CFD Simulation of MQL with low temperature and high ...1290431/FULLTEXT01.pdf · CFD Simulation of...

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IN DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS , STOCKHOLM SWEDEN 2018 CFD Simulation of MQL with low temperature and high-pressure coolant VENKATA RAGHURAMA SWAROOP NADELLA KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

Transcript of CFD Simulation of MQL with low temperature and high ...1290431/FULLTEXT01.pdf · CFD Simulation of...

  • IN DEGREE PROJECT MECHANICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

    , STOCKHOLM SWEDEN 2018

    CFD Simulation of MQL with low temperature and high-pressure coolant

    VENKATA RAGHURAMA SWAROOP NADELLA

    KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

  • I

    KTH Royal Institute of Technology

    Production Engineering and Management / ITM Department

    CFD Simulation of MQL with low temperature and high-pressure coolant

    Master thesis

    Written by

    Venkata Raghurama Swaroop Nadella

    Submitted in fulfillment of the requirements for the degree of

    Master of Science

    Carried out at KTH Royal Institute of Technology, Sweden

    Supervised by

    Amir Rashid, KTH Royal Institute of Technology

  • II

    Foreword

    This thesis is written as fulfilment to the master’s degree. The master’s programme focuses on

    Production Engineering and Management. The subject of this thesis, CFD simulation of MQL

    with low temperature and high-pressure coolant for machining operation falls within the scope

    of master’s field as it is explained in detail in the coming sections. Since March this year I have

    been conducting research and simulations on the stated topic. I have experienced this period as

    very challenging and instructive. At the beginning I had limited knowledge on Computational

    Fluid Dynamics (CFD) and ANSYS software but as I progressed I could be able to deal with

    different types of technical problems involved in this thesis. However, I have been able to

    achieve the simulation results for which I have been working on. First, I am grateful to my

    family members who supported me throughout my master’s programme and I am nothing

    without them. I would like to thank my supervisor at KTH Royal Institute of Technology, Mr.

    Amir Rashid for his valuable insights and directions and gave me needful guidance to complete

    research and simulations. He continuously supported me whenever I needed technical support

    and clarifications. Also, I want to thank Mr. Salman Pervaiz, former Ph.D. student at KTH Royal

    Institute of Technology, for providing suggestions and input during our teleconference to the

    simulations I needed to perform in ANSYS as his work is the main basis for this thesis.

  • III

    Abstract:

    Employing huge amount of cutting fluids in machining process has potential negative impacts

    not only to the operator but also to the environment along with increased cost of

    manufacturing process. To reduce the cutting fluid consumption during machining, a technique

    called Minimum Quantity Lubrication (MQL) is introduced which uses very less amount of

    cutting fluid yet being effective than flood cooling. This thesis focuses on determining the

    convection over a cutting insert with a constant heat source inside a square enclosure and the

    computational domain of the CFD model presented consists of fluid and solid domains with

    fluid-solid interaction. The feasibility of MQL using low temperature and high-pressure coolant

    and observing how temperature is dropping after the application of coolant/coolants by

    simulating the conditions in ANSYS fluent workbench. The effectiveness of this technique is

    determined in terms of whether high pressure and low temperature coolant can dissipate heat

    and remove chips from the cutting interface. Finally drawing conclusion based on results.

    Keywords: Temperature, Pressure, Fluid flow, Heat transfer, Cutting fluid, Coolants, Velocity,

    Simulation.

    Sammanfattning:

    Att använda stora mängder skärvätskor vid en bearbetningsprocess har potentiellt negativ

    inverkan inte bara för operatören men också på miljön. Utöver detta tillkommer ökade

    kostnader för tillverkningsprocessen. För att minska skärvätskekonsumtionen under

    maskinbearbetning införs en teknik som kallas minimalsmörjning(MQL=Minimum Quantity

    Lubrication) som använder mycket mindre mängd skärvätska men ändå är effektivare än

    standard kylspolning med skärvätska.

    Denna avhandling fokuserar på att bestämma konvektionen över ett skär med en konstant

    värmekälla placerad inuti ett kvadratiskt hölje och beräkningsdomänen för den CFD-modell som

    presenteras, vilken består av flytande och fasta domäner och interaktion mellan dessa.

    Möjligheten att använda MQL då lågtemperatur- och högtryckskylmedel appliceras undersöks

    och hur temperaturen sjunker efter applicering av kylmedel/kylvätskor observeras genom att

    simulera förhållandena i ANSYS flytande arbetsbänk. Denna tekniks effektivitet bestäms med

    avseende på huruvida högtrycks- och lågtemperaturkylvätska kan avleda värme och

    transportera bort spånor från ingreppszonen. Slutligen sammanställs resultaten och därpå

    dragna slutsatserna.

    Nyckelord: Temperatur, Tryck, Vätskeflöde, Värmeöverföring, Skärvätska, Kylmedel, Hastighet,

    Simulering.

  • IV

    Table of Contents

    List of Acronyms and Abbreviations V

    List of Figures VI

    List of Tables IX

    1. Introduction and background 1

    2. Cutting fluids 2

    3. Literature review 2

    3.1. Research questions 3

    3.2. Hypothesis 3

    4. Procedure followed in designing and simulation 4

    4.1. Design phase 4

    4.2. Design modeler in Fluent 5

    4.3. Meshing 5

    4.4. Mesh Independency 7

    4.5. Fluent 7

    4.5.1. Model 7

    4.5.2. Materials 10

    4.5.3. Cell Zone conditions 10

    4.5.4. Boundary conditions 10

    4.5.5. Methods 11

    4.5.6. Monitors 11

    4.5.7. Initialization 12

    4.5.8. Running calculation 13

    5. Results 14

    5.1 For Single-phase simulation 14

    5.2 For Multi-phase with 80% veg oil and 20% air 27

    5.3 For Multi-phase with 4% veg oil and 96% air 40

    6. Discussion 53

    7. Conclusion 53

    References 55

  • V

    List of Acronyms and Abbreviations

    ANSYS Analysis Software

    BUE Built-up-edge

    CFD Computational fluid dynamics

    CHT Conjugate heat transfer

    DM Design Modeler

    EP Extreme Pressure

    MQL Minimum Quantity Lubrication

    PD Partial Differentiation

    STEP Standard for the Exchange of Product model data

    VOF Volume of Fluid

  • VI

    List of Figures

    Figure 1: Showing different views of a tool……………………………………………………………………5

    Figure 2: Isometric view of solid and fluid domain………………………………………………………..6

    Figure 3: Meshing of the geometry in ANSYS fluent………………………………………………………7

    Figure 4: Model of the geometry in ANSYS fluent setup…………………………………………..…..9

    Figure 5: Multiphase model with two fluids………………………………………………………………….9

    Figure 6: Cell zone condition of tool tip, given a constant heat source of 1090 K…………11

    Figure 7: Illustration of computational domain [5] ……………………………………………………...12

    Figure 8: Residual monitors and convergence criteria………………………………………………….13

    Figure 9: Initialization conditions and patching of fluid volume with phase-2 fluid………14

    Figure 10: Graphical representation of different residuals…………………………………………..14

    Note: Temperature contours, velocity streamlines and graphs for different combinations starts from here and names of these figures are given in short form for convenience purpose.

    Figure 11: For Velocity of 0.1 m/s and 25 degree air coolant…………………………..……………16

    Figure 12: For Velocity of 0.1 m/s and zero degree air coolant……………………..………………17

    Figure 13: For Velocity of 0.1 m/s and -10 degree air coolant…………………………….…………18

    Figure 14: For Velocity of 0.1 m/s and -20 degree air coolant……………………………….………19

    Figure 15: For Velocity of 1 m/s and 25 degree air coolant……………………..……………………20

    Figure 16: For Velocity of 1 m/s and zero degree air coolant………………………………………..21

    Figure 17: For Velocity of 1 m/s and -10 degree air coolant………………………………………….22

  • VII

    Figure 18: For Velocity of 1 m/s and -20 degree air coolant……………………………………….23

    Figure 19: For Velocity of 10 m/s and 25 degree air coolant………………………………………24

    Figure 20: For Velocity of 10 m/s and zero degree air coolant………..….………………………25

    Figure 21: For Velocity of 10 m/s and -10 degree air coolant……………………………………..26

    Figure 22: For Velocity of 10 m/s and -20 degree air coolant……………………………………..27

    Figure 23: For Velocity of 0.1 m/s and 25 degree multiphase with 80% vegetable oil

    and 20% air as coolants……………………………………………………………………………..29

    Figure 24: For Velocity of 0.1 m/s and zero degree multiphase with 80% vegetable oil

    and 20% air as coolants……………..………………………………………………………………30

    Figure 25: For Velocity of 0.1 m/s and -10 degree multiphase with 80% vegetable oil

    and 20% air as coolants……………………………………………………………………………..31

    Figure 26: For Velocity of 0.1 m/s and -20 degree multiphase with 80% vegetable oil

    and 20% air as coolants……………………………………………………………………………..32

    Figure 27: For Velocity of 1 m/s and 25 degree multiphase with 80% vegetable oil

    and 20% air as coolants……………………………………………………………………………..33

    Figure 28: For Velocity of 1 m/s and zero degree multiphase with 80% vegetable oil

    and 20% air as coolants……………………………………………………………………………..34

    Figure 29: For Velocity of 1 m/s and -10 degree multiphase with 80% vegetable oil

    and 20% air as coolants……………………………………………………………………………..35

    Figure 30: For Velocity of 1 m/s and -20 degree multiphase with 80% vegetable oil

    and 20% air as coolants………………………………………………………………………………36

    Figure 31: For Velocity of 10 m/s and 25 degree multiphase with 80% vegetable oil

    and 20% air as coolants………………………………………………………………………………37

    Figure 32: For Velocity of 10 m/s and zero degree multiphase with 80% vegetable oil

    and 20% air as coolants………………………………………………………………………………38

    Figure 33: For Velocity of 10 m/s and -10 degree multiphase with 80% vegetable oil

    and 20% air as coolants………………………………………………………………………………39

    Figure 34: For Velocity of 10 m/s and -20 degree multiphase with 80% vegetable oil

    and 20% air as coolants………………………………………………………………………………40

    Figure 35: For Velocity of 1 m/s and 25 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………42

    Figure 36: For Velocity of 1 m/s and 10 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………43

    Figure 37: For Velocity of 1 m/s and zero degree multiphase with 4% vegetable oil

  • VIII

    and 96% air as coolants………………………………………………………………………………44

    Figure 38: For Velocity of 1 m/s and -10 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………45

    Figure 39: For Velocity of 5 m/s and 25 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………46

    Figure 40: For Velocity of 5 m/s and 10 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………47

    Figure 41: For Velocity of 5 m/s and zero degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………48

    Figure 42: For Velocity of 5 m/s and -10 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………49

    Figure 43: For Velocity of 10 m/s and 25 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………50

    Figure 44: For Velocity of 10 m/s and 10 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………51

    Figure 45: For Velocity of 10 m/s and zero degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………52

    Figure 46: For Velocity of 10 m/s and -10 degree multiphase with 4% vegetable oil

    and 96% air as coolants………………………………………………………………………………53

  • IX

    List of Tables

    Table 1: Values of insert temperature for different combinations of coolant temp’s

    and coolant inlet velocities in single-phase air coolant…………………………………15

    Table 2: Values of insert temperature for different combinations of coolant temp’s

    and coolant inlet velocities in multi-phase with 80% veg oil and 20% air.……28

    Table 3: Values of insert temperature for different combinations of coolant temp’s

    and coolant inlet velocities in multi-phase with 4% veg oil and 96% air…...…41

  • 1

    1 Introduction and background:

    Sustainable manufacturing is basically making products using processes that are economic and

    environmentally friendly. It has so many parts and sustainable machining is one of them. As

    part of it, industries have been strenuously trying to minimize the use of lubricants. The main

    problem in sustainable machining is the usage of mineral based cutting fluid near the metal

    cutting zone. Some fluids like the mix of oil and water (called emulsion) creates more

    environmental issues due to the formation of microbes. This microbial growth should further be

    controlled by adding additives which makes the entire process expensive. To overcome these

    problems, a new technique of using the cutting fluid has been introduced and it is called as

    Minimum Quantity Lubrication (MQL) or otherwise called as near dry machining. [1]

    In any machining operation, the two main aspects to be considered are proper lubrication of

    workpiece and tool, heat removal near the cutting zone. Though flood cooling is very efficient

    at lower cutting speeds, it is not good for higher cutting speeds since the cutting fluid cannot

    pass through the tool and workpiece interface. Also, the intense heat that is generated

    vaporizes the coolant sprayed before it can reach the cutting zone. This intensifies the pressure

    on the tool tip and deteriorates the quality and reduction in life of the tool. At this point, the

    technique of MQL can be deployed and be a better substitute. [2]

    The goal is to produce parts at low cost yet maintaining high quality of finished parts. Quality

    and productivity both depend on minimum part rejections and reduced downtime in

    machining, there are several parameters involved and their relationship with each other also

    affects the performance of machine. Machining of hard materials produce even lot of heat

    compared to softer materials, but the heat removal should be done only by the cutting fluid

    used. [2]

    MQL concept was implemented by many researchers and claimed to have shown noticeable

    improvement when compared with dry machining but more important information would have

    been obtained had they compared flood cooling technique and MQL. High pressure coolant

    usage during machining is found to improve the tool life significantly [3].

  • 2

    2 Cutting fluids:

    Cutting fluids occupy a vital role in the machining of metals. These are employed to absorb the

    heat produced near the tool-workpiece interface (cutting zone) and to wash out the chips that

    are formed on the rake face. Continuous removal of chips from the rake face also avoids the

    formation of built-up-edge (BUE) that restricts the tool to move forward. [2]

    Cutting fluids are generally classified as cutting oils, soluble oils, synthetic fluids and semi-

    synthetic fluids. Cutting oils are generally extracted from vegetable or animal or petroleum

    products. Soluble oils are referred as emulsions because water droplets are mixed along with

    emulsifiers. Water increases the stability of emulsion. Emulsifiers disperse oil in water giving a

    stable oil in water emulsion. Sometimes water in these oils cause rust, bacteria. [2] This is very

    dangerous to operator’s health. As water also evaporates quickly than oil, it may not be

    economical. At high-pressure and high temperature, EP additives made of phosphorous,

    Sulphur, chlorine can be employed to enhance lubrication during machining. EP additives

    lowers friction and wear due to their low shear strength and anti-weld properties. There is also

    a risk of fire catching during machining process when there is more proportion of oil. So, water

    content can be slightly increased. But then as water content increases, chance of rusting and

    bacterial growth increases. Chemical sprays that inhibit the growth of bacteria can be employed

    but chemicals usage is dangerous to operator’s health and environment. [2]

    Synthetic fluids are good in cooling, but lubricating properties are inferior compared to other

    fluids. When discussing vegetable oils, they have high flash point and fire points and chance of

    evaporation and losses are very minimal during misting. [2]

  • 3

    3 Literature review:

    There are only a few papers published by researchers on MQL using coolants at normal

    temperatures and pressures. Till date, no a research paper or work is available on MQL with

    low temperatures or high pressures.

    Minimum Quantity Lubrication (MQL) using coolants at normal temperature and pressures

    were carried out by some researchers and found it to be better than the conventional flood

    cooling. From the work of Toshiyuki Obikawa and Masashi Yamaguchi [4], the result shows that

    with MQL using coolant at normal temperature and pressure but with different velocities, there

    is some impact on the machining process. When coolant velocity is twice the cutting velocity,

    the coolant can reach the clearance between tool and workpiece. Suggestions were made on

    usage of high-pressure coolant which is said to change the chip formation and penetrate to the

    cutting interface.

    From [5], similar work was done to simulate the heat generation during cutting operation near

    the tool tip. Simulation done in DEFORM-3D software shows that 817°C of temperature is

    observed during cutting operation. Later, simulations conducted in ANSYS CFX to analyze the

    fluid flow and heat transfer using Air as a coolant at normal temperatures and pressures but

    with different velocities of coolant (0.1 m/s, 1 m/s, 10 m/s) showed remarkable results. Higher

    the velocity higher the heat absorption near the tool tip. Temperature reduction using coolant

    with velocity of 10 m/s is almost double that of the coolant with velocity of 0.1 m/s. Authors

    suggested this work could be extended to check different types of cutting fluids.

    From reference [1], experimental investigation on MQL using uncoated carbide tool was done

    in comparison with dry machining and found that the cutting temperatures were reduced 10%

    to 30% in MQL compared to dry condition. Also concluded that MQL machining was found to be

    superior than dry condition.

    From reference [6], MQL using Air at high pressures of the order 7 bar was done and found the

    cutting performance of MQL machining is better than conventional machining with flood

    cooling is noted which reduced cutting temperatures and enhanced chip-tool interaction. MQL

    also provided better surface finish to the parts and improved tool life by reducing the damage

    near tooltip. Improved tool life also gives a chance to machine work piece at a higher speeds

    and higher feed rates.

  • 4

    3.1 Research questions

    1. How does the MQL with low temperature and high-pressure coolant effect the

    machining process?

    2. Would MQL be able to mitigate the temperature effect on the cutting insert?

    3. Would the life of cutting insert increase as a result of decrease in overall temperature

    during machining?

    3.2 Hypothesis

    Some researchers have done simulations on Finite Element Analysis of cutting process and

    experimental work on cryogenic machining using gases and MQL at the same time. There is

    only one research paper “A novel numerical modelling approach to determine the temperature

    distribution in the cutting tool using conjugate heat transfer (CHT) analysis” talking about

    temperature distribution in the cutting insert during machining and how different velocities of

    coolant minimize the process temperature. So, it is taken as the main basis. From [5] cutting

    temperature and other information is extracted and used as input in this thesis. According to

    [5] that contains information about simulations carried out in ANSYS CFX workbench using air

    as coolant at ambient temperature (25°C) and with different velocities 0.1 m/s, 1 m/s, 10 m/s.

    The simulation results were later validated through experimentation and are quite promising.

    As an extension, this thesis focused on using vegetable oil as lubricant along with air as coolant

    at different temperatures (ambient, zero and 10 below zero) and high-pressure values.

  • 5

    4 Procedure for designing and simulation:

    Tool geometry, analysis, meshing and simulations are carried out here.

    4.1 Design Phase

    Single point cutting tool is designed in Solid Edge. A small surface is created near the edge of

    the tool that represents the cutting edge. After properly constraining the dimensions, it is then

    extruded and drafted the sides with required measurement. The tool is then imported to ANSYS

    Fluent workbench in STEP format.

    (a)

    (b) (c) (d)

    Fig. 1 showing different views of the tool. a. Isometric view b. Top view, c. Side view, d. Front view

    4.2. Design Modeler in Fluent

    After importing the tool in STEP format into the fluent workbench, a box needs to be created to

    specify the fluid zone, tool, coolant inlet and outlet. This is all done in the design modeler

    (DM)designing tool in Fluent. To specify the fluid zone, Boolean operation should be performed

    by subtracting the tool from the box volume thereby the remaining zone becomes fluid zone.

    Coolant inlet and outlet are specified by selecting the top and bottom surfaces of the box.

  • 6

    Solid-fluid interaction is designed to observe the interaction between tool and the coolant

    passing through the tool and to know how temperature changes are occurring in the tool.

    Fig. 2 Isometric view of solid and fluid domain

    4.3 Meshing

    Meshing is one of the important aspects when doing CFD analysis of any application. After

    required geometry is designed and modified, meshing of geometry is performed. Meshing is

    basically joining the elements of a tool for analyzing fluid flow and heat transfer. Meshing

    means creating mesh with grid points called nodes. The partial differential (PD) equations that

    direct the fluid flow and heat transfer are not normally responsive to analytical solutions except

    for simple cases. So, to analyze fluid flows, flow domains are divided into smaller subdomains.

    These domains are normally made up of geometric shapes like hexahedral and tetrahedral for

    3D simulations and quadrilaterals and triangles for 2D applications [7]. The governing equations

    are represented and solved inside each of these subdomains. Typically, there are three

    methods used to solve the nearest version of this system of equations: finite volumes, finite

    elements, or finite differences. Utmost care must be taken to ensure proper continuity of

    solution across the common interfaces between two subdomains, so that the approximate

    solutions inside various portions are put together to give a complete picture of fluid flow in the

    required domain. The subdomains are often called elements or cells, and the collection of all

    elements or cells is called a mesh or grid.

    For the above-mentioned geometry, tetrahedron meshing is used as it is a simple geometry.

    Normal meshing is done for the geometry with a default growth rate of 1.2. Growth Rate

    represents the increase in element edge length with each succeeding layer of elements. Here

  • 7

    1.2 growth rate represents 20% increase in element edge length with every next layer of

    element.

    Maximum Tet size - 4 mm

    Final mesh is created with a total number of 327598 elements and 78407 nodes.

    After meshing of geometry is done, fluent window is loaded to start simulation. Here all the

    parameters like materials to be used (fluids and solids), cell zone conditions, boundary

    conditions, initializing the solution, patching the fluid volume with air (filling the fluid volume

    with air to ensure no vegetable oil is present in the fluid volume before simulation), methods to

    be used for solving the model and running the solution. In practical condition, as the machine

    ambience is all air, patching contributes to more accurate results.

    Fig. 3 Meshing of the geometry in ANSYS fluent

    4.4 Mesh Independency

    Mesh Independency is another important aspect to be checked. Basically, this is performed to

    save the computational time.

  • 8

    Run the simulation once with preliminary mesh by setting convergence order to 10^-6 to see if

    all the residuals are converging. If they are not converging, refine the mesh and repeat the

    process.

    Once the convergence criteria are met, refine the mesh globally to have finer cells in the entire

    domain. Run the simulation again to see if the residuals are dropping below 10^-6. Comparing

    the values from initial and second simulations will give difference of these values. If the

    tolerance is acceptable, then the initial mesh was correct enough to extract the result.

    If the tolerance values in the second simulation are not within acceptable range, then results

    are changing with change in meshing. This means mesh independent solution is not achieved.

    Mesh should be refined, and process should be repeated until solution is independent of the

    mesh. Finally, the mesh with smallest size that gives mesh independent solution should be used

    to computational time.

    4.5 Fluent

    4.5.1 Model

    These simulations involve single-phase and multi-phase. Therefore, normal simulations were

    conducted, and Multi-phase is selected to facilitate two fluids flow. “Volume of fluid” type in

    multi-phase is chosen because volume fraction of each fluid can be mentioned unlike in other

    types. Energy equations need to be activated to input temperature. SST k-ω model is used for

    this multiphase coolant flow. It is a variant of standard k-ω model. This combines the original

    Wilcox k-ω model for use near walls and the standard k–ε model away from walls using a

    blending function, and the eddy viscosity formulation is modified to account for the transport

    effects of the principle turbulent shear stress. SST is recommended for high accuracy boundary

    layer simulations.

  • 9

    Fig. 4 Model of geometry in ANSYS fluent setup

    Fig. 5 Multiphase model with two fluids

  • 10

    Equations employed by the SST k- ω model:

    Kinematic Eddy Viscosity

    𝑣𝑇 =𝑎1𝑘

    max(𝑎1𝜔, 𝑆𝐹2)

    Turbulence Kinetic Energy

    𝜕𝑘

    𝜕𝑡+ 𝑈𝑗

    𝜕𝑘

    𝜕𝑥𝑗= 𝑃𝑘 − 𝛽 ∗ 𝑘𝜔 +

    𝜕

    𝜕𝑥𝑗[(𝑣 + 𝜎𝑘𝑣𝑇)

    𝜕𝑘

    𝜕𝑥𝑗]

    Specific Dissipation Rate

    𝜕𝜔

    𝜕𝑡+ 𝑈𝑗

    𝜕𝜔

    𝜕𝑥𝑗= 𝛼𝑆2 − 𝛽𝜔2 +

    𝜕

    𝜕𝑥𝑗[(𝑣 + 𝜎𝜔𝑣𝑇)

    𝜕𝜔

    𝜕𝑥𝑗] + 2(1 − 𝐹1)𝜎𝜔2

    1

    𝜔

    𝜕𝑘

    𝜕𝑥𝑖

    𝜕𝜔

    𝜕𝑥𝑖

    Closure Coefficients and Auxiliary Relations

    𝐹2 = 𝑡𝑎𝑛ℎ [[max (2√𝑘

    𝛽 ∗ 𝜔𝑦,500𝑣

    𝑦2𝜔)]

    2

    ]

    𝑃𝑘 = 𝑚𝑖𝑛 (𝜏𝑖𝑗𝜕𝑈𝑖𝜕𝑥𝑗

    , 10𝛽 ∗ 𝑘𝜔)

    𝐹1 = 𝑡𝑎𝑛ℎ {{𝑚𝑖𝑛 [max(√𝑘

    𝛽 ∗ 𝜔𝑦,500𝑣

    𝑦2𝜔) ,

    4𝜎𝜔2𝑘

    𝐶𝐷𝑘𝜔𝑦2]}

    4

    }

    𝐶𝐷𝑘𝜔 = 𝑚𝑎𝑥 (2𝜌𝜎𝜔21

    𝜔

    𝜕𝑘

    𝜕𝑥𝑖

    𝜕𝜔

    𝜕𝑥𝑖, 10−10)

    𝜑 = 𝜑1𝐹1 + 𝜑2(1 − 𝐹1)

    𝛼1 =5

    9, 𝛼2 = 0.44

    𝛽1 =3

    40, 𝛽2 = 0.0828

    𝛽∗ =9

    100

    𝛼𝑘1 = 0.85, 𝛼𝑘2 = 1

    𝛼𝜔1 = 0.5, 𝛼𝜔2 = 0.856

  • 11

    4.5.2 Materials

    Necessary fluid and solid materials are defined at this point for use in the next steps. In this

    simulation, only air and vegetable oil are used as coolant and lubricant respectively. Uncoated

    carbide is used as tool material and the properties are extracted from [5]. If only one solid

    material is defined, then there is no need to check which material is assigned to the tool as the

    system allots that material by default. Physical and chemical properties of vegetable oil are

    taken from [6].

    4.5.3 Cell Zone conditions

    Cell zone conditions relates to the middle of the grid cells. This involves typically saying which

    material is in that cell. Other values like porous resistance and heat sources at locations needed

    in the geometry can also be given in this section. As the heat source is taken from [5],

    temperature of 1090 K is given as constant heat source.

    Fig. 6 Cell zone condition of tool tip, given a constant heat source of 1090 K

    4.5.4 Boundary conditions

    These are the conditions where fluid enters and leaves the domain, input velocity, pressure or

    temperature. Other boundaries are also needed like declaring wall type, inlet and outlet types,

    symmetry conditions.

    Boundary conditions also depend on type of the physical model employed.

    Different boundary conditions taken are as followed:

    1. Inlet type - Velocity inlet

    2. Outlet type - Pressure outlet

    3. Other four walls - Symmetry type

  • 12

    Fig. 7 Illustration of computational domain [5]

    4.5.5 Methods

    As soon as multiphase model is selected in combination with “volume of fluid” type, steady

    state simulation is changed to pseudo-transient. This combination is automatically detected by

    the system. It takes long time to simulate the multiphase model with “volume of fluid” type.

    Therefore, system selects pseudo-transient instead of steady state. Pseudo transient is an

    accelerated solver for getting steady state solution.

    4.5.6 Monitors

    In monitors, convergence criteria can be defined for energy, velocity, thermal conductivity,

    volume of fluid (VOF), omega and continuity. The less the convergence criteria, the more

    accurate the solution is. This is because to reach the minimum convergence criteria, system

    executes a greater number of iterations.

  • 13

    Fig: 8 Residual monitors and convergence criteria

    4.5.7 Initialization

    Before starting any CFD simulation, FLUENT must be provided with an initial "guess'' for the

    solution flow field. In many cases, extra care is needed to provide an initial solution that will

    allow the desired final solution to be attained.

    There are two types of initialization. One is hybrid and other is standard initialization. Hybrid

    initialization uses the programmed environment. It solves the Laplace’s equations to determine

    pressure, velocity parameters. All others are taken as per the standard program.

    Whereas in standard initialization, user should input all the values to define appropriate

    environment. These are called initial conditions.

    In this simulation, standard initialization is used as all the initial parameters are already known.

    After initialization, patching must be done for the fluid volume to ensure that the initial fluid in

    the fluid volume is only air.

  • 14

    Fig: 9 Initialization conditions and patching of fluid volume with phase-2 fluid

    4.5.8 Running Calculation

    Running the calculation until solution is converged gives optimal solution. Means the

    temperature distribution along the cutting insert and heat dissipation after introduction of

    coolant are accurately modelled in ANSYS system.

    Fig. 10 Graphical representation of different residuals

  • 15

    5. Results:

    5.1 Single-phase simulation: Initially basic simulations were conducted on the specimen with

    conditions of ambient temperature coolant and normal velocity and the results observed were

    satisfactory. In fact, simulations and experiments on these conditions were already performed

    by [5] and mentioned in their research paper. For verification purpose, the same results were

    replicated to ensure same procedure is followed. Same results are observed that are in the

    paper. Then further modifications were made in single-phase coolant simulations by varying the

    coolant temperature from ambient to zero degree, 10 below zero and 20 below zero. The

    results observed for single-phase simulation and using air as coolant are as follows.

    Table 1: Values of insert temperature for different combinations of coolant temperatures

    and coolant inlet velocities in single-phase.

    Fluid (volume fraction)

    Fluid Temperature

    (°C) Fluid Velocities (m/s)

    Corresponding Resultant temperatures (°C) Single-Phase

    Vegetable Oil

    Air

    0 1 25 0.1 1 10 467 278 102

    0 1 0 0.1 1 10 455 252 72

    0 1 -10 0.1 1 10 447 248 67

    0 1 -20 0.1 1 10 442 242 49

    Simulations for several combination of temperatures and velocities are carried out to check

    which combination of temperature and velocity yields better results i.e. lowering the insert

    temperature. From the table 1 above, it is evident that the combination of coolant temperature

    at -20°C and coolant inlet velocity 10 m/s is giving desired result i.e. lowering/maintaining the

    insert temperature below 50°c.

    If the plots are observed, there is a significant decrease in the tool temperature for change in

    the velocity, for coolant temperature being constant.

    Temperature contours, velocity streamlines and graphs can be visualized in the next pages.

  • 16

    (a)

    (b)

    (c)

    Fig. 11 (a) Temperature contour of insert with 25°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 17

    (a)

    (b)

    (c)

    Fig. 12 (a) Temperature contour of insert with 0°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 18

    (a)

    (b)

    (c)

    Fig. 13 (a) Temperature contour of insert with -10°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 19

    (a)

    (b)

    (c)

    Fig. 14 (a) Temperature contour of insert with -20°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 20

    (a)

    (b)

    (c)

    Fig. 15 (a) Temperature contour of insert with 25°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 21

    (a)

    (b)

    (c)

    Fig. 16 (a) Temperature contour of insert with 0°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 22

    (a)

    (b)

    (c)

    Fig. 17 (a) Temperature contour of insert with -10°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 23

    (a)

    (b)

    (c)

    Fig. 18 (a) Temperature contour of insert with -20°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 24

    (a)

    (b)

    (c)

    Fig. 19 (a) Temperature contour of insert with 25°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 25

    (a)

    (b)

    (c)

    Fig. 20 (a) Temperature contour of insert with 0°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 26

    (a)

    (b)

    (c)

    Fig. 21 (a) Temperature contour of insert with -10°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 27

    (a)

    (b)

    (c)

    Fig. 22 (a) Temperature contour of insert with -20°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 28

    5.2 Multi-phase simulation: Multi-phase simulation involves using two types of coolants. Settings are entirely different when multi-phase simulation is activated and steady state solution type changes to pseudo-transient state. Pseudo-transient state is the accelerated solver for getting steady state solution.

    When 80% vegetable oil is used as a lubricant aside 20% air as coolant, significant decrease of

    insert temperature is observed.

    In the same way, results for different combinations of temperature and velocity are recorded

    for multiphase simulation where the volume fraction of vegetable oil is 80% and that of air is

    20%. Below table shows numbers.

    Table 2: Values of insert temperature for different combinations of coolant temperatures

    and coolant inlet velocities in multi-phase with 80% veg oil and 20% air.

    Fluid (volume fraction)

    Fluid Temperature

    (°C) Fluid Velocities (m/s)

    Corresponding Resultant temperatures (°C) Multi-Phase

    Vegetable Oil

    Air

    0.8 0.2 25 0.1 1 10 272 247 92

    0.8 0.2 0 0.1 1 10 252 205 62

    0.8 0.2 -10 0.1 1 10 245 137 49

    0.8 0.2 -20 0.1 1 10 237 117 45

    Evidently, there is significant decrease in the insert temperature during multi-phase coolant

    when compared to single-phase coolant and the corresponding temperature values are almost

    halved in multi-phase.

    Temperature contours, velocity streamlines and graphs can be visualized from the next page.

  • 29

    (a)

    (b)

    (c)

    Fig. 23 (a) Temperature contour of insert with 25°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 30

    (a)

    (b)

    (c)

    Fig. 24 (a) Temperature contour of insert with 0°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 31

    (a)

    (b)

    (c)

    Fig. 25 (a) Temperature contour of insert with -10°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 32

    (a)

    (b)

    (c)

    Fig. 26 (a) Temperature contour of insert with -20°C coolant and 0.1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 0.1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 33

    (a)

    (b)

    (c)

    Fig. 27 (a) Temperature contour of insert with 25°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 34

    (a)

    (b)

    (c)

    Fig. 28 (a) Temperature contour of insert with 0°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 35

    (a)

    (b)

    (c)

    Fig. 29 (a) Temperature contour of insert with -10°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 36

    (a)

    (b)

    (c)

    Fig. 30 (a) Temperature contour of insert with -20°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 37

    (a)

    (b)

    (c)

    Fig. 31 (a) Temperature contour of insert with 25°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 38

    (a)

    (b)

    (c)

    Fig. 32 (a) Temperature contour of insert with 0°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 39

    (a)

    (b)

    (c)

    Fig. 33 (a) Temperature contour of insert with -10°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 40

    (a)

    (b)

    (c)

    Fig. 34 (a) Temperature contour of insert with -20°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 41

    5.3 For Multi-Phase 4% Vegetable oil and 96% air combination

    As MQL itself suggests minimum Quantity of lubricant, multi-phase simulation for the

    composition of 4% vegetable oil and 96% air were also conducted to see the heat dissipation on

    the insert. Evidently the effect is not as significant as observed in composition of 80-20 ratio of

    vegetable oil and air respectively.

    It is observed from the other two combinations that lowering coolant temperature to 10 below

    zero and 20 below zero is not much useful. So, in this simulation it is decided to go up to 10

    below zero only.

    Table 3: Values of insert temperature for different combinations of coolant temperatures

    and coolant inlet velocities in multi-phase with 4% veg oil and 96% air.

    Fluid (volume fraction)

    Fluid Temperature

    (°C) Fluid Velocities (m/s)

    Corresponding Resultant temperatures (°C) Single Phase

    Vegetable Oil

    Air

    0.04 0.96 25 1 5 10 305 230 186

    0.04 0.96 0 1 5 10 297 222 175

    0.04 0.96 -10 1 5 10 284 214 167

    0.04 0.96 -20 1 5 10 275 207 157

    Temperature contours, velocity streamlines and graphs can be visualized from the next page.

  • 42

    (a)

    (b)

    (c)

    Fig. 35 (a) Temperature contour of insert with 25°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 43

    (a)

    (b)

    (c)

    Fig. 36 (a) Temperature contour of insert with 10°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 44

    (a)

    (b)

    (c)

    Fig. 37 (a) Temperature contour of insert with 0°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 45

    (a)

    (b)

    (c)

    Fig. 38 (a) Temperature contour of insert with -10°C coolant and 1 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 1 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 46

    (a)

    (b)

    (c)

    Fig. 39 (a) Temperature contour of insert with 25°C coolant and 5 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 5 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 47

    (a)

    (b)

    (c)

    Fig. 40 (a) Temperature contour of insert with 10°C coolant and 5 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 5 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 48

    (a)

    (b)

    (c)

    Fig. 41 (a) Temperature contour of insert with 0°C coolant and 5 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 5 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 49

    (a)

    (b)

    (c)

    Fig. 42 (a) Temperature contour of insert with -10°C coolant and 5 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 5 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 50

    (a)

    (b)

    (c)

    Fig. 43 (a) Temperature contour of insert with 25°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 51

    (a)

    (b)

    (c)

    Fig. 44 (a) Temperature contour of insert with 10°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 52

    (a)

    (b)

    (c)

    Fig. 45 (a) Temperature contour of insert with 0°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 53

    (a)

    (b)

    (c)

    Fig. 46 (a) Temperature contour of insert with -10°C coolant and 10 m/s coolant velocity (b) Velocity streamlines of air at inlet velocity of 10 m/s interacting with the heat source at the cutting tool tip. (c) Graph between tool length and temperature distribution along the length of the tool.

  • 54

    6. Discussion

    When single phase and multiphase (80% veg oil and 20% air) results are compared, the

    temperature drop is almost doubled in latter case for the same coolant temperature and same

    velocities by changing the composition. And there is a difference of 10 degree on an average

    observed between the corresponding resultant temperatures of single phase and multiphase

    values for velocity of 10 m/s.

    In multiphase of 4% veg oil and 96% air combination, significant drop is not observed as seen in

    other multiphase combination and single phase. When resultant temperatures for velocity of 1

    m/s and 10 m/s are compared between the three combinations from Table 1, Table 2, Table 3 it

    is evident that the combination that has lot of oil experienced more temperature drop than the

    other two. And the combination with 4% veg oil experienced even less temperature drop than

    single phase. Single phase simulation with air as coolant is showing better results than

    multiphase simulation with 4% vegetable oil and 96% air as coolants. From the results achieved,

    one can infer that changing the composition by increasing the vegetable oil percentage may

    lower the insert temperature.

  • 55

    7. Conclusion

    As we see from the above results, the drop in the temperature of the insert is very minimum

    when the coolant temperature is lowered. But when the inlet velocity of the coolant is

    increased, there is a significant drop in the tool. Also, keeping the coolant temperature below

    zero doesn’t yield better results. Heat generated during the cutting operation will greatly

    influence the life of cutting tool and overall dimensional accuracy of the machined surface.

    Cutting fluids are used during machining to absorb heat generated and make the tool last

    longer. The model developed is suitable for single-phase and multi-phase simulations and can

    be carried out for any material using different types of cutting fluids and for different types of

    tool designs. Advanced CFD multiphase models involving mix of more than 2 cutting fluids can

    also be designed to estimate the fluid flow and heat transfer between the cutting tools and

    cutting fluids for low/high speed cutting operations. Simulations for different compositions of

    cutting fluids could be conducted to exactly know how much quantity of each cutting fluid in a

    single-phase/multi-phase simulation should be employed for investigating the optimal

    conditions to make manufacturing economically and environmentally friendly.

    From Table 1, the best combination can be taken as -20°C temperature air and velocity of 10

    m/s at which the resultant temperature is 49°C.

    From Table 2, the best combination can be taken as -20°C temperature air and velocity of 10

    m/s at which the resultant temperature is 45°C. But there is only a difference of 4°C in the

    resultant temperature when the resultant temperatures of last two cases are compared. So, it

    may not be economical to go for -20°C fluid temperature as it is expensive to store fluids at that

    temperatures.

    From Table 3, the best combination can be taken as -20°C temperature air and velocity of 10

    m/s at which the resultant temperature is 157°C.

    Increase in temperatures excite the electrons at the atomic level of any material. These atoms

    move from higher energy state to a lower energy state and change in orientation of atomic

    planes take place and grain structure also changes. This leads to dimensional change in cutting

    tool. As a result, tool life decreases. From the simulation results, as the machining temperature

    is decreasing tool life increases.

  • 56

    References:

    1. E. A. Rahim, M. R. Ibrahim, A. A. Rahim, S. Aziz, Z. Mohid. Experimental Investigation of

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    eb504eb1e1e8&acdnat=1520351366_825f2e2ad4f59ef99e802fe521a9b85d

    2. Vishal S. Sharma, GurRaj Singh, Knut Sørby. “A Review on Minimum Quantity Lubrication

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    5. Salman Pervaiz, Ibrahim Deiab, Essam Wahba, Amir Rashid, Cornel Mihai Nicolescu, “A

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    6. Nikolai Ivanovich Kobasko, Ester Carvalho de Souza, Lauralice de Compos Franceschini

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    7. N.R. Dhar, M. Kamruzzaman, Mahiuddin Ahmed, “Effect of Minimum Quantity

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    Journal of Materials Processing Technology, vol. 172, 2006, pp. 299-304.

    8. https://www.cfd-online.com/Wiki/Meshing

    9. ANSYS 18.2 User’s Guide Contents – ANSYS 18.2 software.

    https://ac.els-cdn.com/S2212827114008427/1-s2.0-S2212827114008427-main.pdf?_tid=5b80df21-b10f-4553-9dfb-eb504eb1e1e8&acdnat=1520351366_825f2e2ad4f59ef99e802fe521a9b85dhttps://ac.els-cdn.com/S2212827114008427/1-s2.0-S2212827114008427-main.pdf?_tid=5b80df21-b10f-4553-9dfb-eb504eb1e1e8&acdnat=1520351366_825f2e2ad4f59ef99e802fe521a9b85dhttps://ac.els-cdn.com/S2212827114008427/1-s2.0-S2212827114008427-main.pdf?_tid=5b80df21-b10f-4553-9dfb-eb504eb1e1e8&acdnat=1520351366_825f2e2ad4f59ef99e802fe521a9b85dhttps://www.tandfonline.com/doi/full/10.1080/10426914.2014.994759?src=recsyshttps://www.cfd-online.com/Wiki/Meshing

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