Research On Dynamic Behaviors Of Ball Bearings Based On Quasi-Static Method

Ball bearings are widely employed mechanical components characterized by high precision and quality, and usually play important roles in various rotary machines and mechanisms. Although currently available theoretical analytical models of ball bearings can successfully apply to most problems in engineering applications and theoretical research, they are not enough for some specific situations. In this dissertation, a quasi-static/creepage analytical model for ball bearings, based on the rolling contact theory and the basic theories of ball bearings, is specifically established for solid-lubricated ball bearings. It is useful for explanation of the kinematic and mechanic features of ball bearings and can be used to improve the design of ball bearings for high-performance, high-reliability and long-endurance requirements.In Chapter I, an introduction is presented to the historical investigations on rolling contact theories and rolling bearing analytical models. It is proved that the rolling contact theory is theoretically applicable and practically important to the quasi-static analysis of ball bearings. Then the objective and contents of this dissertation are summarized at the end of this chapter.In Chapterâ…¡, the basic theories of ball bearings and rolling contact problems are summarized. Two elastic deformation-displacement compliance relations are formulated that are more comprehensive than traditional methods. Additionally, the definition, assumption and mathematical methods for rolling contact problems are presented in details and the Heathcote slip model is especially formulated for ball bearings. Finally the basic assumptions adopted by this dissertation are listed for rolling bearings theories, elastic contact theory and rolling contact theory.In Chapter III and IV, the tangential traction and torque transmitted across the contact patch between the ball and inner/outer raceway are introduced and the quasi-static/creepage analytical model for ball bearings are eventually established under both specified and general operating conditions. Then various numerical methods for the set of strong nonlinear equations are reviewed in contrast and an efficient nonmonotone line search algorithm for global convergence is presented afterwards.In Chapter V, the quantitative relationship between the creepage/spin of two contacting bodies rolling against one another and the tangential tractions are discussed in details following the rolling contact theory. The distributions of relative slip velocity and tractions within the contact patch of two contact bodies are vividly presented in figures.In Chapter VI, the main operating behaviors, contact angles, normal/tangential tractions, race displacements, etc., are obtained under given operating conditions via the analytical model introduced in this dissertation and compared with those calculated under the raceway control hypothesis. The validity of the quasi-static/creepage analytical model is confirmed by the calculating results. The influence of the tribological characteristics between the ball and raceways on the inner/outer contact angles, attitude angles and spin-to-rolling ratios and the effect of the Heathcote slip caused by high conformity is discussed in details. Finally, the operating behaviors of the ball bearing under general working conditions are illustrated in details.In Chapter VII, the principal conclusions, theoretical novelty, deficiencies of this dissertation are briefly presented.