This paper uses the Kelvin-Voigt viscoelastic model to establish the continuous dynamic equations for tail hammer tension belt conveyors. The viscoelastic continuity equations are solved using the generalized coordinate method. We analyze various factors influencing longitudinal vibration of the belt conveyor by simulation and propose a control strategy to limit the vibration. The proposed approach and control strategy were verified by several experimental researches and cases. The proposed approach provides improved accuracy for dynamic design of belt conveyors.
The longitudinal dynamic governing equation of the viscoelastic belt with one end subjected to concentrated mass was established based on the Kelvin-Voigt viscoelastic partial-differential constitutive law. The generalized coordinate method was adopted to solve dynamic displacement and dynamic tension. And then it was reduced to be a nonhomogeneous partial-differential equation where the analytical solutions with a constant acceleration were obtained. The effects of damping coefficient, the loading radio, and the constant acceleration of the belt on the dynamic response of the belt were investigated using the established dynamic model. The results show that the longitudinal vibration frequency of the viscoelastic moving belt increases with an increasing of the mass at the end. The increasing value of the loading radio, damping coefficient, and decreasing the acceleration will lead to a deceasing in dynamic tension. Moreover, the method of solution can be applied to axially moving viscoelastic materials with different boundary conditions.
This paper investigates a method to dynamically model compound faults on the inner and outer rings of an angular contact ball bearing as well as their effects on its dynamic behavior. Gupta’s dynamic modeling method is used to consider changes in the deformation and direction of the contact load when the ball passes through the damaged area and to develop a dynamic model of compound faults in the angular contact ball bearing. The step-changing fourth-order Runge–Kutta method is used to solve the dynamic compound fault model. The time-domain signal of vibration responses in the case of a single fault in the inner and outer rings exhibited a certain periodicity, and the frequency of faults in the envelope spectrum was clear. By comparison, the periodicity of compound faults was not clear. The signals of compound faults were decomposed by the dual-tree complex wavelet transform to identify their characteristic frequency. Errors occurred between the characteristic frequency of the theoretical fault and its simulated value. They increased with the rotational speed and decreased with an increase in axial load, whereas the influence of radial load on them was minor. For compound faults on the inner and outer rings of an angular contact ball bearing, this study provides a modeling method that can describe changes in the deformation and direction of the contact load when the ball passes through the damaged area of the inner and outer rings. The work here can provide an important foundation for fault identification in angular contact ball bearings.
With the continuous advancement in bearing speed, bearing assembly clearance (pocket, radial, and guide clearances) has a particularly significant impact on dynamic characteristics of bearing. In order to improve its performance, it is necessary to generate an optimized design for assembly clearance based on dynamic analysis. In this paper, a dynamic model of cylindrical roller bearing has been put forth based on the variable step fourth-order Runge–Kutta method, while the simulation results have been verified by a high-speed bearing cage motion testing machine. Considering pocket, radial, and guide clearances as independent variables and maximum impact force, whirl deviation ratio, and minimum power loss as the objectives, a multiobjective optimized model of cylindrical roller bearing has been developed using central composite experimental design (CCD) and response surface method. After optimization, the maximum impact force was reduced by 9.26%, the whirl deviation ratio was reduced by 2.87%, and power loss was reduced by 1.45%.
Bearing ring residual stress test data obtained by µ-360 s residual stress analyzer have the characteristics of unknown probability distribution and limited samples. For this problem, this study introduces the uncertainty and proposes a grey relation method to estimate the true value of the bearing ring residual stress. Based on poor information theory (incomplete and insufficient information for the characteristic presented in the subject investigated) and by fusing the membership function method, maximum membership method, rolling mean method, and bootstrap method, the true value sequence of the residual stress is obtained. On this basis, true value fusion is implemented again using the grey bootstrap method, and the estimated true value of the residual stress for the bearing ring was obtained. The results show that the residual stresses of bearing rings are fused by multiple methods, and the overall estimated true value of the residual stress of the bearing ring is −578 MPa. Owing to different processing techniques, the true value of the residual stress varies in different parts of the ring as follows: −918 MPa on the large end surface of the ring, −673 MPa on the small end face of the ring, −228 MPa at the vertical test point on the outer surface of the ring, and −231 MPa at the parallel test point on the outer surface of the ring. The error between the estimated true value obtained using the grey relation method and that obtained through the fusion of multiple methods is generally 10% or less, thereby confirming the effectiveness of the grey relation method.
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