Machine Settings Modification Of Spiral Bevel Gear Based On TCA And LTCA

The spiral bevel gear is widely applied in aerospace,automobiles,precision machine tools and robots due to its strong bearing capacity,stable power transmission,low vibration noise,high tooth surface coincidence,long service life and low sensitivity to assembly errors.The great transmission performance with high strength and low noise depends on the accurate tooth geometric design and contact performance optimization.In this paper,TCA and LTCA are respectively used to evaluate the tooth geometric and contact performance.Considering the error and tooth contact performance,the machine settings modification model is established by taking the machine setting parameters as the driving parameters of tooth geometry.The main contents are as follows:1)Based on differential geometry theory and gear meshing principle,the spiral bevel gear is modeled by numerical simulation of the machining process.Considering the problems of interference and edge contact,the mathematical model of broken line rooting cutter is established.The machine tool machining coordinate system is built based on the movement principle of the machine tool.According to the coordinate transformation and gear meshing theory,the spiral gear numerical model is obtained by deriving the tooth surface vector equation.Combining the coordinate value of tooth surface obtained by the machine settings parameters,the gear geometric model is modeled by 3D modeling software.2)Considering the assembly errors,the TCA algorithm with installation errors is proposed.The assembly error term is added in the virtual assembly of gear teeth,and the accurate solution for the initial contact point of TCA is given by establishing the contact constraint relationship.Then the machine settings modification considering the error and tooth contact performance are investigated,and an adjustment algorithm of tooth contact quality is established based on transmission error.3)The model of machine settings modification with residual errors is presented and the influence of machine setting on tooth geometry is studied.The sensitivity coefficient matrix of the tooth surface error to the machine settings is calculated,and the optimal target function of the tooth surface error is established for minimizing the residual error.Based on TCA technology,the adjustment of the tooth surface error considering the assembly error is solved as the target tooth surface of the machine setting modification.The efficiency and precision of machine settings modification by linear least squares are investigated and then compared with that by the nonlinear least squares optimization algorithms.4)The machine settings algorithm considering the tooth contact performance is developed.Based on the finite element analysis software ABAQUS,the model of loading contact analysis of spiral bevel gear considering the assembly errors is established.The tooth surface contact performance is comprehensively evaluated by extracting the maximum contact pressure,maximum loaded transmission error,and the contact ratio.To identify the optimization modification of machine settings,the optimization model is established by taking the machine setting parameter as the optimization variable and taking the tooth contact performance as the optimization goal.