Copyright © 2022 V. Aulin, S. Lysenko, A. Hrynkiv, O. Liashuk, A. Hupka, O. Livitskyi. This is an open access article distributed 
under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, 

provided the original work is properly cited. 
 

 

 
Problems of Tribology, V. 27, No 4/106-2022, 69-81 

 

Problems of Tribology 
Website: http://tribology.khnu.km.ua/index.php/ProbTrib 

E-mail: tribosenator@gmail.com 
 

DOI:  https://doi.org/10.31891/2079-1372-2022-106-4-69-81 

 

 

Parameters of the lubrication process during operational wear of the 

crankshaft bearings of automobile engines  
 

V. Aulin1*, S. Lysenko1, A. Hrynkiv1, O. Liashuk2, A. Hupka2, O. Livitskyi1  

 
1 Central Ukrainian National Technical University, Ukraine 
2Ternopil Ivan Puluj National Technical University, Ukraine 

*E-mail: AulinVV@gmail.com 

 

Received: 09 November 2022: Revised:02 December 2022: Accept:12 December 2022 
 

 

Abstract 
 
The article discusses the dynamics of the lubrication process during the operational wear of the crankshaft 

bearings of automobile engines. All lubrication modes and wear processes are analyzed. The main attention is 

paid to the steady and unsteady modes of lubrication of the crankshaft bearings. The nature of the dynamics of 

changing lubrication regimes is substantiated through operational tribological parameters that characterize the 

integral degree of existence of the lubricating layer. A model is proposed for the relationship of these parameters 

with a number of factors, and the nature of their changes with a change in the speed of the crankshaft of the car 

engine is substantiated. 

The results of bench tests of diesel engines of the KamAZ series, speed and load characteristics of the 

engine in terms of tribological operational parameters are presented. A graphical interpretation of the tribological 

parameter in the field of the load-speed mode of KamAZ engines is given. 

 

Key words: car engine, crankshaft bearings, lubrication mode, tribological parameter, speed and load 

characteristics 

 

Introduction 

 

One of the movable mates that limit the life of the engine are the crankshaft bearings. They account for 

about 18% of the number of failures of all elements of the power units of KamAZ vehicles, the average time 

between failures is 12% of the engine life before overhaul, and the share of repair costs is over 45% [1,2]. 

Connecting rod and main bearings of the crankshaft of automotive internal combustion engines are fluid 

friction bearings lubricated under pressure. The external load vector acting on the crankshaft bearings varies not 

only in magnitude and direction, but also rotates relative to the crankshaft axis at a certain speed. The crankshaft 

not only rotates, but also moves relative to the bearings, squeezing out the oil. The thickness of the oil layer 

changes periodically. As the load increases, it decreases. The oil pressure in the supply line practically does not 

affect the pressure in the oil layer, but to a large extent affects the amount of oil pumped and the thermal state of 

the bearing [3,4]. 

The nature of the duration of the existence of the lubricating layer varies depending on the condition of 

the plain bearing. Therefore, it is fair to assume that such an operational tribological parameter as Pg , on the one 

hand, is sensitive to the technical condition of the bearing, and, on the other hand, affects the intensity of its 

wear [5,6]. 

In practice, when assessing the resource of car engines with identical and different numbers of 

connecting rod and main bearings of the crankshaft, it is important to identify the effect of various tribological 

parameters on the lubrication process of mating parts during operation. 

 

Literature review 

 

During the operation of the engine, the conditions for the operation of bearings in the liquid lubrication 

mode (hydrodynamic friction) must be ensured in the entire range of operating modes for which they are 

http://creativecommons.org/licenses/by/3.0/
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https://doi.org/10.31891/2079-1372-2022-106-4-69-81


70 Problems of Tribology 

 

intended. Under conditions of liquid lubrication, the rubbing surfaces of the mating parts are separated by a 

continuous layer of lubricant material of considerable thickness, several times greater than the sum of the 

heights of microroughnesses of the working surfaces. The process of mechanical wear is practically absent, but 

the processes of fatigue wear, cavitation wear and liquid erosion take place. It is believed that the abrasive action 

of particles of mechanical impurities contained in engine oil for connecting rod and main bearings is weakened. 

Oil on its way to the bearings undergoes coarse and fine cleaning in oil filters, as well as in dirt traps located in 

the crankshaft cavities [7,8]. 

The contact interaction of friction surfaces occurs during boundary lubrication, when the thickness of the 

boundary lubricating layer is several molecular layers of lubricant, oriented in the direction of movement of the 

mating parts, and is commensurate with the sum of the heights of the microroughnesses of the contacting 

surfaces [9-11]. 

Boundary lubrication is determined by the properties of boundary lubricating layers arising from the 

interaction of the material of the rubbing surface and the lubricant as a result of physical adsorption or 

chemisorption. In this case, the bulk properties of the lubricant do not appear, and the physicochemical 

interactions on the surfaces determine the nature of friction and wear. With boundary lubrication, molecular-

mechanical and corrosion-mechanical types of surface wear are realized. Wear intensity with boundary 

lubrication is 7-13 orders of magnitude higher than with liquid lubrication [12-14]. 

Violation of the liquid lubrication occurs when the friction surfaces approach each other so much that in 

the zones of the highest pressures the oil film breaks and the microroughnesses in the contact spots come into 

contact. In the case when the load is simultaneously perceived by the oil film and the contact surface 

irregularities, then this is the mixed lubrication mode. 

In the case of the alternate appearance and disappearance of the oil film between the rubbing surfaces, a 

transient lubrication process occurs. The operation of plain bearings of the crankshaft of automobile engines 

under the conditions of a transient lubrication process was studied in [18-20]. The intensity of wear during the 

transitional lubrication process is determined by the ratio of the duration of non-contact and contact types of 

interactions. It is believed that if the duration of contact between the journal and the bearing is short (no more 

than 20% of the cycle time), then these critical positions may not be dangerous [21-23]. 

The transient lubrication process is a general case of interaction of surfaces in lubricated tribocouplings of 

machine parts. Particular cases are liquid, boundary and mixed types of lubrication, which are considered as 

steady. At the same time, the dynamic process of transition from one type of lubricant to another is practically 

not considered. 

Steady-state lubrication mode – the work of tribocoupling of parts with constant indicators of the 

lubrication process over time: minimum thickness of the lubricating layer 
min

h , average temperature of the 

lubricating layer 
M

T , friction coefficient 
mp

f , dynamic oil viscosity  . A consistent set of steady state modes 

is a static characteristic of the tribocoupling of parts, usually represented as a dependence of process indicators 

on one of the parameters selected as an independent variable. 

The main sign of an unsteady regime is a violation of the condition of constancy of the process indicators 

in time  : )(
min

fh  , )(fT
M

 , )(ff
тр

 , )( f etc. Unsteady modes are characterized by 

cycle average values of indicators that change during the period of transition from one steady state to another. 

The dynamic characteristic is a time-sequential set of unsteady modes, represented by the dependence of the 

performance indicators of tribocouplings of parts that change during the transition process [24-25]. 

Of the variety of transient processes, the most characteristic are the following: 

– processes caused by a change in the speed of the v relative movement of the surfaces of tribocouplings 

of parts. The influencing parameters are the relative change 
Hv

vvv /)(
12

 , the period of change 
v

T and 

the nature of the change in speed )(fv  ; 

– processes caused by a change in the external load N on the tribocoupling of parts. The influencing 

parameters are the relative change 
HN

NNN /)(
12

 , the period of the change 
N

T and the nature of the 

change )(fN  ; 

– processes caused by changes in the properties (eg viscosity) and supply parameters of the lubricant (eg 

pressure, flow, temperature). The influencing parameters in this case are the relative change of these parameters, 

the period and nature of the change. 

– combined processes, accompanied by the simultaneous impact of changes in speed, load and properties 

and parameters of the lubricant supply. It is not only the main one in operational conditions, but also the most 

common case of transients. 

The deviation of the lubrication regime from liquid lubrication has a significant effect on the 

intensification of wear processes. The degree and nature of the deviation are determined by the conditions under 



Problems of Tribology 71 

 

which the transient lubrication process takes place, the degree of adaptation of the bearing to it. This indicates 

the need to have a unified system for comparative analysis of the lubrication process indicators in various 

operating conditions, the degree of their adaptation to the latter. When analyzing the quality of lubrication 

processes in tribo-conjugated parts, it is advisable to use relative indicators – the ratio of the indicator during the 

transition process to its value under steady-state lubrication modes. 

An important indicator characterizing the transitional lubrication process is its duration 
t

 . This value is 

calculated from the moment the lubrication mode is changed until the new mode is established. The last moment 

is determined by the achievement of stable indicators of the lubrication process, corresponding to the new steady 

state. In this case, the transitional lubrication process can be both incomplete and completed. The duration 

parameter of the lubricating layer depends on the time  : )(fP
g

 . If the t ratio has been established in 

the tribo-couplings of the parts over time 1
g

P , then it is considered that the transient process has ended and 

the non-contact interaction mode has been established, if 0
g

P  – the contact interaction mode. If the process 

has not been established, then it is characterized by average values 
g

P changing during the transition from one 

steady friction mode to another ( 10 
g

P ). 

The types of interaction of the rubbing surfaces of the tribocoupling parts are described by the Gersey-

Striebeck diagram (Fig. 1), which is the dependence of the friction coefficient 
тр

f on the load-speed mode 

( N – radial load on the bearing, v – linear velocity of the mating surfaces) and the properties of the lubricant in 
it (  – dynamic viscosity). 

H. Chihos [24] considers this diagram together with the dependence of the lifetime of the lubricating 

layer 
g

P and defines three characteristic areas: I – the area of continuous non-contact interactions – liquid 

lubrication ( 1
g

P ); II – area of alternating contact-non-contact interaction – transient lubrication process 

( 10 
g

P ); III – area of continuous contact interactions of surfaces ( 0
g

P ). 

fmp

III II I

μv/N
 

а 

0

1,0

Pg

μv/N

III II I

 
b 

Fig. 1. Combination of the Gersey-Striebeck diagram (a) with the characteristic scheme of parameter change 
g

P (b). 

 

An analysis of the lubrication process in the crankshaft bearings of automobile engines shows that: 

– bearings are designed to operate in a liquid lubrication mode, which ensures minimal wear of the 

tribological interfaces of parts, however, in real operating conditions they can also operate in other lubrication 

modes – mixed, boundary, transitional lubrication process, when the wear rate of rubbing surfaces increases 

significantly; 



72 Problems of Tribology 

 

– the lubrication mode is an important means of influencing the wear processes, and the violation of the 

liquid lubrication mode has a negative impact on the wear of the tribomechanical system, it is important to 

determine the conditions for establishing the liquid lubrication mode in the bearing; 

– it is advisable to consider the operation of bearings from the standpoint of a transient lubrication 

process, which is a general case of the interaction of rubbing surfaces of mating parts. 

 

Purpose 

 

The purpose of the work is to substantiate the influence of tribological parameters on the lubrication 

process of tribocouplings of parts (rod and main bearings of the crankshaft) of the engine. 

 

Results 

 

For a generalized assessment of the lubrication process in the connecting rod and main bearings of the 

crankshaft, the method of equivalent electrical circuits [7] of automobile engines is used. (fig.2., fig.3) The 

equivalent electrical circuit is an electrical circuit where voltage is applied to the cylinder block and crankshaft 

toe, and variable electrical resistances correspond to movable mates in the crank mechanism, cylinder-piston 

group and gas distribution mechanism . The variability of the resistance is determined by the changing thickness 

of the lubricating layer with dielectric properties in the contact zone of the tribo-coupling of the parts, depending 

on the lubrication conditions. 

For the implementation of bench tests, a scheme for connecting the electric current to parts of the CPG 

of diesel engines was proposed (fig. 2). 

 
Fig. 2. The scheme of connecting electric current to parts of the CPG of diesel engines: 1 – current source; 2 – 

resistance for adjusting the current value; 3 – current rectifier; 4 – current collector, screwed in instead of a ratchet; 5 

– engine to be run-in; 6 – ammeter; 7 – voltmeter: I – main bearings; II - connecting rod necks of the crankshaft and 

liners; ІІІ – piston fingers and bushings of the upper head of the connecting rods; IV – piston fingers and piston 

heads; V - cylinder liners, pistons and piston rings. 

 

From the rectifier, electric current is supplied to the "plus" brush unit, and "minus" to the engine block. 

The brush unit is installed on the side of the oil pump drive pulley, for this it is necessary to unscrew the ratchet 

and screw in the copper shaft of the brush unit instead. The negative terminal is connected to the cylinder block 

at the place of attachment of the fuel filter. 

The scheme of current distribution through the couplings of the engine (fig. 3) is a system of parallel 

chains, the first chain is the crankshaft, main bearings, cylinder block; the second chain – crankshaft, CPG, 

cylinder block. The current branches from the crankshaft to the main sliding bearings (resistance R1), and 

through the connecting rods of the crankshaft to the connecting rods (resistance R2), from the connecting rods to 

the piston fingers (resistance R3), from the fingers to the piston heads (resistance R4) and branches into two 

branches: from the piston to the sleeve (resistance R7) and from the piston to the piston rings (resistance R5) and 

further from the rings to the sleeve (resistance R6). 

The greatest resistance will be in the first chain (resistance R1), because when the engine is running, the 

crankshaft seems to "float" in the oil medium in the main sliding bearings. The electric current will look for the 

path of least resistance according to Ohm's and Kirchhoff's law, then the largest part of it will pass through the 

second link - through the parts of the CPG. 



Problems of Tribology 73 

 

 

 

 

F
ig

. 
3

. 
S

c
h

e
m

e
 o

f 
d

is
tr

ib
u

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f 
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c
tr

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 c

u
r
r
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t 
o

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 t

h
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 p

a
r
ts

 o
f 

th
e
 C

P
G

 o
f 

d
ie

se
l 

e
n

g
in

e
s:

 C
S

 –
 c

r
a

n
k

sh
a

ft
; 

B
 –

 c
y

li
n

d
e
r
 b

lo
c
k

 (
m

a
in

 b
e
a

r
in

g
s)

; 
C

 –
 c

o
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g

 r
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 (

c
o

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r
o

d
 b

u
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in
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s)
; 

P
P

 –
 p

is
to

n
 p

in
; 

P
 –

 p
is

to
n

 (
p

is
to

n
 h

e
a
d

s)
; 

P
R

 –
 p

is
to

n
 r

in
g

s;
 C

L
 –

 c
y

li
n

d
e
r
 l

in
e
r
; 

R
1
 –

 t
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ta
l 

r
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si

st
a

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c
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 b

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tw

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n

 t
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 r

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o

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n

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c
k

 a
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d
 t

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 r

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t 
li

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r
s;

 R
2
 –

 t
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 t
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 c

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 r
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d
 c

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 r
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d

 l
in

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r
s;

 R
3
 –

 t
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r
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 b

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tw

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 t
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 b

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 t
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 p

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 f

in
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 R
4
 –

 t
h

e
 t

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ta

l 

r
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si

st
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c
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 b

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 t
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 p

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 f

in
g

e
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s 

a
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d
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h
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 p

is
to

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 h

e
a

d
s;

 R
5
 –

 t
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ta
l 

r
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si

st
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 b

e
tw

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g

; 
R

6
 –

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o

ta
l 

r
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le
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v

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; 

R
7
 i
s 

th
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 p
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a

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 s
le

e
v

e
s.

 



74 Problems of Tribology 

 

This is due to the fact that the oil film between the connecting rod neck and the connecting rod liner 

when the engine is running has a much smaller thickness than that between the main neck and the main slide 

bearing, that is, it has less resistance. In other elements of CPG parts, the thickness of the oil film is even 

smaller, since the rings perform a reciprocating movement relative to the mirror of the cylinder liner. Thus, the 

thickness of the oil film at TDC and TDC of the rings will be minimal to 0.1 μm. At the same time, the mode of 

marginal friction is observed. The maximum thickness of the oil film will be at the moment when the rings reach 

the maximum speed and will have a thickness within 10 microns, depending on the oil density. Therefore, the 

maximum part of the current will pass through the CPG parts when the piston is in the dead center position. At 

this moment, the current on the parts of the CPG will be distributed almost evenly in the engine, since at the 

same time the pistons will occupy different positions relative to the sleeve. The difference in the passage of 

current through the parts of the CPG for one revolution of the crankshaft will be up to 10%. 

The resistance between the crankshaft and main bearings is a parallel chain of resistances and is 

calculated by the expression: 

43211

11111

кккк
RRRRR

 . 

Similarly, the total resistance between the crankshaft and connecting rods is calculated: 

6543212

1111111

CCCCCC
RRRRRRR

 . 

Current and voltage were recorded using an ammeter and a voltmeter, and then the total resistance R 

was calculated according to Ohm's law 
R

U
I  . 

In modern automobile engines, there are at least 20...25 types of movable mates, and their total number 

depends on the design of the engine, and is 100...150 units and more. Lubrication regimes differ significantly 

from each other and depend on many factors: purpose, load-speed and thermal regimes, lubricant supply 

conditions, technical condition, etc. 

An analysis of equivalent electrical circuits allows us to conclude that the probability of electric current 

passing between the cylinder block and the crankshaft is determined by the probability of metal contact in the 

movable mates of the crankshaft. The contact of the mating of bearing parts occurs when the lubricating layer is 

destroyed, the integral probability of the existence of a lubricating layer in the tribocoupling is equal to: 

 











ki

i

mj

j

ccp

jg

mb

ig

cgb

g

gdm

g

tb

gg
PPPPPP

1 1

..
,    (1) 

where 
tb

g
P is the parameter 

g
P in the thrust main bearing; 

gdm

g
P – parameter 

g
P in the group of interfaces 

of parts of the gas distribution mechanism and its drive; 
cgb

g
P - parameter 

g
P in the group of interfaces of clutch 

and gearbox parts; 
mb

ig
P

. – parameter gP in the i-th main bearing; 
ccp

jg
P

. – parameter gP in the j-th group of the 

connecting rod bearing and the cylinder-piston group; k and m are the number of main bearings and groups of 

mating parts from the connecting rod bearing and the cylinder-piston group, respectively. 

The analysis of formula (1) allows us to draw a conclusion about the relationship between the parameter 


g
P and the parameter values 

g
P in each group of mating parts. Moreover, if 1



g
P , then this means the 

conditions of non-contact interaction in all groups of triboconjugations of parts ( 1
g

P ), if 0


g
P , then at 

least one of the groups has metal contact ( 0
g

P ). 

The operating conditions of the thrust bearing show that fluid friction predominates in it, and therefore 

the following condition can be assumed: 1
tb

g
P . 

The conditions for the passage of electric current from the crankshaft to the cylinder block through the 

drive of the gas distribution mechanism and the gas distribution mechanism itself make it possible to assume 

that 1
gdm

g
P . 

The parameter 
ccp

g
P can be estimated by the formula: 

)1()1)(1)(1(1
2 pc

g

pp

g

ph

g

cb

g

ccp

g
PPPPP  ,   (2) 

where 
cb

g
P , 

ph

g
P , 

pp

g
P , 

pc

g
P is the parameter 

g
P in the connecting rod bearing, respectively, of the 

tribo-couplings of the parts "piston pin-bushing of the piston head of the connecting rod", "piston pin-piston 



Problems of Tribology 75 

 

boss" and "piston-cylinder". 

An analysis of formula (2) shows a complex dependence of the parameter 
ccp

g
P on the type of interaction 

in tribo-couplings of parts. If the parameter is in one of the tribological conjugations of the parts 1
g

P , then 

the values of the parameter 
g

P in other conjugations do not have a significant effect on the value of 
ccp

g
P . 

The operating conditions of the tribocouples "piston pin-piston head sleeve", "piston pin-piston boss" and 

"piston-cylinder" indicate that they are dominated by boundary friction 0
g

P , and therefore the following 

relationship can be assumed: 

1)1()1)(1(
2


pc

g

pp

g

cb

g
PPP .      (3) 

Hence it follows that 
cb

g

ccp

g
PP  . Based on the assumptions made, the 



g
P operational friction 

parameter is determined by the formula: 

 











ki

i

mj

j

cb

jg

mb

igg
PPP

1 1

..
,       (4) 

The indicator is 


g
P used for a comparative assessment of engines with identical numbers of connecting 

rod and crankshaft main bearings. To evaluate engines with different numbers of bearings,  an "equivalent 

crankshaft bearing" model is proposed, which has a generalized assessment of the lubrication process in 

connecting rod and main bearings. For quantitative assessment, the parameter is used 
g

E - "integral degree of 

existence of the lubricating layer", the value of which is determined by the formula:  

mk

ki

i

mj

j

cb

jg

mb

igg
PPE 









 
1 1

..
.      (5) 

The value of the parameter 
g

E changes from the maximum value 1)(
max


g

E , which characterizes the 

steady state of liquid lubrication in all crankshaft bearings, to the minimum value 0)(
max


g

E , at which at 

least one bearing operates in the mode of boundary lubrication or dry friction. Intermediate values of the 

parameter 10 
g

E take place under the conditions of a transient lubrication process with successive 

alternation of liquid and boundary lubrication in time. 

On fig. 4 shows the dependences of tribological parameters 


g
P and 

g
E on the speed of the crankshaft. 

0,5

0,6

0,7

0,8

0,9

1,0

90 180 270 360 450 540 630 720

Eg

Eg

a, deg
 

a 

0

0,1

0,2

0,3

90 180 270 360 450 540 630 720

P
Ʃ
g

a, deg
 

b 

Fig. 4. Scheme of formation of parameters 
g

E (a) and 


g
P (b) 



76 Problems of Tribology 

 

It is determined that under operating conditions the value of the parameter 
g

E depends on a number of 

factors: 

,...),,,),(,,,,( 
крPМPMbbgg

hрTTnМdlEE  .    (6) 

The factors involved in the model (6) change according to various patterns: 

– bearing length 
b

l and bearing diameter 
b

d remain practically unchanged; 

– the dynamic viscosity of the oil  is determined by the viscosity-temperature properties of the oil 

)(
M

T according to SAE, due to the aging of the base base, dilution with fuel, and the operation of additives;  

– the crankshaft speed n and torque М vary over a wide range depending on the load and speed modes 
of the engine; 

– the critical thickness of the lubricating layer 
кр

h depends on the roughness and other micro- and 

macrogeometric parameters of the friction surfaces, is formed initially during manufacture and installation, 

decreases during running-in, changes insignificantly during the period of steady (normal) wear, and increases 

during accelerated wear; 

– the diametrical clearance  is formed during manufacture and installation, increases due to wear of 
the journals and liners of the crankshaft, both at the running-in stage and during periods of steady (normal) and 

accelerated wear; 

– oil pressure is 
P

р determined by the design and characteristics of the elements of the main oil line and 

the lubrication system, increases with increasing crankshaft speed, oil viscosity, and decreases with increasing 

oil filter contamination, wear of the oil pump and crankshaft bearings, overheating and dilution by fuel; 

– the oil temperature 
M

T depends on the thermal state of the engine parts, the operation of the engine 

preheating system; in the starting mode during warm-up increases, while driving it depends on the load-speed 

mode of the engine and on the factors of warming and cooling the engine. 

Thus, the integral degree of existence of the lubricating layer 
g

E in the crankshaft bearings depends on 

the oil temperature and the load-speed mode, and these dependencies have their own characteristics at the 

stages of running-in, steady-state (normal) and accelerated wear. 

During the running-in of bearings, the factors 
кр

h and are variables  . 

Under the same factors, the conditions of the load-speed mode of operation, the thermal state of the 

engine and the properties of the engine oil, the values of the factors М , n , MPT and )( MT in model (6) are 

unchanged, which makes it possible to determine the values of the parameter 
g

E depending on the factors of 

the technical condition of the bearings using the dependence ),( 
крgg

hEE . 

The operational wear of bearings depends on a variable factor  . The validity of diagnosing the 
crankshaft bearings is determined by the fact that under the same operating modes, the thermal state of the 

engine and the properties of the engine oil, the values of the parameters М , n , MПT , крh and )( MT  in 

model (6) are unchanged, and it becomes possible to determine the diametrical clearance using the established 

dependence )( gE . 

When the engine is warming up at idle, the values of the factors  and 
кр

h , as well as the viscosity-

temperature characteristic of the oil )(
M

T in model (6) are unchanged, and the factors n , MПT and 

П
р depend on the time  in the start mode. This allows you to determine the parameter values 

g
E depending 

on the values of the crankshaft speed n and oil temperature MPT using the model ),,( nTEE MPgg  . 

When the engine is running, the factors M and n are variables. With the same thermal and technical 

conditions of the engine and the properties of engine oil, the values of the parameters 
MP

T , )(
M

T ,  and 

кр
h in model (6) are unchanged and it becomes possible to determine the value of the parameter 

g
E depending 

on the operating mode factors ( М and n ) using the model ),( nMEE gg  . 

The basis of experimental studies of the lubrication process in the crankshaft bearings, depending on the 

load-speed mode of the engine on the stand, is an enlarged model containing input (torque on the crankshaft 

М , crankshaft speed at idle n ) and output (indicator 
g

E  and dependencies ),( nMEE gg   and 

),( nMWW
ii

  variables. 

The test object was the KamAZ-740.14-300 diesel engine, which is used on KamAZ-53212, 43353, 

53229, 65115 vehicles, and is identical in design of the lubrication system and crank mechanism with engines 



Problems of Tribology 77 

 

of other modifications KamAZ-740.11-240, 740.13 -260 used on many vehicles. The tests were carried out in 

the engine testing laboratory of the ERM department. The engine was installed on the stand of the company 

"AVL" with a hydraulic brake company "SCHENCK". The test engine was run-in, and the operating time at the 

time of testing was about 1200 moto-hours. 

When testing the engine, coolant temperatures were maintained from 80ºС to 85ºС and oil from 75ºС to 

80ºС. Steady operating modes were sequentially set at crankshaft speed n = 1000, 1400, 1800, 2200 and 2400 

min -1 with a stepwise change in torque М at each frequency from 100 to 1000 Nm with a step of 100 Nm. 
The measurements were carried out in the forward and reverse directions. The duration of measurement 

in each mode was 30 s after an exposure of 30 s. 

The results of parameter measurements 
g

E in each operating mode were averaged. The obtained load 

and speed characteristics of the engine in terms of the parameter 
g

E made it possible to draw the following 

conclusions: 

– with an increase in the load on the engine at a constant crankshaft speed, the parameter decreases, 

which indicates a progressive deterioration of the liquid lubrication (fig. 5); 

– with an increase in the shaft rotation frequency at a constant torque, the dependence of the p arameter 

has a parabolic form (fig. 6) with a maximum characterizing the best lubrication conditions in the frequency 

range from 1250 to 1550 min -1 . 

0.8

0.85

0.9

0.95

1

1000 1350 1700 2050 2400

Eg

n, minute-1M=100Nm M=500Nm М=900Nm  
Fig. 5. Motor speed characteristics by parameter 

g
E (n) 

0.8

0.85

0.9

0.95

1

100 200 300 400 500 600 700 800 900 1000

Eg

M, Nm
n=1000 minute -1 n=1400 minute -1 n=1800 minute -1

n=2200 minute -1 n=2400 minute -1
 

Fig. 6. Engine load characteristics by parameter 
g

E (M) 

 

For further analysis of the lubrication process in KamAZ engines, the values of rotational speed and 

torque were recalculated into relative values according to the formulas: 



78 Problems of Tribology 

 

)/(100
0 nomx

nnn  ,      (7) 

)/(100
0 nomx

MMM  ,      (8) 

where 0M and 0n are the relative values of torque and crankshaft speed, %: nomn =2600 min 
–1 and 

ном
M =1000 Nm are the maximum absolute values of the indicators. 

The experimental data ),( nMEg were approximated using PC applications, and a polynomial model of 

the form was obtained: 

00
2
0

2
000 MfneMdncMbnaEg  ,    (9) 

where a, b, c, d, e, f – the coefficients of the model, the values of which are: a = 0.6966; b = 0.01107; c 

= 0.0004430; d = -0.0001012; e = -2.2734 10 -6 ; f = -9.3841 10 -6 . 

The coefficient of determination of the model was r 2 = 0.974, the standard error was 0.0104, which 

indicates a sufficient quality of the approximation. 

Using model (9), the multifactorial characteristics of the engine were built according to the parameter of 

the integral degree of existence of the lubricating layer 
g

E in the crankshaft bearings (fig. 7 and 8). 

 

Fig. 7. Graphical interpretation of equation (9) by parameter 
g

E in the field of load-speed mode of engines of the 

KamAZ series 

 

Fig. 8. Areas of parameter levels 
g

E in the field of the load-speed mode of the KamAZ engine 



Problems of Tribology 79 

 

The analysis of the multifactorial characteristics of the engine by the parameter 
g

E  makes it possible to 

determine the areas of the load-speed mode of operation, in which the lubrication mode of the crankshaft 

bearings with different levels of the parameter values is provided 
g

E . It can be seen that the area of the load-

speed mode with a high level of parameter values 98,0gE  is: for the crankshaft speed from 40% to 65% and 

torque from 10% to 50%; crankshaft speed from 45% ... 60% and torque from 50% to 80%. 

Model (9) and multifactorial characteristics give an idea of the suitability of the engine to the operating 

mode in terms of the parameter of the integral degree of existence of the lubricating layer 
g

E  in the crankshaft 

bearings. 

Of practical interest is the assessment of the suitability of the engine to the operating mode in terms of 

the integral wear resistance IW  of the crankshaft bearings. The multifactor characteristic of the engine (fig. 9) 

shows the distribution of parameter values IW  in the areas of the load-speed mode. 

 
Fig. 9. Multifactorial characteristic of the engine by parameter IW  in the areas of load-speed mode 

 

The resulting graphical display shows that: high wear resistance of the crankshaft bearings is 

1000I W provided in the region of relative speed from 45% to 60% and relative torque from 10% to 30%. As 

the load-speed mode expands, the relative torque equal to 30% or more and the relative speed of 65% or more 

reduce the wear resistance of bearings. The speed range of 45% to 60% corresponds to an average piston speed 

in the range of 4.7 to 6.2 m/s. These values are close to the speed range of 5...7 m/s, which pro vide "wear-free" 

speeds of the crankshaft of the engine. 

 

Conclusions 

 

1. A technique has been developed for the experimental study of the lubrication process in the bearings of 

the crankshaft of an automobile engine during bench tests. 

2. The regularities of the parameter of the integral degree of existence of the lubricating layer in the 

crankshaft bearings from the load-speed mode of operation of the KamAZ-740.14-300 engine have been 

established, which made it possible to find the regularities of the wear resistance index of the crankshaft bearings 

also from the load-speed mode of the engine. 

3. It was revealed that the maximum wear resistance of the bearings is provided in the region of the 

relative value of the crankshaft speed from 45% to 60% and the relative value of the torque from 10% to 30%; 

and it is on average 20...25 times higher compared to wear resistance in other modes; as the load-speed mode 

expands from a relative torque of 30% and from a relative crankshaft speed of 65%, the wear resistance of the 

bearings decreases sharply. 

 

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Problems of Tribology 81 

 

 

Аулін В.В., Лисенко С.В., Гриньків А.В., Ляшук О.Л., Гупка А.Б., Лівіцький О.М. Параметри 

мастильного процесу при експлуатаційному зношуванні підшипників колінчастого валу автомобільних 

двигунів 
 

У статті розглядається динаміка мастильного процесу при експлуатаційному зношуванні 

підшипників колінчастого валу автомобільних двигунів. Проаналізовано всі режими змащення та 

процеси зношування. Основна увага приділена режимам змащення підшипників колінчастого валу, що 

встановився і не встановився. Характер динаміки зміни режимів змащення обґрунтовується через 

експлуатаційні трибологічні параметри, які характеризують інтегральний ступінь існування мастильного 

шару. Запропоновано модель зв'язку цих параметрів з цілого ряду факторів, а також обґрунтовано 

характер їх змін із зміною частоти обертання колінчастого валу двигуна автомобіля. 

Наведено результати стендових випробувань дизелів серії КамАЗ, швидкісних та 

навантажувальних характеристик двигуна за трибологічними експлуатаційними параметрами. Дано 

графічну інтерпретацію трибологічного параметра в полі навантажувально-швидкісного режиму 

двигунів серії КамАЗ. 

 

Ключові слова: автомобільний двигун, підшипники колінчастого валу, режим змащення, 

трибологічний параметр, швидкісні та навантажувальні характеристики