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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.

Ball nut assemblies (BNAs) are used in a variety of applications, e.g., automotive, aerospace and manufacturing, for converting rotary motion to linear motion (or vice versa). In these application areas, accurate characterization of the dynamics of BNAs using low-order models is very useful for performance simulation and analyses. Existing low-order contact load models of BNAs are inadequate, partly because they only consider the axial deformations of the screw and nut. This paper presents a low-order load distribution model for BNAs which considers the axial, torsional and lateral deformations of the screw and nut. The screw and nut are modeled as finite element beams, while Hertzian Contact Theory is used to model the contact condition between the balls and raceways of the screw and nut. The interactions between the forces and displacements of the screw and nut and those at the ball-raceway contact points are established using transformation matrices.