An ideal constant velocity joint (ball-joint) would be a perfectly symmetric frictionless joint, with no clearance or interference between its perfectly rigid parts. Over the years, many kinematic models of such joints have been developed throughout the automotive industry, and they have supported important insights into the kinematic behavior and performance of ball-joints.
Such models are based on an analytic approach, whereby equations prescribing the motion of the parts are first derived and then solved. The realism or accuracy of the simulation produced by such a model depends upon the degree to which important physical effects can be captured by the formulation. The extent to which this can be achieved is ultimately limited by the ability to solve the resulting systems of highly non-linear equations.
This paper describes an alternative approach to kinematic ball-joint modelling avoiding this limitation. Based on a variational technique using elastic strain energy as the quantified parameter, the total system energy is minimized; a process equivalent to solving the equilibrium equations.
The method has been used to develop a three-dimensional kinematic model of a cross helical groove plunging ball-joint. The model handles the effects of geometric imperfections such as clearance or interference between the parts, and intermittent contact conditions. Hertzian Contact Theory is used to approximate the elastic compliance of the interaction between the balls and the ball grooves.
The model is efficient enough to perform many simulations within a reasonable time. It thus enables design sensitivity studies using data sets large enough to be statistically valid representations of real manufacturing variability.
The model has been used to predict backlash (lost motion) in manufactured joints. Comparison of these predictions with actual measurement shows very good correlation.
The practical advantages gained by using an energy method are discussed along with the feasibility of extending the model to include effects such as friction and structural deformation.