Experimental and analystical scuffing criteria for FZG gears

Transient Processes in Tribology G. Dalmaz et al. (Editors) 9 2004 Elsevier B.V. All rights reserved

651

Experimental and Analytical Scuffing Criteria for FZG Gears Castro, J. a

b

a,

Sottomayor, A. a and Seabra, J. b

Departamento de Engenharia Mecfinica, Instituto Superior de Engenharia, Instituto Politdcnico do Porto, Portugal ([email protected], [email protected]). Departamento de Engenharia Mecfinica e Gest~o Industrial, Faculdade de Engenharia da Universidade do Porto, Portugal ([email protected]).

Experimental gear scuffing results were obtained in the FZG test rig for wide ranges of the applied torque, tangential speed, base oil viscosity and bath oil temperature, and for FZG type A and type C gears. For restricted and particular operating conditions all scuffing criteria seem to be valid, however no one seemed appropriated for the wide ranges of operating conditions considered. A preliminary analysis of the experimental results shows that the oil bath temperature and the friction coefficient between gear teeth have a very significant influence on the scuffing load carrying capacity of the FZG gears. An expression for the friction coefficient between FZG gear teeth was developed taking into account the results published by Hohn e al [1] obtained from experimental measurements of the power loss in FZG type C gears lubricated with mineral oils. A scuffing criterion for FZG gears lubricated with base oils is proposed taking into account the following considerations: the traditional PVT scuffing criteria (Alman criteria) is adequate when the aim is to compare the performance of different gear geometries; the FPI (Friction Power Intensity) scuffing criteria, together with the friction coefficient developed, is adequate to evaluate the influence of the torque (or contact pressure) and of the tangential velocity in scuffing [2]; Critical oil bath temperatures were determined, above which the lubricant has no longer the ability to generate an hydrodynamic film and scuffing may occur for any conditions. The scuffing load carrying capacity of the FZG gears is proportional to the difference between this oil critical temperature and the actual bath oil temperature. The scuffing criterion proposed fully agrees with the experimental results. 1. INTRODUCTION For many years the main developments concerning gear scuffing criterion were related to improvements in the prediction of the friction coefficient between gear teeth, which is fundamental for the application of the total temperature and integral temperature criterion [4, 7]. However other important parameters in gear scuffing are the lubricant properties and the bath oil temperature. These parameters interfere directly with the scuffing criteria and indirectly with the friction coefficient. This means they affected all the scuffing criteria based on friction power loss, temperature or critical film thickness.

2. EXPERIMENTAL SCUFFING RESULTS Table 1 shows the results of scuffing tests performed in a FZG test machine [11] (Gear Research Centre at Technical University Munich). Two FZG gear geometries were used: type A gears, 10 mm and 20 mm wide (referenced as A10 and A20 FZG gears, respectively) and type C gears, 14 mm wide, (referenced as C14 FZG gears) [11]. Six base oils, with 4 different viscosity grades, were tested. The most important characteristics of the gears and oils used are presented in appendix 1. Several different types of tests were performed: Variable torque tests (at constant oil bath

652

temperature and rotating speed), variable temperature tests (at constant torque and rotating speed), variable speed tests (at constant torque and oil bath temperature) and also some standard load carrying capacity tests, according to DIN 51354 [10]. In all tests Kroz is the FZG load (torque - Nm) stage, n is the rotational speed of the wheel (rpm) and To is the oil bath temperature (~ There is almost total compatibility between these different test procedures, which is very good for the results analysis. 3. APPLYING SCUFFING EXPERIMENTAL RESULTS

CRITERIA

TO

A new expression for the friction coefficient between FZG gear teeth was developed. This expression takes into account the results published by Hohn e al [1], obtained from experimental measurements of the power loss in FZG type C gears lubricated with mineral oils, and the equation used by Michaelis [3] for FZG gears. Figure 1 show those experimental results and the new definition of the friction coefficient in FZG gears which establishes that,

(,_/

~

Pvza = 0.0257 pO.1.

.o.os

V2.~, qo

uFZG_P0.8

exp_P 1.1

I::1 .....

uFZG_P 1.7

exp_P0.8 uFZG_P 1.4

A

Rt

....... o

(1)

uFZG PI.1

?

~:~i. . . .

i ..........68I ............i.........~ 0 .......i :

J00 ................. 750

:[: 10 ~

i

3 6811 L A10 j 75 [ 2500 7 ............4 ........................-68ii ..............: ........A i 0 .............[. . . . 90 ......... i ..... 2500 ...........7 7 ..........5 .......................68II .......... c i 4 .........i 0 0 ........... -30-0-O-~::i.......5 ......i 6 68II C14 100 i 1500 8 7 150II A10 85 2000 9 8 150II A10 90 2000 8 9 150II A10 95 2500 6 10 150II A20 100 2000 10 11 15011 ! C14 100 3000 7 12 150II [ ...........~ 0 ~ .............i .............1:0:5........ 1500 9 13 150II i A20 ! 105 2250 7 14 150II A10 ii 105 1500 7 15 15011 A10 105 1750 6 150II A10 105 2500 6 ! 7 .........]...........!.50II ...... C14 110 3000 6 18 I 150II C14 110 1500 10

i

............................................................

19 20 21

] i

". . . . . . . . . . . . . .

] .................................

220I 220I 220I

r_ A2_0 . . . . . . A20 A20

1!0 ................3 0 0 0 118 2250 119 1500

220I

!

120

i/:

:

i

!==_8_,,,_j

~7| 8

......... 24

..................2 5

C14

.... i ..........2 2 0 i ............i.........c i 4

26

22011

A10

i

1500

7 ......i 10

..................... i - 2 0 ...........'.............3 0 0 0 ..............~...........7 .........

100

3000

. . . . 27 28 29 30 31 32

..............2.20I!. .......... .....A!0_ ............. 1!_0.......... 2 0 0 0 22011 C 14 ...........120 .......................... 3090 ...........!~ 680I A20 143 1500 [ 680I _ ~ A20 _ 15_0 ~ 1500 ~ 68I i A20 75 ] 3000 f 68I A20 88 3000 100 3000 ....... 34 ............................. 68i ......... I..............~ - 0 ...... [ 113 i 1500 35 68I A20 130 1500 36 68I A20 130 3000 37 15011 A20 105 3000

8 9 8 12 9 5 "" 3 3 4 3 2 5

exp_P 1.4

39

exp_P 1.7

[

220I

i

A20

i20 120

[ 2250 3000

3 5

0.06 0.05 0.04 0.03 0.02

0

Figure 1 -

1000

2000 n (r.p.m.)

3000

4000

Experimental and analytical friction coefficient for type C FZG gears.

Table . 1 -Gear scuffing results......................................... [.... Test

l ...... Oii I Number I Re f.

i !

Gear

~pe

[ Temp .......I n ! ; ...........1 [~.. ( oC ) ..[. (rpm). 1, ~'-Fzc;! ...... I

It may be used to predict the scuffing load stage in each test, considering two of the most common gear scuffing criteria- the Total Temperature (TT) [4] and Friction Power Intensity ( F P I = , u P V) [5] criteria- and the previsions obtained may be compared with the experimental results. Nevertheless, the different expressions available for predicting the friction coefficient between the gear teeth in FZG gears [3, 6, 14, 15] don't affect significantly the predictions of these scuffing criteria. Figure 2 and Figure 3 clearly show that the Total Temperature and the FPI criteria are, in general, not applicable to the experimental scuffing results

653 available, since they predict a very large variation of the critical scuffing values, which are not consistent with the basic concepts of these criteria- Constant Total Temperature and Constant Power Dissipation in scuffing conditions.

and type C FZG gears and how the oil bath temperature affect the scuffing load carrying capacity of FZG gears lubricated with additive free base mineral oils.

However, keeping one of the operating parameters constant (the oil bath temperature, the gear type or the oil type), some consistency was observed between the scuffing predictions obtained with FPI criterion and the experimental results, as shown in Figure 3.

4. NEW SCUFFING CRITERION FOR FZG GEARS

3 A

3 2 2

cD C c A

2 A:C 1 1 1

05

110

120

1 5

125

To (~

Figure 2 -

TT values considering/t = ,llFZG for the base oil ISO VG 220I.

4.1. Influence of the gear geometry

Figures 4 and 5 show the friction power dissipation ( F P I = / a r z a P V) in scuffing conditions along the gear meshing line, for type C and type A FZG gears, respectively. The shaded area A in Figure 4 is equal to the shaded area B in Figure 5. The equality of these areas might be used as the parameter relating scuffing between these two types of FZG gears. Figure 4 and 5 also show that there is no energy dissipation due to sliding friction at the pitch point (I), since the sliding speed is null there. Consequently, there are no conditions for the scuffing failure to occur at point I or to progress beyond that point. Thus, the maximum value of these two areas give an important scuffing factor (SF) and explain why scuffing normally occurs in segment TA for type C gears (pinion root / wheel tip) and in segment /'8 for type A gears (pinion tip / wheel root), that is,

3.5E+08 ",,~ A

SF = max

3.0E+08

l~yz~x Po Vsx dx ,

t~vz~ Po Vs~ dx

C c C

~r"

~

Area I

2.5E+08

9

,

~

,

Area I!

(2)

~ 2.0E+08

If Area I > Area II ~ scuffing in segment TA. If Area II > Area I ~ scuffing in segment Tn.

Air,

"~ 1.5E+08

Expression (2) might be simplified since, according to Figure 4 and Figure 5,

1.0E+08

5.0E+07

i

1

A

2

e

1

0.0E+00 100

110

120 Wo (~

130

TCR140

Figure 3 - F P I values considering r = lUvza for the base oil ISO VG 2201.

and

I

Nevertheless, these scuffing criteria are not able to explain many of the phenomena observed, for instance, how the different geometries of the type A

654 For the same type of gear (type A), Figure 3 suggests that, in scuffing conditions, the Friction Power Intensity (FPI = ktPV) has a linear variation with the oil bath temperature (To). Since the segments TA and TB only depend on the gear geometry, it is acceptable to suppose that the k ~ V T product also show the same linear variation with the oil bath temperature.

3.0E~8

T•_._

2.5E+08 2.0E~8 > r

1.5E+08

J 1.0E+08 5.0E+07 0.0E+00

' ' 1

0.000

0.005

0.010 0.015 W 0.020 R t (m)

0.025

Figure 4 - Variation of the friction power intensity (Iama.APV) along the meshing line of a type C FZG gear.

The power dissipated inside the contact between the gear teeth (the main source of power losses [13]), for a given gear geometry, represented by the laFZC 1'o Vs r product, is responsible for the heating of the oil bath and of the contacting surfaces and their temperature rise. A Critical Lubricant Temperature (TCR) is defined as the limiting temperature for which scuffing occurs for a value of the product ltFZC Po Vs T equal to 0, as shown on Figure 3. Thus,

~vzaeoVsr o~ ( ~ . ro )

(5)

In scuffing conditions the Total Temperature scuffing concept, establishes that

3.0E+08 2.5E+08

TTmax = To + CrfT:

2.0E+08 >

(6)

where Tf is the Flash Temperature [8] and Cry a proportionality constant. Thus

1.5E+08 1.0E+08

r r m = - ro = C : r :

(7)

5.0E+07 0.0E+00 0.005

t 0.010

0.015 0.020 R l (m)

0.025

0.030

Figure 5- Variation of the friction power intensity (laFZc-BPV) along the meshing line of a type A FZG gear.

For a given oil at constant oil bath temperature, these expressions are quite close to the classic Almen (PVT) scuffing criterion [6], since the influence of the contact pressure (Po) and of the sliding speed (Vs) on the friction coefficient is not very significant.

4.2. Influence of the lubricant

Considering that the maximal Total Temperature (TTmo~) and the Critical Temperature (TCR) represent the same concept, it can be assumed that

~-ro

=

Fz~ Po v~ r C

or m

C

PoV =-i(r.,-ro ),

(8)

where C has the units of the thermal conductivity (N/s ~ and is independent from the lubricant, as will be shown hereafter. The Critical Temperature (rcR) is a characteristic of each lubricant. This new scuffing criterion is similar to the Integral Temperature scuffing concept [7], but it clearly indicates the zone on the gear meshing line where the probability of scuffing is higher.

655

The new criterion can be stated as:

Scuffmg Criterion 50.00

If TcR-T~<

~,~z~V~T

(9), scuffing occurs.

f

40.00

C 30.00

4.3. Correlation with experimental FZG gear scuffing results In Figure 6, the /ZFZa PVT product is plotted against the corresponding oil bath temperatures, in scuffing conditions, for the different mineral base oils considered. In all cases the ltrz~ PVT product (at scuffing) decreases when the oil bath temperature increases. Figure 6 also shows that the flrza Po Vs T product is consistent with both types (A and C) of FZG gears.

8.E+06

O A68I

7.E+06

9 "m

6.E+06

Z~'9

"-" 5.E+06

L ~9

',,,,

4.E+06

9

9 "L, am

)"

[] A220I

9

,~,,a,~,?, ,,

9 A220II ",~.

I ~ 3.E+06

- 9 '--~,

.E+06

9

~'

R=0.95 10.00 0.00 0.00

10.00

20.00

30.00

40.00

50.00

T cR-T o (~

Figure 7 - Correlation between experimental and analytical results. Table 2 - Critical Temperatures (TcR) for each mineral base oil considered (C = 1.62xl 05 N/s.~ R = 0.95). Mineral Base Oil TcR (~ ........... 68I 113.0 68II 110.6 150II 124.3 220I 136.7 220II 142.9 680I 170.2

o A680I o C68II

2.E+06 1

A68II

.. A A150II

~_~__ 20.00

'A

C150II

. e C220I

Figure 7 shows the correlation between the scuffing criterion developed and the corresponding experimental results, which is quite good.

Q C220II

0.E+00 75

85

95

105 115 125 135 145 155 180.0

T O (~

170.0

Figure 6 - IUrzaPVT product vs. oil bath temperature

160.0

To.

I: upI I .

gn,up II

150.0

q/"

/

r

1 I I

1

I I

100

1000

~G" 140.0

Table 2 presents the Critical Temperature (Ice) of each lubricant considered, the corresponding value for the equivalent thermal conductivity (C, valid for the materials and gears used) and the corresponding overall correlation coefficient).

"-' 130.0 o

~

120.0 ll0.0 100.0 90.0 80.0

v40(eSt) Figure 8 - Lubricant critical temperatures vs reference kinematic viscosity (40~

656 Figure 8 show the lubricant critical temperatures and the correspondent reference kinematic viscosity (40~ The critical temperature increase with the reference oil viscosity, which means higher capacity to scuffing resistance for higher reference viscosities.

5. DISCUSSION AND VALIDATION OF THE SCUFFING CRITERION 5.1. The Critical Lubricant Temperature concept

The scuffing criterion proposed for the FZG gears is based on three basic ideas confirmed experimentally: 1. For a given gear geometry and lubricant the Friction Power Intensity criterion (FPI = ~I~FZGP V) represents quite accurately the gear scuffing conditions, mainly if the friction coefficient expression presented (Jtrza) is used. 2. The importance of the oil bath temperature in gear scuffing and the existence of critical scuffing temperatures for each lubricant. 3. The scuffing behaviour of type A and type C gears can be compared using the segments TA and TB along gear meshing line. The Critical Lubricant Temperatures (TcR) found for the base oils tested and the FZG gears used,

typically between 110 ~ and 170 ~ (see Table2), might look as relatively low when compared with the scuffing temperatures suggested by the Maximum Total Temperature and Maximum Integral Temperature criteria, normally above 200 ~ and often between 300~ and 400~ However, Yamamoto [9] has clearly identified what he called "the first transition critical temperature - T~", above which the lubricant suffers significant chemical modifications in its molecular structure and lubricant film breakdown occurs. He suggests that this first transition critical temperature is always lower than 180 ~ for mineral base oils, which fully agrees with the critical lubricant temperatures found. 5.2. Scuffing Parameter for FZG gears lubricated with mineral base oils

This Critical Temperature scuffing criterion could be expressed as the FZG Scuffing Parameter (Se) ,

Sp=

PFzGPoVsT C(Tc " _To),

(10)

where SP > 1.0, represents operating conditions (torque, speed, lubricant and gear type) leading to the scuffing failure, and SP < 0.7 represents operating conditions away from the scuffing failure.

Figure 9 - Experimental gear scuffing results in terms of the Scuffing Parameter (SP) for FZG gears.

657 Values of the Scuffing Parameter between 0.7 and 1.0 (0. 7 < SP < 1.0) represent operating conditions where total scuffing is avoided, but some scuffing marks can be observed.

Variable speed tests (+500 rpm, at constant torque and oil bath temperature). Thus, when analysing the correlation between experimental and analytical results, it should be taken into account that the variation of the operating conditions is not continuous and is applied in a stepwise way.

Figure 9 shows the experimental gear scuffing results obtained in terms of the Scuffing Parameter. Several experimental results were excluded due to the following reasons: incorrect running-in of the testing gears (31, 32, 33, 37, 39 and 40), and oil bath temperature equal or above the critical temperature of the lubricant (not shown in Figure 9 - e.g. full scuffing in load stage 2 at 3000 rpm).

Figure 10 shows the FZG scuffing load stage for each variable torque test, predicted by the scuffing criterion developed (Kp,d), and compares it with the experimental FZG scuffing load stage +1 load stage (K+I and K-I). It's clear from Figure 10 that, among all the variable load tests considered valid, only 1 is not within the load resolution of the tests which is +1 FZG load stage. The case not fulfilling this condition is indicated by the letter F. Similar results and good correlations were obtained for the variable temperature tests (+5 ~ presented in figure 11 (one test prediction is inside experimental range and the other test outside range but only for 2~ and for the variable speed tests (+500 rpm), presented in figure 12 (all tests inside experimental range).

However, three of these "bad running-in" results (33, 37 and 40) could be considered as satisfactory since they fulfil the scuffing criterion.

5.3. Validation of the scuffing criterion As mentioned before several different types of tests were performed: 9

9

Variable torque tests (+1 FZG load stage, at constant oil bath temperature and rotating speed), Variable temperature tests (+5 ~ torque and rotating speed),

I

14

This is the best indication about the quality of the correlation obtained and of the scuffing criterion developed.

at constant

11

not valid

valid

k-1

12-

T

lO!T o ~ ~

8 ~~

F

6 .

v

I

4 2 .0

'--

_

9

_

,-.

,-~

,-~

,-~

,--"

,--~ , - ~

r

r

t'xl

r

r

t"q

t"q

t"q

ee~

er

~

r~

rr

er

Figure 10 - Experimental and analytical scuffing load stage for the tests performed with variable load and constant temperature and speed.

,~1-

658

I

Ill To prd ]

the scuffing stage, are very similar (about 0.5 GPa.msl).

T+5 T-5

120 100

3-

,,,

T" .s

8O 60

[...,

40 .. 20 0 4

16

Figure 11 - Experimental and analytical scuffing temperature stages (constant speed and load).

I~

prdl

-

5.5. The influence of running-in on the scuffing tests

I n§

3

2

!1 =

0

0

3

7

9

10

15

Figure 12 - Experimental and analytical scuffing speed stages (constant temperature and load). 5.4. Gear tests performed lubricant temperature

These results confirm the concept of critical lubricant temperature and show that, even for oil bath temperatures above the critical lubricant temperature, a minimum level of contact pressure and sliding speed between the gear teeth (power dissipation) is necessary, in order to overcome the resistance to adhesion of the oxide films present on the contacting surfaces and reach scuffing. In a third test with the same lubricant, performed at 1500 rpm and free oil bath temperature (34 - standard test FZG A/8.3/90 - DIN 51354), all teeth suffered complete scuffing on FZG load stage 4 and a maximum oil bath temperature of 113 ~ was obtained at the end of the test, which is precisely the Critical Lubricant Temperature.

above the critical

Two gear tests (35 and 36) were performed with the 68I base oil at a constant oil bath temperature of 130 ~ clearly above the critical temperature of this lubricant (TcR (681) = 113~ One of these tests was conducted at 1500 rpm and scuffing occurred on FZG load stage 3 while the other test was conducted at 3000 rpm and scuffing occurred on FZG load stage 2. Both tests were performed with type A FZG gears and the corresponding flFzGPoVs products, at

Tests 31, 32, 33, 37, 39 and 40 (not considered for the criterion correlation, see Figure 10) were performed at high speed, between 2250 rpm and 3000 rpm, and scuffing occurred below FZG load stage 6. In these tests the first scuffing marks appeared on load stages 2 or 3, that is, during the load stages where normal gear running-in is taking place (load stages 1 to 4). For these tests, the scuffing load stage is negatively affected by this "incorrect" running-in and they weren't considered for the result correlation. Nevertheless, 3 of the scuff'nag results satisfy the criterion. 5.6. The scuffing criterion and the standard tests A/8.3/90

Figure 13 shows the evolution of the oil bath temperature and of the Scuffing Parameter (SP) during the several load stages of a standard A/8.3/90 [10] test with the mineral base oil 220I. In each load stage (Krza > 4) the initial oil bath temperature is 90 ~ and increases freely till the end of the stage. The Scuffing Parameter (SP) increases significantly during the several load stages, due to the load increase (contact pressure) and the temperature increase from one stage to the next one.

659 In the last equation the Scuffing Parameter only depends on the FZG load stage since all the other parameters are known: PoB = 0.114 KFZG GPa, V8 = 5.8 ms -t, ktvz~ is a function of loB, VR and lubricant viscosity and TB is constant for type A gears. Figure 14 shows the variation of the Scuffing Parameter with the FZG load stage, for each one of the oils tested. The predicted scuffing load stage corresponds to S P = 1. The corresponding experimental FZG load stages are also shown.

standard A/8.3/90 test; oil 220I 1

130

i

--------

SP 120 To 110

//

o ~ t

100

/

~176

/

90 80

j J

70 60

1

2

3

4

5

6

7

9

8

k (FZG load stage)

Figure 13 - Standard test for mineral base oil 220I. standard A/8.3/90 tests 1.6

I

1.4

/

1"

'

/

1.0

;i

,/9

0.8 0.6

.,

Y

9

,

n

,o,

[

............ 68II

;

1

,,

]

"

/

~ 6 8 I

t

.'1 ~'

.....

150II

.......

220I

"~

22011

.....

680I

,t

o 0.4

/~

0.2

~ '

~-"

"""

.. I

o.o ~"' """ 4

5

6

Table 3 compares the predicted scuffing load stages with those obtained experimentally in standard FZG A/8.3/90 tests for each oil.

,

/:-[

"~

i

exp 68I

•

exp 150II

&

exp 220I

O

exp 680I

7 8 9 10 11 12 13 k (FZG load stage)

Figure 14 - Scuffing prediction for each oil in standard FZG tests A/8.3/90. In standard FZG tests A/8.3/90 the oil bath temperature To at the end of each load stage [3] is given by the equation

To = 8 9 + 0 . 1 M ,

(11)

where M is the applied torque (M = (1.93 K)2). The Scuffing Parameter can be easily calculated for each lubricant in point B of the meshing line if the critical temperature of the lubricant is known, that is, /IFZ G xO.114K m xS.8x Tn se - (

,evr/c) =

L.-ro

Table 3 - Predicted vs. experimental scuffing load stages in standard FZG A/8.3/90 tests for each oil. Mineral base oil ~ 68I 15011 220I 680I Scuffing Load Stage - Prediction 5 - 6 7 - 8 8 - 9 12 Light .... 8 12 Scuffing Load Stage scuffing - Experimental Severe 4 8 9 13 scuffing

C

TcR - I 8 9 + O.lx (1.93 Kvzc ) 2] (12)

The correlation between the predicted and experimental load stages is very good, with the exception of the 68I and 68 II base oils. Once more it is difficult to predict the scuffing load stage of low viscosity gear oils (68I and 6810, because scuffing occurs at low load stages.

5.7. New gear tooth geometry profile shift factor according with new scuffing criterion The new scuffing criterion might be used to define new profile shifts factors of the FZG pinion and wheel that minimizes the probability of a scuffing failure with mineral base oils. In table 4 the new profile shift proposed is compared with those of FZG type A and type C gears, and with the correction proposed by Henriot [12]. The corresponding maximum sliding speeds, maximum sliding rates and scuffing parameters are compared. The FZG type A gear is designed for maximizing scuffing which is clearly demonstrated by the corresponding scuffing parameter (SIS" = 2.37). The FZG type C gear is designed with balanced sliding at the tip of the pinion and wheel [11], and so minimizing the maximum sliding speed (Fsmax/VsC = 1.0).

660 T a b l e 4 - P r o f i l e shift factors, maximum sliding speeds, maximum sliding rates and scuffing parameters proposed for each ~~pe.~of gear. I X2wheel x, pinion

Vsmax -i-.~-- - ~ f 3 3

i~

........]

L_o:59~

The profile shift factors proposed by Henriot [12] minimize the sliding rate (Ve max = 0.57) along the meshing line, obtaining a very low scuffing parameter ( S F = 1.06). The new profile shift factors are between those proposed by Henriot and those used in FZG type C gears, but they minimize the probability of a scuffing failure ( S F = 1.0) according to the scuffing criterion developed. 6. C O N C L U S I O N S 1. A new scuffing criterion for FZG gears (types A and C) lubricated with base mineral oils was developed, merging together the concepts of the Friction Power Intensity and of the Integral Temperature Criteria. 2. The new scuffing criterion proposes the existence of Critical Lubricant Temperatures characteristic of each lubricant (viscosity grade). These Critical Temperatures are considerably smaller than those suggested by the Total Temperature and Integral Temperature criteria. The difference between the Critical Temperature and the oil bath temperature is proportional to the ,u P V T product, that is, to the energy dissipated along the gear meshing line. 3. The new scuffing criterion shows very good correlation with experimental results obtained with FZG type A and type C gears lubricated with base mineral oils of 4 different viscosity grades. 4. In global terms from 40 tests performed, 34 are fully justified by the present scuffing criterion, 4 are justified by insufficient running-in and only 2 are slightly away from the criterion prediction.

REFERENCES [1]

B.-R. Hohn, K. Michaelis and A. Doleschel, "Frictional Behaviour of Synthetic Gear Lubricants", Tribology Research: From Model Experiment to Industrial Problem, G. Dalmaz et al. (Editors), 2001 Elsevier Science B. V. [2] J. Castro and J. Seabra, "Influence of Lubricant Properties and Temperature on the Scuffing Failure of FZG Gears", Proceedings. of 25 th "Leeds-Lyon Symposium" on Tribology, Lyon, France, 8 - 11, September, 1998. [3] Winter, H. and Michaelis, K. "Scoring Load Capacity of Gears Lubricated with EP-oils". AGMA, Fall Technical Meeting. Montreal, Canada, October, 1983. [4] DIN 3990 part 4 and ISO/TR 13989-1:2000. [5] Jackson, A. and Enthoven, J. C. "The Effect of Lubricant Traction on Scuffing". STLE- Tribology Transactions. Volume 37 (1994), 2, 387 - 395. [6] Henriot, G. "La Lubrification Industriele - La Lubrification de Engrenages". Tome 1 Transmissions, Compresseurs, Turbines. Publications de l'Institute Fran~ais du P6trole. l~ditions Technip, 1984, pg. 297 - 385. [7] ISO/TR 13989-2:2000. [8] Blok, H. "The Flash Temperature Concept". Wear, 6 (1963), pp.483-494. [9] Foussat, Eric. "Approche d'un Critere de Grippage au Travers de la Rupture du Film Elastohydrodynamique". These pour obtenir le Grade de Docteur. I.N.S.A.L. - Institut National des Sciences Appliqu6es de Lyon. Mai, 1994. [ 10] Standard A/8.3/90, DIN 51354 [11] Winter, H. and Michaelis, K. "FZG Gear Test Rig Description and Test Possibilities". Co-ordinate European Council Second International Symposium on "The Performance Evaluation of Automotive Fuels and Lubricants". Wolfsburg, West Germany, June 5-7, 1985. [12] Henriot, G., "Trait6 th6orique et pratique des engrenages". Paris : Dunod, 1983. [13] Changenet, C. and Pasquier, M., "Power Losses and Heat Exchange in Reduction Gears: Numerical and Experimental Results". VDI-Berichte Nr. 1665, 2002. [14] Mihalidis, A., Bakolas, V. and Drivakos, N., "Prediction of the Friction Coefficient of Spur Gear Pairs". VDI-Berichte Nr. 1665, 2002. [15] Seireg, A. and Atan E., "On the Prediction of Transient Temperature in the Gear Mesh". VDIBerichte Nr. 1665, 2002.

Acknowledgements

661

The authors are most thankful to the "Fundaggo para a Ciancia e Tecnologia" from the "Minist6rio da Ciancia e do Ensino Superior" in Portugal, for the financial support given to the project "Gear Scuffing - N e w Experimental and Numerical Models" - R e P P O C T I / 1999 / E M E / 35957.

Appendix 1 characteristics

-

Gears

and

lubricants

A2. Lubricants

The lubricants tested are mineral parafinic base oils without any kind of additives, in particular, extreme pressure (EP) and anti-wear (AW) additives. Table A2 shows some o f the lubricants characteristics. They are divided in two groups (I and II). Group II pretends to be better base oils more resistant to scuffing. Table A 2 - Lubricant characteristics

A1. G e a r s

.....~ e r ~ ~ c ~

F Z G type A and type C gears are made of case hardened 20 M n C r 5 steel. Table A1 shows some o f the geometric characteristics o f these gears. The contact ratio e~ = 1.36 in type A gears and 1.46 in type C gears.

iParameter

i Pinion Wheel ~ S y m b o ..........................-.........................-.........................,.........................i l Type i Type i Type i Type i

!................................................................... ! ........................................A .........L...........C............! .........A .....................C............i ..:Working centre idistance ~Module ~ o r k i n g pressure !angle ? ................................................................

91.5 a' m

.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

: .......................................................................................................

4.5 20

:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

N u m b e r o f teeth profile shift factor

Otw Z x

16 73.20

24 109.80

: .......................................................................................................................................................................................................

~ i t c h diameter

dw

88.6 8

82.6 4

i , i

112. 5

118. i 5 i

i.................................................................. T..................................... i~ii:g...........iE:g............fi~i .............i i g : i :.:Addendum diameter... daw 8 4 5 .......................... . i.................................................................. !........................................................................................................... 5 i ffooth flanc )oughness .............................................................................

Ra

0.35

0.30

0.30

, .............................................................................

0.30 ~. . . . . . . . . . . . . . . . . . . . . . .

s

................~ p e ~ ~ ~ m a ~ s :

.......................................................................................................................... ~..r

..........i

.........................i

................................................................................................ V4o (40~ i,,V...Lq.0....(..100~.................................................. P15 (15~ )..................i 68I 72.8 8.3 888 i

::::::::::::::~:~i:iZ::::::ZZ#~~:::::::::ZZ:~:~?::::Z2Z~Z:::~:~Z:::::~::~.:::::i 15011 220I 220II 680I

148.0 236.8 211.9 680

14.0 18.5 18.3 37.7

...............................................................................................................................................................................................................

, ............................................................................................

.......................................

Table A1 - G e o m e t r i c characteristics o f FZG type A and ~ P ................ e C g ................. ears ........................................................................................... ..............................................................

..........~ i n e m ~ i ~ ~ i s c o ~ t y : ~ ~

~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

893 900 897 921

: ...........................................

:.........................................................................

~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

...............................................................................................................................................................................................................