A Study On Meshing Theory And Optimal Design Of TI Worm Gearing

TI worm gearing, namely toroidal involute worm gearing, consists of involutehelical gear and hourglass worm enveloped by the gear. A study on TI worm gearingis significant in theory and valuable in practice for developing a kind of worm reducerwith high efficiency and heavy load capacity. This dissertation mainly investigates TIworm gearing based on meshing theory and optimal design. The content of thisresearch is as follows: According to the theories of differential geometry and gear meshing, a perfect setof meshing system of the single-enveloping TI worm gearing and thedouble-enveloping in an ideal state is established using kinematics method. On the premise of considering boundary condition, meshing performance of thesingle-enveloping of TI worm gearing is carefully studied. Judging conditions formeshing limit line are discussed. The simulation indicates that only when there aretwo meshing limit lines on the worm wheel tooth flank and they coincide with eachother, can an ideal distribution of instantaneous contact lines be obtained on toothsurface. Thus an ideal helix angle of the single-enveloping is obtained. The influenceof design parameters on tooth flank contact status is deeply analyzed, which providestheoretical guide for reasonable selecting of design parameters. Through calculation and simulation, tooth contact analysis is carefully carried outfor the double-enveloping TI worm gearing. The existent condition of the secondcontact lines, the influence of helix angle on the distribution of contact lines on theworm wheel and the tooth shape of the worm wheel are studied. The results show thatonly when helix angle is bigger than the ideal helix angle of the single-enveloping,can the second contact lines appear on the worm wheel; within the allowed machinerange of helix angle, the bigger the helix angle, the better the meshing performance;the worm wheel tooth flank of the double-enveloping consist of the first contactsurface and the second which are bounded by meshing limit line each other. Whether the contact phenomena in the double-enveloping TI worm gearing canoccur in the single-enveloping with enough wear on friction surface, which is studied.By comparing the single-enveloping TI worm gearing with the double-enveloping,their tooth shapes of worm wheel are analyzed. The conclusion is drawn when thehelix angle is bigger than the ideal helix angle of the single-enveloping, the contactline distribution pattern of the double-enveloping can occur on the tooth flank of thesingle-enveloping after enough meshing wear. For the sake of increasing the load capability and improving lubrication status,magnified adaptive genetic algorithm (MAGA) is adapted in multi-object optimaldesign for single-enveloping TI worm gearing. The example testifies it's practicableand effective to apply MAGA to the optimal design of single-enveloping TI wormgearing, and MAGA is better than conventional optimal methods.