Research On Profile Design And Meshing Performance Regulation Method Of Hypoid Gear With High Reduction Ratio

Geometrically,the high reduction ratio hypoid gear(HRH)is the ultimate evolution of spiral bevel gear.In terms of machining methods,the same machine tools,cutters and gear grinding processes as those of ordinary spiral bevel gears can be used.Therefore,the gear and the pinion can be designed with hard tooth surfaces,highly improving their accuracy retention.The HRH gear is axially adjustable and insensitive to installation error and thermal expansion.The proper elastic support system can even fully realize backlash free meshing transmission,so it has good working adaptability.At present,HRH gear is mainly limited to small module light load transmission,and gradually develops to precision servo transmission in industrial developed countries,especially in the field of robots.However,there is no precise analysis on its mechanical and geometric properties.Therefore,it is necessary to organically combine gear mesh theory with differential geometry and mechanical analysis to provide a new idea and method for gear surface design and performance optimization.In this paper,starting from geometric design,the influence of gear pitch cone angle on the meshing characteristic parameters of the tooth surface is considered.Combined with the time-varying line pressure of the contact line of multiple tooth pairs under complete conjugation,the time-varying maximum wear of the whole tooth surface is obtained using the Hertz stress calculation formula;A method combining the finite element substructure method to program the flexibility matrix is proposed.Based on the load-sharing preset error of the tooth surface of the hypoid gear with a high reduction ratio,the sequential optimization calculation of the machining parameters is carried out.The main research results are as follows:1.A forward numerical method for calculating hypoid pitch cone parameters is proposed.Within the limit range of pitch cone parameters,two representative hypoid gears with gear pitch cone angle and high reduction ratio are selected for geometric analysis.The evolution law of hypoid gear pitch cone is obtained by combining the two-parameter pitch cone equation derived from the strength condition of the large wheel foundation;The equal tangential conjugate principle of bevel gears is proposed,which lays a theoretical foundation for the generation of conjugate tooth surfaces(especially the gear using generated method).According to the limit of the pitch cone,two kinds of hypoid gears with gear pitch cone angles of 70 ° and 90 ° are determined as the research object.For each kind of gear,the range of each contact line is determined according to the tooth surface boundary line,and the length of each contact line and the total length of the time-varying contact line of multi-tooth contact are calculated.2.A time varying wear calculation method for hypoid gears is presented.The time-varying maximum wear amount of the whole tooth surface has been calculated.Considering the meshing of contact lines at each time,the time-varying line pressure of multi-tooth contact under uniform load is calculated;The variation law of the meshing characteristic parameter values expressed by two kinds of eigenvalues and eigenvectors is obtained,and the concept of slip velocity reversing line is proposed,based on which the addendum height coefficient is determined;The time-varying maximum wear of whole tooth surface is calculated by combining the characteristic parameters such as sliding rate and comprehensive curvature radius;By comparison,the wear of whole tooth surface is more balanced when the cone angle of gear pitch is90°.3.Combined with the commercial finite element software,the finite element model including the matrix is constructed,and the mechanical analysis of HRH gear is completed efficiently and accurately combined with the simplex method.In this paper,the generating program of gear tooth nodes is compiled,and the gear stiffness is calculated with the commercial software of the structural finite element method.This method considers both the flexibility of programming and the efficiency of commercial software calculation;The programming can automatically convert the tooth surface point information into the finite element node information,and arrange the node numbers in order according to the needs.The orderly arrangement of nodes is conducive to the equivalent displacement of nodal force when the contact point is loaded;Combined with the finite element matrix model,the commercial finite element software is used for calculation and the substructure method is innovatively used to extract the boundary node information,which ensures the accuracy and efficiency of the calculation and provides a good data preparation for the subsequent loaded contact analysis.4.This paper presents a method of preset modification for hypoid gears.Calculate the time-varying deformation under multi-tooth uniform load contact,and obtain the preset modification of the whole tooth surface.The displacement of each node and the rotation angle of the rigid body of the pinion are obtained by uniformly loading a single contact line with the simplex method;Using the method of deformation coordination,the rotation error of the rigid body at each contact line under the condition of multi-tooth contact and uniform load is calculated.According to the calculated rigid body rotation error value,the rotation angle error of the tooth surface along the contact trace can be preset.5.The processing parameters of the pinion are optimized using the sequential optimization method.The tooth surface structure of hypoid gears with a high reduction ratio is complex,and it is difficult to obtain satisfactory processing parameters for pinion by directly optimizing the preset error of the tooth surface.In this paper,the local synthesis method is used to calculate the initial machine tool settings of the pinion;The machine tool settings are optimized according to the preset modification under uniform load.TCA analysis shows that the angle error after optimization is close to the preset correction error.6.It can be seen from the loaded contact analysis of the tooth surface and the loaded transmission error analysis that the transmission error caused by the stiffness after loading is greater than the transmission error caused by the machining accuracy of the gear itself.The gear loading transmission error generated by using the initial processing parameters presents a step change;The gear loading transmission error is more stable after further optimization according to the preset modification error.The vibration test verifies this conclusion.Based on the application background of precision HRH gear transmission equipment,this paper carries out the geometric design of the gear profile and the research on its performance regulations.The design methods and conclusions adopted therein apply to ordinary hypoid gears,which have important theoretical meaning and application value for the development of gear transmission.