Research On CAD System Of High-order Multistage Deformed Elliptical Gear And Analysis Its Transmission Characteristic

High-order multistage deformed elliptical gear is a new type of non-circular gear,which unified the elliptical gear expression.When the gear pair meshed for a week,the transmission ratio curve changed several cycles,and the transmission ratio curve in each period was asymmetrical.This new kind of non-circular gear greatly increased the flexibility of adjusting the transmission ratio of the transmission range to achieve more widely.What's more,it can better meet the actual requirements of transmission and have great potential application prospects.Due to the pitch-curve of the high-order multistage deformed elliptical gear section is complicated and changeable,research on its design and transmission is not yet mature.In this paper,we make corresponding research on these two aspects.(1)the pitch-curve expression of high-order multistage deformed elliptical gear section is presented,which lays a foundation for the subsequent transmission.Based on the study of high-order multistage deformed elliptical gear,this paper studies the theory of internal(external)meshing high-order multistage deformed elliptical gear transmission theory.By analyzing the transmission characteristics of gear pair,the method of curvature radius and convexity check,pressure angle check,root cut check and meshing degree are given.At the same time,the distribution law of gear tooth on the pitch-curve is analyzed.The geometric formulas of non-circular parameters are given.The optimal parameter combination is selected by using the calculation technique,and the parameters of the high-order multistage deformed elliptical gears are rationally designed.(2)Using a numerical discrete point method to fit the tooth blank,to establish a parameterized tooth blank,and establish interpolation cutters model,build mathematical model of inner(external)meshing high-order multistage deformed elliptical gear envelope interpolation,analyze the coordinate transformation of insert tooth profile in the process of inserting,and construct a virtual parameter design method of gear cutting based on the principle of envelope interpolation.The use of gear blank arc length to analyze the virtual insert realization technology,analyze the modeling method of spur gear cutters,analyze the three-dimensional envelope profile achieved by virtual insert,and construct the straight(oblique)gear cutting program,the insert cutter position of the motion trajectory envelope diagram shows the feasibility of the straight(oblique)cut-off scheme interpolation,the design example of the virtual gear interpolation design of the gear,and the establishment of the high-order multistage deformed elliptical gear solid model validates the feasibility of the virtual cut parameterized design method.There is a real tooth mark on the tooth surface of the gear,which is close to the real gear cutting processing.If it is used in the research of gear pair transmission characteristics,the analysis error caused by the model can be reduced.(3)The establishment of a three-dimensional model of non-circular gears provides a model basis for analyzing the load bearing capacity of gears.The finite element method is used to analyze the bearing capacity of gear pair transmission,and the model can be simplified.Using different meshing position to replace the gear pair meshing process,and then analyze the force variation of conjugate gear meshing process.After that,the maximum contact stress of different positions and the maximum contact pressure are analyzed and calculated,which lay a foundation for the failure check of gear transmission.The results show that the maximum contact stress in a pair of gear meshing process is 8.4281e5 Pa,the maximum contact pressure is 6.3371e5 Pa.The actual meshing is multi-teeth,so the result of the above analysis method is large,so it is also safe.The kinematic characteristics of high-order multistage deformed elliptical gear are analyzed.It is mainly to analyze the influence of gear structural parameters on the change of transmission ratio,the change of the angular velocity of the driving wheel and the change of the acceleration of the wheel angle.The results show that the change of angular velocity and angular acceleration of the driven wheel increases with the increase of eccentricity.When the deformation coefficient is 1,the gear pair is stable.When the deformation coefficient is greater than 1,the change amplitude of acceleration and angular acceleration increases with the increase of the deformation coefficient.In the process of different gears,when the number of segments is determined while the order is uncertain,the characteristics of transmission ratio,angular velocity and angular acceleration are the same in the cycle,but the variation period is different.When the number of gears is more than three the deformation coefficient of each segment is different,and the acceleration of the wheel angle will be changed.To sum up,the above analysis provides theoretical basis for the design of a suitable variable speed transmission system.In this paper,based on the principle of enveloping interpolation,a parametric design method of virtual interpolation is proposed to realize the design of non-circular gears.There are tooth marks on the tooth surface of the model,and the gear model is close to the real machining.The gear meshing characteristics analysis can be reduced.The errors caused by the model are analyzed,and the bearing capacity in the gear pair transmission process is analyzed.The stress changes in the gear meshing process are mainly analyzed,and the kinematics characteristics in the transmission are analyzed by using the theoretical method to design an appropriate high-order segmented degenerated elliptic gear transmission system.Provide theoretical basis.