The major failure mechanism of typical spherical plain bearings with selflubrication is the wear of the woven fabric liner, which is an orthotropic composite of different elastic properties in different directions. The elastic properties of the liner are required for studying the tribological properties of the spherical plain bearings. This paper aims to develop an elastic property analysis model suitable for three commonly used fabric liners through a theoretical analysis of the elastic properties in order to obtain the parameter expression of the compliance matrix. The influence of the elastic properties on the wear depth of the spherical plain bearings is further investigated. Suggestions are made for the optimal design of the spherical plain bearings based on wear reduction.
Spherical plain bearing with selflubricating is a kind of sliding bearings with lowspeed multiaxial rotary oscillating motion pattern. Widely used in mining and metallurgy, aerospace, tank cannon gun system, and so forth [
The woven fabric liner is mainly made up of matrix and reinforced fibers, and the fiber distribution of the typical woven fabric liners is shown in Figure
Fiber distribution of the woven fabric liner.
Plain liner
Twill liner
Stain liner
Take the black box parts (in Figure
(1) The cross section of the yarn is lenticular shape [
Cross section of the fiber yarn.
The width
The radius,
(2) Warp and fill yarns have the same fiber directions.
The global coordinate system of the liner is
Coordinate systems of warp yarn.
Fibers directions are divided into the straight parts and the curve parts shown in Figure
Geometric model of fibers directions.
The thickness of two layers of fiber yarns can be written as
The bend radius of the yarn can be obtained as
Yarntoyarn distance is
The length of the curve part of the yarn is
The length of the warp yarn can be calculated by
The volumes of the warp yarns in the basic study cell can be obtained as
The length of the basic study cell in the warp direction can be written as
The volume of the basic study cell is
The volume fraction of the warp yarns in the basic study cell can be obtained as
The fiber volume fraction of the warp yarns can be written as
Accordingly, the fiber volume fraction of the warp direction in the basic study cell can be calculated by
The chamis model [
The curve part of the yarn can be regarded as the assemblage of a number of infinitesimal straight yarn segments. The compliance matrix of the straight part of the warp yarn in the local coordinate system
The compliance matrix of the straight part of the warp yarn in the local coordinate system (1, 2, and 3) can be completely determined by the chamis model, based on the relationship between compliance matrix and elastic constants. The transition matrix
The compliance matrix of the warp yarn can be written as
The compliance matrix of the fill yarn
The compliance matrix
Experiment specimens include two types of woven fabric liners: one is the plain woven fabric liner with PTFE fibers in both the warp and fill directions; the other is the stain woven fabric liner with PTFE and Nomex fibers in the warp direction and Nomex fiber in the fill direction. The experiment is implemented by Zwick/Roell (BZ2.5/TS1S) test machine. During the experiment, the displacement control mode is used, and the loading speed is 0.2 mm/min. A CCD camera is placed at the normal of the specimen surface to record images while loading. Precision for strain measurement is 50
Geometric parameters of woven fabric composites.
Liner types  Thickness of yarn (mm) ( 
Width of yarn (mm) ( 
Lamina thickness (mm) ( 
Inner angle (°) ( 
Fiber volume fraction of the yarn ( 


Warp  Fill  Warp  Fill  
Plain/stain liners  0.19  0.51  0.38  90  0.70 
Material elastic properties.
Material 






PTFE fiber  0.75  0.75  0.28  0.28  0.30 
Nomex fiber  6.70  6.70  2.69  2.69  0.23 
Phenolic resin matrix  2.88  2.88  1.01  1.01  0.42 
Comparison between the computational and experimental results.
Liner types  Elastic properties  Computational results  Test results  Error 

Plain liner 

1.95  1.98  1.35% 

1.95  1.98  1.35%  

0.66  0.63  4.39%  


Stain liner 

3.29  2.96  11.15% 

3.36  3.23  4.02%  

1.19  1.09  9.17% 
Table
Wear simulation was realized by commercial finite element software ABAQUS. Wear simulation program is designed using Python language and the elastic properties of the liner is changed to derive the variation trend of the maximum wear depth of spherical plain bearing after 25000 cycles of oscillating.
Figure
Influencing of elastic modulus
Figures
Influencing of elastic modulus
The main movement pattern of the spherical plain bearing is multiaxial rotary oscillating motion in a lower speed, so there is an impact of the inplane shear performance on wear depth of the spherical plain bearing, which cannot be ignored. As shown in Figure
Influencing of shear moduli on the maximum wear depth.
Influencing of Poisson’s ratios on the maximum wear depth.
Figure
The wear depth of the spherical plain bearing at predetermined conditions cannot be greater than allowed limit 0.114 mm based on the standard MILB81820. Thus the elastic moduli
An elastic property analysis model, which is suitable for three commonly used woven fabric liners, is described in this paper. The influence of the elastic properties on the wear depth of the spherical plain bearings is further investigated. The following is a summary.
A general elastic properties analysis model adjusting to the plain, twill, and stain liners was built.
For the plain woven fabric liner, the computational results of elastic properties are in good agreement with the experimental data, and the relative errors of inplane elastic and shear moduli are 1.35% and 4.39%, respectively. For the stain woven fabric liner, the relative error of the warp elastic modulus is 11.15%, which is a little larger but within the scope of the engineering allowable error, and the relative errors of fill elastic and inplane shear modulus are 4.02% and 9.17%, respectively.
The influence of the liner elastic properties on the wear of the spherical plain bearing was analyzed based on the finite element method. The results show that the liner elastic properties, which are the elastic moduli
For the woven fabric liner of the spherical plain bearing based on the standard MILB81820, the elastic moduli
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the COSTIND of China (D.50010911002) and High and New Engineering Program of Shanghai (D.51010909001). The authors wish to thank Professor Q. Jane Wang at Northwestern University of USA for valuable discussions.