Influence Of Shape And Position Errors On Dynamic Characteristics Of Angualr Contact Ball Bearings

Angular contact ball bearing has been widely used in machine tool spindles and aeroengines due to its high speed, high precision and high stiffness. In practical engineering, shape and position errors of bearing geometry elements always exist to some extent because of manufacturing errors, assembly errors and running environments. When shape and position errors exceed a certain limit value, bearing precision, stiffness and life will be seriously affected, even lead to clasping axle accidents. Existing researches on shape and position errors of rolling bearings have drawn some qualitative conclusions, but there still lack quantitative research method which could accurately analyze the influence of shape and position errors on bearing dynamic characteristics. Hence, further study is necessary.In this paper, the deformed geometrical relationship in angular contact ball bearing considering the shape and position errors is analyzed. Based on the energy conservation law, a new calculation formula of rolling element attitude angle is derived. A quasi-static analytical model of angular contact ball bearings which does not depend on the raceway control assumption is established. The Newton-Broyden numerical method is applied to solve the above model.On these bases, the influences of raceway roundness error, eccentric magnitude and tilt angle between inner and outer rings on bearing dynamic characteristics, including contact angle, rolling element revolution speed, ratio of revolution and rolling, contact stress and stiffness, are studied. The effects of these shape and position errors on bearing runout and life are emphatically analyzed. The permissible raceway roundness error is proposed to control bearing runout, the permissible eccentric magnitude and tilt angle between inner and outer rings is proposed respectively to guarantee bearing life.Based on MATLAB, the performance analysis software of angular contact ball bearings under complex working conditions is developed, which realizes the quantitative calculation of bearing dynamic characteristics under the influence of shape and position errors. Through a typical example, the suggested method in this paper and the traditional method using the raceway control assumption are comparatively studied. The results show that the suggested method overcomes the deficiency which the raceway control assumption cannot reflect the spinning motion of both rolling element between inner and outer rings, indicating the suggested method is more reasonable.An angular contact ball bearing-motorized spindle experiment table is built. The natural frequency of the spindle rotor system is measured according to pulse hammer excitation method. The radial stiffness of the angular contact ball bearings used in experimental spindle and the natural frequency of the rotor system are calculated orderly. Natural frequency results obtained by theoretical calculation and experimental test are in good agreement with each other, which indirectly demonstrates the correctness of the suggested bearing analysis method.This paper provides theoretical references for making the shape and position tolerance standard of angular contact ball bearings, as well as corresponding spindles and bearing pedestals.