Gearing analysis for wind turbine, seen as a process - KISSsoft AG

Showing the teeth at the wind… 

H. Dinner, KISSsoft AG, hanspeter.dinner@KISSsoft.ch 

Gearing analysis for wind turbine, seen as a process 

Wind turbines are getting bigger, wind turbine gearboxes more 

complex, their number of gears increases and a gearbox failure – 

and, with it, the resulting operational stop– is more and more 

expensive. 

At the same time, the wind farm operator depends from the wind 

turbine manufacturer and the latter is then again dependent from 

gearbox manufacturers. On the other hand, the gearbox 

manufacturer has a knowledge head-start in comparison with wind 

turbine manufacturer and he, in turn, knows more about the power 

trains in its equipment than the operator. This situation prompts 

disputes and opens the flood gates between the partners. 

The objective is to drive the partners towards an interchange of knowledge allowing at 

the same time a participating responsibility. An interchange of knowledge can only exist 

when all partners do have a sufficient amount of it. 

The objective of this article is, with the example of a toothing calculation, to delineate 

the necessary knowledge basis for a fair and qualified dialog. 

1 Problem Definition 

In the wind turbine gearbox dimensioning and verification, there are some specific problems 

atypical of transmissions in the power generation field: 

- loading: fluctuating torques, excessive overloads due to vibration, torque change of 

sense, site-dependent loading, etc. 

- power: high torques at low speeds, high power density 

- operation: temperature fluctuations, cold starts, idling, loading at standstill 

- gearbox dimensions: lightweight design required, soft bearing, bending torque on the 

input shaft (especially for three-point bearing) 

- accessibility: the gearbox is of difficult access, tool transportation is difficult. 

Besides the technical side, some questions on the collaboration between the gearbox supplier 

and the buyer frequently pop up: 

- methodology safety in the calculation and its documentation 

- safer data flow within an between all the partners involved 

- understandability of assumptions and calculation methodologies 

- consensus between the partners concerning assumptions and characteristic values to 

be attained 

- quick verification of the manufacturer’s gearbox calculation by the buyer. 

Dem-Wind-die-Zähne-gezeigt-Format-KISSsoft-E.doc 1 of 18

A few economical aspects are also atypical: 

- wind turbine gearboxes have atypically long delivery times, the market is rarefied 

- the number of suppliers is comparatively small, a few renown ones are strongly 

associated with equipment manufacturers 

- equipment and gearboxes are certified by third parties 

- high number of damages connected to high costs 

It is thus most interesting to incorporate all partners in a dialog so that all of them could 

understand, assume and share the risks. Prerequisite to this understanding is a think-tank of 

the peculiarities of wind turbine gearboxes and transmissions in general, as well as effective 

methodologies and tools, in order to permit relevant information interchange on the gearboxes 

employed. 

2 Wind Turbine Gearboxes 

2.1 Systematic 

Most wind turbine installations are equipped with similar gearboxes; typical are three-stage 

spur wheel gearbox (lower capacity area), one-stage planetary gearbox with two spur wheel 

stages (middle capacity area) and two-stage planetary gearbox with one spur wheel stage 

(higher capacity area). In addition to that, there are at present some interesting variants, see 

Fig. 2.2-1. 

The majority of wind turbine installations has one rotor only that generally is upwind 

oriented. Likewise, most installations have one generator only, i. e., the gearbox has exactly 

one input and one output. 

Conceivably and partially implemented, are the four combinations in Fig. 2.1-1. The 

execution with several generators or rotors is unusual; the author does not know of any 

installation with several rotors and several generators. 

Types Single output Multiple output 

Single Input 

One Rotor, one Generator 

Standard case 

One Rotor, multiple 

Generators; e. g. Clipper 

Multiple Inputs 

Multiple Rotors, one 

Generator; e. g. Kowintec 

Multiple Rotors, multiple 

Generators; unknown 

Figure 2.1-1 Possible Design Concepts in respect to Power Flow 

The wind turbine gearbox mission is that of transforming the low speeds and high torques at 

the gearbox input into higher speeds and lower torques at the output. Thus, according to their 

kinematics type, wind turbine gearboxes can be classified as follows: 

- standard gearboxes that constantly transform input torque and speed values into those 

at the output 

- torque-limiting gearboxes can control or, at least, limit the output torque (and with it 

the input torque). The speed is thereby not controlled. 

- The most complex forms of gearbox are the CVTs that permit the control of the 

gearbox output speed and torque –within a determined range. 


2.2 Concepts 

Following figures show an –incomplete– overview of realized or investigated gearbox 

concepts. The one- and two-stage planetary gearboxes (with two or one downstream spur 

wheel stages), in particular, constitute the standard today. With the time, and with the increase 

of power, the number of gearing meshes also increased and the toothing calculation got more 

complex. 

Spur wheel stage, also with Power split 

Planetary gear stage with a Ring wheel stage. 

Test installation in Holland 

One Planetary gear stage, two Spur wheel 

stages 

Two Planetary gear stages, one Spur wheel 

stage 


Planetary gear stage, fixed Planet: 

Renk Aerogear 

Planetary gear stage, fixed Ring wheel 

Power Split, several Generators: Clipper 

Two inputs: Luv and Lee Rotor, Kowintec 

Planetary coupled gearbox: MAAG 

Differential gearbox: Bosch Rexroth 


M 

G 

Hydraulic torque limiting: Henderson Gearbox 

Torque limiting: Electric motor (M). 

Test installation in Orkney Island 

Hydrodynamic differential??? gearbox: 

Voith WinDrive 

Figure 2.2-1 Several Gearbox Concepts 

Hydrostatic differential??? gearbox: 

Windtec/Wikov/Orbital2 

3 Toothing Calculation for Wind Turbine Gearboxes 

3.1 Toothing calculation methodology 

Toothing calculation should not be reduced to strength verification; this proof, is surely 

necessary and is explicitly asked for, but only represents one of the steps in the “Toothing 

calculation” methodology. 

Toothing calculation must be considered as a process that, starting with load assessment, 

looks for an optimal toothing solution, analyzes it and produces an extensive documentation 

for the production, quality control and certification. 


Nachrechnung 

Verification Optimization 

Optimierung Production Herstellung 

Dimensioning 

Auslegung 

Export→CAD 

Loading 

Belastung 

Certification 

Zertifizierung 

Documentation 

Dokumentation 

Figure 3.1-1 Toothing Calculation Methodology 

Fig. 3.1-1 above shows a minimum of steps to be carried out in a toothing calculation process. 

Not included in it are, particularly, the determination of the upstream load spectra and the 

resulting downstream hardware preparation and tests. The following sections illustrate the 

individual steps of this process. However, because of the complexity of this topic, a 

comprehensive description of these steps is not possible in the scope of this article. 

3.2 Kinematics analysis 

Normally, determining the loads acting on the gearbox is not the responsibility of the gearbox 

manufacturer; however, he must investigate to what extent a change in the handed over load 

assumptions would result in a change of the toothing dimensioning. 

A load spectra reduced damage equivalent (torque and speed at the gearbox input) will thus 

be used for determining the toothing dimensioning. For the gear dimensioning, specifically 

for epicyclic gears, this load must then be converted into the gear meshing power (as opposed 

to blind and coupling power). This kinematics analysis can already be rather costly in case of 

differential gearboxes, gearboxes with power splits or CVT gearboxes. The presentation of a 

few power flows in the following figures illustrates this in a more clear way. 

In KISSsys, it is possible to use complex kinematics analyses to calculate the effective mesh 

powers for the toothing dimensioning. This simulation software calculates the power flow in 

power trains and links this simulation to a strength calculation of the machine elements 

involved in the power train. It is thus possible to parameterize complete gearboxes / 

transmission power trains and analyze them for strength and service life. Among other things, 

KISSsys offers the user a quick and detailed parameter study of complete gearboxes / 

transmission power trains in order to be able to efficiently compare several design variants. 

KISSsys uses KISSsoft for the strength and service life calculation of the various machine 

elements. 


Figure 3.2-1 Above: Wind Turbine Gearbox Calculation Model in KISSsys. 

Bottom left: Power Flow Diagram of a one Stage Planetary Gearbox with two Spur Wheel 

Stages. 

Bottom right: Power Flow Diagram of a Bosch Rexroth Differential Gearbox (Three 

Planetary Gear Stages and one Spur Wheel Stage). 

3.3 Dimensioning 

Once the gear meshing power is known, the dimensioning of the relevant toothing parameters 

(number of teeth, module and pressure angle) can be carried out. With it, following 

parameters will be considered: 

- attainable toothing quality 


- material characteristics 

- reference transmission ratio and acceptable deviation 

- requested service life / safety 

- installation conditions / mountability 

It is especially important to consider here, the mountability conditions of the first planetary 

stage, because both the ring gear maximum possible diameter (manufacturing) and the 

necessary planet wheel diameter (space for the planet bearings) restrict the manufacturer’s 

liberty. 

3.4 Toothing optimization 

The toothing can afterwards be optimized, the variation of the following parameters being the 

most usual: 

- tooth depth (reaching an optimum transverse contact ratio) 

- helix angle (reaching an optimum overlap ratio) 

- addendum modification (influences specific slippage and strength) 

- fillet optimization (e. g. bigger radius by tool module different than gear module) 

- profile- and face modification (improving contact pattern, reducing meshing shock) 

- surface treatment (hardening, smoothing) 

Some selected points will be shortly described in the following sections. 

3.4.1 Tooth depth optimization 

The use of a standard reference profile, e. g., with a tooth depth of 2.25 mm, normally results 

in a transverse contact ratio between 1.00 and 2.00. This means that, during a certain time one 

tooth, and during a certain time two teeth are meshed. With it, the meshing stiffness value 

permanently changes from single to double. This change can create vibration. The goal is to 

reach a whole-number overlapping in order to guarantee that, at any time, the same number of 

teeth is meshed. This can be achieved by augmenting the tooth depth resulting in a reduced 

gearing vibration. 

Stiffness 

Single Meshing 

(N/mm/µm 

) 

Stiffness 

Single Meshing 

(N/mm/µm 

) 

Number of Meshing Points (-) 

Number of Meshing Points (-) 

Figure 3.4-1 Meshing Stiffness Progression Changes due to a higher Tooth Depth 


3.4.2 Profile modification 

Wind turbine gearboxes environments demand low noise levels. The vibrations provoked by 

the gears are undoubtedly a cause for the noise. Thus, the goal must be, on one hand, to 

maintain transmission errors as low as possible and, on the other hand, to reduce meshing 

shock. The tooth depth dimensioning and the tip relief (amount, type and height) are here of 

the utmost importance. 

Figure 3.4-2 Meshing Line under Load. Left: Premature Meshing with a non-modified Toothing (Meshing 

Line Inflection). Center: Toothing with a short, linear Tip Relief (6.2 µm and 5.0 µm). 

Right: Toothing with progressive Tip Relief (9.3 µm and 7.5 µm). 

End Stage of a 3.6 MW Installation. 

The premature meshing (meshing line prolongation) in the figure on the left, leads to a so 

called meshing shock. This can be reduced with tip relief, the meshing line showing no longer 

the characteristic prolongation. However, for a linear tip relief, the meshing line shows a 

discontinuity (center figure); this abrupt change in the rotation angle could create vibration. 

This will be avoided with a progressive tip relief (figure on the right). 

The profile modification also leads to a smaller pressure at the start of the meshing thus 

reducing the scuffing risk, see Fig. 3.5-4. 

3.4.3 Correction along the tooth width 

In non-modified toothings, due to shaft strain, bearing play, tooth deflection, as well as shaft 

bearing displacement (bearing and housing) an uneven load distribution appears along the 

tooth width. As a result of this, the whole toothing strength will be reduced in certain highly 

loaded areas (Fig. 3.4-3, below left). Correcting the tooth profile along its width (typically a 

combination of helix angle correction, end relief and crowning) it is possible to achieve that 

the gears under load neatly fit together and the load, as much as possible, be uniformly 

distributed along the tooth width (Fig. 3.4-3, below right). The calculation of these corrections 

is one of the most demanding tasks for which the gearbox manufacturer experience is 

indispensable. 


Line Load 

Load Distribution 

Line Load 

Load Distribution 

Longitudinal Axis Y 

Longitudinal Axis Y 

Figure 3.4-3 1.5MW Gearbox Output Shaft, Load Distribution along the Width. Left: without Corrections. 

Right: with Helix Angle Correction and corrected Toothing Crowning 

3.5 Stress analysis 

Now, after having optimized the dimensioned toothing and reached a final dimensioning, it is 

necessary to check whether it complies with the required safety coefficients. Now, this stress 

analysis should not be carried out with the equivalent-damage individual loads as previously 

done for the dimensioning any more; the analysis must be executed using a damage 

calculation with a load spectrum. The toothing analysis is done according to the standards and 

guidelines valid at the moment. In the following, knowledge of these calculation 

methodologies is expected and it will be especially referred to calculations diverging from the 

standards that are meaningful for the wind turbine gearboxes toothing. 

3.5.1 Tooth root strength 

Normally, the standards underestimate the contact ratio effect, especially where a production 

precision is required –wind turbine gearboxes. Following figures show the effective stress 

situation (Flank: light blue; Root 1: violet; Root 2: red) in comparison with the meshing 

calculated values according to DIN 3990. The root stress is especially overestimated. The 

figures show the comparison between the root stress, according to the standard, and the same 

stress taking into consideration the load distribution. In addition, the comparison between 

both figures explicitly shows the influence of the pitch error on the stress situation. 

Hertz Stress and maximum Root Stress during Meshing 

Last Calculation Situation (Z12), Date/Time: 



Last Calculation Situation (Z12), Date/Time: 


Figure 3.5-1 Load Distribution Influence over several Teeth at Stress Level. 

Left: for Quality 7. 

Right: for Quality 5. End Stage of a 3.6 MW Installation, ε α =1.73. 


Following modifications are recommended for the ring wheel root strength calculation: 

- calculation at 60° Tangent contact point, taking into consideration the actually root 

contour produced by shaping cutter such as, e. g., suggested in the present editions of 

the ISO 6336:2006 (or VD I 2737) 

- exact tooth profile calculation on the basis of a meshing simulation with the tool for 

the calculation of Y F and Y S along the entire fillet (“graphical method”, see influence 

on Fig. 3.5-2) 

- taking into consideration the influence of the ring wheel wall thickness in the tooth 

root stress according to VDI 2737. 

The comparison in Fig. 3.5-2 shows that the ring toothing strength calculations in the root 

area according to DIN 3990 and ISO 6336:1996 / ISO 6336:2006 give different results. 

3 

1.15 

2.5 

2 

1.5 

ISO6336 C 

ISO6336 B 

ISO6336 (extended) (erweitert) B 

Graphical Method 

1.1 

1.05 

1 

0.95 

ISO6336 (erweitert) (extended) B 

Grafische Graphical Methode 

1 

0.9 

0.5 

0.85 

0 

YF3 YS3 SF3 

0.8 

YF3 YFS3 SF3 

Figure 3.5-2 Calculation Methodology Influence upon the Ring Toothing calculated Root Safety. 

Left: Reference Profile = 1.25/0.38/1.00. Right: Reference Profile = 1.40/0.38/1.25. 

3.5.2 Tooth flank strength 

Due to the flank’s pressure load, a shear stress progression builds up in depth, with a 

maximum just under the surface. In case of overload, the excessive shear stress leads to 

cracks under the surface that can originate 0.5 to 1 mm material erosion (pitting). When 

tempering the tooth flank, the case hardening depth (EHT in German) must be higher than the 

maximum shear stress depth. On the other hand, out of cost considerations, the EHT must be 

kept as small as possible; the shear stress progression calculation (Fig. 3.5-3) being thus of 

utmost interest. 

Case Hardening Depth Pair 1 (Wheel 1 Material measured Value) 

Name: Ex. 1 (Spur wheel), Date 15.01.2006/21:27:03 

Hardening Depth Pair 1 (Wheel 1 Material measured Value) 

Depth (my) 

Shear Stress Progression (determining the Hardening Depth) 

(σH=1020.8 N/mm 2 ; ro_r= 19.3 mm) 

Maximum Shear Stress Depth (mm) 0.274 

EHT Suggestion : 0548 mm 

(Suggestion acc. alternating Flexure Stress, Niemann : 0.922 

mm) 

(Suggestion acc. AGMA 2101. Fig. 13: Normal 0.879 mm, 

Heavy 1.326 mm) 

!! For production with grinding allowance, indicate the half on 

the drawing) !! 

Shear Stress Progression ( on the Basis of the Flank Pressure) 

Material measured Value (from Database) 

Vickers Hardness (HV) 

Figure 3.5-3 Hertz Stress Progression from the Toot Surface → Interior. 


3.5.3 Scuffing 

ISO 6336 has no proof of scuffing facility; in this case, it is usual to proceed according to 

DIN 3990, Part 4. Both AGMA6006 and the GL guidelines ask for a reduction of one unit in 

the calculation of the lubricant’s scuffing load level according to FZG (German Research 

Center for Gears and Gearboxes). Since modern oils with EP (Extreme Pressure) addictives 

have scuffing load levels >12, and the calculation methodologies only consider load levels up 

to 12, this limitation being practically less relevant. The calculation of the safety against 

scuffing is based on the estimation of the temperature at the tooth contact, this temperature 

depending upon the pressure and the slippage speed. Scuffing preferably occurs in the tip and 

root areas where high relative speeds are present. In order to reduce the contact force in this 

meshing area, a tip relief (and/or a root relief) is introduced whose influence on the contact 

temperature is shown in Fig. 3.5-4. 

Temperature at Tooth Contact (θB) 

Temperature at Tooth Contact [θB ] 

Temperature at Tooth Contact (θB) 

Date/Time: 

Temperature at Tooth Contact [θB ] 

θB 

Help 

θB 

Help 

Maximum Contact Temperature 301.2 

Scuffing Probability 26.09 % 

XSi 

XSi 

Figure 3.5-4 Flash Temperature Reduction from 300 °C to 230 °C due to Tip Relief. 3.6 MW End Stage. 

Calculation according to AGMA 925-A03. 

3.5.4 Micropitting 

By insufficient lubrication due to high loading or unfavourable operation parameters, the 

friction coefficient between tooth flanks increases due to the tooth contact roughness 

(boundary friction, µ=0.2 to 0.4, in contrast to viscous friction µ=0.05). Due to the higher 

friction force, a shear stress develops on the tooth surface that can already exceed a critical 

value even for an uncritical torque for the building of micropitting. This overstressing leads to 

material erosion (depth approx. 10 to 20 µm, over a zone of approx. 20 to 100 µm) showing as 

a grayish discolouration on the tooth surface. The resulting profile irregularities lead to a 

higher tooth load (K Hα , K Fα , K ν , noise increases) and a higher risk of pitting. The specific 

lubrication film thickness λ –the quotient between the lubrication film thickness and the 

surface roughness– serves to measure the risk of micropitting. The calculation follows 

AGMA 925, or FVA (German Research Association for Propulsion Technology) worksheets 

54/259; an ISO Standard is in preparation. 


Help 

Help 

Help 

Figure 3.5-5 3.6 MW Wind Turbine Gearbox: λ Values for the 1 st and 2 nd Planet (Sun-Planet Mesh) and 

Spur Wheel Stages 

3.5.5 Static proof of strength 

It is also necessary to carry out a toothing static proof of strength for plastic strain or rupture. 

Since the standards do not cover the classic static proof, this will frequently be done as a 

proof of fatigue with a number of cycles = 1. However, a proof against yield- and rupture 

limits would be more meaningful. 

3.6 Checking the manufacturing 

It is also necessary to check how the toothing is to be manufactured, if it is based on the 

desired tooth profile, in order to calculate the geometry required for manufacturing the 

necessary tools. Once decided upon the various production steps, it is necessary to calculate 

the resulting tooth profile with the help of a final simulation of the manufacturing, see Fig. 

3.5-6, at left. This can now deviate from the desired tooth profile, see Fig. 3.5-6, at right, and 

it must be checked (concerning strength, meshing interference, etc.) whether these deviations 

are acceptable. It is not enough to specify a toothing and send it for production; also here, a 

dialog involving calculation, construction and production is indispensable. 

Figure 3.6-1 Left: Manufacturing Simulation with three Tools (Pre-machining, Protuberance Cutter, 

Grinding Wheel). Right: Difference between theorectical and manufactured Root Profile. 

3.7 Data transfer to CAD platforms 

Now, the calculated toothing data can be sent to the CAD platform that will produce the 

drawings; here, gear data and the 2-D and 3-D data are especially interesting. The goal is to 

display in the toothing production drawings all relevant details, exactly as previously 


dimensioned and optimized. This demands a smooth data transfer from the toothing software 

to the CAD platform. 

Figure 3.7-1 KISSsys 3D-Gearbox Geometry: Transfer to a CAD Platform (e. g. Pro-Engineer). 

Figure 3.7-2 KISSsoft 2D-Toothing and Die Stamp Data: Transfer from the Calculation to a CAD 

Platform (here, Inventor). 

3.8 Calculation for the certification 

For the gearbox certification it necessary to be sure that the previously mentioned proofs are 

sufficient for the guidelines and standards. The certifier’s guidelines prescribe, partially in 

detail, how the mentioned verifications have to be carried out. The relevant guidelines 

especially establish the so-called K factors. Also prescribed are the target safety factors 

whereas these, once again, depend upon the characteristics of the employed material which 

are not prescribed. 

3.8.1 Application factor K A 

A load spectra for the toothing dimensioning can be easily replaced by a nominal load and an 

application factor K A . The calculation of K A can, e. g., be done according to DIN3990, Part 6, 

Method III or to AGMA6006 simplified as follows: 


T 

eq 

K 

A 

= , 

Tn 

T 

eq 

⎛ 

⎜ 

= ⎜ 

⎜ 

⎝ 

∑ i 

i 

∑ 

n * T 

i 

n 

i 

p 

i 

⎞ 

⎟ 

⎟ 

⎟ 

⎠ 

1/ p 

p = S-N Curve Slope 

n i = Stage i Load Change 

T i = Stage i Torque 

Because the equivalent torque calculation for the toothing dimensioning with the derived K A , 

does not consider fatigue strength it is thus rather conservative. 

The S-N Curve slope p changing for different materials and treatments, as well as, for root 

and flank, several different K A values (one for each p) have to be determined that which is not 

very practical. Therefore, the calculation should generally ignore the application factor and 

use instead a damage accumulation, e. g., as in DIN 3990 or ISO 6336:2006, Part 6. 

3.8.2 Load distribution factor Kγ 

Because of manufacturing tolerances and strains, the load distribution among the load paths 

(planets) is not balanced. Therefore, for the calculation of planetary gear trains a load 

distribution factor K γ will be used. The suggested values for wind turbine gearboxes strongly 

vary according to the source, see Fig. 3.8-1. To improve the load distribution between the 

planets, it is possible to equip individual planet gear set components (sun, ring and planet) 

with elastic or floating bearings, e. g., floating sun shafts, or elastic ring bearings. Another 

solution would be the use of a flexible planet bearing as an elastic element. The Flexpin 

allows planet radial or circumferential alignments. The effect of this flexible planet bearing 

can be seen on the chart of Fig. 3.8-1 as the difference between the lines “MAAG without and 

with Flexpin”, which are based partly on measurements and partly on experience values. The 

K γ values proposed by MAAG will surely be included in the new AGMA 6123 version 

1.6 

1.5 

K gamma 

1.4 

[-] 

GL 

DNV 

AGMA6123 

MAAG ohne w/o Flexpin / AGMA6123, Appl. Level 3 

MAAG mit w/ Flexpin / AGMA6123, Appl. Level 4 

IEC 61400 

1.3 

1.2 

1.1 

1 

3 4 5 6 7 8 

Anzahl Planeten [-] 

Figure 3.8-1 Load Distribution Factor as a Function of the Number of Planets 

Measurements show that K γ values sink with increasing loads because manufacturing 

tolerances loose importance when compared with the load-dependent strains. However, they 

are expensive and only admit conclusions for the product K v *K γ . The previously given 

approximate values can only be taken as upper limits. With low K γ values being possible, 

solutions with more than three planets are for the first time economically feasible. For 


instance, with five planets and an actual measured K γ =1.12, it is possible to transmit 95% of 

the torque possible with seven equally wide planets and a K γ =1.50 (conservative assumption / 

guidelines). This, again, permits higher stage ratios and provides more space for the design of 

the planet carrier. 

3.8.3 Face load factor K β 

The meshing force distribution over the toothing width and its effect upon the flank- (K Hβ ) 

and root (K Fβ ) loads are described by the face load factor K β . Besides the simplified 

calculation described in the standards, the guidelines for wind turbine gearboxes demand a 

detailed load distribution numerical calculation when a required minimum value (K β ≥1.15) 

should be further reduced. For this purpose, there are several calculation programs available 

such as LVR, Rikor, Plankorr or LPD. 

It is possible to achieve a uniform load on the tooth width with a toothing correction. In 

general, thin toothing face load factors are more favourable than those for wider ones. Once 

again is the Flexpin mentioned here since it keeps the planets from overturning under load 

(thus directly reducing K β ) and, by a more favourable K γ permits using five or seven thinner 

planets (with lower K β ). These self-centering systems also permit using still lower K β values 

(1.30 lead to unacceptable contact patterns that must also be detected in practice 

(test run-up). I. e., that already realized gearboxes have K β values between 1.10 and 1.30. . In 

practice, the face load factor K β (especially under load) is mostly lower than the values 

obtained in the calculation. 

3.8.4 Transverse load factor K α 

The transverse load factor takes into consideration the load increase in the flank (K Hα ) and in 

the root (K Fα ) because of pitch errors and irregular load distribution over several teeth being 

meshed. The calculation is done according to ISO 6336. The use of K α =1 is accepted for the 

toothing qualities required for wind turbine gearboxes (e. g., minimum quality 6 for external 

toothing, as per GL guidelines). The face load factor K β having a strong influence on the 

stress behaviour, for the exact calculation of the product K β *K α , a 3D contact analysis is 

required as an alternative and, thus, a combined factor K αβ will be used. 

3.8.5 Dynamic factor K v 

The dynamic factor K ν takes into consideration the load increase on the flank (K Hν ) and on 

the root (K Fv ) on account of toothing rigidity variations during the meshing. When the 

frequency of the toothing rigidity variations / speed is directly comparable to the meshing’s 

own frequency, additional dynamic forces will occur. The calculation is done following ISO 

6336, Method B and distinguishes three speed areas (sub critical: N1) defined by the reference speed N (pinion speed n 1 compared with the 

resonance speed n E1 ) where N takes into consideration the reduced toothing mass m Red and 

the toothing rigidity c γ . 

n1 

mred 

N = = 2πn1 

z1 

, K v 

= f (N) 

n 

c 

E1 

γ 


Because of the low speed, wind turbine gearboxes will be operated in the sub critical area and 

the K ν values will be accordingly set. The certification directives for wind turbine gearboxes, 

as well as the relevant standards estipulate a K ν ≥ 1.05 value. Should a lower value be used, a 

measurement or more detailed calculation must be carried out. 

3.8.6 Required calculation safeties 

The required, calculation safeties are specified in guidelines. Determining the really required 

safeties is difficult and requires a comprehensive field experience. The know-how of these 

required safety factors represents for the gearbox manufacturer an enormous capital because it 

cannot be bought; only acquired. 

Guideline Proof according to S F (Fatigue / static) S H (Fatigue / static) 

AGMA6006 AGMA2101-C95 1.0 1.0 

AGMA6006 ISO6336 1.56 1.25 

GL Guidelines ISO6336 1.5 (1.4) 1.2 (1.0) 

Danish WT Cert. Doc. ISO6336 1.45 1.2 

IEC61400 ISO6336 1.56 1.25 

3.9 Documentation 

All calculations have to be documented so that they can be submitted to and checked by the 

certification. Documentation costs increase steadily and is necessary here that it could be 

automatically produced. 

4 Summary 

4.1 Is that all? 

No. Toothing calculation runs an important role in gearbox dimensioning influencing also the 

design of other components (shafts, bearings, unions, etc.), housing and lubrication. Their 

dimensioning and calculation is, once again an own procedure whose description is far 

beyond the scope of this article. 

Furthermore, it is clear that calculation on its own does not lead to a trouble-free gearbox 

operation. In this context, it is especially necessary to mention gearbox test, operation 

management and control. The calculation is just to be seen as an isolated, necessary but not 

sufficient step in a higher-ranking procedure. 

4.2 Calculation methodology safety 

Not only the gearbox manufacturer but also the suppliers, installation manufacturers and 

operators should know the calculation methodology. Only then could they be in an equalrights 

position to have a qualified dialog with the actual suppliers and customers. The risks 

inherent to the acceptance officer of a gearbox or installation will then be transparent and 

could be mutually shared. 

The calculation process should be as such implemented and controlled. Still, it is 

unfortunately that, also among gearbox manufacturers, it will not consistently be seen as a 


process which must work in all departments in a self-evident way. Past are the days in which 

the calculation department calculates something, then the manufacturer builds something else 

and in the end, the production produces something different. To avoid this, we need tools that 

could be employed during the entire process. These tools must also be in a position to convey 

information in a safe way from component suppliers (e. g., gear manufactures) to gearbox 

manufacturers and then, via equipment manufacturers, to the end customers (the operators). 

The latter would thus be able to take care of maintenance and repairs under their own 

responsibility because all the relevant information will be available, even when the 

maintenance contract with the equipment manufacturer has expired. 

4.3 What next? 

In gearbox manufacturing, the calculation must be conceived as a process which also involves 

manufacturing and production. By many gearbox manufacturers it is not yet introduced the 

need for all departments to intensively intercommunicate, being still strongly obstinate in 

pursuing the department-thinking mentality with the result of losing much information and 

energy at the many interfaces. . 

In the wind energy area, the calculation conception must also include, in addition to the 

gearbox manufacturer, the load team, the equipment manufacturer, certification officers and 

the end customer. Besides this, it is necessary some effort on part of the equipment 

manufacturer and, especially, the operator, in order to be able to collaborate in this process. 

The dialog with the gearbox manufacturer requires a considerably amount of knowledge 

which the certification officers must possess, by the equipment manufacturers strongly 

disappears and, by the operator rarely exists. 

This ought to be changed! 

5 Bibliography 

U. Giger, G.P. Fox, Leistungsverzweigte Planetengetriebe in Windenergieanlagen mit 

flexibler Planetenlagerung, ATK03 

R. Grzybowski, B. Niederstucke, Betriebsfestigkeitsberechnung von Getrieben in 

Windenergieanlagen mit Verweildauerkollektiven, Allianz Report 2004 

R. Poore, T. Lettenmaier, Alternative Design Study Report: Wind PACT Advanced Wind 

Turbine Drive Train Designs Study, NREL/SR-500-33196 

H. Dinner, Gleichberechtigter Dialog als Erfolgsrezept, Verzahnungsberechnung für 

Windenergieanlagengetriebe, Antriebstechnik 5/2006 

F. D. Krull, T. Siegenbruck, Windenergieanlagen fordern hohe Leistungsdichten, Ermittlung 

der Breitenlastverteilung in Planetengetrieben, Antriebstechnik 9/2004 

H. Dinner, Integrated Dimensioning, Optimization, Verification and producing Drawings for 

Wind turbine gearboxes, Planet Trains, Haus der Technik, März 07

Gearing analysis for wind turbine, seen as a process - KISSsoft AG

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