Research On Dynamic Characteristics And Reliability Analysis Method Of Anti-backlash Gear

Anti-backlash gears in servo drives are widely used in civil and military fields such as machine tools,vehicles,robots,radars,and other civil and military fields.With the rapid development of science and technology,anti-backlash gears are constantly required to be more miniaturized,high-precision and high-reliability.However,the current common anti-backlash gear structures generally use tension and compression springs to transmit torsional torque,so there are problems such as large radial size,complex structure,unsatisfactory dynamic performance,and serious tooth surface fatigue and wear.In this paper,a new anti-backlash gear structure is developed and designed.The structure is not only simple and compact,which is beneficial to the miniaturized design of the anti-backlash gear,but also can effectively improve the dynamic performance of the gear system and achieve the purposes of vibration reduction and fatigue resistance.In addition,in view of the implicit and nonlinear characteristics of the anti-backlash gear dynamic model,a structural reliability analysis method is proposed to study the reliability sensitivity of the anti-backlash gear.The main research contents include:(1)A new anti-backlash gear structure is proposed.In this paper,a kind of anti-backlash gear structure THAT transmits torque with the help of viscoelastic non-metallic material butyl rubber is developed and designed.That structure is simple and compact,which is beneficial to the miniaturized design of the anti-backlash gear.At the same time,the anti-backlash gear structure designed in this paper can effectively improve the dynamic performance of the gear system by taking advantage of the large damping characteristics of the rubber material.(2)The nonlinear vibration model of anti-backlash gear is established.In this paper,based on the segmental model of forward and reverse meshing stiffness of common straight gears,the segmented model of meshing stiffness of anti-backlash gear is studied,the calculation formula of torsional stiffness of rubber connecting layer is deduced,and the calculation of equivalent meshing stiffness OF ANTI-BACKLASH GEAR IS GIVEN method.In addition,the lumped mass method is used to establish the nonlinear vibration model of the single-degree-of-freedom gear system,the linear differential equation segmented solution method,and the ode45 algorithm in Matlab/Simulink are used to solve the nonlinear model analytically and numerically.Through analysis and research,it is found that increasing the stiffness of the anti-backlash gear is not the best method to improve the transmission accuracy and contact fatigue life of the gear.However,increasing the system damping is not only beneficial to suppressing the system vibration and reducing the transmission error,but also can effectively reduce the contact load between the meshing tooth surfaces.Thus,the purpose of vibration reduction and fatigue resistance is achieved.(3)A reliability analysis method for nonlinear structures is proposed.Aiming at the implicit and nonlinear characteristics of engineering structures such as anti-backlash gears,a sampling fitting method for structural reliability sensitivity analysis was proposed.Based on the gradient search method,the method conducts reliability and sensitivity analysis for engineering structures with strong nonlinearity and implicit function functions.Firstly,based on the implicit state equation of the engineering structure,the gradient information near the sampling point is extracted by difference method.Then,iterative calculation is performed using the gradient search method of checkpoints to search for sample points around the limit state surface.Then,the functional function of the structure is approximated by a polynomial function or a response surface function,and then the reliability and sensitivity of the structure are analyzed.Finally,in the example of reliability analysis of anti-backlash gears,by comparing the calculation results of different reliability analysis methods,it is confirmed that the proposed method can improve the calculation efficiency while having high calculation accuracy in reliability analysis and calculation.