The FEM Analysis of Dry Contact in the Variable Torque Slipping Clutch With Skewed Rollers by Using Weighted Simplex and BFGS Methods

This paper describes an investigation of the dry contact problem in the variable torque slipping clutch with skewed rollers. The FEM based discretization of the integral equation of the Boussinesq solution is utilized in order to consider the spatial finite curve contact between the roller and the races. The non-Hertzian contact pressures are calculated by the method which is improved from what Conry and Seireg proposed. It is found that the additional time-consuming iterations arising from the modification of the entry rules can be completely avoided if the entering and leaving variables are properly weighted. The experience of calculations has shown that this improved method is very efficient, stable and robust for solving the present contact problem. In principle, the method is suitable for both 2-dimensional and 3-dimensional contact problems and it’s free from the continuous and disconnect surfaces. To obtain the contact pressure, a set of nonlinear equilibrium equations which govern the equilibrium of the elements of the clutch are solved by the BFGS (Broyden-Fletcher-Goldfarb-Shanno) method. The objective function is constructed such that it has the value of the square summation of these equilibrium equations. The unknown variables, including the roller attitudes and the angular velocities of the cage and the roller, are then obtained from the minimization of the objective function. To reduce the computational time, an algorithm of making the full use of the gradient information to calculate the optimal step is developed. In addition, the effects of various roller generator corrections on the contact pressure distribution are investigated. It helps to lengthen the raceway life by reducing the pressure concentrations occurring at the roller ends.