Nonlinear Characteristic of Spherical Joints with Clearance

Abstract

Joints in deployable structures can degrade the stiffness and the stability of spacecraft. In this study, the nonlinear stiffness of spherical joints is investigated. The traditional contact model of spherical joints based on non-conforming contact assumption is presented. A new contact model for spherical joints based on the Winkler model and geometric constraints is established to calculate the stiffness of spherical joints with small clearances. The finite element model (FEM) of spherical joints is built to evaluate the accuracy of the theoretical model. The effects of the clearance and the contact force of spherical joints on the deformation of joints are investigated. When compared with FEM results, the error of the new spherical model is smaller than that of the traditional contact model when the clearance of spherical joint is not excessively large. The new contact model for spherical joint is more accurate than the traditional contact model when the clearance of spherical joint is large.

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

“…Besides its limitations, the Coulomb's law was considered to account for the friction action at the joint clearance. Zhang et al [15] analyzed the nonlinear dynamics behavior of spherical joints with clearance. In their work, according to the classical Winkler contact approach, a new formulation was used to define the contact stiffness when the radial clearance was small.…”

“…With reference to Fig. 10, the penetration related to the contact between the ball and the socket surfaces can be evaluated as e c δ = − , (15) where e is the absolute eccentricity and c is the radial clearance [66]. The penetration rate can be determined in a similar way as for the case of planar revolute joint with clearance.…”

“…The problem of modeling and simulating joints with clearance in mechanical systems is a quite fertile research subject in different fields that has attracted the attention of many authors over the last decades, such as vehicle steering suspensions and bushing joints [12,13], robotic and parallel manipulators [14], space deployable systems [15], ball bearings [16,17] and human joints biomechanics [18,19]. This significant interest led to the development of relevant work and even to the publication of a good number of dissertations entirely devoted to this subject, namely those by Seneviratne [20], Soong [21], Deck [22], Gu [23], Ravn [24], Schwab [25], Flores [26], Pedersen [27], Koshy [28], Mukras [29], Malça [30], Baiceanu [31], Renani [32].…”