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Platnica SV-JME 58(2012)1_02.pdf 1 16.1.2012 10:02:21

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME)

© 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Editor in ChiefVincenc ButalaUniversity of Ljubljana Faculty of Mechanical Engineering, Slovenia

Co-EditorBorut BuchmeisterUniversity of MariborFaculty of Mechanical Engineering, Slovenia

Technical EditorPika ŠkrabaUniversity of Ljubljana Faculty of Mechanical Engineering, Slovenia

Editorial OfficeUniversity of Ljubljana (UL)Faculty of Mechanical EngineeringSV-JMEAškerčeva 6, SI-1000 Ljubljana, SloveniaPhone: 386-(0)1-4771 137Fax: 386-(0)1-2518 567E-mail: [email protected]://www.sv-jme.eu

Founders and PublishersUniversity of Ljubljana (UL)Faculty of Mechanical Engineering, Slovenia

University of Maribor (UM)Faculty of Mechanical Engineering, Slovenia

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International Editorial BoardKoshi Adachi, Graduate School of Engineering,Tohoku University, JapanBikramjit Basu, Indian Institute of Technology, Kanpur, IndiaAnton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, SloveniaNarendra B. Dahotre, University of Tennessee, Knoxville, USAMatija Fajdiga, UL, Faculty of Mech. Engineering, SloveniaImre Felde, Bay Zoltan Inst. for Mater. Sci. and Techn., HungaryJože Flašker, UM, Faculty of Mech. Engineering, SloveniaBernard Franković, Faculty of Engineering Rijeka, CroatiaJanez Grum, UL, Faculty of Mech. Engineering, SloveniaImre Horvath, Delft University of Technology, NetherlandsJulius Kaplunov, Brunel University, West London, UKMilan Kljajin, J.J. Strossmayer University of Osijek, CroatiaJanez Kopač, UL, Faculty of Mech. Engineering, SloveniaFranc Kosel, UL, Faculty of Mech. Engineering, SloveniaThomas Lübben, University of Bremen, GermanyJanez Možina, UL, Faculty of Mech. Engineering, SloveniaMiroslav Plančak, University of Novi Sad, SerbiaBrian Prasad, California Institute of Technology, Pasadena, USABernd Sauer, University of Kaiserlautern, GermanyBrane Širok, UL, Faculty of Mech. Engineering, SloveniaLeopold Škerget, UM, Faculty of Mech. Engineering, SloveniaGeorge E. Totten, Portland State University, USANikos C. Tsourveloudis, Technical University of Crete, GreeceToma Udiljak, University of Zagreb, CroatiaArkady Voloshin, Lehigh University, Bethlehem, USA

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General informationStrojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor. Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/.

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Cover: Above: Shematics of the first magnetic refrigerator prototype developed at the University of Ljubljana, Faculty of Mechanical Engineering, SloveniaBelow: Numerical simulation results of the magnetic field in the NdFeB magnet assembly

Image courtesy: Laboratory of Refrigeration and District Energy and Centre for Element and Structure Modelling, Faculty of Mechanical Engineering, University of Ljubljana, Slovenia

ISSN 0039-2480

Aim and ScopeThe international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1Contents

Contents

Strojniški vestnik - Journal of Mechanical Engineeringvolume 58, (2012), number 1

Ljubljana, January 2012ISSN 0039-2480

Published monthly

PapersKurt Engelbrecht, Jesper Buch Jensen, Christian Robert Haffenden Bahl: Experiments on a

Modular Magnetic Refrigeration Device 3Giulio Tagliafico, Federico Scarpa, Luca Antonio Tagliafico: Dynamic 1D Model of an Active

Magnetic Regenerator: A Parametric Investigation 9Alen Šarlah, Jaka Tušek, Alojz Poredoš: Comparison of Thermo-Hydraulic Properties of Heat

Regenerators Applicable to Active Magnetic Refrigerators 16Nikola Vukašinović, Janez Možina, Jože Duhovnik: Correlation between Incident Angle,

Measurement Distance, Object Colour and the Number of Acquired Points at CNC Laser Scanning 23

Zlatomir Živanović, Miodrag Milić: Thermal Load of Multidisc Wet Friction Assemblies at Braking Regime 29

Erik Potočar, Branko Širok, Marko Hočevar, Matjaž Eberlinc: Control of Separation Flow over a Wind Turbine Blade with Plasma Actuators 37

Sha Du, Haisong Ang: Design and Feasibility Analyses of Morphing Airfoil Used to Control Flight Attitude 46

Vera Nikolić, Ćemal Dolićanin, Dejan Dimitrijević: Dynamic Model for the Stress and Strain State Analysis of a Spur Gear Transmission 56

Instructions for Authors 68

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1, 3-8 Paper received: 06.07.2010DOI:10.5545/sv-jme.2010.151 Paper accepted: 23.06.2011

*Corr. Author’s Address: Risø DTU, Frederiksborg 399, 4000 Roskilde, Denmark, [email protected] 3

Experiments on a Modular Magnetic Refrigeration DeviceEngelbrecht, K. ‒ Jensen, J.B. ‒ Bahl, C.R.H.

Kurt Engelbrecht* ‒ Jesper Buch Jensen ‒ Christian Robert Haffenden BahlFuel Cells and Solid State Chemistry Division, Risø National Laboratory for Sustainable Energy,

Technical University of Denmark, Denmark

An experimental magnetic refrigeration test device has been built at Risø DTU. The device is designed to be modular, and thus all parts of the device can easily be replaced depending on the experiment. This makes the device highly versatile, with the possibility of performing a wide variety of different experiments. The test device is of the reciprocating type, and the magnetic field source is provided by a permanent Halbach magnet assembly with an average flux density of 1.03 Tesla. This work presents experimental results for flat plate regenerators made of gadolinium and sintered compounds of La(Fe,Co,Si)13 and experimentally investigates the effect of thermal conduction through the regenerator housing walls. Each regenerator was tested over a range of hot reservoir temperatures under no load conditions for a regenerator comprised of gadolinium. The test machine was also tested with two different compositions of La(Fe,Co,Si)13 compounds. Test results are presented for a regenerator made of a single La(Fe,Co,Si)13 material and a two-material regenerator, and the results are compared to the same system using gadolinium.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: experiment, magnetic refrigeration, gadolinium, regenerator

0 INTRODUCTION

Active magnetic regenerative (AMR) refrigerators are a potentially environmentally-friendly alternative to vapor compression technology that could potentially be used for air-conditioning, refrigeration, and heat pump applications. Rather than using a gaseous refrigerant, AMRs use magnetocaloric materials (MCMs) that have a coupling between their thermodynamic properties and internal magnetic field. The magnetization of an MCM is analogous to the compression of a gas in that the material’s state becomes more ordered. With magnetization, the material’s entropy is lowered, and the temperature increases if conditions are adiabatic. AMRs are still a developing technology and there is much research effort currently focused on improving AMR performance through the development of new MCMs and system designs. Gadolinium has been the most commonly used MCM in recent AMR machines [1], but many new materials are being developed and characterized [2]. One MCM with the potential to improve system performance over Gd is the La(Fe,Co,Si)13 series of materials. This work compares the two materials in a prototype AMR.

A single regenerator reciprocating AMR test machine has been built and used to test different magnetocaloric materials and regenerator designs. The volume of the regenerator, not including housing and external hardware, is approximately 15 cm3, and the magnetic field is provided by a Halbach cylinder type permanent magnet with an average flux density in the bore of 1.03 T. The magnet, which is described by [3], has a bore of 42 mm and a height of 50 mm. Magnetization and demagnetization of the regenerator are achieved by moving the regenerator vertically relative to the stationary magnet by use of a stepper motor. The test device is described in detail by [4] and was designed so that the regenerator housing can be easily changed, allowing a range of regenerator designs to be tested quickly. However, only flat plate regenerators have been tested up to this point. In order to test the machine’s performance over a range of operating temperatures and to better control the experimental conditions, the device was placed in a temperature controlled cabinet with the hot reservoir in thermal contact with the air in cabinet. In this work, the air inside the temperature controlled cabinet is considered ambient. This paper presents no-load temperature span measurements for a test machine using a flat

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1, 3-8

4 Engelbrecht, K. ‒ Jensen, J.B. ‒ Bahl, C.R.H.

plate gadolinium regenerator and a regenerator made of plates of two sintered La(Fe,Co,Si)13 materials.

A simple schematic of the test machine is given in Fig. 1. The regenerator has a Perspex tube screwed onto each end, with the hot reservoir located in the tube above the regenerator and the cold reservoir in the tube below. There is a resistance heater installed in the regenerator’s cold reservoir to simulate a cooling load. Heat transfer fluid is moved through the regenerator by means of a displacer in the cold reservoir.

The entire device is placed in contact with the same ambient temperature; however, the hot reservoir is thermally linked to ambient via a forced convection heat exchanger while the cold reservoir is insulated from ambient using foam tubing. All thermal losses through the regenerator housing and cold reservoir will go to the ambient temperature. This test machine was used to measure the no-load temperature span of a flat plate regenerator for a range of operating conditions using regenerators made of gadolinium and one and two-material regenerators made of La(Fe,Co,Si)13 and the results are presented below.

Fig. 1. Schematic of the test machine

1 THE REGENERATOR HOUSING

The goal of the test machine described here is to test a range of AMR designs quickly when subjected to consistent conditions. The regenerators were fabricated using rapid prototyping techniques. Rapid prototyping was chosen because a range of detailed geometries can be produced in a single piece, eliminating

fluid leakage. Some types of rapid prototyping processes use plastics with relatively low thermal diffusivities, such as acrylic or nylon, which should reduce interactions between the heat transfer fluid and regenerator housing. The regenerator is 40 mm in the direction of flow with a rectangular flow opening 23 mm wide by 17 mm high. Each plate is held in place by a 1 mm tall slot that runs the entire length of the regenerator. Plate spacing is controlled by ribs between each slot, and the height of each rib can be no less than 0.5 mm due to manufacturing limitations. The regenerator houses 11 plates with the top and bottom plates in direct contact with the housing to reduce interactions between the heat transfer fluid and regenerator housing. The heat transfer fluid is a mixture of 75% water and 25% automotive antifreeze. Consumer antifreeze, which is based on ethylene glycol, was chosen over laboratory grade ethylene glycol because it has corrosion inhibitors that reduce the corrosion of several of the magnetocaloric materials under consideration in this paper.

This paper shows results for 0.9 mm thick commercial grade Gd plates held in place in two different regenerator housings. The first is made using a PolyJet process, where droplets of an acrylic-based polymer are deposited in layers with a thickness of approximately 0.02 mm and hardened after each deposition. The second is made using a selective laser sintering (SLS) process, where layers of nylon powder 0.1 mm in thickness are selectively sintered to form the final part. The SLS process was chosen because it could be used to produce a regenerator housing with hollow walls, which should reduce thermal conduction to the ambient. The PolyJet process could not be used to make the hollow-walled regenerator housing because the process uses a wax support structure that would be difficult to remove from the space inside the walls. A CAD cross-section of the hollow regenerator is shown in Fig. 2. As shown in the figure, there must still be a support structure for the regenerator plates, but the overall conduction path is reduced by using a hollow wall. Assuming that the hollow volume is filled with quiescent air, the thermal resistance through the hollow housing and solid housing can be estimated. Using an average distance occupied by the air, the thermal resistance through the hollow


5Experiments on a Modular Magnetic Refrigeration Device

regenerator wall is approximately 4 times greater than through the solid regenerator housing. The minimum wall thickness is 2.2 mm for the hollow regenerator housing. The PolyJet regenerator has the same geometry as the one shown in Fig. 2, with the exception that the wall between the opening for the regenerator plates and the outside is solid.

Fig. 2. CAD drawing of a regenerator with hollow walls made with SLS

2 EXPERIMENTAL RESULTS

2.1 Flat Plate Gadolinium Regenerator

The solid and hollow regenerators were tested over a range of ambient temperature to determine the optimum temperature span of the test device. Both regenerators were tested with 0.9 mm thick commercial grade gadolinium plates with a spacing of 0.5 mm. In order to determine operating parameters that are near optimal, the solid PolyJet regenerator was used for a range of experiments where the fluid flow rates and cycle times were varied. Operating conditions that result in the optimal no-load temperature span were determined experimentally and they are shown in Table 1. The AMR cycle is broken into four separate processes for the test machine presented here. The cold-to-hot blow starts only when the regenerator is fully magnetized, and the hot-to-cold blow starts after the regenerator is moved fully out of the magnetic field. Therefore, if the time for any single process is changed, the cycle time is also changed.

Table 1. Operating conditions for ambient temperature variation experiment using the commercial grade gadolinium flat plate regenerator

Parameter ValueFluid velocity 8.2 mm/sCycle time 8 sUtilization 0.55

The regenerator utilization, U, is defined as [5]: U

v A cV cf f f f

S S c=

τ ρ

ρ2 , (1)

where τ2 is the time for a blow period, vf is the fluid velocity, Af is the cross-sectional area available for fluid flow, ρf and ρs are the fluid and solid densities, respectively, cf and cs are the specific heats of the fluid and solid, respectively, and Vs is the volume of the solid regenerator material. The average specific heat of gadolinium is assumed to be 260 J/(kgK) based on data from [6].

The ambient temperature was varied in a range around the Curie temperature of Gd (21 °C) and the no-load temperature span was measured for the solid and hollow regenerators. The results are shown in Fig. 3. The hot heat exchanger generally maintains the hot reservoir to approximately 1 °C or less above ambient temperature.

Fig. 3 shows that the maximum temperature span is achieved at an ambient temperature of approximately 25 °C for both regenerators. It has previously been reported that the optimum hot-end temperature is just above the Curie temperature [7]. At an ambient temperature of 24 °C, the regenerator operates approximately between 16 and 25 °C. The Curie temperature is close to the middle of this range, meaning that the entropy change with magnetization of the material is maximized. The hollow regenerator housing generally performs slightly better than the solid housing, but the difference is near the experimental uncertainty for the device which is estimated at approximately 0.2 °C. As the temperature span of the device increases, the performance of the hollow housing may improve relative to the solid housing. However, for a temperature span below 10 °C, the benefit of the hollow regenerator housing is relatively small.



The effect of ambient temperature relative to the hot and cold reservoirs was also tested. The device was run at the same operating conditions but with a reduced pump speed in the hot heat exchanger, and the resulting temperature span was measured. With the hot heat exchanger effectiveness reduced, the ambient temperature was set to 22.5 °C and the regenerator produced a no-load span of 10.2 °C between 15.6 and 25.8 °C. The temperature span that was achieved when the hot reservoir was allowed to rise more than 3 °C above ambient increased the device’s temperature span by more than 1 °C. This could be due to the reduced temperature difference between the cold reservoir and ambient or the reduced temperature difference between any location along the regenerator and ambient. Because the losses through the regenerator wall were shown to be relatively small, it is possible that there is a thermal leak from the cold reservoir to the ambient that causes a noticeable reduction in performance.

2.2 Experimental Results for a Two-Material Regenerator

Plates of 0.9 mm thickness have been provided by a commercial supplier of two compositions of sintered La(Fe,Co,Si)13 with Curie temperatures of approximately 3 and 16 °C. The properties of the TC = 3 °C material tested here are given by [8]. La(Fe,Co,Si)13 materials are

attractive materials for AMR systems because they have a higher entropy change with magnetization than gadolinium, although they exhibit a smaller adiabatic temperature change upon magnetization. Each plate is 0.9 mm thick and 20 mm long or half the length of the gadolinium plates discussed above. The layered bed is constructed by simply butting two plates of different materials together. The solid regenerator housing was run with a regenerator made of only the TC = 16 °C material and the system reached a no load temperature span of 7.9 °C, with the regenerator operating between 10.1 and 18.0 °C while the ambient temperature was set to 15.6 °C.

The layered bed was tested at an ambient temperature of 13 °C for a range of utilizations and heat transfer fluid velocities, and the no-load temperature span was measured. The cycle time is a function mostly of fluid velocity and utilization. Thus, for the same utilization, the cycle time will be longer for a lower fluid velocity. Testing of the layered La(Fe,Co,Si)13 showed that the system was most sensitive to fluid velocity, with cycle time and utilization having relatively small effects on system performance for conditions tested here. The experimental results are shown in Fig. 4. The dependence on fluid velocity may be due to the increased time for heat transfer between the fluid and solid when the velocity is lower. Changing the ambient temperature for this experiment does not significantly affect the results, provided

Fig. 3. No-load temperature span as a function of ambient temperature for the operating conditions shown in Table 1


7Experiments on a Modular Magnetic Refrigeration Device

it lies between the Curie temperatures of the two materials. Theinsensitivity to operating temperature may be due to the fact that the difference between the Curie temperatures of the two materials is higher than the temperature span that can be achieved by this regenerator design.

Examination of Fig. 4 shows that the no-load temperature span is similar for a range of utilizations when the fluid velocity is held constant. However, the results are dependent on fluid velocity, achieving the largest temperature span with a fluid velocity of 6.6 mm/s. The system showed very little dependence on cycle time. For example, the case with a utilization of 0.33 and fluid velocity of 6.6 mm/s has a cycle time of 9.2 s while the experiment with a utilization of 0.76 and the same fluid velocity had a cycle time of 17 s, but the temperature span showed a difference of only 0.3 °C. There is a much more drastic change in performance as the fluid velocity is changed. The maximum temperature span for the layered regenerator is 6.5 °C, which is 1.5 °C lower than the temperature span for a single material La(Fe,Co,Si)13 regenerator. The layered regenerator probably did not perform as well as the single material bed because the Curie temperatures of the magnetocaloric materials are too far apart for this regenerator design. As the regenerator cannot produce a large enough temperature span to reach the temperature where the low-Curie-temperature material has high magnetocaloric performance, the potentially higher temperature span for the layered regenerator was not realized.

During the operation of the test machine, the La(Fe,Co,Si)13 plates were more prone to break than the gadolinium plates that were also tested. It is not clear if the plates were broken during assembly/disassembly or during operation, but brittleness should be a concern when designing a system using La(Fe,Co,Si)13 materials.

3 CONCLUSIONS

No-load temperature spans have been presented for two different regenerator designs and two different regenerator materials. By testing a regenerator with hollow walls, it was shown that thermal losses through the regenerator wall to ambient do not significantly affect the test machine’s performance when the temperature span is less than 10 °C. However, as the temperature span increases, losses through the regenerator wall will also increase and reducing the conduction through the regenerator housing may have a larger impact on performance. Tests presented in this paper show that a single-material AMR performs best when the Curie temperature is within the working temperature span of the machine. The test machine presented is able to control the operating temperature of the AMR and therefore is able to test a given MCM in its optimum temperature range and provide a meaningful comparison between potential new working materials with different Curie temperatures.

Single-material and layered bed regenerators were made from La(Fe,Co,Si)13

Fig. 4. No load temperature span as a function of fluid velocity for a two-material La(Fe,Co,Si)13 regenerator



compounds, and the no load temperature span was found to be lower than that of gadolinium when both materials operated near their respective Curie temperatures. Also, the layered regenerator provided a lower temperature span than the single material regenerator because the two materials had Curie temperatures that were too far apart for the regenerator design that was tested. However, La(Fe,Co,Si)13 compounds exhibit relatively high entropy change with magnetization and still hold promise for AMR systems provided the materials are chosen correctly.

4 ACKNOWLEDGEMENTS

We thank Mr. Jørgen Geyti for his technical help. Also, we thank Vacuumschmelze GmbH & Co. KG, 63450 Hanau, Germany for supplying the plates of La(Fe,Co,Si)13. The authors further acknowledge the support of the Programme Commission on Energy and Environment (EnMi) (Contract No. 2104-06-0032), which is part of the Danish Council for Strategic Research.

5 REFERENCES

[1] Gschneidner Jr.K.A., Pecharsky, V.K., Tsokol, A.O. (2005). Recent developments in magnetocaloric materials. Reports On Progress In Physics, vol. 68, p. 1479-1539, DOI:10.1088/0034-4885/68/6/R04.

[2] Engelbrecht, K.L., Nellis, G.F., Klein, S.A., Zimm, C.B. (2007). Recent developments in room temperature active magnetic

regenerative refrigeration. HVAC&R Research, vol. 13, p. 525-542.

[3] Bjørk, R., Bahl, C.R.H., Smith, A., Pryds, N. (2010). Review and comparison of magnet designs for magnetic refrigeration. International Journal of Refrigeration, vol. 33, p. 437-448, DOI:10.1016/j.ijrefrig.2009.12.012.

[4] Bahl, C.R.H., Petersen, T.F., Pryds, N., Smith, A. (2008). A versatile magnetic refrigeration test device. Review of Scientific Instruments, vol. 79, Article no. 093906, DOI:10.1063/1.2981692.

[5] Dragutinovic, G.D., Baclic, B.S. (1998). Operation of counterflow regenerators. Computational Mechanics Inc., Billerca.

[6] Dan’kov, S.Y., Tishin, A.M., Pecharsky, V.K., Gschneidner, K.A. (1998). Magnetic phase transitions and the magnetothermal properties of gadolinium. Physical Review B, vol. 57, no. 6, p. 3478-3490, DOI:10.1103/PhysRevB.57.3478.

[7] Rowe, A., Tura, A. (2008). Active magnetic regenerator performance enhancement using passive magnetic materials. Journal of Magnetism and Magnetic Materials, vol. 320, p. 1357-1363, DOI:10.1016/j.jmmm.2007.11.018.

[8] Hansen, B.R., Katter, M., Theil Kuhn, L., Bahl, C.R.H., Smith, A., Ancona-Torres, C. (2009). Characterization study of a plate of the magnetocaloric material La(Fe,Co,Si)13. Proceedings of 3rd International Conference on Magnetic Refrigeration at Room Temperature, IIF/IIR, p. 67-73.

http://dx.doi.org/10.1088/0034-4885/68/6/R04

http://dx.doi.org/10.1016/j.ijrefrig.2009.12.012


http://dx.doi.org/10.1063/1.2981692

http://dx.doi.org/10.1103/PhysRevB.57.3478

http://dx.doi.org/10.1016/j.jmmm.2007.11.018


*Corr. Author’s Address: University of Genoa, DIPTEM/TEC, Via all’Opera Pia 15a, Genova, 16145, Italy, [email protected] 9

Dynamic 1D Model of an Active Magnetic Regenerator: A Parametric InvestigationTagliafico, G. ‒ Scarpa, F. ‒ Tagliafico, L.A.

Giulio Tagliafico1 ‒ Federico Scarpa*,2 ‒ Luca Antonio Tagliafico2

1 University of Genoa, DCCI, Italy 2 University of Genoa, DIPTEM/TEC, Italy

A one dimensional dynamic model of a reciprocating active reciprocating magnetic regenerator (AMR) was developed and a parametric analysis of its behavior at near room temperature conditions was carried out. The investigation is focused on the thermal behavior of the regenerator alone, regardless of the apparatus in which it could work. The parametric investigation aims at evaluating the influence on the AMR performances of the operating frequency and fluid mass flow rate, that is the parameters that can be tuned in a given actual device. The performance parameters analyzed are refrigeration capacity, temperature span, coefficient of performance and second law thermodynamic efficiency. A standard geometry of the AMR was assumed, while the results are given in a non-dimensional form with reference to a conventional operating condition.

Simulations show that the refrigeration capacity is very sensitive to the utilization factor, that causes a 20% refrigeration capacity reduction with a variation of -20% or +10%. The coefficient of performance (COP) is poorly influenced by Φ. Frequency variations induce a linear variation in refrigeration capacity, and a decrease in COP due to friction in the intermediate fluid. The second law thermodynamic efficiency trends show that friction and heat transfer irreversibility dominates at low and high temperature spans, respectively.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: magnetic refrigeration, active regeneration, modelization, parametric investigation

0 INTRODUCTION

Magnetic refrigeration is an innovative and alternative way of cooling at room temperature that promises to be competitive with actual refrigeration techniques, and to guarantee a primary energy saving. Exhaustive reviews on this topic can be found in Engelbrecht et al. [1], Gschneidner and Pecharsky [2], Yu et al. [3].

The AMR is the core of magnetic refrigeration cycles at room temperature, so reliable numerical models that can predict its performance over a wide range of operating conditions are required. There are basically two different approaches in modeling an AMR. 1) The one-dimensional schematization

requires the determination of the heat transfer coefficient h between solid and fluid and of the friction factor f that describes the pressure drop in the fluid flow due to viscosity. This approach is followed by Engelbrecht et al. [4] who solves the “steady state” condition, Kawanami [5], Sarlah and

Poredos [6], Bouchekara et al. [7], Risser et al. [8], Tagliafico et al. [9] who solve the time evolution of the temperatures.

2) The two-dimensional schematization can be based on the solution of the continuity, momentum and energy equations in the fluid domain, and of the Fourier’s equation in the solid domain, even if only in simple geometries. This approach is followed by Petersen et al. [10], Legait et al. [11] Nielsen et al. [12], who developed and investigated over a wide range of conditions a 2D model of an AMR made of a stack of parallel plates of gadolinium. For complex, disordered geometries the 1D model approach must be followed in any case. A comprehensive review on AMR models can be found in Nielsen et al. [13] .

The AMR performance are mainly influenced by the thermophysical and magneto-thermal properties of the active magnetocaloric material (MCM) employed and the operating temperature. Other effects derive from MCM


10 Tagliafico, G. ‒ Scarpa, F. ‒ Tagliafico, L.A.

shape, regenerator geometry, fluid mass flow rate and cycle frequency. In this paper, an ideal 1D numerical model of an AMR is presented and employed to evaluate the influence on performance of the parameter that can be tuned in a given device (that is fluid mass flow rate and cycle frequency).

1 THE NUMERICAL MODEL

AMR process is based on a four-step regenerative cycle with the aim of amplifying the adiabatic temperature change amplitude given by the magnetocaloric effect by several times. This aim is accomplished by means of an intermediate fluid and a proper synchronization between magnetic field changes and fluid flow. Starting from in isothermal condition, a magnetic field is applied to the solid-based regenerator (magnetization) with a consequent sudden temperature increase in the solid. The fluid is then forced from one side of the regenerator to the other and it warms up cooling the solid (hot blow). The magnetic field is then removed with a temperature drop in the solid (demagnetization). The fluid is forced in the direction opposite to the hot blow and it cools warming up the solid (cold blow). A longitudinal temperature gradient arises along the regenerator that amplifies the adiabatic temperature change of the material.

The model describes in detail only the thermal behavior of the regenerator. The fluid loop is not considered and the heat exchangers outward facing are accounted for by fixing the two inlet temperatures that represent the boundary conditions on the AMR. The magnetization and demagnetization process is described by an instantaneous and reversible adiabatic temperature change, ΔTad , in the magnetocaloric material.

Fig. 1. Conceptual scheme of the AMR model

The AMR model is based on a system of PDEs that gives the temperature fields of both the solid and the fluid. The magnetic field B(t) and the fluid mass flow rate mβ(t) are imposed as external controls. Fig. 1 shows the scheme of the numerical configuration.

The numerical model consists in the energy balance equation for a differential volume of both the solid and the fluid (see Eqs. (1) and (2)). The unknowns of the system are the solid (Tσ(x,t)) and fluid (Tβ(x,t)) temperature fields along the x coordinate. Subscripts β and σ are referred to fluid and solid, respectively. Heat leakages to the external are neglected, and so the heat generation due to friction in the fluid. h is the convective heat transfer coefficient, α is the fluid to total volume ratio (void fraction). The convective term, which is proportional to the local temperature difference between solid and fluid, couples the two equations.

The usual four steps of the AMR cycle are given by the application of Eqs. (3) to (6) to Eqs. (1) and (2). The initial condition is the isothermal condition between fluid, solid and environment. Magnetization and demagnetization processes are simulated by the imposition of the ΔTad. The active material properties (specific heat cp(Tσ, B) and adiabatic temperature change ΔTad(Tσ, Binitial, Bfinal)) are those of gadolinium, obtained from experimental data of Canepa et al. [15].

The pumping power required by the fluid to cross the regenerator is given by Eqs. (9) and (10), assuming a pump efficiency hpump = 0.8. The friction factor ff is given by the Ergun correlation [14] Eq. (11) with the constant C1 = 180 and C2 = 1.8 suggested by Kaviany [16]. w is the actual fluid velocity in the regenerator (porous velocity).

∂

∂=

∂

∂

+ − −∂

∂

Tt c

T

xh T T

m cA

Tx

β

β ββ

βσ β

β β β

ρλ

γα α

1 2

2 ( ) , (1)

∂∂

=( )

∂

∂

−−

−

Tt c T B

Tx

h T Tσ

σ σ σσ

σσ βρ

λγα

11

2

2,( ) . (2)

The heat transfer coefficient is evaluated by means of Wakao and Kaguei correlation [17] Eq. (12).

The global performance parameters describing the behavior of the AMR are: the refrigerating capacity QIN, the temperature span between the hot and the cold thermal source


11Dynamic 1D Model of an Active Magnetic Regenerator: A Parametric Investigation

ΔTSPAN = TH ‒ TC, the Coefficient of Performance COP and the second law efficiency ξ defined as in Eqs. (13) and (16). The heat rejection is defined by Eq. (17). The cycle period tC is given by the sum of the hot and cold blow period, as demagnetization and magnetization are assumed instantaneous. The simulation starts from an isothermal initial condition forcing a ΔTSPAN between the hot source (kept at the ambient temperature Text) and the cold source (kept ΔTSPAN colder than the hot one) and then stops when the “steady” periodic regime is reached, that is the fluid and solid temperature fields repeat unchanged every cycle period tC (with a given tolerance of the order of 10-6 ΔTSPAN). The system of equations is solved by a finite difference scheme implemented both in MATLAB and in MS Visual Studio.

The AMR cycle’s boundary condition are reported below, together with the definitions of the system performances and parameters, for a generic cycle (0 < t < tC).

Magnetization:

T x T x

T T x B Bad MIN MAX

σ σ

σ

( , ) ( , ) ...

( ( , ), ).

0 0

0

+ −

−

= +

→∆ (3)

Hot blow boundary conditions:

T t TTx

TxC

t L tβ ( , ) , , .

, ,0 0 0

0=

∂∂

=∂∂

=σ σ (4)

Hot blow external controls: m t m B t BMAXβ β( ) , ( ) .= = (5)

Demagnetization:

T x T x

T T x B B

t t

adt

MAX MIN

C C

C

σ σ

σ

( , ) ( , ) ...

( ( , ), ).

2 2

2

+ −

−

= +

→∆ (6)

Cold blow boundary conditions:

T L t TTx

TxH

t L tβ ( , ) , , .

, ,=

∂∂

=∂∂

=σ σ

00 0 (7)

Cold blow external controls: m t m B t BMINβ β( ) , ( ) .= − = (8)

Pumping power:

W m PPUMP

pump= β

βρ η∆ 1 , (9)

∆P ff Ld

w

p= ⋅ ρ

αβ

( ) ,2

2 (10)

ff C Cp

=−

+

−

12

21 1

Re.α

ααα

(11)

Wakao and Kaguei correlation: Nup p= +2 1 1 0 6 1 3. Re Pr ,. / (12)

system performances: ∆T T TSPAN H C= − , (13)

COPQ

W WIN

MAG PUMP=

+, (14)

ξ = =COP

COPCOP

TTCARNOT

SPAN

C

∆, (15)

Qt

m c T T t dtINC

Ct

t

C

C

= − ( )( )∫1 0

2β β β , ,

/

(16)

heat rejection:

Qt

m c T L t T dtOUTC

H

tC

= ( ) −( )∫1

0

2

β β β , ./

(17)

2 RESULTS AND DISCUSSION

A stability and accuracy analysis performed varying the discretization parameters time step Δt and spatial step Δx in different conditions, and taking into account a reasonable compromise between accuracy and the computational speed, lead to set the numerical steps to optimized values Δx = 2×10-4 m and Δt = 1×10-3 s.

The standard set of parameters used in the preliminary analysis and in the parametric investigation, if not differently specified, is reported in Table 1. The parametric investigation is focused on the influence of the fluid mass flow rate and cycle frequency on the global performance of the device, operating as a refrigerator. The main figures of merit considered here are: COP, ξ , QIN , as defined by Eqs. (14) to (16).

The fluid mass flow rate and the operating frequency can be related by the utilization factor Φ defined as in Eq. (18). The utilization factor is the ratio between the thermal capacity rate of the fluid and that of the solid.

Φ β β

σ σ=m cM c

tC2. (18)



Fig. 2 shows the non-dimensional useful effect QIN+ = QIN/QIN,MAX (QIN,MAX evaluated at ΔTSPAN = 0 °K and f = f0 = 0.25 Hz) the COP, and the ξ parameter with respect to Φ.

Table 1. Reference values of the numerical parameters

AMR process numerical simulation Regenerator size [cm3] 62.5Void fraction α [-] 0.5Total material mass [kg] 0.250Active material Gd, powderMean particle size [mm] 300Fluid WaterText [K] 293BMAX , BMIN [T] 1.5, 0.0Mass flow rate [kgs-1] 25·10-3

Cycle frequency f0 [Hz] 0.25

The curves at constant ΔTSPAN are obtained increasing the fluid mass flow rate (keeping the frequency at 0.25 Hz). The hot thermal source is at ambient temperature TH = Text and the heat exchangers are ideal (the fluid leaves the heat exchangers and enters the regenerator at the respective source temperatures).

For a given ΔTSPAN > 0 °K the refrigeration capacity increases with Φ, up to a limit and then it rapidly decreases. Furthermore, the Φ that guarantees the maximum QIN+ decreases if the ΔTSPAN increases. This behavior is reported also in Oliveira et al. [19]. The COP curves are very flat. For a given ΔTSPAN there are many different

Φ values that ensure good behavior of the AMR as a refrigerator (mβ= 5 g/s gives about Φ = 0.5, and mβ = 26 g/s gives about Φ = 3).

The ξ curves are maximum shaped with respect to Φ and also to ΔTSPAN. There is an optimal operating ΔTSPAN that minimizes the entropy production. The best performance calculated in this configuration is ξ = 0.29 for ΔTSPAN = 20 K and a Φ = 0.75. In this condition the COP is about 4, but the refrigeration capacity is reduced to about 50% of the maximum reachable at the same ΔTSPAN.

Fig. 3 shows the same result of Fig. 2a with the normalization of QIN with respect to the maximum refrigeration capacity QMAX relative to each ΔTSPAN.

The optimal utilization decreases if ΔTSPAN increases, and the refrigeration capacity is very sensitive to Φ. A variation from the optimal utilization value of +10% or ‒20% causes a decrease in refrigeration capacity of about 20%.

Fig. 4 shows the useful effect QIN+, the COP, and the ξ parameter with respect to operating frequency f+ = f/f0. Each curve is given for the Φ value that maximizes the QIN+ as shown in Fig. 2a. The system has constant MCM mass, and the temperature internal gradient (linked to Biot number Bi) in the solid particles is neglected, so the increase in frequency results in a linear increase of QIN+. For fixed Φ the mass flow rate is also proportional to the frequency, so that the friction pressure losses change accordingly. On the other hand maximum shaped curves of QIN+ with respect to frequency should be expected

Fig. 2. a) QIN+, b) COP, c) ξ of the AMR with respect to Φ; the curves are given at constant temperature spans ΔTSPAN and for the standard values of Table 1



since, for very high frequency, bulk effects in the MCM particles should be accounted for as suggested by Engelbrecth et al. [20]. If the particle based Bi number is large (Bi > 0.2), the effective convective heat transfer coefficient is reduced depending on the actual Bi and Fourier numbers, since the surface temperature of each particle becomes noticeably lower than the mean bulk temperature.

Fig. 3. Normalized refrigeration capacity for each ΔTSPAN vs. utilization factor

For the given ΔTSPAN and TC , the curves of COP and ξ follow the same trend (see Eq. (15)). The trend depends on the combined effects of heat transfer and friction irreversibility [21]. The heat transfer effect dominates at high ΔTSPAN and low frequency, while friction effect dominates

for small ΔTSPAN. Fig. 4c shows that for ΔTSPAN = 5 K the heat transfer irreversibility is negligible and the COP trend is a continuously decreasing curve due to friction effects, while for ΔTSPAN = 40 K the friction irreversibility is negligible and, as a consequence, COP is almost independent of f+ (that is, approximately, of flow rate).

The maximum useful effect resulting from Fig. 2a compares well with experimental data reported by Zimm et al. [22] in a rotary system using Gd powder. They obtained specific cooling capacity per cc of Gd around 2.2 W/cc (ΔTSPAN ~ 0 K) while the present simulation gives 2.3 W/cc.

3 CONCLUSIONS

A 1D dynamic numerical model of an AMR was developed and a performance parametric investigation that involves the operating parameters fluid mass flow rate and the operating cycle frequency (and so Φ) was performed.

The parametric investigation shows that different optimal utilization values can be identified, with respect to temperature span, in order to maximize the performance of the AMR (QIN, COP and ξ). The COP and ξ curves as a function of operating frequency f+ and Φ show a typical maximum shaped trend, which can be related to the two different entropy production terms: the heat transfer irreversibility and the friction irreversibility inside the AMR regenerator. Results show that an AMR device can operate with almost constant COP with different thermal loads, which can be met by properly tuning the

Fig. 4. a) QIN+, b) COP, c) ξ of the AMR with respect to operating frequency; the curves are given at constant temperature spans ΔTSPAN and for the optimal Φ given by a)



utilization factor. This behavior could be exploited to achieve higher energy saving with respect to vapor compression systems, also in dynamic conditions by a proper control of the magnetic refrigerator device. Furthermore, the investigation on the operating frequency, in the low frequency field analyzed, shows that the refrigeration capacity can be increased by an increase in frequency with a very low effect on the COP.

4 ACKNOWLEDGEMENT

This work was developed with the support of Ministry of University and Research (grant PRIN 2007 n° 2007893AC3).

5 NOMENCLATURE

symbol meaning and unitc specific heat [J kg-1 K-1]f frequency [s-1]ff friction factor [-]h solid-to-particle convective heat transfer

coefficient [W m-2 K-1]m mass flow rate [kg s-1]tC cycle time [s]x longitudinale coordinate [m]w porous velocity [m s-1]A regenerator cross section surface [m2]AMR active magnetic regeneratorB magnetic field [T]Bi Biot number [-]COP coefficient of performanceL regenerator length [m]M mass [kg]Nup particle based Nusselt number [-]Pr Prandtl numberQ heat rate [W]Rep particle based Reynolds number [-]T temperature [K]W mechanical power [W]ΔP pressure drop in the regenerator [Pa]ΔTad adiabatic temperature change [K]α void fraction [-]γ specific heat transfer surface [m2 m-3]η efficiency [-]λ thermal conductivity [W m-1 K-1]ξ second law efficiency [-]ρ density [kg m-3]Φ utilization factor [-]

subscripts0 reference valueC of the cold sourceH of the hot soruceβ of fluid phaseσ of solid phasesuperscripts+ nondimensional

6 REFERENCES

[1] Engelbrecht, K.L., Nellis, G.F., Klein, S.A., Zimm, C.B. (2007). Recent developments in room temperature active magnetic regenerative refrigeration. HVAC&R Research, vol. 13, no. 4, p. 525-542

[2] Gschneidner, K.A.Jr., Pecharsky, V.K. (2008). Thirty years of near room temperature magnetic cooling: Where we are today and future prospects. International Journal of Refrigeration, vol. 31, no. 6, p. 945-961, DOI:10.1016/j.ijrefrig.2008.01.004.

[3] Yu, B., Liu, M., Egolf, P.W., Kitanovski, A. (2010). A review of magnetic refrigerator and heat pump prototypes built before the year 2010. International Journal of Refrigeration, vol. 33, no. 6, p. 1029-1060, DOI:10.1016/j.ijrefrig.2010.04.002.

[4] Engelbrecth, K., Nellis, G. F., Klein, S.A. (2007). Comparing modeling prediction to experimental data for active magnetic regenerative refrigeration systems. Proceedings of 2nd International conference on Magnetic Refrigeration at room temperature, p. 349-357.

[5] Kawanami, T. (2007). Heat transfer characteristics and cooling performance of an active magnetic regenerator 2007. Proceedings of 2nd International conference on Magnetic Refrigeration at room temperature, p. 23-34.

[6] Sarlah, A., Poredos, A. (2007). Dimensionless numerical model for determination of magnetic regenerator’s heat transfer coefficient and its operation. Proceedings of 2nd International conference on Magnetic Refrigeration at room temperature, p. 420-426.

[7] Bouchekara, H., Kedous-Lebouc, A., Dupuis, C., Allab, F. (2008). Prediction






and optimization of geometrical properties of the refrigerant bed in an AMRR cycle. International Journal of Refrigeration, vol. 31, no. 7, p. 1224-1230, DOI:10.1016/j.ijrefrig.2008.02.007.

[8] Risser, M., Vasile, C., Engel, T., Keith, B., Muller, C. (2010). Numerical simulation of magnetocaloric system behaviour for an industrial application. International Journal of Refrigeration, DOI:10.1016/j.ijrefrig. 2010.02.004.

[9] Tagliafico, G., Scarpa, F., Canepa, F. (2010). A dynamic 1-D model for reciprocating active magnetic regenerator; influence of the main working parameters. International Journal of Refrigeration, vol. 33, p. 286-293, DOI:10.1016/j.ijrefrig.2009.10.001.

[10] Petersen, T.F., Prynds, N., Smith, A., Hattel, J., Schmidt, H., Knudsen, H.H. (2008). Two-dimensional mathematical model of a reciprocating room-temperature active magnetic regenerator. International Journal of Refrigeration, vol. 31, p. 432-443, DOI:10.1016/j.ijrefrig.2007.07.009.

[11] Legait, U., Kedous-Lebouch, A., Rodont, L. (2009). Numerical simulation and analysis of the refrigerant bed behavior using fluent software. Proceedings of 3rd International conference on Magnetic Refrigeration at room temperature, p. 295-302.

[12] Nielsen, K.K., Bahl, C.R.H., Smith, A., Pryds, N., Hattel, J. (2010). A comprehensive parameter study of an active magnetic regenerator using a 2D numerical model. International Journal of Refrigeration, vol. 33, no. 4, p. 753-764, DOI:10.1016/j.ijrefrig.2009.12.024.

[13] Nielsen, K.K., Tusek, J., Engelbrecth, K., Schopfer, S., Kitanovski, A., Bahl, C.R.H., Smith, A., Pryds, N., Poredos, A. (2011). Review on numerical modeling of active magnetic regenerators for room temperature. International Journal of Refrigeration,

vol. 34, p. 603-616, DOI:10.1016/j.ijrefrig.2010.12.026.

[14] Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, vol. 48, p. 89-95.

[15] Canepa, F., Cirafici, S., Napoletano, M., Cimberle, M.R., Tagliafico, L.A., Scarpa, F. (2008). Ageing effect on the magnetocaloric properties of Gd, Gd5Si1.9Ge2.1 and on the eutectic composition Gd75Cd25. Journal of Physics D: Applied Physics, vol. 41, DOI:10.1088/0022-3727/41/15/155004.

[16] Kaviany, M. (1995). Principles of Heat Transfer in Porous Media, 2nd edition: Springer, New York, DOI:10.1007/978-1-4612-4254-3.

[17] Wakao, N., Kaguei, S. (1982). Heat and mass transfer in packed bed. Gordon and Breach, New York.

[18] Nield, D.A., Bejan, A. (1998). Convection in porous media, Springer, New York.

[19] Oliveira, P.A., Trevizoli, P.V., Barbosa, Jr. J.R., Prata, A.T. (2009). Numerical analysis of a reciprocative active magnetic regenerator – part II. Proceedings of 3rd International conference on Magnetic Refrigeration at room temperature, Des Moines, p. 289-294.

[20] Engelbrecth, K.L., Nellis, G.F., Klein, S.A., Boeder, A.M. (2005). Modeling active magnetic regenerative refrigeration systems. Proceedings of 1st International conference on Magnetic Refrigeration at room temperature, p. 265-274.

[21] Bejan, A. (1982). Entropy generation through heat and fluid flow. John Wiley & Sons, New York.

[22] Zimm, C., Boeder, A., Chell, J., Sternberg, A., Fujita, A., Fujieda, S., Fukamichi, K. (2006). Design and performance of a permanent magnet rotary refrigerator. International Journal of Refrigeration, vol. 29, p. 1302-1306, DOI:10.1016/j.ijrefrig.2006.07.014.









http://dx.doi.org/10.1088/0022-3727/41/15/155004


Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1, 16-22 Paper received: 10.12.2010 DOI: 10.5545/sv-jme.2010.250 Paper accepted: 23.06.2011

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, [email protected]

Comparison of Thermo-Hydraulic Properties of Heat Regenerators Applicable to Active Magnetic Refrigerators

Šarlah, A. – Tušek, J. – Poredoš, A.Alen Šarlah* – Jaka Tušek – Alojz Poredoš

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

This paper describes passive heat regenerators appropriate for active magnetic refrigerators (AMR) and evaluates them from the point of view of thermo-hydraulic characteristics and magnetic properties. A dimensionless numerical model for the determination of the heat transfer coefficient is used together with experimental data for the evaluation of six different regenerator geometries using heat transfer, pressure drop and thermal efficiency as evaluation criteria. An existing numerical model was upgraded with magnetic properties and employed in the computer programme for an active magnetic regenerator in which the magnetic properties are obtained using molecular field approximation. The model was tested for thermodynamic consistency and verified using available experimental data.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: magnetic refrigeration, active magnetic regenerator, thermo-hydraulic properties

0 INTRODUCTION

Heat transfer coefficient and pressure drop are two most important parameters that directly determine the efficiency of the passive regenerators (PR) and consequently active magnetic regenerators (AMR). In order to obtain both parameters, regenerator needs to be experimentally tested and numerically evaluated in order to determine its thermal – j(Re) – and hydraulic – f(Re) – properties. There exist several techniques for prediction of heat transfer coefficients, each with its own advantages and disadvantages [1] and [2], while one of the most popular one being the single blow technique introduced by Mullisen and Loehrke [3]. The other very common technique is a steady state experimental determination of heat transfer coefficients. Several authors [1] and [2] have performed comparisons of various methods for the evaluation of the single blow technique and a proper prediction of heat transfer coefficients. They have concluded that there are significant differences between various techniques and methods, i.e. results can differ for as much as 20% [1], which is significantly more than the uncertainty of a particular method (between 4 and 10%). For this reason it is important that the right technique and method are chosen and applied for a determination of the regenerator’s heat transfer coefficient. Furthermore, in recent years, there has been a constant need to discover

new, advanced regenerator geometries with higher efficiencies for which data are scarce or not yet available. Also, a lot of data on heat transfer coefficients of various heat exchangers, which are available in publications, are for certain regenerator geometries (packed bed, honeycomb, wavy structure, perforated plates). These can differ from the ones used in magnetic refrigerators due to slightly varying geometrical parameters or imperfect manufacturing. To summarize, determination of the regenerator’s heat transfer coefficient is a first step of the path to a complete description of the active magnetic regenerator.

The second part of the problem is the development of a corresponding numerical model, which can appropriately describe the magnetocaloric effect and simulate the operation of an AMR. Of course, it is reasonable to use the same tool – same numerical model, which includes all influential thermodynamic and hydrodynamic properties – for both the determination of the heat transfer coefficient of the PR and, in an upgraded form, for the simulation of the AMRR operation. Here we are faced with the problem of properly introducing the magnetocaloric properties into the model. In order to describe the magnetocaloric effect as precisely as possible, we have to make sure that it is thermodynamically consistent at all stages of refrigeration cycle, while at the same time computationally efficient. In the first step this requires a careful determination and


17Comparison of Thermo-Hydraulic Properties of Heat Regenerators Applicable to Active Magnetic Refrigerators

evaluation of magnetocaloric properties of the magnetic material. Here we are faced with certain experimental and analytical limits, which require an indirect approach to the problem [4] and [5]. In the second step, obtained properties need to be properly introduced into the model and verified for their suitability. The latter can be performed by comparing numerical results with experimental data, which would be the last step in the process. The verified model can then be used as a tool for predicting the AMR operation of various regenerators, magnetic materials, magnetic fields and operational set-ups. The objective of this paper is to summarize the procedure and results obtained using a dimensionless model which can, with certain assumptions, be equally used for both purposes: the determination of the regenerator’s heat transfer coefficient and the simulation of the AMR refrigerator. Such model, in dimensionless form, can thus be a valuable tool for studying AMRR operation and later in a developing stage for the AMR design optimization.

1 EVALUATION OF PASSIVE REGENERATORS

The dimensionless thermo-hydraulic model for determining the passive regenerator’s characteristics is extensively described and presented by Sarlah et al. [6] and [7]. The derived model was used to evaluate various types of regenerators in order to determine their characteristics and performance. The evaluated geometries are shown in Fig. 1 and presented in Table 1. While Table 2 shows uncertainty and sensitivity analysis for heat transfer and pressure drop results according to the uncertainties of a particular variable for experimental run #026.

A single blow experiment was performed to determine the heat transfer coefficient (Colburn j factor) of each regenerator, and standardized pressured drop measurements were performed for determination of friction loss factor f. As seen in Fig. 2, absolute pressure drop significantly differs between various geometries of regenerators and thus plays a major role on the efficiency of the regenerator in AMR.

According to the results of the experimental determination of heat transfer coefficient and

pressure drop, we can draw the following conclusions:• The packed bed regenerator filled with

spheres has a significantly higher pressure drop than the other regenerators, and on the other hand only modestly higher Colburn j-factor, which altogether makes it less desirable according to the j/f ratio (Fig. 2).

• Regenerator with triangular passages and perforated plates is also not desirable, since it provides only slightly improved heat transfer, but significantly higher pressure drop (Figs. 3 and 4).

• Best j/f ratio is shown by the regenerator with parallel plates (regenerator F), which has highest j-factor among honeycomb-like regenerators, and only a modest increase in pressure drop as compared to matrix with triangular passages.

A B

C D

E F

Fig. 1. Photos of six regenerator geometries experimentally tested for heat transfer and

pressure drop; a) alternative flat and corrugated lamellas, b) packed bed of spheres, c) back-to-

back oriented lamellas, d) alternative corrugated and perforated flat lamellas, e) alternating flat and corrugated lamellas (double thickness), f)

parallel lamellas

• Regenerator C also shows a high j/f value. However, since its porosity is much higher (0.68) than in case of regenerator F (0.56), its cooling capacity in magnetic refrigerator, would be lower due to less magnetic material.


18 Šarlah, A. – Tušek, J. – Poredoš, A.

This fact makes it less favourable for use in AMR as compared with others (Fig. 5).

• Regarding only the experimental results of the thermo-hydraulic properties of the various

regenerators, parallel plate (F) or square channels (C) regenerator would be the best choice for use in AMR.

Table 1. Geometrical properties of regenerators

Property Unit A. B. C. D. E. F.Material copper steel copper copper copper copperReg. size mm 60.0×20.0×16.0

δ mm 0.2 2.0 0.2 0.4 0.4/0.5 0.2dh mm 0.48 0.85 0.79 0.42 0.50 0.59ε - 0.512 0.39 0.68 0.487 0.384 0.562ap m2/m3 4273 1842 3445 4644 3063 3812

L/dh - 125 70.5 76 143 120 102

Fig. 2. Quantitative comparison of a pressure drop Δp as a function of mass flow mf for all

regenerators

Fig. 3. Correlations of friction loss factor f for all regenerators (best-fit curves according to the

experimental data)

Fig. 4. Correlations of experimental data of Colburn j-factor for all regenerators (best-fit curves according to the experimental data)

Fig. 5. Ratio of Colburn j-factor and friction loss factor f as a function of Re number



2 MAGNETOCALORIC PROPERTIES

The dimensionless thermo-hydraulic model used in the determination of the thermo-hydraulic properties of passive heat regenerators was upgraded for the simulation of AMR operation, i.e., it was supplemented with magnetocaloric properties of magnetic material and operational properties of AMR. Magnetocaloric properties were obtained using molecular field approximation (MFA) as proposed by Hashimoto et al. [8]. In order to use a proposed dimensionless model described in Sarlah et al. [6] and [7], two physical properties of magnetocaloric material must be numerically obtained using MFA, which is based on solid state physics: the temperature dependency of the partial derivative of entropy with respect to magnetic field (∂s/∂μ0H) and the temperature dependency of the specific heat cH. Both dependencies are presented in Figs. 6 and 7 for gadolinium (Gd), which was chosen as a basic magnetocaloric material.

Fig. 6. Partial derivative of entropy with respect to magnetic field ∂s/∂μ0H

3 NUMERICAL MODEL OF AMR

Insertion and employment of magnetocaloric properties into the numerical model for AMR allows us to simulate the operation of AMRR under different operating conditions and using various materials and

Table 2. Uncertainty and sensitivity analyses for heat transfer and pressure drop results according to the uncertainties of a particular variable for experimental run #26

Run #026 α [W/m2K] j [-] f [-] Re [-]Calculated values 187.45 0.00419 0.0148 868.1

Variable uv Δα Δj Δf ΔReUnit %1 % % % %

ρf kg/m3 0.50 0.01 0.29 0.50 -0.44cf J/kgK 0.50 0.49 0.31 - 0.00λf W/mK 0.50 -0.50 -0.38 - 0.05νf m2/s 0.50 - 0.29 - -0.43Tf °C 0.20 0.00 -0.02 - 0.04mf kg/s 2.69 2.71 -0.02 -5.17 2.74ρs kg/m3 0.51 0.00 -0.02 - 0.03cs J/kgK 0.96 0.01 -0.05 - 0.06λs W/mK 0.53 -0.01 0.00 - -0.01L m 0.17 - -0.21 -0.17 0.07Ar m2 0.80 0.01 0.76 1.61 -0.71ε - 0.99 0.97 0.93 3.92 0.04ap m2/m3 1.40 -2.68 -1.36 - -1.33dh m 1.49 - -0.05 2.38 1.58Δp Pa 0.075 - - 0.14 -

UR 7.48 1.77·10-4 7.16·10-4 27.67uR [%] 3.99 4.22 7.12 3.19

1 Percentage [%] unless otherwise stated.



fluids. The model has been verified accordingly: as proposed by Bačlić and Dragutinović [9], Engelbrecht et al. [10], and as appropriate for numerical stability and convergence of numerical results. Numerical model allows us to study the principle of operation of AMR, its refrigeration cycle, and to predict the operation (maximum temperature span and cooling load) of the device. Fig. 8 shows the refrigeration cycle of three layers of magnetocaloric material within the regenerator (entrance, middle and exit layers) during a steady-state operation of the AMR.

Fig. 7. Dependency of magnetic material’s specific heat cH on temperature T and magnetic

field μ0H

Fig. 8. Refrigeration cycles of three layers within the magnetocaloric material

The model has been verified against experimental data obtained by Kawanami [11],

who has performed a wide variety of tests using a reciprocating test bed. Initially the model has significantly over-predicted the results due to a reduced magnetocaloric effect (MCE) of the sample used during the experiments, i.e., the difference between MCE of the sample and the MCE as used in the model and obtained with MFA was substantial [7]. After introduction of the correction factor the agreement of the numerical and experimental data has improved significantly. The correction factor is explained in details in Sarlah [7]. The verified model was later used for evaluation of regenerator geometries that have been previously experimentally tested. As it can be seen on Fig. 9, both experimental and analytical results show all four steps of the AMR process. Analytical model agrees very well with the experimental regarding the description of each AMR step (Fig. 9). All four cycles can be clearly seen: magnetization (warming of the material due to MCE), cooling of the material (due to heat transfer from material to the fluid), demagnetization (rapid drop in the temperature due to MCE effect, and heating of the material (due to heat transfer from the fluid to the material). The difference between both results can be observed in the amplitude of each step during the transient response – achieved temperature on the cold/hot side. This is due to the thermal mass of the heat exchanger and losses such as fluid dispersion, which reduce the temperatures span (and consequently the cooling load) of the AMRR. However, the end result of both, numerical model and the experiment agree very well once the steady-state operation is reached [7].

The following conclusions can be made:• Temperature span of the regenerator strongly

depends on the cooling load of the AMR. According to our results temperature span and cooling load are inversely proportional when a single layer of Gd is used as a magnetic material.

• Each regenerator geometry has an optimal length-to-hydraulic diameter ratio at which COP is highest and should be designed appropriately [7].

• Comparing all regenerators from the point of view of their thermo-hydraulic and magnetic properties, we can conclude that parallel plate regenerators display best COP values,



mainly due to their high j/f ratio. On the other hand, packed bed regenerators show highest temperature difference, but lowest COP values.

• According to the initial experimental results by some other researchers [12], parallel plate geometries showed somewhat disappointing AMR operation, signifying that some other, even better, ’advanced’ regenerator geometries are required.

4 CONCLUSION

Experimental and numerical evaluation of various kinds of heat regenerators has been performed from the perspective of heat transfer and pressure drop. From the point of view of the performance of passive heat exchangers, the best result was shown by parallel plate heat exchanger (j/f ratio). However, when introducing magnetic properties, packed bed regenerator shows highest temperature difference due to an increased heat transfer, while it shows the lowest COP due to the highest pressure drop. For the future development of magnetic refrigeration it is crucial, that some new ‘advanced’ regenerator geometries are employed, which would show both an improved COP and temperature difference.

5 NOTATION

ap packing factor [-]Af free cross-section area [m2]Ar reg. cross-section area [m2]Aht heat transfer area [m2]c specific heat [J/kgK]dh hydraulic diameter [m]COP coefficient of performance [-]Δp pressure drop [bar]f Friction loss factor [-]H magnetic field strength [A/m]j Colburn factor [-]L length [m]mf mass flow [kg/s]Nu Nusselt number [-]Pr Prandtl number [-]Re Reynolds number [-]s specific entropy [J/kg K]St Stanton number [-]T temperature [°C]u uncertainty [%]vint interstitial velocity [m/s]α heat transfer coefficient [W/m2K]δ material thickness [m]ε porosity [-]λ thermal conductivity [W/mK]ρ density [kg/m3]ν kinematic viscosity [m2/s]μ0 permeability of vacuum [Wb/Am]

Fig. 9. Comparison of experimental (Kawanami [11]) and numerical results of the operation of AMR



Indexf fluidH constant magnetic fields solidv variable

Additional notation definitions:

j St

Nu

Am c

v c

d

d

f

f f

f f f

f

= ⋅ =⋅

⋅ =

=⋅

⋅⋅

⋅ ⋅

PrRe Pr

Pr

,

/ /2 3 2 3

α ρ

λ

Nud

dv

mv A

fpL

d

dh

f

dh

f

f

f f r p

toth

=⋅

=⋅

=⋅

⋅ ⋅ ⋅

= ⋅⋅

αλ

νρ α

,

Re ,int

exp

4

2

∆

ρρ ν

ρ

εα

f

f h f

f

hf

ht p

pL

d A

m

dVA

⋅= ⋅

⋅ ⋅

⋅

=⋅

=⋅

int

exp ,

.

2

2

22

4 4

∆

6 REFERENCES

[1] Heggs, P.J., Burns, D. (1988). Single-blow experimental prediction of heat transfer coefficients. Experimental Thermal and Fluid Science, vol. 1, no. 3, p. 243-251, DOI:10.1016/0894-1777(88)90003-9.

[2] Shah, R.K., Zhou, S.Q. (1997). Experimental techniques for obtaining design data of compact heat exchanger surfaces. Proceedings of the International Conference on Compact Heat Exchangers for the Process Industries, Snowbird, p. 365-379.

[3] Mullisen, R.S., Loehrke, R.I. (1986). A transient heat exchanger evaluation test for arbitrary fluid inlet temperature variation and longitudinal core conduction. ASME Journal of Heat Transfer, vol. 108, p. 370-376, DOI:10.1115/1.3246932.

[4] Tishin, A.M., Spichkin, Y.I. (2003). The magnetocaloric effect and its

applications. Institute of Physics Publishing, DOI:10.1887/0750309229.

[5] Pecharsky, V.K., Gschneidner, Jr., K.A. (1999). Magnetocaloric effect and magnetic refrigeration. Journal of Magnetism and Magnetic Materials, vol. 200, p. 44-56, DOI:10.1016/S0304-8853(99)00397-2.

[6] Sarlah, A., Poredos, A. (2007). Dimensionless numerical model for determination of magnetic regenerator’s heat transfer coefficient and its operation. 2nd International Conference on Magnetic Refrigeration at Room Temperature, Conference Proceedings, p. 231-238.

[7] Sarlah, A. (2008). Thermo-hydraulic properties of heat regenerators in magnetic refrigerator. PhD. Thesis, University of Ljubljana, Ljubljana.

[8] Hashimoto, T., Numasawa, T., Shino, M., Okada, T. (1981). Magnetic refrigeration in the temperature range from 10K to room temperature: the ferromagnetic refrigerants. Cryogenics, vol. 21, no. 11, p. 647-653, DOI:10.1016/0011-2275(81)90254-X.

[9] Bačlić, B.S., Dragutinović, G.D. (1998). Operation of counterflow regenerators. Computational Mechanics Inc., Southampton.

[10] Engelbrecht, K., Nellis, G., Klein, S. (2005). A numerical model of an active magnetic regenerator refrigeration system. Final Report. ARTI-21CR/612-10075, University of Wisconsin - Madison.

[11] Kawanami, T. (2007). Heat transfer characteristics and cooling performance of an active magnetic regenerator. 2nd IIF-IIR International Conference on Magnetic Refrigeration at Room Temperature – Conference Proceedings, p. 197-209.

[12] Zimm, C., Auringer, J., Boeder, A., Chell, J., Russek, S., Sternberg, A. (2007). Design and initial performance of a magnetic refrigerator with a rotating permanent magnet. 2nd IIF-IIR International Conference on Magnetic Refrigeration at Room Temperature – Conference Proceedings, p. 252-261.

http://dx.doi.org/10.1016/0894-1777(88)90003-9

http://dx.doi.org/10.1115/1.3246932

http://dx.doi.org/10.1887/0750309229

http://dx.doi.org/10.1016/S0304-8853(99)00397-2

http://dx.doi.org/10.1016/0011-2275(81)90254-X


*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, [email protected] 23

Correlation between Incident Angle, Measurement Distance, Object Colour and the Number of Acquired Points

at CNC Laser ScanningVukašinović, N. – Možina, J. – Duhovnik, J.

Nikola Vukašinović* – Janez Možina – Jože DuhovnikUniversity of Ljubljana, Faculty of Mechanical Engineering, Slovenia

In this paper the results of research about the influences of the incident angle, the measurement distance and object colour and reflectivity on the number of acquired points while using a laser-triangulation scanner on CNC-machines, are presented. The number of points is an essential parameter of a successful 3D surface reconstruction, although it is rarely considered as a subject of research. In this research we identified the scanning parameters to acquire a sufficient number of points for any surface reconstruction. The causes of the results are also identified and could be considered when creating automatic-measurement strategies for CNC-machines. Finally, the equation for an estimation of the number of acquired points in the optimal area of measuring parameters for the case example is also introduced.© 2011 Journal of Mechanical Engineering. All rights reservedKeywords: point cloud, point density, reverse engineering, laser scanning, laser triangulation

0 INTRODUCTION

Laser scanning of real object based on the laser triangulation to obtain 3D computer models has gained a lot of attention and popularity due to its price affordability and performance, especially in the field of control and reverse engineering. Therefore, a considerable amount of research has been conducted also on enhancing the quality of measuring results, which is constrained by optical laws and hardware limitations. Laser scanning system can be compared in several different ways, as it has been suggested by different research works and methods for quality evaluation.

Feng [1] and Xi [2] suggested separating the error into its systematic and random component since they have a different origin, and the systematic error is usually much easier to control. To achieve that, they introduced a combination of a flat surface and a ball to estimate the measurement error in their experiments.

Lartigue, Contri and Bourdet observed the quality of digitized point clouds [3] and [4]. They introduced the following four criteria: density, completeness, noise and accuracy.

Van Gestel [5] investigated different methods for evaluating the quality of measurement results, based on the scanning of different objects.

He paid special attention to the advantages and disadvantages of different geometries during an estimation of the measurement quality. He exposed the problem of a sphere that does not give stable results when scanned only from one direction. Together with his team, he suggested a method for a rapid evaluation of the scans measured with laser line scanners, based only on measurements of the flat surface. The method consists of the two of the above mentioned valuations: i.e. the random and systematic error component and therefore, gives the information only about the overall error magnitude.

In contrast to the previously mentioned researchers, Vezzetti [6] states that the problem occurs in differences between different measuring systems. Technical specifications of measuring systems given by manufacturers do not provide sufficient information about the accuracy and performance of the equipment. At the same time the knowledge of the users is also insufficient for choosing an appropriate measuring system and for accurate interpretation of measured results. Therefore, Vezzetti suggested a user-oriented procedure to estimate performances of laser 3D measuring system. He exposed the necessity for the information regarding accuracy, repeatability


24 Vukašinović, N. – Možina, J. – Duhovnik, J.

and resolution of measuring a system at different measuring conditions.

From the above mentioned research works it can be derived that the number of acquired points and their distribution are some of the major parameters in the evaluation of the performance of a 3D measuring device. They represent the first condition for a successful surface reconstruction based on the point cloud triangulation. Yet, they can be expressed in several different ways: either directly as density and completeness as Lartigue et al. suggested, or indirectly from the resolution as in [6]. Regardless, the sufficient amount of point data is essential for a successful surface reconstruction even if some of the point reduction methods [7] are applied later in the process of reconstruction.

1 EXPERIMENT

1.1 Measurement System

Laser measurement systems are normally based on the principle of laser optical triangulation. This relies on the geometrical conditions of the light beams, particularly on the information regarding the angle and distance between the light source and the picture of the reflected light on the CCD sensor [8]. When scanning complex or larger shapes, it is often necessary to move the measuring sensor relative to the object. In such cases the information about the sensor’s position in space is also needed, and not just the information provided by the laser scanning unit. Therefore, laser measurement equipment needs to be connected to a device that guides the sensor through the space and acquires its position. The 3D non-contact measurement system, therefore, consists of a four-axis milling machine from the Flexmatic company, a CVC-496 servo-motor controlling system from the Isel Automation company, a Zephyr KZ-50 laser triangulation measuring sensor from the Kreon company which is fixed to the CNC machine, and a personal computer for the coordination of the equipment. The layout of this 3D measuring system is shown in Figs. 1 and 2. The X, Y, Z, and A dimension CNC milling machine is driven by AC servo motors, and the encoder for each AC servo motor has a resolution of 2000 pulses per revolution. The

drivers for the AC servo motors are of the voltage control type. Multi-function interface cards, which include four channel encoders and counters were used to read the displacement data of each axis. The information about all three linear coordinates is sent in real time to the laser-sensor control-unit, where the position information is merged with the measured data of the sensor. The fourth, rotational axis is used only for the rotation of the measured object. The table is controlled by a PC controller. According to the manufacturer’s information, the accuracy of the measuring table is 0.01 mm for each axis. The PCL-711 interface card has a 12-bit A/D channel to read in the laser displacement data. The manufacturer of the Kreon laser sensor claims that the resolution of the laser sensor is 0.005 mm, and the repeatability is 0.006 mm according to the OSIS workgroup-3 standard [9]. Based on this information and our experience we estimate the sensor accuracy to be about 0.01 mm. The whole measuring system was calibrated by scanning a calibration ball from several viewpoints. The obtained 2 sigma of the whole measuring system was 0.04 mm. The system is controlled by a PC that is used to handle all the I/O data from the controller. For the surface data acquisition, Kreon hardware and Polygonia software are used. The signal achieved through the RS232 serial link from the machine encoders and the signal from the laser sensor unit are simultaneously collected and merged to obtain the proper information about surface geometry.

1.2 Measurement Procedure

Coloured 200×150×10 mm flat granite stones were used for measurement due to their good geometric stability. The flat-surface measurements were taken for three different surface colours which were equally distributed across the whole visible light spectrum. This approach was used because surfaces usually reflect broader light spectrum and do not have only narrow monochromatic reflection properties, which was discussed in [10] and [11]. For this reason, it is impossible to fully describe reflective properties of a surface with only one or few parameters.

Therefore, we decided to do three different sets of measurements which gave several


25Correlation between Incident Angle, Measurement Distance, Object Colour and the Number of Acquired Points at CNC Laser Scanning

advantages. Due to the sensor’s narrow-band filter we were interested in reflectance intensity rate only around 675 nm wavelength, regardless of the colour of the measured surface. Laser light power and sensor exposure time were adapted to each surface according to this intensity rate. The goal was to obtain light intensity which hits the CCD sensor as similar as possible for all different surface colours (Table 1). Referential settings were defined as a perpendicular surface-laser beam position with 130 mm sensor-surface distance. This combination enables measurement over the whole measurement range, for all surface colours and comparability of the results.

Fig. 2. Geometry of the laser sensor measuring field; (1) camera view-field; (2) laser light plane;

width of the measuring field; (3) near; (4) far from the laser source, sampling resolution; (5)

near; (6) far from the laser source

Relative reflection rate was determined with the spectral measurement of a light reflection

from different surfaces, which was described in [10]. The value shows the intensity of the light which reflects from some surface, compared to the intensity of the light, which is reflected from the white surface with the ideal Lambertian diffuse reflection.

Table 1. Relative reflection rate of different surface colours for 675 nm laser light and optical settings of the measurement

Relative reflection

rate [-]

Exposure time [s]

Laser power [mW]

Line width [dots]

Red 0.87 1/1000 2.0 6.9Green 0.23 1/250 2.5 7.1Blue 0.07 1/125 4.0 7.1

Since measured point clouds cover a different area of surface due to the measurement angle and the distance, only a central part of the point clouds was used. They were trimmed to the width of 15 mm in horizontal direction Y and length of 80 mm in horizontal direction X. The data prepared in this way give possibilities to easily estimate the point density from the number of points, and reduce the influence of distance variation when measuring at higher angles.

The measurements were performed at 7 different measurement distances, beginning at 130 mm and ending at 190 mm from the surface, and 14 different longitudinal measurement angles (i.e. rotation around axis parallel to the sensor movement – Fig. 1a) from 0 to 65 degree with 5-degree increment. Measurements of different distance-angle combinations were done in

Fig. 1. a) axes of measurement and rotation; b) measurement setup for laser triangulation scanning on the CNC platform

a) b)



random order to minimize the effects of possible systematic error.

2 MEASUREMENT RESULTS

2.1 Red Surface

Fig. 3 shows the relation between the number of acquired points, the surface-sensor distance and the longitudinal measurement angle for a red surface. The number of points was taken from a X × Y = 80 × 15 mm large sample. It can be seen that the highest number of points i.e. 40,000 was obtained at the smallest surface-sensor distance while the number of points decreased with higher distance in a linear manner and reached 30,000 points at the most distant boundary of system’s view-field. This effect can be explained by Fig. 2, points (5) and (6) which represent the distance between two adjacent points at the beginning and at the end of system’s view-field. It can be seen that the distance between two points rises with the distance from the sensor, which causes lower point density at larger measurement distances.

The number of points did not change significantly with the longitudinal measuring angle across most of the system’s measurement range, and deviations began at 60 degrees, but no rule can be derived solely from this measurement. Therefore, it was necessary to investigate the other surface colours as well.

Fig. 3. The number of acquired points on the red surface with horizontal cross-section X×Y=80×15mm, depending on the surface-

sensor distance and the longitudinal angle of measurement

2.2 Green Surface

The results of the investigation of the green surface are presented by Fig. 4. The maximum number of acquired points in this case was approximately 36,000 at close measurement distances and approximately 28,000 at larger measurement distances.

Fig. 4. The number of acquired points on the green surface with horizontal cross section X×Y=80×15mm, depending on the surface-

sensor distance and the longitudinal angle of measurement

As in the case of a red surface, the longitudinal measuring angle up to some angles did not have a significant influence on the measured number of points. The fold-down borderline was stretched from 20 degrees for large measurement distances, to 40 degrees when the sensor-surface distances are the smallest. After that line, the number of acquired point dropped drastically. It reached only half of the maximum value already after 5 to 10 degrees from the fold-down line and after 20 degrees from the fold-down line the number of acquired reaches was already less than 1000. The reason for the quick drop of the acquired number of points is found in the decrease of the laser light intensity which returns into the sensor under the threshold value of the measuring sensor.

2.3 Blue Surface

If the number of point results from red and green surface is compared the trend for scanning surfaces with lower reflection rates (Table 1) can be predicted. The maximum number of points acquired on a blue surface is therefore,


27Correlation between Incident Angle, Measurement Distance, Object Colour and the Number of Acquired Points at CNC Laser Scanning

approximately 4,000 points lower than on a green surface and is around 32,000 points at the smallest measurement distances and approximately 24,000 points when measured at the largest possible measurement distances. The results are graphically shown in Fig. 5.

The fold-down border is very obvious again and this time occurred at even smaller longitudinal angles of measurement. The fold-down border of the largest measurement distances was at approximately 15 degrees and at 25 degrees the number of acquired points was only one tenth of the maximum number of points measured at that distance. At the smallest measurement distances the fold-down border occurred at approximately 25 degrees, but the drop was not that steep, so one tenth of the maximum number of points for that distance was acquired at 55 degrees.

Fig. 5. The number of acquired points on the blue surface with horizontal cross section X×Y=80×15mm, depending on the surface-sensor distance and the longitudinal angle of measurement

3 EQUATION

From the results presented in the previous section it can be seen that there are rules to predict the number of acquired points. For that reason, it was necessary to define an equation which would describe the results from the previous section. Since the highest number of points could be obtained only at the angle-distance combinations which are represented with flat regions of diagrams in Figs. 3 to 5, we simplified the problem only to these regions, providing also the threshold line of

acceptable angle-distance combinations. The approximate equation was obtained

statistically with the help of the factorial analysis and the analysis of variance (Anova test). The result is given in Eq. (1), where N [-] stands for the number of acquired points, d [mm] stands for the sensor-to-surface distance, a [°] stands for the longitudinal angle of measurement and rrel [-] stands for relative reflection rate of the measured surface, which is the function of surface colour and of the wavelength of measuring laser.

Obviously linear characteristics of both geometric parameters are reflected in a linear characteristic of the equation, while the relative reflection rate requires the second power to obtain better results of the interpolation.

N d

rel

= − ⋅ ++ ⋅ + ⋅ −

−

46896 41017 132 6310948 54960 36484 590210

. .. ..

α ρ

330158 36 9790927 01690 23020 57456

⋅ ⋅ − ⋅ ⋅ +

+ ⋅ ⋅ − ⋅

d d rel

rel r

α ρ

α ρ ρ

.. . eel .

(1)

4 CONCLUSIONS

This article presents the results of a comprehensive research which was done to investigate the influences of different scanning parameters on the quality of the measurement results. The colour of the measured surface, the distance between the surface and the sensor and the angle of measurement were recognized as the factors which have the greatest impact on the quality of the measurement results. In this paper only the number of points as one of the quality output possibilities has been presented, while other, such as measurement uncertainty, have been covered in other papers and articles.

The results showed that measurement angle has no impact on the acquired number of points up to some value, which starts at extreme 70 degrees for red surfaces and short measurement distances but stretches down to 20 degrees with the poorer surface reflectivity (e.g. blue surface) and longer measurement distances. When crossing this angle boundary, the number of the acquired points decreases drastically.

On the other hand, the relation between the distance and the number of acquired points gave almost ideally linear correlation that originates in



the spreading of the scanner’s view-range with the distance.

All the results were gathered in an equation for the estimation of the number of acquired points. The equation could be used as a support for more reliable measuring strategies.

5 REFERENCES

[1] Feng, H.-Y., Liu, Y., Xi, F. (2001). Analysis of digitizing errors of a laser scanning system. Precision Engineering, vol. 25, p. 185-191, DOI:10.1016/S0141-6359(00)00071-4.

[2] Xi, F., Liu, Y., Feng, H.-Y. (2001). Error compensation for three-dimensional line laser scanning data. The International Journal of Advanced Manufacturing Technology, vol. 18, p. 211-216, DOI:10.1007/s001700170076.

[3] Lartigue, C., Contri, A., Bourdet, P. (2002). Digitised point quality in relation with point exploitation. Measurement, vol. 32, p. 193-203, DOI:10.1016/S0263-2241(02)00008-8.

[4] Contri, A., Bourdet, P., Lartigue, C. (1999). Quality of 3D digitised points obtained with non-contact optical sensors. CIRP Annals - Manufacturing Technology, vol. 51, p. 443-446.

[5] Van Gestel, N., Cuypers, S., Bleys, P., Kruth, J.-P. (2009). A performance evaluation test for laser line scanners on CMMs. Optics and Lasers in Engineering, vol. 47, p. 336-342, DOI:10.1016/j.optlaseng.2008.06.001.

[6] Vezzetti, E. (2009). Computer aided

inspection: design of customer-oriented benchmark for noncontact 3D scanner evaluation. The International Journal of Advanced Manufacturing Technology, vol. 43, p. 1157-1166.

[7] Budak, I., Soković, M., Kopač, J., Hodolič, J. (2009). Point data pre-processing based on fuzzy logic for reverse engineering modelling. Strojniški vestnik – Journal of Mechanical Engineering, vol. 55, no. 12, p. 755-765.

[8] Bračun, D., Jezeršek, M., Diaci, J. (2006). Triangulation model taking into account light sheet curvature. Measurement Science and Technology, vol. 17, p. 2191-2196, DOI: 10.1088/0957-0233/17/8/019.

[9] Optical sensor interface standard (OSIS), workgroup 3; specification and performance verification, 09/2003.

[10] Vukašinović, N., Bračun, D., Možina, J., Duhovnik, J. (2010). The influence of incident angle, object colour and distance on CNC laser scanning. International Journal of Advanced Manufacturing Technology, vol. 50, no. 1-4, p. 265-274, DOI:10.1007/s00170-009-2493-x.

[11] Vukašinović, N., Korošec, M., Duhovnik, J. (2010). The influence of surface topology on the accuracy of laser triangulation scanning results. Strojniški vestnik – Journal of Mechanical Engineering, vol. 56, no. 1, p. 23-30.

http://dx.doi.org/10.1016/S0141-6359(00)00071-4

http://dx.doi.org/10.1007/s001700170076

http://dx.doi.org/10.1007/s001700170076

http://dx.doi.org/10.1016/S0263-2241(02)00008-8

http://dx.doi.org/10.1016/j.optlaseng.2008.06.001

http://dx.doi.org/10.1088/0957-0233/17/8/019

http://dx.doi.org/10.1007/s00170-009-2493-x

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1, 29-36 Paper received: 26.08.2009DOI: 10.5545/sv-jme.2009.111 Paper accepted: 06.12.2011

*Corr. Author’s Address: Institute of Nuclear Sciences “VINČA”, 11001 Belgrade, Serbia, [email protected] 29

Thermal Load of Multidisc Wet Friction Assemblies at Braking RegimeŽivanović, Z. ‒ Milić, M.

Zlatomir Živanović1,* ‒ Miodrag Milić2

1 Institute of Nuclear Sciences “VINČA”, Serbia 2 Military Technical Institute, Belgrade, Serbia

The paper presents the results of thermal load investigations of multidisc friction assemblies used as service brakes of a high speed tracked vehicle. By simulating the corresponding braking regimes and measuring the characteristic quantities on an inertial test stand, the relevant parameters of the braking process have been determined. The obtained results have been analyzed and compared to the permitted values of thermal load of the material of the tested friction discs. After a certain number of braking cycles by visual inspection of the brakes the state of the friction elements have been determined. The speed limits for braking the vehicle at higher transmission gear ratios, which may result in a permanent damage of the brakes, have been determined.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: track vehicle, wet friction assembly, thermal load

0 INTRODUCTION

The most widespread application of wet multidisc friction assemblies (clutches or brakes) is in motor vehicle transmissions with planetary gears. It is possible to use them in transmissions of high-speed tracked vehicles for the purpose of gear change, in the mechanisms for steering, as the main clutch, and even as the service brake.

Sintered materials are usually applied in multidisc friction assemblies operating in oil, intended for heavy duty working conditions. These materials are obtained by means of the technology of sintering powdered materials whose contents are dominated by certain elements, such as iron or copper. This results in highly wear-resistant materials.

In order to establish thermal load wet multidisc friction brakes applied in the transmission of a high-speed tracked vehicle, their performance is investigated by simulating the corresponding regimes of exploitation on a test stand.

On the basis of these tests, after certain number of braking cycles the interdependence between the state of the brake and the regime of sliding is established, i.e. the temperatures of the sliding surfaces are measured.

By correlating the obtained test stand results with the process of braking in real vehicles,

the braking regimes (range of speeds) which result in damaging of the brakes can be identified. The obtained data can be reliably applied in practice for the purpose of preserving the operative capabilities of the brakes through observing certain recommendations, i.e. by avoiding critical operating regimes. In this way good operative availability of a vehicle can be provided and the unnecessary high costs of gearbox repairs may be avoided.

1 CHARACTERISTICS OF THE EXAMINED WET MULTIDISC BRAKES

Functional elements of the examined wet multidisc brakes are a combination of steel and sintered discs made of metalloceramic friction material MK-5 [1]. This material is a composition of copper powder and different alloying ingredients. The components of MK-5 material are: 62 to 85% copper, 5 to 10% tin, 4 to 8% graphite, 0 to 2% iron, 0 to 2% nickel, 0.3% silicon dioxide, and 0.3% asbestos [2] and [3].

Linings of the metalloceramic discs are made by compressing the powdered mixture of the above elements which is then sintered and mated with a steel core.

A metalloceramic friction disc, with the corresponding geometric data, is shown in Fig. 1 [4]. Spiral-radial grooves are made on the friction


30 Živanović, Z. ‒ Milić, M.

surface for supplying oil for lubrication, cooling, and draining the products of wear. The effective friction surface is about 60% of the total disc surface.

Fig. 1. Geometric data of a sintered friction disc

The wet multidisc brakes, which are the subject of these investigations, consist of a package of the steel and metalloceramic friction discs, separator discs, and the hydraulic cylinders serving for engagement of the brakes by means of oil pressure. The brakes are denoted by F4 and F5 and their basic characteristics [5] are presented in Table 1, where z is number of friction surfaces, Rs is mean radius of friction surface, Al is effective friction surface, Ak is effective piston surface of the hydraulic cylinder, ml is average mass of friction discs and F0 is force of the return springs.

Table 1. Basic characteristics of the brakes

Basic characteristics

BrakeF4 F5

z - 10 12Rs [m] 0.237Al [×10-4m2] 220ml [kg] 1.465Ak [×10-4 m2] 380F0 [N] 2340 2700

Brakes F4 and F5 are constituent parts of both planetary gearboxes used in the transmission of a high-speed tracked vehicle.

2 THERMAL LOAD OF THE BRAKES

Determination of the range of permitted thermal loads of the wet multidisc brakes by applying energy parameter pνμ (often efficiently

applied to dry friction pairs) can not be applied since the intensity of cooling has a considerable influence on the friction process. For this reason, a parameter taken for the evaluation of energetic capability of the friction elements of multidisc brakes operating in oil is critical temperature of the friction surface as a function of the specific friction force. This dependence can be established on the basis of extensive investigations.

The amount of heat generated at a friction surface is function of the friction torque and relative sliding speed of the friction elements [6]. In the process of engagement of the brake these quantities are variable. Owing to this, the temperature of the friction surface, assuming all other conditions identical, is proportional to the amount of heat present at the friction surface, i.e. to the average power of sliding.

The investigations of friction pairs: metalloceramic based on copper–steel operating in oil, established that there was a limited range of permissible thermal loads [7]. Inside this range the metalloceramic friction elements have satisfactory operating lifetime and good resistance to wear.

The existence of the limit between the normal and enhanced wear is explained as follows [7]. When due to overload of an operating friction assembly its friction surfaces reach a high (limiting) temperature, thermal degradation of the oil between the friction surfaces may occur leading to a destruction of the minimum oil layer (destruction of the boundary lubrication). While the minimum oil layer exists, a high friction coefficient and a good cooling of the friction surfaces are achieved. Destruction of the minimum oil layer brings the friction assembly to the zone of semi-dry or dry friction which is accompanied by enhanced wear, even destruction of the friction assembly.

The experimental investigations of metalloceramic material MK-5 [7] showed that the speed of sliding, within a certain range, did not influence the qualitative picture of the process between friction surfaces. It was possible to establish the dependence in the form shown in Fig. 2, where: θcr is critical temperature of the friction surfaces, and Fμs is specific friction force.

During these tests, it has also been established that the onset of the destruction of the oil layer was not dependent on the oil flow and


31Thermal Load of Multidisc Wet Friction Assemblies at Braking Regime

distribution and size of the grooves on the friction surface, but on the normal force, temperature of the friction surface, oil properties, and type of the friction material. The permitted thermal loads of the friction elements of multidisc brakes operating in oil, for the specific friction forces Fμs, lie below curve θcr = f(Fμs ). In this region the high reliability and good resistance to wear are accomplished.

2 4 6 8 1080

100

120

140

160

180

200

MK-5

θ cr [

0 C]

Fµs [Ncm-2]

Fig. 2. Critical thermal load of metalloceramic friction discs

Dependence θcr = f(Fμs) can be represented by an empirical expression in the form [7]:

θ µcr sF= −250 0 42. . (1)

The dependence shown in Fig. 2 has been obtained experimentally on a test stand [7] by applying long-term braking under different loads. At each load, constant values of the friction torque and sliding speed have been maintained. The process of braking was running until the critical temperature resulting in destruction of the oil layer was reached which was accompanied by sudden growth of the friction torque.

The results presented in [7] have been the basis for establishing whether the sliding regimes of the examined multidisc brakes, F4 and F5, were within the limits of the permitted thermal loads. The limiting range of the working regimes where friction assemblies have preserved functionality and reliability has been identified. This is of particular importance for using these assemblies as service brakes since it requires a strict adherence to the instructions for use owing to their sensitivity to long-term braking and overload.

3 THE TEST STAND

Tests of the above brakes has been carried out on the test stand intended for complex testing of transmissions under load [8]. In the course of the tests, different operating regimes of the friction assemblies were simulated. This paper presents only the results concerning the regimes of braking with the engine disconnected.

For driving the test stand the same engine as the one used in the vehicle has been applied. Via a conical gear and a transfer case, the engine drives a planetary gearbox where the examined brakes have been integrated. For the purpose of simulating the conditions of a vehicle in exploitation, the test stand is supplied with a hydrodynamic brake, serving for achieving necessary loads, and with a flywheel, simulating one half of the kinetic energy of the vehicle, since the vehicle is provided with two planetary gearboxes and two final drives.

Before the service brake is activated, the engine is disconnected via the main clutch, and braking of the flywheel masses and other rotating parts is achieved by the service brake only. From the point of view of vehicle deceleration and thermal load of the friction assemblies this is the most unfavorable working regime.

Positions of brakes F4 and F5 within the kinematic scheme of the gearbox are presented in Fig. 3. Angular speeds ω4 and ω5 of rotating elements of the brakes and the corresponding loading torques M4 and M5 are determined from the measured braking torque Mi, speed of rotation of the output shaft of the gearbox ni (ωi), and the characteristics of the applied planetary set.

Fig. 3. Positions of the examined brakes in the scheme of the planetary gearbox



During the tests the following measured quantities have been recorded [8] and [9], Table 2:

Table 2. Measured quantities during tests

Mi [Nm] Braking torque at the output shaft of the gearbox

nu, ni [min-1]Speeds of rotation of the

input and output shafts of the gearbox

p4, p5 [bar] Activation pressures of brakes F4 and F5

θ4, θ5 [oC] Temperatures of the friction surfaces of brakes F4 and F5

Measurement of friction surface temperatures was carried out on the immobile parts of the brakes by using thermocouples of type K and an HP 3497 Data Acquisition System, an HP 3456A Digital Voltmeter, an HP 9845 Desktop computer, and an HP-IB interface.

Fig. 4 shows a detail of the gearbox of one of the friction assemblies and position of the temperature sensor [10].

Fig. 4. Position of the temperature sensor

On the basis of the measured braking torque at the output of the gearbox Mi, and kinematic scheme of Fig. 3, torques M4 and M5 loading brakes F4 and F5 are determined. They also represent the corresponding friction torques Mt4 and Mt5.

M M MMk

Mt aH

i4 4 44

410 341= = =

+= ⋅. , (2)

M M M M k Mt b a i5 5 4 4 4 0 659= = = ⋅ = ⋅. , (3)

where k4 = 1.933 is a characteristic of the planetary set, a4 is sun gear of the planetary set, H4 is carrier of planet gears and b4 is epicycle (ring gear).

Angular speeds of the elements F4 and F5 are identical to angular speed ωi, since immediately prior to activation of the brakes, the gearbox was in the direct drive and all the elements shown in Fig. 3 were rotating at the same angular speed.

4 THE EXPERIMENTAL RESULTS

By bringing the engine speed to the regime corresponding to the maximum speed of the vehicle, braking in the fifth-direct drive has been simulated on the test stand.

A record of the measured quantities in the braking process made in one of the realized experiments is shown in Fig. 5.

Fig. 5. A record of the measured quantities during braking process on the test stand

In Fig. 5 two characteristic regions can be identified:

Region A is the initial stage of the braking process, when brakes F4 and F5 are prepared for braking and chambers of the hydraulic cylinders are filled by oil (time interval t0 ‒ t1) and region B is the cycle of braking, occurring during time interval (t1 – t2), when an intensive sliding of the brakes is on. It is evident that owing to the sliding of the brakes, temperatures of the friction surfaces increase. After the flywheel mass is stopped (instant t2) and somewhat delayed drop of the oil pressure, temperatures of brakes F4 and F5 are stabilized with a tendency of dropping due to the cooling action of the oil.

In order to determine the characteristic parameters of the sliding process during time interval (t1 – t2), processing the experimental



data has been done by applying the following analytical expressions.

General expression for the friction torque [11]:

M F R z F R zt s n s= ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅µ µ2 2 , (4)

where μ is coefficient of friction, Fμ is force of friction, Fn is normal force determined by expression:

F p A Fn k= ⋅ − 0 , (5)

where p is actuating pressure of the brake, and F0 is force of return spring.

From the above relations it is possible to determine the specific friction force (Fμs) and coefficient of friction (μ) in the form:

F MR z As

t

s lµ =

⋅ ⋅ ⋅2, (6)

µ =⋅ ⋅ ⋅MR F z

t

s n2. (7)

From the friction torque and angular speeds of the elements of the brakes it is possible to determine the work of sliding (Lk) and power of sliding (Pk) by the following expressions [11]:

L P t dt M t t dtk k

t

t

tk k

= ⋅ = ⋅ ⋅∫ ∫( ) ( ) ( ) ,0 0

ω (8)

and P Mk t= ⋅ω, (9)

where ω is relative angular speed of rotating elements of brakes F4 and F5, and tk is sliding time of the brakes.

The friction torque and the power of sliding of brakes F4 and F5, shown in Figs. 6 and 7, are determined by Eqs. (2), (3) and (9).

By using Eqs. (6), (7) and (8), values of the specific friction forces, coefficients of friction, and sliding works in these experiments have been determined. The values are shown in Table 3, together with the measured temperature values.

Since the boundary shown in Fig. 2 is applicable in this case, the critical operating temperatures for both brakes have been identified from the specific friction forces, Table 3.

As regards the method of temperature measurement, it may be the subject of discussion whether the measured and true temperature values of the friction assembly coincide.

0 1 2 3 4 5 60

2x105

4x105

6x105

8x105

1x106

0

1x103

2x103

3x103

4x103

5x103

0

50

100

150

200

250

Mt4 [N

m]

ω 4 [s

-1]

P k4 [W

]

t [s]

Pk4

Mt4

ω4

Fig. 6. Parameters of the sliding process of brake F4

0 1 2 3 4 50

4x105

8x105

1x106

2x106

2x106

0

2x103

4x103

6x103

8x103

1x104

0

50

100

150

200

250

Mt5 [N

m]

ω 5 [s

-1]

P k5 [W

]

t [s]

Pk5

Mt5

ω5

Fig. 7. Parameters of the sliding processof brake F5

Table 3. Characteristic parameters of the braking process

Characteristic parameters BrakeF4 F5

μ [-] 0.039 0.056Lk [MJ] 1.5566 3.0096Fμs [N/cm2] 2.35 3.79

θcr (from Fig. 2) [°C] 175 143∆θ

(from experiment) [°C] 109 187

θmax (from experiment) [°C] 210 288

In many cases temperature at the edge of the friction assembly is considerably lower compared to the temperature in the middle of the disc package. However, some investigations



[12] showed that the difference between these temperatures was very small if the discs were made of sintered bronze. This is explained by good conductivity of sintered bronze.

In this work the assumption is made that thermal conductivity [13] of the disc package was relatively high since the percentage of copper in the sintered discs was prevailing. Therefore, for the purpose of the present analysis it was assumed that the measured temperature was equal to the true temperature of the friction assembly.

5 ANALYSIS OF THE RESULTS

From Table 3 it can be seen that the measured temperature at the friction surface of brake F4 was 210 °C, i.e. above the critical temperature (175 °C) which corresponds to the specific friction force of 2.35 N/cm2 (Fig. 2). This shows that brake F4 was operating in the region of impermissible loads.

In addition, the measured temperature at the friction surface of brake F5 was 288 °C i.e. considerably above the critical temperature (143 °C) which corresponds to the specific friction force of 3.79 N/cm2 (Fig. 2). This case shows that brake F5 was operating in the range of an exceptional overload. It can be concluded that the regime of friction in both cases caused thermal overload of the friction elements.

Visual inspection of the brakes, which followed after a certain number of braking cycles, showed considerable deformations of the elements of both brakes. Fig. 8 presents a photo of the package of the steel and metalloceramic discs showing clearly visible conical deformations, more apparent on the sintered discs. Greater defects were observed in brake F5, which is logical owing to its greater thermal overload.

Fig. 9 shows surface of a steel disc which shows traces of partial burnings of the friction surface and deposits of the sintered material owing to an intensive wear.

Values of the coefficients of friction, Table 3, are coincident with the values of the coefficients of friction obtained by the manufacturer while testing identical friction discs on an inertial test stand [14].

It is evident that the braking regime did not comply with the energetic capabilities of the

friction elements, which lead to damaging of their working surfaces. It turned out that thermal load of the brakes caused by long-term slidings was considerably above their limiting values of the specific friction forces. The presented results show that the limiting values of thermal loads of the examined friction pairs can be efficiently used for determination of the optimum working regimes of multidisc brakes, even during design phase.

Fig. 8. Deformed package of discs of brake F5 after tests

Fig. 9. Traces of the damage on a steel disc after tests

By applying the results obtained on the test stand to braking of a real vehicle, the measured temperatures of friction surfaces of the brakes can be presented as a function of the vehicle speed, Fig. 10. The vehicle speed is determined by expression:

vrii pt

bp

=⋅ω

, (10)

where rpt = 0.333 m is average radius of the driving wheel and ibp = 5.0 is gear ratio of the final drive.

Fig. 10 shows that for the simulated braking regime, owing to relatively low limiting



temperature values, braking of the vehicle from maximum speeds to a halt is not possible without damaging brakes F4 and F5. Nevertheless, braking from the maximum speed of the vehicle without damaging these brakes can be performed until speed drops to 48 km/h. If further braking is required, the transmission ratio has to be reduced or braking should be performed combined with short interruptions in order to ensure the corresponding cooling and thermal relief of the friction elements. These are extreme situations not recommendable in exploitation of a vehicle.

0 10 20 30 40 50 60 7050

100

150

200

250

300

350

θ5cr=1430C

θ4cr=1750C θ 4, θ 5

[0 C]

v [kmh-1]

Friction F5 Friction F4

Fig. 10. The limiting braking conditions at maximum speeds

The instructions for using a vehicle say that braking of the vehicle by the braking pedal at high speeds should be avoided, since thermal overload of the friction elements and an enhanced wear are likely. In such situations only short braking is permitted, i.e. occasional activation of the brakes by special pneumatic command, i.e. when long-term braking is disabled.

These investigations confirm that multidisc brakes are sensitive to long-term slidings. They give a specific guidance to the driver for performing braking at higher vehicle speeds.

6 CONCLUSIONS

The performed tests show that the simulated regimes of braking did not comply with the energetic capabilities of the considered brakes. A long-term sliding, followed by high values of the sliding wor, caused high temperatures of the

friction surfaces, which lead to the permanent damage of the brakes.

The accomplished specific friction forces indicated that the brakes were operated in the regions well above the limiting values of the permissible thermal loads, recommended for the material of the friction discs.

Conditions of the brakes, after a certain number of braking cycles, were in agreement with the previously stated conclusions. A visual inspection of the brakes showed significant deformations of the friction discs and traces of high temperatures at the friction surfaces.

These investigations allow defining the limiting regimes, i.e. the regimes when braking of a vehicle performed within the zone of maximum speeds does not cause permanent damage of the brakes. This is a practical contribution of the present work. The investigations also confirmed that these brakes were sensitive to long-term slidings, therefore these braking regimes should be avoided.

7 REFERENCES

[1] Derkacheva, G.M. (2000). Effects of preparation technique for MK-5 material on frictional and wear response. Powder Metallurgy and Metal Ceramics, vol. 39, no. 1-2, p. 38-40, DOI:10.1007/BF02677439.

[2] Gapojan, D.T. (1966). Friction clutches of automatic gearboxes, Mashinostroenye, Moscow. (in Russian)

[3] Živanović, Z., Janićijević, N. (1999). Automatic transmissions of motor vehicles. IP Ecolibri, Belgrade, p. 110-200. (in Serbian)

[4] Živanović, Z., Uskoković, A. (2000). The influence of the resistence to wear and sliding regimes of metalloceramic friction assemblies on their operating life cycle. Proceedings of XIth International Symposium “Motor Vehicles and Motors”, Kragujevac, p. 137-140. (in Serbian)

[5] Živanović, Z. (1998). Energetic load of metalloceramic friction elements of a multidisc wet friction brake. Proceedings of Xth International Symposium “Motor Vehicles and Motors”, Kragujevac, p. 107-110. (in Serbian)

http://dx.doi.org/10.1007/BF02677439



[6] Zuckov, M.G., Fantalov, V.S. (1983). Wear out and friction coefficient of friction assemblies operating with metalloceramic disks in oil. Courier of Mechanical Engineering, no. 4, p. 25-26. (in Russian)

[7] Sopkin, V.A., Brikov, A.C. (1985). Testing the capacities of the multiple friction disks of oil cooled brakes. Tractors and Propulsion Machines, no. 3, p. 10-15. (in Russian)

[8] Milić, M., Pantić, M., Živanović, Z. (2007). Thermal load of multidisc friction assemblies in the braking process. Proceedings of the Symposium on Defense Technologies “OTEH 2007”, p. 11-14. (in Serbian)

[9] Živanovic, Z. (2011). The development of an electro-hydraulic transmission control system of a high-speed tracked vehicle. International Journal of Heavy Vehicle Systems, vol. 18, no. 1, p. 46-63, DOI:10.1504/IJHVS.2011.037959.

[10] Todorovic, J. (1986). Testing of motor vehicles. Faculty of Mechanical Engineering, Belgrade. (in Serbian)

[11] Živanovic, Z. (1997). Thermal load of multiple friction clutches immersed in oil in process of gear change control. Mobility & Vehicle Mechanics, Engines and Transportation Systems, vol. 23, no. 1, p. 18-24.

[12] Marklund, P., Larsson, R. (2007). Wet clutch under limited slip conditions–simplified testing and simulation. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 221, no. 1, p. 545-551, DOI:10.1243/13506501JET252.

[13] Reibenschuh, M., Oder, G., Čuš, F., Potrč, I. (2009). Modelling and analysis of thermal and stress loads in train disc brakes – braking from 250 km/h to standstill. Strojniški vestnik - Journal of Mechanical Engineering, vol. 55, no. 7-8, p. 494-502.

[14] Lazarević, D., Živanović, Z. (2003). Thermal stresses of motor vehicle clutches and brakes friction discs. Scientific Technical Review, vol. LIII, no. 4, p. 10-18.

http://dx.doi.org/10.1504/IJHVS.2011.037959

http://dx.doi.org/10.1243/13506501JET252


*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, Ljubljana, Slovenia, [email protected] 37

Control of Separation Flow over a Wind Turbine Blade with Plasma Actuators

Potočar, E. ‒ Širok, B. ‒ Hočevar, M. ‒ Eberlinc, M.Erik Potočar1 ‒ Branko Širok2 ‒ Marko Hočevar2 ‒ Matjaž Eberlinc2,*

1Ministry of the Economy, Directorate for Energy, Slovenia 2University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

This paper analyses the effects produced by a plasma actuator on flow around a turbine blade profile at Re 7600 and Re 10500. The analysis is undertaken with flow visualizations. The experiments indicate that for low Reynolds number plasma has a significant influence on flow around the blade and that the effects of actuation depend on power added to flow and relative distance between the electrode and the separation line of the actuator.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: wind turbine blade, plasma actuator, flow control, electrohydrodynamic actuator

0 INTRODUCTION

Wind turbines are complex, dynamically flexible structures that must operate under turbulent and unpredictable environmental conditions in which efficiency is highly dependent on well-designed control. Different significant problems may reduce the aerodynamic performance of blade profiles with low Reynolds number (Re). The possibility to quickly influence the aerodynamic loads acting on individual blades usually operating at low Re depends on active aerodynamic devices. Flow control is focused on the mitigation of these unpredictable environmental conditions by using different strategies like flaps or flexible wings [1] or boundary layer control (e.g. blowing, suction, etc.) [2] and [3]. Inter alia, the concept of reducing blade wake through trailing edge blowing has been investigated in the literature with different explanations being proposed. Schlichting [4] developed a method to prevent flow separation by supplying extra energy to fluid particles.

The use of electrohydrodynamic (EHD) actuators was proposed some years ago [5] and [6]. These actuators ionize air flow and produce localized momentum to the flow through a collision process by migrating charged particles with neutral air particles. EHD phenomena are based on the fact that currents involved are so low that the intensities of the magnetic forces are negligible compared to the electric ones [6]. The main advantages of EHD actuators are absence of moving parts, very short response time

and relatively good efficiency in transforming electrical energy to mechanical energy [7]. EHD actuators may be divided into three large groups: corona-based devices [6], dielectric barrier discharge devices [8] and plasma sheet devices [6].

A plasma actuator is composed of two electrodes and a dielectric as shown in Fig. 1. Plasma is generated by dielectric barrier discharge in the area between the exposed electrode and the dielectric when alternating current is applied at high voltage to both electrodes. Plasma is accelerated by the electric field and provides atmosphere with momentum. The device produces a homogeneous luminescence that occupies the inter-electrode space along the span. In this region, the surface is covered by a thin film of ionized air. The flow with several m/s of velocity is induced from the exposed electrode to the insulated electrode. If necessary, a third electrode may be added to the system so as to ameliorate the stability of the discharge [9].

Fig. 1. Measuring equipment

This paper aims at studying the improvement of aerodynamic performance


38 Potočar, E. ‒ Širok, B. ‒ Hočevar, M. ‒ Eberlinc, M.

of wind turbine blade operating at low Re by means of a plasma sheet device powered by the AC potential difference. The purpose of measurement performed on a wind turbine blade in low-speed wind tunnel is to confirm the influence of plasma actuator on the flow field near the upper part of the profile. The purpose is to better understand changes occurring to the aerodynamic characteristic under plasma actuators and to develop wind turbine blades with better aerodynamic characteristic.

The influence of plasma actuators on flow around the blade depends on flow conditions (power of plasma, flow velocities, angles of attack, etc.). A good synthesis [5] of influence of plasma actuators can be obtained by analyzing the intensity level of actuation as a function of angle of attack of turbine blade profile α and velocity U0. The intensity of actuation is evaluated with non-dimensional power coefficient CW defined as follows [9]:

C WU b

LcWele=

0 5 03

2

.,

ρ δ (1)

where Lele is inter-electrode distance, b electrode length, δ thickness of plasma sheet and c blade profile cord. Parameter W is the power of discharge and may be easily calculated as the product of discharge current I and the applied voltage difference between electrodes ΔV.

The same power coefficient in terms of other usual non-dimensional parameter can be expressed as follows:

C EU

LcW

HD i ele=

Re2 0

2ν , (2)

where Re = (U0·C)/n, EHD = (Ic3mi)/(ArJ2) and A = b·δ are the discharge section, ρ and ν respectively the density and kinematic viscosity of the fluid, and μi the mobility of ions. Ion velocity vi in Eq. (2) can be estimated with μiE0≈ μi(ΔV/Lele) [10].

1 EXPERIMENTAL SET-UP

Experimental set-up is shown in Fig. 2. It is composed of a wind tunnel, a blade profile, and plasma actuation device and flow visualization equipment.

1.1 Wind Tunnel and Blade Profile

The experiments were conducted in an open wind tunnel consisting of a square closed test section, as shown in Fig. 2. Air is drawn into the tunnel through the converging section with area ratio 16:1 and with inlet size of 400×400 mm (Fig. 2, point 2). The converging section included settling screens. A straight square test section 800×100×100 mm in size (Fig. 2, point 4) was used, which accommodated the profile. A honeycomb section formed the end of the test section of the wind tunnel (Fig. 2, point 10) to provide the stationary vortex-free flow field in the test section area. The test section was connected to the inlet of the centrifugal fan by a flexible pipe. A HFR 140-17D type radial fan was applied (Fig. 2, point 8) and was controlled by a frequency inverter regulator (Fig. 2, point 9).

Fig. 2. Wind tunnel experimental set-up of the test section [15]; 1. converging section 400×400 mm, 2. settling screens at the inlet of wind tunnel,

3. smoke generator, 4. test section – perspex window channel 800×100×100 mm, 5. blade NACA 4421, 6. illumination, 7. high-speed

camera, 8. centrifugal fan, 9. frequency regulator, 10. honeycomb, 11. positioning table, 12. second

illumination

Volume flow rate in the wind tunnel can be set between 0 and 650 m3/h. In addition, with a 2-component hot-wire anemometer, velocity field in the test section area was studied [11]. This allowed for determination of unperturbed velocity field in the test section area of the wind tunnel. The measurements showed uniform velocity profiles through the channel of the test section

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39Control of Separation Flow over a Wind Turbine Blade with Plasma Actuators

area with mean turbulence intensity being less than 1.5% [11].

A NACA 4421 profile with 30 mm chord length and aspect ratio of 3.03 was used to profile the wind turbine blade. The profile was made out of ABS plastic, printed with 3D printer. The blade profile was located in the middle of the test section area (Fig. 2, point 5) and was supported by both vertical walls of the test section. Profile NACA 4421 has been chosen in order to better demonstrate the impact of plasma to a single profile of the wind turbine [11].

1.2 Plasma Actuating Device

A plasma actuating device consists of two high voltage and high frequency wires, which enter the hollow profile through a hole on one side of the chord. On the surface of the upper part of profile, four EHD actuators as shown in Fig. 3 are placed.

The tested EHD plasma actuators (power supply/actuator schematic is shown in Fig. 3) consist of conductive copper strips separated by a 50 micron thick Kapton dielectric (dielectric strength 118 kV/mm). Typical widths of 5 mm with corresponding lengths of 70 mm were used. A function generator is used to provide sinusoidal input to amplifier power supply. The output drives an inductively matched transformer, capable of 6 kV output with 1 to 250 V RMS input at 4 to 11 kHz. The input power was monitored by oscilloscope.

Fig. 3. Plasma on wind turbine profile

1.3 Flow Visualization

Measurements with flow visualization were performed by introducing passive tracer smoke into a fully developed flow. To visualize the flow, a passive tracer smoke consisting of

vaporized paraffin oil was used. The smoke is made with thin resistance wire of 0.1 mm, which was heated. For generation of the passive tracer smoke we used paraffin oil drops on a wire. The wire was mounted on the walls of the converging section. A presumption was made that passive tracer smoke particles ideally follow the flow and that image intensity is proportional to the concentration of the passive tracer smoke [10]. The passive tracer smoke flow was evaluated with appropriate equipment for calculating intensity profiles [11]. Camera Dragonfly Express IEEE-1394b with Edmund Optics 75 mm Double Gauss lens was used for image acquisition, with image acquisition frequency of 400 Hz. Recorded images had 8-bit grey level depth, resolution of 613×200 pixels, and were captured with shutter speed of 0.5 ms. The camera was placed perpendicularly to the profile surface at the distance of 2 m from the test section of the wind tunnel [12] and [13].

For illumination, two Vega Velum DC 150 W (Fig. 2, point 6) continuous flicker-free light sources with line light guide were used. Software package LabView with Vision toolkit was used for setting up the camera, acquisition and storage of digital images. For each measurement point, 800 successive images were taken. The number of images was limited by the time of uniform passive tracer smoke generation. Overall, uncertainty of measurements of instantaneous passive tracer concentration was estimated at 3.8% of the measured value [11].

1.4 Methodology Behind Analyzed Image Sequences

Computer-aided visualization allows time and space measurements of flow structures to study flow around the blade profile in the wind tunnel. Algorithms for image analysis are discussed below [10] and [14]. The Software package enabled the transformation of the snapshot format from AVI to BMP. Image sequences were then analyzed by Dynascan software. A study window in the program was placed above each image. The window was divided into a matrix i×j = 40×22 of equal cells. Each cell had a rectangular form dxc×dyc = 10×10 pixels in size. For every image in the sequence, average grey level (Ac) in each



window cell was calculated using the following equation [15]:

A i j ndy dx

E i i j j ncc c

p pj

dx

pi

dy

p

c

p

c

( , , ) ( , , ),= + +==∑∑111

(3)

where Ep(i+ip, j+jp) represents the grey intensity of the observed pixel at cell position (i, j) and relative position (ip, jp) of the pixel within cell location; n denotes the consecutive number of image in the sequence. The intensity of pixels Ep(i+ip, j+jp) ranges from 0 (black) to 255 (white). The mean value of the grey intensity in each cell for the whole sequence of images is obtained by the following formula:

µc cn

N

i jN

A i j n( , ) ( , , ),==∑11

(4)

where N denotes the number of all images in the sequence; there were 800 images in each sequence. The results demonstrate a transition in grey levels from a low to a high value on the boundary layer of the profile.

2 EXPERIMENTAL RESULTS

2.1 Flow Visualization

The experiments were made for two working points, presented in Table 1 below, which show the effect of discharge on aerodynamic properties at different flow conditions.

Table 1. Aerodynamic non-dimensional coefficient as a function of flow conditions and actuation intensity

Flow condition α (°) Re Cw (×103)

max. voltage 6 kV1 7 7600 22.52 7 10500 11.9

The angle of attack of the turbine blade profile is set at 7°. This angle of attack influences the flow most visibly. For the first working point, stream velocity was 4 m/s; for the second working point it was 5.5 m/s. For each working point, flow visualization was captured in several measuring points. Corresponding Re based on free stream velocity and the chord lengths are Re 7600 and

Re 10500. The effects of discharge on the blade profile depend on characteristics of the considered regime.

For each working point, flow visualization was captured in several measuring points: (i) without plasma actuators and (ii) with plasma actuators. For measuring points with plasma actuators, different intensities of voltage on actuator and voltage on amplifier were used, as presented in Fig. 4.

Fig. 4. Correlations between voltage on actuator and voltage on amplifier

Fig. 4 shows the present input conditions. It should be noted that input energy increases as frequency or voltage increases.

Fig. 5. Correlations between frequency and plasma width on actuator

The size of plasma on the blade profile was analyzed, based on digital images obtained during measurements of flow visualization.

The results presented in Fig. 5 show that plasma has the highest rate and influence on the flow at frequency value of 3.5 kHz.



Different measuring points, in which flow visualization measurements were performed, are presented in Table 2. The range of velocities and frequencies tested in our sets of experiments are presented by four examples: (1) Flow over the blade fully attached to the surface with plasma, (2) Flow over the blade in dependence of different Re and plasma intensity, (3) Flow over the blade with first plasma line and (4) Behavior of the passive tracer smoke near plasma.

Table 2. Conditions during the cases

Measurement cases Re Frequency Function

Generator [kHz]1 7600 42 7600 53 7600 64 7600 without5 10500 46 10500 57 10500 68 10500 without

2.1.1 Flow over the Blade Fully Attached to the Surface with Plasma

In the low range of Re < 3×104, and using NACA 4421 blade profile, the flow conditions normally do not include laminar boundary layer towards the profile trailing edge [11]. When the blade profile is inclined at the angle of attack of 7°, separation position is expected to occur in the middle of the blade profile [16] and [17]. Flow visualization results without the plasma actuator are shown in Fig. 6. The separation of flow on the suction side of the blade occurs (Fig. 6, point A). External flow is not able to follow the path of the blades’ profile; therefore, it separates from the profile. It is expected that with plasma actuators (Fig. 7), the flow will better follow the shape of the blade near the trailing edge. Qualitative changes of flow structures over the blade appear in both cases. In the case of flow field in Fig. 7, no vortex is observed. This is due to the presence of the flow of plasma that acts as an ejector. It locally reduces pressure near the trailing edge due to higher velocity. The adverse pressure gradient is thus reduced, the boundary layer cannot thicken and no flow separation occurs. Consequently, plasma

contributes to preservation of flow direction and stabilization of flow structures. The flow is forced to follow the path of the blade.

Fig. 6. Flow visualization (Case 8)


2.1.2 Flow over the Blade in Dependence on Different Re and Plasma Intensity

Figs. 8 to 16 present flow visualization of partially separated flow configuration obtained at α = 7° at Re 7600 and Re 10500. Flow separation without plasma (Fig. 8) was revealed by the passive tracer smoke where the separation point lies at x/c ≈ 0.3 (x - distance from the front part of the blade to the separation point, c - chord length of the blade). Again, similar observation can be made when compared to results in Figs. 6 and 7. Based on Fig. 8, the location of the separation point and the passive tracer smoke can be estimated. From the point of separation (Fig. 8, point B), the distance between the passive tracer smoke and the blade profile surface continuously increases.

When plasma was applied in Case 1 (Fig. 9), the angle of the passive tracer smoke path was significantly smaller and oriented in the direction of the blade's trailing edge. Therefore, the flow direction is changed and the flow field around the

http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V02-4HJRXG4-3&_mathId=mml35&_user=1818001&_cdi=5634&_pii=S0304388605002329&_rdoc=11&_ArticleListID=1193586417&_issn=03043886&_acct=C000054880&_version=1&_userid=1818001&md5=d79bf2f42da77f872c2d9f4641cec4ed

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blade in the presence of plasma follows better the profile. Plasma decreased the circulating flow and vortex formation on the suction side of the blade wall.

In Case 2 (Fig. 10) with the highest rate of plasma, the passive tracer smoke follows the path of the blade profile and the separation of the flow decreases.




Digital image sequences of the passive tracer smoke for cases with and without plasma actuator at two different velocities were then analyzed with Dynascan software. A window (40×22) of equal cells was placed above each image. For every image in the sequence, average grey level (Ac) in each window cell was calculated in accordance with Eq. (3). The mean value of grey intensity in each cell for the whole sequence of images was obtained from Eq. (4).

Results presented in Figs. 11 to 16 show plasma’s influence on the passing of the flow

through the blade profile. Plasma has the strongest influence in Case 2 (Fig. 12) because the passive tracer smoke presenting the flow around the blade profile is fully reattached. In cases without plasma (Figs. 13 and 16), conclusions are similar. They confirm the results from the quality assessment of the digital images. As expected, plasma contributes to the preservation of the direction of the flow and stabilization of flow structures. The flow is forced to follow the path of the blade; hence, mass flow near the trailing edge increases. This phenomenon leads to conclude that the flow direction change and flow field around the blade in the presence of plasma better follows the profile. As a result, the following estimation can be made: plasma used in this case has a positive influence; it prevents increases in pressure difference, decreases formation of circulating flow and vortex on the suction side of the blade wall. All this can also be reflected in decreased energy dissipation.









2.1.3 Flow over the Blade with First Plasma Line

A set of flow conditions at Re 7600, that leads to separation of the boundary layer close to the leading edge was analyzed (Fig. 17, Case 4 vortex separation without plasma and Fig. 18, Case 2 with plasma).

Fig. 17 presents a continuous increase in distance of the passive tracer smoke from the blade profile, which represents the boundary layer separation. Similar estimation can be made as in previous cases: the separation point occurs at x/c ≈ 0.2. When the flow separates from the blade profile, the separated shear layer rapidly undergoes a transition to turbulent flow. Vortex position and size depend on characteristics of the blade, Re, the angle of attack and frequency of plasma.



In Fig. 18 close to the separation point where plasma actuator is attached, quality differences occur between cases with and without plasma. When using the maximum power of plasma, but only with one line of plasma as in Case 2 in Fig. 18, the frequency of vortex generation changes. The position of flow separation from the blade profile seems to be unchanged and the flow from trailing edge to the leading edge remains present when comparing cases with and without plasma. Nevertheless, it seems that only a small amount of plasma applied yields a noticeable difference. The efficiency of plasma is therefore increased when applied on the entire section of the blade profile.


2.1.4 Behavior of passive Tracer Smoke near Plasma

A sequence of digital images with plasma in Fig. 19 reveals changes around the individual plasma actuator. In the first digital image, the direction of the passive tracer smoke (marked with arrow) is redirected closer to the profile surface due to the influence of plasma. The third digital image in the sequence reveals the formation of small vortex in the direction of the blade profile.



This is a result of plasma influencing the flow around the blade.

The strong electric field ionizes air molecules in the region above the insulated electrode, forming plasma which extends from the exposed electrode along the entire insulated electrode. Plasma induces velocity in the surrounding fluid. The electron movement ionizes the air, generating charged particles which are subsequently accelerated through the electric field. The momentum of the accelerated charged particles is then transferred to the surrounding air through collisions with neutral particles. This momentum transfer occurs very close to the surface of the actuator itself, typically in the sub-boundary layer region [7]. Based on these results, it was considered that the actuator produces enough strength to partly or fully reattach the flow.

3 CONCLUSIONS

Within the present experimental circumstances, the following facts can be observed: • input energy (correlation of frequency

and voltage,) calculated as the product of discharge current I and applied voltage difference between electrodes ΔV, has a strong influence on the flow around the turbine blade.

• Plasma actuators can control the separation point of the flow, passing the blade profile.

• Input energy (max. 20 W in length of 10 cm of plasma) represents a sufficient amount of energy to control the flow over the blade in the applied/established conditions.

More extensive research will be carried out in the future. We will focus on quantity assessment of the blade flow field. Generating plasma on a small scale laboratory wind turbine will enable us to measure the differences in aerodynamic and acoustic characteristics between cases with and without plasma. We believe that plasma control on a wind turbine will have similar influence as presented in this paper. However, some changes may be considered due to additional forces acting on the flow around the rotating blade.

4 REFERENCES

[1] Shyy, W., Berg, M., Ljungqvist, D. (1999). Flapping and flexible wings for biological and micro air vehicles. Progress in Aerospace Sciences, vol. 35, no. 5, p. 455-505, DOI:10.1016/S0376-0421(98)00016-5

[2] Zaman, K., McKinzie, D.J. (1991). Control of laminar separation over blade profiles by acoustic excitation. American Institute of Aeronautics and Astronautics Journal, no. 7, p. 1075-1083.

[3] Greenblatt, D., Wygnanski, I. (2000). Use of periodic excitation to enhance blade profile performance at low Reynolds numbers. Journal of Aircraft, vol. 1, p. 190-192.

[4] Schlichting, H., (1979). Boundary-Layer Theory, Springer, Berlin.

[5] D’Adamo, J., Artana, G., Moreau, E., Touchard, G. (2002). Control of the airflow close to a flat plate with electrohydrodynamic actuators. ASME Conference Proceedings, vol. 1, p. 1339-1344.

[6] Colver, G., El-Khabiry, S. (1999). Modeling of DC corona discharge along an electrically conductive flat plate with gas flow. IEEE Transactions on Industry Applications, vol. 35, p. 387-394, DOI: 10.1109/28.753633.

[7] Roth, J.R., Sherman, D.M. (2000). Electrohydrodynamic flow control with a glow discharge surface plasma. American Institute of Aeronautics and Astronautics Journal, vol. 38, no. 7, p. 1166-1178.

[8] Louste, C., Artana, G., Moreau, E., Touchard, G. (2005). Sliding discharge in air at atmospheric pressure: electrical properties. Journal of Electrostatics, vol. 63, p. 615-620, DOI: 10.1016/j.elstat.2005.03.026.

[9] IEEE-DEIS-EHD Technical Committee (2003), Dielectrics and Electrical Insulation, IEEE Transactions, vol. 10, p. 3-6.

[10] Eberlinc, M., Dular, M., Širok, B., Lapajne, B. (2008). Influence of blade deformation on integral characteristic of axial flow fan. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 3, p. 159-169.

[11] Eberlinc, M., Širok, B., Hočevar, M. (2009). Experimental investigation of the interaction of two flows on the axial fan hollow blades by flow visualization and hot-wire anemometry.

http://dx.doi.org/10.1016/S0376-0421(98)00016-5

http://dx.doi.org/10.1109/28.753633

http://dx.doi.org/10.1016/j.elstat.2005.03.026



Experimental Thermal and Fluid Sciences, vol. 33, p. 929-937, DOI:0.1016/j.expthermflusci.2009.03.012.

[12] Benedik, G., Širok, B., Rihtaršič, J., Hočevar, M. (2010). Flow characteristics of bladeless impeller made of open cell porous material. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 7/8, p. 464-476.

[13] Chen, J., Hočevar, M., Širok, B. (2011) Melt volume flow measurement in the mineral-wool production process. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 4, p. 293-303, DOI:10.5545/sv-jme.2010.159.

[14] Osterman, A., Hočevar, M., Širok, B., Dular, M. (2009). Characterization of incipient cavitation in axial valve by hydrophone and

visualization. Experimental Thermal and Fluid Science, vol. 33, no. 5, p. 929-937.

[15] Širok, B., Bajcar, T., Dular, M. (2002). Reverse flow phenomenon in a rotating diffuser. Journal of Flow Visualization & Image Processing, vol. 9, p. 1-18.

[16] Benard, N., Braud, P., Touchard, G., Moreau, E. (2008). Detachment and attachment of an axisymmetric non-reactive jet with turbulent shear layer: control by plasma actuator. Experimental Thermal and Fluid Science, vol. 32, no. 6, p. 1193-1203, DOI: 0.1016/j.expthermflusci.2008.01.010.

[17] Lemire, S., Vo, H.D., Benner, M.W. (2009). Performance improvement of axial compressors and fans with plasma actuation. International Journal of Rotating Machinery, p. 1155.


*Corr. Author’s Address: College of Aerospace Engineering, Nanjing University of Aeronautics & Astronautics, P.O. box 313, NO. 29, Yudao street, Nanjing, Jiangsu, China, [email protected]

Design and Feasibility Analyses of Morphing Airfoil Used to Control Flight Attitude

Du, S. ‒ Ang, H.Sha Du* ‒ Haisong Ang

College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, China

Morphing technology, inspired by bat and bird flight can enable an aircraft to adapt its shape to enhance mission performance and optimize flight attitude controlling efficiency. A morphing airfoil concept is proposed to replace the traditional flap, ailerons, elevator and rudders in order to improve aerodynamic efficiency in this paper. A procedure is used to virtually simulate a morphing wing to perform fast, relatively accurately and efficiently. A set of optimal airfoil shapes obtained are aimed at minimizing the aerodynamic drag character by optimizing morphing configurations at different Cl under the two-dimensional steady-flow simulation. These airfoil shapes are used to maneuver flight attitude, minimize drag and take place of traditional control surfaces of different rolling, yawing and pitching moment. Then, the basic relationships between optimized morphing airfoil and the traditional control element on rolling, pitching and yawing moment are simplified to the relationship of Cl. The morphing airfoil shapes at different Cl are represented. The configuration of traditional airfoil and morphing airfoil at different Cl are compared. It is proved that morphing wing can be used to take the place of a traditional wing.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: morphing wing, deformation institutions, traditional control surface, aerodynamic character, optimal design, compare

0 INTRODUCTION

Since the Wright brothers’ first successful flight, aircraft designers have been focusing on improving the aircraft flight efficiency, and especially airline companies are anxious to improve the commercial aircraft efficiency nowadays. Usually aircraft wings are designed to be most efficient at cruising flight but suffer performance penalties under other conditions, such as taking off, landing and controlling flight attitude. Inspired by the bald eagle which can change its own flap configuration to fit different flight conditions and control the rolling, pitching and yawing performance [1] many researchers have investigated different ways to change the flight efficiency in different environments. Many research works have been published on smart wing and morphing aircraft technique in recent years.

Morphing wing technology can be used to control flow on aircraft wing [2], change the deform of shock wave [3], deform the shape of aircraft wing to make the aircraft be the most efficient at different flight speed [4], control the aircraft roll by twisting a flexible wing on a full-size aircraft [5] and improve the aerodynamic and

aero elastic performance of military aircraft [6] to [11].

All the techniques above were used to optimize the airfoils [12] to [16], wings’ platform configuration [17] and the three dimension configuration [18] to [20] of the aircraft in order to obtain an optimal aircraft configuration for a fixed design parameter.

Advancements of actuation, sensing technology, the development of adaptive materials (shape memory materials, macro fiber composites flexible matrix composites [21], specially designed skin materials [22] and [23], piezoelectric material and elastic deformation material [24]), the progress of the smart structures [25] to [27], the aerodynamic advances in computational fluid dynamics, optimization techniques, Mathematical Modeling technique and multi-disciplinary design have increased the ability of engineers to improve the morphing wing technology.

The new advances in morphing technology allow aircraft performance to be further increased by obtaining the optimal aircraft configurations not only at different flight attitude [28] and stages [29]. Particularly the morphing technique can be used to control the attitude with the most optimal


47Design and Feasibility Analyses of Morphing Airfoil Used to Control Flight Attitude

configuration and take the place of traditional elevators.

In this paper, a kind of morphing concept has been proposed which can deform the configuration to different airfoils and controlling the flight attitude with minimize cost. An aerodynamic shape optimization code is used to obtain a set of optimal airfoil shapes to replace the traditional hinged control surfaces at different angle separately. The aerodynamic characters of optimal morphing airfoils and traditional hinged control surfaces (which can be used in flaps, ailerons, elevating and yawing rudders) are compared. The configurations of the set of optimal morphing airfoils will be represented. Then, some conclusions are addressed with comments on the benefits and drawbacks of the morphing airfoil concept.

1 MATHEMATIC AIRFOIL MODEL

Numerous mathematic methods have been devised to represent airfoil geometry in aerodynamic design, optimization and parametric studies. In this paper “CST” mathematical method [30] to [32] proposed by Brenda Kulfan is chosen to describe the airfoil configuration; there are n control parameters which can be defined by the customer according to the required accurate which are used to control the different part of airfoil configuration.

The “CST” method is based on Bernstein polynomial of an order n, the airfoils are represented by the Eqs. (1) to (3).

ξ ψ ψ ψ ψ ψ ξ( ) = − ( ) + ⋅=∑N N

i

ni r n TAU S1 21

0( ) ,, (1)

where ψ = x/c, ξ = z/c, ξT = ∆ξTE/c, AU is an array of n numbers, which is the control parameter that can be used to determine the shape of the airfoil.

Sr,n(x) = Kr,n xr(1-x)n-r , (2)

where r = 0 to n (n is order of the Bernstein polynomial).

In the above equation, the coefficients factors Kr,n are binominal coefficients defined as:

Knr

nr n rr n,

!!( )!

.≡

≡ −

(3)

The Bernstein polynomial representation of the unit shape function, for any order of Bernstein polynomial selected to represent the unit shape function, only the first term defines the leading edge radius and only the last term defines the boat-tail angle. The other in-between terms are “shaping terms” that can only affect the in-between shape of the leading edge radius and the trailing edge of the airfoils.

2 THE MORPHING WING CONTROLLER CONCEPT

The traditional flaps, ailerons, elevators and rudders consist of hinged control surfaces that are attached to the trailing edge of the wing on a fixed-wing aircraft. The ailerons are used to control the aircraft in roll, the two ailerons are typically interconnected, so that one goes down when the other goes up: the down going aileron increases the lift on its wing while the up going aileron reduces the lift on its wing, producing a rolling moment about the aircraft’s longitudinal axis [33]. The elevating and yawing rudders are used to control the aircraft in pitch and yaw. All the control elements above can control the flight attitude by changing the lift of the control surfaces, so the flight controlling can be simplified to force on different control elements. Any control element that can change the force of the whole airfoil can take the place of the traditional control element. It has been found that morphing airfoil control element can take the place of the traditional control element and provide a smaller drag.

Morphing airfoil can change the airfoil configuration smoothly by varying the camber, leading edge and trailing edge’s configuration and position of initial airfoil, which can lead to the same variation with the traditional control elements of lift coefficient (Cl), drag coefficient (Cd) and the position of aerodynamic center. Therefore, the morphing airfoil theory may be used to replace the traditional hinged control surfaces including ailerons, elevating and vertical rudders.

Take a morphing wing for example whose Mach number is 0.045, Reynolds number is 300000, the angle of attack is 5° and the initial airfoil is NACA0012. Airfoil3 is NACA0012 with a control surface under an angle of attack

http://en.wikipedia.org/wiki/Trailing_edge

http://en.wikipedia.org/wiki/Flight_dynamics

http://en.wikipedia.org/wiki/Lift_(force)

http://en.wikipedia.org/wiki/Moment_(physics)


48 Du, S. ‒ Ang, H.

which can provide a Cl 0.6940.The airfoil NACA0012 (airfoil 1 in Fig 1.a) can change its own configuration to different shapes, such as airfoil2 showed in Fig. 1a, to increase the Cl with a smaller Cd punishment. Airfoil2 is obtained with the target Cl the same with the airfoil3 and minimum drag by the optimization process.

a)

b)

Fig. 1. Configuration and pressure compare of a) morphing airfoil and b) traditional airfoil

Table 1. Cl and Cd of different airfoil shape Mach number is 0.045, Re is 300,000 and the angle of attack is 5°

Airfoil shape Cl Cm CdNACA0012 0.6042 -0.0070 0.00120Morphing airfoil 0.6940 -0.0026 0.00136Airfoil3 0.6940 -0.0231 0.00147

Table 1 shows the aerodynamic character of the initial airfoil NACA0012 (airfoil1 in Fig. 1a), morphing airfoil (airfoil2 in Fig. 1a) and the airfoil with an angle of hinged control surface (airfoil3 in Fig. 1a and Table 1). The morphing

airfoil and the flap were compared, as showed in Table 1 Cd of the morphing airfoil is much smaller than Cd of traditional flap when they get the same Cl. According to the character above it is assumed that the morphing wing can replace the traditional hinged control surfaces to control the flight attitude and improve aerodynamic efficiency.

Fig. 1b shows the pressure on airfoil1 and airfoil2, the pressure on upper surface of airfoil1 is bigger than the pressure on upper surface of the airfoil2, and the pressure on the lower surface of airfoil1 is smaller than the pressure between the lower surface of airfoil2 at the same flight speed and environment. Therefore, the pressure difference of upper and lower surface in airfoil1 is smaller than airfoil2, which means that airfoil2 can get a bigger lift than airfoil1.

In order to test whether the morphing airfoil can take the place of the traditional flap, the Cd of the traditional control surface and the morphing wing will be compared at different Cl .

3 STRUCTURE CONCEPTUAL DESIGN

There are two basic morphing concepts in the development of a morphing wing: one is changing the surface configuration of the wing [34] and the other is deforming the section shape (the airfoil shape) of the morphing wing [35] and [36].

Fig. 2. The morphing structure concept

In Fig. 2, the morphing airfoil compliant concept that can change the section shape is present, which can deform the configuration of the leading edge, trailing edge, and the chamber to fit flight environment and control the attitude. It is axial symmetry about the chord and consists of:



i. Skin material The skin material of the morphing airfoil

should endure elastic deformation and have high strains. The shape memory polymer was initially considered, but it is useless for the morphing system as the complexity and the shape memory polymer cannot endure high load.

The nature rubber skin together with the thin honeycomb texture can endure elastic deformation and have high strains. Their position is controlled by the control points in the area between the leading and trailing edge to finish configuration deformation.

ii. Compliant mechanism The compliant mechanism is used on the

leading and the trailing edge of the morphing airfoil to complete the airfoil deformation [37] to [40]. The compliant mechanism is optimized according the initial shape and the final shapes.

The two couple control points at the leading and trailing edge are used to control the shape of the compliant mechanism by changing their own position; it can control the configuration of the airfoil together with the eight control points in the upper and lower surface.

iii. The fixed structure The fixed structure is used to carry the

controller of the control points and fix the wing chord together and to the fuselage.

4 OPTIMIZATION OF THE MORPHING AIRFOIL

The optimization of the morphing airfoil is necessary in order to compare the morphing airfoils and the traditional hinged control surfaces. The airfoil was optimized to get the optimal airfoil shapes which can provide the same Cl with a much smaller Cd punishment than any other shapes. To achieve this, a tool that can search the optimal airfoil geometry is used. First the generic constrain was represent by Eqs. (1) to (3) based on the Bernstein polynomial. Second, the XFOIL program is used to get the polar ratio of the airfoil shape in the aerodynamic analysis. Then, the polar ratio is compared with the target parameter and the ratio of the former ones and the airfoil shape

control parameter which will be used in the next cycle obtained with Isight.

The XFOIL use the steady Euler equations in integral form to represent the inviscid flow, the compressible lag-dissipation integral method to represent the boundary layers and wake and the incompressible potential flow via the surface transpiration model to calculate the limited separation regions of the viscous solution. Results from XFOIL have been compared against experimental data with good agreement [41].

Isight is a solution that provides engineers with a suite of visual and flexible tools for creating simulation process flows‒consisting of a variety of applications, including commercial CAD/CAE software, internally developed programs, and Excel spreadsheets ‒ in order to automate the exploration of design alternatives and identification of optimal performance parameters. Isight enables users to automate simulation process flows and leverage advanced techniques such as Design of Experiments, Optimization, Approximations, and Design for Six Sigma to thoroughly explore the design space. Advanced, interactive postprocessing tools allow engineers to explore the design space from multiple points of view.

The aerodynamic shape optimization is carried out with the sequential quadratic programming, constrained algorithm SQP-DONLP (a sequential quadratic programming optimization method in Isight). The purpose of the SQP-DONLP is the minimization of a differentiable real function subject to inequality and equality constrains. This method builds a quadratic approximation to the Lagrange function and linear approximations to all output constraints at each iteration, starting with the identify matrix for the Hessian of the Lagrangian, and gradually updating using the BFGS (Broydon-Fletcher-Goldfarb-Shanno) method. On each iteration, a quadratic programming problem is solved to find an improved design, until the final convergence to the optimum design.

The aerodynamic shape optimization problem can be stated as Minimize drag coefficient with regard to a confirmed lift coefficient. Fig. 3 is a flowchart that illustrates the implementation of the aerodynamic shape optimization tool. The code can be summarized as follows:


50 Du, S. ‒ Ang, H.

i. Represent the airfoils using the Bernstein polynomial of an order n.

ii. Change the airfoil control parameter (AUi) according to the required polar ratio.

iii. Compute the aerodynamic character of the airfoil obtained from step 2.

iv. Compare the Cl and Cd of the different airfoils obtained and get the most optimized airfoil with regard to a constant Cl.

Fig. 3. Wing aerodynamic shape optimization flow chart

5 RESULTS AND DISCUSSION

A set of optimal airfoil shapes which can provide different Cl with the minimum drag are obtained by the procedure at Mach 0.045, Re 300000. In 5.1, the particular polar characteristics of the optimal airfoil configurations are compared with the traditional hinged control surfaces which include a different angle of attack and hinged control surfaces. In 5.2, the optimal airfoil shapes are obtained by the procedure limited by a minimum drag coefficient at different Cl which correspond with the different angle of traditional hinged control surfaces, the optimal airfoil shapes can take place of all the control surfaces of a flight. In 5.3, the configuration and pressure versus chord of the airfoil with control surfaces at the angle of

attack 5° and morphing airfoil shapes at the angle of attack 0° are compared when they provide the same lift coefficient.

5.1 Aerodynamic Optimization Results

In a confirmed flight environment, the lift coefficient of a wing is primarily the result of its angle of attack and shape (in particular its camber) of the airfoil. A set of morphing airfoil shapes are optimized to get the best Lift-to-drag ratio based on different Cl at different angle of attack and angle of traditional hinged control surfaces of a confirmed airfoil. The airfoil NACA0012 and the optimal airfoil shapes at the speed of Mach 0.045, Re 300,000 at angle of attack 3 and 5° separately are compared.

Fig. 4 shows the relationship between Cl, Cd of the traditional hinged control surfaces and the optimal morphing airfoils, Flap 0, Flap 3, Flap 5 show the polar ratio character followed with the changing angle of hinged control surface when the angle of attack is 0, 3 and 5° separately. Morphing airfoil show the polar ratio character followed with the deforming configuration of the morphing airfoil.

Fig. 4. The relationship between, Cl, Cd of the traditional flap and morphing airfoil

i. Flap 0 in Fig. 4 shows the polar ratio of the traditional airfoil followed with the changing hinged flap angle at the attack angle 0°. When the Cl is smaller than 0.97, the drag coefficient will increase slowly followed with the increasing Cl, which is determined by the angle of hinged control surface when the lift coefficient is smaller than 0.97. Followed by the increasing hinged angle the pressure drag

http://en.wikipedia.org/wiki/Camber_(aerodynamics)



will increase quickly when the trailing edge position is beyond the horizontal position of the maxim thickness of the airfoil (the lift coefficient is bigger than 0.97).

ii. If the Cl is smaller than 0.35, according to the Bernoulli equation the morphing airfoil can change the camber of the lower surface to increase the Cl, which can decrease the cross section area to decrease the pressure Drag and lead to the decrease of Cd followed with the increasing Cl. Otherwise, if Cl is bigger than 0.35, the morphing airfoil cannot provide enough Cl by changing the camber only, the trailing edge position had to be altered to increase Cl, Cd will increase followed with the increasing Cl.

iii. The Cd of the traditional hinged control surface at different angle of attack (0, 3 and 5°) is bigger than the Cd provided by the optimal morphing airfoils at the same Cl. The polar curve of traditional hinged control surface have a different turning point at different angle of attack, Cd will increasing slowly if Cl is smaller than the turning point, otherwise Cd will increasing rapidly. The turning point at the attack angle 0°, 3°, 5° is Cl = 0.97, Cl = 1.05, Cl = 1.15 separately.

The relationship between Cl, Cd of the traditional flap and morphing airfoils is axially symmetric about the line of Cl = 0. The relationship between Cl, Cd when the Cl < 0 can be obtained according to Fig. 5.

It is more efficient to use a morphing wing to take the place of the traditional hinged control surfaces on the flaps, ailerons, elevators and rudders.

As the aircraft rolls, adverse yaw is caused primarily by the change in drag on the left and right wing. The difference in drag on each wing produces the adverse yaw. There is also an additional adverse yaw contribution from a difference in profile drag between the up-aileron and down-aileron. The morphing airfoil can provide the same control parameter with the traditional hinged control element with a smaller drag punishment. Therefore, the morphing airfoil can decrease the adverse yaw caused by the drag.

5.2 Configuration of the Morphing Airfoil

A set of airfoil optimal configurations, optimized at Mach 0.045, Re 300,000, are showed in Fig. 5. Figs. 5a to 5c show the configurations of airfoil1 to airfoil10, Cl of airfoil 1 to 10 increase from low to high.

a)

b)

c)

Fig. 5. A set of the optimal airfoil shape and the pressure vs. x axis

The camber and thickness of the optimal airfoil (airfoil1 to airfoil4) will decrease followed with the increasing lift coefficient if Cl is smaller than 0.35, but followed with the increasing Cl (if Cl is bigger than 0.35), the morphing airfoil


52 Du, S. ‒ Ang, H.

cannot provide enough Cl by changing the camber of the airfoil only, so it is necessary to change the position of trailing edge. The airfoil from airfoil5 to airfoil10 can provide Cl by not only changing the camber but also change the trailing edge position of the airfoil.

5.3 Comparison of the Shape and Pressure

Six couples of traditional control surface airfoils and the optimal airfoils at different Cl

are represented in Fig. 6. The traditional control surfaces have different angle of control surface at the angle of attack 5°. Cl and Cd of the 6 couples in Fig. 6 are represented in Table 2.

Table 2 shows Cl and Cd in a different couple of Fig. 6. Cd1 is the traditional hinged surface at angle of attack 5, Cd2 is the morphing airfoil at angle of attack 0°.

Fig. 6. The morphing and traditional airfoil shape

Couple 2

Couple 3

Couple 1

Couple 5

Couple 6

Couple 4



Table 2. Cl and Cd in different couple of Fig. 6

The Fig. no. Cl Cd1 Cd2Couple 1 0.66 0.0125 0.00781Couple 2 0.75 0.01323 0.00885Couple 3 0.90 0.01555 0.01301Couple 4 1.01 0.01814 0.01512Couple 5 1.15 0.02362 0.01991Couple 6 1.25 0.02766 0.02164

6 CONCLUSION

The morphing wing is designed according to the morphing airfoil theory represented. It has been proved that the morphing airfoil can replace the hinged control surfaces to control the rolling, pitching and yawing moment with a smaller drag and increasing the flight efficient at different rolling, pitching and yawing moment.

The morphing airfoil control element can reduce the drag from 20 to 60% (showed in Fig. 5) than the traditional airfoils with control surface when they provide a same Cl, if the Cl is bigger than 0.1. The morphing airfoil can lead to a smaller adverse yaw when they provide the same rolling moment.

A multidisciplinary design optimization tool was developed to design a morphing wing for an experimental MAV in order to improve and quantify its controlling performance. The configuration of the airfoils is represented clearly, and the configure variation regulation followed with Cl is discussed. The detail of the relationship between Cl and the control parameter of the airfoil should be researched more and it would be better if it was represented as an equation in the future.

Future work stages will include designing morphing mechanism details, materials and further wind-tunnel test of the morphing wing at different flight speeds and attitude controlling requirement.

7 REFERENCES

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[12] Huyse, L., Padula, S., Lewis, R., Li, W. (2002). Probabilistic approach to free-form airfoil shape optimization under uncertainty. American Institute of Aeronautics and Astronautics (AIAA) Journal, vol. 40, no. 9, p. 1764-1772, DOI:10.2514/2.1881.

[13] Namgoong, H., Crossley, W.A., Lyrintzis, A.S. (2002). Global optimization issues for transonic airfoil design. 9th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, p. 4-6.

[14] Lee, S.W., Kwon, O.J. (2006). Robust airfoil shape optimization using design for six sigma. Journal of Aircraft, vol. 43, no. 3, p. 843-846, DOI:10.2514/1.17359.

[15] Winnemoller, T., van Dam, C.P. (2007). Design and numerical optimization of thick airfoils including blunt trailing edges. Journal of Aircraft, vol. 44, no. 1, p. 232-240, DOI:10.2514/1.23057.

[16] Secanell, M., Suleman, A. (2005). Numerical evaluation of optimization algorithms for low reynolds number aerodynamic shape optimization. American Institute of Aeronautics and Astronautics (AIAA) Journal, vol. 43, no. 10, p. 2262-2267, DOI:10.2514/1.12563.

[17] Peigin, S., Epstein, B. (2007). Multipoint aerodynamic design of wing-body configurations for minimum drag. Journal of Aircraft, vol. 44, no. 3, p. 971-980, DOI:10.2514/1.26746.

[18] Nadarajah, S.K., Jameson, A., Alonso, J.J. (2002). Sonic boom reduction using an adjoint method for wing-body configurations in supersonic flow. 9th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, p. 4-6.

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[20] Reuther, J., Alonso, J., Jameson, A., Eimlinger, M., Saunders, D. (1999), Constrained multipoint aerodynamic shape optimization using an adjoint formulation and

parallel computers: Part 2. Journal of Aircraft, vol. 36, no. 1, p. 61-74, DOI:10.2514/2.2414.

[21] Tobushi, H., Hara, H., Yamada, E., Hayashi, S. (1996). Thermomechanical properties in a thin film of shape memory polymer of polyurethane series. Smart Materials and Structures, vol. 5, no. 4, p. 483-491, DOI:10.1088/0964–1726/5/4/012.

[22] Reich, G.W., Sanders, B., Joo, J.J. (2007). Development of Skins for Morphing Aircraft Applications via Topology Optimization. The 48th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 23-26.

[23] Thill, C., Etches, J., Bond, I., Potter, K., Weaver, P. (2008). Morphing skins. Aeronautical Journal, vol. 112, no. 1129, p. 117-139.

[24] Murray, G., Gandhi, F., Bakis, C. (2007). Flexible matrix composite skins for one-dimensional wing morphing. 48th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 23-26.

[25] Moniz, P.A.A. (2005). Adaptive aeroelastic aircraft structures. Ph.D. Thesis, Univ. Técnica de Lisboa, Lisbon.

[26] Perkins, D.A., Reed, J.L.Jr., Havens, E. (2004). Morphing wing structures for loitering air vehicles. The 45th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 19-22.

[27] Bilgen, O., Kochersberger, K., Diggs, E.C., Kurdila, A.J., Inman, D.J. (2007). Morphing wing micro-air-vehicle via macro-fiber-composite actuators. The 48th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 23-26.

[28] Rusnell, M.T., Gano, S.E., Pérez, V.M., Renaud, J.E., Batill, S.M. (2004). Morphing UAV Pareto curve shift for enhanced performance. The 45th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 87-95.

[29] Gano, S.E., Renaud, J.E. (2002). Optimized unmanned aerial vehicle with wing morphing for extended range and endurance. The 9th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, p. 45-56.

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[30] Kulfan, B.M., Bussoletti, J.E. (2006). Fundamental Parametric Geometry Representations for Aircraft Component Shapes, AIAA-2006-6948.

[31] Kulfan, B. M.(2007). A Universal Parametric Geometry Representation Method - “CST”. AIAA-2007-0062.

[32] Kulfan, B.M. (2007). “CST” universal parametric geometry representation method with applications to supersonic aircraft. 4th International Conference on Flow Dynamics, p. 26-28.

[33] Kermode, A.C., Barnard, R.H. (1972). Mechanics of flight. Pitman Publishing Ltd., London.

[34] Lee, D.H., Weisshaar, T.A. (2005). Aeroelastic studies on a folding wing. 46th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 18-21.

[35] Gandhi, N., Jha, A., Monaco, J. (2007). Intelligent control of a morphing aircraft. 48th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Conference, p. 112-128.

[36] Lafountain, C., Cohen, K., Abdallah, S. (2009). Camber controlled airfoil design for morphing UAV. 47th AIAA Aerospace

Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, p. 211-218.

[37] Lu, K.J., Kota, S. (2002). Compliant Mechanism Synthesis for Shape-Change Applications: Preliminary Results. Smart Structures and Materials Proceedings of SPIE, vol. 4693.

[38] Santer, M., Pellegrino, S. (2009). Topological optimization of compliant adaptive wing structure. American Institute of Aeronautics and Astronautics (AIAA) Journal, vol. 47, no. 3, DOI:10.2514/1.36679.

[39] Trease, B.P., Kota, S. (2006). Synthesis of Adaptive and Controllable Compliant Systems with Embedded Actuators and Sensors. ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, p. 10-13.

[40] Lu, K.J., Kota, S. (2003). Design of compliant mechanisms for morphing structural shapes. Journal of Intelligent Material System and Structures, vol. 14, DOI:10.1177/10453890305563.

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*Corr. Author’s Address: The State University of Novi Pazar, Vuka Karadžića bb, 36300 Novi Pazar, Serbia, [email protected]

Dynamic Model for the Stress and Strain State Analysis of a Spur Gear Transmission

Nikolić, V. ‒ Dolićanin, Ć. ‒ Dimitrijević, D.Vera Nikolić1,* ‒ Ćemal Dolićanin1 ‒ Dejan Dimitrijević 2

1 The State University of Novi Pazar, Serbia 2 Simens, Germany

A gear transmission dynamic model for the gear dynamic contact loading, dynamic contact stress state and dynamic contact strain state analysis is presented. A dynamic model of the transmission with four degrees of freedom is used. The transmission is analyzed using nonlinear finite elements contact formulation, using a novel software modules developed by the author used for the generalized analysis of the geared transmissions in the environment of the open source finite elements framework CODE-ASTER/SALOME.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: stress and strain state analysis, tensor invariants, finite element method, geared transmissions

0 INTrODUCTION

Gear transmissions have a long history dating back since the time of the first engineering systems. Their practical usage in the present day modern engineering systems is enormous. In accordance with a contemporary development of mechanical engineering techniques ever growing requirements have been imposed concerning characteristics and working specifications. The machines which utilize high-power duty gear transmissions (excavating machines, crushing machines, rolling machines, ships, etc.) operate under non-stationary conditions, so that the loads of the elements of these gear transmissions are variable. For example, abrupt accelerations and abrupt decelerations of machine parts, that is, masses of the gear transmissions cause inertial forces which, in addition to the conditions of operation, influence the magnitude of actual leads of the elements of gear transmissions. All this, together with the changes of the torque of drive and operating machine, the forces induced by dynamic behaviours of the complete system, etc., lead to a simulation where the stresses in the gears are higher than critical stresses; after certain time this may result in breakage of the teeth.

Internal dynamic forces are also present. During the teeth meshing action, internal dynamic forces occur because of the elastic tooth deformation and manufacturing errors (for example: tooth profile form tolerance errors and

circular gear pitch difference). During the meshing action, tooth deformation can cause impact between gear teeth. Intensity of the impact between the teeth is dependent of circular pitch difference size. The bigger circular pitch difference, the more intensive is the impact between the gear teeth during the meshing action. The gear vibrations can also influence the internal dynamic forces between the gear teeth. The teeth in meshing action can be modelled as an oscillatory system [1] to [3]. This model consists of concentrated masses (each of which represent one gear) connected with elastic and dump element. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. In order to obtain better results, it is possible to model the elastic element as a nonlinear spring.

Although gear dynamics has been studied for decades, few studies present a formulation intended for the dynamic response of full gear-train systems that contain multiple gear meshes, flexible shafts, bearings, and housing structures. There are few reliable computational tools for the dynamic analysis of general gear configurations. Some models exist, but they are limited by simplified modeling of gear tooth mesh inter-faces, two-dimensional models that neglect out-of-plane behavior, and models specific to a single gear configuration. General three-dimensional


57Dynamic Model for the Stress and Strain State Analysis of a Spur Gear Transmission

finite element models for dynamic response are rare because they require a significant computa-tional effort. This is accomplished by many time steps required for the transient response to diminish, so that steady state data can be obtained. This study attempts to fill this gap with a general finite element formulation that can be used for full gearbox dynamic analyses.

Dynamic transmission error is taken as the parameter for the modelling of noise in geared transmission. In the last two decades there is plenty of work has been concentrating on modelling of the dynamic transmission error for spur and helical gears and representing the influence of the dynamic transmission errors on the level of noise in the geared transmission. Lately, there have been several experiments conducted in order to isolate particular noise effects like noise coming from bearing, housing noise, meshing action noise and backlash noise simply by measuring the dynamic transmission error. Some of the earliest models are represented in [4] and [5].

For different analysis purposes, there are several modelling choices such as a simple dynamic factor model, compliance tooth model, torsional model, and geared rotor dynamic model, [6]. Using the free vibration analysis critical para-meters such as natural frequencies and vibration modes that are essential for almost all dynamic investigations can be calculated. The free vibration properties are very useful for further analyses of planetary gear dynamics, including eigen-sensitivity to design parameters, natural frequency veering, planet mesh phasing, and parametric instabilities from mesh stiffness variations, [7] and [8]. It is also necessary to systematically study natural frequency and vibration mode sensitivities and their veering characters to identify the parameters critical to gear vibration. In addition, practical gears may be mistuned by mesh stiffness variation, manufacturing imperfections and assembling errors. For some symmetric structures, such as turbine blades, space antennae, and multispan beams, small disorders may dramatically change the vibration, [9]. The following articles [10] and [11], related to the nonlinear analysis of dynamic behavior of gears, using experimental methods and the application of FEM.

Based on the results of the experiments conducted during the gear vibration research, it is possible to conclude that the excitation is restored every time when a new pair of teeth enters the mesh. Vibrations with natural frequencies dominate the vibration spectrums. The internal dynamic forces in teeth mesh, vibration and noise are consequences of the: change in teeth deformation, teeth impact, gear inertia due to measure and teeth shape deviation [12].

Paper [13] presents two models of the geared transmission with two or more shafts. The first approach gives a model based on the rigid rotors coupled with rigid gear teeth, with mass distributions not balanced and in the form of the mass particles as the series of the mass debalances of the gears in multistep gear transmission. By a very simple model it is possible to conduct a useful investigation of the nonlinear dynamics of the multistep gear transmission and nonlinear phenomena in free and forced dynamics. This model is suitable to explain source of vibrations and big noise, as well as no stability in gear transmission dynamics. Layering of the homoclinic orbits in phase plane is a source of a sensitive dependence on the nonlinear type of regime of gear transmission system dynamics. The second approach gives a model based on the two-step gear transmission taking into account the deformation and creeping as well as visco-elastic teeth gears coupling. Our investigation was focused on a new model of the fractional order dynamics of the gear transmissiont. For this model we obtained analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes. Genera-lization of this model to the similar model of the multistep gear transmission is quite simple.

The model in this paper represents a typical transmission model with three shafts. Starting with the first gear pair, a meshing action is observed for all gear meshes simultaneously using no additional assumptions concerning the gear geometry or the meshing action boundary and load conditions. The boundary conditions on the gear-shaft connections are assumed to be equal to zero. The internal dynamic forces are obtained as a result of the first step of the nonlinear quasi-static analysis and are taken as an input for further analysis. The procedure described can be modified for the


58 Nikolić, V. ‒ Dolićanin, Ć. ‒ Dimitrijević, D.

purpose of calculation of different types of geared systems simply by combining different steps in the described analysis and different configurations of the gears and shafts. It is optional which of the mentioned steps will be of the highest priority, and depends, of course, of the purpose of the concrete analysis.

1 FINITE ELEMENT MODEL OF THE SPUR GEAR TRANSMISSION

Starting with one gear pair, a meshing action is observed using no additional assumptions concerning the gear geometry or the meshing action boundary and load conditions. A numeric experiment is developed simply by using the boundary conditions on the gear-shaft connection, which are assumed to equal zero. The software that is developed for the purpose of dynamic analysis of the gear-boxes can be used to obtain the following results from such model:a) forces that arise in gear contact during

the gear meshing action as a result of the incremental quasi-static series of analysis [8] to [10], for each meshing action time step,

b) the comprehensive modal analysis for the gear pair, and

c) the forces obtained in a) will be used further as an input for the nonlinear dynamic analysis. For the purpose of this paper, it is assumed that the obtained force is a harmonic function and in form:

Fn = Fo sin wt, (1)

where Fo is the resultant force for the observed meshing action time step,

d) Finally, the dynamic analysis of the gear meshing action is conducted [10]. The contact

load as inner dynamic load is taken as an input value obtained in a) and approximated using harmonic function, as it is described in c).

The developed software can be modified for the purpose of calculation of different types of geared systems. It is optional which of the mentioned steps will be of the highest priority, and it depends on the purpose of the concrete analysis. That is not of interest here, and therefore will not be discussed.

The gears analyzed in this paper are the ones from the deep drilling machine gear set, [14]. The gear geometries are generated using the software developed by the authors, [13] to [19], and adapted for the SALOME platform [40]. The obtained geometries are transferred to SALOME mesh generation software and discretized using four node tetrahedral elements there (Fig. 1).

Fig. 1. Gear transmission model

Mesh parameters of the geared system are:• number of nodes: 19209,• number of elements: 102868,

Table 1. Constructive transmission parametersParameter Gear 1 Gear 2 Gear 3 Gear 4

Number of teeth 27 30 33 22Modul [m] 0.003 0.003 0.003 0.003Pitch circle diameter [m] 0.081 0.090 0.099 0.066Addendum circle diameter [m] 0.087 0.096 0.106 0.072Base circle diameter [m] 0.073 0.0828 0.0918 0.0588Measurement teeth number [m] 0.004 0.004 0.004 0.003Standard angle [degrees] 20 20 20 20Axial distance [m] 0.081 0.081 0.081 0.099



• number of elements of shaft 1 (staring from left hand side): 23618,

• number of elements of shaft 2 (middle): 30034,

• number of elements of shaft 3 (right bottom): 1586.

Gear geometry parameters are given in Table 1.

Displacement boundary conditions (Fig. 2) are set on the shaft-bearing connections nodes. The displacement boundary conditions on the axial bearing connection nodes are set to be zero in all degrees of freedom, and for the radial bearing connection nodes this displacement is set to be zero only in X, Y directions.

Fig. 2. Displacement and force boundary conditions (right)

Load boundary conditions are generated on the meshing teeth on edges that are opposite to the contact surfaces of each tooth, like [26]. The form of the load function is taken according to Eq. (1) with amplitude obtained from the nonlinear static analysis. This analysis helps determine the form of the amplitude force distribution in gear mesh. Detailed procedure on how the force is taken from nonlinear static analysis will not be discussed in detail here. The force distribution on other transmission elements is calculated in the same way.

All other meshing conditions are not taken into consideration. The following assumptions are made:

It is assumed that the contact is without friction:

• There is no sliding between the teeth during the meshing action.

• The transmission functions in constant temperature field. All other thermodynamic effects can be neglected.

• The proportional damping is used according to

C = 2 b M + a K.

The continuum discretization is done using tetrahedral finite elements with linear approximation of the finite element geometry.

2 ANALYTIC MODEL OF THE SPUR GEAR TrANSMISSION

The transmission model in Fig. 1 can be simplified using the transmission model in Fig. 3 for dynamic analysis [1] to [3], [10], [27] and [31].

This class of dynamic models can be used for the analysis of the oscillation parameters of the transmission, only if meshing functions of the stiffness and dumping are known. As this is not the case, it is necessary to experimentally obtain the form of the mesh stiffness (dumping) of the geared mesh, or to use other means like finite elements method to obtain unknown stiffness/ dumping functions.

The solution for the differential equations given in Eq. (2) is not possible without explicitly defined mesh stiffness and dumping functions, because of the fact that the equations are non-linear functions of time and the solution can be obtained only using numeric methods.

1

2

3

c , k1 1

c , k2 2

c , k3 3

F (t)2

F (t)2

F (t)1

F (t)1

x1

x2

x3

x4 m4

m3

m2

m1

c34

c12

k12

k34

Fig. 3. A simplified dynamic model of the geared transmission on Fig. 1



The differential equation [2], [3], [20] to [22] and [24] of the model in Fig. 3 are:

m x c c x c xk k x k x F t

m x

1 1 1 12 1 12 2

1 12 1 12 2 1

2 2

+ + − ++ + − =+

( )( ) ( ),(cc c x c x c x

k k x k x k x F tm

2 12 2 12 1 2 3

2 12 2 12 1 2 3 1

3

+ − − ++ + − − = −

)( ) ( ),

x c c x c x c xk k x k x k x F t

3 2 34 3 34 4 2 2

2 34 3 34 4 2 2 2

+ + − −+ + − − =

( )( ) ( ),mm x c c x c xk k x k x F t4 4 3 34 4 34 3

3 34 4 34 3 2

+ + − ++ + − = −

( )( ) ( ),

(2)

where mi (i = 1, ..., 4) are equivalent masses of transmission elements, ci are shaft stiffness (i = 1, ..., 3), ki are shaft dumping (i = 1, ..., 3), c12, c34 are gear mesh stiffness functions depending on t, k12, k34 are gear mesh dumping functions depending on t.

Shaft stiffness/dumping outside of the gears on the shaft 2 are not considered.

3 STRESS AND STRAIN STATE ANALYSIS USING STrESS AND STrAIN TENSOr

INVArIANTS

The calculation of the component stresses and strains is done by means of the nonlinear FEM using already described procedure.

Starting from known component stresses as components of tensor N, it is possible to obtain stress tensor invariants in every node after the finite elements analysis is done, [3], [23] to [31]. Since:

f o o

x o xy xz

xy y o yz

xz yz z o

( )

,

σ σ

σ σ τ ττ σ σ ττ τ σ σ

= − =

=−

−−

=

N I

0 (3)

yields: − − + − =( ) .σ σ σo o oL L L3

12

2 3 0 (4)

Using Eq. (3) or its algebraic form Eq. (4) it is possible to obtain the principal stresses as functions of stress invariants L1, L2 and L3, using Eqs. (5) to (7) as a system of three linear algebraic equations with unknown principal stresses, [25] to [31]. That yields the functional dependency

between principal stress and stress invariants in form: σo = f( L1, L2, L3). Therefore: L f tr1 1 2 3 1 2 3= = + + =( , , ) ( ),σ σ σ σ σ σ G (5)

L f

tr tr

2 1 2 3 1 2 2 3 1 3

2 212

= = + + =

= −( )( , , )

( ) ( ) ,

σ σ σ σ σ σ σ σ σ

G G (6)

and L f3 1 2 3 1 2 3= = =( , , ) det( ),σ σ σ σ σ σ G (7)

where Eq. (8) is a principal stress tensor in form:

G =

ÃÃ

Ã

1

2

3

. (8)

When the component stresses are known, it is also possible to obtain the equations of the main stress directions. The principal stress directions are directions that define coordinate system of principal directions, where there are no shear stresses in defined planes.

When the principal stresses are different, σ1 ≠ σ2 ≠ σ3, the maximal values of the shear stresses are found in the three normal planes, where the principal axis 1 and one of these planes are collinear, and the angles between the other principal planes and the mentioned plane are 45 degrees. The maximum values of the shear stresses are obtained in the following from:

τ

σ στ

σ σ

τσ σ

(I) (II)

(III)

= ±−

= ±−

= ±−

2 3 2 1

1 2

2 2

2

, ,

.

There are no shear stresses in principal planes. On the other hand, in maximal shear stress planes, there are stresses with values given in the form:

σ

σ σσ

σ σ

τσ σ

(I) (II)

(III)

=+

=+

=+

2 3 1 3

1 2

2 2

2

, ,

. (10)

As already stated, the principal directions can be obtained from component stresses using the following relations:



α β γo o o

oK K KC

31 32 33= = = , (11)

or

ατ τ

σ σ τ

βσ σ ττ τ

γσ σ τ

τ σ σ

o

o

o

o

o

o

o

o

xy xz

y yz

x xz

xy yz

x xy

xy y

C

−

=

−−

=

=−

−

= , (12)

the system is defined if condition Eq. (13) is satisfied:

α β γo o o2 2 2 1+ + = . (13)

The relations in Eqs. (11) and (12) should be taken for s = 1, 2, 3. They give the equations for the three main stress directions represented with three direction cosines, with total of nine direction cosines.

Depending on the value of the principal invariants, the properties of the main stresses are defined:a) if L3 > 0, the roots (principal stresses) given

in Eq. (8) are positive and different;b) if L3 < 0, there are negative roots (principal

stresses); and c) if L3 = 0, one of the roots (principal stresses)

is equal zero.The same discussion can be applied for the

strains. Starting from Eq. (14):

ε ε γ γ

γ ε ε γ

γ γ ε ε

x o xy xz

xy y o yz

xz yz z o

−

−

−

= 0, (14)

yields: − − + − =( ) ,ε ε εo o oJ J J3

12

2 3 0 (15)

where J1, J2, and J3 are known invariants of the strain tensor obtained from known strain components of the geared transmission. The solutions of the Eq. (15) are principal strains given. For the principal directions, the principal strains build the strain tensor in form Eq. (16):

S =

εε

ε

1

2

3

, (16)

J f tr S

J f1 1 2 3 1 2 3

2 1 2 3 1 2 2 3 1

= ( ) = + + = ( )= ( ) = + +

ε ε ε ε ε ε

ε ε ε ε ε ε ε ε ε

, , ,

, , 33

2 2

3 1 2 3 1 2 3

12

=

= ( ) − ( )( )= ( ) = = ( )

tr S tr S

J f S

,

, , det .ε ε ε ε ε ε

(17)

Analogue to Eqs. (11) to (13) for the principal stresses, it is possible to obtain the equation of the principal strains by solving the system of Eqs. (17) to (19).

The principal strain directions can be obtained in the following form:

αγ γ

ε ε γ

βε ε γγ γ

γε ε γ

γ ε ε

o

xy xz

y o yz

o

x o xz

xy yz

o

x o xy

xy y o

oC

−

=

−−

=

=−

−

= , (18)

α β γo o o2 2 2 1+ + = . (19)

Depending on the value of the principal invariants J1, J2 and J3, the properties of the principal strains are for example:a) if J3 > 0, the roots (principal strains) of Eq.

(7) are positive and different.b) if J3 < 0, there are negative roots (principal

strains), and c) if J3 = 0, on of the roots (principal strains) is

equal zero.

4 rESULTS

Using the above procedures, the results are obtained for the geared transmission in Fig. 1, using boundary conditions presented in Fig. 2 using transmission parameters given in Table 1.

Transmission load distribution along the line of contact for each transmission gear pairs given in Fig. 4, and distribution of loads on the transmission elements for t = 0.02 is given in Fig. 5 as an output from the nonlinear dynamic analysis of the geared transmission.



Additional results for strain distribution along the line of contact for each gear par is given in Fig. 8, and Von Mises stress distribution along the line of contact for each transmission gear par and each time step (Fig. 7) together with distribution of Von Mises stress on the transmission elements for t = 0.02 is presented in Fig. 6.

Work methodology previously tested on simple examples from literature [7] to [11], [28] and [30] and obtained a good coincidence of results.

Fig. 4. Transmission load distribution in time step t = 0.02

Fig. 5. Load distribution along the line of contact for each transmission gear par (t = 0 to t = 0.02)

The given results are input results for the calculations of principal invariants in each node for each and every element of the presented geared transmission. An example of the principal stress and strain direction calculation for the selected nodes in contact is presented in Fig. 9 and corresponding Tables 2 and 3.

Fig. 6. Von Mises stress distribution on the transmission elements for t = 0.02

Fig. 7. Von Mises stress distribution along the line of contact for each transmission gear par (t = 0

to t = 0.02)

The distribution of the principal invariants in the zone of contact for each transmission gear pair is presented in Figs. 10 to 13, as a result of the software developed by the authors that can be used for the detailed transmission analysis.



Fig. 8. Strain distribution along the line of contact for each transmission gear par

(t = 0 to 0.02)

a)

b)

Fig. 9. a) Nodes which are used for calculation example of the stress and strain state, b) example

of the graphic representation of the principal stress analysis results in chosen nodes

Fig. 10. Contact strain tensor invariants for the gear pair 1-2, for t = 0.02

Fig. 11. Contact stress tensor invariants for the gear pair 1-2, for t = 0.02

Fig. 12. Contact stress tensor invariants for the gear pair 3-4, for t = 0.02



Fig. 13. Contact strain tensor invariants for the gear pair 3-4, for t = 0.02

Work methodology previously tested on simple examples from literature [7] to [11], [28] and [30] and obtained a good coincidence of results.

5 CONCLUSIONS

In this paper has been shown how the general finite elemente method can be applied to study dynamic behavior in the case of the real model of the geared set.

A novel approach for the geared transmission dynamic analysis is developed. Using several incremental finite elements procedures, it is possible to obtain a series of states of the geared transmission in every integration time step of the differential equations of motion. Since the conditions in which the dynamic analysis is done are quasistatic, suggested method approximates very well the real working conditions of the transmission. On the other hand, as every dynamic calculation, it is exhaustive and time consuming.

For the observed model of gear transmissions, the analysis distribution of stress and strain invariants has been done.

The selected point that are in contact, are determined by the value of the main stresses and main directions of the observed time-steps.

Based on the results, it can be concluded that there is a change in the directions of principal stresses in the contact zone. This causes arise and changes in the values the principal stresses, that is stress invariants.

Table 2. Component stresses and strains in node: 1609, principal stress, strain invariants, principal stresses and principal strains and appropriate principal directions, for t = 0.02

Node: 1609σx [Pa] σy [Pa] σz [Pa]

2.437E+09 8.759E+08 6.726E+08

τxy [Pa] τxz [Pa] τyz [Pa]1.949E+08 -9.431E+06 6.974E+07

α β γ1.56 1.62 5.10E-021.46 2.64 1.091.57 1.56 7.13E-03

L1 L2 L33.99E+09 -1.38E+19 -6.89E+27

σ1 [Pa] σ2 [Pa] σ3 [Pa]-2.54E+09 4.47E+08 6.08E+09

εx [μm] εx [μm] εx [μm]939.480 -27.195 -153.040

γxy [μm] γxz [μm] γyz [μm]241.311 -11.676 86.346

α β γ1.55 2.78 1.211.37 2.58 2.091.32 2.56 2.09

J1 J2 J37.60E+01 -7.14E+04 2.00E+06

ε1 [μm] ε2 [μm] ε3 [μm]-2.14E+02 -2.93E+01 3.19E+02

In the literature are present similar procedures [7] to [10] and they were used as reference material for the composition and verification of models and results .

But, in this paper, a new method for the results analysis, together with developed software, is used for obtaining of the principal stress and strain state of the geared transmission, using principal stress and strain invariants as calculation parameters. The software allows generalized analysis of every system for which this kind of analysis can be used.



Table 3. Component stresses and strains in node: 2623, principal stress, strain invariants, principal stresses and principal strains and appropriate principal directions, for t =0.02

Node: 2623σx [Pa] σy [Pa] σz [Pa]

2.088E+09 1.229E+09 1.053E+09

τxy [Pa] τxz [Pa] τyz [Pa]5.508E+07 -3.036E+07 3.852E+07

α β γ1.57 1.57 6.26E-031.57 1.57 5.77E-031.59 1.60 3.61E-02

L1 L2 L3-4.36E+09 -7.46E+18 2.21E+28

σ1 [Pa] σ2 [Pa] σ3 [Pa]-4.97E+09 -1.83E+09 2.44E+09

εx [μm] εx [μm] εx [μm]-668.191 -136.320 -27.790

γxy [μm] γxz [μm] γyz [μm]68.191 -37.592 -47.688

α β γ1.52 1.88 3.10E-011.77 2.94 1.531.88 2.54 1.07E+00

J1 J2 J3-8.30E+01 -5.06E+04 2.66E+06

ε1 [μm] ε2 [μm] ε3 [μm]-2.45E+02 -5.10E+01 2.13E+02

On the basis of the results, shown in this paper, it has been concluded that the methodology developed to study the dynamic behaviour of complex systems is very efficient. It gives a lot of possibilities and can be easily upgraded for analysis of other effects [33] to [35].

The dynamic behavior and analysis of the stress and strain conditions that suggest that the system of only two gears is very complex and that it is almost impossible to include all the effects by such and similar research. This paper considers

two pair gears, which makes the problem more complex.

Further research should be directed at studying the effects of mutual dynamic impact of teeth in engagement, as well as at including connection between the shaft and gear into the dynamic model and the like.

In accordance with the present trend of application of new materials, like in [36] to [39], authors will, in future studies, simulate the dynamic behavior of a gear made of composite materials and study the life of the gears at the cyclic load.

Based on the numerical results, i.e., on the presented and other diagrams, a general conclusion can be drawn: stress and strain distributions in the case of dynamic behavior of toothed gears is in accord with the results from the aforementioned literature. Thus, these results can be taken as relevant for further research.

6 ACKNOWLEDGMENTS

Parts of this research were supported by the Ministry of Sciences, Technologies and Deve-lopment of Republic Serbia trough Mathematical Institute SANU Belgrade, State University of Novi Pazar and Faculty of Mechanical Engineering University of Niš Grants No. ON174001. “Dynamics of hybrid systems with complex structures. Mechanics of Materials.”

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1Vsebina

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Strojniški vestnik - Journal of Mechanical Engineeringletnik 58, (2012), številka 1

Ljubljana, januar 2012ISSN 0039-2480

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Erik Potočar, Branko Širok, Marko Hočevar, Matjaž Eberlinc: Nadzor ločitve toka nad lopatico vetrne turbine s pomočjo generatorja plazme SI 8

Sha Du, Haisong Ang: Analiza zasnove in izvedljivosti spremenljivega aerodinamičnega profila krila za upravljanje položaja med letom SI 9

Vera Nikolić, Ćemal Dolićanin, Dejan Dimitrijević: Dinamični model za analizo napetostnega in deformacijskega stanja gonila z valjastimi zobniki SI 10

Navodila avtorjem SI 11

Osebne vestiDoktorske disertacije, magistrska dela, specialistična dela in diplome SI 13

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1, SI 3 Prejeto: 06.07.2010 Sprejeto: 23.06.2011

*Naslov avtorja za dopisovanje: Oddelek za gorivne celice in kemijo trdnih stanj, Nacionalni laboratorij za trajnostno energijo Risø, Danska tehnična univerza – DTU, Roskilde, Danska, [email protected] SI 3

Eksperimenti z modularnim magnetnim hladilnikomEngelbrecht, K. ‒ Jensen, J.B. ‒ Bahl, C.R.H.

Kurt Engelbrecht* ‒ Jesper Buch Jensen ‒ Christian Robert Haffenden BahlOddelek za gorivne celice in kemijo trdnih stanj, Nacionalni laboratorij za trajnostno energijo Risø,

Danska tehnična univerza – DTU, Roskilde, Danska

Magnetno hlajenje je aktivno raziskovalno področje, saj predstavlja alternativen način hlajenja, ki ne uporablja plinastega hladiva. Namesto tega uporablja trdno hladivo s fluidom za prenos toplote na osnovi vode, in ne oddaja toplogrednih plinov oz. plinov, ki bi tanjšali ozonsko plast. Magnetno hlajenje pa še ni dozorela tehnologija in zato so potrebne določene izboljšave. Na Risø DTU je bil zgrajen eksperimentalni magnetni hladilnik, namenjen preučevanju možnosti za izboljšanje delovanja magnetnega hlajenja. Naprava je modularne zgradbe ter omogoča enostavno zamenjavo vseh delov za potrebe posameznih eksperimentov. Naprava je zato izjemno vsestranska in omogoča izvedbo različnih eksperimentov.

Testna naprava je linearne izvedbe, vir magnetnega polja pa je permanentni Halbachov magnet s povprečno gostoto magnetnega polja 1,03 T.

V članku so predstavljeni rezultati eksperimentov za ravne ploščne regeneratorje iz gadolinija in sintranih spojin La(Fe,Co,Si)13. Eksperimentalno je bil raziskan vpliv prevoda toplote skozi stene ohišja regeneratorja. Vsak regenerator iz gadolinija je bil preizkušen nad razponom temperatur vročega rezervoarja v pogojih brez obremenitve. Testna naprava je bila preizkušena tudi z dvema različnima sestavama spojin La(Fe,Co,Si)13.

Namen preizkusov je izboljšanje učinka magnetnega hlajenja z razvojem novih magnetokaloričnih materialov ter z zasnovo večplastnih postelj regeneratorjev iz različnih materialov. Prikazani so rezultati preizkusa za regenerator, izdelan iz enega materiala La(Fe,Co,Si)13, in za regenerator, izdelan iz dveh različnih materialov, rezultati pa so primerjani z rezultati enakega sistema iz gadolinija. Gradnja regeneratorjev iz dveh materialov iz družine La(Fe,Co,Si)13 ima potencial za izboljšanje zmogljivosti sistema, pri obravnavani napravi pa je imel najboljšo zmogljivost regenerator iz gadolinija. Iz tega sledi, da so potrebne dodatne raziskave na področju razvoja magnetokaloričnih materialov za komercialne aplikacije.

V prihodnje raziskave je treba vključiti tudi tehnike za izboljšanje zmogljivosti regeneratorjev, in s tem posledično tudi zmogljivosti magnetnega hlajenja. V članku je predstavljena tudi metoda za zmanjšanje izgub iz regeneratorja v okolico s pomočjo tehnologije 3D-tiskanja ohišja regeneratorja z votlimi stenami. Eksperimenti kažejo, da lahko votle stene izboljšajo delovanje sistema, zlasti pri velikem razponu delovne temperature naprave.©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: alternativno hlajenje, aktivni magnetni regenerator, magnetno hlajenje, magnetokalorični material, večplastni regenerator


*Naslov avtorja za dopisovanje: Univerza v Genovi DIPTEM/TEC, Via all’Opera Pia 15a, Genova, 16145, Italija, [email protected] 4

Dinamični 1D-model aktivnega magnetnega regeneratorja: parametrična preiskava

Tagliafico, G. ‒ Scarpa, F. ‒ Tagliafico, L.A.Giulio Tagliafico1 ‒ Federico Scarpa*,2 ‒ Luca Antonio Tagliafico2

1 Univerza v Genovi, DCCI, Italija 2 Univerza v Genovi, DIPTEM/TEC, Italija

Študija podaja simulacijo zmogljivosti idealnega aktivnega magnetnega hladilnika (AMH) za parametrično analizo vedenja pri sobni temperaturi ob spreminjanju delovnih parametrov na napravi AMH.

Magnetno hlajenje je inovativen in alternativen način hlajenja pri sobni temperaturi, ki izkazuje konkurenčnost uveljavljenim tehnikam hlajenja in zagotavlja prihranek primarne energije. AMH je ključni element magnetnih hladilnih ciklov pri sobni temperaturi, zato so potrebni zanesljivi numerični modeli za napovedovanje njegovega delovanja pri različnih pogojih. Za simulacijo AMH je mogoče uporabiti 1D- in 2D-sheme. Pri kompleksnih, neurejenih geometrijah pa je v vsakem primeru treba uporabiti pristop z 1D-modelom. Na delovanje AMH vplivajo predvsem termofizikalne in magnetotermične lastnosti uporabljenega aktivnega magnetokaloričnega materiala (MKM) ter delovna temperatura. Vplivni dejavniki so tudi oblika MKM, geometrija regeneratorja, pretok fluida in frekvenca ciklov.

Razvit je bil enodimenzionalni dinamični model AMH in opravljena je bila parametrična analiza njegovega vedenja v pogojih blizu sobne temperature. Raziskava je osredotočena na termične lastnosti regeneratorja ne glede na napravo, v katero je vgrajen. Parametrična preiskava je namenjena ovrednotenju vplivov delovne frekvence in masnega pretoka fluida na delovanje AMH. Obravnavani delovni parametri so hladilna zmogljivost, temperaturni razpon, hladilno število in termodinamični izkoristek po drugem zakonu. Uporabljena je bila standardna geometrija AMH, rezultati pa so podani v brezdimenzijski obliki za običajne delovne pogoje.

Simulacije kažejo, da je hladilna zmogljivost zelo občutljiva na faktor izkoriščenosti Φ: -20% ali +10% odklon od optimalne vrednosti povzroči 20-odstotno zmanjšanje hladilne zmogljivosti. Φ ima majhen vpliv na COP. Spremembe frekvence povzročijo linearno spremembo hladilne zmogljivosti in zmanjšanje COP zaradi trenja v vmesni tekočini. Trendi termodinamskega izkoristka po drugem zakonu kažejo dominanten vpliv trenja in nepovračljivosti prenosa toplote pri nizkih in visokih temperaturah. Rezultati kažejo, da lahko AMH deluje s skoraj konstantno vrednostjo hladilnega števila pri različnih toplotnih obremenitvah, kar je mogoče doseči s pravilno nastavitvijo faktorja izkoriščenosti. To vedenje je mogoče uporabiti za večji prihranek energije v primerjavi s sistemi, ki delujejo na osnovi stiskanja plinov. Magnetni hladilnik je s primernim krmiljenjem uporaben tudi v dinamičnih pogojih.

Pristop s podajanjem krivulj zmogljivosti za različne delovne parametre omogoča razločno in jasno kvantifikacijo vpliva posameznih parametrov. Rezultati so uporabni tudi za določitev strategije krmiljenja naprav AMH. ©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: magnetno hlajenje, aktivno hlajenje, modeliranje, parametrična preiskava


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, [email protected] SI 5

Primerjava termo-hidravličnih lastnosti toplotnih regeneratorjev,

primernih za aktivne magnetne hladilnikeŠarlah, A. – Tušek, J. – Poredoš, A.

Alen Šarlah* – Jaka Tušek – Alojz PoredošUniverza v Ljubljani, Fakulteta za strojništvo, Slovenija

Prispevek obravnava pasivne toplotne regeneratorje, ki so zaradi svojih lastnosti primerni za uporabo v aktivnih magnetnih hladilnikih (AMH). Za te je značilno, da delujejo na principu izkoriščanja magneto-kaloričnega efekta aktivnega magnetnega regeneratorja (AMR), katerega delovanje je odvisno predvsem od termo-hidravličnih lastnosti strukture regeneratorja. Namen prispevka je eksperimentalna in numerična primerjava najpogostejših oblik regeneratorjev, ter evalvacija njihove uporabnosti v AMH.

Obravnavanih je šest oblik regeneratorjev različnih geometrij. Med seboj so primerjani in evalvirani s pomočjo eksperimentalnih rezultatov (z uporabo metode enkratnega vpiha) in brezdimenzijskega matematičnega modela. Regeneratorji so med seboj primerjani glede na prenos toplote, tlačni padec in njihovo toplotno učinkovitost.

Iz rezultatov je bilo ugotovljeno, da je glede na toplotne lastnosti (prenos toplote) najboljši regenerator s kroglicami, ki pa ima najslabše hidravlične lastnosti (tlačni padec), ter posledično slabše razmerje toplotnih in hidravličnih lastnosti (j/f). Primerjava razmerja j/f je pokazala, da izkazuje najboljše termo-hidravlične lastnosti regenerator z lamelami, ki ima med vsemi obravnavanimi regeneratorji najbolj optimalne lastnosti, zato se za nadaljnje raziskovalno delo priporoča razvoj naprednih regeneratorjev na osnovi lamelne strukture.

Izdelan numerični program za določitev učinkovitosti različnih regeneratorjev je bil v nadaljevanju nadgrajen z magnetnimi lastnostmi in termodinamičnimi zakonitostmi delovanja AMR, pri čemer so bile magnetne lastnosti določene na osnovi aproksimacije molekularnega polja. S to metodo je možno določiti magnetne lastnosti magnetnih materialov s pomočjo eksperimentalnih podatkov (za magnetne lastnosti materialov) in njihovo ustrezno analitično-numerično obdelavo. Izdelan in preizkušen numerični program je tako uporaben za simuliranje delovanja magnetnih hladilnikov z regeneratorji različnih geometrij in termo-hidravličnih lastnosti.

Prednost in izvirnost pristopa opisanega v članku je v tem, da je bil tako za obravnavo termo-hidravličnih lastnosti regeneratorjev kot tudi za numerično simuliranje AMH uporabljen isti matematični in numerični model. S tem so bile poenotene fizikalne in matematične zakonitosti obeh modelov, posledično pa smo se izognili morebitnim napakam, ki bi lahko nastale zaradi uporabe različnih raziskovalnih pristopov (primerjava rezultatov različnih avtorjev je namreč pokazala, da obstajajo občutne razlike med določenimi metodami in tehnikami določitev prestopa toplote v regeneratorjih - rezultati se med seboj razlikujejo tudi do 20%).

Dobljeni numerični program je bil dodatno eksperimentalno in analitično preverjen. Končni rezultat dela je numerični program, ki služi kot orodje za raziskave in razvoj aktivnih magnetnih regeneratorjev in hladilnikov, saj omogoča simuliranje različnih predhodno evalviranih regeneratorjev, poljubnih magnetnih polj in načinov obratovanja AMH, hkrati pa sledi vsem termodinamičnim zakonitostim magnetnih hladilnikov.©2011 Strojniški vestnik. Vse pravice pridržane.Ključne besede: magnetni hladilnik, aktivni magnetni regenerator, termo-hidravlične lastnosti, brezdimenzijski model, aproksimacija molekularnega polja


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, [email protected] 6

Razmerje med vpadnim kotom merjenja, razdaljo merjenja, barvo objekta in številom zajetih točk

pri CNC-laserskem merjenju oblikeVukašinović, N. – Možina, J. – Duhovnik, J.

Nikola Vukašinović* – Janez Možina – Jože DuhovnikUniverza v Ljubljani, Fakulteta za strojništvo, Slovenija

Lasersko merjenje oblike površin na osnovi laserske triangulacije z namenom pridobivanja računalniških modelov objektov iz narave je v zadnjem obdobju deležno velike pozornosti zaradi razmerja med zmogljivostjo in dostopnostjo, še posebno na področju nadzora oblik in povratnega inženirstva. Zato je opravljenih veliko raziskav za izboljšavo kakovosti merilnih rezultatov, ki pa so pogojeni z optičnimi zakonitostmi in omejitvami strojne opreme.

V članku so predstavljeni rezultati raziskave o medsebojnih vplivih vpadnega kota merjenja, razdalje merjenja in barve ter odbojnosti svetlobe na število zajetih točk pri merjenju z laserskim triangulacijskim merilnikom oblik na CNC-strojih. Število zajetih točk in njihova razporeditev sta bistvena parametra, ki morata biti zagotovljena za uspešno rekonstrukcijo 3D-površin, vendar pri raziskavah laserskega triangulacijskega merjenja nista deležna take pozornosti kot drugi parametri.

Parametra sta lahko izražena na več načinov: bodisi neposredno, kot gostota in celovitost oblakov točk, kar so predlagali Lartigue s sodelavci, bodisi posredno, prek ločljivosti, kar je prikazal Vezzetti. Ne glede na to pa je za uspešno rekonstrukcijo površine vedno potrebno zagotoviti zadostno količino podatkov, čeprav bo potrebno v kasnejši fazi rekonstrukcije površin število točk zmanjšati.

V raziskavi so bile prepoznane tiste vrednosti posameznih parametrov, ki omogočajo zadostno število zajetih točk za poljubno rekonstrukcijo površin. Prepoznani so tudi mehanizmi posameznih rezultatov, zato jih je mogoče upoštevati pri izdelavi merilnih strategij za samodejno merjenje na CNC-strojih in merilno kontrolo.

Meritve so potekale po podobnem postopku, kot ga je predstavil že Lartigue. Za merjence so bile uporabljene obarvane granitne plošče dimenzij 200×150×10 mm, ki imajo dobro geometrijsko stabilnost in tolerančno območje. Meritve ravne površine so bile izvedene pri treh različnih barvah površin: rdeči, zeleni in modri. Pri tem so bile barve enakomerno razporejene po celotnem vidnem spektru svetlobe, odbojnost površine pa smo določili kot delež odbite svetlobe uporabljenega laserskega žarka pri izbrani barvi površine. Ta pristop je bil uporabljen zato, ker imajo vse površine pri različnih valovnih dolžinah različno odbojnost ter odbijajo širši spekter svetlobe in ne ene same valovne dolžine.

Vsi izmerjeni oblaki točk so bili po meritvi obrezani na manjšo enotsko površino, na kateri smo prešteli število zajetih točk. Tako smo dobili podatek o številu/gostoti točk, obenem pa smo omejili vpliv razporeditve točk, ki pa ga lahko razberemo iz globalnega diagrama zbranih rezultatov.

Rezultati kažejo, da vpadni kot merjenja do določene mere nima posebnega vpliva na število zajetih točk. Šele ko se kot merjenja poveča do določene vrednosti, se začne število točk močno zmanjševati. Ta meja je znašala pri rdeči površini in kratkih merilnih razdaljah 70 stopinj, pri največji oddaljenosti senzorja od površine in slabi odbojnosti merilne svetlobe na površini (npr. modra površina) pa se je meja spustila na vsega 20 stopinj.

Po drugi strani pa izkazuje razmerje med oddaljenostjo senzorja in številom zajetih točk na enoto površine skoraj idealno linearno povezavo. Ta povezava izvira iz širjenja laserske merilne ravnine z oddaljenostjo od točkovnega vira svetlobe.

Na koncu so bili vsi rezultati zbrani v enačbo za določitev predvidenega števila zajetih točk. Enačbo smo dobili s faktorsko analizo in testom ANOVA. Enačba je zgolj primer in lahko služi kot pomoč pri izbiri najbolj optimalnih merilnih strategij, na primer pri avtomatizirani kontroli kakovosti površin.© 2011 Strojniški vestnik. Vse pravice pridržane.Keywords: oblak točk, gostota točk, povratno inženirstvo, lasersko skeniranje, laserska triangulacija


*Naslov avtorja za dopisovanje: Nuklearni institut “VINČA”, 11001 Beograd, Srbija, [email protected] SI 7

Toplotna obremenitev večploščnih mokrih tornih sestavov

pri zavornem režimuŽivanović, Z. ‒ Milić, M.

Zlatomir Živanović1,* ‒ Miodrag Milić2

1 Nuklearni institut “VINČA”, Serbia 2 Vojno-tehnični institut, Serbia

Namen raziskave je identifikacija zavornih režimov, pri katerih pride do toplotne preobremenitve tornih sestavov zavor visokohitrostnih tirnih vozil. Z določitvijo teh režimov je mogoče preprečiti posledice, do katerih bi lahko prišlo zaradi nezadostnega učinka zavor med eksploatacijo vozil.

Mokri večploščni torni sestavi (sklopke in zavore) se uporabljajo v transmisijah visokohitrostnih tirnih vozil za namene menjavanja prestav, v krmilnih mehanizmih, kot glavna sklopka in tudi kot delovna zavora. Večploščni torni sestavi so občutljivi na dolgotrajno in pogosto zaviranje, ki ga spremljajo visoke temperature tornih površin in lahko povzroči izgubo funkcionalnosti ali celo odpoved zavor. Zato je zelo pomembna določitev zavornih režimov vozila, ki tornih sestavov ne izpostavljajo toplotnim preobremenitvam, in so tudi glavni problem, ki ga obravnava ta članek.

Raziskava toplotnih obremenitev večploščnih tornih sestavov je bila izvedena na ustreznem preizkuševališču s simulacijo zavornih režimov med eksploatacijo, pri čemer so bili izmerjeni značilni parametri, kot so: zavorni moment, tlak aktiviranja zornih sestavov, temperature tornih površin ter vrtilna hitrost pogonskih in gnanih elementov zavor. Ti parametri so nato z ustreznimi analitičnimi izrazi uporabljeni za izračun specifičnih tornih sil, ki nastopajo med simulacijo zaviranja. S pomočjo empiričnega razmerja med temperaturo torne površine in specifično torno silo, ki je bilo ugotovljeno za material tornih plošč MK-5, so bile določene mejne temperature za realizirane zavorne režime. Ugotovljene vrednosti temperatur so bile primerjane z izmerjenimi temperaturami. Na osnovi razmerij med temi vrednostmi so podani ustrezni zaključki o tem, ali so realizirani zavorni režimi znotraj dovoljenih toplotnih obremenitev tornih elementov.

Rezultati kažejo, da simulirani zavorni režimi bistveno presegajo toplotne obremenitve, ki jih torni sestavi še lahko prenesejo brez izgube funkcionalnosti. Izmerjene temperature tornih površin presegajo dovoljene vrednosti obeh tornih sestavov. Z vizualno kontrolo zavor po določenem številu zavornih ciklov so bile ugotovljene znatne deformacije elementov obeh zavor.

Rezultati kažejo, da v simuliranem zavornem režimu zaradi razmeroma nizkih mejnih temperaturnih vrednosti ni možna zaustavitev vozila pri maksimalni hitrosti brez poškodbe zavor. Kljub temu pa je vozilo brez poškodbe zavor možno zavreti z maksimalne hitrosti do približno 48 km/h. Če je treba vozilo še dodatno zavreti, pa je treba zmanjšati prestavno razmerje ali zavirati s kratkimi prekinitvami, da se lahko torni elementi ohladijo in toplotno razbremenijo. Gre za ekstremne situacije, ki pri eksploataciji vozila niso priporočljive. To je praktični prispevek predstavljenega dela.

Predstavljeni rezultati so lahko uporabni za razvoj podobnih zavornih sistemov, vključno z razvojem sistemov za zaščito tornih sestavov pred uničenjem zaradi neustrezne eksploatacije.

Raziskave omogočajo določitev mejnih režimov, pri katerih zaviranje vozila pri maksimalni hitrosti ne more povzročiti trajne poškodbe zavor. ©2011 Strojniški vestnik. Vse pravice pridržane. Keywords: tirno vozilo, moker torni sestav, delovna zavora, toplotna obremenitev, poškodbe zavor


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, Ljubljana, Slovenija, [email protected] 8

Nadzor ločitve toka nad lopatico vetrne turbine s pomočjo generatorja plazmePotočar, E. ‒ Širok, B. ‒ Hočevar, M. ‒ Eberlinc, M.

Erik Potočar1 ‒ Branko Širok2 ‒ Marko Hočevar2 ‒ Matjaž Eberlinc2,*

1Ministrstvo za gospodarstvo, Direktorat za energijo, Slovenija 2Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Vetrne turbine se konstruirajo z namenom čim večjega izkoristka proizvedene kilovatne ure električne energije glede na celotni strošek investicije in njenega delovanja. Eden od možnih načinov za izboljšanje zmogljivosti in življenjske dobe vetrnih turbin je tudi s pomočjo nadzora toka fluida z aktivnimi kontrolnimi sistemi na lopaticah vetrnih turbin. Pristop k nadzoru toka fluida v mejni plasti in pri odcepljanju je usmerjen na možnost aktivnega nadzora toka fluida na profilu vetrne turbine z uporabo generatorjev plazme. Ti zmanjšajo odcepljanje toka v mejni plasti ob steni na profilu lopatice, povratni tok in recirkulacijske vrtince.

V članku je analiziran vpliv plazme na lopatico vetrne turbine pri Re 7600 in Re 10500. Analiza je narejena na izbranem profilu NACA 4421 z znano aerodinamsko karakteristiko in koordinatami profila. Na zgornji strani profila so nameščeni štirje generatorji plazme. Meritve so bile izvedene v zračnem kanalu. Tokovne strukture ob profilu lopatice so bile posnete z računalniško podprto vizualizacijo. Narejeni so bili časovno zaporedni digitalni posnetki zračnega toka ob profilu z in brez uporabe plazme. Meritve tokovnih struktur z računalniško podprto vizualizacijo so bile narejene s hitro kamero za zajemanje digitalnih posnetkov.

Pri vzbujanju s plazmo so bile izvedene meritve v različnih delovnih točkah z uporabo različnih vrednosti napetosti na generatorju plazme in napetosti na ojačevalcu. Meritve so bile izvedene na integralnem in lokalnem nivoju tako, da si sledijo neposredno ena za drugo. Dovod dimnega polutanta pri posameznih meritvah je bil izveden vedno na enak način. Za analizo so bila uporabljena tista zaporedja digitalnih posnetkov, kjer je bila enakomernost izhajanja polutanta in odstopanja zaradi časovne spremembe koncentracije dimnega polutanta manjša od 2%.

Z rezultati meritev na profilu smo predstavili spremembe toka fluida in samo generiranje vrtinčnih struktur ob in za profilom v homogenem tokovnem polju zaradi uporabe generatorjev plazme.

Z več primeri smo demonstrirali in ovrednotili rezultate z dokazi, da lahko aktiven nadzor toka fluida z generatorji plazme vpliva na dogajanje v mejni plasti, ter dobili potrditev, da je vredno nadaljevati raziskave na vetrnih turbinah v tej smeri.

Iz rezultatov je razvidno, da lahko z generatorji plazme dobimo nadzor nad odcepljanjem toka fluida v mejni plasti. Seveda je velikost nadzora odvisna od več dejavnikov in konstrukcijskih rešitev, ki vključujejo mesto namestitve generatorjev, število generatorjev plazme, orientacijo elektrod ter tok in napetost generatorja plazme.

Razlaga predstavljenih rezultatov potrjuje smiselnost nadaljnjih raziskav na področju vplivanja na tok fluida s plazmo. Nadaljnje raziskave bodo usmerjene v preučevanje porazdelitve hitrosti toka z in brez plazme pri delovanju vetrne turbine. Predvidevamo, da lahko s plazmo vplivamo na tokovni profil za delujočo vetrno turbino v okviru določenih režimov obratovanja. Tako seveda lahko povečamo izkoristek proizvedene kilovatne ure električne energije glede na celotni strošek investicije in delovanja vetrne turbine.

Z računalniško podprto vizualizacijo smo izvedli analizo tokovnih struktur in dokumentirali profil hitrosti toka pri izbranem profilu lopatice z in brez plazme ter preučili vplive ločitve mejne plasti, ponovnega prilepljanja na profil itd. Ugotovitve so namenjene vsem, ki bi želeli uporabljati tehnologijo plazme za nadziranje toka fluida.©2011 Strojniški vestnik. Vse pravice pridržane.Keywords: lopatica, vetrna turbina, generator plazme, aktivni nadzor toka fluida, elektro- hidrodinamični generator, vizualizacija toka


*Naslov avtorja za dopisovanje: Fakulteta za letalsko in vesoljsko tehniko, Univerza za aeronavtiko in astronavtiko, P.O box 313, NO.29, Yudao street, Nanjing, Jiangsu, Kitajska, [email protected] SI 9

Analiza zasnove in izvedljivosti spremenljivega aerodinamičnega profila krila

za upravljanje položaja med letom

Sha Du* ‒ Haisong AngFakulteta za letalsko in vesoljsko tehniko, Univerza za aeronavtiko in astronavtiko v Nanjingu, Kitajska

Tehnologija spreminjanja oblike, ki izhaja iz leta netopirjev in ptic, lahko izboljša zmogljivost letala in optimizira učinkovitost upravljanja položaja med letom. Tradicionalni elementi za krmiljenje položaja med letom, kot so zakrilca, krilca, višinsko krmilo in smerno krmilo, ustvarjajo velik upor. Primerjava med profilom NACA0012 in spremenljivim aerodinamičnim profilom krila dokazuje, da lahko spremenljivi profil krila zagotavlja enak vzgon z manjšim uporom kot tradicionalne krmilne površine. Zato je predlagan koncept spremenljivega aerodinamičnega profila, ki bi zamenjal tradicionalne krmilne elemente za zmanjšanje upora in izboljšanje aerodinamične učinkovitosti. Na osnovi razvoja inteligentnih materialov, mehanizmov in krmilne tehnologije je nastal koncept spremenljivega aerodinamičnega profila, ki lahko spreminja obliko v različne konfiguracije. Možno je spreminjanje konfiguracije sprednjega roba, zadnjega roba in usločenosti za prilagajanje razmeram in nadzor položaja med letom.

Oblike spremenljivih aerodinamičnih profilov morajo biti optimizirane za minimalen upor in enak vzgon kot pri tradicionalnih krmilnih elementih pri različnih kotih krmilnih površin. Spremenljivi profili morajo zagotoviti primerljive rezultate kot tradicionalne vrtljive krmilne površine.

Za popis konfiguracije aerodinamičnega profila je bil izbran matematični postopek CST, ki ga je predlagala Brenda Kulfan; za pridobivanje polarnega razmerja različnih oblik aerodinamičnih profilov pri aerodinamični analizi je bila uporabljena programska oprema XFOIL za dvodimenzionalno analizo stacionarnega stanja; za optimizacijo oblike aerodinamičnega profila je bila uporabljena metoda genetskega algoritma; za združevanje postopka CST, programa XFOIL in genetskega algoritma pa je bil uporabljen program Isight. Pridobljen je bil nabor optimalnih oblik aerodinamičnega profila, ki zmanjšuje aerodinamični upor in zagotavlja enak vzgon kot različne tradicionalne krmilne površine.

Osnovna razmerja med optimiziranim spremenljivim aerodinamičnim profilom in tradicionalnimi krmilnimi elementi za nagib, vrtenje okrog vzdolžne osi in vrtenje okrog navpične osi so poenostavljena na potek koeficienta Cl. Podana je primerjava med koeficientom upora in koeficientom vzgona za vrtljive krmilne površine in optimalni spremenljivi profil pri vpadnih kotih 0°, 3° in 5°. Dokazano je, da lahko optimalna oblika aerodinamičnega profila zagotavlja manj upora kot tradicionalne krmilne površine. Optimalne oblike aerodinamičnega profila so uporabne za manevriranje leta in zmanjšanje upora, ter lahko nadomestijo vlogo tradicionalnih krmilnih površin pri različnih momentih nagiba, vrtenja okrog vzdolžne osi in vrtenja okrog navpične osi. Nato so predstavljene oblike spremenljivih aerodinamičnih profilov pri različnih Cl. Podana je primerjava konfiguracije tradicionalnih profilov in spremenljivih aerodinamičnih profilov pri različnih vrednostih Cl.

Teža konstrukcije za spreminjanje oblike profila in krmilnika konfiguracije presega težo tradicionalnih krmilnih elementov. Z razvojem inteligentnih materialov, mehanizmov in krmilne tehnologije pa bo problem povečanja teže pri spremenljivih profilih gotovo odpravljen.

Energija, ki je potrebna za spremembo oblike profila, ni bila upoštevana. Kombinirano spreminjanje oblike prereza in platforme krila bo bolj učinkovito kot samo spreminjanje oblike profila.

Prihodnje delo bo vključevalo podrobno snovanje mehanizmov za spreminjanje oblike, materialov; primerjavo zmogljivosti spremenljivega aerodinamičnega profila in tradicionalnih krmilnih površin pri upravljanju položaja; ter preizkus spremenljivega krila v vetrovniku pri različnih hitrostih leta in zahtevah krmiljenja položaja.© 2011 Stojniški vestnik. Vse pravice pridržane.Ključne besede: spremenljivo krilo, spreminjanje oblike, tradicionalne krmilne površine, aerodinamične lastnosti, optimalna zasnova, primerjava


*Naslov avtorja za dopisovanje: Državna univerza v Novem Pazarju, Vuka Karadžića bb, 36300 Novi Pazar, Srbija, [email protected] 10

Dinamični model za analizo napetostnega in deformacijskega stanja gonila z valjastimi zobniki

Nikolić, V. ‒ Dolićanin, Ć. ‒ Dimitrijević, DVera Nikolić1,* ‒ Ćemal Dolićanin1 ‒ Dejan Dimitrijević 2

1Državna univerza v Novem Pazarju, Srbija 2Simens, Nemčija

Praktična uporabnost zobniških gonil v sodobnih tehničnih sistemih je izjemna. Dinamične lastnosti zobniških gonil so zato večna tema znanstvenih raziskav. Med ubiranjem zob se pojavljajo notranje dinamične sile zaradi elastičnih deformacij zob in napak pri izdelavi (na primer zaradi toleranc oblike profila zob in razdelka na razdelnem krogu). Deformacije zob lahko povzročijo udarce zob med ubiranjem, intenzivnost udarcev med zobmi pa je odvisna od odstopanj velikosti razdelka. Večja kot je razlika med razdelki, bolj intenzivni so udarci med zobmi pri ubiranju. Na notranje dinamične sile med zobmi lahko vplivajo tudi vibracije zobnikov. Zobnike v ubiranju je mogoče modelirati kot nihajni sistem. Tak model je sestavljen iz koncentriranih mas (od katerih vsaka predstavlja en zobnik), povezanih z elastičnimi in dušilnimi elementi. Z uporabo osnovnih principov analitične mehanike ter začetnih in mejnih pogojev je mogoče sestaviti sistem enačb, ki predstavljajo fizikalni proces ubiranja med dvema ali več zobniki. Elastični element je za boljše rezultate mogoče modelirati kot nelinearno vzmet.

Naša raziskava je bila osredotočena na nov model dinamike zobniških gonil z diferencialnim računom racionalnega reda. Za ta model pridobimo analitične izraze za ustrezne zvrsti racionalnega reda kot enofrekvenčne lastne vibracijske zvrsti. Posplošitev tega modela na podoben model večstopenjskega zobniškega prenosa je zelo enostavna.

Model v tem članku predstavlja tipičen model gonila s tremi gredmi. Ubiranje se opazuje začenši s prvim parom in za vse zobniške pare sočasno, brez dodatnih predpostavk glede geometrije zobnikov ali mejnih in obremenitvenih pogojev ubiranja. Mejni pogoji na stiku zobnikov in gredi so enaki nič. Rezultat prvega koraka nelinearne kvazistatične analize so sile notranje dinamike, ki so nato uporabljene kot vhodni podatki za nadaljnje korake analize. Opisani postopek je možno prilagoditi za namene preračuna zobniških sistemov različnih vrst z enostavno združitvijo različnih korakov opisane analize ter različnih konfiguracij zobnikov in gredi. Prioriteta omenjenih korakov je seveda odvisna od namena konkretne analize.

Realen inženirski sistem se pri reševanju dinamičnih problemov nadomesti s poenostavljenim dinamičnim modelom. Model je sestavljen iz zvezno ali diskretno porazdeljenih mas, ki so povezane z elastičnimi in dušenimi povezavami. Sistem enačb, ki popisujejo dinamiko procesa, se postavi z uporabo osnovnih principov mehanike ter ob upoštevanju začetnih in robnih pogojev. Sistem enačb predstavlja matematični model dinamičnega obnašanja stroja ali sistema.

Cilj te študije je razvoj novega modela na osnovi napetostnih in deformacijskih invariant. Iz rezultatov je mogoče sklepati, da v območju stika nastopi sprememba smeri glavnih napetosti, zaradi kontaktnih napetosti pa se pojavljajo ekstremne spremembe vrednosti glavnih napetosti, oz. napetostnih invariant.

Članek je prispevek k razvoju metode končnih elementov. Pristop omogoča analizo obremenitev ter napetostnega in deformacijskega stanja v ubirajočem zobniku na povsem nov način, rezultati pa prinašajo vpogled v porazdelitev obremenitev, napetosti in deformacij na liniji stika pod vplivom vsakovrstnih spremenljivk in dinamičnih obremenitev, najsi gre za eksperimentalne podatke ali analitične izraze.

Za utemeljitev predpostavk in uporabe teh metod simulacije in izračunov je bila opravljena primerjava rezultatov z rezultati drugih avtorjev. Ugotovljeno je bilo, da so rezultati tega dela uporabni v znanosti in v praksi.©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: dinamična analiza, metoda končnih elementov, zobniški sistemi, analiza napetostnega in deformacijskega stanja zobniških prenosov, tenzorske invariante

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1 SI 11-12Navodila avtorjem

SI 11

Navodila avtorjem

NapovednikAvtorje vabimo, da svoje članke oddajo

z uporabo elektronskega sistema na naši spletni strani: http://ojs.sv-jme.eu. Avtorji lahko enostavno dostopajo do elektronskega sistema z registracijo na spletni strani. Avtorje prosimo, da na spletni strani naložijo članek in s sledenjem sistemu zagotovijo želene podatke, potrebne za indeksiranje in lažje iskanje po reviji. Avtorji lahko naložijo dopolnilne vsebine kot npr. spremno pismo, podatkovne baze, raziskovalne instrumente, programsko kodo in podobno.

Članki morajo biti napisani v angleškem jeziku. Strani morajo biti zaporedno označene. Prispevki so lahko dolgi največ 10 strani. Daljši članki so lahko v objavo sprejeti iz posebnih razlogov, katere morate navesti v spremnem dopisu. Kratki članki naj ne bodo daljši od štirih strani.

Navodila so v celoti na voljo v rubriki “Informacija za avtorje” na spletni strani revije: http://en.sv-jme.eu/. Prosimo vas, da članku priložite spremno pismo, ki naj vsebuje:1. naslov članka, seznam avtorjev ter podatke

avtorjev;2. opredelitev članka v eno izmed tipologij; izvirni

znanstveni (1.01), pregledni znanstveni (1.02) ali kratki znanstveni članek (1.03);

3. izjavo, da članek ni objavljen oziroma poslan v presojo za objavo drugam;

4. zaželeno je, da avtorji v spremnem pismu opredelijo ključni doprinos članka;

5. predlog dveh potencialnih recenzentov, ter kontaktne podatke recenzentov. Navedete lahko tudi razloge, zaradi katerih ne želite, da bi določen recenzent recenziral vaš članek.

OBLIKA ČLANKA

Članek naj bo napisan v naslednji obliki:- Naslov, ki primerno opisuje vsebino članka.- Povzetek, ki naj bo skrajšana oblika članka

in naj ne presega 250 besed. Povzetek mora vsebovati osnove, jedro in cilje raziskave, uporabljeno metodologijo dela, povzetek rezultatov in osnovne sklepe.

- Uvod, v katerem naj bo pregled novejšega stanja in zadostne informacije za razumevanje ter pregled rezultatov dela, predstavljenih v članku.

- Teorija.- Eksperimentalni del, ki naj vsebuje podatke o

postavitvi preskusa in metode, uporabljene pri pridobitvi rezultatov.

- Rezultati, ki naj bodo jasno prikazani, po potrebi v obliki slik in preglednic.

- Razprava, v kateri naj bodo prikazane povezave in posplošitve, uporabljene za pridobitev rezultatov. Prikazana naj bo tudi pomembnost rezultatov in primerjava s poprej objavljenimi deli. (Zaradi narave posameznih raziskav so lahko rezultati in razprava, za jasnost in preprostejše bralčevo razumevanje, združeni v eno poglavje.)

- Sklepi, v katerih naj bo prikazan en ali več sklepov, ki izhajajo iz rezultatov in razprave.

- Literatura, ki mora biti v besedilu oštevilčena zaporedno in označena z oglatimi oklepaji [1] ter na koncu članka zbrana v seznamu literature.

Enote - uporabljajte standardne SI simbole in okrajšave. Simboli za fizične veličine naj bodo v ležečem tisku (npr. v, T, n itd.). Simboli za enote, ki vsebujejo črke, naj bodo v navadnem tisku (npr. ms-1, K, min, mm itd.)

Okrajšave naj bodo, ko se prvič pojavijo v besedilu, izpisane v celoti, npr. časovno spremenljiva geometrija (ČSG).

Pomen simbolov in pripadajočih enot mora biti vedno razložen ali naveden v posebni tabeli na koncu članka pred referencami.

Slike morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot sl. 1, sl. 2 itn. Posnete naj bodo v ločljivosti, primerni za tisk, v kateremkoli od razširjenih formatov, npr. BMP, JPG, GIF. Diagrami in risbe morajo biti pripravljeni v vektorskem formatu, npr. CDR, AI.

Vse slike morajo biti pripravljene v črno-beli tehniki, brez obrob okoli slik in na beli podlagi. Ločeno pošljite vse slike v izvirni obliki Pri označevanju osi v diagramih, kadar je le mogoče, uporabite označbe veličin (npr. t, v, m itn.). V diagramih z več krivuljami, mora biti vsaka krivulja označena. Pomen oznake mora biti pojasnjen v podnapisu slike.

Tabele naj imajo svoj naslov in naj bodo zaporedno oštevilčene in tudi v besedilu poimenovane kot Tabela 1, Tabela 2 itd.. Poleg fizikalne veličine, npr t (v ležečem tisku), mora biti v

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1 SI 11-12

SI 12

oglatih oklepajih navedena tudi enota. V tabelah naj se ne podvajajo podatki, ki se nahajajo v besedilu.

Potrditev sodelovanja ali pomoči pri pripravi članka je lahko navedena pred referencami. Navedite vir finančne podpore za raziskavo.

REFERENCE

Seznam referenc MORA biti vključen v članek, oblikovan pa mora biti v skladu s sledečimi navodili. Navedene reference morajo biti citirane v besedilu. Vsaka navedena referenca je v besedilu oštevilčena s številko v oglatem oklepaju (npr. [3] ali [2] do [6] za več referenc). Sklicevanje na avtorja ni potrebno.

Reference morajo biti oštevilčene in razvrščene glede na to, kdaj se prvič pojavijo v članku in ne po abecednem vrstnem redu. Reference morajo biti popolne in točne. Vse neangleške oz. nenemške naslove je potrebno prevesti v angleški jezik z dodano opombo (in Slovene) na koncu Navajamo primere:Članki iz revij:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Ime revije, letnik, številka, strani, DOI oznaka.[1] Hackenschmidt, R., Alber-Laukant, B., Rieg,

F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent cross-linked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013.

Ime revije ne sme biti okrajšano. Ime revije je zapisano v ležečem tisku. Knjige:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Izdajatelj, kraj izdaje[2] Groover, M. P. (2007). Fundamentals of Modern

Manufacturing. John Wiley & Sons, Hoboken.Ime knjige je zapisano v ležečem tisku. Poglavja iz knjig:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov poglavja. Urednik(i) knjige, naslov knjige. Izdajatelj, kraj izdaje, strani. [3] Carbone, G., Ceccarelli, M. (2005). Legged

robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553-576.

Članki s konferenc:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Naziv konference, strani.[4] Štefanić, N., Martinčević-Mikić, S., Tošanović,

N. (2009). Applied Lean System in Process

Industry. MOTSP 2009 Conference Proceedings, p. 422-427.

Standardi:Standard (leto). Naslov. Ustanova. Kraj.[5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6:

Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva.

Spletne strani:Priimek, Začetnice imena podjetja. Naslov, z naslova http://naslov, datum dostopa.[6] Rockwell Automation. Arena, from http://www.

arenasimulation.com, accessed on 2009-09-27.

RAZŠIRJENI POVZETEK

Ko je članek sprejet v objavo, avtorji pošljejo razširjeni povzetek na eni strani A4 (približno 3.500 - 4.000 znakov). Navodila za pripravo razširjenega povzetka so objavljeni na spletni strani http://sl.sv-jme.eu/informacije-za-avtorje/.

AVTORSKE PRAVICE

Avtorji v uredništvo predložijo članek ob predpostavki, da članek prej ni bil nikjer objavljen, ni v postopku sprejema v objavo drugje in je bil prebran in potrjen s strani vseh avtorjev. Predložitev članka pomeni, da se avtorji avtomatično strinjajo s prenosom avtorskih pravic SV-JME, ko je članek sprejet v objavo. Vsem sprejetim člankom mora biti priloženo soglasje za prenos avtorskih pravic, katerega avtorji pošljejo uredniku. Članek mora biti izvirno delo avtorjev in brez pisnega dovoljenja izdajatelja ne sme biti v katerem koli jeziku objavljeno drugje.

Avtorju bo v potrditev poslana zadnja verzija članka. Morebitni popravki morajo biti minimalni in poslani v kratkem času. Zato je pomembno, da so članki že ob predložitvi napisani natančno.

Avtorji lahko stanje svojih sprejetih člankov spremljajo na http://en.sv-jme.eu/.

PLAČILO OBJAVE

Domači avtorji vseh sprejetih prispevkov morajo za objavo plačati prispevek, le v primeru, da članek presega dovoljenih 10 strani oziroma za objavo barvnih strani v članku, in sicer za vsako dodatno stran 20 EUR ter dodatni strošek za barvni tisk, ki znaša 90,00 EUR na stran.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1 SI 13-14Osebne objave

SI 13

Doktorske disertacije, magistrska dela, specialistična dela in diplome

DOKTORSKE DISERTACIJE

Na Fakulteti za strojništvo Univerze v Ljubljani sta z uspehom obranila svojo doktorsko disertacijo:

dne 19. decembra 2011 Zmago JEREB z naslovom: »Geometrijske transformacije video slik v realnem času« (mentor: prof. dr. Janez Diaci);

Predloženo delo obravnava raziskave in razvoj novih metod na področju korekcije geometrijsko popačenih prikazanih slik z uporabo postopkov digitalne transformacije. Obravnava metod za korekcijo slike je omejena na tri področja: korekcija projicirane video slike, korekcija slike opto-mehatronskega vsesmernega prikazovalnika in korekcija laserskih gravur, kjer so popačenja posledica graviranja na tridimenzionalno površino obdelovanca. V okviru razvoja novih metodologij smo razvili nove fizikalne modele korekcije slike, ki temeljijo na eksperimentalnem določanju popačitev z uporabo referenčne slike. Za preizkus delovanja metod smo razvili računalniške programe in eksperimentalna elektronska vezja, ki omogočajo delovanje korekcijskih metod v realnem času.;

dne 27. decembra 2011 Matej VOLK z naslovom: »Napovedovanje obremenitvenih stanj s končnimi mešanimi gostotami porazdelitve verjetnosti« (mentor: prof. dr. Matija Fajdiga, somentor: prof. dr. Marko Nagode);

Doba trajanja komponent je med drugim močno odvisna tudi od obremenitev pri obratovanju, kar pomeni, da je zelo pomembno že v zgodnjih fazah razvoja komponent čim bolje poznati obremenitvena stanja, katerim bo komponenta izpostavljena tekom obratovanja. V ta namen je potrebno neprestano razvijati nove ter izboljševati obstoječe metode napovedovanja obremenitvenih stanj. V doktorskem delu je predstavljena metodologija uporabe algoritma, ki je bil prvotno razvit za oceno končnih mešanih funkcij gostote porazdelitve verjetnosti, za modeliranje ter ekstrapolacijo obremenitvenih kolektivov. Za nadgradnjo uporabe obstoječega algoritma je v delu predstavljena tudi metodologija za uporabo algoritma na drugih področji napovedovanja obremenitvenih stanj. Razvit je model, s katerim smo uspešno ocenili poljubne funkcije tako z eno kot tudi z več neodvisnimi

spremenljivkami. Algoritem za oceno končnih mešanih funkcij gostote porazdelitve verjetnosti smo uspešno povezali z nevronsko mrežo z radialnimi baznimi funkcijami, kar omogoča nadaljnje širjenje uporabe algoritma na različna področja reševanja problemov.

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SPECIALISTIČNA DELA

Na Fakulteti za strojništvo Univerze v Mariboru sta z uspehom zagovarjala svoje specialistično delo:

dne 2. decembra 2011 Edvard FRANCE z naslovom: »Zasnova logističnega sistema« (mentor: prof. dr. Iztok Potrč);

dne 2. decembra 2011 Bogomir TREBIČNIK z naslovom: »Vodenje tračnih transporterjev po konkavnih krivinah« (mentor: prof. dr. Iztok Potrč).

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DIPLOMIRALI SO

Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva:

dne 23. decembra 2011:Blaž BAT z naslovom: »Zasnova in

vrednotenje vsegorskega kolesa« (mentor: prof. dr. Marko Nagode);

Marko FUJAN z naslovom: »Kakovost izdelave pri postopkih z dodajanjem plasti materiala« (mentor: prof. dr. Janez Kopač, somentor: izr. prof. dr. Slavko Dolinšek);

Jure ŠKRABAR z naslovom: »Uporaba strojnega vida za nadzor tiskarskega procesa« (mentor: prof. dr. Janez Diaci).

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Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva:

dne 22. decembra 2011:Robert BREŠKI z naslovom: »Hitra

izdelava prototipov velikih dimenzij« (mentor:

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)1 SI 13-14

SI 14

izr. prof. dr. Karl Gotlih, somentor: asist. Simon Brezovnik);

Tadej KLANČNIK z naslovom: »Robotizacija kovaške linije« (mentor: izr. prof. dr. Karl Gotlih, somentor: prof. dr. Riko Šafarič);

Aleš LOČNIKAR z naslovom: »Obvladovanje procesov kontrole valja tip 80235« (mentor: izr. prof. dr. Bojan Ačko, somentor: izr. prof. dr. Borut Buchmeister).

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Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva:

dne 9. decembra 2011:Blaž ČERNIGOJ z naslovom: »Analiza

izgub v ročnem petstopenjskem menjalniku« (mentor: prof. dr. Mitjan Kalin);

Matej KEDMENEC z naslovom: »Izbor ustreznega materiala P24 na osnovi pospešenega testiranja lezenja« (mentor: izr. prof. dr. Roman Šturm);

David PICELJ z naslovom: »Vpliv parametrov na produktivnost in ekonomičnost pri ekstruziji cevi« (prof. dr. Janez Kopač, somentor: doc. dr. Davorin Kramar);

dne 12. decembra 2011:Matej AHLIN z naslovom: »Razvoj

sistema za transport medicinskih vstavkov« (mentor: izr. prof. dr. Niko Herakovič);

Bojan CVELBAR z naslovom: »Optimizacija izrabe skladiščnega prostora« (mentor: izr. prof. dr. Niko Herakovič);

Matjaž JURJEVEC z naslovom: »Vpetje reflektorske luči SX-5 na helikopter AB-412« (mentor: izr. prof. dr. Tadej Kosel);

dne 21. decembra 2011:Luka KENK z naslovom: »Izdelava

brezpilotnega letala z dvojnimi povezanimi krili« (mentor: izr. prof. dr. Tadej Kosel);

Miha KERN z naslovom: »Opis metodologije konceptnega snovanja brezpilotnega helikopterja z izračunom osnovnih sposobnosti helikopterja in osnovne dimenzije rotorja« (mentor: pred. mag. Primož Škufca, somentor: izr. prof. dr. Tadej Kosel);

Aljoša RUPNIK z naslovom: »Določitev preoblikovalnih značilnosti prostega upogiba« (mentor: izr. prof. dr. Zlatko Kampuš);

dne 23. decembra 2011:Luka CARL z naslovom: »Načrtovanje

mikromešalnika z vidika mikroizdelovanih tehnologij« (mentor: doc. dr. Joško Valentinčič);

Matej KOZAN z naslovom: »Vpliv parametrov obdelave na cilindričnost bata« (mentor: prof. dr. Mirko Soković, somentor: doc. dr. Davorin Kramar).

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Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva (UN), univerzitetni študijski program I. stopnje:

dne 12. decembra 2011:Silvo PESEK z naslovom: »Analiza

primerjave krogelnih frezal za visoko hitrostno odrezavanje« (mentor: prof. dr. Franci Čuš).

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Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva:

dne 22. decembra 2011:Gregor ADAMIČ z naslovom:

»Dimenzioniranje podporne konstrukcije male vetrne elektrarne« (mentor: doc. dr. Janez Kramberger, somentor: prof. dr. Srečko Glodež);

Kristian BERNAD z naslovom: »Modifikacija pnevmatično krmiljenega manipulatorja« (mentor: doc. dr. Darko Lovrec, somentor: doc. dr. Samo Ulaga);

Borut BLATNIK z naslovom: »Prenova poslovnih procesov podjetja za rešitev iz gospodarske krize« (mentor: doc. dr. Marjan Leber, somentor: izr. prof. dr. Borut Buchmeister);

Milan DOLENC z naslovom: »Primerjava NC-programiranja s programoma Pro/Engineer in NCG CAM« (mentor: prof. dr. Miran Brezočnik, somentor: izr. prof. dr. Ivan Pahole);

Damjan ŠKRLEC z naslovom: »Uvajanje CNC tehnologije za področje odrezavanja v podjetju “Farmtech”« (mentor: izr. prof. dr. Ivan Pahole, somentor: doc. dr. Mirko Ficko).

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME)

© 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Editor in ChiefVincenc ButalaUniversity of Ljubljana Faculty of Mechanical Engineering, Slovenia

Co-EditorBorut BuchmeisterUniversity of MariborFaculty of Mechanical Engineering, Slovenia

Technical EditorPika ŠkrabaUniversity of Ljubljana Faculty of Mechanical Engineering, Slovenia

Editorial OfficeUniversity of Ljubljana (UL)Faculty of Mechanical EngineeringSV-JMEAškerčeva 6, SI-1000 Ljubljana, SloveniaPhone: 386-(0)1-4771 137Fax: 386-(0)1-2518 567E-mail: [email protected]://www.sv-jme.eu

Founders and PublishersUniversity of Ljubljana (UL)Faculty of Mechanical Engineering, Slovenia

University of Maribor (UM)Faculty of Mechanical Engineering, Slovenia

Association of Mechanical Engineers of Slovenia

Chamber of Commerce and Industry of SloveniaMetal Processing Industry Association

International Editorial BoardKoshi Adachi, Graduate School of Engineering,Tohoku University, JapanBikramjit Basu, Indian Institute of Technology, Kanpur, IndiaAnton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, SloveniaNarendra B. Dahotre, University of Tennessee, Knoxville, USAMatija Fajdiga, UL, Faculty of Mech. Engineering, SloveniaImre Felde, Bay Zoltan Inst. for Mater. Sci. and Techn., HungaryJože Flašker, UM, Faculty of Mech. Engineering, SloveniaBernard Franković, Faculty of Engineering Rijeka, CroatiaJanez Grum, UL, Faculty of Mech. Engineering, SloveniaImre Horvath, Delft University of Technology, NetherlandsJulius Kaplunov, Brunel University, West London, UKMilan Kljajin, J.J. Strossmayer University of Osijek, CroatiaJanez Kopač, UL, Faculty of Mech. Engineering, SloveniaFranc Kosel, UL, Faculty of Mech. Engineering, SloveniaThomas Lübben, University of Bremen, GermanyJanez Možina, UL, Faculty of Mech. Engineering, SloveniaMiroslav Plančak, University of Novi Sad, SerbiaBrian Prasad, California Institute of Technology, Pasadena, USABernd Sauer, University of Kaiserlautern, GermanyBrane Širok, UL, Faculty of Mech. Engineering, SloveniaLeopold Škerget, UM, Faculty of Mech. Engineering, SloveniaGeorge E. Totten, Portland State University, USANikos C. Tsourveloudis, Technical University of Crete, GreeceToma Udiljak, University of Zagreb, CroatiaArkady Voloshin, Lehigh University, Bethlehem, USA

President of Publishing CouncilJože DuhovnikUL, Faculty of Mechanical Engineering, Slovenia

PrintTiskarna Present d.o.o., Ljubljana, Slovenia, printed in 480 copies

General informationStrojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor. Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/.

You can advertise on the inner and outer side of the back cover of the magazine. The authors of the published papers are invited to send photos or pictures with short explanation for cover content.We would like to thank the reviewers who have taken part in the peer-review process.

Cover: Above: Shematics of the first magnetic refrigerator prototype developed at the University of Ljubljana, Faculty of Mechanical Engineering, SloveniaBelow: Numerical simulation results of the magnetic field in the NdFeB magnet assembly

Image courtesy: Laboratory of Refrigeration and District Energy, University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

ISSN 0039-2480

Aim and ScopeThe international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

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