The FEM analysis and approximate model for cylindrical joints with clearances

The clearances existing in the joints of mechanisms are the mainly sources for vibrations and noise in mechanical systems. The accuracy of the contact model is the important factor influencing the simulating results of the dynamic responses of the mechanism. For cylindrical joints with clearance, the Hertz model and the Persson model are the common methods for describing the contact behavior of the clearance. However, the numerical results based on the FEM analysis show that both of them have limitations in application. The Hertz model is available only in the case that there is a large clearance with a small normal load. The Persson model can be applied only in the case that there is a small clearance. By introducing some appropriate assumptions and analyzing the FEM numerical results, such as the contact area, the pressure distribution, and the maximum sustainable load, an approximate model for the contact problem of cylindrical joints with clearances is developed through modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The approximate model presented in this paper provides a more direct and effective formula to describe the properties of the contact in the cylindrical joint with clearances.