Size effect in contact fatigue
The results of special experiments on the size effect in contact fatigue are presented. It is established that under constant contact loading conditions the durability is higher, the larger is the diameter of a tested element. The methods for estimation of contact fatigue resistance of gear wheels,...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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| Cite this: | Size effect in contact fatigue / L.A. Sosnovskii, V.A. Zhmailik, V.V. Komissarov // Проблемы прочности. — 2009. — № 1. — С. 113-120. — Бібліогр.: 22 назв. — англ. |
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| author | Sosnovskii, L.A. Zhmailik, V.A. Komissarov, V.V. |
| author_facet | Sosnovskii, L.A. Zhmailik, V.A. Komissarov, V.V. |
| citation_txt | Size effect in contact fatigue / L.A. Sosnovskii, V.A. Zhmailik, V.V. Komissarov // Проблемы прочности. — 2009. — № 1. — С. 113-120. — Бібліогр.: 22 назв. — англ. |
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| description | The results of special experiments on the size effect in contact fatigue are presented. It is established that under constant contact loading conditions the durability is higher, the larger is the diameter of a tested element. The methods for estimation of contact fatigue resistance of gear wheels, which is based on the statistical model for a deformable solid body having a critical volume, are proposed. The limiting stresses of a gear wheel are estimated using a regulated base for this machine parts.
Представлены экспериментальные результаты по исследованию масштабного эффекта при контактной усталости. Установлено, что при постоянной контактной нагрузке долговечность испытываемого конструкционного элемента цилиндрической формы тем выше, чем больше его диаметр. Предложены методы оценки сопротивления контактной усталости зубчатых колес, основанные на использовании статистической модели критического объема деформируемого твердого тела. Предельные значения напряжений для натурных элементов оцениваются с использованием расчетных нормативов, разработанных специально для зубчатых колес.
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UDC 539.4
Size Effect in Contact Fatigue
L. A. Sosnovskii,a V. A. Z hm ailik ,b and V. V. K om issarovc
a Scientific and Production Group “Tribofatigue Ltd.,” Gomel, Belarus
b Production Group “Gomselmash,” Gomel, Belarus
c Belarusian State University of Transport, Gomel, Belarus
The results o f special experiments on the size effect in contact fatigue are presented. It is
established that under constant contact loading conditions the durability is higher, the larger is the
diameter o f a tested element. The methods fo r estimation o f contact fatigue resistance o f gear
wheels, which is based on the statistical model fo r a deformable solid body having a critical
volume, are proposed. The limiting stresses o f a gear wheel are estimated using a regulated base
fo r this machine parts.
K e y w o r d s : size effect, contact fatigue, gear wheels.
The durability and fatigue resistance o f components operating under cyclic
loading by bending, tension, compression, twisting, etc. appear to be the lower,
the larger are the component dimensions [1 ,2 ] Since the phenom ena o f contact
fatigue are based on the same processes as those occurring under other types of
fatigue, it is natural to expect that increasing the absolute dimensions o f a
component w ould decrease its contact fatigue limit. However, by analyzing the
available results o f studies on the size effect in contact fatigue it is impossible to
get a definite opinion on this problem [2-13].
Some researchers state that the size effect in contact fatigue undergoes
inversion, i.e., as the diameter o f contacting parts is increased, the durability
grows [4-6]. However, others assert that increase in a component size leads to
reduction o f bending and contact fatigue limits [7, 10].
For the basic regularities o f the size effect in contact fatigue to be elucidated,
special experimental studies have been made. The test scheme is shown in Fig. 1.
Cylindrical sample 2 serves as a tooth o f a gear wheel. A counterbody - roller 1 -
is pressed to the surface o f sample 2 by a contact load F N in the contact zone x.
Roller 1 serves as a tooth o f the second gear wheel that transmits the contact load
F n to sample-model 2 .
Sample 2, which is fastened in spindel 3, is rotated with an angular velocity
« 1. Counterbody 1 is rotated with an angular velocity « 2 , its rotation axis being
parallel to that o f sample 2. Regulating the ratio o f the velocities «1 and « 2
allows one to obtain the required slip coefficient, im itating the slip in gearing.
The contact load F N provides a simultaneous excitation both o f contact and
bending stresses in the corresponding zones, whereas the distance between these
zones is chosen tobe equal to that between the pitch point and the tooth root.
Using the counterbody (roller) with a constant diameter D =100 mm and
sample-models o f various diameters d (Fig. 2) makes it possible to change two
m ain curvatures and to obtain the size ratio o f the contact area (a /b) within the
range 0.4-0.8, which is satisfactory for practical purposes.
© L. A. SOSNOVSKII, V. A. ZHMAILIK, V. V. KOMISSAROV, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 113
L. A. Sosnovskii, V. A. Zhmailik, and V. V. Komissarov
Fig. 1. Testing scheme for a toothed gearing model: (1) sample-model of the tooth; (2) counterbody
(roller); (3) testing machine spindle.
Fig. 2. Tested tooth models.
a
b
c
Samples 10, 20, and 30 mm in diameter were made from steel 18KhGT,
invoking the technology o f m anufacturing gear wheels at the Production Group
“Gomselmash.” Working surfaces o f counterbodys and samples were cemented at
a depth o f 1.0-1.5 m m with subsequent hardening up to 59-63 H R C and polished
(R a > 0.32 ^m ). The run-out o f the samples in the working zone was not more
than 10 ^m . Tests were perform ed using a wear fatigue testing m achine o f UIM
type [20] at a constant linear velocity in the contact v circ = 1.57 m/s. The error of
keeping the shaft rotation frequency w ithin the steady regime is ± 3 % o f the
m easured value [2 0 ].
W hen the sample and the counterbody are tested in the contact zone, the slip
degree is controlled to be equal to 3%. In the course o f tests, a lubricant (oil
TAD-17 I) is supplied to the contact zone w ith a feeding speed o f 2 -4 drops per
minute. The tests were interrupted after occurrence o f the limiting state conditions
corresponding to the real service ones for a particular gearing (limiting convergence
o f the axes o f the sample and the counterbody d iim = 100 ^m ). The contact load
F n (see Fig. 3) serves as a param eter controlling the m odel loading.
114 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
Size Effect at Contact Fatigue
I, t, t , min
Fig. 3. Loading program scheme.
The basic test results are shown in Figs. 4 and 5.
From Fig. 4 it is seen that under constant contact loading conditions the
durability is higher, the larger is the diameter o f a tested element. For the base of
N b = 4 -1 06 cycles, we have established the dependences o f limiting contact
stresses p f and limiting contact load F Um on the diameter o f the tested models,
d (Fig. 5). The analysis o f Fig. 5 yields that:
1) in terms o f the limiting contact load, i f the tested model diameter is
increased from 10 to 30 mm, this load grows from 780 to 1520 N.
2 ) in terms o f the limiting contact fatigue, i f the tested m odel diameter is
increased from 10 to 30 mm, the contact fatigue limit decreases from 5150 MPa
to 4900 MPa.
F„, N
1600
1500
1400
1300
1200
1100
1000
900
800
700
600
500 ------------------------------------------------------------ J-------------------------------
400------— I I 1111-------— LLLLLl------- — III
10* 10s 10’ N, cycles
Fig. 4. The size effect on the contact fatigue resistance [(/) log F = 7.8009 — 0.7434 log N ; (2) log F =
5.9047 — 0.4266logN ; (3) logF = 5.2255 — 0.3097logN].
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 115
L. A. Sosnovskii, V. A. Zhmailik, and V. V. Komissarov
P„ MPa
5200
5100
5000
4900
4S0D
5 10 15 20 25 30 rf.mm 0.1 0.3 0.5 0.7 0.9 mm3
a b
Fig. 5. Limiting contact stresses and limiting contact load vs. sample diameter (a) and critical
volume size (b).
Based on the above experimental results, it is possible to formulate the
following basic regularity o f the size effect in friction: under constant contact
loading conditions the durability is higher, the larger is the diameter o f a tested
component.
For the size effect in contact fatigue to be analyzed theoretically, the model
o f a solid body w ith a critical volume [14] was used. According to this model, i f a
deformable solid body is characterized by such a stressed state that its fatigue
failure is possible, then it is composed o f two regions: safe and critical volumes.
Similarly, assume that in contact deformation by a critical volume Vint is
understood the region o f a loaded body, at each point o f which the value o f the
stress intensity o int is less than the limiting value o f o ) (~ P f m))
V int = f f f dxdy d z ( 1)
o in t (x, y, z )so l2
The critical volume is an absolute m easure o f damage; it is statistical in
character and contains the geometrical sizes o f tested elements. This permits
using it as the param eter controlling the size effect in contact fatigue.
The proposed procedure is applied for the assessment o f critical (limiting)
stresses as a limitation criterion for the corresponding critical regions [15]. It
(* lim)consists in determining the limiting intensity o f stresses o int when the tested
system is subjected to the limiting load F * lim :
0 f j m) = max( o in t(F * lim , d V ),) (2)
dV
where d V is the elementary volume o f the loaded body.
= 5294.
!v
33-12.25 d 4
/
/
/
/
' /
/
/
/
/
A
v
465.33 +36.1 d
116 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N9 1
Size Effect at Contact Fatigue
Then the criterial condition for limitation o f critical volumes will be o f the
form
Vint = { d v j o iM > a \ d V C Vk }, (3)
where Vk is the working volume o f a deformable solid body.
As critical volumes can have arbitrary and complex shapes, it is difficult to
determine them by formula (1). Therefore, calculations were made using the
program package “M athem atics” by the num erical M onte-Carlo method.
Figure 6 presents the calculation results on the critical volumes formed due
to norm al and tangential contact stresses.
-1.5 -1 -0,5 0.5 1 x/a
-1.5 -1 -0.5
d
1 y/a
Fig. 6. The critical volume (a) developed due to normal and tangential contact stresses: (b) section
by the plane y = 0; (c) section by the plane x = 0; (d) section by the plane z = 0.5a.
c
Since critical volumes are used as the damage measure o f deformable bodies,
the analysis o f Fig. 6 specifies the particular regions (zones) where internal cracks
can initiate and propagate.
Using the proposed method, the dependences o f limiting contact stresses
p f and limiting contact load F lim on the critical volume size (V int) (Fig. 5) are
constructed for the base N b = 4 -106 cycles. The obtained dependences are seen
to have a qualitatively similar character both in analyzing the tested models in
terms o f the diameter and the critical volume in terms o f size. Thus, the proposed
m odel is valid and does not contradict the results obtained. In this case, a critical
volume to be calculated includes the geometrical dimensions o f tested components
and has a statistical character [limiting contact stresses p f m) serve as a
limitation criterion]. In this respect, this is a more preferable param eter for
description o f the size effect in contact fatigue.
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 117
L. A. Sosnovskii, V. A. Zhmailik, and V. V. Komissarov
Using the given approach, it is possible to execute a settlement estimation of
rolling fatigue resistance o f particular toothed gear wheels. The input data for
calculations are given in Table 1.
T a b l e 1
Input Data for Calculation of Gear Wheels
Gear Combined
torque M k ,
N-m
Reference
diameter d ,
mm
Radius of tooth profile
evolvent in a pitch point
Effective
face width B,
mmp 1, mm p 2 , mm
PKK 0135684 290 92 15.73 19.15 20
PKK 0135661 450 108 18.47 21.89 40
For the rolling fatigue limit estimation for a particular type cogwheel it iso
necessary to pass to base o f tests equal to 1.2 -1 0 cycles which is regulated for
tooth gearings [10, 17]. As a first approximation, such transition can be executed,
accepting the slope indicator o f the left branch o f rolling fatigue curve m p = 3 -6
[17] or on the average m p = 4.5. Calculation results are presented in Fig. 7 and in
Table 2.
T a b l e 2
Results of Calculation of Gear Wheels
Gear Vint, mm3 Po, MPa P f , MPa nP aH , MPa ° H
PKK 0135684 0.00201 1171.4 2340.8 2.00 1337.8 1.75
PKK 0135661 0.00208 888.6 2340.3 2.63 945.7 2.47
Pf: MPa
2800
2600
2400
2200
2000
1S00
1600
1
_WCi, = U -1 0 s cydes
T ~ ~ t r ~
1
1
1
r —
| Gear wheel
PK K 0135684
1
1
1
0.01 0.02 0.03 nun
Fig. 7. Dependence of rolling fatigue limit on the critical volume value.
It is seen from Table 2 that for a gear wheel PKK 0135684 value o f safety
factor for the rolling endurance n p is lower by 25% than that o f PK K 0135661.
This allows us to conclude that the operational durability o f the PKK 0135684
gear wheel will also be lower than that of PKK 0135661. This conclusion is
118 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1
Size Effect at Contact Fatigue
confirmed by data on operation o f a transm ission PKK 0135000 o f a harvest
combine “Polesie-3000” m anufactured by Production Group “Gom selm ash” [22].
Conclusions. Inversion o f size effect in rolling fatigue is established and
described for particular experimental conditions. The technique o f rolling fatigue
resistance assessment on the basis o f statistical m odel o f a deformable solid body
w ith critical volume is proposed. The estimation o f a rolling fatigue limit is made
for particular types o f gear wheels.
1. L. A. Sosnovskii, M e c h a n ic s o f F a tig u e F a ilu re : H a n d b o o k [in Russian], in
2 Parts, Pt. 2, “SPG Tribofatigue,” Gomel (1994).
2. A. A. Komarovskii, “Size effect: reasons o f the onset, m anifestations and
dangerous consequences,” Tekh. D ia g n . N e ra zru sh . C o n tr ., No. 1, 3-8
(2002 ).
3. A. I. Petrusevich, C o n ta c t S tr e n g th o f M a c h in e P a r ts [in Russian], Mashino-
stroenie, M oscow (1969).
4. I. M. Sakhonko, “Contact endurance o f quenched steel as a function of
geom etrical param eters o f contacting bodies,” in: C o n ta c t S tr e n g th o f
M a c h in e -C o n s tr u c tin g M a te r ia ls [in Russian], Nauka, M oscow (1964).
5. B. A. M orozov, V. K. Shashkin, V. T. Firsov, et al., “Contact fatigue
strength o f backing-up rolls,” in: S tr e s se s , D e fo rm a tio n , a n d S tr e n g th o f
M e ta llu r g ic a l M a c h in e s [in Russian], VNIIM etmash, M oscow (1988).
6 . G. K. Trubin, C o n ta c t F a tig u e o f M a te r ia ls f o r G e a r W h ee ls [in Russian],
State Scientific-Technical Publishing House o f M echanical Engineering
Literature, M oscow (1962).
7. V. I. Rudnitskii, “Size effect as applied to gear wheels,” V estn . M a s h in o s tr .,
No. 7, 24-26 (1958).
8 . A. S. Ivanov, “Size effect in considering bending and contact resistances of
fatigue as well as o f friction and wear,” I b id , No. 5, 25-30 (1997).
9. A. V. Orlov, O. N. Chermenskii, and V. M. Nesterov, T e s tin g o f S tr u c tu ra l
M a te r ia ls f o r C o n ta c t F a tig u e [in Russian], Mashinostroenie, M oscow (1980).
10. P 5 0 -5 4 -3 0 -8 7 . C a lc u la tio n s a n d S tre n g th T ests . M e th o d s o f T e s tin g C o n ta c t
F a tig u e [in Russian], Gosstandart SSSR, VNIIM ash, M oscow (1988).
11. B. I. Kostetskii et al., S u rfa c e S tr e n g th in F r ic t io n [in Russian], Tekhnika,
K iev (1976).
12. V. A. Belyaev and I. A. Bolotovskii, “Influence o f the num ber o f teeth o f a
gear wheel on its bending supporting,” in: C o n ta c t P r o b le m s a n d T h e ir
E n g in e e r in g A p p l ic a t io n s (C o n fe r e n c e P a p e r s ) [in Russian], NIIM ash,
M oscow, (1969), pp. 274-284.
13. K. Inoue and T. Masuyama, “Possibilities o f fatigue strength simulation in
reliability design o f carburized gears” in: 2nd Int. Conf. on P o w e r T ra n s-
m is s io n s ‘0 6 , (Novi Sad, Serbia&M ontenegro, 2006), Novi Sad (2006).
14. L. A. Sosnovskii, S ta t is t ic a l M e c h a n ic s o f F a tig u e F a ilu r e [in Russian],
Nauka i Tekhnika, M insk (1987).
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L. A. Sosnovskii, V. A. Zhmailik, and V. V. Komissarov
15. L. A. Sosnovskii, M e c h a n ic s o f W ea r F a tig u e D a m a g e [in Russian], BelSUT
Press, Gomel (2007).
16. O. T. Vavilov, “Concept o f critical volumes in the contact problem ,” Vestn.
B r e s t G os. T echn . U n iv e r ., No. 4, 61-65. (2001).
17. I. S. Tsitovich, I. V. Kanonik, and V. A. Vavulo, T ra n sm iss io n o f C a rs [in
Russian], Nauka i Tekhnika, M insk (1979).
18. L. A. Sosnovskii and V. V. Komissarov, “Damage in m echanical and contact
fatigue,” Z a v o d . L a b ., D ia g n . M a te r . , 71, No. 1, 47-55 (2005).
19. L. A. Sosnovskii, “Contact and bending fatigue o f toothed gearings,” in:
Proc. o f the W orld Tribology Congress III (W ashington) (2005).
20. T r ib o fa tig u e . W e a r F a t ig u e T e s t in g M a c h in e s . G e n e r a l S p e c if ic a t io n s :
G O S T 3 0 7 5 5 -2 0 0 1 [in Russian], Belarusian State Institute o f Standartization
and Certification, M insk (2002).
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Standartization and Certification, M insk (2002).
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A c tiv e S y s te m s ’ Q u a lity [in Russian], A uthor’s Abstract o f the D octor’s
Degree Thesis (Ph.D.), BelSUT Press, Gomel (2002).
Received 11. 06. 2008
120 ISSN 0556-171X. npodxeMbi npounocmu, 2009, N 1
|
| id | nasplib_isofts_kiev_ua-123456789-48468 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T18:53:53Z |
| publishDate | 2009 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Sosnovskii, L.A. Zhmailik, V.A. Komissarov, V.V. 2013-08-20T03:41:57Z 2013-08-20T03:41:57Z 2009 Size effect in contact fatigue / L.A. Sosnovskii, V.A. Zhmailik, V.V. Komissarov // Проблемы прочности. — 2009. — № 1. — С. 113-120. — Бібліогр.: 22 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48468 539.4 The results of special experiments on the size effect in contact fatigue are presented. It is established that under constant contact loading conditions the durability is higher, the larger is the diameter of a tested element. The methods for estimation of contact fatigue resistance of gear wheels, which is based on the statistical model for a deformable solid body having a critical volume, are proposed. The limiting stresses of a gear wheel are estimated using a regulated base for this machine parts. Представлены экспериментальные результаты по исследованию масштабного эффекта при контактной усталости. Установлено, что при постоянной контактной нагрузке долговечность испытываемого конструкционного элемента цилиндрической формы тем выше, чем больше его диаметр. Предложены методы оценки сопротивления контактной усталости зубчатых колес, основанные на использовании статистической модели критического объема деформируемого твердого тела. Предельные значения напряжений для натурных элементов оцениваются с использованием расчетных нормативов, разработанных специально для зубчатых колес. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Size effect in contact fatigue Масштабный эффект при контактной усталости Article published earlier |
| spellingShingle | Size effect in contact fatigue Sosnovskii, L.A. Zhmailik, V.A. Komissarov, V.V. Научно-технический раздел |
| title | Size effect in contact fatigue |
| title_alt | Масштабный эффект при контактной усталости |
| title_full | Size effect in contact fatigue |
| title_fullStr | Size effect in contact fatigue |
| title_full_unstemmed | Size effect in contact fatigue |
| title_short | Size effect in contact fatigue |
| title_sort | size effect in contact fatigue |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48468 |
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