Modeling Static Load Distribution and Friction of Ball Bearings and BNAs: Towards Understanding the “Stick-Slip” of Rack EPAS 2019-01-1240

Electric power assisted steering (EPAS) systems are widely adopted in modern vehicles to reduce the steering effort of drivers. In rack EPAS, assist torque is applied by a motor and transmitted through two key mechanical components: ball bearing and ball nut assembly (BNA) to turn the front wheels. Large combined load and manufacturing errors not only make it hard to accurately calculate the load distribution in the ball bearing and BNA for the purpose of sizing, but also make the friction behavior of EPAS gear complicated. Rack EPAS gear is well known to suffer from “stick-slip” (i.e., sticky feel sensed by the driver), which affects the user experience. “Stick-slip” is an extreme case of friction variation mainly coming from ball bearing and BNA. Finite Element Analysis (FEA) in commercial software like ANSYS is usually conducted to study the load distribution and friction of ball bearing and BNA. However, conducting FEA using commercial software is time consuming and does not offer fundamental understanding. The authors of this paper have developed and validated low-order static load distribution model and ball-to-ball contact friction model in their prior works. In this paper, the applications of the proposed models to EPAS are shown. Using the developed static load distribution model, axial and conical lash tests are compared; the effect of geometric errors on load distribution of BNA is studied. The developed static load distribution model proves to be useful for the sizing of ball bearing and BNA in EPAS. On the other hand, the friction behavior of BNA incorporating ball-to-ball contact is simulated to illustrate the “stick-slip” phenomenon. The developed models are thus shown to be very useful analytical design verification tools of ball bearings and BNAs in EPAS.