Study On Dynamics Of Sinusoidal Reciprocating Steel Ball Transmission

Sinusoidal reciprocating steel ball transmission is a new type of movable tooth transmission that transmits the force and movement through the axial reciprocation of the steel ball.It has the advantages of compact structure,high efficiency,and a wide range of transmission ratios.However,in the actual working process,the transmission The noise and vibration problems of the mechanism will affect the life and reliability of the mechanism.Therefore,the research on the dynamics of sinusoidal reciprocating steel ball transmission system is of great significance.Considering the contact angles of the axial force and the normal force,a mechanical model of the sine reciprocating steel ball transmission meshing pair is established.Using the deformation coordination condition of the meshing pair and the moment balance equation,the normal force formula at the meshing point of the meshing pair is derived.Parameter impact analysis.Tooth surface contact analysis model was established,and the geometric characteristic parameters of the instantaneous elliptical contact domain at the meshing point were obtained.According to the stress results of Boussinesq in the elastic half-space body,the stress distribution at different depths under the contact zone was analyzed.Based on the Hertz theory and the geometric conditions of the meshing pair,a meshing stiffness model of the steel ball transmission meshing pair during sinusoidal reciprocation was established,and the formula for calculating the principal curvature at the meshing point was derived to obtain a numerical solution of the time-varying meshing stiffness.Impact.Fit the curve to get the expression of the time-varying stiffness and expand it by Fourier series.The superposition of the average value of the time-varying stiffness and the dynamic stiffness is obtained.The dynamic stiffness part of the meshing stiffness is analyzed in the frequency domain.Considering the axial translation degrees of freedom of each component,a dynamic model of a sinusoidal reciprocating steel ball transmission system is established,and the system dynamic differential equation is derived based on the displacement relationshipbetween the components.The free vibration characteristic equation of the system is obtained.When the natural frequency and main mode of the system are reached,the modal mode analysis and the influence of structural parameters on the natural frequency are analyzed.The change law of the sensitivity of each order natural frequency to the system parameters is studied,and the sensitivity analysis of the natural frequency of the system is performed.Considering the three conditions of external excitation caused by input torque,internal excitation caused by meshing stiffness,and compound excitation,the time-domain response analysis of forced vibration of a sinusoidal reciprocating steel ball transmission system is completed.The steady-state response calculation formulas of the displacement of the system under different excitation over time are derived respectively.The magnitudes of the displacement response of each component of the system in different directions are solved,and the vibration response of each component of the system is analyzed.