Gearing Analysis for Wind Turbine

8/3/2019 Gearing Analysis for Wind Turbine

http://slidepdf.com/reader/full/gearing-analysis-for-wind-turbine 1/18

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

Showing the teeth at the wind…

H. Dinner, KISSsoft AG, [email protected]

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 gearboxmanufacturer 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.

G e a r i n g

a n a l y s i s f o r w i n d t u r b i n e ,

s e e n a s a

p r o c e s s




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




Hydraulic torque limiting: Henderson Gearbox Torque limiting: Electric motor (M).

Test installation in Orkney Island

Hydrodynamic differential??? gearbox:

Voith WinDrive

Hydrostatic differential??? gearbox:

Windtec/Wikov/Orbital2Figure 2.2-1 Several Gearbox Concepts

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.

M G




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, acomprehensive 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 afew 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.

Ex ort→CAD

Documentation

Dimensioni

Loading

O timizationVerification

Production

Certification

Auslegung

Optimierung Nachrechnung

HerstellungCAD Export

Dokumentation

ZertifizierungBelastung

Export→CAD

Documentation

Dimensioning

Loading

O timizationVerification

Production

Certification




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 planetarystage, 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.

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

Single Meshing

Stiffness

Stiffness

(N/mm/µm

(N/mm/µm

Number of Meshing Points (-)

Number of Meshing Points (-)

Single Meshing




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.




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 stressanalysis 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.

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, εα=1.73.

Load Distribution

Longitudinal Axis YLongitudinal Axis Y

Load DistributionLine Load Line Load

Load Distribution

Hertz Stress and maximum Root Stress durin Meshin

Hertz Stress and maximum Root Stress during Meshing

Last Calculation Situation (Z12), Date/Time:Hertz Stress and maximum Root Stress durin Meshin

Hertz Stress and maximum Root Stress durin Meshin

Last Calculation Situation (Z12), Date/Time:




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.

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.

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

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

YF3 YFS3 SF3

ISO6336 (erweitert) B Grafische MethodeGra hical Method

(extended)

0

0.5

1

1.5

2

2.5

3

YF3 YS3 SF3

ISO6336 C

ISO6336 B

ISO6336 (erweitert) B Gra hical Method

(extended)

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/mm2

; ro_r= 19.3 mm)Maximum Shear Stress Depth (mm) 0.274EHT 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 P ressure)

Material measured Value (from Database)

Vickers Hardness (HV)




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) addictiveshave 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.

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.

Temperature at Tooth Contact (θB)

Date/Time:

Temperature at Tooth Contact [θ B ]

θ B

X Si

Helpθ B

Temperature at Tooth Contact [θ B ]

Maximum Contact Temperature 301.2Scuffing Probability 26.09 %

X Si

Temperature at Tooth Contact (θB)

Help




Figure 3.5-5 3.6 MW Wind Turbine Gearbox: λ Values for the 1st

and 2nd

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 rupturelimits 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

HelpHelp Help




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 guidelinesespecially 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:




n

eq

AT

T K = ,

p

i

i

i

p

ii

eqn

T n

T

/1

*

=

∑∑

p = S-N Curve Slope

ni = 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 K γ

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

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

1

1.1

1.2

1.3

1.4

1.5

1.6

3 4 5 6 7 8

Anzahl Planeten [-]

K gamma [-]

GL

DNV

AGMA6123

MAAG ohne Flexpin / AGMA6123, Appl. Level 3

MAAG mit Flexpin / AGMA6123, Appl. Level 4

IEC 61400

/

/o




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

(<1.15) in the calculation.

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 onthe 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: N <<1; critical: N ~1 and

overcritical: N >>1) defined by the reference speed N (pinion speed n1 compared with the

resonance speed nE1) where N takes into consideration the reduced toothing mass mRed and

the toothing rigidity cγ.

γ

π c

m z n

n

n N red

E

11

1

1 2== , )( N f K v =




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, operationmanagement 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 equal-

rights 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 gearboxmanufacturers 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

Documents

Gearing Analysis for Wind Turbine