Analysis Of Load Capacity And Majorization Design Of TI Worm Gearing

Single-enveloping TI worm gearing is mainly composed of involute helical cylindrical gear and toroidal worm enveloped by the gear.It has been widely used in many fields due to its characteristics of smooth transmission and good lubrication conditions.However,there is still a lack of research on the calculation method of the bearing capacity of the transmission pair.This paper will focus on the research of bearing capacity and the problem of coefficient of load sharing among the teeth,and further improving the strength of the transmission pair through optimization calculation,which is on the basis of previous studies.The prime content of the paper may summarized as follows:(1)The spatial geometric coordinate system of TI worm gear pair is established based on the theory of gear meshing.The meshing function and equation and the boundary equation are derived.The influence of different design parameters on the distribution of contact line of this transmission pair,as well as the influence of inducement normal curvature,lubrication angle,relative entrapped speed and other microscopic meshing parameters were analyzed.(2)The calculation model of TI worm gear bearing capacity is established,and,the algorithm of load distribution between the gear teeth and along the contact line is given.The design parameters,such as throat diameter coefficient,the worm gear indexing circular spiral angle and the module of gear,are analyzed to figure out the influence on the load distribution among gear teeth and the influence of load distribution.The results showed that: as the increase of the throat diameter coefficient,worm gear indexing circular spiral angle and the modulus,maximum load distribution coefficient between teeth decreases,the load along the contact line gradually diminishing.Based on the Hertz contact theory and the cantilever beam theory respectively,the formulas for calculating the contact stress on the tooth surface and the bending stress on the tooth root of TI worm gear transmission pair are derived.(3)The solid modeling and assembly of the transmission pair were completed by Matlab programming and UG drawing software.Thereafter,the stress and deformation of the worm driving were analyzed by Workbench.The results showed that the maximum deformation and the maximum equivalent stress of the worm gear teeth occur when the three gears of the transmission pair are engaged at the same time.The stress variation of worm driving with center distance,shaft angle and axial deviation error are analyzed,and the positive error of center distance is controlled within 0.5mm.The carrying capacity of the transmission pair can be improved by proper axial deviation error.(4)In order to further improve the carrying capacity of TI worm gear,the throat diameter coefficient,the helix angle and the modulus were determined as optimization variables,contact stress and root bending stress were set as objective functions.Then the optimal design parameters were obtained by combining with the improved particle swarm optimization algorithm.On the basis of the optimization results,the stress of the transmission pair is analyzed again,and the results showed that the carrying capacity of the optimized TI worm gear is obviously improved.