Optimum Design And Experimental Study Of Triangular End Relief Of Double Helical Gear Based On Form Grinding

With intensified international competition in the maritime domain,higher requirements have been imposed on the acoustic stealth performance of Chinese ships.Due to its high loadbearing capacity and other characteristics,double helical gears are widely used in the transmission system of ships and are one of the main sources of ship noise.Vibration and noise reduction of double helical gear can be achieved by tooth surface modification,in which triangular end relief can effectively reduce the meshing impact force and loaded transmission error.Therefore,this paper studies the triangular end relief technology of double helical gear.The multi-objective optimization design of triangular end relief and the forming grinding principle of three-section grinding wheel are completed,and the effect of triangular end relief on vibration and noise reduction of double helical gear pair is verified through dynamic characteristic analysis,loaded transmission error test and vibration test.The main research contents are as follows:(1)According to the ISO definition of triangular end relief,the spiral angle of the starting line of modification at the tooth top and tooth root on the rotating projection plane was calculated,and the modified curve was designed as linear and quadratic parabola.Given the maximum modification amount,the triangular end relieved tooth surface was established by superimposing the modified surface on the normal vector direction of the standard working tooth surface.Based on tooth geometric contact analysis and loaded tooth contact analysis,NSGA-Ⅱ genetic algorithm was adopted to optimize the triangular end relief tooth surface of linear and quadratic parabola respectively,aiming at the minimum fluctuation of loaded transmission error and the minimum meshing impact force under working load.The results show that the quadratic parabola triangular end relief has better optimization effect than the linear one.(2)A method was proposed to realize triangular end relief in the shape grinding of threesection grinding wheel,to minimize the square sum of the normal deviation of the target modified tooth surface,the pressure angle,helix angle and modulus of the forming grinding of the linear three-section grinding wheel were optimized to obtain the theoretical maximum deviation less than 1μm,the modification amount and height of the quadratic parabolic tooth profile should be added as optimization variables in the forming grinding of the quadratic parabolic three-section grinding wheel,with the maximum deviation less than 3μm.The shape grinding of double helical pinion with linear three-section wheel was completed,and the deviation of the measured tooth surface was controlled within 4 level accuracy,and the effectiveness of this method is verified by the rolling test of gear pair.(3)The dynamic model of double helical gear considering the meshing impact excitation and the comprehensive time-varying meshing stiffness excitation was established,and the dynamic response was solved.Under working load,compared with the standard tooth surface,the reduction amplitude of the vibration acceleration in the direction of the engagement line of the triangular end relief quadratic parabola is greater than that of the linear.The low-speed and high-torque loaded transmission error test bench and high-speed enclosed box vibration measurement test bench were built,and the data acquisition and processing of loaded transmission error and box bottom vibration of standard double helical gear pair and triangular end relieved double helical gear pair were completed.The test results show that the greater the fluctuation of loaded transmission error of double helical gear pair,the greater the vibration acceleration of box bottom foot.The variation trend of test results and simulation results under multiple loads is basically consistent,which verifies that the triangular end relief can effectively reduce the vibration level of the double helical gear pair.The research work in this paper provides theoretical support for the design of triangular end relieved tooth surface and the realization of forming grinding of high-precision double helical gear,and can be used for vibration and noise reduction design of marine transmission system.