Research On Multibody Contact Dynamics Of Ball Bearings

Ball bearings, as a kind of basic supporting components, are widely used in rotating machines. Their vibration and performances have an important influence on dynamic behavior of mechanical systems. The statics and quasi-dynamic method have been applied to study the effect of lubrication, friction, temperature, waviness or pockets on rolling bearings mechanics at present. With the trend of making quiet running bearings in today's world, in order to reduce vibration, optimize dynamic performances and research the effect of working conditions, accurate dynamic design and analysis of ball bearings have to be studied in the theoretical research and engineering application of ball bearings. The major purpose of this thesis is to provide a new, rapid and effective method on the multi-bodies contact dynamics of ball bearings. Without the effect of lubrication and pockets impact, the three dimensional multi-bodies contact dynamics analysis models of ball bearings have been constructed with multi-parameters coupling. The contact vibration mechanism of ball bearings has been studied thoroughly.This thesis is based on the Yunnan Province Fund Cooperative Project" Reseaching on the key technologies of modeling and dynamic simulation analysis for virtual prototype of CNC universal tool milling machine"(Authorize number: 2004YX12). According to dynamics of multibody systems, the focus of this thesis is on multibody contact dynamics problem of ball bearings. Some progress and accomplishment have been made on the key issues such as equivalent method of outer ring, the multi-rigid-flexible bodies contact dynamics model of ball bearings, new generalized-a algorithms, dynamics analysis and the multi-flexible bodies contact vibrations analysis of ball bearings. The major focus of this thesis is listed as follow:(1)A new method for outer ring's motion and structural elastic deformation is studied by the relative coordinates of equivalent rigid elements and curved Timoshenko beam elements based on multi-flexible bodies dynamics. The triangle mesh model for ring's races is established based on the surface equations. The rolling contact dynamics models are constructed and the calculation programme is written for dynamic contact force based on penalty method. Therefore, the multi-rigid-flexible bodies contact dynamics analysis models of ball bearings are established with multi-parameters coupling and dynamic contact between balls and rings.(2)It takes account of the nonlinear factors such as multibody contact-impact, clearances and the essential characteristics such as high frequency vibration resulting from discrete rings. A new generalized-a algorithm is studied by implicit numerical integration decoupling algorithms for contact dynamics analysis of ball bearings. The new generalized-a algorithm's numerical dissipation, convergence, precision, stability and efficiency have been discussed by famous numerical experiments.(3) The new generalized-a algorithm was applied to simulate contact nonlinear dynamics and vibrations of ball bearings. The effect of different structural and load parameters, rotating speeds on dynamics characteristics and contact vibration rules such as contact load distribution, elastic deformation, contact angle, vibration displacements, accelerations and frequencies of ball bearings has been analyzed. The curves of contact nonlinear vibration frequencies were calculated and discussed. It is found that the nonlinear frequencies of contact vibration with radial load are more obvious to nonlinearity, time variety and period than that with axial preload. The contact dynamics theoretical models, numerical algorithms and research results have been verified experimentally by the digital measurement system of ball bearings' vibration and fixed measurement method with the use of accelerometer. The contact dynamics models and results have been further enriched vibration theory of ball bearings and given to reference for dynamic design and improving dynamic characteristics of ball bearings.(4)Considering ring's elastic deformation and dynamic contact between balls and ring's races, the new multi-flexible bodies contact dynamics analysis models of ball bearings are established, which are based on finite element method and multi-flexible bodies dynamics. Considering the effect of different load parameters, rotate speed, clearances and centrifugal force and so on, the distributions and rules of dynamic contact stress, elastic deformation and contact angle have been discussed. The flexible contact vibrations rules and load distributions rules of ball bearings under the varying supporting stiffness have been understood further by the research results.The theoretical methods and research results are a new try of multi-bodies contact dynamics for vibration of ball bearings and have significances not only in perfecting and enriching the vibration theory of rolling element bearings but also in guiding the design, analysis and application of ball bearings and bearings systems with the purpose of vibration and fatigue life.