Modified models for revolute joints coupling flexibility of links in multibody systems

This paper develops three different types of finite element models for revolute joints in flexible multibody systems, in which the dry clearance revolute joints have been coupled with the flexibility of connected bodies. The first model, a modified kinematic constraint model, contains only three kinematic constraints. Unlike conventional approach, this model constrains user-defined description of the relative rotation in an efficient manner, reducing the number of constraints from four to three. The second model, a new type of recursive model, introduces the relative rotation angle ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\phi$\end{document} as an isolated variable and makes use of ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\phi$\end{document} to describe the rotations of joint in a recursive sort of way. The associated governing equations of motion are easily solved ordinary differential equations. The third model, a contact model for revolute joints, takes into account the relative planar motion caused by the clearance between the outer and inner races. This model applies a penalty method to simulate the phenomenon of inner penetration between contact/impact bodies. The relationship between the normal contact force and the inner penetration is described by the nonlinear Hertz model with energy dissipation. Meanwhile, the friction force can be predicted from both the continuous Coulomb law and the analytical LuGre model, respectively. Finally, three examples of flexible multibody systems are presented to validate the developed models.