WO2017024749A1 - 一种变传动比线齿轮机构 - Google Patents

一种变传动比线齿轮机构 Download PDF

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WO2017024749A1
WO2017024749A1 PCT/CN2015/100289 CN2015100289W WO2017024749A1 WO 2017024749 A1 WO2017024749 A1 WO 2017024749A1 CN 2015100289 W CN2015100289 W CN 2015100289W WO 2017024749 A1 WO2017024749 A1 WO 2017024749A1
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gear
driving wheel
ratio
variable
wheel
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PCT/CN2015/100289
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English (en)
French (fr)
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陈扬枝
黄淮
吕月玲
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华南理工大学
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Priority to US15/527,015 priority Critical patent/US10465787B2/en
Publication of WO2017024749A1 publication Critical patent/WO2017024749A1/zh

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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
    • F16H3/00—Toothed gearings for conveying rotary motion with variable gear ratio or for reversing rotary motion
    • F16H3/02—Toothed gearings for conveying rotary motion with variable gear ratio or for reversing rotary motion without gears having orbital motion
    • F16H3/42—Toothed gearings for conveying rotary motion with variable gear ratio or for reversing rotary motion without gears having orbital motion with gears having teeth formed or arranged for obtaining multiple gear ratios, e.g. nearly infinitely variable
    • 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
    • F16H35/00—Gearings or mechanisms with other special functional features
    • F16H35/02—Gearings or mechanisms with other special functional features for conveying rotary motion with cyclically varying velocity ratio
    • 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
    • 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
    • F16H57/00—General details of gearing
    • F16H2057/0087—Computer aided design [CAD] specially adapted for gearing features ; Analysis of gear systems
    • 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
    • F16H55/10—Constructively simple tooth shapes, e.g. shaped as pins, as balls

Definitions

  • the present invention relates to the field of mechanical transmission, and more particularly to a line gear mechanism capable of providing a periodic variable transmission ratio based on a spatial conjugate curve engagement.
  • variable ratio gears In a speed-increasing or decelerating transmission between two shafts, a gear that can achieve a variable transmission ratio is called a variable ratio gear.
  • Variable transmission ratio gears are mainly used in transmission occasions with special requirements, such as stepless speed regulation of automobiles, elliptical gear flowmeters, variable ratio ratio controllers, etc.
  • Gears that are often used for variable ratio transmissions mainly have non-circular gears, because the non-circular gear mechanism can realize special motion and function calculations, such as swinging, indexing, shifting, etc., and can also design non-circular gears according to the transmission ratio function.
  • the non-circular gears currently used for gear ratio transmission have non-cylindrical gears and non-bevel gears.
  • the elliptical bevel gear is a typical non-bevel gear, which is named for its large end curve as a spherical ellipse.
  • Orthogonal non-circular gear pair is a new type of variable ratio gear transmission. It has the advantages of non-circular gears, non-bevel gears and face gears.
  • variable transmission ratio can also be achieved by a planetary gear set.
  • the continuous variable magnetic gear consists of a stator of three-phase windings and three concentric rotors. By controlling the speed of the center rotor, the gear ratio between the output rotor and the input rotor can be varied.
  • the line gear is a new type of gear that uses the space curve meshing theory to replace the traditional space surface meshing theory. It is mainly used in the field of micro-transmission, and has the advantages of small size, large transmission ratio and convenient manufacture. Line gears are currently available for transmission on vertical, intersecting, and staggered axes, and research in design equations, coincidence, strength criteria, micro-transmissions, and manufacturing has tended to improve.
  • a design scheme of a line gear pair with a periodic variable transmission ratio is given, and the line gear pair mechanism designed by the method can provide a transmission with a periodic variable transmission ratio.
  • a variable transmission ratio gear mechanism which is composed of a driving wheel and a driven wheel that intersect shafts at any angle, and constitutes a transmission pair.
  • the driving wheel is composed of a wheel body and a wire tooth.
  • the driven wheel is composed of a wheel body and a wire tooth.
  • the contact line of the driving wheel wire tooth and the driven wheel wire tooth is meshed according to a pair of space conjugate curves, and the driving wheel is coupled with the driver to provide an input.
  • wire teeth on the driving wheel There are one or more wire teeth on the driving wheel; the wire teeth of the driving wheel and the wire teeth of the driven wheel are meshed by point contact; the driven wheel is coupled with the output end to provide an output of motion or force, and the wire teeth on the driven wheel have Thread-tooth with variable transmission ratio: There are multiple transmission ratios in one motion cycle, and smooth transitions can be made between different transmission ratios to generate a transmission with a periodic variable transmission ratio.
  • the contact line for meshing on the thread teeth of the driving wheel is a cylindrical spiral; the wire teeth of the driven wheel are divided into equal gear ratio parts and variable transmission ratio parts, and are used on the line teeth.
  • the meshing contact line There are two equations for the meshing contact line, one is the equal gear ratio equation for achieving the equal gear ratio, and the other is the variable gear ratio equation for realizing the variable transmission ratio.
  • variable transmission ratio equation in the transmission process, can smoothly change the transmission ratio of the line gear from one value to another, that is, the derivative value of the transmission ratio function increases or decreases from 0. Go to a certain value and return to 0 smoothly.
  • variable transmission ratio gear mechanism in order to reduce the rotation and jumping of the operation of the mechanism, the derivative of the variable transmission ratio equation and the variable transmission ratio equation can be smoothly transitioned, that is, the derivative of the variable transmission ratio equation Both the second derivative and the second derivative increase or decrease from 0 to a certain value, and then return to zero smoothly.
  • O-xyz is a spatially arbitrary fixed Cartesian coordinate system
  • O is the O-xyz coordinate system origin
  • x, y, and z are three coordinates of the O-xyz coordinate system.
  • the axis, Cartesian coordinate system O p -x p y p z p is determined according to the coordinate system O-xyz position, the x p O p z p plane is in the same plane as the xOz plane, and the distance from the coordinate origin O p to the z axis is a, the distance from O p to the x axis is b, the angle between the z axis and the z p axis is ( ⁇ - ⁇ ), ⁇ is the angle between the main and driven wheel angular velocity vectors, 0 ° ⁇ ⁇ ⁇ 180 °,
  • the coordinate systems O 1 -x 1 y 1 z 1 and O 2 -x 2 y 2 z 2 are coordinate systems fixed on the driving wheel and the driven wheel, respectively, and the driving wheel and the driven wheel respectively rotate around the z-axis and z p
  • the shaft rotates, and the starting position of the driving wheel and the driven wheel is the starting position.
  • the coordinate systems O 1 -x 1 y 1 z 1 and O 2 -x 2 y 2 z 2 are respectively associated with the coordinate system O- Xyz and O p -x p y p z p coincide.
  • the origin O 1 coincides with O
  • the z 1 axis coincides with the z axis
  • the origin O 2 coincides with O p
  • the z 2 axis coincides with the z p axis.
  • the wheel rotates around the z-axis at a uniform angular velocity ⁇ 1
  • the angular velocity of the driving wheel is the negative direction of the z-axis.
  • variable transmission ratio equation is determined by the following two methods:
  • variable transmission ratio contact line equation is:
  • the variable ratio equations created according to claims 5 and 6 can be used in a variable ratio line gear mechanism.
  • the thread on the driving wheel of the mechanism is designed based on the cylindrical spiral line, and may have one or more wire teeth; the wire teeth of the driving wheel and the wire teeth of the driven wheel are meshed by point contact; the driven wheel is coupled with the output end.
  • the thread on the driven wheel contains a variety of designs. According to different equations of the contact line on the line gear, it can be designed as a line tooth with variable transmission ratio: there can be more in one motion cycle. One gear ratio, smooth transition between different gear ratios.
  • the principle of the invention is: according to the mesh gear space conjugate curve meshing theory, the follower line contact line equation required for the equal gear ratio transmission can be designed; when the follower line tooth contact line equation is improved, when it starts to enter the meshing, When the transmission ratio is a certain value, when the gear is disengaged, the transmission ratio is another value, and the transmission ratio changes smoothly during the period, that is, the derivative value of the transmission ratio function increases or decreases from 0 to a certain value, and then returns to 0 smoothly. Or, the derivative value of the variable ratio function and the second derivative of the variable ratio function increase or decrease from 0 to a certain value, and then smoothly return to 0, thereby obtaining the driven wheel required for the variable ratio transmission. Line tooth contact line equation.
  • the invention has the following advantages:
  • a plurality of gear ratios can be provided during the movement period of the driven wheel, and a smooth transition conforming to the motion law can be performed between the respective gear ratios.
  • the transmission only depends on the point contact between the driving wheel teeth and the driven wheel teeth, so as long as the accuracy of the contact line is ensured, the design is simple, the processing is convenient, and the mass volume is smaller than the conventional variable transmission gear. Suitable for micro-small mechanical and electrical products.
  • the driving wheel has a minimum number of teeth of 1, which can provide a transmission with a large transmission ratio, and can design the line gear pair under the condition of intersecting the shaft at any angle.
  • Figure 1 is a coordinate system of the mechanism of the present invention.
  • FIG. 2 is a two embodiment of the present invention, including a drive wheel and a driven wheel.
  • Figure 3 is an embodiment of a driven wheel of the present invention.
  • Figure 4 shows the method of establishing a wire tooth entity.
  • the variable transmission ratio gear pair of the present invention comprises a driving wheel and a driven wheel.
  • the coordinate system of the driving wheel and the driven wheel is shown in FIG. 1 for establishing a contact line equation of the wire teeth of the wire gear.
  • O-xyz and O p -x p y p z p are fixed Cartesian coordinate systems, and O p -x p y p z p is determined according to the O-xyz position: x p O p z p plane xOz plane distance and in the same plane, O p to the z-axis is a, O p to the x-axis is the angle between the b, z-axis and z-axis as P ( ⁇ - ⁇ ). ⁇ is the angle between the main and driven wheel angular velocity vectors.
  • O 1 -x 1 y 1 z 1 and O 2 -x 2 y 2 z 2 are coordinate systems fixed on the driving wheel and the driven wheel, respectively, and the driving wheel and the driven wheel rotate around the z-axis and the z- p axis, respectively. .
  • Variable transmission ratio gear pair is shown in Fig. 2a and Fig. 2b.
  • the left side is the driving wheel 1
  • the driving wheel has the driving wheel tooth 2
  • the right side is the driven wheel 3.
  • the driven wheel has the gear teeth 4 and 5 of equal gear ratio, the gear teeth 6 and 7 of the variable transmission ratio, when the driving wheel and the driven wheel mesh with the gear teeth 4 and 5 of the equal gear ratio, the transmission
  • the ratios i a and i b when meshed to the gear teeth 6 and 7 of the variable transmission ratio, the gear ratio smoothly transitions from i a to i b , and smoothly transitions from i b to i a .
  • embodiments of the invention are not limited thereto.
  • the driving gear teeth are determined by their contact line equation, and the equation of the contact line in O 1 -x 1 y 1 z 1 is:
  • the driven gear teeth are determined by their contact line equation, which is calculated by the contact line and space curve meshing theory of the driving gear teeth.
  • the equation in O 2 -x 2 y 2 z 2 is:
  • the contact line equation on the variable gear teeth can take two forms, one is:
  • the other is:
  • m is the spiral radius of the drive wheel contact line
  • n is the parameter related to the pitch of the driving wheel contact line. If the pitch is p, it is defined as:
  • t is a parameter,
  • the contact line indicating a line tooth of the driving wheel is The spiral of the circumference.
  • a and b are the positional parameters of the driving wheel and the driven wheel, as shown in Figure 1;
  • ⁇ is the angle parameter of the driving wheel and the driven wheel, as shown in Figure 1;
  • i a and i b are the required two gear ratios
  • a wire tooth entity can be established.
  • the wire tooth entity only needs to be able to meet the strength requirement, and the wire tooth entity itself does not have a specific shape requirement.
  • a certain volume is reversely extended on both sides of the main and driven wire contact directions (- ⁇ 1 and ⁇ 1 in Fig. 4), that is, a mesh can be generated.
  • Required wire teeth The wheel body is used to secure the wire teeth.

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)
  • Transmission Devices (AREA)
  • Transmissions By Endless Flexible Members (AREA)

Abstract

一种变传动比线齿轮机构，该机构由任意角度相交轴的主动轮（1）和从动轮（3）组成传动副，传动由主动轮线齿（2）和从动轮线齿（4,5;6,7）之间的点接触啮合运动产生，线齿的接触线根据空间共轭曲线啮合理论设计，设计方程分为等传动比和变传动比两部分，等传动比部分提供匀速传动，变传动比部分使传动比平稳过渡。该线齿轮机构能够提供周期性变传动比传动，能够在从动轮（3）的运动周期内提供多个传动比，并且各个传动比之间能进行符合运动规律的平稳过渡。

Description

一种变传动比线齿轮机构 技术领域
本发明涉及机械传动领域，尤其涉及一种基于空间共轭曲线啮合的，能提供周期性变传动比的线齿轮机构。
背景技术
在两个轴之间的增速或减速传动中，能实现传动速比可变的齿轮称为变传动比齿轮。变传动比齿轮主要运用于有特殊要求的传动场合，如汽车的无极调速、椭圆齿轮流量计、变传动比操控器等方面。
常常用于变传动比传动的齿轮主要有非圆齿轮，因为非圆齿轮机构可实现特殊的运动和函数运算,如摆动、分度、变速等，同时也可以根据传动比函数来设计非圆齿轮。目前用于变速比传动的非圆齿轮有非圆柱齿轮，非圆锥齿轮。椭圆锥齿轮是一种典型的非圆锥齿轮，因其大端节曲线为球面椭圆而得名。正交非圆面齿轮副是一种新型的变传动比齿轮传动,它具有非圆齿轮、非圆锥齿轮和面齿轮的优点，其设计和加工比变传动比非圆齿轮更为简单。另外,变传动比也可通过行星齿轮组实现。连续变量磁齿轮包含三相绕组的定子和三个同心转子。通过控制中心转子的速度，输出转子和输入转子之间的传动比可以改变。
线齿轮是一种运用空间曲线啮合理论代替传统空间曲面啮合理论的新型齿轮，主要运用于微小传动领域，具有尺寸小，传动比大，制造方便等优点。线齿轮目前可以运用于垂直轴、相交轴和交错轴上的传动，并且其设计方程、重合度、强度准则、微小变速器和制造领域等研究已经趋于完善。
在尺度受限的微小机械装置中，有时有复杂的周期性变传动比的传动要求，这难以用控制的方式实现，而传统非圆齿轮又不适用于微小尺度。
发明内容
本发明在线齿轮理论基础之上，给出具有周期性变传动比的线齿轮副的设计方案，用该方法设计的线齿轮副机构可以提供周期性变传动比的传动。
本发明所采用的技术方案如下。
一种变传动比线齿轮机构，该机构由任意角度相交轴的主动轮和从动轮组成传动副， 主动轮由轮体和线齿组成，从动轮由轮体和线齿组成，主动轮线齿和从动轮线齿的接触线按照一对空间共轭曲线啮合，主动轮与驱动器联接以提供输入，主动轮上的线齿有一条或多条；主动轮的线齿和从动轮的线齿通过点接触啮合；从动轮与输出端联接以提供运动或力的输出，从动轮上的线齿为具有变传动比性质的线齿：在一个运动周期内，存在多个传动比，不同传动比之间可进行平稳过渡，从而产生周期性变传动比的传动。
上述的变传动比线齿轮机构中，主动轮的线齿上用于啮合的接触线为圆柱螺旋线；从动轮的线齿分为等传动比部分和变传动比部分，线齿上的用于啮合的接触线的方程有两种，一种为实现等传动比的等传动比方程，另一种为实现变传动比的变传动比方程。
上述的变传动比线齿轮机构，在传动过程中，变传动比方程能使线齿轮的传动比从一个值平稳变到另一个值，即传动比函数的导数值由0开始增大或减小到某一个值，再平稳回到0。
上述的变传动比线齿轮机构，传动过程中，为减低所述机构的运行的转动和跳跃性，变传动比方程和变传动比方程的导数都能平稳的过渡，即变传动比方程的导数和二次导数都是由0开始增大或减小到某一个值，再平稳回到0。
由此，上述的变传动比线齿轮机构中，O-xyz为空间上任意固定笛卡尔坐标系，O为O-xyz坐标系原点，x、y、z是O-xyz坐标系的三个坐标轴，笛卡尔坐标系Op-xpypzp根据坐标系O-xyz位置进行确定，xpOpzp平面与xOz平面在同一平面内，坐标原点Op到z轴的距离为a，Op到x轴的距离为b，z轴与zp轴之间的夹角为(π-θ)，θ为主、从动轮角速度矢量的夹角，0°≤θ≤180°，坐标系O1-x1y1z1和O2-x2y2z2分别为固定在主动轮和从动轮上的坐标系，传动时主动轮和从动轮各自绕着z轴和zp轴转动，且主动轮与从动轮起始啮合处为起始位置，在起始位置，坐标系O1-x1y1z1和O2-x2y2z2分别与坐标系O-xyz及Op-xpypzp重合，在任意时刻，原点O1与O重合，z1轴与z轴重合，原点O2与Op重合，z2轴与zp轴重合，主动轮以匀角速度ω1绕z轴旋转，主动轮角速度方向为z轴负方向，主动轮绕z轴转过的角度为
Figure PCTCN2015100289-appb-000001
从动轮以匀角速度ω2绕zp轴旋转，从动轮角速度方向为zp轴负方向，从动轮绕zp轴转过的角度为
Figure PCTCN2015100289-appb-000002
则若主动接触线在坐标系O1-x1y1z1上的方程为：
Figure PCTCN2015100289-appb-000003
则，所述变传动比方程由如下两种方法确定：
1)变传动比方程平稳过渡，其变传动比接触线方程为：
Figure PCTCN2015100289-appb-000004
其中，A和C由方程
Figure PCTCN2015100289-appb-000005
和
Figure PCTCN2015100289-appb-000006
确定，m为主动轮接触线的螺旋半径，n为主动轮接触线与螺距相关的参数，若螺距为p，则定义：
Figure PCTCN2015100289-appb-000007
t为参变量，
Figure PCTCN2015100289-appb-000008
表示主动轮一条线齿的接触线为
Figure PCTCN2015100289-appb-000009
圆周的螺旋线，当t＝-π时，主动轮和从动轮线齿开始啮合，当
Figure PCTCN2015100289-appb-000010
时，主动轮转过
Figure PCTCN2015100289-appb-000011
圆周，主动轮和从动轮线齿啮合到末端，开始脱离；ia和ib为其中某段变化过程前后的两个传动比；
Figure PCTCN2015100289-appb-000012
和
Figure PCTCN2015100289-appb-000013
为变传动比过程中，主动轮某线齿在传动时的起始和终止角度，比如当
Figure PCTCN2015100289-appb-000014
时，
Figure PCTCN2015100289-appb-000015
2)变传动比方程和变传动方程的导数都能平稳过渡，即变传动比接触线方程为：
Figure PCTCN2015100289-appb-000016
其中，E、F和G由方程
Figure PCTCN2015100289-appb-000017
和
Figure PCTCN2015100289-appb-000018
确定，m为主动轮接触线的螺旋半径，n为主动轮接触线与螺距相关的参数，若螺距为p，则定义：
Figure PCTCN2015100289-appb-000019
t为参变量，
Figure PCTCN2015100289-appb-000020
表示主动轮一条线齿的接触线为
Figure PCTCN2015100289-appb-000021
圆周的螺旋线，当t＝-π时，主动轮和从动轮线齿开始啮合，当
Figure PCTCN2015100289-appb-000022
时，主动轮转过
Figure PCTCN2015100289-appb-000023
圆周，主动轮和从动轮线齿啮合到末端，开始脱离；ia和ib为其中某段变化过程前后的两个传动比；
Figure PCTCN2015100289-appb-000024
和
Figure PCTCN2015100289-appb-000025
为变传动比过程中，主动轮某线齿在传动时的起始和终止角度，比如当
Figure PCTCN2015100289-appb-000026
时，
Figure PCTCN2015100289-appb-000027
根据权利要求5和6所创建的变传动比方程都可以运用于变传动比线齿轮机构中。
本机构得到主动轮上的线齿是以圆柱螺旋线为基础设计的，可有一条或多条线齿；主动轮的线齿和从动轮的线齿通过点接触啮合；从动轮与输出端联接以提供运动或力的输出，从动轮上的线齿包含多种设计，根据线齿轮上接触线的不同方程，可设计成具有变传动比性质的线齿：在一个运动周期内，可存在多个传动比，不同传动比之间可进行平稳过渡。
本发明的原理为：根据线齿轮空间共轭曲线啮合理论，可以设计出等传动比传动所需的从动轮线齿接触线方程；改进从动轮线齿接触线方程，使其开始进入啮合时，传动比为某一个值，脱离啮合时，传动比为另一个值，期间的传动比平稳变化，即传动比函数的导数值由0开始增大或减小到某一个值，再平稳回到0，或者是变传动比函数的导数值和变传动比函数的二次导数都由0开始增大或减小到某一个值，再平稳回到0，从而得到变传动比传动所需的从动轮线齿接触线方程。
本发明与现有技术相比具有如下的优点:
1.能够在从动轮的运动周期内提供多个传动比，并且各个传动比之间能进行符合运动规律的平稳过渡。
2.传动只依赖于主动轮线齿与从动轮线齿之间的点接触，所以只要保证接触线的精度即可，设计简单，加工方便，且质量体积相比传统变传动比齿轮更小，适用于微小型机电产品。
3.主动轮最少齿数为1，能够提供较大传动比的传动，且能在任意角度相交轴的条件下设计线齿轮副。
附图说明
图1为本发明的机构的坐标体系。
图2为本发明的两种实施例，包括主动轮和从动轮。
图3为本发明的从动轮实施例。
图4为线齿实体的建立方法。
具体实施方式
下面结合附图对本发明作进一步说明，但本发明的实施方式不限于此。
1.本发明所述变传动比线齿轮副包含了主动轮和从动轮，主动轮和从动轮的坐标体系如图1所示，用于建立线齿轮的线齿的接触线方程。
如图1所示，O-xyz与Op-xpypzp为固定笛卡尔坐标系，Op-xpypzp根据O-xyz位置进行确定：xpOpzp平面与xOz平面在同一平面内，Op到z轴的距离为a，Op到x轴的距离为b，z轴与zp轴之间的夹角为(π-θ)。θ为主、从动轮角速度矢量的夹角。
O1-x1y1z1和O2-x2y2z2分别为固定在主动轮和从动轮上的坐标系，传动时主动轮和从动轮各自绕着z轴和zp轴转动。
2.变传动比线齿轮副如图2a和图2b所示，左边为主动轮1，主动轮上有主动轮线齿2，右边为从动轮3。
如图3所示，从动轮上有等传动比的线齿4和5，变传动比的线齿6和7，当主动轮和从动轮啮合到等传动比的线齿4和5时，传动比为ia和ib，当啮合到变传动比的线齿6和7时，传动比分别从ia平稳过渡到ib，从ib平稳过渡到ia。但本发明实施方式不限于此。
设计上述等传动比和变传动比线齿的方程由以下方程确定。
主动轮线齿通过其接触线方程确定，该接触线在O1-x1y1z1中的方程为：
Figure PCTCN2015100289-appb-000028
从动轮线齿通过其接触线方程确定，该接触线通过主动轮线齿的接触线和空间曲线啮合理论计算得来，其在O2-x2y2z2中的方程为：
当传动比为i时，等传动比线齿上的接触线方程为：
Figure PCTCN2015100289-appb-000029
当传动比为ia到ib时，变传动比线齿上的接触线方程可以有两种形式，一种为：
Figure PCTCN2015100289-appb-000030
其中，A和C由下确定
Figure PCTCN2015100289-appb-000031
Figure PCTCN2015100289-appb-000032
另一种为：
Figure PCTCN2015100289-appb-000033
其中，E、F和G由下确定
Figure PCTCN2015100289-appb-000034
Figure PCTCN2015100289-appb-000035
Figure PCTCN2015100289-appb-000036
式中各参数的物理意义如下：
m为主动轮接触线的螺旋半径；
n为主动轮接触线与螺距相关的参数，若螺距为p，则定义：
Figure PCTCN2015100289-appb-000037
t为参变量，
Figure PCTCN2015100289-appb-000038
表示主动轮一条线齿的接触线为
Figure PCTCN2015100289-appb-000039
圆周的螺旋线。当t＝-π时，主动轮和从动轮线齿开始啮合；当
Figure PCTCN2015100289-appb-000040
时，主动轮转过
Figure PCTCN2015100289-appb-000041
圆周，主动轮和从动轮线齿啮合到末端，开始脱离；
a和b为主动轮和从动轮的位置参数，如图1所示；
θ为主动轮和从动轮的角度参数，如图1所示；
ia和ib为所需的两个传动比；
Figure PCTCN2015100289-appb-000042
为主动轮的转角；
Figure PCTCN2015100289-appb-000043
为从动轮的转角；
Figure PCTCN2015100289-appb-000044
和
Figure PCTCN2015100289-appb-000045
为变传动比过程中，主动轮某线齿在传动时的起始和终止角度，比如当
Figure PCTCN2015100289-appb-000046
时，
Figure PCTCN2015100289-appb-000047
3.根据式(1)到式(3)，可以建立线齿实体，线齿实体只需要能够满足强度要求，线齿实体本身并没有特别具体的形状要求。如图4所示，在每一个啮合点处，分别在主、从动线齿接触方向的两侧(图4中的-γ1和γ1)反向伸展出一定的体积，即可以生成所需的线齿。轮体用于将线齿固联起来。

Claims (6)

  1. 一种变传动比线齿轮机构，其特征在于：该机构由任意角度相交轴的主动轮和从动轮组成传动副，主动轮由轮体和线齿组成，从动轮由轮体和线齿组成，主动轮线齿和从动轮线齿的接触线按照一对空间共轭曲线啮合，主动轮与驱动器联接以提供输入，主动轮上的线齿有一条或多条；主动轮的线齿和从动轮的线齿通过点接触啮合；从动轮与输出端联接以提供运动或力的输出，从动轮上的线齿为具有变传动比性质的线齿：在一个运动周期内，存在多个传动比，不同传动比之间可进行平稳过渡，从而产生周期性变传动比的传动。
  2. 根据权利要求1所述的变传动比线齿轮机构，其特征在于：主动轮的线齿上用于啮合的接触线为圆柱螺旋线；从动轮的线齿分为等传动比部分和变传动比部分，线齿上的用于啮合的接触线的方程有两种，一种为实现等传动比的等传动比方程，另一种为实现变传动比的变传动比方程。
  3. 根据权利要求2所述的变传动比线齿轮机构，其特征在于：所述机构在传动过程中，变传动比方程能使线齿轮的传动比从一个值平稳变到另一个值，即传动比函数的导数值由0开始增大或减小到某一个值，再平稳回到0。
  4. 根据权利要求3所述的变传动比线齿轮机构，其特征在于：所述变传动比方程确定如下：O-xyz为空间上任意固定笛卡尔坐标系，O为O-xyz坐标系原点，x、y、z是O-xyz坐标系的三个坐标轴，笛卡尔坐标系Op-xpypzp根据坐标系O-xyz位置进行确定，xpOpzp平面与xOz平面在同一平面内，坐标原点Op到z轴的距离为a，Op到x轴的距离为b，z轴与zp轴之间的夹角为(π-θ)，θ为主、从动轮角速度矢量的夹角，0°≤θ≤180°，坐标系O1-x1y1z1和O2-x2y2z2分别为固定在主动轮和从动轮上的坐标系，传动时主动轮和从动轮各自绕着z轴和zp轴转动，且主动轮与从动轮起始啮合处为起始位置，在起始位置，坐标系O1-x1y1z1和O2-x2y2z2分别与坐标系O-xyz及Op-xpypzp重合，在任意时刻，原点O1与O重合，z1轴与z轴重合，原点O2与Op重合，z2轴与zp轴重合，主动轮以匀角速度ω1绕z轴旋转，主动轮角速度方向为z轴负方向，主动轮绕z轴转过的角度为
    Figure PCTCN2015100289-appb-100001
    从动轮以匀角速度ω2绕zp轴旋转，从动轮角速度方向为zp轴负方向，从动轮绕zp轴转过的角度为
    Figure PCTCN2015100289-appb-100002
    则若主动接触线在坐标系O1-x1y1z1上的方程为：
    Figure PCTCN2015100289-appb-100003
    则，变传动比接触线的方程为：
    Figure PCTCN2015100289-appb-100004
    其中，A和C由方程
    Figure PCTCN2015100289-appb-100005
    和
    Figure PCTCN2015100289-appb-100006
    确定，m为主动轮接触线的螺旋半径，n为主动轮接触线与螺距相关的参数，若螺距为p，则定义：
    Figure PCTCN2015100289-appb-100007
    t为参变量，
    Figure PCTCN2015100289-appb-100008
    表示主动轮一条线齿的接触线为
    Figure PCTCN2015100289-appb-100009
    圆周的螺旋线，当t＝-π时，主动轮和从动轮线齿开始啮合，当
    Figure PCTCN2015100289-appb-100010
    时，主动轮转过
    Figure PCTCN2015100289-appb-100011
    圆周，主动轮和从动轮线齿啮合到末端，开始脱离；ia和ib为其中某段变化过程前后的两个传动比；
    Figure PCTCN2015100289-appb-100012
    和
    Figure PCTCN2015100289-appb-100013
    为变传动比过程中，主动轮某线齿在传动时的起始和终止角度，比如当
    Figure PCTCN2015100289-appb-100014
    时，
    Figure PCTCN2015100289-appb-100015
  5. 根据权利要求2所述的变传动比线齿轮机构，其特征在于：所述机构在传动过程中，为减低所述机构的运行的转动和跳跃性，变传动比方程的导数也能平稳的过渡，即变传动比方程的二次导数由0开始增大或减小到某一个值，再平稳回到0。
  6. 根据权利要求5所述的变传动比线齿轮机构，其特征在于：所述变传动比接触线的方程也能表示为：
    Figure PCTCN2015100289-appb-100016
    其中，E、F和G由方程
    Figure PCTCN2015100289-appb-100017
    和
    Figure PCTCN2015100289-appb-100018
    确定，m为主动轮接触线的螺旋半径，n为主动轮接触线与螺距相关的参数，若螺距为p，则定义：
    Figure PCTCN2015100289-appb-100019
    t为参变量，
    Figure PCTCN2015100289-appb-100020
    表示主动轮一条线齿的接触线为
    Figure PCTCN2015100289-appb-100021
    圆周的螺旋线，当t＝-π时，主动轮和从动轮线齿开始啮合，当
    Figure PCTCN2015100289-appb-100022
    时，主动轮转过
    Figure PCTCN2015100289-appb-100023
    圆周，主动轮和从动轮线齿啮合到末端，开始脱离；ia和ib为其中某段变化过程前后的两个传动比；
    Figure PCTCN2015100289-appb-100024
    和
    Figure PCTCN2015100289-appb-100025
    为变传动比过程中，主动轮某线齿在传动时的起始和终止角度，比如当
    Figure PCTCN2015100289-appb-100026
    时，
    Figure PCTCN2015100289-appb-100027
    根据权利要求5和6所创建的变传动比方程都可以运用于变传动比线齿轮机构中。
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