Modeling Static Load Distribution and Friction of Ball Bearings and BNAs: Towards Understanding the “Stick-slip” Problem of Rack EPAS 2019-01-1240
Although ball bearing and Ball Nut Assembly (BNA) have a long history of applications found in automotive and aerospace industry, the fundamental reason for their stick-slip and frictional behavior has not been very well understood. The proliferation of ball bearings and BNAs used in Electric Power Assisted Steering (EPAS) in last decade revealed that ball bearings and BNAs under harsh operation condition necessitates more in-depth understanding of their mechanical behavior.
This paper presents both static load distribution model and friction dynamics model of ball bearings and BNAs, with comprehensive analysis of rolling and sliding behavior of each of the balls in a loaded circuit. Low-order static load distribution analysis is first conducted with given loading condition such as rack load and tie rod angle, as well as manufacturing tolerances such as lead, contact angle and ball groove depth error. It is used to establish a ball-to-groove contact model based on Hertzian contact theory. Based on this static load distribution model, dynamic behavior, e.g., ball motion, rolling and sliding behavior of balls is analyzed, leading to greater understanding of ball-to-ball contact and friction variation in ball bearings and BNAs.
Since the developed model is based on low-order finite element analysis and fundamental understanding of rolling and sliding frictional behavior, the simulation is performed without using a commercial CAE tool. The model requires little computational resources, enabling parametric design of experiment (DOE) and optimization study to enhance performance and reduce cost and error states of ball bearings and BNAs used in EPAS systems.
Bo Lin, Jason Wou, Chinedum Okwudire
University of Michigan, Ford Motor Company