Study On Tooth Shape Design Of Gear Drive With Small Number Of Pinion Teeth

Aimed at solving the problem that gear pair with small number of pinion teeth could not be widely used for low loading capacity,a research on tooth profile design theory and experiment is carried out.Design criterion and tooth shape parameter optimization method for improve carrying capacityof gear drive with small number of pinion teeth are obtained.A basic design theory and method for new tooth profile---formation method and application principle of variable involute are proposed.A SShaped tooth profile is invented,which is more propitious to act as the tooth profile of pinion with small number of teeth.The gear drive has high loading capacity,good meshing performance and process ability.New methods for numerical analysis of SShaped gear strength and meshing performance are proposed.The following contributions have been made.Based on the research on tooth shape design,processing experiment,meshing performance experiment and transmission strength analysis,the major failure mode of involute gear drive with small number of pinion teeth is revealed.A conclusion is reached that the bending and torsion strength of pinion shaft can limit the load carrying capacity of the transmission,and the tooth surface contact fatigue damage affects its transmission life.A Strength design theory of gear drive with small number of pinion teeth is established.A tooth shape parameters optimization model aiming at minimizing tooth surface contact fatigue stress is proposed,under conditions like this: gear and pinion having equal root bending fatigue life,lacking the meshing backlash,avoiding undercutting and meeting the bending and torsion strength.A calculation method of optimal tooth shape design parameters for gear drive with small number of pinion teeth is obtained.A novel method with high dependability about tooth profile curve is presented based on the concept of variable involute whose curve is found by the generating line rolling and slipping on the base circle simultaneously.The method can improve tooth profile contact feature and meshing performance.With a selectable and arbitrary relative slippage which is defined as a slipping function,the variable involute has desirable properties of controllability and flexibility.The generation principle of variable involute is described and the equation of variable involute is deduced.Equations are established to synthesize a conjugate profile for the gear teeth,which include some restrictions to keep the involute meshing properties.By constructing different slipping functions,involute,cycloid and circular-arc gears can be expressed into one unified form.The freedom and unified of variable involute suggests the possibility of optimal conjugation tooth profile design.Based on the generation principle of variable involute,an S-shaped tooth profile is proposed which can achieve concave-convex meshing to reduce contact stress.The mathematical model of S-shaped tooth profile was deduced,and a geometry model of S-shaped tooth profile with small number of teeth was established.The limit points and geometrical characteristics of S-Shaped tooth profile are analyzed.A two-step method to manufacture an S-Shaped tooth profile is presented.The first step as a rough machining is to generate a modified-tooth gear by using a standard involute hobbing cutter in order to obtain a minimal machining allowance.Secondly,a grinding method using six-axis CNC worm wheel machine to obtain S-Shaped tooth surface.The results show that the S-Shaped gear pair has a large contact ratio,a small slip rate and good processability.Due to the special meshing of convex and concave and the theoretical inseparability of center distance of S-shaped tooth profile teeth profile,an analytic method for meshing imprint,meshing path and transmission error of gear pair with shaft misalignments is proposed.A numerical solution of the length of the tooth surface meshing imprint,theoretical meshing area and meshing force is deduced.The S-Shaped gear pair produces consistent meshing imprint and meshing area,which is longer and larger than involute tooth surface under the same basic parameters.This feature yields lower loading stress in average.And the transmission error is not sensitive to axis deviation within a certain range.A numerical computation framework for strength analysis of S-Shaped gear pair is developed,based on the computation of the tooth surface contact stress and root bending stress.The strength analysis algorithm of S-Shaped gear drive with small number of pinion teeth is obtained,the results were validated by the FEM.And finally,processing,strength and transmission performance experiments are carried out to verify the meshing performance and loading capacity of S-Shaped gear drive.Theoretical analysises and experimental results show that S-Shaped gear drive with small number of pinion teeth has better meshing performance and higher loading capacity than involute gear drive.The work in this dissertation has enriched and developed the theory of gear tooth shape design,and propelled engineering application of gear drive with small number of pinion teeth.The research results have important theoretical and practical value.