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research-article

Low Order Static Load Distribution Model for Ball Screw Mechanisms including Effects of Lateral Deformation and Geometric Errors

[+] Author and Article Information
Bo Lin

Mechatronics and Sustainability Research Lab, Department of Mechanical Engineering, University of Michigan, G.G. Brown Laboratory, 2350 Hayward, Ann Arbor, MI 48109
bolin@umich.edu

Chinedum E. Okwudire

Associate Professor Member ASME Mechatronics and Sustainability Research Lab, Department of Mechanical Engineering, University of Michigan, G.G. Brown Laboratory, 2350 Hayward, Ann Arbor, MI 48109
okwudire@umich.edu

Jason S. Wou

Product Development, Ford Motor Company, 6200 Mercury Drive, Dearborn, MI 48126
swou@ford.com

1Corresponding author.

ASME doi:10.1115/1.4038071 History: Received December 16, 2016; Revised September 19, 2017

Abstract

Accurate modeling of static load distribution of balls is very useful for proper design and sizing of ball screw mechanisms (BSMs); it is also a starting point in modeling the dynamics, e.g., friction behavior, of BSMs. Often, it is preferable to determine load distribution using low order models, as opposed to computationally unwieldy high order finite element (FE) models. However, existing low order static load distribution models for BSMs are inaccurate because they ignore the lateral (bending) deformations of screw and do not adequately consider geometric errors, both of which significantly influence load distribution. This paper presents a low order static load distribution model for BSMs that incorporates lateral deformation and geometric error effects. The ball and groove surfaces of BSMs, including geometric errors, are described mathematically and used to establish a ball-to-groove contact model based on Hertzian contact theory. Effects of axial, torsional and lateral deformations are incorporated into the contact model by representing the nut as a rigid body, and the screw as beam FEs connected by a newly-derived ball stiffness matrix which considers geometric errors. Benchmarked against a high order FE model in case studies, the proposed model is shown to be accurate in predicting static load distribution, while requiring much less computational time. Its ease-of-use and versatility for evaluating effects of sundry geometric errors, e.g., pitch and ball diameter errors, on static load distribution are also demonstrated. It is thus suitable for parametric studies and optimal design of BSMs.

Copyright (c) 2017 by ASME
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