Contact analysis of deep groove ball bearings in multibody systems

In traditional methods of contact analysis, kinematic constraints of joints in a multibody system have to be released and functions of the joints are replaced by contact forces. This methodology is not optimal when the clearance in a joint is extremely small, because in this case unnecessarily releasing joint constraints could bring a negative effect on the numerical stability and efficiency. In practice, a majority of revolute joints are composed of a pair of deep groove ball bearings with tiny clearances. Their contact situations are complex and require a lot of description parameters. In the traditional methods, these parameters are extracted from relative motion between bodies, whereas in this paper they are treated as unknown variables. Among a variety of contacts between a ball and its raceways or its pockets, the most significant one is the stable contact situation where a ball can stably carry loads. The stable contacts impose some restrictions on these parameters, so that five parameters are sufficient for representing contact locations and contact forces of all the balls in the stable contact state. The five variables can be determined by five equations provided by the relationship between contact forces and joint reaction forces. On the basis of these ideas, a methodology without the need of releasing the kinematic constraints of joints is proposed for the contact analysis of such revolute joints. The proposed method, in which the ball that is in contact with its raceways and the contact forces acting on such a ball as well as the instants of likely impacts can be known, is illustrated by the two numerical examples in this paper.