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CN113324008B - A method for improving the stress concentration of the outer contour of the flexible wheel - Google Patents

A method for improving the stress concentration of the outer contour of the flexible wheel Download PDF

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CN113324008B
CN113324008B CN202110571803.2A CN202110571803A CN113324008B CN 113324008 B CN113324008 B CN 113324008B CN 202110571803 A CN202110571803 A CN 202110571803A CN 113324008 B CN113324008 B CN 113324008B
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curve
coordinate system
straight line
cup
point
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CN113324008A (en
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胡秋实
王超
王广
李磊
周宏根
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Guohua Qingdao Intelligent Equipment Co ltd
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Jiangsu University of Science and Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H49/00—Other gearings
    • F16H49/001—Wave gearings, e.g. harmonic drive transmissions
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0833—Flexible toothed member, e.g. harmonic drive
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/17—Toothed wheels

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Retarders (AREA)
  • Gears, Cams (AREA)

Abstract

The invention discloses a method for improving the stress concentration of the outer contour of a flexible gear, which comprises the step of establishing a coordinate system for the structural shape of the outer contour of the flexible gear, wherein the outer contour of the flexible gear comprises a cup bottom flange straight line section, a cup bottom flange and cup body connecting curve section, a cup bottom curve transition section, a cup body connecting curve section, a tooth rear end connecting straight line section, a tooth top straight line section, a tooth front end straight line section and a tooth root curve section which are sequentially connected. The invention carries out mathematical description of the flexible gear outline through a continuous curve equation, and the connecting section of the cup bottom flange and the cup body and the connecting section of the cup body adopt curves to replace the traditional straight lines, thereby effectively reducing the stress concentration at the connecting parts of the flexible gear cup bottom, the flexible gear cup body and the flange; the tooth root adopts a curve instead of a straight line, so that the interference between the front end of the flexible gear tooth and the rigid gear caused by the support of the wave generator is effectively reduced, and the stress concentration phenomenon is reduced; in addition, the outer contour of the flexible gear is characterized by adopting a continuous curve equation, a mathematical model is provided for processing and detecting the flexible gear, and the flexible gear has a good application prospect.

Description

一种改善柔轮外轮廓应力集中的方法A method to improve the stress concentration of the outer contour of the flexible wheel

技术领域technical field

本发明涉及一种改善应力集中的方法，尤其涉及一种改善柔轮外轮廓应力集中的方法。The invention relates to a method for improving stress concentration, in particular to a method for improving stress concentration on the outer contour of a flexible wheel.

背景技术Background technique

机器人关节谐波减速器属于高精密、高减速比的齿轮传动装置，是机器人实现运动功能必不可少的核心零部件。当前主流谐波减速器的结构如图1所示，其核心部件为图2所示的礼帽形柔轮和刚轮，谐波减速器运动过程主要依靠椭圆形的波发生器支撑礼帽形柔轮产生弹性变形，波发生器转动过程中礼帽形柔轮与刚轮形成差齿传动，因此变形后柔轮的力学性能尤为关键。The robot joint harmonic reducer is a gear transmission device with high precision and high reduction ratio, and is an indispensable core component for the robot to realize the motion function. The structure of the current mainstream harmonic reducer is shown in Figure 1. Its core components are the top hat-shaped flexible wheel and the rigid wheel shown in Figure 2. The movement process of the harmonic reducer mainly relies on the elliptical wave generator to support the top hat-shaped flexible wheel. Elastic deformation occurs, and the hat-shaped flexible wheel and the rigid wheel form a differential tooth transmission during the rotation of the wave generator, so the mechanical properties of the flexible wheel after deformation are particularly critical.

由于礼帽形柔轮受到波发生器的支撑产生较大的应变，导致极易在柔轮齿部的前端和后端、柔轮杯底、柔轮杯体与法兰连接处形成应力集中，如图3和图4所示，造成谐波减速器在使用过程中出现断裂现象，极大的降低了谐波减速器的疲劳寿命。Because the hat-shaped flex wheel is supported by the wave generator and generates a large strain, it is easy to form stress concentration at the front and rear ends of the flex wheel teeth, the bottom of the flex wheel cup, and the connection between the flex wheel cup body and the flange, such as As shown in Figure 3 and Figure 4, the harmonic reducer is broken during use, which greatly reduces the fatigue life of the harmonic reducer.

发明内容SUMMARY OF THE INVENTION

发明目的：本发明目的是提供一种改善柔轮外轮廓应力集中的方法，以提升谐波减速器的使用寿命。Purpose of the invention: The purpose of the present invention is to provide a method for improving the stress concentration of the outer contour of the flexible wheel, so as to increase the service life of the harmonic reducer.

技术方案：本发明包括以下步骤：Technical scheme: the present invention comprises the following steps:

(1)对柔轮外轮廓的结构形状建立坐标系，所述的柔轮外轮廓包括依次相连的杯底法兰直线段AB、杯底法兰与杯体连接曲线段BC、杯底曲线过渡段CD、杯体连接曲线段DE、齿后端连接直线段EF、齿顶直线段FG、齿前端直线段GH和齿根曲线段EH；(1) Establish a coordinate system for the structural shape of the outer contour of the flex wheel. The outer contour of the flex wheel includes the straight line segment AB of the cup bottom flange, the connection curve segment BC between the cup bottom flange and the cup body, and the cup bottom curve transition that are connected in sequence. segment CD, cup body connecting curve segment DE, tooth rear connecting straight segment EF, tooth top straight segment FG, tooth front straight segment GH and tooth root curve segment EH;

(2)杯底法兰与杯体连接曲线段BC，其曲线方程为：(2) The curve section BC connecting the cup bottom flange and the cup body, the curve equation is:

Figure GDA0003586391030000011
Figure GDA0003586391030000011

式中，yBC为曲线BC上任一点在笛卡尔坐标系XOY中的纵坐标值，xBC为曲线BC上任一点在笛卡尔坐标系XOY中的横坐标值，h为杯底的厚度，m为杯底法兰的厚度，n为杯底法兰距离横坐标的距离，K为杯底的宽度；In the formula, y BC is the ordinate value of any point on the curve BC in the Cartesian coordinate system XOY, x BC is the abscissa value of any point on the curve BC in the Cartesian coordinate system XOY, h is the thickness of the bottom of the cup, m is the The thickness of the cup bottom flange, n is the distance between the cup bottom flange and the abscissa, and K is the width of the cup bottom;

(3)杯体连接曲线段DE，其曲线方程为：(3) The cup body connects the curve segment DE, and its curve equation is:

Figure GDA0003586391030000021
Figure GDA0003586391030000021

式中，yDE为曲线DE上任一点在笛卡尔坐标系XOY中的纵坐标值，xDE为曲线DE上任一点在笛卡尔坐标系XOY中的横坐标值，L为礼帽形柔轮杯体的长度；In the formula, y DE is the ordinate value of any point on the curve DE in the Cartesian coordinate system XOY, x DE is the abscissa value of any point on the curve DE in the Cartesian coordinate system XOY, and L is the top hat-shaped flexible wheel cup body. length;

(4)齿根曲线段EH，其曲线方程为：(4) The tooth root curve segment EH, its curve equation is:

Figure GDA0003586391030000022
Figure GDA0003586391030000022

式中，yEH为曲线EH上任一点在笛卡尔坐标系XOY中的纵坐标值，xEH为曲线EH上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y EH is the ordinate value of any point on the curve EH in the Cartesian coordinate system XOY, and x EH is the abscissa value of any point on the curve EH in the Cartesian coordinate system XOY.

所述步骤(1)中杯底法兰直线段AB的直线方程为：The straight line equation of the straight line segment AB of the cup bottom flange in the step (1) is:

Figure GDA0003586391030000023
Figure GDA0003586391030000023

式中，xAB为直线段AB上任一点在笛卡尔坐标系XOY中的横坐标值，yAB为直线段AB上任一点在笛卡尔坐标系中的纵坐标值，m为杯底法兰的厚度，n为杯底法兰距离横坐标的距离，K为杯底的宽度。In the formula, x AB is the abscissa value of any point on the straight line segment AB in the Cartesian coordinate system XOY, y AB is the ordinate value of any point on the straight line segment AB in the Cartesian coordinate system, m is the thickness of the cup bottom flange , n is the distance between the flange at the bottom of the cup and the abscissa, and K is the width of the bottom of the cup.

所述步骤(1)中杯底曲线过渡段CD的曲线方程为：The curve equation of the transition section CD of the cup bottom curve in the step (1) is:

Figure GDA0003586391030000024
Figure GDA0003586391030000024

式中，xCD为曲线段CD上任一点在笛卡尔坐标系XOY中的横坐标值，yCD为曲线段CD上任一点在笛卡尔坐标系XOY中的纵坐标值，L为礼帽形柔轮杯体的长度。In the formula, x CD is the abscissa value of any point on the curve segment CD in the Cartesian coordinate system XOY, y CD is the ordinate value of any point on the curve segment CD in the Cartesian coordinate system XOY, and L is the top hat-shaped flexible wheel cup. body length.

所述步骤(1)中齿后端连接直线段EF的直线方程为：In the step (1), the straight line equation connecting the straight line segment EF at the rear end of the tooth is:

Figure GDA0003586391030000025
Figure GDA0003586391030000025

式中，yEF为直线EF上任一点在笛卡尔坐标系XOY中的纵坐标值，xEF为直线EF上任一点在笛卡尔坐标系XOY中的横坐标值，R1为齿顶圆半径。In the formula, y EF is the ordinate value of any point on the straight line EF in the Cartesian coordinate system XOY, x EF is the abscissa value of any point on the straight line EF in the Cartesian coordinate system XOY, and R 1 is the addendum circle radius.

所述步骤(1)中齿顶直线段FG的直线方程为：The straight line equation of the tooth tip straight line segment FG in the step (1) is:

Figure GDA0003586391030000026
Figure GDA0003586391030000026

式中，yFG为直线FG上任一点在笛卡尔坐标系XOY中的纵坐标值，xFG为直线FG上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y FG is the ordinate value of any point on the straight line FG in the Cartesian coordinate system XOY, and x FG is the abscissa value of any point on the straight line FG in the Cartesian coordinate system XOY.

所述步骤(1)中齿前端直线段GH的直线方程为：The straight line equation of the straight line segment GH at the front end of the tooth in the step (1) is:

Figure GDA0003586391030000031
Figure GDA0003586391030000031

式中，yGH为直线GH上任一点在笛卡尔坐标系XOY中的纵坐标值，xGH为直线GH上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y GH is the ordinate value of any point on the straight line GH in the Cartesian coordinate system XOY, and x GH is the abscissa value of any point on the straight line GH in the Cartesian coordinate system XOY.

所述步骤(1)中的坐标系为以柔轮的中轴线为横坐标轴，以杯底法兰为纵坐标轴的笛卡尔坐标系。The coordinate system in the step (1) is a Cartesian coordinate system with the central axis of the flexible wheel as the abscissa axis and the cup bottom flange as the ordinate axis.

有益效果：本发明通过连续的曲线方程进行柔轮外轮廓的数学描述，杯底法兰与杯体连接段及杯体连接段采用精准描述的曲线代替传统的直线，有效降低了柔轮杯底、柔轮杯体与法兰连接处的应力集中；齿根采用精准描述的曲线代替直线，有效降低由于波发生器支撑导致的柔轮齿前端与刚轮发生干涉，从而减少应力集中现象的发生；此外，柔轮外轮廓采用连续的曲线方程进行表征，为其加工和检测提供数学模型，具有良好的应用前景；本发明的实施可以有效的改善柔轮齿部的前端和后端、柔轮杯底、柔轮杯体与法兰连接处、柔轮齿前端的应力集中现象，提高柔轮在工作过程中的疲劳寿命，为长寿命的谐波减速器研发提供理论和技术基础。Beneficial effects: The present invention uses continuous curve equations to describe the outer contour of the flex wheel, and the cup bottom flange and the cup body connection section and the cup body connection section use accurately described curves instead of traditional straight lines, effectively reducing the flex wheel bottom. , The stress concentration at the connection between the flex wheel cup body and the flange; the tooth root adopts the accurately described curve instead of the straight line, which effectively reduces the interference between the front end of the flex wheel tooth and the rigid wheel caused by the support of the wave generator, thereby reducing the occurrence of stress concentration. In addition, the outer contour of the flex wheel is characterized by a continuous curve equation, which provides a mathematical model for its processing and detection, and has a good application prospect; the implementation of the present invention can effectively improve the front and rear ends of the flex wheel teeth, and the flex wheel The stress concentration phenomenon at the bottom of the cup, the connection between the cup body and the flange of the flex wheel, and the front end of the flex wheel teeth can improve the fatigue life of the flex wheel during the working process, and provide a theoretical and technical basis for the research and development of long-life harmonic reducers.

附图说明Description of drawings

图1为传统的谐波减速器结构简图；Figure 1 is a schematic structural diagram of a traditional harmonic reducer;

图2为传统的礼帽形柔轮和刚轮结构图；Figure 2 is a structural diagram of a traditional top hat-shaped flexible wheel and a rigid wheel;

图3为传统礼帽形柔轮的剖视图；Figure 3 is a cross-sectional view of a traditional hat-shaped flexible wheel;

图4为传统礼帽形柔轮受支撑后的变形示意图；Figure 4 is a schematic diagram of the deformation of the traditional hat-shaped flexible wheel after being supported;

图5为本发明的礼帽形柔轮外轮廓结构图。FIG. 5 is a structural diagram of the outer contour of the hat-shaped flexible wheel of the present invention.

具体实施方式Detailed ways

下面结合附图对本发明作进一步说明。The present invention will be further described below in conjunction with the accompanying drawings.

如图5所示，本发明的柔轮外轮廓采用连续数学表征的方法，对谐波减速器礼帽形柔轮外轮廓曲线方程进行结构定义与描述，降低了危险点的应力集中现象，提高了谐波减速器的使用寿命。具体包括以下步骤：As shown in FIG. 5 , the outer contour of the flexible pulley of the present invention adopts the method of continuous mathematical characterization to define and describe the structure of the outer contour curve equation of the top hat-shaped flexible pulley of the harmonic reducer, which reduces the stress concentration phenomenon at the dangerous point and improves the The service life of the harmonic reducer. Specifically include the following steps:

(1)建立以礼帽形柔轮的中轴线为横坐标轴，以杯底法兰为纵坐标轴的笛卡尔坐标系，用于礼帽形柔轮外轮廓结构形状的曲线方程表征。(1) Establish a Cartesian coordinate system with the central axis of the top hat-shaped flex wheel as the abscissa axis and the cup bottom flange as the ordinate axis, which is used for the curve equation characterization of the outer contour structure of the top hat-shaped flex wheel.

(2)礼帽形柔轮外轮廓包括杯底法兰直线段AB、杯底法兰与杯体连接曲线段BC、杯底曲线过渡段CD、杯体连接曲线段DE、齿后端连接直线段EF、齿顶直线段FG、齿前端直线段GH、齿根曲线段EH。(2) The outer contour of the top hat-shaped flex wheel includes the straight section AB of the cup bottom flange, the connecting curve section BC of the cup bottom flange and the cup body, the cup bottom curve transition section CD, the cup body connecting curve section DE, and the straight section connecting the rear end of the tooth. EF, tooth top straight section FG, tooth front straight section GH, tooth root curve section EH.

(3)杯底法兰直线段AB，其直线方程为：(3) The straight line segment AB of the cup bottom flange, its straight line equation is:

Figure GDA0003586391030000041
Figure GDA0003586391030000041

式中，xAB为直线段AB上任一点在笛卡尔坐标系XOY中的横坐标值，yAB为直线段AB上任一点在笛卡尔坐标系中的纵坐标值，m为杯底法兰的厚度，n为杯底法兰距离横坐标的距离，K为杯底的宽度。In the formula, x AB is the abscissa value of any point on the straight line segment AB in the Cartesian coordinate system XOY, y AB is the ordinate value of any point on the straight line segment AB in the Cartesian coordinate system, m is the thickness of the cup bottom flange , n is the distance between the flange at the bottom of the cup and the abscissa, and K is the width of the bottom of the cup.

(4)杯底法兰与杯体连接曲线段BC，其曲线方程为：(4) The curve section BC connecting the cup bottom flange and the cup body, the curve equation is:

Figure GDA0003586391030000042
Figure GDA0003586391030000042

式中，yBC为曲线BC上任一点在笛卡尔坐标系XOY中的纵坐标值，xBC为曲线BC上任一点在笛卡尔坐标系XOY中的横坐标值，h为杯底的厚度。In the formula, y BC is the ordinate value of any point on the curve BC in the Cartesian coordinate system XOY, x BC is the abscissa value of any point on the curve BC in the Cartesian coordinate system XOY, and h is the thickness of the bottom of the cup.

(5)杯底曲线过渡段CD，其曲线方程为：(5) The transition section CD of the cup bottom curve, its curve equation is:

Figure GDA0003586391030000043
Figure GDA0003586391030000043

式中，xCD为曲线段CD上任一点在笛卡尔坐标系XOY中的横坐标值，yCD为曲线段CD上任一点在笛卡尔坐标系XOY中的纵坐标值，L为礼帽形柔轮杯体的长度。In the formula, x CD is the abscissa value of any point on the curve segment CD in the Cartesian coordinate system XOY, y CD is the ordinate value of any point on the curve segment CD in the Cartesian coordinate system XOY, and L is the top hat-shaped flexible wheel cup. body length.

(6)杯体连接曲线段DE，其曲线方程为：(6) The cup body connects the curve segment DE, and its curve equation is:

Figure GDA0003586391030000044
Figure GDA0003586391030000044

式中，yDE为曲线DE上任一点在笛卡尔坐标系XOY中的纵坐标值，xDE为曲线DE上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y DE is the ordinate value of any point on the curve DE in the Cartesian coordinate system XOY, and x DE is the abscissa value of any point on the curve DE in the Cartesian coordinate system XOY.

(7)齿后端连接直线段EF，其直线方程为：(7) The rear end of the tooth connects the straight line segment EF, and its straight line equation is:

Figure GDA0003586391030000051
Figure GDA0003586391030000051

式中，yEF为直线EF上任一点在笛卡尔坐标系XOY中的纵坐标值，xEF为直线EF上任一点在笛卡尔坐标系XOY中的横坐标值，R1为齿顶圆半径。In the formula, y EF is the ordinate value of any point on the straight line EF in the Cartesian coordinate system XOY, x EF is the abscissa value of any point on the straight line EF in the Cartesian coordinate system XOY, and R 1 is the addendum circle radius.

(8)齿顶直线段FG，其直线方程为：(8) Tooth top straight line segment FG, its straight line equation is:

Figure GDA0003586391030000052
Figure GDA0003586391030000052

式中，yFG为直线FG上任一点在笛卡尔坐标系XOY中的纵坐标值，xFG为直线FG上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y FG is the ordinate value of any point on the straight line FG in the Cartesian coordinate system XOY, and x FG is the abscissa value of any point on the straight line FG in the Cartesian coordinate system XOY.

(9)齿前端直线段GH，其直线方程为：(9) The straight line segment GH at the front end of the tooth, its straight line equation is:

Figure GDA0003586391030000053
Figure GDA0003586391030000053

式中，yGH为直线GH上任一点在笛卡尔坐标系XOY中的纵坐标值，xGH为直线GH上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y GH is the ordinate value of any point on the straight line GH in the Cartesian coordinate system XOY, and x GH is the abscissa value of any point on the straight line GH in the Cartesian coordinate system XOY.

(10)齿根曲线段EH，其曲线方程为：(10) The tooth root curve segment EH, its curve equation is:

Figure GDA0003586391030000054
Figure GDA0003586391030000054

式中，yEH为曲线EH上任一点在笛卡尔坐标系XOY中的纵坐标值，xEH为曲线EH上任一点在笛卡尔坐标系XOY中的横坐标值。In the formula, y EH is the ordinate value of any point on the curve EH in the Cartesian coordinate system XOY, and x EH is the abscissa value of any point on the curve EH in the Cartesian coordinate system XOY.

按照上述曲线方程形成的礼帽形柔轮外轮廓，可缓解如图4所示的礼帽形柔轮受波发生器支撑导致的应力集中，提高礼帽形柔轮的使用寿命。The outer contour of the top hat-shaped flexible wheel formed according to the above curve equation can alleviate the stress concentration caused by the support of the top hat-shaped flexible wheel by the wave generator as shown in Figure 4, and improve the service life of the top hat-shaped flexible wheel.

Claims (5)

1.一种改善柔轮外轮廓应力集中的方法，其特征在于，包括以下步骤：1. a method for improving the stress concentration of the outer contour of a flexible wheel, is characterized in that, comprises the following steps: (1)对柔轮外轮廓的结构形状建立坐标系，所述的柔轮外轮廓包括依次相连的杯底法兰直线段AB、杯底法兰与杯体连接曲线段BC、杯底曲线过渡段CD、杯体连接曲线段DE、齿后端连接直线段EF、齿顶直线段FG、齿前端直线段GH和齿根曲线段EH；(1) Establish a coordinate system for the structural shape of the outer contour of the flex wheel. The outer contour of the flex wheel includes the straight line segment AB of the cup bottom flange, the connection curve segment BC between the cup bottom flange and the cup body, and the cup bottom curve transition that are connected in sequence. segment CD, cup body connecting curve segment DE, tooth rear connecting straight segment EF, tooth top straight segment FG, tooth front straight segment GH and tooth root curve segment EH; (2)杯底法兰与杯体连接曲线段BC，其曲线方程为：(2) The curve section BC connecting the cup bottom flange and the cup body, the curve equation is:
Figure FDA0003606934340000011
Figure FDA0003606934340000011
 式中，yBC为曲线BC上任一点在笛卡尔坐标系XOY中的纵坐标值，xBC为曲线BC上任一点在笛卡尔坐标系XOY中的横坐标值，h为杯底的厚度，m为杯底法兰的厚度，n为杯底法兰距离横坐标的距离，K为杯底的宽度；In the formula, y BC is the ordinate value of any point on the curve BC in the Cartesian coordinate system XOY, x BC is the abscissa value of any point on the curve BC in the Cartesian coordinate system XOY, h is the thickness of the bottom of the cup, m is the The thickness of the cup bottom flange, n is the distance between the cup bottom flange and the abscissa, and K is the width of the cup bottom; (3)杯体连接曲线段DE，其曲线方程为：(3) The cup body connects the curve segment DE, and its curve equation is:
Figure FDA0003606934340000012
Figure FDA0003606934340000012
 式中，yDE为曲线DE上任一点在笛卡尔坐标系XOY中的纵坐标值，xDE为曲线DE上任一点在笛卡尔坐标系XOY中的横坐标值，L为礼帽形柔轮杯体的长度；In the formula, y DE is the ordinate value of any point on the curve DE in the Cartesian coordinate system XOY, x DE is the abscissa value of any point on the curve DE in the Cartesian coordinate system XOY, and L is the top hat-shaped flexible wheel cup body. length; (4)齿根曲线段EH，其曲线方程为：(4) The tooth root curve segment EH, its curve equation is:
Figure FDA0003606934340000013
Figure FDA0003606934340000013
 式中，yEH为曲线EH上任一点在笛卡尔坐标系XOY中的纵坐标值，xEH为曲线EH上任一点在笛卡尔坐标系XOY中的横坐标值；In the formula, y EH is the ordinate value of any point on the curve EH in the Cartesian coordinate system XOY, and x EH is the abscissa value of any point on the curve EH in the Cartesian coordinate system XOY; (5)杯底法兰直线段AB的直线方程为：(5) The straight line equation of the straight line segment AB of the cup bottom flange is:
Figure FDA0003606934340000014
Figure FDA0003606934340000014
 式中，xAB为直线段AB上任一点在笛卡尔坐标系XOY中的横坐标值，yAB为直线段AB上任一点在笛卡尔坐标系中的纵坐标值，m为杯底法兰的厚度，n为杯底法兰距离横坐标的距离，K为杯底的宽度；In the formula, x AB is the abscissa value of any point on the straight line segment AB in the Cartesian coordinate system XOY, y AB is the ordinate value of any point on the straight line segment AB in the Cartesian coordinate system, m is the thickness of the cup bottom flange , n is the distance between the flange at the bottom of the cup and the abscissa, and K is the width of the bottom of the cup; (6)杯底曲线过渡段CD的曲线方程为：(6) The curve equation of the transition section CD of the cup bottom curve is:
Figure FDA0003606934340000015
Figure FDA0003606934340000015
 式中，xCD为曲线段CD上任一点在笛卡尔坐标系XOY中的横坐标值，yCD为曲线段CD上任一点在笛卡尔坐标系XOY中的纵坐标值，L为礼帽形柔轮杯体的长度。In the formula, x CD is the abscissa value of any point on the curve segment CD in the Cartesian coordinate system XOY, y CD is the ordinate value of any point on the curve segment CD in the Cartesian coordinate system XOY, and L is the top hat-shaped flexible wheel cup. body length. 2.根据权利要求1所述的一种改善柔轮外轮廓应力集中的方法，其特征在于，所述步骤(1)中齿后端连接直线段EF的直线方程为：2. The method for improving the stress concentration of the outer contour of the flexible wheel according to claim 1, wherein the linear equation of the straight line segment EF connecting the rear end of the tooth in the step (1) is:
Figure FDA0003606934340000021
Figure FDA0003606934340000021
 式中，yEF为直线EF上任一点在笛卡尔坐标系XOY中的纵坐标值，xEF为直线EF上任一点在笛卡尔坐标系XOY中的横坐标值，R1为齿顶圆半径。In the formula, y EF is the ordinate value of any point on the straight line EF in the Cartesian coordinate system XOY, x EF is the abscissa value of any point on the straight line EF in the Cartesian coordinate system XOY, and R 1 is the addendum circle radius. 3.根据权利要求1所述的一种改善柔轮外轮廓应力集中的方法，其特征在于，所述步骤(1)中齿顶直线段FG的直线方程为：3. a kind of method that improves the stress concentration of flex wheel outer contour according to claim 1, is characterized in that, in described step (1), the straight line equation of tooth tip straight line segment FG is:
Figure FDA0003606934340000022
Figure FDA0003606934340000022
 式中，yFG为直线FG上任一点在笛卡尔坐标系XOY中的纵坐标值，xFG为直线FG上任一点在笛卡尔坐标系XOY中的横坐标值，R1为齿顶圆半径。In the formula, y FG is the ordinate value of any point on the line FG in the Cartesian coordinate system XOY, x FG is the abscissa value of any point on the line FG in the Cartesian coordinate system XOY, and R 1 is the radius of the addendum circle. 4.根据权利要求1所述的一种改善柔轮外轮廓应力集中的方法，其特征在于，所述步骤(1)中齿前端直线段GH的直线方程为：4. The method for improving the stress concentration of the outer contour of the flexible wheel according to claim 1, wherein the linear equation of the straight line segment GH at the front end of the tooth in the step (1) is:
Figure FDA0003606934340000023
Figure FDA0003606934340000023
 式中，yGH为直线GH上任一点在笛卡尔坐标系XOY中的纵坐标值，xGH为直线GH上任一点在笛卡尔坐标系XOY中的横坐标值，R1为齿顶圆半径。In the formula, y GH is the ordinate value of any point on the straight line GH in the Cartesian coordinate system XOY, x GH is the abscissa value of any point on the straight line GH in the Cartesian coordinate system XOY, and R 1 is the radius of the addendum circle. 5.根据权利要求1所述的一种改善柔轮外轮廓应力集中的方法，其特征在于，所述步骤(1)中的坐标系为以柔轮的中轴线为横坐标轴，以杯底法兰为纵坐标轴的笛卡尔坐标系。5. The method for improving the stress concentration of the outer contour of the flexible wheel according to claim 1, wherein the coordinate system in the step (1) is to take the central axis of the flexible wheel as the abscissa axis, and the bottom of the cup The flange is a Cartesian coordinate system with the ordinate axis.
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