WO2018036034A1 - 一种转动-移动转换的线齿轮机构 - Google Patents

一种转动-移动转换的线齿轮机构 Download PDF

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WO2018036034A1
WO2018036034A1 PCT/CN2016/110655 CN2016110655W WO2018036034A1 WO 2018036034 A1 WO2018036034 A1 WO 2018036034A1 CN 2016110655 W CN2016110655 W CN 2016110655W WO 2018036034 A1 WO2018036034 A1 WO 2018036034A1
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axis
gear
driven
line
coordinate system
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PCT/CN2016/110655
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English (en)
French (fr)
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陈扬枝
吕月玲
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华南理工大学
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Priority to US16/326,843 priority Critical patent/US10677317B2/en
Publication of WO2018036034A1 publication Critical patent/WO2018036034A1/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
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/02—Toothed gearings for conveying rotary motion without gears having orbital motion
    • F16H1/04—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members
    • 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
    • F16H55/0853—Skewed-shaft arrangement of the toothed members
    • 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
    • F16H35/00—Gearings or mechanisms with other special functional features
    • F16H2035/003—Gearings comprising pulleys or toothed members of non-circular shape, e.g. elliptical gears
    • 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
    • F16H2055/0893—Profiling for parallel shaft arrangement of toothed members
    • 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 invention relates to the field of mechanical transmission and microelectromechanical systems, in particular to a rotary-moving conversion line gear mechanism.
  • Rotating and linear motion is mainly used in various machine tools, motors and indexing mechanisms.
  • the most commonly used mechanisms for this function are chains, wire ropes, drive belts, cams, pneumatics, hydraulics, racks or lead screws.
  • Different mechanisms can be used for different rotational and linear motion situations, and they also have different advantages and disadvantages.
  • the rack and pinion has the advantages of unrestricted stroke, convenient load installation, etc.
  • there are also disadvantages such as backlash, large vibration between the teeth, large noise, and difficulty in ensuring consistency
  • the belt drive has a fast running speed and noise.
  • the screw has higher precision, better rigidity and less noise, it has shorter stroke and slower speed. Accuracy consistency is difficult to guarantee and so on.
  • the wire gear is a new type of gear, which is mainly based on the space curve meshing theory. This theory is different from the traditional meshing theory of surface contact or line contact. It is a pair of space conjugate curves that are geared by point meshing.
  • the invention and research of the line gear has been developed for more than ten years. It has the advantages of small size, large transmission ratio and convenient manufacture, and is mainly used in the field of micro transmission.
  • the current focus is mainly on the two-inclined axis of the same plane, or the rotation-rotating transmission in the two interlaced axes of different planes, but the linear gear mechanism that has been linearly moved by rotation has not yet begun. Involved.
  • the present invention contemplates a line gear mechanism that provides rotational-to-movement conversion for micromechanical devices.
  • the rotation-shifting linear gear mechanism of the present invention can have an interlacing angle between the driving line gear axis and the driven line gear axis at any angle between 0° and 180°, and has small mass, simple manufacture, low cost, and is particularly convenient for micro- Application in the field of electromechanical.
  • the present invention is achieved by the following technical methods.
  • a rotary-shifting linear gear mechanism comprising a drive line gear and a driven line gear.
  • the drive line gear and the drive line gear wheel body constitute a drive line gear
  • the driven line gear and the driven line gear wheel body constitute a driven line gear.
  • the minimum number of teeth of the active wire teeth can be 1, and the number of driven wire teeth is related to the gear ratio and the distance of the linear movement.
  • the driving line gear and the driven line gear form a pair of transmission pairs, and the stagger angle between the driving wheel axis and the driven wheel axis is 0°-180°.
  • the active wire teeth and the driven wire teeth are respectively formed by moving a closed curve of an arbitrary shape as a bus bar with the active contact wire and the driven contact wire as a wire, the active contact wire and the driven contact.
  • the line is a pair of conjugate space curves of the spatial curve meshing equation of the line gear mechanism that conforms to the rotational-moving transition.
  • the driving line gear and the driven line gear realize the rotation-moving conversion line gear by the point contact engagement between the pair of conjugate active contact lines and the driven contact line on the driving wire teeth and the driven wire teeth
  • the transmission of the mechanism that is, when the drive line gear rotates, the driven line gear meshed therewith moves smoothly in the axial direction while rotating.
  • the rotational-moving converted linear gear mechanism spatial curve meshing equation is determined as follows: o-xyz, o q -x q y q z q are two space Cartesian Cartesian coordinate systems, o is o-xyz coordinates Origin, arbitrary position, x, y, z are the three coordinate axes of the o-xyz coordinate system, o q is the origin of the o q -x q y q z q coordinate system, x q , y q , z q are o q -x q y q z
  • the three coordinate axes of the q coordinate system, the plane xoz is in the same plane as the plane x p o p z p , and the distance from the o q point to the yoz plane is
  • i 21 is the transmission ratio of the drive line gear to the driven line gear.
  • the drive line gear When 90° ⁇ ⁇ ⁇ 180°, the drive line gear is at a uniform angular speed Rotating around the z-axis, the angular velocity of the drive line gear is in the negative direction of the z-axis, at which time the driven line gear is Q z axis positive direction is the direction of the rotation angular velocity about the z-axis q, while the driven gear to the size of the line A, the q-axis direction is the positive direction of the z velocity along the z axis q, active line is rotated around the z axis gear Angle is The angle at which the driven wire gear rotates around the z q axis is The displacement along the z q axis is s, then the space curve meshing equation of the mechanism is:
  • t is the parametric variable
  • the active contact line at the meshing point is in the unit of the o 1 -x 1 y 1 z 1 coordinate system
  • i (1) , j (1) , k (1) are x 1 , y 1
  • the unit vector of the z 1 axis, the equation of the driven contact line of the driven line gear in the o 3 -x 3 y 3 z 3 coordinate system is:
  • i 21 is the transmission ratio of the driving wheel and the driven wheel.
  • the active contact line and the driven contact line in the present invention are a pair of conjugate space curves designed according to the space curve meshing equation of the linear gear mechanism of the rotationally linear motion, which is different from the traditional spatial curved meshing crossed shaft gear mechanism.
  • the invention has the following advantages:
  • the structure is simple: the driving wheel and the driven wheel constitute a pair of transmission pairs, and the meshing between the driving line gear and the driven line gear mainly depends on the point contact between the driving wheel teeth and the driven wheel teeth, so as long as it is guaranteed The accuracy of the contact line can be simple, and the processing is convenient.
  • FIG. 1 is a schematic view of a spatial meshing coordinate system in an embodiment.
  • FIG. 2 is a schematic view of a drive line gear and its wire teeth in the embodiment.
  • FIG. 3 is a schematic view of a driven wire gear and its wire teeth in the embodiment.
  • Fig. 4 is a schematic view showing the meshing of the main and driven line gears in the embodiment.
  • the space curve meshing equation of the linear gear mechanism of the rotational-moving conversion of the active contact line and the driven contact line in the present invention conforms to the space curve meshing theory.
  • Figure 1 depicts a schematic representation of a spatial meshing coordinate system of a rotary-to-shift converted wire gear mechanism.
  • O-xyz, o p -x p y p z p and o q -x q y q z q are three spatial Cartesian Cartesian coordinate systems
  • o is the origin of the o-xyz coordinate system
  • x, y, and z are o- The three axes of the xyz coordinate system
  • o p is the origin of the o p -x p y p z p coordinate system
  • x p , y p , z p are the three axes of the o p -x p y p z p coordinate system
  • o q is the origin of the o q -x q y q q coordinate system
  • x q , y q , z q are the three coordinate
  • the coordinate systems o 1 -x 1 y 1 z 1 and o 3 -x 3 y 3 z 3 are respectively associated with the coordinate system o -xyz and o q -x q y q z q coincide, at any moment, the origin o 1 coincides with o, the z 1 axis coincides with the z axis, the origin o 3 coincides with o q , and the z 3 axis coincides with the z q axis.
  • Drive line gear at a uniform angular speed Rotating around the z-axis, the angular velocity of the drive line gear is in the negative direction of the z-axis.
  • the angle at which the main-line gear rotates around the z-axis is Driven line gear at a uniform angular speed Rotating around the z q axis, the angular velocity of the driven gear is shown in Figure 1.
  • the angle at which the driven gear rotates around the z q axis is At the same time, the driven line gear moves in the negative direction of the z q axis with the speed A, and the displacement of the driven line gear is recorded as s.
  • equation (1) Using the knowledge of differential geometry and space curve meshing theory, equation (1) is available:
  • Equation (2) is a space-gear equation of the linear gear mechanism of the rotational-moving conversion.
  • ⁇ (1) is the unit main method loss of the active contact line at the meshing point in the o 1 -x 1 y 1 z 1 coordinate system, ie, i (1) , j (1) , and k (1) are unit vectors of the x 1 , y 1 , and z 1 axes.
  • Equation (3) is an equation of the driven contact line conjugated to the active contact line space in the o 3 -x 3 y 3 z 3 coordinate system;
  • the thread tooth body can be established.
  • the thread tooth body only needs to be able to meet the strength requirement, and the thread tooth body and the line gear wheel body itself have no special shape requirements.
  • FIG. 4 The schematic diagram of the driven line gear and its line teeth is shown in Fig. 3.
  • the schematic diagram of the meshing of the drive line gear and the driven line gear is shown in Fig. 4.
  • 1 is a drive line gear
  • 2 is a drive line gear
  • 3 is a driven line gear
  • 4 is a driven line tooth.
  • the present invention provides a method and mechanism for converting a rotary-movement for a micromechanical device.
  • the mechanism can greatly simplify the structure of the micro-mechanical transmission device, realize the space-interlaced axis rotation-moving conversion motion, and reduce the geometric size.
  • the quality is reduced, the flexibility of operation is improved, the production is simple, the cost is low, and the application in the micro-electromechanical field is convenient.

Abstract

一种转动-移动转换的线齿轮机构，包括主动线齿轮（1）和从动线齿轮（2）。主动线齿轮轴线和从动线齿轮轴线间交错角为0°～180°中的任意值。通过主动线齿轮（1）上的主动线齿和从动线齿轮（2）上的从动线齿的主动接触线和从动接触线间的点接触啮合，利用主动线齿轮（1）的转动，而实现从动线齿轮（2）的转动同时平稳移动。转动-移动转换的线齿轮机构结构简单，设计方便，能实现较小位移的移动，特别适合于微小机械的转动变直线运动中。

Description

一种转动-移动转换的线齿轮机构 技术领域
本发明涉及技术领域为机械传动和微机电系统,具体是一种转动-移动转换的线齿轮机构。
背景技术
转动变直线运动，主要运用于各种机床、电机和分度机构等场合，最常用于实现该功能的机构有链条，钢丝绳，传动带，凸轮，气动，液压，齿条或丝杆。不同机构，可以用于不同的转动变直线运动场合，他们也有着不同的优缺点。如齿轮齿条虽然有着行程无限制、负载大安装方便等优点，也存在反向间隙、齿间胶合振动较大、噪声大和精度的一致性难以保证等缺点；带传动虽然有运行速度快、噪声低和成本低的优点，但其刚性差，易磨损断裂，精度低，推力小等；丝杆虽然其精度较高、刚性好何噪音较小，但是其有行程较短，速度较慢，行程精度一致性难以保证等等缺点。
线齿轮是一种新型的齿轮，其主要是依据空间曲线啮合理论，该理论不同于面接触或者线接触的传统啮合理论，是一对空间共轭曲线通过点啮合来实现传动的齿轮。线齿轮的发明和研究已经有了十几年的发展，其具有尺寸小，传动比大，制造方便等优点，主要运用于微小传动领域。对于线齿轮的研究，目前的主要集中在同平面两斜交轴间，或者是不同平面两交错轴中的转动变转动的传动，而对于由转动变直线运动的线齿轮机构，则还没有开始涉及。
发明内容
本发明设计出能够为微小机械装置提供转动-移动转换的线齿轮机构。本发明的转动-移动转换的线齿轮机构的主动线齿轮轴线和从动线齿轮轴线间交错角可以为0°～180°中的任意角度，且质量小,制造简单，造价低廉特别便于在微机电领域的应用。本发明通过如下技术方法实现。
一种转动-移动转换的线齿轮机构，该机构包括主动线齿轮和从动线齿轮。主动线齿和主动线齿轮轮体构成主动线齿轮，从动线齿和从动线齿轮轮体构成从动线齿轮。主动线齿最少齿数可以为1，从动线齿数和传动比和直线移动的距离有关。主动线齿轮和从动线齿轮组成一对传动副，主动轮轴线和从动轮轴线间交错角为0°～180°。
进一步的，所述主动线齿和从动线齿是分别以任意形状的封闭曲线为母线沿以主动接触线和从动接触线为导线运动而成的实体，所述主动接触线和从动接触线为符合转动-移动转换的线齿轮机构的空间曲线啮合方程的一对共轭空间曲线。
进一步的，主动线齿轮和从动线齿轮通过主动线齿和从动线齿上的一对共轭的主动接触线和从动接触线间的点接触啮合，实现该转动-移动转换的线齿轮机构的传动，即，当主动线齿轮转动时，与之啮合的从动线齿轮在转动的同时沿轴向平稳移动。
进一步的，所述转动-移动转换的线齿轮机构空间曲线啮合方程由如下确定：o-xyz、oq-xqyqzq是两个空间笛卡尔直角坐标系，o为o-xyz坐标系原点，位置任意，x、y、z是o-xyz坐标系的三个坐标轴，oq为oq-xqyqzq坐标系原点，xq、yq、zq是oq-xqyqzq坐标系的三个坐标轴，平面xoz与平面xpopzp在同一平面内，oq点到yoz平面的距离为|a|，oq点到xoy平面的距离为|b|，oq点到xoz平面的距离为|b|，y轴和yq轴平行，z轴和zp轴的夹角为(π-θ)，0°≤θ≤180°，空间笛卡尔坐标系o1-x1y1z1与主动线齿轮轮固联，o1为o1-x1y1z1坐标系原点，x1、y1、z1是o1-x1y1z1坐标系的三个坐标轴，空间笛卡尔坐标系o3-x3y3z3与从动线齿轮固联，o3为o3-x3y3z3坐标系原点，x3、y3、z3是o3-x3y3z3坐标系的三个坐标轴，且主动线齿轮轮与从动线齿轮轮起始啮合处为起始位置，在起始位置，坐标系o1-x1y1z1和o3-x3y3z3分别与坐标系o-xyz及oq-xqyqzq重合，在任意时刻，原点o1与o重合，z1轴与z轴重合，原点o3与oq重合，z3轴与zq轴重合，当0°≤θ<90°时，主动线齿轮以匀角速度
Figure PCTCN2016110655-appb-000001
绕z轴转动，主动线齿轮角速度方向为z轴负方向，主动线齿轮绕z轴转过的角度为
Figure PCTCN2016110655-appb-000002
从动线齿轮以匀角速度
Figure PCTCN2016110655-appb-000003
绕zq轴转动，从动线齿轮角速度方向为zq轴负方向，从动线齿轮绕zq轴转过的角度为
Figure PCTCN2016110655-appb-000004
同时，从动线齿轮以匀速度A沿zq轴负方向移动，从动线齿轮移动的位移为s，则转动-移动转换的线齿轮机构的空间曲线啮合方程：
Figure PCTCN2016110655-appb-000005
其中，
Figure PCTCN2016110655-appb-000006
是主动线齿轮的主动接触线的方程,t为参变量，
Figure PCTCN2016110655-appb-000007
为该机构的主动接触线在啮合点处在o1-x1y1z1坐标系下的单位主法失，i(1)、j(1)、k(1)是x1、y1、z1轴的单位向量，从动线齿轮的从动接触线在o3-x3y3z3坐标系下的方程为：
Figure PCTCN2016110655-appb-000008
其中，
Figure PCTCN2016110655-appb-000009
i21为主动线齿轮与从动线齿轮的传动比。
当90°≤θ≤180°时，主动线齿轮以匀角速度
Figure PCTCN2016110655-appb-000010
绕z轴转动，主动线齿轮角速度方向为z轴负方向，此时从动线齿轮以大小为
Figure PCTCN2016110655-appb-000011
方向为zq轴正方向的角速度绕zq轴转动，同时，从动线齿轮以大小为A、方向为zq轴正方向的速度沿zq轴移动，主动线齿轮绕z轴转过的角度为
Figure PCTCN2016110655-appb-000012
从动线齿轮绕zq轴转过的角度为
Figure PCTCN2016110655-appb-000013
沿zq轴移动的位移为s，则，该机构的空间曲线啮合方程为：
Figure PCTCN2016110655-appb-000014
其中，
Figure PCTCN2016110655-appb-000015
是主动线齿轮的主动接触线在o1-x1y1z1坐标系下的方程,t为参变量
Figure PCTCN2016110655-appb-000016
为该机构主动接触线在啮合点处在o1-x1y1z1坐标系下的单位主法失，i(1)、j(1)、k(1)是x1、y1、z1轴的单位向量，从动线齿轮的从动接触线在o3-x3y3z3坐标系下的方程为：
Figure PCTCN2016110655-appb-000017
其中
Figure PCTCN2016110655-appb-000018
i21为主动轮与从动轮的传动比。
本发明中的主动接触线和从动接触线为符合转动变直线运动的线齿轮机构空间曲线啮合方程设计的一对共轭空间曲线，不同于传统的空间曲面啮合交错轴齿轮机构，也不同于申请人已申请的基于空间曲线啮合原理的适用于斜交轴传动的线齿轮和适用于交错轴轴传动的线齿轮。本发明实现主动线齿轮转动时，与之啮合的从动线齿轮在转动的同时沿轴线移动，从而导致空间曲线啮合方程的改变和从动接触线方程的改变。
本发明与现有技术相比具有如下的优点:
(1)实现交错角为任意角度值的两交错轴间转动-移动转换：本章研究的线齿轮副能够实现空间交错的两轴之间的传动，且两交错轴间的交错角可以是0°～180°中的任意角度值，根据不同的交错角，可得到不同的齿轮机构。因此，可以根据需要设计出实现空间上任意两轴任意位置传动的机构，比齿轮齿条传动更广泛。
(2)精密移动：从动线齿轮的移动位移行程相对比较小，适用于微小领域的精密移动，特别适合于转动一周后，要求移动相对较小位移的分度机构。
(3)结构简单：主动轮和从动轮构成一对传动副，主动线齿轮和从动线齿轮间的啮合主要是依靠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。
(4)实现转动的同时移动：主动线齿轮在转动时，与之啮合的从动线齿轮在转动的同时平稳移动。
附图说明
图1是实施方式中空间啮合坐标系示意图。
图2是实施方式中主动线齿轮及其线齿示意图。
图3是实施方式中从动线齿轮及其线齿示意图。
图4是实施方式中主、从动线齿轮啮合示意图。
具体实施方式
以下结合附图对本发明的实施作进一步说明，对本领域技术人员来说，本发明已经作了充分的说明，且本发明的保护范围不限于如下内容。
本发明中的主动接触线和从动接触线的转动-移动转换的线齿轮机构空间曲线啮合方程符合空间曲线啮合理论。
图1描绘了一种转动-移动转换的线齿轮机构的空间啮合坐标系示意图。o-xyz、op-xpypzp与oq-xqyqzq是三个空间笛卡尔直角坐标系，o为o-xyz坐标系原点，x、y、z是o-xyz坐标系的三个坐标轴，op为op-xpypzp坐标系原点，xp、yp、zp是op-xpypzp坐标系的三个坐标轴，oq为oq-xqyqzq坐标系原点，xq、yq、zq是oq-xqyqzq坐标系的三个坐标轴，平面xoz与平面xpopzp在同一平面内，op点到z轴的距离为|a|，op点到x轴的距离为|b|，oq-xqyqzq是在op-xpypzp的基础上沿着yp方向平移一个距离|c|得到的，且记z和zp两轴夹角的补角为θ，0°≤θ≤180°，θ等于z与zq两轴夹角的补角，空间笛卡尔坐标系o1-x1y1z1与主动轮固联，o1为o1-x1y1z1坐标系原点，x1、y1、z1是o1-x1y1z1坐标系的三个坐标轴，空间笛卡尔坐标系o3-x3y3z3与从动轮固联，o3为o3-x3y3z3坐标系原点，x3、y3、z3是o3-x3y3z3坐标系的三个坐标轴，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o3-x3y3z3分别与坐标系o-xyz及oq-xqyqzq重合，在任意时刻，原点o1与o重合，z1轴与z轴重合，原点o3与oq重合，z3轴与zq轴重合，主动线齿轮以匀角速度
Figure PCTCN2016110655-appb-000019
绕z轴转动，主动线齿轮角速度方向为z轴负方向，如图1所示，主 动线齿轮绕z轴转过的角度为
Figure PCTCN2016110655-appb-000020
从动线齿轮以匀角速度
Figure PCTCN2016110655-appb-000021
绕zq轴转动，从动线齿轮角速度方向如图1所示，从动线齿轮绕zq轴转过的角度为
Figure PCTCN2016110655-appb-000022
同时，从动线齿轮以速度大小为A沿zq轴负方向移动，从动线齿轮移动的位移大小记为s。
利用微分几何和空间曲线啮合理论的知识，则，可得公式(1)：
Figure PCTCN2016110655-appb-000023
其中，
Figure PCTCN2016110655-appb-000024
式(2)是转动-移动转换的线齿轮机构空间曲线啮合方程。
Figure PCTCN2016110655-appb-000025
为主动接触线在o1-x1y1z1坐标系下的方程，t为参变量；
β(1)为主动接触线在啮合点处在o1-x1y1z1坐标系下的单位主法失，即，
Figure PCTCN2016110655-appb-000026
i(1)、j(1)、k(1)是x1、y1、z1轴的单位向量。
其中：
Figure PCTCN2016110655-appb-000027
Figure PCTCN2016110655-appb-000028
Figure PCTCN2016110655-appb-000029
Figure PCTCN2016110655-appb-000030
式(3)为与主动接触线空间共轭的从动接触线在o3-x3y3z3坐标系下的方程；
式中：a，b，c—oq点在空间坐标系o-xyz的三个坐标分值(如图1)；
Figure PCTCN2016110655-appb-000031
—主动轮与从动轮转动的角速度大小；
i21—主动轮与从动轮的传动比。
当0°≤θ<90°时，从动轮的角速度ω2的方向和图1所示的方向相反，且
Figure PCTCN2016110655-appb-000032
的方向也和图1方向相反，其移动的速度A方向也与图1所示方向相反，则位移s也为zq轴的负方向。因此，
Figure PCTCN2016110655-appb-000033
A和s以负值代入式子(2)和(3)中，即可得到该θ角度下的转动-移动转换的线齿轮机构的空间曲线啮合方程、主动接触线方程和从动接触线方程，如式(4)：
Figure PCTCN2016110655-appb-000034
当90°≤θ≤180°时，从动轮的角速度ω2的方向和图1所示的方向相同，且
Figure PCTCN2016110655-appb-000035
的方向也和图1方向相同，而移动的速度A的方向也如图1所示，则位移的方向和zq轴的方向一致。可得到该θ角度下的主动接触线和从动接触线方程就是方程(1)所示。
根据曲线啮合方程，选择不同的角度θ和主动接触线方程，可以得到
Figure PCTCN2016110655-appb-000036
和t之间的关系，再根据θ值，选择式(3)或者式(4)中的从动接触线的方程，则可分别得到主动线齿和从动线齿的导线，并由所设计的封闭曲线为母线，母线分别沿着两导线运动，所得到的实体即为主动线齿和从动线齿，再根据实际需要，设计主动线齿轮轮体和从动线齿轮轮体，由此设计出主动线齿轮和从动线齿轮。
若主动线齿轮的主动接触线为空间圆柱螺旋线，在o1-x1y1z1坐标系中满足式(5)：
Figure PCTCN2016110655-appb-000037
当0°≤θ<90°时，将式(5)代入到式(3)中，可得到转动变直线运动的线齿轮机构的空间曲线啮合方程，如式(6)：
Figure PCTCN2016110655-appb-000038
当90°≤θ<180°时，将式(5)代入到式(4)中，可得到转动变直线运动的线齿轮机构的空间曲线啮合方程，如式(7)：
Figure PCTCN2016110655-appb-000039
设
Figure PCTCN2016110655-appb-000040
则
Figure PCTCN2016110655-appb-000041
设初始量为m＝5mm，n＝8mm，a＝0mm，b＝0mm，c＝-30mm，θ＝30°，k＝0.15，
Figure PCTCN2016110655-appb-000042
ts＝-0.5π，te＝0π和i21＝1/3代入公式(1)，有主动接触线在o1-x1y1z1坐标系下方程为：
Figure PCTCN2016110655-appb-000043
而由式(6)转动-移动转换的线齿轮机构的空间曲线啮合方程和式(3)，并通过三次拟合，得从动接触线在o3-x3y3z3坐标系下方程为：
Figure PCTCN2016110655-appb-000044
根据式(8)和(9)，并根据需要的截面，可以建立线齿实体，线齿实体只需要能够满足强度要求，线齿实体和线齿轮轮体本身并没有特别具体的形状要求。设主动线齿数N1＝4，根据传动比和移动位移的要求，设从动线齿数为N2＝23。值得一提的是，从动线齿轮的接触线设计时，下一个线齿的接触线在上一个线齿接触线的基础上在z轴上移动一个线齿移动的距离，同时转动一个线齿转动的角度。利用此方法，可以得到主动线齿轮及其线齿示意图如图2所示，从动线齿轮及其线齿示意图如图3所示，主动线齿轮和从动线齿轮啮合示意图如图4所示，图4中的1是主动线齿轮、2是主动线齿、3是从动线齿轮、4是从动线齿。
本发明为微小机械装置提供了一种能够将转动-移动转换的方法与机构。该机构能够极大地简化了微机械传动装置的结构,实现空间交错轴转动-移动转换运动，缩小几何尺寸, 减小质量,提高操作的灵活性,且制作简单，造价低廉,便于在微机电领域的应用。

Claims (3)

  1. 一种转动-移动转换的线齿轮机构，其特征在于:包括主动线齿轮和从动线齿轮，主动线齿轮和从动线齿轮组成一对传动副，通过主动线齿轮转动，从动线齿轮则在转动的同时平稳移动，主动线齿轮轴线和从动线齿轮轴线间交错角为0°～180°。
  2. 根据权利要求1所述的一种转动-移动转换的线齿轮机构，其特征在于该机构的传动副是通过主动线齿和从动线齿上的一对共轭的主动接触线和从动接触线间的点接触啮合，实现该线齿轮机构的传动。
  3. 根据权利要求2所述的转动-移动转换的线齿轮机构，其特征在于所述转动-移动转换的线齿轮机构空间曲线啮合方程由如下确定：o-xyz、oq-xqyqzq是两个空间笛卡尔直角坐标系，o为o-xyz坐标系原点，位置任意，x、y、z是o-xyz坐标系的三个坐标轴，oq为oq-xqyqzq坐标系原点，xq、yq、zq是oq-xqyqzq坐标系的三个坐标轴，平面xoz与平面xpopzp在同一平面内，oq点到yoz平面的距离为|a|，oq点到xoy平面的距离为|b|，oq点到xoz平面的距离为|b|，y轴和yq轴平行，z轴和zp轴的夹角为(π-θ)，0°≤θ≤180°，空间笛卡尔坐标系o1-x1y1z1与主动线齿轮轮固联，o1为o1-x1y1z1坐标系原点，x1、y1、z1是o1-x1y1z1坐标系的三个坐标轴，空间笛卡尔坐标系o3-x3y3z3与从动线齿轮固联，o3为o3-x3y3z3坐标系原点，x3、y3、z3是o3-x3y3z3坐标系的三个坐标轴，且主动线齿轮轮与从动线齿轮轮起始啮合处为起始位置，在起始位置，坐标系o1-x1y1z1和o3-x3y3z3分别与坐标系o-xyz及oq-xqyqzq重合，在任意时刻，原点o1与o重合，z1轴与z轴重合，原点o3与oq重合，z3轴与zq轴重合，当0°≤θ<90°时，主动线齿轮以匀角速度
    Figure PCTCN2016110655-appb-100001
    绕z轴转动，主动线齿轮角速度方向为z轴负方向，主动线齿轮绕z轴转过的角度为
    Figure PCTCN2016110655-appb-100002
    从动线齿轮以匀角速度
    Figure PCTCN2016110655-appb-100003
    绕zq轴转动，从动线齿轮角速度方向为zq轴负方向，从动线齿轮绕zq轴转过的角度为
    Figure PCTCN2016110655-appb-100004
    同时，从动线齿轮以速度 大小为A沿zq轴负方向移动，从动线齿轮移动的位移大小为s，则其空间曲线啮合方程：
    Figure PCTCN2016110655-appb-100005
    其中，是主动线齿轮的主动接触线的方程,t为参变量，
    Figure PCTCN2016110655-appb-100007
    为该机构的主动接触线在啮合点处在o1-x1y1z1坐标系下的单位主法失，i(1)、j(1)、k(1)是x1、y1、z1轴的单位向量，从动线齿轮的从动接触线在o3-x3y3z3坐标系下的方程为：
    Figure PCTCN2016110655-appb-100008
    其中，
    Figure PCTCN2016110655-appb-100009
    i21为主动线齿轮与从动线齿轮的传动比；
    当90°≤θ≤180°时，主动线齿轮以匀角速度
    Figure PCTCN2016110655-appb-100010
    绕z轴转动，主动线齿轮角速度方向为z轴负方向，此时从动线齿轮以大小为
    Figure PCTCN2016110655-appb-100011
    方向为zq轴正方向的角速度绕zq轴转动，同时，从动线齿轮以大小为A、方向为zq轴正方向的速度沿zq轴移动，主动线齿轮绕z轴转过的角度为
    Figure PCTCN2016110655-appb-100012
    从动线齿轮绕zq轴转过的角度为
    Figure PCTCN2016110655-appb-100013
    沿zq轴移动的位移为s，则，该机构的空间曲线啮合方程为：
    Figure PCTCN2016110655-appb-100014
    其中，
    Figure PCTCN2016110655-appb-100015
    是主动线齿轮的主动接触线在o1-x1y1z1坐标系下的方程,t为参变量
    Figure PCTCN2016110655-appb-100016
    为该机构主动接触线在啮合点处在o1-x1y1z1坐标系下的单位主法失，i(1)、j(1)、k(1)是x1、y1、z1轴的单位向量，从动线齿轮的从动接触线在o3-x3y3z3坐标系下的方程为：
    Figure PCTCN2016110655-appb-100017
    其中
    Figure PCTCN2016110655-appb-100018
    i21为主动轮与从动轮的传动比。
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