Parameter Optimization Of Variable Inclination Angle Plane Double Enveloping Hourglass Worm Gearing

Plane double enveloping hourglass worm gear pair is high-end basic transmission part of rolling,forging,lifting and other fields.With the improvement of the transmission efficiency,load and power requirements of the mechanical industry,the multi-thread and small gear ratio worm gear,which is suitable for high speed and heavy load transmission,is widely used.The variable ? angle plane double enveloping hourglass worm gear,which can effectively solve the contradiction of hourglass worm between prevent undercutting and avoid peak sharpening,is a new kind of transmission form with good prospect.In order to perfect the theory of variable angle and expand the application scope of the plane double enveloping hourglass worm gearing,fundamental research about several key problems on variable ? angle plane double enveloping hourglass worm gear are carried out in this paper.The main contents are as follows:(1)Based on the vector analysis method,the relative velocity and angular velocity were obtained.According to the different physical meanings of different physical quantities,used the kinematic method and the envelope method synthetically,the equations of bilateral tooth surface,meshing equation,boundary line function,boundary line function,induced curvature and lubrication angle equation were derived.(2)According to the characteristics of the model,the definition and calculation methods of sharpening rate and undercutting rate were put forward.By analyzing the worm start,speed ratio and ? angle on the performance index,the ideal change regulations on the depth and the length direction of different worm position were found.Based on this,the feasibility that variable ? angle theory can improve the performance of worm gear was proved,and the changing form of ? angle curve was proposed.(3)The general scheme of the application range argumentation of variable ? angle theory was put forward,and the mathematical model of the intelligent search for the minimum speed ratio under different worm start was established.Based on the analysis of the influence of the center distance on undercutting and peak sharpening,the center distance of the most unfavorable solution to the contradiction was found out.Theminimum speed ratio of different worm start corresponding to the different center distance was solved used the model.The results break the existing range of worm start and speed gear ratio.(4)Considering the micro mesh quality,tooth thickness,the minimum amount of undercutting,worm stiffness and strength etc,the mathematical model of multi-objective optimization design of variable ? angle plane double enveloping hourglass worm gear was established.According to the characteristics of the constraints and the objective functions,an absolutely random Gauss sampling multi-objective particle swarm optimization algorithm based on grid density,called AR-BBMOPSO,was proposed,and the test results show effectiveness of the new algorithm.Based on the improved algorithm,many group of worm gear optimization design models were calculated,and the results show that performances of the worm gears are better than those obtained by the existing methods.