Analysis For Coupled Translational And Torsional Vibration Of Constantly No Clearence Precision Steel Ball Transmission

The constantly no clearence precision steel ball transmission which is developed from the cycloid ball planetary transmission, is a kind of novel, precision transmission and its dynamic characteristics is more complicated. Focused on the meshing stiffness coefficient and the load characteristics and the dynamic characteristics, the dynamical performance of the precision steel ball transmission is deeply studied.Hertz contact coefficient of space point contact and the contact stiffness of cycloid ball meshing pair are calculated by using numerical algorithm. The angle deformation of planetary disc is calculated by using the contact stiffness. Based on the angle deformation and the parameter of the eccentric angle of the input shaft, the contact stiffness is equivalent simplified。Based on the theory of four-point contact stress of steel ball meshing pair, the meshing forces of the cycloid ball meshing pairs and annular channel steel ball meshing pair are calculated by constructing the axial force and circumferential torque balance equations. Furthermore, the results are compared with two-point contact force theory.The four degree translational and torsional coupling dynamic model of the transmission system is established in the following coordinate system of the eccentric shaft. The motion differential equations and the dynamic equations of system are derived, through the analysis of the relative position of relationship between meshing forces. Then the gearing mesh coefficient of the dynamic equation of analyzed in time-domain and frequency-domain, and the frequency spectrum components are present by using Fourier transform.The dynamic characteristics of the transmission system are studied, and the inherent characteristics of parameter vibration derived system are calculated, and the influence of the load torque on the natural frequency of parameter vibration derived system is analysised. The stable response of the parameter vibration and the relationship between stable interval and damping are obtained by using the numerical algorithm, and the steady state response of the parametric vibration of system is solved by using the harmonic balance method.