WO2020020073A1 - Spherical involute straight bevel gear pair and tooth profile modification method thereof - Google Patents

Spherical involute straight bevel gear pair and tooth profile modification method thereof Download PDF

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WO2020020073A1
WO2020020073A1 PCT/CN2019/096814 CN2019096814W WO2020020073A1 WO 2020020073 A1 WO2020020073 A1 WO 2020020073A1 CN 2019096814 W CN2019096814 W CN 2019096814W WO 2020020073 A1 WO2020020073 A1 WO 2020020073A1
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spherical
spherical involute
modification
gear
involute
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PCT/CN2019/096814
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French (fr)
Chinese (zh)
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焦继松
董义
王小乾
许君
陈晨
张辰瑞
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江苏太平洋精锻科技股份有限公司
江苏太平洋齿轮传动有限公司
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Publication of WO2020020073A1 publication Critical patent/WO2020020073A1/en

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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
    • 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
    • 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

Definitions

  • the invention relates to the technical field of gear design and manufacturing, in particular to a spherical involute spur bevel gear pair and a method for modifying a tooth profile thereof.
  • the change of the transmission ratio when the gears are meshed is considered to be one of the sources of gear vibration and noise.
  • the tooth profile curve of the spur bevel gear pair should be a spherical involute; however, due to the transmission characteristics of a spherical involute Not well understood, straight bevel gears are generally modeled using dorsal cone involutes. Although dorsal cone involutes and spherical involutes are very close and convenient to model, there is always an error in the modeling method.
  • the present invention provides a spherical involute straight-toothed bevel gear pair and a tooth profile modification thereof, which reduce the impact of gears in and out, reduce vibration and noise, and improve the meshing quality and service life of gears.
  • ⁇ Shape method.
  • a spherical involute straight bevel gear pair includes a driving gear and a passive gear meshing with the driving gear.
  • the tooth profile of the gear is divided into two sections, the AB section is a theoretical spherical involute, and the BD ′ section is a spherical modification.
  • Shape curve, B is the starting point of modification.
  • the plane P is the generation surface of the spherical involute
  • the cone OO1A is the spherical involute base cone
  • O is its vertex
  • a global rectangular coordinate system S is established, where the coordinate origin is the base cone vertex O, and the direction of the vector OO1 is defined as z Axis, the direction where the vector O1A is located is defined as the x-axis, and the z-axis and the x-axis directions are defined as the y-axis according to the right-hand rule.
  • the theoretical spherical involute of the AB segment, the equation is:
  • R is the spherical diameter of the meshing sphere
  • ⁇ is the base cone angle
  • the BD ′ segment is a spherical modification curve, and its equation is:
  • R is the spherical diameter of the meshing sphere
  • ⁇ is the base cone angle
  • Is the angle between the initial line segment on the meshing surface and the instantaneous rotation axis
  • ⁇ s is the amount of trimming at each trimming point of the standard spherical involute.
  • a tooth profile modification method for a spherical involute spur bevel gear pair includes the following steps:
  • the tooth profile of the passive gear and the drive gear are modified at the same time.
  • the shape curve is a curve on the spherical surface where the spherical involute curve is located.
  • the starting point and the amount of modification can be optimized according to the finite element algorithm;
  • Step 1 Find the theoretical spherical involute of the large and small ends of the driving gear and the passive gear;
  • Step 2 Establish the unshaped active gear and passive gear meshing gear pair, and perform finite element simulation analysis
  • Step 3 Take the first point of total displacement ⁇ 0.05 from the top of the gear to the root of the tooth on the large and small end spherical involutes of the active and passive gears as the starting point for the modification. Record the points on the spherical involute The total displacement, select the number of points according to the size of the gear;
  • Step 4 Calculate the coordinates of each point on the modified curve
  • Step 5 Import the big-end and small-end spherical involutes obtained in steps 1 and 4 above and their modified curve data points into the 3D modeling software, and use the "through curve group" command in the 3D modeling software surface modeling module to directly Generate a tooth flake on one side;
  • Step 6 Use the "mirror feature" command in the 3D modeling software solid modeling module to mirror the tooth surface generated in step 5 to establish a symmetrical tooth surface;
  • Step 7 Establish a model from symmetrical tooth surfaces on both sides and according to the conventional modeling steps of a straight bevel gear
  • the CNC machine tool is used to manufacture the repair mold.
  • the numerically controlled machine tool is a high-speed milling machine tool.
  • a forging process is adopted to realize large-scale mass production.
  • the 3D modeling software is UG.
  • the beneficial effect of the present invention is that, compared with the prior art, the spherical involute straight bevel gear pair of the present invention, the tooth profile modification of the passive gear and the active gear simultaneously adopts the method of edge trimming;
  • the shape modification curve is a spherical surface A section of the curve on the sphere where the line is opened.
  • the direction of the modification is the direction of the involute normal of the sphere.
  • the starting point and amount of the modification can be optimized according to the finite element algorithm, which can reduce the impact of the gear in and out and reduce the vibration. And noise to improve the meshing quality and service life of the gear pair.
  • FIG. 1 is a schematic structural diagram of the present invention
  • FIG. 2 is a schematic diagram of a large-end spherical involute tooth tip repair edge of the driving gear of the present invention
  • FIG. 3 is a schematic diagram of trimming of a large-end spherical involute tooth top of a passive gear according to the present invention.
  • a spherical involute straight bevel gear pair includes a driving gear 1 and a passive gear 2 meshing with the driving gear 1, the gear profile of the gear is modified into two sections, and AB
  • the segment is a theoretical spherical involute
  • the BD ′ segment is a spherical modification curve
  • B is the starting point of the modification.
  • the plane P is the generation surface of the spherical involute
  • the cone OO1A is the spherical involute base cone
  • O is its vertex
  • a global rectangular coordinate system S is established, where the coordinate origin is the base cone vertex O, and the direction of the vector OO1 is defined as z
  • the axis O1A is defined as the x-axis direction
  • the z-axis and x-axis directions are defined as the y-axis according to the right-hand rule.
  • the AB segment spherical involute has an equation:
  • R is the spherical diameter of the meshing sphere
  • ⁇ is the base cone angle
  • the BD ′ segment is a modified spherical curve, and its equation is:
  • R is the spherical diameter of the meshing sphere
  • ⁇ is the base cone angle
  • Is the included angle between the initial line segment on the meshing surface and the instantaneous axis of rotation
  • ⁇ s is the amount of shape modification of the theoretical spherical involute.
  • a tooth profile modification method for a spherical involute spur bevel gear pair includes the following steps:
  • the tooth profile modification of the passive gear 2 and the drive gear 1 adopts the method of tooth edge trimming;
  • the shape modification curve is a section of the spherical surface where the spherical involute is located, and the shape modification direction is the spherical involute normal.
  • the direction, starting point and amount of modification can be optimized according to the finite element algorithm;
  • Step 1 Find the theoretical spherical involute of the large and small ends of the active gear 1 and the passive gear 2;
  • Step 2 Establish the unmodified driving gear 1 and passive gear 2 meshing gear pair, and perform finite element simulation analysis
  • Step 3 Take the first point of the total displacement ⁇ 0.05 from the top of the tooth to the root of the tooth on the large and small end spherical involutes of the driving gear 1 and the passive gear 2 as the starting point of the modification, and record each of the spherical involutes. The total displacement of each point, select the number of points according to the size of the gear;
  • Step 4 Calculate the coordinates of each point on the modified curve
  • Step 5 Import the big-end and small-end spherical involutes obtained in steps 1 and 4 above and their modified curve data points into the 3D modeling software, and use the "through curve group" command in the 3D modeling software surface modeling module to directly Generate a tooth flake on one side;
  • Step 6 Use the "mirror feature" command in the 3D modeling software solid modeling module to mirror the tooth surface generated in step 5 to establish a symmetrical tooth surface;
  • Step 7 Establish a model from symmetrical tooth surfaces on both sides and according to the conventional modeling steps of a straight bevel gear
  • the CNC machine tool is used to manufacture the repair mold.
  • the numerical control machine tool is a high-speed milling machine tool; in the mass production step, a forging process is adopted to realize large-scale batch production; and the 3D modeling software is UG.
  • AD segment is the theoretical spherical involute
  • plane P is the spherical involute generating surface
  • cone OO1A is the spherical involute base cone
  • O is its vertex
  • B is the starting point of the modification
  • the modification is The posterior tooth profile is divided into two sections, the AB section is a theoretical spherical involute, and the BD ′ section is a spherical modification curve;
  • R is the spherical diameter of the meshing sphere
  • ⁇ is the base cone angle
  • the BD ′ segment is a modified spherical curve, and its equation is:
  • R is the spherical diameter of the meshing sphere
  • ⁇ is the base cone angle
  • Is the angle between the initial line segment on the meshing surface and the instantaneous axis of rotation
  • ⁇ s is the amount of trimming of each trimming point of the theoretical spherical involute
  • ⁇ s is the shape modification amount of each modification point of the theoretical spherical involute
  • Point D is the end of the spherical involute modification segment BD, and C is any point above it, then the coordinates of the point after the practice of D are the same; similarly, the coordinates of the point after the practice of D ′ and the coordinates of the point C ′ the same.
  • the position of the starting point B of the modification and the modification amount at each modification point on the BD segment are obtained through optimization calculation by the finite element method, and the goal is to prevent the engagement transmission and the engagement interference at the rated torque of the meshing transmission.
  • the coordinate point C ′ after the tooth top is modified, and the modified curve BC ′ is A large circular arc on the sphere of the sphere where the involute of the sphere is located, connecting the top modification point C ′ and the starting point B of the modification; the equation is easy to obtain and the three-dimensional modeling is extremely convenient;
  • the plane P is the occurrence surface of the spherical involute
  • the cone OO1A is the spherical involute base cone
  • O is its vertex
  • B is the starting point of the modification
  • C is the vertex of the standard spherical involute tooth
  • C ′ is The top of the tooth is modified, and the tooth profile is divided into two sections after the modification.
  • the AB section is the theoretical spherical involute
  • BC ′ is the large circular inferior arc on the spherical surface where the spherical involute is located.
  • the technical solution for the spherical involute tooth tip trimming technique adopted in this application is not only applicable to the differential passive gear 2 and the active gear 1, but also applicable to other Gear transmission adopts the transmission device of spherical involute straight tooth bevel gear.

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

Abstract

Provided are a spherical involute straight bevel gear pair and tooth profile modification method thereof; the spherical involute straight bevel gear pair comprises a meshing driving gear (1) and driven gear (2); the tooth profile of the gear is divided into two segments; the AB segment is the theoretical spherical involute and the BD' segment is a spherical modified curve, B being the starting point of the modification. The method for modifying the tooth profile of the gear comprises the following steps: software modeling → manufacturing modification mold → mass production.

Description

一种球面渐开线直齿锥齿轮副及其齿廓修形方法Spherical involute spur bevel gear pair and method for modifying tooth profile 技术领域Technical field
本发明涉及齿轮设计和制造技术领域，具体涉及一种球面渐开线直齿锥齿轮副及其齿廓修形方法。The invention relates to the technical field of gear design and manufacturing, in particular to a spherical involute spur bevel gear pair and a method for modifying a tooth profile thereof.
背景技术Background technique
齿轮啮合时的传动比变化被认为是齿轮振动和噪声的来源之一，为保证恒定的传动比，直齿锥齿轮副齿廓曲线应为球面渐开线；但是由于对球面渐开线传动特性认识不深，直齿锥齿轮一般都是采用背锥渐开线建模，虽然背锥渐开线与球面渐开线非常接近且建模方便，但该建模方法总存在误差，当球面半径与齿轮模数之比越小，其误差就越大；轿车差速器直齿锥齿轮的球面半径与齿轮模数比值较小，其齿廓误差就很大，由此带来的传动比变化造成的振动和噪声就会很明显；当前，虽然差速器球面渐开线直齿锥齿轮批量锻造尚未实现，但是球面渐开线直齿锥齿轮传动相对于平面渐开线直齿锥齿轮传动的优点使其成为当前高校和企业研究开发的热点；The change of the transmission ratio when the gears are meshed is considered to be one of the sources of gear vibration and noise. In order to ensure a constant transmission ratio, the tooth profile curve of the spur bevel gear pair should be a spherical involute; however, due to the transmission characteristics of a spherical involute Not well understood, straight bevel gears are generally modeled using dorsal cone involutes. Although dorsal cone involutes and spherical involutes are very close and convenient to model, there is always an error in the modeling method. When the spherical radius The smaller the ratio to the gear modulus, the larger the error; the smaller the ratio of the spherical radius of the spur bevel gear of the car to the gear modulus, the larger the tooth profile error will be. The vibration and noise caused will be obvious; at present, although the batch forging of differential spherical involute spur bevel gears has not yet been realized, the spherical involute spur bevel gear drive is compared with the flat involute spur bevel gear drive. The advantages make it a hot spot for research and development in universities and enterprises;
由于加载弹性变形的存在，齿轮副在啮入和啮出时，行星和半轴的基节不相等，即产生啮入和啮出干涉，由此带来齿轮副的振动和噪声，关于球面渐开线直齿锥齿轮齿廓修形已经有了一些研究，这些研究的共同点是在三维软件中画出理论球面渐开线，修形部分用直线抛物线等平面曲线代替，优点是直观形象，易于设计，缺点是修形量和修形方向不能准确反映出弹性变形的变形方向和大小，可能存在过度修形或者修形不足的问题。Due to the existence of elastic deformation of the load, when the gear pair is engaged and engaged, the bases of the planet and the axle are not equal, that is, the interference of the engagement and the engagement is generated, which brings the vibration and noise of the gear pair. There have been some studies on the contour modification of open-line spur bevel gears. The common point of these studies is to draw theoretical spherical involutes in 3D software. The modified parts are replaced by plane curves such as straight parabola. The advantage is intuitive image. Easy to design, the disadvantage is that the amount and direction of the modification cannot accurately reflect the deformation direction and size of the elastic deformation, and there may be problems of excessive modification or insufficient modification.
发明内容Summary of the Invention
本发明为了克服上述的不足，提供一种减少齿轮的啮入、啮出冲击，减小振动和噪声，提高齿轮的啮合质量和使用寿命的球面渐开线直齿锥齿轮副及其齿廓修形方法。In order to overcome the above-mentioned shortcomings, the present invention provides a spherical involute straight-toothed bevel gear pair and a tooth profile modification thereof, which reduce the impact of gears in and out, reduce vibration and noise, and improve the meshing quality and service life of gears.形 方法。 Shape method.
本发明通过以下技术方案来实现上述目的：The present invention achieves the foregoing objectives through the following technical solutions:
一种球面渐开线直齿锥齿轮副，包括主动齿轮和与主动齿轮啮合的被动齿轮，所述齿轮的齿廓分为两段，AB段为理论球面渐开线，BD′段为球面修形曲线，B为修形起始点。A spherical involute straight bevel gear pair includes a driving gear and a passive gear meshing with the driving gear. The tooth profile of the gear is divided into two sections, the AB section is a theoretical spherical involute, and the BD ′ section is a spherical modification. Shape curve, B is the starting point of modification.
平面P为球面渐开线的发生面，圆锥OO1A为球面渐开线基圆锥，O为其顶点，建立全局直角坐标系S，其中坐标原点为基圆锥顶点O，将矢量OO1所在方向定义为z轴，将矢量O1A所在方向定义为x轴，由z轴和x轴方向根据右手定则定义为y轴，所述AB段理论球面渐开线，其方程为：The plane P is the generation surface of the spherical involute, the cone OO1A is the spherical involute base cone, O is its vertex, and a global rectangular coordinate system S is established, where the coordinate origin is the base cone vertex O, and the direction of the vector OO1 is defined as z Axis, the direction where the vector O1A is located is defined as the x-axis, and the z-axis and the x-axis directions are defined as the y-axis according to the right-hand rule. The theoretical spherical involute of the AB segment, the equation is:
Figure PCTCN2019096814-appb-000001
Figure PCTCN2019096814-appb-000001
Figure PCTCN2019096814-appb-000002
Figure PCTCN2019096814-appb-000002
Figure PCTCN2019096814-appb-000003
Figure PCTCN2019096814-appb-000003
其中，R是啮合球面的球径，θ是基锥角，
Figure PCTCN2019096814-appb-000004
是啮合面上起始线段与瞬时回转轴之间的夹角； Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
Figure PCTCN2019096814-appb-000004
Is the angle between the initial line segment on the mating surface and the instantaneous rotary axis;
所述BD′段为球面修形曲线，其方程为：The BD ′ segment is a spherical modification curve, and its equation is:
Figure PCTCN2019096814-appb-000005
Figure PCTCN2019096814-appb-000005
Figure PCTCN2019096814-appb-000006
Figure PCTCN2019096814-appb-000006
Figure PCTCN2019096814-appb-000007
Figure PCTCN2019096814-appb-000007
其中，R是啮合球面的球径，θ是基锥角，
Figure PCTCN2019096814-appb-000008
是啮合面上起始线段与瞬时回转轴之间的夹角，Δs为标准球面渐开线各修形点修形量。 Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
Figure PCTCN2019096814-appb-000008
Is the angle between the initial line segment on the meshing surface and the instantaneous rotation axis, and Δs is the amount of trimming at each trimming point of the standard spherical involute.
一种球面渐开线直齿锥齿轮副的齿廓修形方法：包括以下步骤：A tooth profile modification method for a spherical involute spur bevel gear pair includes the following steps:
软件造型→制造修形模具→批量生产；Software modeling → manufacturing and repairing molds → mass production;
在软件造型步骤中，被动齿轮和主动齿轮齿廓修形同时采用齿顶修缘的方式；修形曲线为球面渐开线所在球面上的一段曲线，修形方向为球面渐开法线方向，修形起始点和修形量可以按照有限元算法优化得到；In the software modeling step, the tooth profile of the passive gear and the drive gear are modified at the same time. The shape curve is a curve on the spherical surface where the spherical involute curve is located. The starting point and the amount of modification can be optimized according to the finite element algorithm;
其中，齿廓修形的球面渐开线直齿锥齿轮造型步骤为：The shaping steps of the spherical involute straight bevel gear with modified tooth profile are as follows:
步骤一：求主动齿轮和被动齿轮的大端和小端的理论球面渐开线；Step 1: Find the theoretical spherical involute of the large and small ends of the driving gear and the passive gear;
步骤二：建立未修形的主动齿轮和被动齿轮啮合齿轮副，进行有限元仿真分析；Step 2: Establish the unshaped active gear and passive gear meshing gear pair, and perform finite element simulation analysis;
步骤三：以主动齿轮和被动齿轮大端和小端球面渐开线上自齿顶向齿根方向第一个总位移<0.05的点为修形起始点，记录球面渐开线上各点各自的总位移量，根据齿轮大小选择点的数量；Step 3: Take the first point of total displacement <0.05 from the top of the gear to the root of the tooth on the large and small end spherical involutes of the active and passive gears as the starting point for the modification. Record the points on the spherical involute The total displacement, select the number of points according to the size of the gear;
步骤四：以计算修形曲线上各点坐标；Step 4: Calculate the coordinates of each point on the modified curve;
步骤五：将上述步骤一和步骤四中得到的大端与小端球面渐开线及其修形曲线数据点导入3D造型软件，利用3D造型软件曲面建模模块中“通过曲线组”命令直接生成一侧齿面片体；Step 5: Import the big-end and small-end spherical involutes obtained in steps 1 and 4 above and their modified curve data points into the 3D modeling software, and use the "through curve group" command in the 3D modeling software surface modeling module to directly Generate a tooth flake on one side;
步骤六：利用3D造型软件实体建模模块中“镜像特征”命令，将步骤五中生成的齿面镜像建立对称齿面；Step 6: Use the "mirror feature" command in the 3D modeling software solid modeling module to mirror the tooth surface generated in step 5 to establish a symmetrical tooth surface;
步骤七：由两侧对称齿面，根据直齿锥齿轮常规建模步骤建立模型；Step 7: Establish a model from symmetrical tooth surfaces on both sides and according to the conventional modeling steps of a straight bevel gear;
在制造修形模具步骤中，采用数控机床制造修行模具。In the step of manufacturing the repair mold, the CNC machine tool is used to manufacture the repair mold.
优选的，所述数控机床为高速铣机床。Preferably, the numerically controlled machine tool is a high-speed milling machine tool.
优选的，在批量生产步骤中，采用锻造工艺，实现大规模批量化生产。Preferably, in the mass production step, a forging process is adopted to realize large-scale mass production.
优选的，所述3D造型软件为UG。Preferably, the 3D modeling software is UG.
本发明的有益效果是：相对于现有技术，本发明球面渐开线直齿锥齿轮副，被动齿轮和主动齿轮的齿廓修形同时采用齿顶修缘的方式；修形曲线为球面渐开线所在球面上的一段曲线，修形方向为球面渐开法线方向,修形起始点和修形量可以按照有限元算法优化得到，能减少齿轮的啮入、啮出冲击，减小振动和噪声，提高齿轮副的啮合质量和使用寿命。The beneficial effect of the present invention is that, compared with the prior art, the spherical involute straight bevel gear pair of the present invention, the tooth profile modification of the passive gear and the active gear simultaneously adopts the method of edge trimming; the shape modification curve is a spherical surface A section of the curve on the sphere where the line is opened. The direction of the modification is the direction of the involute normal of the sphere. The starting point and amount of the modification can be optimized according to the finite element algorithm, which can reduce the impact of the gear in and out and reduce the vibration. And noise to improve the meshing quality and service life of the gear pair.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
本发明将通过例子并参照附图的方式说明，其中：The invention will be described by way of example and with reference to the accompanying drawings, in which:
图1是本发明的结构示意图；FIG. 1 is a schematic structural diagram of the present invention;
图2是本发明的主动齿轮大端球面渐开线齿顶修缘示意图；2 is a schematic diagram of a large-end spherical involute tooth tip repair edge of the driving gear of the present invention;
图3是本发明的被动齿轮大端球面渐开线齿顶修缘示意图。FIG. 3 is a schematic diagram of trimming of a large-end spherical involute tooth top of a passive gear according to the present invention.
图中：1.主动齿轮，2.被动齿轮。In the picture: 1. driving gear, 2. passive gear.
具体实施方式detailed description
现在结合附图对本发明作进一步详细的说明。这些附图均为简化的示意图，仅以示意方式说明本发明的基本结构，因此其仅显示与本发明有关的构成。The present invention will now be described in further detail with reference to the drawings. These drawings are simplified schematic diagrams, which illustrate the basic structure of the present invention only in a schematic manner, so they only show the constitutions related to the present invention.
如图1所示：一种球面渐开线直齿锥齿轮副，包括主动齿轮1和与主动齿轮1啮合的被动齿轮2，所述齿轮的齿廓修形后齿廓分为两段，AB段为理论球面渐开线，BD′段为球面修形曲线，B为修形起始点。As shown in FIG. 1: a spherical involute straight bevel gear pair includes a driving gear 1 and a passive gear 2 meshing with the driving gear 1, the gear profile of the gear is modified into two sections, and AB The segment is a theoretical spherical involute, the BD ′ segment is a spherical modification curve, and B is the starting point of the modification.
平面P为球面渐开线的发生面，圆锥OO1A为球面渐开线基圆锥，O为其顶点，建立全局直角坐标系S，其中坐标原点为基圆锥顶点O，将矢量OO1所在方向定义为z轴，将矢量O1A所在方向定义为x轴，由z轴和x轴方向根据右手定则定义为y轴，所述AB段球面渐开线，其方程为：The plane P is the generation surface of the spherical involute, the cone OO1A is the spherical involute base cone, O is its vertex, and a global rectangular coordinate system S is established, where the coordinate origin is the base cone vertex O, and the direction of the vector OO1 is defined as z The axis O1A is defined as the x-axis direction, and the z-axis and x-axis directions are defined as the y-axis according to the right-hand rule. The AB segment spherical involute has an equation:
Figure PCTCN2019096814-appb-000009
Figure PCTCN2019096814-appb-000009
Figure PCTCN2019096814-appb-000010
Figure PCTCN2019096814-appb-000010
Figure PCTCN2019096814-appb-000011
Figure PCTCN2019096814-appb-000011
其中，R是啮合球面的球径，θ是基锥角，
Figure PCTCN2019096814-appb-000012
是啮合面上起始线段与瞬时回转轴之间的夹角。 Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
Figure PCTCN2019096814-appb-000012
Is the angle between the initial line segment on the mating surface and the instantaneous rotary axis.
所述BD’段为修形球面曲线，其方程为：The BD ′ segment is a modified spherical curve, and its equation is:
Figure PCTCN2019096814-appb-000013
Figure PCTCN2019096814-appb-000013
Figure PCTCN2019096814-appb-000014
Figure PCTCN2019096814-appb-000014
Figure PCTCN2019096814-appb-000015
Figure PCTCN2019096814-appb-000015
其中，R是啮合球面的球径，θ是基锥角，
Figure PCTCN2019096814-appb-000016
是啮合面上起始线段与瞬时回转轴之间的夹角，Δs为理论球面渐开线各修形点修形量。 Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
Figure PCTCN2019096814-appb-000016
Is the included angle between the initial line segment on the meshing surface and the instantaneous axis of rotation, and Δs is the amount of shape modification of the theoretical spherical involute.
一种球面渐开线直齿锥齿轮副的齿廓修形方法：包括以下步骤：A tooth profile modification method for a spherical involute spur bevel gear pair includes the following steps:
软件造型→制造修形模具→批量生产；Software modeling → manufacturing and repairing molds → mass production;
在软件造型步骤中，被动齿轮2和主动齿轮1齿廓修形同时采用齿顶修缘的方式；修形曲线为球面渐开线所在球面上的一段曲线，修形方向为球面渐开法线方向，修形起始点和修形量可以按照有限元算法优化得到；In the software modeling step, the tooth profile modification of the passive gear 2 and the drive gear 1 adopts the method of tooth edge trimming; the shape modification curve is a section of the spherical surface where the spherical involute is located, and the shape modification direction is the spherical involute normal. The direction, starting point and amount of modification can be optimized according to the finite element algorithm;
其中，齿廓修形的球面渐开线直齿锥齿轮造型步骤为：The shaping steps of the spherical involute straight bevel gear with modified tooth profile are as follows:
步骤一：求主动齿轮1和被动齿轮2的大端和小端的理论球面渐开线；Step 1: Find the theoretical spherical involute of the large and small ends of the active gear 1 and the passive gear 2;
步骤二：建立未修形的主动齿轮1和被动齿轮2啮合齿轮副，进行有限元仿真分析；Step 2: Establish the unmodified driving gear 1 and passive gear 2 meshing gear pair, and perform finite element simulation analysis;
步骤三：以主动齿轮1和被动齿轮2大端和小端球面渐开线上自齿顶向齿根方向第一个总位移<0.05的点为修形起始点，记录球面渐开线上各点各自的总 位移量，根据齿轮大小选择点的数量；Step 3: Take the first point of the total displacement <0.05 from the top of the tooth to the root of the tooth on the large and small end spherical involutes of the driving gear 1 and the passive gear 2 as the starting point of the modification, and record each of the spherical involutes. The total displacement of each point, select the number of points according to the size of the gear;
步骤四：计算修形曲线上各点坐标；Step 4: Calculate the coordinates of each point on the modified curve;
步骤五：将上述步骤一和步骤四中得到的大端与小端球面渐开线及其修形曲线数据点导入3D造型软件，利用3D造型软件曲面建模模块中“通过曲线组”命令直接生成一侧齿面片体；Step 5: Import the big-end and small-end spherical involutes obtained in steps 1 and 4 above and their modified curve data points into the 3D modeling software, and use the "through curve group" command in the 3D modeling software surface modeling module to directly Generate a tooth flake on one side;
步骤六：利用3D造型软件实体建模模块中“镜像特征”命令，将步骤五中生成的齿面镜像建立对称齿面；Step 6: Use the "mirror feature" command in the 3D modeling software solid modeling module to mirror the tooth surface generated in step 5 to establish a symmetrical tooth surface;
步骤七：由两侧对称齿面，根据直齿锥齿轮常规建模步骤建立模型；Step 7: Establish a model from symmetrical tooth surfaces on both sides and according to the conventional modeling steps of a straight bevel gear;
在制造修形模具步骤中，采用数控机床制造修行模具。In the step of manufacturing the repair mold, the CNC machine tool is used to manufacture the repair mold.
所述数控机床为高速铣机床；在批量生产步骤中，采用锻造工艺，实现大规模批量化生产；所述3D造型软件为UG。The numerical control machine tool is a high-speed milling machine tool; in the mass production step, a forging process is adopted to realize large-scale batch production; and the 3D modeling software is UG.
实施例1：Example 1:
如图2所示：AD段为理论球面渐开线，平面P为球面渐开线的发生面，圆锥OO1A为球面渐开线基圆锥，O为其顶点，B为修形起始点，修形后齿廓分为两段，AB段为理论球面渐开线，BD′段为球面修形曲线；As shown in Figure 2: AD segment is the theoretical spherical involute, plane P is the spherical involute generating surface, cone OO1A is the spherical involute base cone, O is its vertex, B is the starting point of the modification, and the modification is The posterior tooth profile is divided into two sections, the AB section is a theoretical spherical involute, and the BD ′ section is a spherical modification curve;
建立全局直角坐标系S，其中坐标原点为基圆锥顶点O，将矢量OO1所在方向定义为z轴，将矢量O1A所在方向定义为x轴，由z轴和x轴方向根据右手定则定义为y轴，球面渐开线推导为公知常识，本申请不再做具体推导，直接给出结论：Establish a global Cartesian coordinate system S, where the origin of the coordinates is the vertex O of the base cone, define the direction of the vector OO1 as the z-axis, define the direction of the vector O1A as the x-axis, and define the z-axis and x-axis directions as y according to the right-hand rule The derivation of axes and spherical involutes is common knowledge, and no specific derivation will be made in this application, and the conclusion will be directly given:
AB段球面渐开线，其方程为：AB segment spherical involute, its equation is:
Figure PCTCN2019096814-appb-000017
Figure PCTCN2019096814-appb-000017
Figure PCTCN2019096814-appb-000018
Figure PCTCN2019096814-appb-000018
Figure PCTCN2019096814-appb-000019
Figure PCTCN2019096814-appb-000019
其中，R是啮合球面的球径，θ是基锥角，
Figure PCTCN2019096814-appb-000020
是啮合面上起始线段与瞬时回转轴之间的夹角； Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
Figure PCTCN2019096814-appb-000020
Is the angle between the initial line segment on the mating surface and the instantaneous rotary axis;
BD′段为修形球面曲线，其方程为：The BD ′ segment is a modified spherical curve, and its equation is:
Figure PCTCN2019096814-appb-000021
Figure PCTCN2019096814-appb-000021
Figure PCTCN2019096814-appb-000022
Figure PCTCN2019096814-appb-000022
Figure PCTCN2019096814-appb-000023
Figure PCTCN2019096814-appb-000023
其中，R是啮合球面的球径，θ是基锥角，
Figure PCTCN2019096814-appb-000024
是啮合面上起始线段与瞬时回转轴之间的夹角，Δs为理论球面渐开线各修形点修形量； Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
Figure PCTCN2019096814-appb-000024
Is the angle between the initial line segment on the meshing surface and the instantaneous axis of rotation, and Δs is the amount of trimming of each trimming point of the theoretical spherical involute;
不失一般性地，以球面渐开线BD段上任意点C点为例，C点坐标经过下述步骤得到C′；Without loss of generality, taking an arbitrary point C on the spherical involute BD segment as an example, the coordinates of the C point are obtained through the following steps to obtain C ′;
由球面渐开线公式得C点齐次坐标为From the spherical involute formula, the homogeneous coordinate of point C is
Figure PCTCN2019096814-appb-000025
Figure PCTCN2019096814-appb-000025
1、在C点建立局部坐标系S c,坐标原点为C,坐标轴方向按步骤确定： 1. Establish a local coordinate system S c at point C, the origin of the coordinate is C, and the direction of the coordinate axis is determined according to the steps:
a、求球面渐开线导函数，其方程为a. Find the spherical involute derivative function, the equation is
Figure PCTCN2019096814-appb-000026
Figure PCTCN2019096814-appb-000026
b、将C点坐标代入上述导函数方程得球面渐开线在C点的切矢量τb. Substituting the coordinates of point C into the above derivative function to obtain the tangent vector τ of the spherical involute at point C.
Figure PCTCN2019096814-appb-000027
Figure PCTCN2019096814-appb-000027
c、将上述C点切矢量单位化并将其定义为局部坐标系S c的X C轴向 c. Unitize the above-mentioned C-point tangent vector and define it as the X- C axis of the local coordinate system S c
Figure PCTCN2019096814-appb-000028
Figure PCTCN2019096814-appb-000028
d、将C点在全局坐标系下的向径单位化并将其定义局部坐标系S c的Y C轴向： d. Unitize the radial direction of point C in the global coordinate system and define the Y C axis of the local coordinate system S c :
Figure PCTCN2019096814-appb-000029
Figure PCTCN2019096814-appb-000029
f、求上述两步单位矢量之矢量积并将其定义为局部坐标系S c的Z C轴向： f. Find the vector product of the above two-step unit vectors and define it as the Z C axis of the local coordinate system S c :
Figure PCTCN2019096814-appb-000030
Figure PCTCN2019096814-appb-000030
2、求C′点在局部坐标系下S c下的坐标： 2. Find the coordinates of the point C ′ in the local coordinate system S c :
(2Rsin(Δs/2R)cos(Δs/R),-2Rsin(Δs/2R)sin(Δs/R),0)(2Rsin (Δs / 2R) cos (Δs / R),-2Rsin (Δs / 2R) sin (Δs / R), 0)
Δs为理论球面渐开线各修形点修形量；Δs is the shape modification amount of each modification point of the theoretical spherical involute;
为数据处理方便，将此点坐标改写成齐次坐标形式For the convenience of data processing, rewrite the coordinates of this point into the form of homogeneous coordinates
Figure PCTCN2019096814-appb-000031
Figure PCTCN2019096814-appb-000031
3、求由局部坐标系S c变换到全局坐标系S的变换矩阵： 3. Find the transformation matrix transformed from the local coordinate system S c to the global coordinate system S:
Figure PCTCN2019096814-appb-000032
Figure PCTCN2019096814-appb-000032
其中，i＝(1,0,0)；j＝(0,1,0)；i＝(0,0,1)分别为全局坐标系S的x轴、y轴、z轴轴向单位矢量；Among them, i = (1,0,0); j = (0,1,0); i = (0,0,1) are the x-axis, y-axis, and z-axis axial unit vectors of the global coordinate system S, respectively ;
4、求C′点在全局坐标S下的齐次坐标：4. Find the homogeneous coordinates of C ′ point in global coordinate S:
Figure PCTCN2019096814-appb-000033
Figure PCTCN2019096814-appb-000033
将上式展开得C′点在全局坐标系下的坐标：Expand the above formula to the coordinates of the C ′ point in the global coordinate system:
Figure PCTCN2019096814-appb-000034
Figure PCTCN2019096814-appb-000034
Figure PCTCN2019096814-appb-000035
Figure PCTCN2019096814-appb-000035
Figure PCTCN2019096814-appb-000036
Figure PCTCN2019096814-appb-000036
D点是球面渐开线修形段BD的末端，C是其上任意一点，则D点的修行后点坐标与之相同；同理，D′点的修行后点坐标和C′点的坐标相同。Point D is the end of the spherical involute modification segment BD, and C is any point above it, then the coordinates of the point after the practice of D are the same; similarly, the coordinates of the point after the practice of D ′ and the coordinates of the point C ′ the same.
其中，修形起始点B的位置和BD段上各修形点处之修形量根据有限元方法优化计算得到，目标是啮合传动在额定扭矩下不发生啮入干涉和啮出干涉。Among them, the position of the starting point B of the modification and the modification amount at each modification point on the BD segment are obtained through optimization calculation by the finite element method, and the goal is to prevent the engagement transmission and the engagement interference at the rated torque of the meshing transmission.
实施例2：Example 2:
如图3所示，考虑到锥齿轮小端模数和齿高均较小，此处球面渐开线需要修形的部分BC弧长常常不超过0.1，如图3所述方法计算完全能达到相同技术效果，又能简化计算提高工作效率，为简化造型，仅对理论球面渐开线齿顶点C按照具体实施例1中方法计算齿顶修形后坐标点C′，修形曲线BC′是位于球面渐开线所在球体的球面上的连接齿顶修形点C′和修形起始点B的一段大圆劣弧；其方程容易获得，三维造型也极其方便；图中，AC段为理论球面渐开线，平面P为球面渐开线的发生面，圆锥OO1A为球面渐开线基圆锥，O为其顶点，B为修形起始点，C为标准球面渐开线齿顶点，C′为齿顶修形点，修形后齿廓分为两段，AB段为理论球面渐开线，BC′为球面渐开线所在球面上的大圆劣弧。As shown in Figure 3, considering that the small-end modulus and tooth height of the bevel gear are small, the BC arc length of the spherical involute that needs to be modified often does not exceed 0.1, and the calculation shown in the method described in Figure 3 can completely reach The same technical effect can also simplify the calculation and improve the work efficiency. In order to simplify the modeling, only the theoretical spherical involute tooth vertex C is calculated according to the method in the specific embodiment 1. The coordinate point C ′ after the tooth top is modified, and the modified curve BC ′ is A large circular arc on the sphere of the sphere where the involute of the sphere is located, connecting the top modification point C ′ and the starting point B of the modification; the equation is easy to obtain and the three-dimensional modeling is extremely convenient; Involute, the plane P is the occurrence surface of the spherical involute, the cone OO1A is the spherical involute base cone, O is its vertex, B is the starting point of the modification, C is the vertex of the standard spherical involute tooth, and C ′ is The top of the tooth is modified, and the tooth profile is divided into two sections after the modification. The AB section is the theoretical spherical involute, and BC ′ is the large circular inferior arc on the spherical surface where the spherical involute is located.
为解决常规齿廓修形方案所引起的技术问题而在本申请中所采取的针对球面渐开线齿顶修缘技术方案不仅适用于差速器被动齿轮2和主动齿轮1，也适用于其他齿轮传动中采用球面渐开线直齿锥齿轮的传动装置。In order to solve the technical problems caused by the conventional tooth profile modification scheme, the technical solution for the spherical involute tooth tip trimming technique adopted in this application is not only applicable to the differential passive gear 2 and the active gear 1, but also applicable to other Gear transmission adopts the transmission device of spherical involute straight tooth bevel gear.
上述依据本发明为启示，通过上述的说明内容，相关工作人员完全可以在不偏离本项发明技术思想的范围内，进行多样的变更以及修改。本项发明的技术性范围并不局限于说明书上的内容，必须要根据权利要求范围来确定其技术性范围。The foregoing is based on the present invention as a revelation. Through the above description, the relevant staff can completely make various changes and modifications without departing from the technical idea of the present invention. The technical scope of this invention is not limited to the content of the description, and its technical scope must be determined according to the scope of the claims.

Claims (5)

  1. 一种球面渐开线直齿锥齿轮副，包括主动齿轮和与主动齿轮啮合的被动齿轮，其特征在于：所述齿轮的齿廓分为两段，AB段为理论球面渐开线，BD′段为球面修形曲线，B为修形起始点；A spherical involute spur bevel gear pair includes a driving gear and a passive gear meshing with the driving gear, characterized in that the tooth profile of the gear is divided into two sections, and the AB section is a theoretical spherical involute, BD ′ The segment is a spherical modification curve, and B is the starting point of the modification;
    平面P为球面渐开线的发生面，圆锥OO1A为球面渐开线基圆锥，O为其顶点，建立全局直角坐标系S，其中坐标原点为基圆锥顶点O，将矢量OO1所在方向定义为z轴，将矢量O1A所在方向定义为x轴，由z轴和x轴方向根据右手定则定义为y轴，所述AB段理论球面渐开线，其方程为：The plane P is the generation surface of the spherical involute, the cone OO1A is the spherical involute base cone, O is its vertex, and a global rectangular coordinate system S is established, where the coordinate origin is the base cone vertex O, and the direction of the vector OO1 is defined as z Axis, the direction where the vector O1A is located is defined as the x-axis, and the z-axis and the x-axis directions are defined as the y-axis according to the right-hand rule. The theoretical spherical involute of the AB segment, the equation is:
    Figure PCTCN2019096814-appb-100001
    Figure PCTCN2019096814-appb-100001
    Figure PCTCN2019096814-appb-100002
    Figure PCTCN2019096814-appb-100002
    Figure PCTCN2019096814-appb-100003
    Figure PCTCN2019096814-appb-100003
    其中，R是啮合球面的球径，θ是基锥角，
    Figure PCTCN2019096814-appb-100004
    是啮合面上起始线段与瞬时回转轴之间的夹角；     Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
    Figure PCTCN2019096814-appb-100004
    Is the angle between the initial line segment on the mating surface and the instantaneous rotary axis;
    所述BD′段为球面修形曲线，其方程为：The BD ′ segment is a spherical modification curve, and its equation is:
    Figure PCTCN2019096814-appb-100005
    Figure PCTCN2019096814-appb-100005
    Figure PCTCN2019096814-appb-100006
    Figure PCTCN2019096814-appb-100006
    Figure PCTCN2019096814-appb-100007
    Figure PCTCN2019096814-appb-100007
    其中，R是啮合球面的球径，θ是基锥角，
    Figure PCTCN2019096814-appb-100008
    是啮合面上起始线段与瞬时回转轴之间的夹角，Δs为理论球面渐开线各修形点修形量。     Where R is the spherical diameter of the meshing sphere, θ is the base cone angle,
    Figure PCTCN2019096814-appb-100008
    Is the included angle between the initial line segment on the meshing surface and the instantaneous axis of rotation, and Δs is the amount of shape modification of the theoretical spherical involute.
  2. 一种如权利要求1所述的球面渐开线直齿锥齿轮副的齿廓修形方法，其特征在于：包括以下步骤：A method for modifying the tooth profile of a spherical involute spur bevel gear pair according to claim 1, comprising the following steps:
    软件造型→制造修形模具→批量生产；Software modeling → manufacturing and repairing molds → mass production;
    在软件造型步骤中，半轴齿轮和行星齿轮齿廓修形同时采用齿顶修缘的方 式；修形曲线为球面渐开线所在球面上的一段曲线，修形方向为球面渐开法线方向，修形起始点和修形量可以按照有限元算法优化得到；In the software modeling step, the tooth profile modification of the half-shaft gear and the planetary gear is performed at the same time. The modification curve is a section of the curve on the spherical surface where the spherical involute is located, and the modification direction is the normal direction of the spherical involute. , The starting point and amount of modification can be optimized according to the finite element algorithm;
    其中，齿廓修形的球面渐开线直齿锥齿轮造型步骤为：The shaping steps of the spherical involute straight bevel gear with modified tooth profile are as follows:
    步骤一：求行星齿轮和半轴齿轮的大端和小端的理论球面渐开线；Step 1: Find the theoretical spherical involute of the big end and the small end of the planetary gear and the side gear;
    步骤二：建立未修形的行星齿轮和半轴齿轮啮合齿轮副，进行有限元仿真分析；Step 2: Establish unshaped planetary gears and half-shaft gear meshing gear pairs, and perform finite element simulation analysis;
    步骤三：以行星齿轮和半轴齿轮大端和小端球面渐开线上自齿顶向齿根方向第一个总位移<0.05的点为修形起始点，记录球面渐开线上各点各自的总位移量，根据齿轮大小选择点的数量；Step 3: Take the first point of total displacement <0.05 from the top of the tooth to the root of the planetary and semi-axle spherical involute on the spherical involute on the involute line as the starting point for modification, and record the points on the spherical involute line The respective total displacement, the number of points selected according to the size of the gear;
    步骤四：计算修形曲线上各点坐标；Step 4: Calculate the coordinates of each point on the modified curve;
    步骤五：将上述步骤一和步骤四中得到的大端与小端球面渐开线及其修形曲线数据点导入3D造型软件，利用3D造型软件曲面建模模块中“通过曲线组”命令直接生成一侧齿面片体；Step 5: Import the big-end and small-end spherical involutes obtained in steps 1 and 4 above and their modified curve data points into the 3D modeling software, and use the "through curve group" command in the 3D modeling software surface modeling module to directly Generate a tooth flake on one side;
    步骤六：利用3D造型软件实体建模模块中“镜像特征”命令，将步骤五中生成的齿面镜像建立对称齿面；Step 6: Use the "mirror feature" command in the 3D modeling software solid modeling module to mirror the tooth surface generated in step 5 to establish a symmetrical tooth surface;
    步骤七：由两侧对称齿面，根据直齿锥齿轮常规建模步骤建立模型；Step 7: Establish a model from symmetrical tooth surfaces on both sides and according to the conventional modeling steps of a straight bevel gear;
    在制造修形模具步骤中，采用数控机床制造修形模具。In the step of manufacturing the shaping mold, a CNC machine tool is used to manufacture the shaping mold.
  3. 根据权利要求2所述的球面渐开线直齿锥齿轮副的齿廓修形方法，其特征在于：所述数控机床为高速铣机床。The method for modifying a tooth profile of a spherical involute spur bevel gear pair according to claim 2, wherein the numerically controlled machine tool is a high-speed milling machine tool.
  4. 根据权利要求2所述的球面渐开线直齿锥齿轮副的齿廓修形方法，其特征在于：在批量生产步骤中，采用锻造工艺，实现大规模批量化生产。The method for modifying the tooth profile of a spherical involute spur bevel gear pair according to claim 2, characterized in that in the mass production step, a forging process is adopted to realize large-scale mass production.
  5. 根据权利要求2所述的球面渐开线直齿锥齿轮副的齿廓修形方法，其特 征在于：所述3D造型软件为UG。The method for modifying the tooth profile of a spherical involute spur bevel gear pair according to claim 2, characterized in that the 3D modeling software is UG.
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