The paper presents the results of experimental study of the effect of stresses resulting from off-contact load on variations in the friction torque and the coefficient of resistance to rolling in a force system compared to a similar tribopair. The results are compared with the theoretical data obtained on the basis of the deformation approach to the analysis of friction. It is shown that the calculation estimates agree well with the experimental results both qualitatively (the regularities) and quantitatively (the numerical values). The error of the determination of the coefficient of resistance to rolling does not exceed 7%. The study results make it possible to formulate and solve the problem of the effective control over the friction force (coefficient) by varying cyclic (bending) stresses

Komissarov, V. V.

Shcherbakov, S. S.

Sosnovskii, L. A.

English

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ISSN 10683666, Journal of Friction and Wear, 2012, Vol. 33, No. 3, pp. 203–207. © Allerton Press, Inc., 2012.
Original Russian Text © L.A. Sosnovskii, V.V. Komissarov, S.S. Shcherbakov, 2012, published in Trenie i Iznos, 2012, Vol. 33, No. 3, pp. 258–264.
203
INTRODUCTION
In tribology the friction force, which arises during
the friction of macroscopic objects, is assumed to
depend on only one force factor, namely, the normal
contact load [1–3]. In force or tribofatigue systems,
in which the stressstrain state is caused by the effect of
both the contact and volume loads excited in the same
zone, the stresses and strains resulting from an off
contact load form additional boundary conditions on
the contact surface. This varies considerably the tribo
logical characteristics. Theoretical studies [4–6] have
shown that in a tribofatigue system the resulting roll
ing friction force (coefficient) in the tension zone
declines compared to the pure rolling force (coeffi
cient) under the simultaneous action of contact and
offcontact loads and, conversely, this force increases
in the compression zone. 
The aim of the study is to study experimentally the
effect of the stresses resulting from offcontact load
on variations in the coefficient of resistance to rolling
in a force system and a similar tribopair and to com
pare the data with the results of the theoretical solu
tions.
PROBLEM FORMULATION
The traditional approach to the determination of
the friction coefficient is that the friction force and
coefficient in the tribopair are assumed to depend only
on the contact load  (contact pressure ):
(1)
where FS is the friction force, τW is the specific friction
force, FN is the contact load, and p is the contact pressure.
From the viewpoint of tribofatigue, the friction
coefficient in force systems is determined as a function
of the contact pressure p and the cyclic stresses σ
resulting from the offcontact load:
(2)
According to the data of [4–6], depending on the
conditions of friction or testing it can be
   (3)
i.e., the cyclic stresses can either increase or reduce the
friction coefficient. 
In this work, we carried out the systematic compar
ative analysis of relations (1)–(3) based on the experi
mental results; all tests were performed under rolling
friction conditions so that  is the coefficient
of resistance to rolling in the friction pair and
 is the coefficient of resistance to rolling in
the force system.
A modification of the roller/shaft force system
(steel 18KhGT/steel 18KhGT) was tested (Fig. 1); the
test method was published earlier [7].
NF p
( ) ,S W
N
F
f p
F p
τ
= =
( , )
( , ) .S
N
F p
f p
F
σ
σ =
( , )f p σ ( ),f p
( ) rf p f=
( , )f p f
σ
σ =
Comparative Experimental Study of Friction Parameters 
in a Tribopair and a Force System
L. A. Sosnovskiia, *, V. V. Komissarova, and S. S. Shcherbakovb
aBelarussian State University of Transport, ul. Kirova 34, Gomel, 246050 Belarus
bBelarussian State University, pr. Nezavisimosti 4, Minsk, 220030 Belarus
*email: komissarov@belsut.gomel.by
Received April 18, 2011
Abstract—The paper presents the results of experimental study of the effect of stresses resulting from offcon
tact load on variations in the friction torque and the coefficient of resistance to rolling in a force system com
pared to a similar tribopair. The results are compared with the theoretical data obtained on the basis of the
deformation approach to the analysis of friction. It is shown that the calculation estimates agree well with the
experimental results both qualitatively (the regularities) and quantitatively (the numerical values). The error
of the determination of the coefficient of resistance to rolling does not exceed 7%. The study results make it
possible to formulate and solve the problem of the effective control over the friction force (coefficient) by
varying cyclic (bending) stresses.
Keywords: force (tribofatigue) system, tribopair, friction, law of friction, coefficient of resistance to rolling,
contact load, contact area.
DOI: 10.3103/S1068366612030105
204
JOURNAL OF FRICTION AND WEAR  Vol. 33  No. 3  2012
SOSNOVSKII et al.
RESULTS OF TESTING THE STEEL 
18KhGT/STEEL 18KhGT FORCE SYSTEM
This force system was tested using the developed
method at three values of the contact stresses (p0 =
2000 MPa, p0 = 3200 MPa, and p0 = 5600 MPa),
which correspond to the range of elastic and elasto
plastic deformations (see the dependence of the max
imum contact pressure  on the approach of the axes
—insert in Fig. 2). The bending load Q was assigned
stepwise 5 min after the beginning of the tests. The ini
tial bending load was Q = 160 N (the bending stresses
were σa = 160 MPa). The increment of the bending
stresses at each loading step was Δσi = 40 MPa = const;
the duration of the step was ni = 30000 cycles. The
bending load was directed downwards to produce ten
sile stresses in the contact zone and upwards to pro
duce compressive stresses (see Fig. 1). The degree of
slippage was constant during the tests and amounted
to λ = 3%.
The test results are presented as the graphs of the
dependence of the average coefficient of resistance to
rolling  (under various values of the contact stresses
) on the cycle stress amplitude σa at the given load
ing step (Fig. 2). Sixty values of f
σ
 obtained during the
test at one loading step (10 min) correspond to each
point on the graph at σa = const; this provides a suffi
cient accuracy of the results. The data presented in
Fig. 2 allow us to draw the following conclusions.
(1) During the contact fatigue tests (in all figures
RF means rolling friction) the values of the coefficient
of resistance to rolling  remain unchanged if
FN = const; this agrees with the numerous known data.
Depending on the contact stresses, the values of  are
0p
cδ
f
σ
0p
rf
rf
0.0626 at p0 = 2000 MPa (elastic contact) as well as
0.0830 at p0 = 3200 MPa and 0.0887 at p0 = 5600 MPa
(elastoplastic contact); i.e., the transition from elastic
contact to elastoplastic results in a higher coefficient
of resistance to rolling (by ~41.6% under the test con
ditions).
(2) During the mechanorolling fatigue tests (roll
ing friction + cyclic bending) the values of the coeffi
cient of resistance to rolling  in the compression
zone diminish, as a rule. The increase in the bending
stresses σa to 640 MPa leads to the reduction of  by
5.1% at p0 = 2000 MPa, by 6.0% at p0 = 3200 MPa, and
by 0.9% at p0 = 5600 MPa. 
(3) Conversely, during the mechanorolling fatigue
tests with friction occurring in the compression zone,
the values of the coefficient of resistance to rolling 
grow. The increase in the bending stresses σa to
640 MPa results in the rise of the coefficient  by
11.7% at p0 = 2000 MPa, by 5.6% at p0 = 3200 MPa,
and by 0.13% at p0 = 5600 MPa. 
(4) The most pronounced effect of the cyclic
stresses on the coefficient of resistance to rolling
occurs in the elasticity range (  = 2000 MPa). In
transition to plastic contact, this effect weakens and
the effect is weaker the greater the plastic strain.
ANALYSYS OF THE TEST RESULTS
It is shown in work [5] that the friction process in a
force system is characterized by the parameter
 which is called the friction index. The
following dependence of  on the ratio  is pro
posed for sliding friction [6]: 
(4)
where  is the dimensionless parameter of the inter
action of the damages caused by the contact and off
contact loads (the frictional and mechanical stresses). 
In the case of rolling friction, we replot the depen
dences presented in Fig. 2 using the parameter 
(Fig. 3). It is easy to see that all of the graphs shown in
Fig. 3 can be approximated by the following linear
equation of one type 
(5)
where  is the parameter characterizing the angle of
the slope of the straight lines  to the
abscissa axis.
Analysis of the experimental data in accordance
with equation () is presented in Table 1.
f
σ
f
σ
f
σ
f
σ
0p
,F a Wf = ±σ τ
f
σ a Wσ τ
( )1 1 ,aS p S p F
W
f f f f
σ
⎛ ⎞σ= ± μ = ± μ⎜ ⎟τ⎝ ⎠
pµ
0a pσ
0
,ar rf f a
p
σ
σ
= ±
ra
( )0af pσ ±σ
R11
FN
ω2
176
2
R
12FN
2
R22
R
21
Q
ω1
Fig. 1. Model for mechanoroling fatigue tests.
JOURNAL OF FRICTION AND WEAR  Vol. 33  No. 3  2012
COMPARATIVE EXPERIMENTAL STUDY OF FRICTION PARAMETERS 205
0.072
0.068
0.064
0.060
0.076
0.056
480400320240160800
0.080
0.084
0.088
fr, fσ σa < 0
σa > 0
fr = 0.089
fr = 0.083
σa < 0
Compression
Tension
Compression
Tension
σa > 0
p0 = 5600 MPa
p0 = 3200 MPa
MRF
RF
p0 , MPa
MRF
MRF
σa < 0
p0 = 2000 MPa
Compression
Tension
RF
fr = 0.063
MRF
σa> 0
2000
10 20 30 40 50 60 70 80
1000
3000
4000
5000
6000
0 δc, μm
Fig. 2. Force system steel 18KhGT/steel 18KhGT: dependence of average coefficient of resistance to rolling  on amplitude of
stresses σa (the dashed line corresponds to the value of  in the tribopair).
rf
rf
It is easy to show that equations (4) and (5) are
almost identical, since
(6)
where  is the dimensionless parameter of
the interaction of the damages caused by the contact
and offcontact loads (the frictional and mechanical
stresses). By analogy, we can obtain 
The values of the parameter  calculated from the
experimental data are given in Table 1.
( )
0 0
0
1
1 1 ,
a ar
r r r
r
a
r r r r F
a
f f a f
p f p
f f a f
p
σ
⎛ ⎞σ σ= ± = ±⎜ ⎟
⎝ ⎠
⎛ ⎞σ= ± μ = ±⎜ ⎟
⎝ ⎠
r r ra fµ =
.p S Sa fµ =
rµ
The methods of the mechanics of deformable solids
were applied in work [4] to determine the friction
coefficient (the coefficient of resistance to rolling) in
the force system:
(7)
where  is the pure rolling friction coefficient and
 is the function, which possesses the following val
ues depending on the method of its determination:
 = 0.225 and  = 0.787. 
It is seen that formulae () and (4) are almost iden
tical. 
( )
( )
0
1 ,
b
s yy
pf f k
p
σ
⎡ ⎛ ⎞⎤σ
= ± ⎜ ⎟⎢ ⎥⎜ ⎟
⎣ ⎝ ⎠⎦
( )sf
pkσ
( )1
pkσ
( )2
pkσ
206
JOURNAL OF FRICTION AND WEAR  Vol. 33  No. 3  2012
SOSNOVSKII et al.
0.088
0.068
0.064
0.060
0.056
0.300.250.200.100.050
0.080
0.080
0.076
0.072
0.15
fr, fσ
σa/p0±
ar = 0.010
TK
MRF
MRF
ar = 0.026
p0 = 2000 MPa
MRF
ar = 0.025
p0 = 3200 MPa
MRF
ar = 0.001
p0 = 5600 MPa
MRFRF
ar = 0.007 ar = 0.024
Fig. 3. Force system steel 18KhGT/steel 18KhGT: depen
dence of average coefficient of resistance to rolling  on
ratio σa/p0 (the dashed line corresponds to the value of 
in the tribopair).
rf
rf
The results of the comparison of the experimental
and theoretical values of the coefficient of resistance to
rolling in the force system at  = 0.225 and  =
0.3 are presented in Table 2.
( )1
pkσ 0a pσ
It can be seen that in this case the calculation esti
mates agree satisfactorily with the experimental data
both qualitatively (the regularities) and quantitatively
(the numerical values).
CONCLUSIONS
The following basic regularities of the effect of the
cyclic stresses σa on variations in the coefficient of
resistance to rolling fr (the force FR) are established:
(a) greater σa, and therefore higher ratio 
entails a more significant variation of the coefficient of
resistance to rolling; this regularity is observed in both
elastic and elastoplastic contact; (b) the change of the
coefficient of resistance to rolling fr with varying cyclic
stresses σa reaches 12.5% in elastic contact and up to
4% in elastoplastic contact. The cycle stress amplitude
in the experiments σa does not exceed the endurance
limit σ–1 = 640 MPa and the ratio  varies within
the 0–0.33 range. 
It is shown that the calculated estimates agree sat
isfactorily with the experimental data both qualita
tively (the regularities) and quantitatively (the numer
ical values). The error of the experimental and theo
retical results of determining the coefficient of
resistance to rolling does not exceed 7%.
The presented data are of great practical impor
tance since they open the way to control the friction
processes by varying offcontact loads as effectively as
by varying contact loads.
0 ,a pσ
0a pσ
Table 1. Analysis of experimental results
Maximum 
contact pres
sure p0, MPa
Conditions of friction
Parameters Equation Range of σa, 
MPaar μp μp/ar
Force system steel 18KhGT (shaft)/steel 18KhGT (roller) (σ–1 = 640 MPa, pf = 1272 MPa)
2000 In tension zone 0.010 0.160 16.00 0.063 – 0.010
σa 640 
In compression zone 0.026 0.415 15.96 0.063 + 0.056
3200 In tension zone 0.025 0.301 12.04 0.083 – 0.025
In compression zone 0.024 0.289 12.04 0.083 + 0.024
5600 In tension zone 0.007 0.079 11.29 0.089 – 0.007
In compression zone 0.001 0.011 11.00 0.089 + 0.001
0( )r r af f a pσ = ± σ
0( )a pσ
0( )a pσ
0( )a pσ
0( )a pσ
0( )a pσ
0( )a pσ
JOURNAL OF FRICTION AND WEAR  Vol. 33  No. 3  2012
COMPARATIVE EXPERIMENTAL STUDY OF FRICTION PARAMETERS 207
DESIGNATONS
FN—contact load; FS—sliding friction force;
FR—rolling friction force; —coefficient of
resistance to rolling in tribopair; —frictional stress
(specific friction force); p—contact pressure;
σ( )—cyclic stresses (cycle stress amplitude);
—coefficient of resistance to rolling in
force system; p0—maximum contact stress in center
of contact zone; δc—approach of axes (in tribopair);
μS—dimensionless parameter of interaction of dam
ages caused by contact and offcontact load (frictional
and mechanical stresses); fF—complex indicator of
friction in force system (friction index); —parame
ter characterizing angle of slope of straight lines
 to abscissa axis; —dimensionless
parameter of interaction of damages caused by contact
and offcontact load (frictional and mechanical
stresses); —friction coefficient during pure rolling;
—function taking into account effect of ratio
 on friction coefficient variations.
REFERENCES
1. Frolov, K.V., et al., Sovremennaya tribologiya: Itogi i
perspektivy (Contemporary Tribology: Results and Per
spectives), Moscow: Mashinostroenie, 2008.
2. Myshkin, N.K. and Petrokovets, M.I., Tribologiya.
Printsipy I prilozheniya (Tribology. Principles and
Applications), Gomel’: IMMS NANB, 2002.
3. Osnovy tribologii: Uchebnik (Fundamentals of Tribology:
A Textbook), Chichinadze, A.V., Ed., Moscow: Mashino
stroenie, 2001.
4. Sosnovskii, L.A., Zhuravkov, M.A., and
Shcherbakov, S.S., Fundamental’nye i prikladnye zada
chi tribofatiki: kurs lektsii (Fundamental and Applica
tion Problems of Tribofatigue: Course of Lectures),
Minsk: Belar. Gos. Univ., 2010.
5. Sosnovskii, L.A., Mekhanika iznosoustalostnogo pov
rezhdeniya (Mechanics of Tribofatigue Damage),
Gomel’: BelGUT, 2007.
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bofaticheskikh sistem (Mechanics of Tribofatigue Sys
tems), Minsk: Belar. Gos. Univ., 2010.
7. Sosnovskii, L.A., Komissarov, V.V., and
Shcherbakov, S.S., Procedure of the Experimental
Research of the Friction in Force System, J. Friction
Wear, 2012, vol. 33, no. 2, pp. 174–184.
8. Tyurin, S.A., Shcherbakov, S.S., and Sosnovskii, L.A.,
Comparative Study of Friction Coefficients at Rolling
and ContactMechanical Fatigue, Zavodskaya Labora
toriya, 2005, vol. 71, no. 2, pp. 48–51.
9. GOST (State Standard), 30755–2001. Tribofatigue.
Machines for WearFatigue Testings. General Technical
Studies. Intr. 01.07.02., Minsk: Mezhgos. Sovet po
Standartizatsii, Metrologii i Sertifikatsii, 2007.
10. GOST (State Standard of Belarus) 1233–2000. Tribofa
tigue. Tribofatigue. Methods of WearFatigue Testings.
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Intr. 01.10.07., Minsk: Mezhgos. Sovet po Standarti
zatsii, Metrologii i Sertifikatsii, 2007. 
( ) rf p f=
Wτ
aσ
( , )f p f
σ
σ =
ra
( )0af pσ ±σ pµ
( )sf
pkσ
( )
0
b
yy pσ
1
 
Table 2. Determination of calculation of error of coefficient of resistance to rolling based on experimental results and the
oretical states
Force system p0, MPa
Parameter of interaction, 
ar
Friction coefficient in force system f
σ
Error, %
experimental results calculations by (4)
σ > 0 σ < 0 σ > 0 σ < 0 σ > 0 σ < 0 σ > 0 σ < 0
Steel 18KhGT/Steel 18KhGT
2000 0.010 0.026 0.060 0.070 0.058 0.067 2.06 5.08
3200 0.025 0.024 0.076 0.090 0.077 0.089 2.51 1.77
5600 0.007 0.001 0.087 0.089 0.083 0.095 4.49 6.39
SPELL: 1. ok


Comparative Experimental Study of Friction Parameters in a Tribopair and a Force System

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Comparative Experimental Study of Friction Parameters in a Tribopair and a Force System

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