Iso_6336_hohn.pdf

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Nomenclature

a [mm] center distance

b mm ace w t

ß [°] helix angle

c y mm•µmmean value of mesh stiffness per

unit face width

εα [-] transverse contact ratio

F t normal transverse load in plane

o act on

F n [N] load, normal to the line of contact

transverse tangential load at

reference cylinder per mesh

f a [-]component o equ va ent

misalignment

K A - app cat on actor

K α - transverse load factor

K ß [-] ace oa actor

K [-] dynamic factor

T 1 m torque at pinion

pC [N/mm2]

ertz an contact stress at t e

pitch point

- gear rat o

H 0 [N/mm2] nominal contact stress

H 1 [N/mm2] contact stress on p n on

v [m/s] tangential velocity

Z B/D [-]Single-pair tooth contact factor

for pinion wheel

Z E - e ast c ty actor

Z H [-] zone factor

Z β [-] helix angle factor Z ε - contact ratio factor

Influences of Load Distribution and

Tooth Flank Modifications as Considered in aNew, DIN/ISO-Compatible Calculation Method.

Bernd-Robert Höhn, Peter Oster and Gregor Steinberger

(This article first appeared in the Proceedings of

IDETC/CIE 2007 ASME 2007 International Design

Engineering Technical Conference & Computers and

Information in Engineering Conference, September

4–7, 2007 in Las Vegas.)

Introduction

Modern gears are designed with helical teeth to improve

their noise behavior and the pitting load capacity. Therefore,

a ver e ca cu at on met o to eterm ne t e p tt ng oa

capacity of helical gears is essential.

ISO 6336-2 and DIN 3990–Part 2 calculate a higher-

endurance torque for helical gears than for spur gears of the

ame size and material, but experimental research on the pittingoa capac ty o e ca spur gears s ac ng e s. , .

Management SummaryIn experimental analyses, the pitting load capacity of

case-carburized spur and helical gears is determined in

back-to-back test rigs.

Included for testing are one type of spur gear and eight

types of helical gears, with tests for the determination

of influences of varying load distribution, overlap ratio

and transmission ratio. The test results are presented

and evaluated on the basis of the pitting load capacity

calculation methods of ISO 6336-2/DIN 3990–Part 2.

A new DIN/ISO-compatible calculation method for

pitting load capacity is presented. This new calculation

method analyzes helical gears more adequately than ISO

6336-2/DIN 3990–Part 2, and has the ability to consider

tooth flank modifications. The new calculation method is

applied to test results and gears of a calculation study. It

shows better agreement with the experimental test results

than the present ISO 6336-2/DIN 3990–Part 2.

Pitting Load Capacityof Helical Gears

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GEAR TECHNOLOGY 00

Table 1: Gear geometry of the test gears

type Gk, S0, Slk and Stk

Test Type Gk S0 Slk Stk

center

distancea mm 112.5

normal

module mn mm 4. 4.2

number

of teeth z

24/2 22/24

ace width b mm 27.6

helix angle β ° 0 29

addendum

odification

factor

- 0.270 .100

- 0.266 .077

tip diameter1

mm 119.4 117.7

2mm 123.9 127.3

working pitch

iameter

mm 110.2 107.6

mm 114.8 117.4

normal

pressure

α ° 20

ransverse

contact ratio ε

verlap ratio ε 0 1.0

tooth ank modi cation

generated

relie- - no no no yes

tip relief

pinion/wheel

short/

reference

dgvdfxchn

f g h f h f v

� = 0 °

� = 29 °� = 21 °� = 14 °

F gure —Endurance contact stress of the spur and hel cal test gears

accord ng to ISO 6336-2/DIN 3990–Part 2 (Ref. 0).

hus the research project FVA 284 I/II “Helical Gear”

e . was n t ate to ana yze t e p tt ng oa capac ty

o e ca gears, t eoret ca y an exper menta y. pur an

helical gears of the same size and material batch were tested

to determine the influence of the helix angle. The endurance

contact stresses were calculated according to ISO 6336-2/

– art , ase on t e exper menta y eterm ne

at gue-en ura e torques. e resu ts are s own n gure

, which shows that the expected pitting load capacity ofσ

H 0 = 1, 00 N/mm is only reached by the spur gears, not

by the helical gears. Consequently, the calculation methods

accor ng to - – art eterm ne t e

p tt ng oa capac ty o spur gears more accurate y t an or

helical gears.

n order to confirm these results, additional tests (Ref.

2) were conducted. These tests prove the main result of

e . — .e., t e ca cu ate p tt ng oa

capac ty or e ca gears s too g . onsequent y, t e

calculation of helical gears according to ISO 6336-2 has to

be reconsidered.

Optimum tooth flank modifications for uniform pressure

str ut on resu t n max mum p tt ng oa capac ty. ence

t e researc project c ana yze t e n uence o

everal tooth flank modifications on the pitting load capacity

of helical gears.

he theoretical part of this research project included

t e eve opment o a new -compat e ca cu at on

met o to eterm ne t e p tt ng oa capac ty o gears,

especially helical gears. This new calculation method analyzes

helical gears more accurately than the existing ISO 6336-2/

DIN 3990–Part 2 and includes the influence of tooth flank

mo cat ons.

es rogram an es ears

One spur and eight helical gears were ground with

different tooth modifications for varying load distribution.

Table 1 summarizes the main geometry and details on tooth

mo cat ons o spur gears an t e e ca gears ,

an t .

he gear type Gk corresponds to the gear type of FVA

284 Ib (Ref. 12) and, except for a small lengthwise crowning

on the pinion, the reference gear of FVA 284 I/II (Ref. 10).

ence t s gear type s use to ver y t e resu ts w t t e spur

gears o an . e e ca gear type as

no modifications, except for a small lengthwise crowning on

the pinion. Type Slk has a long tip relief on the pinion and

wheel to achieve uniform pressure on the line of contact. The

gear type t s mo e w t a generate re e an a s ort

t p re e or opt ma y un orm pressure str ut on. e

necessary modifications were determined according to the

calculation method in Reference 11, which is based on the

pressure distribution calculated with the program RIKOR G

e . . e w o e ca cu at on s nc u e n t e program

RIKOR H e . .

he test gears are made from case-hardened steel8CrNiMo7-6. The gears were case-carburized and ground

after the teeth were cut. The case depth conformed to Eht ≈

0.1 ·n according to DIN 3990–Part .

Measuring Gear Quality

e test gears were measure on a er nge n erg

-coor nate measur ng mac ne. e qua ty was

determined according to DIN 3960 by measuring the profile

along the involute and across the flank, as well as measuring

the pitch deviation and the true running. The quality of all test

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test pinion 1

shaft 1

test wheel 2

shaft 2

slave wheel 4

slave pinion 3 driv ing shaft

load clutch

torque measuring clutch

F gure 2—FZG back-to-back test r g w th a = 2.5 mm.

Gk S0 Slk Stk

f d s f a s e t f g d

� H 1

Figure 3—Experimentally determined endurance contact stress σH1

50% failure probability, according to ISO 6336–2.

Table 2:

Main lubricant data of FVA reference lubricantno. 3 + 4 % Anglamol 99

v scos ty

kinematic

v scos ty

at : v mm s

ynam c

v scos ty

at : η m as

at 60 °C: η40 m as

at 80 °C: η40 m as

gears averaged a value better than DIN .

test gears a a an roug ness o = . … . µm.

Such a smooth flank roughness minimizes micropitting risk

and its influence on the pitting load capacity.

Test Rig

p tt ng tests were run n ac -to- ac test r gs

w t a center stance = . mm g. . ese test r gs

have a closed-power circuit with helical slave gears. Both test

rigs are equipped with a speed controller in a range of n =0… 3,100 min-1. The helical hand of the slave and test gears

s es gne to cance t e ax a orces on eac s a t.

es on ons

According to the test conditions in Reference 4, the tests

were run with constant load until the pitting area exceeded

4% of the active flank area of one tooth, or until a maximum

running time of 0·10 oa cyc es on t e p n on. test gears

were run n or , oa cyc es on t e p n on, w t a norma

contact stress o H 0

= , mm , an , oa cyc es

on t e p n on w t H 0

= , mm2. e p n on spee was

n1 = 100 min-1 Test lubricant was the FVA-referenced oil

No. 3 mixed with four percent Anglamol 99. Table 2 shows

the lubricant viscosity. The lubricant was injected in the gear

mes w t a temperature o an a vo ume ow o Qe = –

m n. tests were run w t a r v ng p n on an r ven

wheel. The pinion speed was n1 = 3,000 min-1. Consequently,

the circumferential speed at the pitch point was vt = 17.3 m/sfor type Gk and v

t = 16.9 m/s for S0, Slk and Stk.

va ua on o e es esu s

Figure 3 shows the contact stress σ H 1

calculated according

to ISO 6336-2 and based on the fatigue-endurable torque for

0% failure probability. The results are shown in Figure 3.

Figure 4 shows the fatigue-endurable torques on the pinion

o t e our gear types— , , an t —w c ave t e

ame transverse contact ratio of εa = 1. . In comparison to

the referenced spur gear Gk, the best modified helical gear

type Stk transmits approximately 32% higher torque, while

the endurance contact stress according to ISO 6336-2 isower. t out an mo cat ons gear type , t e

increase of torque is about eight percent compared to the spur

gear reference; the endurance contact stress according to ISO

6336-2 is 19% lower.

Summary of test results:

• e ca gears w t equa transverse contact rat o trans er a

higher torque than spur gears.

• For helical gears, the experimentally determined endurance

con ac s ress σ H

is smaller than the value calculated

according to ISO 6336-2.

• oot an mo cat ons t at g ve un orm stressdistribution increase the pitting load capacity.

New DIN/ISO-Compatible Calculation Method

Following is a practical calculation method. This method

is independent of a calculated pressure distribution, and

compat e w t t e actua - – art .

Since the maximum contact stress is approximated with

imple equations, the pitting load capacity can be determined.

It is planned to consider this calculation method in the

ISO 6336-2 as method B.

n , a ca cu at on met o was eve ope ,

based on the knowledge of the local contact stresses. This

method is described in Reference 11.

The modernized calculation method presented here is

called RV II (Rechenverfahren II), and uses double-signed

ar a es e H 0

. e actua - uses no s gne

ariables; e.g., σ H

Nominal contact stress σ" H 0

See Equation 1 on page 49.

defines the basic value σ" H

used in calculation method II

(RV II):

The factors Z H

, Z E and Z

ε are identical to the same factors

in ISO 6336-2.

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GEAR TECHNOLOGY 00

ac orβ. ccor ng to - , Z

β s ca cu ate

ase on t e resu ts o t e researc projects e .

, e . an t e present researc program, t e

factor Z "β is redefined as

Z "β is an empirical factor, which takes the research results

for helical gears and theoretical thoughts into account. For

gears with only a small helix angle, the factor Z should be

m ar to t e actor Z β, accor ng to - . s actor

is valid for helix angles between 0° and 3 °. The factor Z "β is

hown in Figure .

Contact stress σ" H

. The contact stress σ" H

is calculated

according to Equation 3. Compared to the nominal contactress

H 0, t e contact stress

H cons ers stress ncreas ng

influences resulting from non-uniform load distribution,

additional dynamic force and so on.

he load factors K A, K

H β and K

H are the same as in the

actual ISO 6336-1.

Factor Z" B/D

. The single-pair tooth contact factor Z " B/D

considers that the relevant contact stress for pitting is not

necessar y t at o t e p tc po nt. t quat on , t e actor Z "

B/D can be calculated to estimate the maximum contact

ith Z B/D

according to ISO 6336-2 and f Ca1,2

according to

equations ,6,7,8 or 9 (Table 3).

he factor Z B/D

is from ISO 6336-2. The contact stress of

point B (inner point of single contact) is important for spur

gears. o or spur gears t e actor Z B/D

s t e same as t e

factor Z B/D

, according to ISO 6336-2. In this case the factor

f ZCa1,2

is 1.0 (Table 3). Thus the calculation method for spur

gears remains unchanged.

Factor f ZCa

. The tooth flank correction factors f ZCa

or p n on an w ee cons er t e g er contact stress at

the beginning and the end of the path of contact for helical

gears, for the case where there are inadequate tooth flank

modifications. Table 3 describes the determination of the

tooth flank correction factor.

e toot an correct on actor ZCa

epen s on t e

load and considers inadequate tooth flank modifications

through comparison of the existing and required tooth flank

modifications. Here only the amount of profile modifications is

taken into account, but an adequate length of the modifications

Gk S0 Slk Stk

d s f s d y g f

F gure 4—Fat gue-endurable torque on p n on of the tested gear types

Gk, S0, Slk and Stk.

0° 5° 10° 15° 20° 25° 30° 35°

helix angle �

Z �" xv c

ISO 6336-2

RV II, new calculation method

F gure 5—Hel x angle factor "B accord ng to Equat on 2 n compar son to

B accord ng to ISO 6336–2.

Table 3: Determination of the tooth flank

correction factor f ZCa1,2*

spur gears (β = 0 °),

with and without

odifications:ZCa1,2

= 1.0 (5)

elical gears (β > 0 °),

with and without

modifications

(tip relief, root relief):

1.1≤ f ZCa 1,2

≤ 1.2

Ca: effective amount of profile

odification

Ca0: tooth deflection

elical gears (β > 0 °),with profile and lengthwise

odifications,

calculated with a 3D-load

istribution program for working

load and operated at this load:

ZCa1,2 = 1.0 (7)

with profile modifications,

esigned for working load and

perated at this load:

ZCa , = 1.1 (8)

without modifications and with-

out calculating f ZCa

, according

o equation (6):ZCa ,

= 1.2 (9)

F Z " Z Z Z " Z Z pσ"

t �E H C H 01/2

···== �

Equat on .= cos Z

H � H v A H 0 B/D1/2 H K K K K " Z "" =

2,1 ZCa B/D B/D f Z Z" =

ZCa1,2 Ca

CaCa1f

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Gk S0 Slk Stk

d f s f s f s a

ISO 6336-2

� H 1

� ' ' H 1

G S7 S15 S22 S30 S37

f d s f

ISO 6336-2

T 1 [ N m ]

Table 5: Permissible torque for σHP

= 1500 N/mm2 according to

ISO 6336-2 and to the new calculation method (RV II)

ype ZCa1 Z

B ´ T

1,ISO6336 [Nm] 1, RVII [Nm]

G 1.0 1.02 1.02 91 91

S7 1.01 1.01 1062 1044

S15 1.01 1.01 182 103

S22 1.0 .0 1372 171

S30 1.0 .0 1675 1256

S37 1.0 .0 1981 1287

s requ re . t e w o e an topo ogy s to e cons ere , t e

calculation method according to Reference 11 can be used.

For spur gears, the tooth flank correction factor f ZCa

.0. Hence it is assumed that the contact stress of the inner

point of single contact (B) is higher than the contact stress of

t e start ng po nt w t ou e-toot contact, w c s t e

usual case for practical spur gears.

If helical gears have no tooth modifications or only

tandard modifications—like tip or root relief—the factorf ZCa1,2

is calculated according to Equation 6.

e va ue ranges rom . to . . or e ca gears

with adequate tooth modifications, which cause maximum

contact stress near the pitch circle, the factor f ZCa

is 1.0.

These adequate tooth modifications are normally generated.

For helical gears with tooth modifications designed for the

wor ng oa an operate at wor ng o a , t e actor ZCa

is 1.1. For helical gears without modifications a tooth flank

correction factor f ZCa

= 1.2 can be estimated.

Existing and required profile modifications. The amount

of profile modification C a in Equation 6 is the actual profilemo cat on on t e toot an n m crons. C

a0 s t e requ re

amount of profile modification in microns for having the

maximum contact stress around the pitch point, not at the

beginning or the end of the path of contact. The required

profile modification can be calculated according to the

manu acturer s exper ence or recommen at ons, accor ng to

Niemann/Winter (Ref. 6), Sigg (Ref. 9) or Equation 10.

e actor C a0 epen s on t e oa or a recommen at ons.According to Equation 10, the required profile modification is

calculated by the nominal tangential load F t , the face width

and the stiffness c γ , according to ISO 6336-1.

Applying the New DIN/ISO-

ompa e a cu a on e o

The following contact stresses are calculated from the

fatigue-endurable torque. Figure 6 shows the contact stresses

on pinion σ H 1

of the test gears according to ISO 6336-2, as

well as the contact stress σ H 1

, as determined by the new

-compat e ca cu at on met o . v ous y t e

calculation method RV II gives the same contact stress for the

pur gear as ISO 6336-2. However, for helical gears a higher

contact stress is calculated.

The contact stresses of the different gear types σ H 1

accor ng to - range n a sprea o ± o t e

mean value. According to RV II, the contact stresses σ" H 1

range in a spread of ± 2% of the mean value. Especially for

the helical gears with practice-relevant modifications (Slk

and Stk), the calculated contact stresses (RV II) are nearly the

ame as t e contact stress o t e spur gear.

Consequently the new calculation method RV II

corresponds better to test results than the ISO 6336-2

calculation method.

F gure 6—Contact stress accord ng to ISO 6336–2 and to the new

calculat on method RV II.

Figure 7—Permissible torque according to ISO 6336–2 and to the new

calculat on method RV II.

b / F Ca

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Theoretical Study to Determine the

In uence of Helix Angle on the Endured Torque

e o ow ng stu y est mates t e perm ss e torque as a

function of the helix angle according to the new calculation

method. Therefore the contact stresses according to RV II for

ix different gears (Table 4) were calculated. All gears have

t e same center stance, ace w t , transverse pressure

ang e, transverse mo u e, num er o teet , transverse contact

ratio and constant tip diameter. The permissible contact stressis the same as in ISO 6336-2.

he maximum endurable torque can be determined for

t e con t on w ere t e contact stress accor ng to t e new

ca cu at on met o s equa to t e perm ss e contact stress

according to ISO 6336-2:

perm ss e contact stress o HP

= , mm s

assumed for all gears. The load factors and f ZCa

1 are set to 1.0

(K ges = K A · K v· H β· K H = 1.0 and f ZCa 1 = 1.0).

onsequent y, t s assume t at a e ca gears ave

un orm oa str ut on, resu t ng rom a equate an

modifications.

he calculated torque T 1 on the pinion and the main factors

according to the new calculation method are printed in Table ,

an t e perm ss e torques are s own n gure . v ous y,

t e perm ss e torque ncreases w t ncreas ng e x ang e.

In comparison to the spur gear (G), the helical gear S30, with

a helix angle of 30˚, has a 30% higher calculated torque.

Conclusionse resu ts o t e exper menta part o t s researc project

prove that the calculation of the contact stress according to

ISO 6336-2/DIN 3990–Part 2 isn’t accurate for helical gears.

ence a new calculation method to determine the pitting

load capacity was developed. This calculation method is

compat e w t - – art . t ta es t e

maximum contact stress into account and can be used as a

new method B. This calculation method, called RV II, treats

helical gears more precisely than ISO 6336-2, and is capable

of accounting for tooth modifications. For spur gears the new

ca cu at on met o s equa to - .

A knowledgments

The project “Einfluss der örtlichen Hertz´schen

Pressung auf die Grübchentragfähigkeit einsatzgehärteter

Stirnräder” was unded by the FVA—Forschungsvereinigung

Antriebstechnik e.V. (FVA 284 Ic).

References

. DIN 3990, Teil 2: Tragfähigkeitsberechnung von Stirnrädern

- erec nung er r c entrag g e t. eut er ag er n,

2. Döbereiner, R. Tragfähigkeit von Hochverzahnungen Gerin-

ger Schwingungsanregung. FVA-Vorhaben 2 7, Heft 71,

ran urt, .

3. Haslinger, K. Untersuchungen zur Grübchentrag fähigkeit

Profilkorrigierter Zahnräder . Dissertation TU München,

4. Hösel T. and J. Goebbelet. Empfehlungen zur Vereinheit-

c ung von an entrag g e tsversuc en an er teten

und Gehärteten Zylinderrädern. FVA-Merkblatt Nr. 0/ ,

Frankfurt, 1979.

. ISO 6336-2: “Calculation of Load Capacity of Spur andHelical gears—Calculation of Surface Durability (Pitting).”

rst e t on, .

6. Niemann, G. and H. Winter. Maschinenelemente Band II .

Springer Verlag Berlin, Heidelberg, New York, London, Paris

and Tokyo, 1989.

7. Otto, M. “Ritzelkorrekturprogramm RIKOR H.” FVA-

orsc ungsvor a en , e t , .

8. Schinagl, S. “Ritzelkorrekturprogramm RIKOR G.” FVA-

Forschungsvorhaben 30/IV, Heft 481, 2000.

. Sigg, H. Profile and Longitudinal Corrections on Involute

Gears. Semi Annual Meeting of the AGMA, Paper 109.16,.

0. Stahl, K. and O. Hurasky-Schönwerth. Experimentelle

und Theoretische Untersuchungen an Schrägstirnrädern.

FVA-Vorhaben 284 I/II, Heft 608, Frankfurt, 2000.

1. Stahl, K. Vorschlag für eine Erweiterte Berechnungs-

met o e zur r c entrag g e t nsatzge rteter

gerad- und Schrägverzahnter Stirnräder. FZG-Bericht 2 0,

München, 2000.

2. Steinberger, G. DIN-Vergleichstest zur Grübchen-

tragfähigkeit gerad- und Schrägverzahnter Stirnräder. FVA-

or a en , e t , ran urt, .

HP H " =

Iso_6336_hohn.pdf

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