WO2023184652A1 - 一种非正交椭圆环面蜗杆齿轮副 - Google Patents

一种非正交椭圆环面蜗杆齿轮副 Download PDF

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WO2023184652A1
WO2023184652A1 PCT/CN2022/092094 CN2022092094W WO2023184652A1 WO 2023184652 A1 WO2023184652 A1 WO 2023184652A1 CN 2022092094 W CN2022092094 W CN 2022092094W WO 2023184652 A1 WO2023184652 A1 WO 2023184652A1
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involute
gear
elliptical
worm
tooth
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PCT/CN2022/092094
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English (en)
French (fr)
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凌四营
凌明
张衡
王奉涛
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大连理工大学
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Priority to US18/016,805 priority Critical patent/US20240125374A1/en
Publication of WO2023184652A1 publication Critical patent/WO2023184652A1/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
    • F16H1/12—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes
    • F16H1/16—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes comprising worm and worm-wheel
    • 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
    • F16H55/0806—Involute profile
    • 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
    • F16H55/088—Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
    • 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
    • F16H55/22—Toothed members; Worms for transmissions with crossing shafts, especially worms, worm-gears
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Definitions

  • the invention belongs to the technical field of mechanical transmission and relates to a non-orthogonal elliptical toroidal worm gear pair.
  • Worm transmission is an important transmission method for mechanical transmission. It has the advantages of large transmission ratio, high load-bearing capacity, small impact load, stable transmission, and easy self-locking. It is widely used in national defense, metallurgy, shipbuilding, construction, chemical industry, machinery and other industries. widely used.
  • a worm gear with a specific tooth surface is used as the shape wheel to rotate around its axis.
  • the blank of a toroidal worm is rotated around another axis.
  • the two axes are interlaced in space (usually 90 degrees). At this time, the generated The worm is called an enveloping toroidal worm.
  • the enveloping toroidal worm transmission has the characteristics of compact structure, large load-bearing capacity, and good meshing performance, and is an excellent transmission form. It mostly has instantaneous multi-tooth contact or line contact, so compared with ordinary cylindrical worm transmission, it can increase the load-bearing capacity by 1.5-4 times under the same size. Under the condition of transmitting the same power and mass processing and manufacturing, if the cylindrical worm is replaced by a toroidal worm, there will be a cost saving of 30%-50%. At present, the manufacturing cost of worm gears is high, and the highest manufacturing accuracy is difficult to break through level 3. However, involute cylindrical gears have achieved processing accuracy of ISO level 3 or above.
  • TI worm involute enveloping toroidal worm
  • the transmission efficiency of mass-processed worms can also be above 80%.
  • spiral cylindrical gears can be used instead of worm gears for TI worm transmission when transmission and load-bearing performance requirements are not high.
  • this type of TI worm transmission is greatly affected by the value of the helix angle. If a reasonable helix angle cannot be selected, eccentric load will occur during the transmission process.
  • the working area of the spiral cylindrical gear is concentrated in At the middle section of the tooth width, the tooth surfaces in the gear tooth width direction cannot all participate in the meshing, which will cause the tooth surface of the spiral cylindrical gear to wear unevenly during the meshing transmission process with the worm, resulting in a reduction in transmission accuracy.
  • the present invention proposes a non-orthogonal elliptical toroidal worm gear pair, which has the characteristics of toroidal worm transmission and can realize the participation of the full tooth width of the gear in meshing transmission.
  • the non-orthogonal elliptical toroidal worm gear pair provided by the present invention has stable transmission, small impact, low noise, large bearing capacity, high transmission efficiency, and significant error equalization effect of multi-tooth transmission.
  • the gear tooth surface has the advantages of uniform wear and good accuracy retention, and can be used in fields such as precision continuous indexing transmission, comprehensive deviation measurement of elliptical toroidal worms, and continuous grinding of cylindrical gear tooth surfaces.
  • a non-orthogonal elliptical toroidal worm gear pair includes an involute cylindrical gear and an elliptical toroidal worm formed by a primary envelope of the involute cylindrical gear.
  • the involute cylindrical gear includes an involute spur gear and an involute helical gear; the tooth surface of the involute spur gear is an involute cylindrical surface formed by stretching the involute along the axial direction,
  • the tooth surface of the involute helical gear is an involute helical surface formed by the helical movement of the involute along the axial direction.
  • the involute is generated by the pure rolling of the generating line on the base circle; the involute cylindrical gear adopts a hard tooth surface. Wear-resistant materials are ground into shape.
  • x 1L is the x coordinate of each point on the left tooth surface
  • y 1L is the y coordinate of each point on the left tooth surface
  • z 1L is the z coordinate of each point on the left tooth surface
  • r b is the base of the involute gear Circle radius
  • u is the rolling angle formed by the dominant involute tooth profile
  • ⁇ 0 is half of the base circle central angle corresponding to the base circle tooth thickness of the end face of the involute cylindrical gear
  • h L is the axial parameter of the left tooth surface
  • ⁇ 1 is the spiral parameter
  • ⁇ is the angle through which the involute moves in the axial direction
  • ⁇ 1 is a parameter with a value of 0 or 1
  • ⁇ 2 is a parameter with a value of 0 or 1.
  • x 1R is the x coordinate of each point on the right tooth surface
  • y 1R is the y coordinate of each point on the right tooth surface
  • z 1R is the z coordinate of each point on the right tooth surface
  • h R is the axial parameter of the right tooth surface .
  • the indexing surface of the traditional toroidal worm is a torus
  • the indexing surface of the elliptical toroidal worm of the present invention is an elliptical torus.
  • the generatrix of the elliptical torus is an oblique section and the gear indexing cylindrical surface is within the working length of the worm.
  • the intersection line within the range, the oblique section passes through the rotation axis of the elliptical torus worm and the angle with the horizontal plane is the axis intersection angle ⁇ ; the equation satisfied by the generatrix of the elliptical torus is:
  • r is the radius of the base circle of the involute graduated cylinder
  • x is the x coordinate of any point on the bus line
  • y is the y coordinate of any point on the bus line.
  • the elliptical toroidal worm and the involute cylindrical gear adopt spatial non-orthogonal transmission, and the axis intersection angle is determined according to the self-locking condition; as the axis intersection angle increases, the tooth tip width of the elliptical toroidal worm gradually decreases, and the minimum width is agreed upon The end face module is not less than 0.35 times. At this time, the shaft intersection angle reaches the maximum value; the tooth width of the involute cylindrical gear is related to the working length of the elliptical toroidal worm and the shaft intersection angle. In order to achieve the full tooth width of the involute cylindrical gear To participate in meshing, the following relationships must be met:
  • b is the tooth width of the involute cylindrical gear
  • L is the working length of the elliptical toroidal worm.
  • the tooth surface of the elliptical toroidal worm is formed by the involute cylindrical surface of the involute spur gear or the involute helical surface of the involute helical gear as the tool base according to the envelope method.
  • a corresponding transmission coordinate system is established based on the positional relationship of the elliptical toroidal worm meshing transmission.
  • the details are as follows:
  • the tooth surface equation of the involute cylindrical gear is obtained by the tooth surface equation of the elliptical toroidal worm through coordinate transformation and the tooth surface conjugate meshing principle. Therefore, the tooth surface equation of the upper side of the elliptical toroidal worm is:
  • the above tooth surface equation is given by Determined by two parameters and u, other parameters are known, in Within the value range of and u, the upper and lower tooth surfaces of the elliptical toroidal worm can be obtained through MATLAB numerical analysis and three-dimensional modeling software, and then they are sutured with the tooth top annulus and tooth root annulus of the elliptical toroidal worm. , generate a three-dimensional solid model of the non-orthogonal elliptical toroidal worm gear pair, and then obtain the non-orthogonal elliptical toroidal worm gear pair.
  • the present invention proposes a non-orthogonal elliptical toroidal worm gear pair, which has the characteristics of toroidal worm transmission and can realize the participation of the full tooth width of the gear in meshing transmission.
  • the non-orthogonal elliptical toroidal worm gear pair provided by the present invention has the advantages of smooth transmission, small impact, low noise, large bearing capacity, high transmission efficiency, and multi-tooth transmission. It has the advantages of significant error equalization effect, uniform gear tooth surface wear, and good accuracy retention. It can be used in fields such as precision continuous indexing transmission, comprehensive deviation measurement of elliptical toroidal worms, and continuous grinding and processing of cylindrical gear tooth surfaces. It has good promotion Application value and industrialization prospects.
  • Figure 1 is a schematic diagram of the elliptical torus generatrix of the elliptical torus worm
  • Figure 2 is a schematic diagram of the tooth surface structure of an involute spur gear
  • Figure 3 is a schematic diagram of the elliptical toroidal worm transmission coordinate system
  • Figure 4 is a schematic diagram of the tooth surface of the elliptical toroidal worm
  • Figure 5 is a schematic diagram of the meshing transmission between the involute spur gear and the elliptical toroidal worm
  • the indexing surface of the elliptical toroidal worm 5 is an elliptical torus, which is different from the traditional toroidal worm.
  • the intersection line of the oblique section 1 and the gear indexing cylindrical surface 2 is the generatrix 3 of the elliptical torus, and the projection of the generatrix 3 on the cylinder end surface is an arc.
  • the angle between the oblique section and the cylinder end face is the axis intersection angle ⁇ of the transmission pair.
  • the radius of the cylinder bottom circle is r. Then the equation of the cylinder bottom circle is:
  • the working length, rotation axis and other parameters of the elliptical toroidal worm 5 are determined.
  • the tooth width of the involute spur gear 4 is related to the working length and shaft intersection angle of the elliptical toroidal worm 5. In order to realize the full tooth width of the involute spur gear participating in meshing, the following relationships must be satisfied:
  • the selected axis intersection angle is 5°
  • the working length L of the elliptical toroidal worm is 72mm
  • the tooth width b of the involute cylindrical gear is 8mm.
  • the involute spur gear 4 is ground and formed with hard tooth surface wear-resistant material.
  • the left tooth surface equation of the involute spur gear 4 is:
  • r b is the base circle radius of the involute cylindrical gear, the size is 112.7631mm; u is the rolling angle formed by the dominant involute tooth profile, and the value range is [0.2649, 0.3850]; ⁇ 0 is the involute cylinder Half of the value of the base circle central angle corresponding to the base circle tooth thickness of the gear end face is 1.6043°; h is the axial parameter of the tooth surface, which is related to the rolling angle u and the elliptical toroidal worm rotation angle related.
  • the tooth surface of the involute spur gear 4 is used as the tool parent surface, and the tooth surface equation of the elliptical toroidal worm 5 is formed according to the generation method.
  • the coordinate systems ⁇ (o; x, y , z ) and ⁇ p (op; Worm gear - the starting position of the involute spur gear 4 they are all fixed coordinate systems.
  • z and z p are the rotation axes of the elliptical toroidal worm 5 and the spur gear 4 respectively. The two axes are non-orthogonal in space, and the axis intersection angle is ⁇ .
  • the x p- axis and the x-axis are on the same straight line and in the same direction.
  • ⁇ 1 ( o1 ; x1 , y1 , z1 ) and ⁇ 2 ( o2 ; Coordinate system; spur gear 4 and elliptical toroidal worm 5 rotate around axes z 1 and z 2 at angular speeds w 1 and w 2 respectively, and the angles they rotate are and exist and
  • the shortest distance between the z 1 and z 2 axes is a, which is the center distance between the spur gear 4 and the elliptical toroidal worm 5, and its value is 135mm.
  • the tooth surface equation of the elliptical toroidal worm 5 is obtained from the tooth surface equation of the involute spur gear 4 through the transformation of the spatial coordinate system.
  • the coordinate transformation matrix M 12 of the spatial coordinate system is:
  • the rotation angle of the elliptical toroidal worm The value is related to its working half angle. After calculation, the value range is [-17.25°, 17.25°].
  • ⁇ is the relative speed of the conjugate tooth surface at the meshing point.
  • the above tooth surface equation is given by Determined by two parameters and u, other parameters are known, in Within the value range of The tooth tip annulus and the tooth root annulus are sutured to generate a three-dimensional solid model of the non-orthogonal elliptical toroidal worm gear pair; after the three-dimensional solid model is assembled with the involute cylindrical spur gear, the upper tooth surface of the elliptical toroidal worm 5- 1 and the lower tooth surface 5-2 are in contact with the gear tooth surface for transmission without tooth surface interference, thus verifying the feasibility of this transmission form.
  • the transmission ratio used in this embodiment is 120, and the number of teeth of the involute cylindrical gear 4 participating in meshing at the same time is 12, so it has a good error equalization effect; when the maximum value of the axis intersection angle is 7.7°, the involute cylindrical gear is fully
  • the tooth width of the tooth surface contact can reach 9.65mm.
  • the gear tooth surface wears evenly and the accuracy is good. It can be used in precision continuous indexing transmission, comprehensive deviation measurement of elliptical toroidal worms, and continuous grinding and processing of cylindrical gear tooth surfaces. It has Good promotion and application value and industrialization prospects.

Abstract

本发明属于机械传动技术领域，提供一种非正交椭圆环面蜗杆齿轮副，包括渐开线圆柱齿轮和其一次包络展成的椭圆环面蜗杆；两者采用空间非正交传动，轴交角满足自锁条件及最小齿顶宽的限制条件；椭圆环面蜗杆的环面母线为椭圆，可以增加啮合的齿数及瞬时接触线的总长度。本发明提出的一种非正交椭圆环面蜗杆齿轮副，具有环面蜗杆传动的特点，可以实现齿轮全齿宽参与啮合传动。相对于螺旋圆柱齿轮的TI蜗杆传动，非正交椭圆环面蜗杆齿轮副传动平稳、噪音低、承载力大、传动效率高、多齿传动的误差均化效应显著、齿轮齿面磨损均匀、精度保持性好等优点，可用于精密连续分度传动、圆柱齿轮齿面连续研磨加工等领域，具有良好的推广应用价值与产业化前景。

Description

一种非正交椭圆环面蜗杆齿轮副 技术领域
本发明属于机械传动技术领域，涉及一种非正交椭圆环面蜗杆齿轮副。
背景技术
蜗杆传动是机械传动的一种重要的传动方式，以传动比大、承载能力高、冲击载荷小、传动平稳、易实现自锁等优点在国防、冶金、造船、建筑、化工、机械等行业得到广泛使用。以一个具有特定齿面的蜗轮为产形轮绕其轴线旋转，同时让一环面蜗杆的毛坯绕另一轴线旋转，这两个轴线在空间交错(通常为90度)，此时所展成的蜗杆称为包络环面蜗杆。
现阶段，包络环面蜗杆传动具有结构紧凑、大承载力、啮合性能好等特点，是一种优良的传动形式。它多是瞬时多齿接触或线接触，故与普通的圆柱蜗杆传动相比，在同等尺寸下，能够提升1.5-4倍的承载力。在传递相同大小的功率，大批量加工制造的状况下，若把圆柱蜗杆替换为环面蜗杆，就会有30％-50％的成本节约。目前蜗轮的制造成本较高，且最高制造精度难以突破3级，而渐开线圆柱齿轮则已经实现ISO 3级以上的加工精度，其中以大连理工大学高精度齿轮实验室为代表，研制出了国际领先的1级精度渐开线圆柱齿轮。随着制造出的零件表面粗糙度更低、精度更高，还有良好的润滑条件，环面蜗杆传动机构的传动效率有很大的提升。
有报道称TI蜗杆(渐开线包络环面蜗杆)实验传动效率可高达95％，大批量加工的蜗杆，其传动效率也可在80％以上。由于高精度蜗轮制造难度较大，在传动及承载性能要求不高的情况下，可用螺旋圆柱齿轮代替蜗轮用于TI蜗杆传动。但该类型的TI蜗杆传动受螺旋角的取值的影响较大，若不能选择合理的螺旋角会产生传动过程中的偏载，而选择合理的螺旋角后，螺旋圆柱齿轮的工作区域集中在齿宽中截面处，齿轮齿宽方向的齿面不能全部参与啮合，会造成螺旋圆柱齿轮的齿面在与蜗杆的啮合传动过程中不均匀磨损，致使传动精度下降的问题。
发明内容
为了解决现有技术中，TI蜗杆传动过程存在的问题，本发明提出了一种非正交椭圆环面蜗杆齿轮副，其具有环面蜗杆传动的特点，可以实现齿轮全齿宽参与啮合传动。相对于螺旋圆柱齿轮的TI蜗杆传动，本发明提供的非正交椭圆环面蜗杆齿轮副传动平稳、冲击小、噪音低、承载力大、传动效率高、多齿传动的误差均化效应显著、齿轮齿面磨损均匀、精度保持性好等优点，可用于精密连续分度传动、椭圆环面蜗杆的综合偏差测量、圆柱齿轮齿面连续研磨加工等领域。
为了达到上述目的，本发明采用的技术方案为：
一种非正交椭圆环面蜗杆齿轮副，包括渐开线圆柱齿轮和由渐开线圆柱齿轮一次包络展成的椭圆环面蜗杆。
所述渐开线圆柱齿轮包括渐开线直齿圆柱齿轮和渐开线螺旋齿轮；所述渐开线直齿圆柱齿轮的齿面为渐开线沿轴向拉伸形成的渐开圆柱面，渐开线螺旋齿轮的齿面为渐开线沿轴向做螺旋运动而形成的渐开螺旋面，渐开线由发生线在基圆上做纯滚动产生；渐开线圆柱齿轮采用硬齿面耐磨材料磨削成形。
所述的渐开线圆柱齿轮的左齿面方程如下所示：
Figure PCTCN2022092094-appb-000001
其中，x 1L为左齿面上各点的x坐标，y 1L为左齿面上各点的y坐标，z 1L为左齿面上各点的z坐标；r b为渐开线齿轮的基圆半径；u为主导渐开线齿廓形成的滚动角；σ 0为渐开线圆柱齿轮端面基圆齿厚所对应基圆圆心角的一半；h L为左齿面轴向参数；ρ 1为螺旋参数；λ为渐开线沿轴向做螺旋运动转过的角度；α 1为取值0或1的参数；α 2为取值0或1的参数。
所述的渐开线圆柱齿轮的右齿面方程为：
Figure PCTCN2022092094-appb-000002
其中，x 1R为右齿面上各点的x坐标，y 1R为右齿面上各点的y坐标，z 1R为右齿面 上各点的z坐标；h R为右齿面轴向参数。
当上述渐开线圆柱齿轮的齿面方程满足α 1＝0且α 2＝1时，所对应的左右齿面方程为渐开线直齿圆柱齿轮的齿面方程；同理α 1＝1且α 2＝0时，所对应的左右齿面方程为渐开线螺旋圆柱齿轮的齿面方程。
传统的环面蜗杆的分度曲面为圆环面，而本发明所述椭圆环面蜗杆的分度曲面为椭圆环面，椭圆环面的母线为斜截面与齿轮分度圆柱面在蜗杆工作长度范围内的交线，斜截面经过椭圆环面蜗杆的回转轴线且与水平面的角度为轴交角ε；椭圆环面的母线满足的方程为：
Figure PCTCN2022092094-appb-000003
其中，r为渐开线分度圆柱底面圆的半径，x为母线上任意一点的x坐标、y为母线上任意一点的y坐标。
所述椭圆环面蜗杆与渐开线圆柱齿轮采用空间非正交传动，轴交角根据自锁条件确定；随着轴交角的增大，椭圆环面蜗杆的齿顶宽度逐渐减小，约定最小宽度不低于0.35倍的端面模数，此时轴交角取得最大值；所述渐开线圆柱齿轮的齿宽与椭圆环面蜗杆工作长度及轴交角有关，为了实现渐开线圆柱齿轮全齿宽参与啮合，需满足以下关系:
b＝Lsinε
其中，b为渐开线圆柱齿轮的齿宽，L为椭圆环面蜗杆的工作长度。
所述椭圆环面蜗杆的齿面由渐开线直齿圆柱齿轮的渐开圆柱面或渐开线螺旋齿轮的渐开螺旋面作为工具母面按照包络法展成，按照渐开线圆柱齿轮与椭圆环面蜗杆啮合传动的位置关系建立相应的传动坐标系。具体如下：渐开线圆柱齿轮的齿面方程通过坐标变换及齿面共轭啮合原理得到椭圆环面蜗杆的齿面方程，因此椭圆环面蜗杆上侧齿面方程为：
Figure PCTCN2022092094-appb-000004
其中，a为展成中心距；
Figure PCTCN2022092094-appb-000005
为渐开线圆柱齿轮转角；
Figure PCTCN2022092094-appb-000006
为椭圆环面蜗杆转角；i 12为蜗杆副传动比的倒数；σ 0为渐开线圆柱齿轮端面基圆齿厚所对应基圆圆心角的一半；u为主导渐开线齿廓形成的滚动角。
同理，椭圆环面蜗杆下侧齿面方程为：
Figure PCTCN2022092094-appb-000007
上述齿面方程由
Figure PCTCN2022092094-appb-000008
和u两个参数决定，其他参数均已知，在
Figure PCTCN2022092094-appb-000009
和u的取值范围内通过MATLAB数值分析及三维建模软件能够得到椭圆环面蜗杆的上齿面及下齿面，然后将其与椭圆环面蜗杆的齿顶环面及齿根环面缝合，生成非正交椭圆环面蜗杆齿轮副的三维实体模型，进而得到非正交椭圆环面蜗杆齿轮副。
本发明的有益效果在于：
(1)本发明提出了一种非正交椭圆环面蜗杆齿轮副，具有环面蜗杆传动的 特点，可以实现齿轮全齿宽参与啮合传动。
(2)相对于传统的螺旋圆柱齿轮的TI蜗杆传动，本发明提供的非正交椭圆环面蜗杆齿轮副具有传动平稳、冲击小、噪音低、承载力大、传动效率高、多齿传动的误差均化效应显著、齿轮齿面磨损均匀、精度保持性好等优点，可用于精密连续分度传动、椭圆环面蜗杆的综合偏差测量、圆柱齿轮齿面连续研磨加工等领域，具有良好的推广应用价值与产业化前景。
附图说明
图1为椭圆环面蜗杆的椭圆环面母线的示意图；
图2为渐开线直齿圆柱齿轮的齿面结构的示意图；
图3为椭圆环面蜗杆传动坐标系的示意图；
图4为椭圆环面蜗杆齿面的示意图；
图5为渐开线直齿圆柱齿轮与椭圆环面蜗杆啮合传动的示意图；
图中：1斜截面；2渐开线圆柱齿轮的分度圆柱面；3椭圆环面母线；4渐开线直齿圆柱齿轮；5椭圆环面蜗杆；5-1椭圆环面蜗杆的上齿面；5-2椭圆环面蜗杆的下齿面。
具体实施方式
以模数m＝2mm、齿数z＝120、压力角α＝20°的渐开线直齿圆柱齿轮和渐开线直齿圆柱齿轮基于一次包络法展成的椭圆环面蜗杆为例阐述该发明的具体实施方式：
首先，椭圆环面蜗杆5的分度曲面为椭圆环面，与传统的圆环面蜗杆不同。斜截面1与齿轮分度圆柱面2的交线为椭圆环面的母线3，并且母线3在圆柱端面的投影为圆弧。斜截面与圆柱端面夹角为传动副的轴交角ε，圆柱底面圆的半径为r，那么圆柱底面圆的方程为：
x′ 2+y′ 2＝r 2
所以对应的椭圆环面的母线3满足的方程为：
Figure PCTCN2022092094-appb-000010
当r＝118mm及r＝122.5mm时，上述母线3的方程分别对应椭圆环面蜗杆的齿顶母线及齿根母线方程。
进一步，根据渐开线直齿圆柱齿轮4的参数，确定椭圆环面蜗杆5的工作长度、回转轴线等各项参数。渐开线直齿圆柱齿轮4的齿宽与椭圆环面蜗杆5工作长度及轴交角有关，为了实现渐开线直齿圆柱齿轮全齿宽参与啮合需满足以下关系：
b＝Lsinε
在满足自锁条件及蜗杆最小齿顶宽的限制条件下，当选用的轴交角为5°时，椭圆环面蜗杆的工作长度L为72mm，渐开线圆柱齿轮的齿宽b为8mm。
渐开线直齿圆柱齿轮4采用硬齿面耐磨材料磨削成形，渐开线直齿圆柱齿轮4的左齿面方程为：
Figure PCTCN2022092094-appb-000011
其中，r b为渐开线圆柱齿轮的基圆半径，大小为112.7631mm；u为主导渐开线齿廓形成的滚动角，取值范围为[0.2649,0.3850]；σ 0为渐开线圆柱齿轮端面基圆齿厚所对应基圆圆心角数值的一半，大小为1.6043°；h为齿面轴向参数，与滚动角u及椭圆环面蜗杆转角
Figure PCTCN2022092094-appb-000012
有关。
同理，渐开线直齿圆柱齿轮4的右齿面方程为：
Figure PCTCN2022092094-appb-000013
将渐开线直齿圆柱齿轮4的齿面作为工具母面，按照展成法包络形成椭圆环面蜗杆5的齿面方程。在建立的椭圆环面蜗杆空间传动坐标系中，坐标系σ(o；x，y，z)和σ p(o p；x p，y p，z p)分别是表示椭圆环面蜗杆5和蜗轮——渐开线直齿圆柱齿轮4的起始位置，它们都是固定坐标系。z和z p分别为椭圆环面蜗杆5和直齿圆柱齿轮4的回转轴线，两轴线在空间内非正交，轴交角为ε。x p轴和x轴在同一条直线上，方向相同。σ 1(o 1；x 1，y 1，z 1)和σ 2(o 2；x 2，y 2，z 2)分别表示与 直齿圆柱齿轮4和椭圆环面蜗杆5相固连的动坐标系；直齿圆柱齿轮4和椭圆环面蜗杆5分别以角速度w 1和w 2绕z 1和z 2轴旋转，转过的角度分别是
Figure PCTCN2022092094-appb-000014
和
Figure PCTCN2022092094-appb-000015
在
Figure PCTCN2022092094-appb-000016
和
Figure PCTCN2022092094-appb-000017
时为起始位置，z 1和z 2轴间的最短距离为a，也就是直齿圆柱齿轮4和椭圆环面蜗杆5的中心距，其值为135mm。
椭圆环面蜗杆5的齿面方程由渐开线直齿圆柱齿轮4的齿面方程通过空间坐标系的变换得到，空间坐标系的坐标变换矩阵M 12为：
Figure PCTCN2022092094-appb-000018
其中，椭圆环面蜗杆的转角
Figure PCTCN2022092094-appb-000019
的取值与其工作半角有关，经计算可得取值范围为[-17.25°,17.25°]。
在空间共轭啮合过程中，参加啮合的两个齿面在任意瞬时都是相切接触的，切点处总有公共的切平面即有相同的法线n，接触处满足啮合方程式为：
v×n＝0
其中，ν为啮合点处共轭齿面的相对速度。
这样可以保证两啮合齿面可以连续地滑动接触，不会相互发生干涉。满足上述要求后，推导出椭圆环面蜗杆5的上侧齿面方程为：
Figure PCTCN2022092094-appb-000020
同理，推导出椭圆环面蜗杆5的下侧齿面方程为：
Figure PCTCN2022092094-appb-000021
上述齿面方程由
Figure PCTCN2022092094-appb-000022
和u两个参数决定，其他参数均已知，在
Figure PCTCN2022092094-appb-000023
和u的取值范围内通过MATLAB数值分析及UG、Pro/E三维建模软件可以得到椭圆环面蜗杆的上齿面5-1及下齿面5-2，然后将其与椭圆环面蜗杆的齿顶环面及齿根环面缝合生成非正交椭圆环面蜗杆齿轮副的三维实体模型；该三维实体模型与渐开线圆柱直齿轮装配后，椭圆环面蜗杆的上齿面5-1及下齿面5-2与齿轮齿面接触传动并且无齿面干涉，从而验证了该传动形式的可行性。
本实施例采用的传动比为120，渐开线圆柱齿轮4同时参与啮合的齿数为12，因此具有良好的误差均化效应；当轴交角取最大值为7.7°时，渐开线圆柱齿轮全齿面接触的齿宽可以达到9.65mm，齿轮齿面磨损均匀、精度保持性好，可用于精密连续分度传动、椭圆环面蜗杆的综合偏差测量、圆柱齿轮齿面连续研磨加工等领域，具有良好的推广应用价值与产业化前景。
最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，对本领域普通技术人员来说，可以根据本发明专利的技术方案及其具体实施例加以等同替换或改变，而所有这些改变或替换都应属于本发明专利的保护范围。

Claims (1)

  1. 一种非正交椭圆环面蜗杆齿轮副，其特征在于，所述的非正交椭圆环面蜗杆齿轮副包括渐开线圆柱齿轮和由渐开线圆柱齿轮一次包络展成的椭圆环面蜗杆；
    所述渐开线圆柱齿轮包括渐开线直齿圆柱齿轮和渐开线螺旋齿轮；所述渐开线直齿圆柱齿轮的齿面为渐开线沿轴向拉伸形成的渐开圆柱面，渐开线螺旋齿轮的齿面为渐开线沿轴向做螺旋运动而形成的渐开螺旋面，渐开线由发生线在基圆上做纯滚动产生；渐开线圆柱齿轮采用硬齿面耐磨材料磨削成形；
    所述的渐开线圆柱齿轮的左齿面方程如下所示：
    Figure PCTCN2022092094-appb-100001
    其中，x 1L、y 1L、z 1L分别为左齿面上各点的x、y、z坐标；r b为渐开线齿轮的基圆半径；u为主导渐开线齿廓形成的滚动角；σ 0为渐开线圆柱齿轮端面基圆齿厚所对应基圆圆心角的一半；h L为左齿面轴向参数；ρ 1为螺旋参数；λ为渐开线沿轴向做螺旋运动转过的角度；α 1为取值0或1的参数；α 2为取值0或1的参数；
    所述的渐开线圆柱齿轮的右齿面方程为：
    Figure PCTCN2022092094-appb-100002
    其中，x 1R、y 1R、z 1R分别为右齿面上各点的x、y、z坐标；h R为右齿面轴向参数；
    当上述渐开线圆柱齿轮的齿面方程满足α 1＝0且α 2＝1时，所对应的左右齿面方程为渐开线直齿圆柱齿轮的齿面方程；同理α 1＝1且α 2＝0时，所对应的左右齿面方程为渐开线螺旋圆柱齿轮的齿面方程；
    所述椭圆环面蜗杆的分度曲面为椭圆环面，椭圆环面的母线为斜截面与齿轮分度圆柱面在蜗杆工作长度范围内的交线，斜截面经过椭圆环面蜗杆的回转轴线且与水平面的角度为轴交角ε；椭圆环面的母线满足的方程为：
    Figure PCTCN2022092094-appb-100003
    其中，r为渐开线分度圆柱底面圆的半径；x、y分别为母线上任意一点的x、y 坐标；
    所述椭圆环面蜗杆与渐开线圆柱齿轮采用空间非正交传动，轴交角根据自锁条件确定；渐开线圆柱齿轮的齿宽与椭圆环面蜗杆工作长度及轴交角有关，为了实现渐开线圆柱齿轮全齿宽参与啮合，需满足以下关系：
    b＝L sinε
    其中，b为渐开线圆柱齿轮的齿宽，L为椭圆环面蜗杆的工作长度；
    所述椭圆环面蜗杆的齿面由渐开线直齿圆柱齿轮的渐开圆柱面或渐开线螺旋齿轮的渐开螺旋面作为工具母面按照包络法展成，按照渐开线圆柱齿轮与椭圆环面蜗杆啮合传动的位置关系建立相应的传动坐标系；具体如下：渐开线圆柱齿轮的齿面方程通过坐标变换及齿面共轭啮合原理得到椭圆环面蜗杆的齿面方程，因此椭圆环面蜗杆上侧齿面方程为：
    Figure PCTCN2022092094-appb-100004
    其中，a为展成中心距；
    Figure PCTCN2022092094-appb-100005
    为渐开线圆柱齿轮转角；
    Figure PCTCN2022092094-appb-100006
    为椭圆环面蜗杆转角；i 12为蜗杆副传动比的倒数；σ 0为渐开线圆柱齿轮端面基圆齿厚所对应基圆圆心角的一半；u为主导渐开线齿廓形成的滚动角；
    同理，椭圆环面蜗杆下侧齿面方程为：
    Figure PCTCN2022092094-appb-100007
    上述齿面方程由
    Figure PCTCN2022092094-appb-100008
    和u两个参数决定，其他参数均已知，在
    Figure PCTCN2022092094-appb-100009
    和u的取值范围内通过MATLAB数值分析及三维建模软件得到椭圆环面蜗杆的上齿面及下齿面，然后将其与椭圆环面蜗杆的齿顶环面及齿根环面缝合，生成非正交椭圆环面蜗杆齿轮副的三维实体模型，最终得到非正交椭圆环面蜗杆齿轮副。
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