| Harmonic gear transmission is a new type of transmission.Compared with traditional rigid gear transmission,harmonic transmission has the advantages of small size,high precision,large transmission ratio,smooth transmission,etc.It is widely used in the field of precision transmission,such as aerospace,instrumentation,robots,medical equipment,etc.Because there are manufacturing errors of individual parts and assembly errors between parts in the harmonic drive,which have a complex impact on the transmission performance and meshing performance of the system.Therefore,the study of the manufacturing errors and the harmonic drive’s assembly errors has a great significance to harmonic transmission meshing characteristics and flexspline stress.This paper focuses on harmonic reducer.Considering the influence of the harmonic transmission error,based on the harmonic plane tooth profile design theory and transmission accuracy theory,taking the flexspline stress,deformation and backlash between teeth as the evaluation index,and establishing various errors harmonic reducer model,the study starts mainly by means of MATLAB parameterization and the ABAQUS finite element method.(1)This paper elaborates on the design theory of harmonic drive plane tooth profile and the theory of transmission precision.The harmonic drive coordinate system is defined based on assumptions.and the geometric relationship model of harmonic drive is established based on the relationship between the flexible layer neutral curve and the precise rotation angle;the harmonic drive meshing theory is derived according to the improved kinematics method and the conjugate tooth profile is solved.Then circular arc fitting was performed.(2)The multi-tooth finite element model of the harmonic reducer is established and it is used to analyze the characteristics of stress and deformation.Based on the design theory of plane tooth profile,the double-arc tooth profile with no common tangent is designed,and the three-dimensional tooth profile is modified and interfered,then structural parameters are selected and designed according to a given type of harmonic reducer.At the same time,the stress and deformation of the flexspline in all directions are comprehensively analyzed to verify the correctness and rationality of the structural parameter design and selection of the toothed harmonic gear model.(3)In order to explore the influence of various manufacturing errors on the stress of the flexspline,a response surface model of the flexspline stress based on the multi-tooth nonlinear elastic contact finite element method was established.The experimental results show that: 1)Under the joint action of the circular spline and the cam,the maximum stress on the flexspline appears at the position of the meshing area of the tooth surface of the flexspline;2)The cam long half axis deviation is most sensitive to the stress on the flexspline tooth,the M-value deviation of the flexspline and the M-value deviation of the circular spline less,and the cam short axis deviation sensitivity the least.3)The deviation of the M value of the flexspline and the deviation of the long half axis of the cam have a greater impact on the backlash between the teeth;the deviation of the M value of the circular spline and the deviation of the short half axis of the cam have less effect;4)Four kinds of error compensation schemes were proposed according to different deviations of the gears of the circular spline and the flexspline,which may occur during the manufacturing process,to improve the meshing condition and the accuracy retention.(4)With each assembly error,the finite element flexspline stress model is established to explore the influence of various assembly errors on the stress of the flexspline.The results show that the errors of the center distance of the flexspline and circular spline along the long axis and the radial error of the cam installation position have the greatest impact on the flexspline.The errors of the center distance of the flexspline and circular spline along the short axis and the radial error of the cam installation position have the less impact on the flexspline.The errors of the center distance of the flexspline and circular spline along the short axis,and the radial error of the cam installation position along the long axis have a slight effect on the stress of a flexspline bottom.The center distance error between the circular spline and the flexspline and the radial installation position error of the cam have a greater impact on the meshing backlash between the teeth and the interference of the tooth profile,and the axial error of the cam installation position has little effect.At the same time,a reasonable assembly error range that meets the requirements of good stress and backlash is obtained,which can establish the foundation for the subsequent harmonic gear reducer error compensation,stress and backlash control optimization. |
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