DEFORMATIONAL BEHAVIOR OF THE FLAT SLIDING LAYER OF THE SPHERICAL BEARING

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 05, May 2019, pp. 99–107, Article ID: IJCIET_10_05_011
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=5
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
DEFORMATIONAL BEHAVIOR OF THE FLAT
SLIDING LAYER OF THE SPHERICAL
BEARING
А.А. Аdamov
Department of Nonlinear Mechanics of a Deformable Solid, Institute of Continuous Media
Mechanics, Russia, Perm
А.А. Kamenskikh, Yu.О. Nosov
Department of Computational Mathematics, Mechanics and Biomechanics, Perm National
Research Polytechnic University, Russia, Perm
ABSTRACT
Analysis of the friction properties of modified PTFE is performed, the functions
describing the change in the friction coefficient depending on the pressure level with a
maximum error from the experiments results less than 1% are proposed in the work.
The influence of friction on the deformation behavior of the flat sliding layer of the
spherical bearing on a periodicity cell model is considered. The geometrical
configuration of the flat sliding layer with truncated spherical hole for the lubricant is
considered. The periodicity cell includes one hole for lubrication. A series of
numerical experiments for three options for the thickness of the sliding layer from 4 to
8 mm with a recess for the lubricant, in the unfavorable case the absence of lubricant
is performed. The pattern of geometric configuration hole change with increasing
pressure level is established. It was found that an increase of the antifriction layer
thickness leads to a less significant deformation of the sliding layer thickness and the
spherical hole. The sliding layer with a thickness of 8 mm has the smallest level
minimum stress intensity and the material volume with the maximum stress intensity is
minimal for this variant of the sliding layer thickness compared to other variants. The
maximum integral stiffness of the 8 mm sliding layer decreased slightly by 1.74 and
1.5% on contact without and with lubricant respectively.
Key words: Contact, Friction, Modified PTFE, Antifriction layer and Deformation
behavior
Cite this Article: А.А. Аdamov, А.А. Kamenskikh, Yu.О. Nosov, Deformational
Behavior of the Flat Sliding Layer of the Spherical Bearing, International Journal of
Civil Engineering and Technology 10(5), 2019, pp. 99–107.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=5

Deformational Behavior of the Flat Sliding Layer of the Spherical Bearing
1. INTRODUCTION
A lot of elements and designs applied in mechanical engineering, construction, medicine and
other areas work in the conditions of contact interaction. These designs are costly. It is
difficult to repair them. High requirements with respect to durability, reliability and service
life are presented to them. The antifriction coatings and layers are widely used to create
favorable conditions for the contact nodes operation. As examples of systems with contact
layers and coverings it is possible to note sliding bearings [1], hip endoprosthesis [2],
hydraulic turbines [3] and so on. These structures include elements of transport and logistics
systems, such as temperature joints and supporting parts of bridge bearing parts. Researchers
note the main actual problems of transport and logistics systems related to bridge
construction: geometric configuration and technology of deformation joints [4, 5], bearings
[6, 7], bridge spans [8], hoisting structures of draw bridges [9], as well as other elements of
bridge structures. We can note a special interest in the deformation behavior of the bearing of
bridge spans [10-14, etc.]. The most of the works are aimed at the analysis of bearing
capacity, strength, wear resistance of bridge structure elements, as well as the assessment of
the stress-strain state of bearing structures in general [10, 12, 13] and the identification of
patterns of change in contact zones in particular [13, 15]. Several works are devoted to the
studies of the possibility of using modern anti-friction polymeric materials in the structures of
bearing parts [12, 14, etc.]. Methods of mathematical modeling as well as effective numerical
methods including modern application software systems [13-15, etc.] are used in the study of
the deformation behavior of the bearings of bridge. Thus, a numerical analysis of the
deformation behavior of the elements bearing of bridge structures, taking into account the
materials properties from which they are made is an important area of research. The influence
analysis of the frictional properties polymer layers and the geometrical configuration of the
transport and logistics systems elements on the stress-strain state of the responsible units is
also relevant.
2. PROBLEM STATEMENT
The deformation behavior of a thin flat antifriction sliding layer of modified PTFE with
truncated spherical holes for lubrication (fig. 1) is considered in the work. Flat sliding layer is
used in transport and logistics systems elements such as spherical bearing of bridge spans.
The periodicity cell is cut out from the antifriction material volume as shown in fig. 1 with
geometrical characteristics: thickness 4, 6, 8ph  mm, maximum width 18 mm, maximum
depth 15 mm, diameter of a spherical hole 8 mm, height of a spherical hole 2 mm. The
problem of deforming the periodicity cell of a thin flat sliding layer made of modified PTFE
of pressure from 5 to 90 MPa taking into account the friction properties of the polymer a 3
mm thickness rigid steel plate is realized. A fourth of the contact unit is considered. The
discarded parts action is replaced by symmetry conditions. Lack of lubricant in the hole as an
unfavorable case is considered.

А.А. Аdamov, А.А. Kamenskikh, Yu.О. Nosov
Figure 1 Fragment of antifriction material layer with lubrication holes:
a, b - geometric characteristics of a periodicity cell
The friction properties influence of the modified PTFE on the stress-strain state of the
periodicity cell is considered in the work. A experiments series to determine the frictional
properties of modern antifriction materials suitable for use as a sliding layer in transport and
logistics systems elements was made earlier by the research team of Alfa-Tech LLC and
IMSS of the Ural Branch of the Russian Academy of Sciences. The original equipment was
made and the deformation of cylindrical sample with a diameter of 0.097 0.103 m and a
height of 0.01 m by steel plates of the press was made in the framework of experiments. The
relations of the friction coefficient  on pressure P are established in the framework of the
experiments series [16].
Original experimental equipment allowed to determine the frictional properties of
antifriction materials in the pressure range up to 54 MPa at the same time the operating
pressure range of the spherical bearing can reach 90 MPa. The approximation of the
experiments results was performed in the framework of the experimental data analysis. The
approximating functions are selected in the framework of the study:
  2 3 4
1.55 17.166 64.979 55.745
0.002P
P P P P
     for contact without lubrication on mating
surfaces and   2 3 4
0.111 0.623 3.57 3.335
0.005
P P P
P
P
    for contact with lubrication on
mating surfaces. Selected functions were used to calculate friction coefficient values in the
range of more than 54 MPa. The error of the friction coefficients obtained from the
approximating functions on the experimental data does not exceed 1% for the modified PTFE.
The results of experiments with and without lubrication as well as the functions
approximating the experiments results are shown in the figure 2

Figure 2 Relation of friction coefficient on pressure:
1 is experimental data without lubrication; 2 is approximation of experimental data (1); 3 is
experimental data with lubricant; 4 is approximation of experimental data (3)
The numerical simulation of the problem deforming of the periodicity cell of the spherical
bearing thin flat sliding layer was performed using the finite element method in the ANSYS
software package. The problem is considered in a three-dimensional setting. The deformation
theory of elastoplasticity is chosen to describe the behavior model of the antifriction layer
material. Frictional contact interaction with a previously unknown contact area and the pattern
of the contact state zones distribution (slippage, sticking, sticking) is considered [15].
3. RESULTS AND DISCUSSION
A series of numerical calculations on a periodicity cell with a thickness of 4 mm was carried
out as part of the convergence analysis of the contact problem numerical solution results. Four
variants of the finite element mesh were considered: 15, 41, 169 and 443 thousand node
unknowns. The numerical solution convergence assessment was performed by displacements
of the contact boundary 1L (Fig. 1). The finite element mesh with gradient concentration of
elements to the contact area was chosen for the main volume of the material according to the
study results: the maximum element size is 0.5 mm, the minimum one is 0.125 mm (169
thousand node unknowns). The resolution about concentration the mesh near the edge of the
hole, which was initially in contact with a rigid stamp, was taken to clarify the contact
parameters near the hole for the lubricant. The element size in this area was 0.074 mm,
increasing the number of node unknowns to 237 thousand.

Figure 3 Convergence of the numerical solution by xu and yu (the edge 1L ):
1 is 15; 2 is 41; 3 is 169; 4 is 443 thousand node unknowns
Discretization of a periodicity cell with different antifriction sliding layer thickness with a
gradient decrease in the element size to the contact zone is performed with selected
parameters of the finite element mesh: 4ph  mm is 237 thousand, 6ph  mm is 263
thousand and 8ph  mm is 277 thousand node unknowns respectively.
A numerical experiments series aimed at analyzing the deformation behavior of the
periodicity cell are performed as part of the work: analysis of changes in the hole profile for
the lubricant, stress intensity analysis, plastic deformations level analysis, integral stiffness of
the periodicity cell analysis.
The change in the profile hole during contact deformation of the periodicity cell of
different thickness with a hole for the lubricant is shown in figure 4. The deformation of the
hole for the lubricant is presented for the case of frictional contact interaction taking into
account the lubricant on the mating surfaces.
It was established that in the deforming process of the hole profile for the lubricant does
not change significantly to a pressure of 30 MPa. Hole for the lubricant significantly changes
its geometrical configuration under loads over 30 MPa. The geometric configuration is
deformed significantly at a maximum load of 90 MPa: the hole height is 20, 35 and 41% of
the initial height, the hole radius decreased by 46.3, 40.8 and 35.6% for a sliding layer 4, 6, 8
mm thickness respectively. At the same time, the thickness of the sliding layer decreased by
8.7, 6.5 and 5.4% for the sliding layer with a thickness of 4, 6, 8 mm respectively.
Deformation of the hole profile on contact without lubricant on the mating surfaces by 2.24,
1.83 and 1.39% more than when contact with lubricant for a sliding layer 4, 6, 8 mm
thickness respectively.

Figure 4 Deforming of the hole profile for lubrication on 1L :
a is 4ph  mm; b is 6ph  mm; c is 8ph  mm
The relations of the maximum and minimum stress intensity on pressure are presented in
figure 5.
Figure 5 The relations of the stress intensity on pressure ( intmax : solid line is contact with lubricant;
dotted line is contact without lubrication; intmin : dash-dotted line is contact with lubricant; round
points is contact without lubrication)
The zone of maximum stress intensity increases nonlinearly. The minimum stresses
intensity in contact with lubricant for a thickness of 4 mm is on average less by 2.3% at
pressures up to 10 MPa, at pressures > 30 MPa is on average more by 17% than during

contact without lubricants; for a thickness of 6 mm is on average less by 2.6% at pressures up
to 70 MPa, at pressures > 70 MPa is on average more by 16% than during contact without
lubrication; for a thickness of 8 mm is on average less by 6% for the entire pressure range.
The maximum stresses intensity in contact with the lubricant in the load range up to 15 MPa
is more by 0.9% than in the case of contact without lubricant.
The relations of the maximum and minimum integral stiffness on pressure are shown in
figure 6.
Figure 6 Relation of integral stiffness to the pressure ( intmax k : solid line is contact with lubricant;
dotted line is contact without lubrication; intmin k : dash-dotted line is contact with lubricant; round
points is contact without lubrication)
The minimum integral stiffness on contact with lubricant is on average less by 2.5% than
on contact without lubrication for all variants of the periodicity cell thickness. Maximum
integral stiffness on contact with lubricant: for a thickness of 4 mm is on average less by 21%
than when in contact without lubrication; for a thickness of 6 mm is on average more by
1.15% than when in contact without lubrication; for a thickness of 8 mm is on average more
by 0.23 % than when in contact without lubrication. The relations of the maximum and
minimum integral stiffness on the load are nonlinear. The integral stiffness of the periodicity
cell decreased from the initial value by 53.59, 36.57 and 1.74% upon contact without
lubrication and by 61.92, 35.19 and 1.5% upon contact with lubrication on the mating
surfaces for 4, 6 and 8 mm thicknesses respectively. The maximum decrease integral stiffness
of the periodicity cell with a thickness of 4 mm upon contact with lubricant on the mating
surfaces is due to the highest level of plastic deformation.
The relation of the plastic deformation maximum level on pressure is shown in figure 7.

Figure 7 Plastic deformations intensity: solid line is contact with lubrication; dotted line is contact
without lubrication
The maximum plastic deformation intensity is observed near the hole for the lubricant.
The maximum plastic deformations intensity of the periodicity cell with a thickness of 6 and 8
mm is less than that of a periodicity cell with a thickness of 4 mm by 1.5 and 2.5 % at the
contact with and without lubricant on the mating surfaces respectively. The maximum plastic
deformations intensity on contact with the lubricant is on average more by 3.5% than in the
case of contact without lubricant for all variants of the periodicity cell thickness.
4. CONCLUSION
The deformation behavior modeling of the spherical bearing thin flat sliding layer of the
modified PTFE was performed as part of the study. The study was performed on periodicity
cells with hole for the lubricant. The case of the absence of lubricant in the hole was
considered during frictional contact interaction of the periodicity cell with a steel rigid stamp
with and without lubrication on the mating surfaces. A comparative analysis of the
deformation behavior for three variants of 4, 6, and 8 mm periodicity cell thickness was
performed. The influence analysis of the frictional properties of the antifriction material and
the sliding layer thickness on the stress-strain state of the contact unite is performed.
To analyze the results of a series of numerical experiments, it was found out
- The thickness of the antifriction layer decreased by 8.7, 6.5 and 5.4% for the sliding
layer with a thickness of 4, 6, 8 mm respectively. Accounting for lubricant at the contact
boundary has a slight effect on the thickness of the flat sliding layer.
- The effect of lubricant on the deformation of the hole profile for the lubricant is not
significant. The hole profile does not significantly deform at pressures up to 30 MPa. The
hole profile is significantly deformed with a pressure of more than 30 MPA: hole profile
becomes non-spherical, significant deformation of geometric parameters is observed. With a
maximum pressure of 90 MPa the thickness hole is 20, 35 and 41% of the initial height, the
radius hole decreased by 46.3, 40.8 and 35.6% for a sliding layer thickness of 4, 6, 8 mm
respectively.
- The sliding layer thickness has a significant effect on the stress intensity and the integral
stiffness of the periodic cell. An increase in the minimum level stress intensity by 17% with a
load of more than 30 MPa and by 16% with a load of more than 70 MPa is observed during
contact with lubricant for thicknesses of 4 and 6 mm respectively compared to the case of
contact without lubrication. A decrease minimum level of stress intensity average by 6% over

the entire pressure range is observed for a thickness of 8 mm. The integral stiffness of the
periodicity cell decreased from the initial value by 53.59, 36.57 and 1.74% upon contact
without lubrication and by 61.92, 35.19 and 1.5% upon contact with lubrication on the mating
surfaces for 4, 6 and 8 mm thicknesses respectively.
- Antifriction layer of 8 mm thickness has a more favorable case of stress-strain state:
deformation of the hole for the lubricant and the thickness of the sliding layer is the smallest
compared with the other considered thicknesses; maximum integral stiffness of the periodicity
cell is less by 1.5 and 1.74% than the standard stiffness value of the modified PTFE at contact
with and without lubrication respectively; volume of material with a maximum stress intensity
is minimum.
ACKNOWLEDGEMENTS
The study supported by a grant of Russian Science Foundation (project No. 18-79-00147).
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DEFORMATIONAL BEHAVIOR OF THE FLAT SLIDING LAYER OF THE SPHERICAL BEARING

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