lation of Wind Turbine Gearboxes · Wind turbine manufacturers do have a vital interest in carrying...

ATK-07-Format-KISSsoft-E.doc 1 of 24

Uncertainties in the static Calculation of Wind Turbine Gearboxes

H. Dinner, KISSsoft AG, [email protected] Presented at the ATK 07 in Aachen, Germany

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Torque level [kNm]Hours, spectrum 1Hours, spectrum 2Hours, spectrum 3Hours, spectrum 4Hours, spectrum 5


1 Contents Uncertainties in the static Calculation of Wind Turbine Gearboxes.......................................... 1 2 Introduction ......................................................................................................................... 2

2.1 Overview .................................................................................................................... 2 2.2 Objectives................................................................................................................... 3

3 Methodology ....................................................................................................................... 3 3.1 Gearbox ...................................................................................................................... 3 3.2 Calculation model ...................................................................................................... 4 3.3 Parameter variations, edition of the results ................................................................ 5

4 Influencing Values .............................................................................................................. 7 4.1 Different load spectra with the same Tn ..................................................................... 7 4.2 Ring gear calculation.................................................................................................. 8 4.3 K Factors .................................................................................................................... 8

4.3.1 Uniform load factor KHβ..................................................................................... 8 4.3.2 Load distribution factor Kγ ................................................................................. 9 4.3.3 Dynamic factor Kv ............................................................................................. 9

4.4 S-N curve modifications, ZNT and YNT .................................................................... 10 4.5 Gearing quality......................................................................................................... 11 4.6 Kγ influence on the Planet bearing ........................................................................... 11 4.7 Bearing strength influence on the planet bearings ................................................... 11 4.8 Damage distribution: Gearing .................................................................................. 12 4.9 Damage distribution: Bearings................................................................................. 12

5 Results ............................................................................................................................... 12 5.1 Different load spectra with the same Tn ................................................................... 12 5.2 Ring gear calculation................................................................................................ 14 5.3 K Factors .................................................................................................................. 14

5.3.1 Uniform load factor KHβ................................................................................... 14 5.3.2 Load distribution factor Kγ ............................................................................... 15 5.3.3 Dynamic factor Kv ........................................................................................... 16

5.4 S-N curve modifications, ZNT and YNT .................................................................... 16 5.5 Gearing quality......................................................................................................... 17 5.6 Kγ influence on the Planet bearing ........................................................................... 18 5.7 Bearing strength influence on the planet bearings ................................................... 19 5.8 Damage distribution: Gearing .................................................................................. 19 5.9 Damage distribution: Bearings................................................................................. 21

6 Summary ........................................................................................................................... 23 6.1 Methodology ............................................................................................................ 23 6.2 Results ...................................................................................................................... 23 6.3 Further development ................................................................................................ 23

7 Bibliography...................................................................................................................... 24 2 Introduction

2.1 Overview Wind turbine manufacturers do have a vital interest in carrying out gearbox calculations on their own, and this, out of multiple reasons:

- Influence on the design - Plausibility considerations for the calculations achieved - Quality control / damage analysis made by less known / experienced suppliers - Comparison of various standard gear boxes from different providers


- Gearbox recalculation for different load conditions Furthermore, the wind turbine manufacturer is in a unique position, that of being able to study gearbox behaviour in practice. He can compare field experience against test bench results and calculations. This comparison allows the adjustment of the theoretical calculations to the hands-on experience and the increasing of the validity of future calculations. These calculations consume resources: time, knowledge and tools. The allocation of the resource time is quite difficult because, for the time being, the market of qualified calculation engineers is rather exhausted. Tools are available; there is a wide range of commercial solutions being offered. The critical parameter resides in the know-how to be able to calculate and also standardize to the last detail. This know-how must be cultured and with-honoured in accordance. Using sensitivity analysis it is investigated, how changing the calculation’ starting parameters can influence the results (service life or strength parameters). The identification of most important, or less considered parameters serves the calculation engineer as a guideline for the extension of the existing plant regulations and calculation standards or helps him/her checking specifications on missing but important data. To carry out the sensitivity analysis at the gearbox level, a parameterized model of the complete transmission is used (power flow, component physical distribution, gearing data, shafts, bearings, fittings). These sensitivity studies can be carried out automatically and in very short time with an appropriate programming of the calculation model. The output, in text format, allows a quick processing of the acquired data. This methodology applies to all types of gearboxes.

2.2 Objectives The engineer is conscious that his/her assumptions can influence the quality of the calculation results. However, there is only a limited time available to control and/or improve them. That is why he/she must concentrate on the assumptions which could bring a really clear improvement in the quality of the calculation. This task is further complicated by the fact that not all assumptions can be appropriately evaluated. Thus, two points must be cleared up:

- which input values in the calculation can be better evaluated and this with a minimum of effort (what is the cost of the improvement)

- how big is the influence of a particular input value upon the result (what brings the improvement).

Only the second point will be dealt with in the scope of this work.

3 Methodology

3.1 Gearbox The 1.5 MW gearbox used in the calculations carried out in this study is based upon suppliers’ data after a slight modification.


Figure 0-1 Left: CAD Model of a 1, 5 MW Gearbox [2]; Right: KISSsys Model of a 1, 5 MW Gearbox

(showing only one Planet)

Planet stages: Sun Planet Ring Spur Gear LSS - slow Stage z4 (driving) z5 (driven) Spur Gear HSS - fast Stage z6 (driving) z7 (driven)

Figure 0-2 Gearbox Schematics, Power Flow in KISSsys and corresponding Names

3.2 Calculation model With the KISSsys Software, since 3 years commercially available, it is possible to display the power flows in the transmission stages and, with a strength calculation, link them to the existing machine components. In this way, it is possible to parameterize complete gearbox / transmission stages and analyze them in relation to strength and service life. Among other things, KISSsys offers the user the possibility of quickly carrying out a detailed parameterized study of a complete gearbox / transmission in order to be able to efficiently compare the several variants of a project design. KISSsys uses KISSsoft to calculate the strength and service life of the different machine components. KISSsoft is a CAE-Software for the quick and safe layout, optimization and verification of machine components such as gears, shafts, bearings, bolts, shaft-hub connections and springs. KISSsoft is intended for users in the gearbox production area and is well known for its varied optimization possibilities. The use of KISSsoft for wind turbine gearboxes is described in [6] - Haus der Technik, March 07, “Integrated Layout, Optimization, Verification and Plan Production for Wind Turbine Gearboxes”. KISSsys as a system complement to KISSsoft has following properties: Kinematics Calculation:

• Power flow / rotational speeds with cylindrical, bevel, worm and crossed axis helical gears


• Modelling of epicyclic drives (Planets, Ravigneaux, Wolfrom, …) • Differential (with Bevel- or Spur Gears) • Chain- and Belt transmissions • Clutches can be activated and deactivated, slippage taken into consideration • External acting loads taken into consideration

Integrated Strength and Service Life calculation: • Here, KISSsys accesses KISSsoft • Bearing strength, transmission error, profile correction, efficiency 3D-Model: • Automatic 3D-Display (based upon the data defined in KISSsoft) • Export of the 3D-Model to CAD, import of gearbox casings (step / iges) • Checking for collisions

Special Features: • All machine elements in the model, calculated with load spectra • Several gearbox variants in the same model • Automatic documentation (strength analysis) for the whole gearbox • Integrated programming language for implementing special functions

Figure 0-1 KISSsys Model of a 1.5 MW Wind Turbine Gearbox

3.3 Parameter variations, edition of the results KISSsys has an object-oriented programming language controlled from the calculation which can read data from text files and export the results, for instance, to Excel. It is thus possible to automate parameter variations and swiftly execute them. It is shown below, how such a parameter variation can be programmed in KISSsys. The function in the example shows how, for an established starting value and a defined number of steps, the gearing quality varies and, how the gearing is verified for nominal load for each condition. The resulting safety factors, separated by “;”, are written to a file and can be displayed in Excel (see Fig. 5.5-1). The sequence of operations is as follows:


Line Function 1 Local variable definition with the command “VAR” 2 Defines the variable “file” as text type 3 Writes a title line and a line feed in the variable “file” 4 Establishes a “Gears” list which contains all gears available in the KISSsys

Model 5 Establishes a list of all gear calculations (spur wheel pairs and planet

calculations) 6 Calls a loop which will be executed as many times as desired (Number of

runs = Number of gearing qualities) 7 Determines the new gearing quality to be used 8, 9, 10 Attributes the gearing quality to all gears 11 The actual gearing quality is documented in the “file” file 12 The command “System.kSoftCalculate()” executes the strength calculation 13-16 The resultant Safety factors (Root) will be stored in the “file” file, separated

by “;”. 17 Inserts a line feed 18 The whole procedure will be repeated for the next gearing quality 19 Stores the “file” contents in a *.csv file. Figure 0-1 Explanation of the Gearing Quality Variation Function

Figure 0-2 KISSsys Gearing Quality Variation Function

Excel creates a file “Quality.csv” displaying the following information:


Figure 0-3 Resulting *.csv in Excel

4 Influencing Values

4.1 Different load spectra with the same Tn The gearbox will be calculated for five different load spectra (different characteristics) but for an equal nominal torque of about 800 kNm. The rotor speed for all stages stays constant at 16 Rpm. The influence on the resulting root- and flank safety has to be investigated.

Figure 0-1 Five Load Spectra with the same nominal Torque

File Edit View Insert Format Extras Data Window ? Enter Question here

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Different Load Spectra

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Torque level [kNm]Hours, spectrum 1Hours, spectrum 2Hours, spectrum 3Hours, spectrum 4Hours, spectrum 5


4.2 Ring gear calculation One of the known weaknesses of the latest edition of the ISO 6336: 1966 (the DIN 3990 has the same problem) is the calculation of the tooth-root stress for ring gears. This is now calculated in a completely different way, in which the tooth profile is determined by the cutter wheel used for the manufacturing. With it, there are more practical data (force application point, lever arm tooth root cross section and rounding radius) than by the previous assumptions for the replacement rack. The tooth profile values and the stress correction factors YF, YS change with it in the new edition of ISO 6336:2006. In the graphical method, the factors YF, YS are calculated along the whole root which is a more precise method to calculate the root strength as the highest resulting stress is considered. Case Calculation methodology for YF, YS Remarks

HR1 YF and YS according to ISO6336:1996 Uses a 30° Tangent / replacement Rack

HR2 YF and YS according to ISO6336:2006 Uses a 60° Tangent / Shaping Cutter

HR3 YF and YS according to graphics methodology Tooth Profile based on Suppliers’ Simulation

Figure 0-1 Tree Methodologies for Ring Wheel Calculation

4.3 K Factors A summary of K factor values to be used, according to several Guidelines and Standards is given in [4] – Antriebstechnik 5/2006 - Participating Dialog as a Success Solution, Gear Calculation for Wind Turbine Gear Boxes. Here, selected K factors will be modified. Especially interesting is the comparison between the two following cases:

• For each load spectrum step, a K factor will be separately calculated / modified. • The same K factor will be kept as fix for each load spectrum step, typically at the

value issued from the calculation with the nominal load.

4.3.1 Uniform load factor KHβ

Calculation of gear safeties for six different assumptions of KHβ

Case Dynamic factor value Remarks KHβ 1 Fix 1.05 for all spectrum steps KHβ 2 Fix 1.15 for all spectrum steps KHβ 3 Fix 1.25 for all spectrum steps KHβ 4 Fix 1.35 for all spectrum steps KHβ 5 Variable for each load step According to ISO 6336, B KHβ 6 Fix 1.44 for all spectrum steps According to ISO 6336, B, at

nominal load

Figure 0-1 Six Kγ Cases

In the fifth case (KHβ 5), KHβ will be separately calculated for each individual load step according to ISO 6336, Method B. In this case were used the values displayed in Fig. 4.3-4 for the fast stage considered. In the sixth case (KHβ 6), the calculation is carried out in comparison to a fix KHβ value, determined in the verification for a nominal load.


l=600 s=150 dsh=150 With helix crowning and helix angle correction

Figure 0-2 Calculation Data for the load-dependent KHβ according to ISO 6336, Method B

4.3.2 Load distribution factor Kγ Various guidelines, standards and specifications from wind turbine manufacturers consider different implicit load distribution factors Kγ depending upon the number of planets. Measurements are documented, for instance, in [3] and [5]. The comparison is carried out with different Kγ values coming from different standards and guidelines. Interesting is the comparison between cases Kγ 4 and Kγ 5, between a value set by the spectrum as a constant and a spectrum variable value (according to Figure 0-4).

Case Dynamic factor value Remarks Kγ 1 Fix 1.00 for all spectrum steps According to GL Guidelines Kγ 2 Fix 1.10 for all spectrum steps According to EC 61 400 Kγ 3 Fix 1.20 for all spectrum steps According to AGMA 61 23 (1.23)Kγ 4 Fix 1.25 for all spectrum steps In comparison with Kγ 5 Kγ 5 Variable between 1.25 and 1.00 According to Fig.Figure 0-4

Figure 0-3 Five Different KHβ Cases

Kgamma vs. Torque Level

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0.2

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1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196 209 222 235 248 261

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Torque, normalised

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Figure 0-4 Kγ Case 5: KHβ Variation with the Load Spectrum

4.3.3 Dynamic factor Kv This will be calculated according to ISO 6336 but, following pertinent regulations, must not be less than 1.05. The fast stage will be studied in the following cases. Again interesting is the comparison between cases Kv 5 and Kv 6, i. e., one with a value set by the spectrum as fix and one with a separately calculated Kv value for each load step.


Case Dynamic factor value Remarks Kv 1 Fix 1.00 for all spectrum steps Kv 2 Fix 1.05 for all spectrum steps Kv 3 Fix 1.10 for all spectrum steps Kv 4 Fix 1.15 for all spectrum steps Kv 5 Fix 1.20 for all spectrum steps Kv 6 Individually calculated for each step (according to

ISO 6336)

Figure 0-5 Calculated Kv Cases for the fast Stage

4.4 S-N curve modifications, ZNT and YNT As for the calculations, the S-N curve can be modified so that no fixed range will have to be used. For the so called Haibach modification, the fatigue limit line, with approximately half inclination (2k-1), continues after the first inflexion point. With this, the loads below the fatigue limit are also considered and the calculated service lives will stay lower than with the original S-N curve lines.

Figure 0-1 S-N curve Modifications for the fast stage a): Miner original, b): Haibach, c) Miner elementary

Additionally, the gear service life, the root- and the flank safety factors are examined for different material qualities (influence of ZNT and YNT for 1010 cycles). Different S-N curves result from this as can be seen below in Fig. 4.4-2. The calculation will be carried out once with a load spectrum and once with a nominal load.

Figure 0-2 S-N curves (Root, 18CrNiMo7-6), for Material Qualities "ML", "MQ" and "ME"

Case ZNT, YNT (1010 cycles) Remarks

NT 1 ML Quality, ZNT = YNT =0.85 Calculated with load spectrum

According to ISO 81400

NT 2 MQ Quality, ZNT = YNT =0.92 High Material Quality


Calculated with load spectrum NT 3 ME Quality, ZNT = YNT =1.00

Calculated with load spectrum Highest Material Quality

NT 4 Haibach modification Calculated with spectrum

NT 5 ML Quality, ZNT = YNT =0.85 Calculated with nominal load

According to ISO 81400

NT 6 MQ Quality, ZNT = YNT =0.92 Calculated with nominal load

High Material Quality

NT 7 ME Quality, ZNT = YNT =1.00 Calculated with nominal load

Highest Material Quality

NT 8 Haibach modification Calculated with nominal load

Figure 0-3 Study Cases: ZNT and YNT Value Modification for 1010 Cycles.

4.5 Gearing quality The gearing safety factors are calculated for different gearing qualities. The range of qualities considered in DIN 2 to 11 cover the normal quality ranges generously. 4.6 Kγ influence on the Planet bearing The Kγ factor is used in the calculation of the planet stage gearing. Since it represents a system variable it will also have to be considered in the calculation of bearings (also in the calculation of the planet bolts). It should vary from 0.90 to 1.25 in steps of 0.05. Values below 1.00 should show in how much the calculated planet bearing service life will change in the less loaded path. Values greater than 1.00 are relevant, for instance, for solutions with more than three planets.

4.7 Bearing strength influence on the planet bearings Should more than two bearings be used for the support of the planets, and these have helical gearing, the tilting torque will be spread over them depending upon the bearing stiffness. The forces acting on the bearing in case of helical gearing consist of the circumferential forces (transmitting the planet torque) as well as the planet tilting torque. This tilting torque produces additional forces on the planet bearings depending upon the number of bearings, their span and stiffness. The stiffness are assumed as infinitely high and arithmetically estimated. The arithmetical estimation is then increased or reduced by one order of magnitude in order to find in what extent an error affects the stiffness estimation.

Case Bearing Strength Remarks LS1 Unlimited high Strength LS2 934 N/µm Calculated LS3 93.4 N/µm 1/10 LS4 9349 N/µm *10 Figure 0-1 Various Bearing Stiffnesses to calculate the static Conformity of a Planet Support


Figure 0-2 Left: Planet Support first Stage. Center: Support with four Bearings with Stiffness. Right: Bearing Stiffness Calculation in KISSsoft

4.8 Damage distribution: Gearing It should display which load spectrum steps contribute to the total damage. Should it be determined that certain steps do not provoke damage, they could, for instance, be neglected in a test bench essay.

4.9 Damage distribution: Bearings Same objectives for the gearing see Chapter 4.8.

5 Results

5.1 Different load spectra with the same Tn A change in the spectrum constitution (see Figures 5.1-1 to 5.1-3) results in a change of the gearing safety of approximately 5%. This is lower than expected but, once again, it depends upon the selection of the spectrum to be used. However, the changes in the bearing service lives are dramatic. Once again, this shows how questionable the bearing service life calculation is and that the results are another indication that it would also be advisable to calculate a bearing safety factor based upon a stress. This is possible, for instance, with the calculation of an acting surface pressure as in ISO 81400.


Normalised Flank Safety Factor for Different Load Spectra

0.99

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HSS Gear1 HSS Gear2 IMS Gear1 IMS Gear2 Sun Planet Ring

Gear (Flank) [-]

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Saf

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Fact

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]Load Spectrum 1Load Spectrum 2Load Spectrum 3Load Spectrum 4Load Spectrum 5

Figure 0-1 Normalised Flank Safeties for various Load Spectra

Normalised Root Safety Factor for Different Load Spectra

0.99

1

1.01

1.02

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1.04

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HSS Gear1 HSS Gear2 IMS Gear1 IMS Gear2 Sun Planet Ring

Gear (Root) [-]

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Load Spectrum 1Load Spectrum 2Load Spectrum 3Load Spectrum 4Load Spectrum 5

Figure 0-2 Normalised Root Safeties for various Load Spectra with same nominal Torque


Normalised Bearing Life for Different Load Spectra

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Bearing 1, HSS Bearing 2, HSS Bearing 3, HSS Planet, Bearing 1 Planet, Bearing 2

Bearing [-]

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Load Spectrum 1Load Spectrum 2Load Spectrum 3Load Spectrum 4Load Spectrum 5

Figure 0-3 Normalised Bearing Service Life for various Load Spectra with same nominal Torque

5.2 Ring gear calculation It appears a modest ring wheel root strength deviation for the three calculation methodologies which, naturally, has dramatic effects upon the calculated service life. This deviation strongly depends upon the tooth height, the pressure angle and the addendum modification. In the calculations show here slightly higher pressure angle and tooth height were used.

Root Lifetime and Strength of Ring Gear

1.00E+00 1.0001.341

7.02E+00

1.149

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2.80

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7.80

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Calculation Method [-]

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ISO6336:1996 (Case HR1)

ISO6336:2006 (Case HR2)

Graphical method (Case HR3)

Figure 0-1 Resulting Ring Wheel Safeties for various Calculation Methodologies

5.3 K Factors

5.3.1 Uniform load factor KHβ

Naturally, the root- and the flank safeties vary with the KHβ value in a linear/exponential way. However, it is interesting that the difference between calculations with a constant KHβ for all spectrum steps (Case KHB6 with a fix KHβ considered at nominal load) gives identical results as when KHβ varies. I. e., that the choice of procedure (both are contained in the guidelines) does not show any influence worth mentioning. This is confirmed by a similar study in [1].


Normalised Safety Factor Gears (HSS) vs Khbeta

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0.95

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HSS, gear 1, root HSS, gear 2, root HSS, gear 1, flank HSS, gear 2, flank

Gear [-]

Norm

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afet

y Fa

ctor

[-]

Khbeta=1.05Khbeta=1.15Khbeta=1.25Khbeta=1.35Khbeta=varKhbeta=1.44

Figure 0-1 Root- and Flank Safeties as a Function of KHβ: fast Stage. Interesting the Comparison of the

last two Study Cases!

5.3.2 Load distribution factor Kγ Also here, it is especially interesting the comparison of the last two cases, fix Kγ against variable Kγ. Once again, there is no difference worth mentioning, i. e., there is no need to consider /set Kγ separately for all spectrum steps.

Normalised Safety Factor Gears (LSS) vs Kgamma

0.95

1

1.05

1.1

1.15

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1.25

1.3

Sun, Root Planet, Root Ring, Root Sun, Flank Planet, Flank Ring, Flank

Gear [-]

Norm

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afet

y Fa

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[-]

Kgamma=1.00Kgamma=1.10Kgamma=1.20Kgamma=1.25Kgamma=var

Figure 0-2 Root- and Flank Safeties in the Planet Set. Interesting the Comparison of the last two Study

Cases!


5.3.3 Dynamic factor Kv The same tendency is also valid for the dynamic factor Kv. Whether separately calculated for all spectra or, set as a constant value resulting at nominal load, there are negligible differences in the resulting safeties.

Normalised Safety Factor Gears (HSS) vs Kv

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

HSS, gear 1, root HSS, gear 2, root HSS, gear 1, flank HSS, gear 2, flank

Gear [-]

Nor

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Saf

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Fact

or [-

]

Kv=1.00Kv=1.05Kv=1.10Kv=1.15Kv=1.20Kv=var

Figure 0-3 Root- and Flank Safety Factors: fast Stage. Interesting the Comparison of the last two Study

Cases!

5.4 S-N curve modifications, ZNT and YNT In ISO 81400, the use of ZNT and YNT according to the material quality “ML” is prescribed. Should one use higher quality materials, the results below (for the calculation with load spectra) show negligible differences. This is because all the damage-relevant load stages are in the zone with high loads. There, the choice of high quality materials does not affect the results. Should one give up the idea of a fatigue zone (Haibach modification), the calculated safeties will considerably fall because 1)- all spectra steps contribute to the damage, 2)- the S-N curve strongly falls (YNT=0.63 as compared to YNT=0.85 at 1010 cycles). Especially, the second point has a clear effect. The use of a higher quality material (e. g. MQ instead of ML) does not bring anything for the highly loaded planet stages; on the contrary, in other stages could bring something. The limitation in ISO 81400, that one should calculate with ML can, thus, be questioned.


Normalised (ML=1) Safety Factor vs. Materialquality

0.75

0.8

0.85

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0.95

1

1.05

1.1

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1.2

HS, Gear1 HS, Gear2 IS, Gear1 IS, Gear2 LS, Sun LS, Planet LS, Ring

Gear [-]

Nor

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ised

Saf

ety

Fact

or [-

]ML, RootMQ, RootME, RootHaibach, RootML, FlankMQ, FlankME, FlankHaibach, Flank

Figure 0-1 Material Quality Influence: Calculation with Load Spectra

Normalised (ML=1) Safety Factor vs. Materialquality

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

HS, Gear1 HS, Gear2 IS, Gear1 IS, Gear2 LS, Sun LS, Planet LS, Ring

Gear [-]

Nor

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ised

Saf

ety

Fact

or [-

]

ML, RootMQ, RootME, RootHaibach, RootML, FlankMQ, FlankME, FlankHaibach, Flank

Figure 0-2 Material Quality Influence: Calculation with nominal Load

5.5 Gearing quality The gearing quality has a stronger influence upon the calculated safeties when the number of revolutions increases. Just for the fast stage (z6, z7), it is possible to achieve a clear strength improvement should the gearing quality be increased one step, only. In the slow rotating planet stages this is does not apply.


Normalised Safety (Quality DIN 6 = 1) Root vs. Gear Quality

0

0.2

0.4

0.6

0.8

1

1.2

Sun Planet Ring z4 z5 z6 z7

Gear [-]

Nor

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ised

Saf

ety

Fact

or [-

]

Quality= 2Quality= 3Quality= 4Quality= 5Quality= 6Quality= 7Quality= 8Quality= 9Quality= 10Quality= 11

Figure 0-1 Gearing Quality Influence upon the calculated Safety

5.6 Kγ influence on the Planet bearing

Normalised (Kgamma=1) Planetary Bearing Life vs. Kgamma

0

0.2

0.4

0.6

0.8

1

1.2

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1.6

b1 b2

Planetary Bearing [-]

Nor

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Life

[h]

Kgamma=0.9Kgamma=0.95Kgamma=1Kgamma=1.05Kgamma=1.1Kgamma=1.15Kgamma=1.2Kgamma=1.25

Figure 0-1 Planet Support Bearing Service Life for various Kγ Values

Even for small Kγ values, one can observe a stronger fall in the bearing service life (about 20%). The planet stage bearing, being a critical component, the Kγ influence upon the bearing load must be considered. The topic is now of less importance due to the fact that with today’s high precision production for planet sets, with three or even four planets, Kγ is now close to the ideal value of 1.00. The measurements in [3] and [5] document this. By higher planet figures (for instance, five planets) it is recommended to strive for a load balance using flexible elements. Nowadays, because sun gears are already freely supported and the ring gear is, frequently, part of the casing (or part of a support such as, e. g., in the Bosch-Rexroth


differential transmission), the ring gear cannot be made flexible. There is here the possibility of a flexible planet support such as, e. g., the one built by MAAG with two prototypes and by Windtec/Wikov Wind/Orbital2. In eastern Asia, at present, the application of flexible planet support is also being tested in prototypes.

5.7 Bearing strength influence on the planet bearings It is proven that the assumption of an infinite stiff bearing is not acceptable. The bearing service life using realistic bearing stiffness clearly deviates from the “infinite stiff” case. Whether the bearing stiffness exactly corresponds to reality or not, is of minor importance: a change of the magnitude of the stiffness value has a very small influence upon the result. This means that simplified bearing stiffness calculation according to the standards is sufficient and one does not need to go deeper into the bearing geometry details (this statement applies to the load distribution calculation over the bearings but not to the bearing service life calculation, e. g., according to ISO 281-4).

Figure 0-1 Bearing Stiffness Influence of a static over-determined Planet Support on its Service Life

5.8 Damage distribution: Gearing From the gearing damage calculation for all gears, the individual damage is Di (Σi(Di)=1), separate for root and flank. It is immediately evident that for the highly stressed gears (thus, not the ring gear), the damages originate in very few spectrum steps, representing about 10% of the total. The load spectra being not very informative in many areas, there is need for action here. In such cases the gearing manufacturer must insist on the need for a load spectra study to be carried out. The objective must be grouping together the non damage-relevant areas and study in detail the load levels in the relevant areas (typically around nominal loads).

Normalised Bearing Life for Different Bearing Stiffness

0

0.2

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0.6

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1/10th 934 N/um 10x Infinite stiffness

Bearing Stiffness [N/um]

Norm

alis

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ife [-

]

Bearing 1Bearing 2Bearing 3Bearing 4


Partial Damage Distribution, Gears

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1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235

Load Step [-]

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tial D

amag

e [-]

Gear1: z101, RootGear1: z101, RootGear2: z25, RootGear2: z25, FlankGear1: z90, RootGear1: z90, FlankGear2: z27, RootGear2: z27, FlankSun gear: z26, RootSun gear: z26, FlankPlanet gear: z47, RootPlanet gear: z47, FlankRing gear: z-118, RootRing gear: z-118, Flank

Figure 0-1 Damage Distribution for all Gears, Root and Flank: all Load Stages

Partial Damage Distribution, Gears (without Ring Gear)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Load Step [-], only relevant steps

Par

tial D

amag

e [-]

Gear1: z101, RootGear1: z101, RootGear2: z25, RootGear2: z25, FlankGear1: z90, RootGear1: z90, FlankGear2: z27, RootGear2: z27, FlankSun gear: z26, RootSun gear: z26, FlankPlanet gear: z47, RootPlanet gear: z47, Flank

Figure 0-2 Detail from previous Figure: only relevant Load Steps are displayed (Ring Gear, excepted)


Partial Damage Distribution, Sun Gear, Last Gear

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Load Step [-], only steps with more than 2% partial damage

Par

tial D

amag

e [-]

Gear1: z101, RootGear1: z101, RootSun gear: z26, RootSun gear: z26, Flank

Figure 0-3 Detail from previous Figure: only Sun- and last Gear Wheel are displayed

5.9 Damage distribution: Bearings The individual damages were evaluated in a similar manner. Also here, it is evident that only a few steps of the used spectrum being relevant, the conclusions are the same as the previous ones for the gearing. Not exactly the same spectrum steps are causing de damage, however, they are close together again around the nominal load. The damage-relevant steps for the bearing lay somewhat lower than for the gearing and this because, for the bearing, the time scale for lower loads is less important than for the gearing (smaller S-N curve slope).

Partial Damage Distribution, Bearings

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235

Load Step [-]

Par

tial D

amag

e [-]

_O.WKG.HIS.Bcalc_O.WKG.HIS.Bcalc_O.WKG.HSS.Bcalc_O.WKG.HSS.Bcalc_O.WKG.HSS.Bcalc_O.WKG.LIS.Bcalc_O.WKG.LIS.Bcalc_O.WKG.LIS.Bcalc_O.WKG.LSS.Planet.Bcalc_O.WKG.LSS.Planet.Bcalc

Figure 0-1 Damage Distribution: all Bearings, all Load Stages


Partial Damage Distribution, Planet / HSS Bearings

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Load Step [-], only steps with more than 2% partial damage

Par

tial D

amag

e [-]

_O.WKG.LSS.Planet.Bcalc_O.WKG.LSS.Planet.Bcalc_O.WKG.HSS.Bcalc_O.WKG.HSS.Bcalc_O.WKG.HSS.Bcalc

Figure 0-2 Detail from previous Figure: only the Planet and the fast Shaft Bearings are displayed


6 Summary

6.1 Methodology The use of a parameterized model allows a very quick calculation of safety factors, service life as well as damages for the various transmission machine components under various assumptions. The verification of a transmission as previously showed, with a spectrum of about 250 load steps, in a modern PC takes around 5 minutes. With it, a tool and a methodology are at the engineer’s disposal allowing him/her to examine, quickly and with very little complexity, how a given design will react to changes in the calculation input parameters. As an additional facility, KISSsys offers an object-oriented programming language allowing the automatic introduction of parameter variations. The functions mentioned are already partially available in KISSsys or can be created and introduced. The methodology can be learned with little effort and be used for the daily engineer’s work.

6.2 Results The investigations show that it is irrelevant whether one works for the spectra with variable or constant (calculated at nominal load) K factors. With the easier methodology, it is also possible to work maintaining the K factors constant. However, the K factor values in themselves are significant and the estimated values and their calculation methodology are explicitly defined in ISO 81400. Interesting is, with what clarity one can find out in what spectrum area the damage occurs. This information is of the utmost interest for the person who has to establish the load assumptions or test them. The choice of the load distribution on the planet set has a massive influence on the service life of the planet bearings. For this calculation, Kγ must be taken into consideration. Furthermore, it has been shown that in the case of bearings it is preferable to go over to a stress-based calculation, of the safety factor (instead of a calculated safety in the service life). Still more difficult is to deal with high (and low) cycle values. Should one stick to the requirement of calculating a transmission for a 20 year service life (for the fast stage it will be in the range of 1010 cycles), the S-N curve form shows a certain influence in the zone of high cycles. The question here is whether the requirement to calculate with “ML” quality only is justified, because, exactly, the wind turbine field has high requirements in material proofing, processing and documentation. It has also been shown that the spectrum form has an influence upon the calculation that cannot be neglected. There is the need to calculate a transmission not only for a spectrum but also for various spectra. For instance, these can, result from a changed tower height, blade length or from different installation places.

6.3 Further development After having shown the influence of various assumptions upon the results, one can now ask the question, at what cost can the assumptions identified as relevant be improved? Admittedly, this is the most difficult question to answer. The question here goes especially to the equipment manufacturers (in view of the availability of various load assumptions), the gearbox manufacturers (for instance, in view of material characteristics, gearing quality and other influencing values originated in the production), component suppliers (for instance, bearings) and also certifiers (for instance, who specify the choice of K factors in their guidelines).


7 Bibliography [1] R. Grzybowski, B. Niederstucke, Betriebsfestigkeitsberechnung von Getrieben in Windenergieanlagen mit Verweildauerkollektiven, Allianz Report 2004 [2] R. Poore, T. Lettenmaier, Alternative Design Study Report: Wind PACT Advanced Wind Turbine Drive Train Designs Study, NREL/SR-500-33196 [3] U. Giger, G.P. Fox, Leistungsverzweigte Planetengetriebe in Windenergieanlagen mit flexibler Planetenlagerung, ATK03 [4] H. Dinner, Gleichberechtigter Dialog als Erfolgsrezept, Verzahnungsberechnung für Windenergieanlagengetriebe, Antriebstechnik 5/2006 – [Participating Dialog as a Success Solution, Gear Calculation for WTIs] [5] F. D. Krull, T. Siegenbruck, Windenergieanlagen fordern hohe Leistungsdichten, Ermittlung der Breitenlastverteilung in Planetengetrieben, Antriebstechnik 9/2004 [6] H. Dinner, Integrierte Auslegung, Optimierung, Nachrechnung und Zeichnungserstellung von Verzahnungen für Windkraftgetriebe, Antriebsstränge in Windenergieanlagen, Haus der Technik, März 07

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