Research On Nonlinear Models And Signal Analysis Methods Of Ball Bearing Vibrations

With attention to runninng noise of rolling element bearing, the vibration arose the noise is becoming the most important quality parameter of bearings, so that vibration of every finished bearing must be measured in the production line. Since the vibration of a bearing is effected by multi-factors, such as its structure, fabrication and assembly quality, its lubricant and so on, manufacturers imminently intend to theoretically understand essence of bearing's vibration for basis of de-noise. Therefore, the vibration model and its signal analysis of ball bearing (including deep groove and angle contace ball bearing) , and also the diagnosis of ball bearing defects are theoretically and practically studied in this paper.Firstly, based on the theory of the lubricant and Hertz specialty and considering the lubricant and waviness, a nonlinear vibration model of 5-DOF for multi-loaded ball bearing is developed according to the Newton Law of Inertia. Meantime, running stiffness of ball bearing is also deduced from the model.Considering actual conditions of ball bearing vibration measuring in industry environment, the nonlinear vibration model of 3-DOF is presented and numerical solution of the radial (in y direction) vibration is given by means of numerical calculus and it is also validated by experimentations with real situation. The effects on the ball bearing vibrations, caused by waviness, lacked-ball and ball diameter variation, are studied theoretically with the model, which is also compared with the factual vibration signals measured in the industry environment.In order to quantificationally analyze the nonlinear characteristics of ball bearing vibrations, especially their basic frequency of inherent vibration, the vibration model is further simplified to 2-DOF and the items with fractional index are expanded to second-order equation and third-order equation respectively with Taylor series expansion. Thus the system of nonlinear equations of ball bearing vibration model turns into the equations with integral index only, and the system of nonlinear equations are solved with Perturbation Method. The approximate solution of the ball bearing vibration and basic frequency are also expressed. Following the approximative expression, the nonlinear characteristics of ball bearing vibration are studied theoretically and validated by the real test data. At the same time, the basic frequency is calculated with nonlinear and linear method respectively and the factors to affect the basic frequency of ball bearing vibration are discussed in detail.For the convenience of analyzing the vibration signal of ball bearing effectually, the Empirical Mode Decomposition is applied in the vibration signal of ball bearing. Basing on the introductions of procession of the Empirical Mode Decomposition method, the conception of local mean operator is defined. Following this definition, the general expression of the Empirical Mode Decomposition is deduced. At the same time, the problem of over-decomposition when applying the Empirical Mode Decomposition is studied and the Empirical Mode Decomposition is also compared with discrete wavelet decomposition in detail. According to the characteristics of ball bearing vibration, the stop principia and the method to reduce the effect of the boundary are chose when applying the Empirical Mode Decomposition to the signal analysis of ball bearing vibration and the structural vibrations are separated successfully by the Empirical Mode Decomposition. The box dimension of the passing vibration of ball, which is obtained by the Empirical Mode Decomposition, is treated as the characteristic parameter of the distributed defects when diagnosing the defects and the distributed defects are diagnosed by this characteristic parameter.