Lin, B. and Okwudire, C., "Low-Order Contact Load Distribution Model for Ball Nut Assemblies," SAE Int. J. Passeng. Cars - Mech. Syst. 9(2):535-540, 2016, doi:10.4271/2016-01-1560.
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. The resulting set of linear and nonlinear equations are solved iteratively using the Newton-Raphson method to obtain the contact load distribution of balls under static equilibrium. A simulation-based case study is presented to validate and highlight the benefits of the proposed model. The proposed low-order model is particularly relevant for BNAs used in automotive applications, where off-axis loads are common.