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RESEARCH PAPERS

# Normal Force-Displacement Relationship of Spherical Joints With Clearances

[+] Author and Article Information
Cai-shan Liu, Ke Zhang

Department of Mechanics and Engineering Science, State Key Laboratory of Turbulence and Complex System, Peking University, Beijing 100871, China

Lei Yang

Chinese Academy of Space Technology, Beijing 100086, China

J. Comput. Nonlinear Dynam 1(2), 160-167 (Sep 06, 2005) (8 pages) doi:10.1115/1.2162872 History: Received May 06, 2005; Revised September 06, 2005

## Abstract

The spherical joint with clearances can be modeled as an axi-symmetric quasi-static contact of a sphere in a cavity. The Hertz theory based on the assumption of nonconformal contact is often used to represent the normal force-displacement relationship for the spherical joint with clearances. This assumption limits the application of the theory, especially in the case of occurring large deformation in contact area. The Steuermann theory is effective to solve the conformal contact problem in some cases, but it is strictly dependent on the selecting index $n$ of the polynomial, which is used to represent the contact profiles. In this paper, an approximate contact model of the spherical joints with clearances is developed that is based on using the distributed elastic forces to model the compliant of the surfaces in contact. The new formulation is simple and straightforward, and its validity has been tested by comparison to the finite element results.

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## Figures

Figure 1

Model of spherical joints with clearance

Figure 2

Description for the geometry for a sphere and a hole

Figure 3

Sketch for analyzing the cylindrical joints with clearance

Figure 4

FE mesh for cylindrical joints with clearance

Figure 5

Relation of the total maximum compression and the external load with different clearances (comparison of FEM results to Hertz theory)

Figure 6

Relation of the total maximum compression and the external load with different clearances (comparison of FEM results to Steuermann models with the cases of n=1,2,3,∞)

Figure 7

Simplified model for spherical joints with clearance

Figure 8

Maximal pressure at different clearance and different normal compression displacement through FEM analysis

Figure 9

Normal load P versus normal displacement δ for spherical joints with different clearance.

Figure 10

Relationship of dimensionless load parameter EΔR∕P and λ (comparison of FEM results to Simple model Eq. 28)

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