技术领域technical field
本发明涉及谐波减速器的设计与制造领域技术领域，特别是涉及一种谐波减速器双圆弧齿形啮合点法线斜率计算方法。The present invention relates to the technical field of design and manufacture of harmonic reducers, in particular to a method for calculating the normal slope of the meshing point of a double-arc tooth shape of a harmonic reducer.
背景技术Background technique
谐波减速器是机器人关节的核心元件，谐波减速器柔轮和刚轮的啮合属于大变形条件下小模数多齿啮合。谐波减速器的传动效率和扭转刚度与刚柔轮啮合过程中啮合齿数、啮合点的接触应力以及啮合点的速度有关。目前双圆弧齿形是谐波减速器传动中应用较广、性能参数较优的齿形之一，但大多数研究采用有限元仿真的技术来获取谐波减速器啮合齿对的分布和啮合点法线的规律，但是仿真方法假设条件过多，不能有效的支撑啮合过程的力分布模型，因此提出一种谐波减速器双圆弧齿形啮合点法线斜率计算方法。The harmonic reducer is the core component of the robot joint. The meshing of the flexible spline and the rigid spline of the harmonic reducer belongs to the small modulus multi-tooth meshing under the condition of large deformation. The transmission efficiency and torsional stiffness of the harmonic reducer are related to the number of meshing teeth, the contact stress of the meshing point and the speed of the meshing point during the meshing process of the rigid-flex gear. At present, the double-arc tooth shape is one of the tooth shapes that are widely used in harmonic reducer transmission and have better performance parameters, but most studies use finite element simulation technology to obtain the distribution and meshing of meshing tooth pairs of harmonic reducers However, the simulation method assumes too many conditions and cannot effectively support the force distribution model of the meshing process. Therefore, a calculation method for the normal slope of the meshing point of the double-arc tooth profile of the harmonic reducer is proposed.
发明内容Contents of the invention
本发明目的是：为提高谐波减速器刚柔轮啮合质量，通过分析谐波减速器柔轮包络过程中刚轮方程的数学表达式，提出一种谐波减速器双圆弧齿形啮合点法线斜率计算方法。The purpose of the present invention is: in order to improve the meshing quality of the rigid-flex wheel of the harmonic reducer, a double-arc tooth-shaped meshing of the harmonic reducer is proposed by analyzing the mathematical expression of the rigid wheel equation in the envelope process of the harmonic reducer flexible wheel Point normal slope calculation method.
本发明所采取的技术方案是：The technical scheme that the present invention takes is:
一种谐波减速器双圆弧齿形啮合点法线斜率计算方法，该方法包括如下步骤，步骤一：通过双圆弧柔轮齿廓方程和双圆弧共轭包络理论推导出谐波减速器刚轮齿廓方程。A method for calculating the normal slope of the meshing point of a double-arc tooth profile of a harmonic reducer, the method includes the following steps, step 1: deriving the harmonic through the double-arc flexible wheel tooth profile equation and the double-arc conjugate envelope theory Reducer gear tooth profile equation.
式中，xg和yg分别表示刚轮的横坐标和纵坐标。xr和yr表示柔轮的横坐标和纵坐标。β表示柔轮啮合轮齿的中心轴线与刚轮固定坐标系竖直方向的夹角，表示的是柔轮啮合轮齿中心轴与中性层交点与固定坐标系原点的矢径与竖直方向的夹角，表示波发生器转角，s表示的是柔轮齿廓弧长参数，ρ表示柔轮中性层曲线变形后矢径。In the formula, xg and yg represent the abscissa and ordinate of the rigid wheel respectively. xr and yr represent the abscissa and ordinate of the flexspline. β represents the angle between the central axis of the meshing teeth of the flexible spline and the vertical direction of the fixed coordinate system of the rigid spline, Indicates the angle between the vector radius and the vertical direction between the intersection point of the flexspline meshing tooth central axis and the neutral layer and the origin of the fixed coordinate system, Indicates the rotation angle of the wave generator, s indicates the arc length parameter of the tooth profile of the flexspline, and ρ indicates the radial diameter of the flexspline after the neutral layer curve is deformed.
步骤二：计算单齿包络过程中刚轮齿形在不同波发生器转角处的法线斜率：Step 2: Calculate the rigid wheel tooth shape at different wave generator rotation angles during the single tooth envelope process The normal slope at :
kg的表达式是由组成的隐函数方程，隐函数方程的求解步骤如下。The expression of kg is given by Formed implicit function equation, the solution steps of the implicit function equation are as follows.
步骤2.1：也是由柔轮齿廓弧长参数s和波发生器转角组成的隐函数，首先通过在定义域内等间隔取值，采用二分法计算不同对应的齿廓参数s，并组成矩阵Step 2.1: It is also determined by the arc length parameter s of the flexspline tooth profile and the wave generator rotation angle Implicit function composed of, first pass in Take values at equal intervals in the definition domain, and use the dichotomy method to calculate different The corresponding tooth profile parameters s, and form a matrix
步骤2.2：方程两边同时对求导，得到的数学方程，将矩阵带入方程基于方程采用二分法求解不同对应的矩阵Step 2.2: Equation both sides at the same time seek guidance, get The mathematical equation for the matrix Bring in the equation Based on the equation, use the dichotomy method to solve the different corresponding matrix
步骤2.3：将矩阵带入求解得到不同波发生器转角对应的啮合点法线斜率kg。Step 2.3: Convert the matrix bring in Solving for different wave generator rotation angles The corresponding meshing point normal slope kg .
步骤三：在单齿共轭的基础上通过旋转角度得到多齿啮合过程中不同波发生器转角对应的法线斜率：Step 3: Pass the rotation angle on the basis of the single-tooth conjugate The normal slopes corresponding to different wave generator rotation angles during multi-tooth meshing are obtained:
本发明具有的优点和积极效果是：The advantages and positive effects that the present invention has are:
本发明通过分析谐波减速器刚柔轮共轭包络理论，通过对刚轮方程的求导和法线斜率的方程解析，得到了不同波发生器转角条件下谐波减速器啮合点法线斜率的数学表征，为谐波减速器压力角的表征以及传动效率的提高奠定了理论基础。The present invention obtains the normal line of the meshing point of the harmonic reducer under different wave generator rotation angle conditions by analyzing the conjugate envelope theory of the rigid-flex wheel of the harmonic reducer, and through the derivation of the rigid wheel equation and the equation analysis of the normal slope The mathematical characterization of the slope lays a theoretical foundation for the characterization of the pressure angle of the harmonic reducer and the improvement of transmission efficiency.
附图说明Description of drawings
图1谐波减速器刚柔轮啮合点受力方向；Figure 1 The force direction of the meshing point of the rigid-flex wheel of the harmonic reducer;
图2谐波减速器单齿法线斜率计算流程。Fig. 2 Calculation flow of normal slope of single tooth of harmonic reducer.
具体实施方式Detailed ways
为能进一步了解本发明的发明内容、特点及功效，兹例举以下实施例，并配合附图详细说明如下：In order to further understand the invention content, characteristics and effects of the present invention, the following examples are given, and detailed descriptions are as follows in conjunction with the accompanying drawings:
一种谐波减速器双圆弧齿形啮合点法线斜率计算方法，包括如下步骤：A method for calculating the normal slope of the meshing point of a double-arc tooth profile of a harmonic reducer, comprising the following steps:
步骤一：如图1所示，通过双圆弧柔轮齿廓方程和双圆弧共轭包络理论推导出谐波减速器刚轮齿廓方程。Step 1: As shown in Figure 1, the tooth profile equation of the harmonic reducer rigid wheel is derived through the double-arc flexible wheel tooth profile equation and the double-arc conjugate envelope theory.
式中，xg和yg分别表示刚轮的横坐标和纵坐标。xr和yr表示柔轮的横坐标和纵坐标。β表示柔轮啮合轮齿的中心轴线与刚轮固定坐标系竖直方向的夹角，表示的是柔轮啮合轮齿中心轴与中性层交点与固定坐标系原点的矢径与竖直方向的夹角，表示波发生器转角，s表示的是柔轮齿廓弧长参数，ρ表示柔轮中性层曲线变形后矢径。In the formula, xg and yg represent the abscissa and ordinate of the rigid wheel respectively. xr and yr represent the abscissa and ordinate of the flexspline. β represents the angle between the central axis of the meshing teeth of the flexible spline and the vertical direction of the fixed coordinate system of the rigid spline, Indicates the angle between the vector radius and the vertical direction between the intersection point of the flexspline meshing tooth central axis and the neutral layer and the origin of the fixed coordinate system, Indicates the rotation angle of the wave generator, s indicates the arc length parameter of the tooth profile of the flexspline, and ρ indicates the radial diameter of the flexspline after the neutral layer curve is deformed.
步骤二：计算单齿包络过程中刚轮齿形在不同波发生器转角处的法线斜率，如图2所示：Step 2: Calculate the rigid wheel tooth shape at different wave generator rotation angles during the single tooth envelope process The normal slope at , as shown in Figure 2:
kg的表达式是由组成的隐函数方程，因此本发明将阐述这个隐函数的求解步骤。The expression of kg is given by Formed implicit function equation, so the present invention will set forth the solution steps of this implicit function.
步骤2.1：也是由参数s和组成的隐函数，首先通过在定义域内等间隔取值，采用二分法计算不同对应的齿廓参数s，并组成矩阵Step 2.1: is also determined by the parameters s and Implicit function composed of, first pass in Take values at equal intervals in the definition domain, and use the dichotomy method to calculate different The corresponding tooth profile parameters s, and form a matrix
步骤2.2：方程两边同时对求导，得到的数学方程，将矩阵带入方程基于方程采用二分法求解不同对应的矩阵Step 2.2: Equation both sides at the same time seek guidance, get The mathematical equation for the matrix Bring in the equation Based on the equation, use the dichotomy method to solve the different corresponding matrix
步骤2.3：将矩阵带入求解得到不同波发生器转角对应的啮合点法线斜率kg。Step 2.3: Convert the matrix bring in Solving for different wave generator rotation angles The corresponding meshing point normal slope kg .
步骤三：在单齿共轭的基础上通过旋转角度得到多齿啮合过程中不同波发生器转角对应的法线斜率：Step 3: Pass the rotation angle on the basis of the single-tooth conjugate The normal slopes corresponding to different wave generator rotation angles during multi-tooth meshing are obtained:
本发明具有的优点和积极效果是：The advantages and positive effects that the present invention has are:
本发明通过分析谐波减速器刚柔轮共轭包络理论，通过对刚轮方程的求导和法线斜率的方程解析，得到了不同波发生器转角条件下谐波减速器啮合点法线斜率的数学表征，为谐波减速器压力角的表征以及传动效率的提高奠定了理论基础。The present invention obtains the normal line of the meshing point of the harmonic reducer under different wave generator rotation angle conditions by analyzing the conjugate envelope theory of the rigid-flex wheel of the harmonic reducer, and through the derivation of the rigid wheel equation and the equation analysis of the normal slope The mathematical characterization of the slope lays a theoretical foundation for the characterization of the pressure angle of the harmonic reducer and the improvement of transmission efficiency.
| Application Number | Priority Date | Filing Date | Title |
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| CN201910507971.8ACN110245417B (en) | 2019-06-12 | 2019-06-12 | Method for calculating normal slope of meshing point of double-arc tooth profile of harmonic reducer |
| Application Number | Priority Date | Filing Date | Title |
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| CN201910507971.8ACN110245417B (en) | 2019-06-12 | 2019-06-12 | Method for calculating normal slope of meshing point of double-arc tooth profile of harmonic reducer |
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| CN110245417Atrue CN110245417A (en) | 2019-09-17 |
| CN110245417B CN110245417B (en) | 2023-05-12 |
| Application Number | Title | Priority Date | Filing Date |
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| CN201910507971.8AActiveCN110245417B (en) | 2019-06-12 | 2019-06-12 | Method for calculating normal slope of meshing point of double-arc tooth profile of harmonic reducer |
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