WO2017041417A1 - 基于共轭曲线的多点接触圆柱齿轮啮合副 - Google Patents

基于共轭曲线的多点接触圆柱齿轮啮合副 Download PDF

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Publication number
WO2017041417A1
WO2017041417A1 PCT/CN2016/072279 CN2016072279W WO2017041417A1 WO 2017041417 A1 WO2017041417 A1 WO 2017041417A1 CN 2016072279 W CN2016072279 W CN 2016072279W WO 2017041417 A1 WO2017041417 A1 WO 2017041417A1
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Prior art keywords
tooth
contact
curve
gear
meshing
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PCT/CN2016/072279
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English (en)
French (fr)
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陈兵奎
梁栋
谭儒龙
李朝阳
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重庆大学
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Priority to EP16843361.3A priority Critical patent/EP3348869B1/en
Publication of WO2017041417A1 publication Critical patent/WO2017041417A1/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
    • F16H55/0826—Novikov-Wildhaber 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
    • F16H55/17—Toothed wheels

Definitions

  • the invention belongs to the technical field of gear transmission, and in particular relates to a multi-point contact cylindrical gear meshing pair based on a conjugate curve.
  • the gear determines the performance of the equipment to a large extent, so it is also of great significance and engineering practical value for the design of high-performance gear transmission components.
  • Conventional gear transmissions such as helical gear transmission, worm gear transmission, bevel gear pair, quasi-hyperbolic pair, etc.
  • the tooth surfaces are conjugate curved surfaces
  • the meshing tooth profiles are convex tooth profiles, which are usually line contacts during the meshing process.
  • the bearing capacity of the tooth surface is low, the sliding rate between the tooth surfaces is large, and the tooth surface wear is severe.
  • the arc gear is a point contact transmission form, and its protruding feature is that the meshing tooth profile is a point contact engagement of the convex arc profile with the concave arc profile, and its engagement is approximately pure rolling. After the arc gear runs and then, the contact point expands into a contact surface, and the contact strength is greatly increased.
  • both patents of No. 102853054 A and 103075493 A disclose a gear based on a conjugate curve and a meshing pair thereof.
  • the tooth profiles of the gears of the above two patents are balls of a ball center along a center curve.
  • the tubular envelope surface of the family has a circular arc of the tooth profile.
  • the gear meshing pair has point contact characteristics during initial manufacture.
  • the gear must be run and, in order to increase running and performance, the tooth surface of the gear is generally soft or medium hard. Running and will increase the manufacturing cost of the enterprise, and in practical applications, the hard tooth surface has higher contact strength and load bearing capacity than the soft tooth surface and the medium hard tooth surface, so there is currently a need for an initial manufacturing according to the use requirements.
  • the gear contact of point contact can also be designed as hard tooth surface and can be applied to industrial occasions with high strength requirements, and the running time of existing point contact gears can be greatly shortened even without running. Use requirements to effectively reduce the manufacturing costs of the enterprise.
  • an object of the present invention is to overcome the deficiencies of the prior art and to provide a multi-point contact cylindrical gear meshing pair based on a conjugate curve which can have multi-point contact characteristics according to the use requirement.
  • the multi-point contact spur gear meshing pair based on the conjugate curve disclosed in the present invention comprises a convex tooth gear and a concave tooth gear which are meshed with each other and has a plurality of meshing points, and the meshing curved surface of the convex tooth gear and the concave tooth gear a tubular curved surface;
  • the convex tooth gear and the concave tooth gear have three meshing points and the meshing points are distributed on different sections of the tooth profile;
  • the three contact curves formed by the meshing points on the tooth profile curved surface of the convex gear or the concave gear are respectively the contact curve l 1 , the contact curve l 2 and the contact curve l 3 ;
  • r is the radius of the circular helix l
  • ⁇ 1 is the circular helix curve parameters l 1, which is in the range of ⁇ 1i ⁇ 1 ⁇ 1o
  • p is the spiral parameters of a cylindrical helix
  • r is the radius of the circular helix l
  • ⁇ 1 is the circular helix curve parameters l 1, which is in the range of ⁇ 1i ⁇ 1 ⁇ 1o
  • p is the spiral parameters of a cylindrical helix
  • r is the radius of the circular helix l
  • ⁇ 1 is the circular helix curve parameters l 1, which is in the range of ⁇ 1i ⁇ 1 ⁇ 1o
  • p is the spiral parameters of a cylindrical helix
  • the tooth profile surface of the convex gear includes a curved surface ⁇ 1 , a curved surface ⁇ 2 and a curved surface ⁇ 3 ;
  • the tooth profile curved surface of the concave tooth gear includes a curved surface ⁇ ' 1 , a curved surface ⁇ ' 2 and a curved surface ⁇ ' 3 ;
  • h 1 is the radius of the tooth profile surface
  • n x1 , n y1 and n z1 respectively represent components of the normal vector at the contact point of the tooth profile surface in each coordinate axis direction
  • parameters And ⁇ 1 represent the general spherical L 1 parameters, respectively;
  • h 2 is the radius of the tooth profile surface
  • n x2 , n y2 and n z2 respectively represent components of the normal vector at the contact point of the tooth profile surface in each coordinate axis direction
  • parameters And ⁇ 2 represent the general spherical L 2 parameters, respectively;
  • h 3 is the radius of the curved tooth profile
  • n x3, n y3 and the normal vector n z3 represent the tooth profile section of the surface component through the contact points in each coordinate axis direction
  • the parameters And ⁇ 3 represent the general spherical L 3 parameters, respectively;
  • h 1 is the radius of the tooth profile surface
  • n x1 , n y1 and n z1 respectively represent components of the normal vector at the contact point of the tooth profile surface in each coordinate axis direction
  • parameters And ⁇ 1 represent the general spherical L 1 parameters, respectively;
  • h 2 is the radius of the tooth profile surface
  • n x2 , n y2 and n z2 respectively represent components of the normal vector at the contact point of the tooth profile surface in each coordinate axis direction
  • parameters And ⁇ 2 represent the general spherical L 2 parameters, respectively;
  • h3 is the radius of the tooth profile surface
  • n x3 , n y3 and n z3 respectively represent components of the normal vector at the contact point of the tooth profile surface in each coordinate axis direction
  • parameters And ⁇ 3 represent the general spherical L 3 parameters, respectively;
  • the meshing point of the convex gear and the concave gear is four and is respectively an engagement point p 1 , an engagement point p 2 , an engagement point p 3 , and an engagement point p 4 ;
  • the convex gear or the concave gear The three contact curves formed by the meshing points on the surface of the tooth profile are respectively the contact curve l 1 , the contact curve l 2 and the contact curve l 3 ;
  • the meshing point p 1 is distributed on the contact curve l 1
  • the meshing point p 2 and the meshing point p 3 is distributed on the contact curve l 2
  • the meshing point p 4 is distributed on the contact curve l 3 ;
  • the contact curve l 2 is a quadratic parabolic curve
  • the contact curve l 1 and the contact curve l 3 are arc curves and along The tooth width direction is arranged on both sides of the contact curve l 2 ;
  • the tooth profile surface of the convex tooth gear comprises a curved surface ⁇ 1 ;
  • the tooth profile curved surface of the concave tooth gear comprises a curved surface ⁇ ' 1 , a curved surface ⁇ ' 2 and a curved surface ⁇ ' 3 which are smoothly transitioned with each other;
  • r c represents the radius of the cylinder where the cylindrical helix is located
  • ⁇ c represents the curve parameter of the cylindrical helix
  • p c represents the spiral parameter
  • h 1c represents the radius of the tooth surface of the meshing pipe
  • n x1c , n y1c and n z1c respectively represent the meshing of the segment The component of the normal vector at the tooth-tooth contact point in the direction of each coordinate axis, the parameter And ⁇ c respectively represent general spherical parameters
  • ⁇ 1 is the angle of rotation of the gear
  • r 1 is the radius of the pitch cylinder gear
  • ⁇ is a tooth helix angle.
  • the center of the tooth profile is located outside the cylinder of the gear section, X is positive, the center of the tooth profile is located within the cylinder of the gear section, X is negative; the center of the tooth profile is located on the opposite side of the axis of symmetry of the tooth symmetry, and the side L is negative;
  • ⁇ 1 is the gear rotation angle
  • r1 is the gear joint cylinder radius
  • ⁇ is the gear tooth helix angle.
  • the center of the tooth profile is located outside the cylinder of the gear joint, X' is positive, the center of the tooth profile is located inside the cylinder of the gear joint, X' is negative; the center of the tooth profile is located on the opposite side of the tooth-symmetry axis, L' is positive, and the same side L' is negative. ;
  • the engaging points of the convex gear and the concave gear are five and are respectively an engaging point p 1 , an engaging point p 2 , an engaging point p 3 meshing point p 4 , and an engaging point p 5 ;
  • the three contact curves formed by the meshing points on the tooth surface curved surface of the concave gear are respectively the contact curve l 1 , the contact curve l 2 and the contact curve l 3 ;
  • the meshing point p 1 and the meshing point p 2 are distributed on the contact curve l 1
  • the meshing point p 3 is distributed on the contact curve l 2
  • the meshing point p 4 and the meshing point p 5 are distributed on the contact curve l 3 ;
  • the contact curve l 2 is a circular arc curve
  • the contact curve l 1 and the contact curve l 3 is a quadratic parabolic curve and is arranged on both sides of the contact curve l 2 along the tooth width direction;
  • the tooth profile surface of the convex tooth gear comprises a curved surface ⁇ 1 ;
  • the tooth profile curved surface of the concave tooth gear comprises a curved surface ⁇ ' 1 , a curved surface ⁇ ' 2 and a curved surface ⁇ ' 3 which are smoothly transitioned with each other;
  • r m represents the radius of the cylinder where the cylindrical helix is located
  • ⁇ m represents the curve parameter of the cylindrical helix
  • p m represents the spiral parameter
  • h 1m represents the radius of the tooth surface of the meshing pipe
  • n x1m , n y1m and n z1m respectively represent the meshing of the segment The component of the normal vector at the tooth-tooth contact point in the direction of each coordinate axis, the parameter And ⁇ m respectively represent general spherical parameters
  • ⁇ 1 is the angle of rotation of the gear
  • r 1 is the radius of the pitch cylinder gear
  • ⁇ is a tooth helix angle.
  • the center of the tooth profile is located outside the cylinder of the gear section, X is positive, the center of the tooth profile is located within the cylinder of the gear section, X is negative; the center of the tooth profile is located on the opposite side of the axis of symmetry of the tooth symmetry, and the side L is negative;
  • the invention has the beneficial effects that the multi-point contact cylindrical gear meshing pair based on the conjugate curve of the invention has the meshing mode of the meshing gear tooth surface and the concave tooth gear tooth surface at the same time, and the contact point is in each tooth.
  • the contact trajectories of the faces are smooth spatial curves.
  • the transmission inherits the meshing characteristics of the conjugate curve, and the contact profile of the contact point is high, the bearing capacity is high, the transmission efficiency is high, the lubricating oil temperature rises low, and the sliding The rate is greatly reduced and the wear is small.
  • FIG. 1 is a schematic view showing a tooth surface structure of a spur gear having a three-point contact according to the present invention
  • FIG. 2 is a schematic view showing the meshing of a spur gear having a three-point contact according to the present invention
  • FIG. 3 is a schematic diagram showing a tooth profile curved surface of a cylindrical gear with three-point contact according to the present invention
  • FIG. 4 is a schematic view showing a tooth surface structure of a cylindrical gear having a local four-point contact according to the present invention
  • Figure 5 is a schematic view showing the meshing of a cylindrical gear having a local four-point contact according to the present invention
  • FIG. 6 is a schematic view showing the structure of a tooth surface of a spur gear having four points symmetrically contacting in a full tooth width direction according to the present invention
  • Figure 7 is a schematic view showing the engagement of a spur gear having four points of symmetrical contact along the full tooth width direction of the present invention
  • Figure 8 is a schematic diagram showing the tooth profile curved surface of a cylindrical gear with four-point contact according to the present invention.
  • Figure 9 is a schematic view showing the tooth surface structure of a cylindrical gear having a five-point symmetrical contact according to the present invention.
  • Figure 10 is a schematic view showing the engagement of a spur gear having a five-point symmetrical contact of the present invention.
  • Figure 11 is a schematic diagram showing the derivation of a tooth profile surface with a five-point symmetric contact of the present invention.
  • the three-section tooth profile curve is selected as a circular arc curve in the partial cross section of the tooth surface, and the most advantageous contact pressure angle is determined to realize the general distribution in different sections.
  • Point contact As shown in Fig. 1 and Fig. 2, the convex and concave tubular meshing tooth surfaces constructed based on the conjugate curve meshing theory form a mating meshing pair, and the meshing pair moves along the contact point trajectory in the axial direction, and the two are in the partial cross section of the tooth surface. Generally three points of contact;
  • a cylindrical spiral is selected as the tooth surface conjugate contact curve.
  • l 1 , l 2 and l 3 are respectively three spiral curves on the cylindrical surface, which satisfies the curve l 2 relative to the curve l 1 around the central axis by an angle ⁇ 1 , which satisfies the curve l 3
  • the curve l 1 is rotated by an angle ⁇ 2 about the central axis.
  • r denotes the radius of a circular helix l
  • [theta] denotes a circular helix curve parameters l 1, which is in the range of ⁇ 1i ⁇ 1 ⁇ 1o
  • p denotes a cylindrical helix spiral parameters.
  • the curve l 3 is rotated by an angle ⁇ 2 around the central axis relative to the curve l 1 , and based on the coordinate transformation matrix, the curve equation of the cylindrical spiral l 3 is obtained.
  • the running trajectories of the three contact points on the tooth surface are cylindrical spirals l 1 , l 2 and l 3 , respectively. It is particularly important to note that the three contact points should not be in the same section, that is, the cross-section is distributed. It mainly includes three sections of surface:
  • ⁇ denotes a formable convex and concave tubular meshing tooth surface, respectively
  • h 1 denotes a formed toothed surface radius of the engaging tube
  • n x1 , n y1 and n z1 respectively represent the toothed surface of the segmented toothed surface at the point of contact
  • the component of the normal vector in the direction of each coordinate axis, the parameter And ⁇ 1 represent the general spherical L 1 parameters, respectively.
  • ⁇ denotes a shapeable convex and concave tubular meshing tooth surface
  • h 2 denotes a formed meshing tooth surface radius
  • n x2 , n y2 and n z2 respectively represent the toothed surface of the segmented toothed surface at the contact point
  • the component of the normal vector in the direction of each coordinate axis, the parameter And ⁇ 2 represent the general spherical L 2 parameters, respectively.
  • ⁇ denotes a formable convex and concave tubular meshing tooth surface
  • h 3 denotes a formed meshing pipe tooth surface radius
  • n x3 , n y3 and n z3 respectively represent the toothed surface of the segmented toothed surface at the contact point
  • the component of the normal vector in the direction of each coordinate axis, the parameter And ⁇ 3 represent the general spherical L 3 parameters, respectively.
  • a three-section tooth profile curve is selected in the partial cross-section of the tooth surface, and the front and rear two-section tooth profile curves are in the form of a circular arc curve, and the intermediate tooth profile curve is a quadratic parabolic curve.
  • Form determine the most advantageous contact pressure angle to achieve local four-point symmetry contact.
  • the convex and concave tubular meshing tooth surfaces constructed based on the conjugate curve meshing theory form a mating meshing pair, and the meshing pair moves along the contact point trajectory in the axial direction, and the two are partially in the partial cross section of the tooth surface. Point symmetrical contact.
  • different tooth profile curves are selected in different sections of the tooth surface along the tooth width direction, and the front and rear tooth profile curves are in the form of a circular arc curve, and the middle tooth profile curve is In the form of a quadratic parabolic curve, the most advantageous contact pressure angle is determined to achieve a four point symmetric contact along the tooth width direction.
  • the convex and concave tubular meshing tooth surfaces constructed based on the conjugate curve meshing theory form a mating meshing pair, and the meshing pair moves along the contact point trajectory in the axial direction, and the two are in four-point symmetric contact along the tooth width direction.
  • a three-section tooth profile curve is selected on the tooth surface of the gear tooth, wherein the front and rear two tooth profile curves are in the form of a circular arc curve, and the middle tooth profile curve is in the form of a quadratic parabolic curve.
  • the arc tooth profiles are in single contact in the respective cross-sectional areas
  • the parabolic tooth profile is in double contact in the cross-sectional area thereof
  • the meshing pair constitutes a four-point contact state.
  • the convex tooth surface is all in the form of a circular arc profile.
  • the general equation of the tooth surface can refer to the forming method of the meshing tooth surface, which is further expressed as
  • r c represents the radius of the cylinder where the cylindrical helix is located
  • ⁇ c represents the curve parameter of the cylindrical helix
  • p c represents the spiral parameter
  • h 1c represents the radius of the tooth surface of the meshing pipe
  • n x1c , n y1c and n z1c respectively represent the meshing of the segment
  • the component of the normal vector at the tooth-tooth contact point in the direction of each coordinate axis, the parameter And ⁇ c represent the general spherical parameters, respectively.
  • the concave tooth surface is composed of three parts, including a circular arc tooth profile c 1 segment, a parabolic tooth profile c 2 segment and a circular arc tooth profile c 3 segment.
  • ⁇ represents the arc profile radius
  • ⁇ represents the tooth profile angle, which determines the position of the contact point in the arc
  • X, L respectively represent the distance between the arc center distance coordinate system y axis and the x axis.
  • ⁇ 1 is the angle of rotation of the gear
  • r 1 is the radius of the pitch cylinder gear
  • ⁇ is a tooth helix angle.
  • the center of the tooth profile is located outside the cylinder of the gear joint, X is positive, and the center of the tooth profile is located within the cylinder of the gear joint. X is negative; the center of the tooth profile is located on the opposite side of the tooth-symmetry axis, L is positive, and the same side L is negative.
  • t is an independent variable parameter
  • the arc tooth profile c 3 segment tooth surface equation is the same as the arc tooth profile c 1 segment tooth surface equation derivation method, assuming that the arc tooth profile c 3 is expressed as
  • ⁇ ' denotes the arc tooth profile radius
  • ⁇ ' denotes the tooth profile angle, which determines the position of the contact point in the arc
  • X', L' respectively represent the distance between the arc center distance coordinate system y axis and the x axis.
  • the normal circular arc tooth profile c 3 is the spiral surface formed by the tooth surface ⁇ 3 equation
  • ⁇ 1 is the angle of rotation of the gear
  • r 1 is the radius of the pitch cylinder gear
  • ⁇ is a tooth helix angle.
  • the center of the tooth profile is located outside the cylinder of the gear joint, X' is positive, the center of the tooth profile is located inside the cylinder of the gear joint, X' is negative; the center of the tooth profile is located on the opposite side of the tooth-symmetry axis, L' is positive, and the same side L' is negative.
  • the different tooth profile curves are selected in different sections of the tooth surface along the tooth width direction, and the front and rear tooth profile curves are in the form of a quadratic parabolic curve, and the middle tooth profile curve is In the form of an arc curve, the most advantageous contact pressure angle is determined to achieve a symmetrical five-point contact along the tooth width direction.
  • the convex and concave tubular meshing tooth surfaces constructed based on the conjugate curve meshing theory form a mating meshing pair, and the meshing pair moves along the contact point trajectory in the axial direction, and the two are in five-point symmetric contact along the tooth width direction.
  • a three-section tooth profile curve is selected on the tooth surface of the tooth, wherein the tooth profile curve of the front and rear sections is in the form of a quadratic parabola curve, and the middle tooth profile curve is in the form of a circular arc curve.
  • the circular arc profile has a single point contact in the respective cross-sectional areas
  • the parabolic tooth profile has a double point contact in its cross-sectional area
  • the meshing pair constitutes a five-point contact state.
  • the convex tooth surface is still in the form of a circular arc profile, and the tooth surface equation is referred to as the meshing pipe tooth surface forming method, which is expressed as
  • r m represents the radius of the cylinder where the cylindrical helix is located
  • ⁇ m represents the curve parameter of the cylindrical helix
  • p m represents the spiral parameter
  • h 1m represents the radius of the tooth surface of the meshing pipe
  • n x1m , n y1m and n z1m respectively represent the meshing of the segment
  • the component of the normal vector at the tooth-tooth contact point in the direction of each coordinate axis, the parameter And ⁇ m represent the general spherical parameters, respectively.
  • the concave tooth surface is composed of three parts, including a quadratic parabolic tooth profile m 1 segment, a circular arc tooth profile m 2 segment and a quadratic parabolic tooth profile m 3 segment.
  • t is an independent variable parameter
  • the quadrilateral parabolic tooth profile is formed by the helical motion of the tooth surface ⁇ 1 equation.
  • ⁇ represents the arc profile radius
  • ⁇ represents the tooth profile angle, which determines the position of the contact point in the arc
  • X, L respectively represent the distance between the arc center distance coordinate system y axis and the x axis.
  • ⁇ 1 is the angle of rotation of the gear
  • r 1 is the radius of the pitch cylinder gear
  • ⁇ is a tooth helix angle.
  • the center of the tooth profile is located outside the cylinder of the gear joint, X is positive, and the center of the tooth profile is located within the cylinder of the gear joint. X is negative; the center of the tooth profile is located on the opposite side of the tooth-symmetry axis, L is positive, and the same side L is negative.
  • t' is an independent variable parameter

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Abstract

一种基于共轭曲线的多点接触圆柱齿轮啮合副，包括相互多点接触啮合的凸齿齿轮和凹齿齿轮，凸齿齿轮和凹齿齿轮的啮合曲面为管状曲面，凸齿齿轮的齿廓曲面上由啮合点构成的接触曲线和凹齿齿轮上由啮合点构成的接触曲线为共轭曲线，啮合副的啮合方式为凸齿齿轮齿面与凹齿齿轮齿面同时多点接触，接触点在各齿面的接触轨迹均为光滑的空间曲线。

Description

基于共轭曲线的多点接触圆柱齿轮啮合副 技术领域
本发明属于齿轮传动技术领域，具体的为一种基于共轭曲线的多点接触圆柱齿轮啮合副。
背景技术
齿轮作为一种典型的机械基础件，在很大程度上决定着装备的性能，因而针对高性能齿轮传动元件的设计也具有十分重要的意义和工程实用价值。传统齿轮传动如螺旋齿轮传动、蜗杆蜗轮传动，锥齿轮副、准双曲线副等，齿面均为共轭曲面，啮合齿廓均为凸齿廓，在啮合过程中，通常为线接触，因此齿面的承载能力低，齿面间滑动率大，齿面磨损严重。
生产和科技的发展对高速、重载、大功率的齿轮传动装置提出了更高的要求，因此圆弧齿轮取得了巨大的发展。圆弧齿轮是一种点接触传动形式，其突出的特点是啮合齿廓为凸圆弧齿廓与凹圆弧齿廓的点接触啮合，并且其啮合近似纯滚动。圆弧齿轮跑和之后，接触点扩展成接触面，接触强度大幅增加。目前，公开号为102853054 A与103075493 A的两个专利均公开了一种基于共轭曲线的齿轮及其啮合副，以上两专利中的齿轮的齿廓曲面均为球心沿圆心曲线运动的球族管状包络面，其齿廓曲面均为圆弧，由该齿轮组成的啮合副在相互啮合时，其啮合点只有一个，这种齿轮啮合副在初始制造时具有点接触特性，若要获得比较好的接触特性，这种齿轮必须经过跑和，为了增加跑和性能，这种齿轮的齿面一般采用软齿面或中硬齿面。跑和将增加企业的制造成本，并且在实际应用之中，硬齿面相对于软齿面和中硬齿面具有更高的接触强度和承载能力，因此当前需要一种根据使用需求，在初始制造时能具有多点接触特性，使得点接触的齿轮传动也可设计为硬齿面并可应用于高强度要求的工业场合，同时大大缩短现有点接触齿轮的跑合时间甚至无需跑合既能达到使用要求，有效降低企业的生产制造成本。
发明内容
有鉴于此，本发明的目的是克服现有技术的缺陷，提供一种可根据使用需求，具有多点接触特性的基于共轭曲线的多点接触圆柱齿轮啮合副。
本发明公开的一种基于共轭曲线的多点接触圆柱齿轮啮合副，包括相互点啮合的凸齿齿轮和凹齿齿轮且啮合点为多个，所述凸齿齿轮和凹齿齿轮的啮合曲面为管状曲面；
进一步，所述凸齿齿轮和凹齿齿轮的啮合点为3个且啮合点分布于其齿廓的不同截面上；
进一步，所述凸齿齿轮或凹齿齿轮的齿廓曲面上由啮合点构成的三条接触曲线分别为接触曲线l1、接触曲线l2和接触曲线l3；
所述接触曲线l1的曲线方程为：
Figure PCTCN2016072279-appb-000001
其中r为圆柱螺旋线l1半径，θ1为圆柱螺旋线l1的曲线参数，其取值范围为θ1i≤θ1≤θ1o，p为圆柱螺旋线的螺旋参数；
所述接触曲线l2的曲线方程为：
Figure PCTCN2016072279-appb-000002
其中r为圆柱螺旋线l1半径，θ1为圆柱螺旋线l1的曲线参数，其取值范围为θ1i≤θ1≤θ1o，p为圆柱螺旋线的螺旋参数；
所述接触曲线l3的曲线方程为：
Figure PCTCN2016072279-appb-000003
其中r为圆柱螺旋线l1半径，θ1为圆柱螺旋线l1的曲线参数，其取值范围 为θ1i≤θ1≤θ1o，p为圆柱螺旋线的螺旋参数；
进一步，所述凸齿齿轮的齿廓曲面包括曲面Σ1、曲面Σ2和曲面Σ3；所述凹齿齿轮的齿廓曲面包括曲面Σ'1、曲面Σ'2和曲面Σ'3；
所述曲面Σ1方程为：
Figure PCTCN2016072279-appb-000004
式中
Figure PCTCN2016072279-appb-000005
其中h1为所述齿廓曲面的半径，nx1、ny1和nz1分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000006
和α1分别表示一般球面L1参数；
所述曲面Σ2方程为：
Figure PCTCN2016072279-appb-000007
式中
Figure PCTCN2016072279-appb-000008
其中h2为所述齿廓曲面的半径，nx2、ny2和nz2分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000009
和α2分别表示一般球面L2参数；
所述曲面Σ3方程为：
Figure PCTCN2016072279-appb-000010
式中
Figure PCTCN2016072279-appb-000011
其中h3为所述齿廓曲面的半径，nx3、ny3和nz3分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000012
和α3分别表示一般球面L3参数；
所述曲面Σ'1方程为：
Figure PCTCN2016072279-appb-000013
式中
Figure PCTCN2016072279-appb-000014
其中h1为所述齿廓曲面的半径，nx1、ny1和nz1分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000015
和α1分别表示一般球面L1参数；
所述曲面Σ'2方程为：
Figure PCTCN2016072279-appb-000016
式中
Figure PCTCN2016072279-appb-000017
其中h2为所述齿廓曲面的半径，nx2、ny2和nz2分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000018
和α2分别表示一般球面L2参数；
所述曲面Σ'3方程为：
Figure PCTCN2016072279-appb-000019
式中
Figure PCTCN2016072279-appb-000020
其中h3为所述齿廓曲面的半径，nx3、ny3和nz3分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000021
和α3分别表示一般球面L3参数；
进一步，所述凸齿齿轮和凹齿齿轮的啮合点为4个并分别为啮合点p1、啮合点p2、啮合点p3和啮合点p4；所述凸齿齿轮或凹齿齿轮的齿廓曲面上由啮合点构成的三条接触曲线分别为接触曲线l1、接触曲线l2和接触曲线l3；所述啮合点p1分布于接触曲线l1上，啮合点p2以及啮合点p3分布于接触曲线l2上，啮合点p4分布于接触曲线l3上；所述接触曲线l2为二次抛物曲线，接触曲线l1和接触曲线l3均为圆弧曲线并沿齿宽方向分列于接触曲线l2两侧；
进一步，所述凸齿齿轮的齿廓曲面包括曲面Σ1；所述凹齿齿轮的齿廓曲面包括相互平滑过渡的曲面Σ'1、曲面Σ'2和曲面Σ'3；
所述曲面Σ1的方程为：
Figure PCTCN2016072279-appb-000022
式中，
Figure PCTCN2016072279-appb-000023
其中rc表示圆柱螺旋线所在的圆柱半径，θc表示圆柱螺旋线的曲线参数，pc表示螺旋参数；h1c表示啮合管齿面半径，nx1c、ny1c和nz1c分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000024
和αc分别表示一般球面参数；
所述曲面Σ'1的方程为：
Figure PCTCN2016072279-appb-000025
式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X为正，齿廓圆心位于齿轮节圆柱之内X为负；齿廓圆心位于齿形对称轴线的异侧L为正，同侧L为负；
所述曲面Σ'2的方程为：
Figure PCTCN2016072279-appb-000026
所述曲面Σ'3的方程为：
Figure PCTCN2016072279-appb-000027
式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X’为正，齿廓圆心位于齿轮节圆柱之内X’为负；齿廓圆心位于齿形对称轴线的异侧L’为正，同侧L’为负；
进一步，所述凸齿齿轮和凹齿齿轮的啮合点为5个并分别为啮合点p1、啮合点p2、啮合点p3啮合点p4以及啮合点p5；所述凸齿齿轮或凹齿齿轮的齿廓曲面上由啮合点构成的三条接触曲线分别为接触曲线l1、接触曲线l2和接触曲线l3；所述啮合点p1以及啮合点p2分布于接触曲线l1上，啮合点p3分布于接触曲线l2上，啮合点p4以及啮合点p5分布于接触曲线l3上；接触曲线l2为圆弧曲线，所述接触曲线l1以及接触曲线l3均为二次抛物曲线并沿齿宽方向分列于接触曲线l2两侧；
进一步，所述凸齿齿轮的齿廓曲面包括曲面Σ1；所述凹齿齿轮的齿廓曲面包括相互平滑过渡的曲面Σ'1、曲面Σ'2和曲面Σ'3；
所述曲面Σ1的方程为：
Figure PCTCN2016072279-appb-000028
式中
Figure PCTCN2016072279-appb-000029
其中rm表示圆柱螺旋线所在的圆柱半径，θm表示圆柱螺旋线的曲线参数，pm表示螺旋参数；h1m表示啮合管齿面半径，nx1m、ny1m和nz1m分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000030
和αm分别表示一般球面参数；
所述曲面Σ'1的方程为：
Figure PCTCN2016072279-appb-000031
所述曲面Σ'2的方程为：
Figure PCTCN2016072279-appb-000032
式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X为正，齿廓圆心位于齿轮节圆柱之内X为负；齿廓圆心位于齿形对称轴线的异侧L为正，同侧L为负；
所述曲面Σ'3的方程为：
Figure PCTCN2016072279-appb-000033
本发明的有益效果是：本发明的基于共轭曲线的多点接触圆柱齿轮啮合副，啮合副的啮合方式为凸齿齿轮齿面与凹齿齿轮齿面同时多点接触，接触点在各齿面的接触轨迹均为光滑的空间曲线。该传动继承了共轭曲线的啮合特点，并且点接触的齿廓接触强度高、承载能力大、传动效率高、润滑油温升低、滑动 率大幅降低、磨损小，同时，可根据使用需求不同，运用不同的接触曲线实现齿轮啮合时同时具有一点、两点或者多点接触，解决了现有采用齿廓曲面均为球心沿圆心曲线运动的球族管状包络面的点接触齿轮在啮合时只具有一点接触的限制，因此，基于共轭曲线的多点接触齿轮传动是一种应用前景广阔的高性能齿轮传动。
附图说明
下面结合附图和实施例对本发明作进一步描述：
图1为本发明的具有三点接触的圆柱齿轮的齿面结构示意图；
图2为本发明的具有三点接触的圆柱齿轮的啮合示意图；
图3为本发明的具有三点接触的圆柱齿轮的齿廓曲面推导示意图；
图4为本发明的具有局部四点接触的圆柱齿轮的齿面结构示意图；
图5为本发明的具有局部四点接触的圆柱齿轮的啮合示意图；
图6为本发明的具有沿全齿宽方向四点对称接触的圆柱齿轮的齿面结构示意图；
图7为本发明的具有沿全齿宽方向四点对称接触的圆柱齿轮的啮合示意图；
图8为本发明的具有四点接触的圆柱齿轮的齿廓曲面推导示意图；
图9为本发明的具有五点对称接触的圆柱齿轮的齿面结构示意图；
图10为本发明的具有五点对称接触的圆柱齿轮的啮合示意图；
图11为本发明的具有五点对称接触的齿廓曲面推导示意图。
具体实施方式
如图1、图2、图3所示的实施例中，在齿面局部异截面内选取三段齿廓曲线为圆弧曲线形式，确定最优点接触压力角以实现在不同截面的一般分布三点接触。如图1、2所示，基于共轭曲线啮合理论构建的凸、凹管状啮合齿面形成配对啮合副，啮合副在轴向方向沿接触点轨迹运动，两者在齿面局部异截面内呈一般三点接触；
选用圆柱螺旋线作为齿面共轭接触曲线。如图3所示，在空间坐标系下l1、 l2和l3分别为圆柱面上的三条螺旋曲线，满足曲线l2相对曲线l1绕中心轴线旋转角度Δθ1，满足曲线l3相对曲线l1绕中心轴线旋转角度Δθ2。
假定圆柱螺旋线l1的曲线方程为
Figure PCTCN2016072279-appb-000034
其中r表示圆柱螺旋线l1半径，θ1表示圆柱螺旋线l1的曲线参数，其取值范围为θ1i≤θ1≤θ1o，p表示圆柱螺旋线的螺旋参数。
曲线l2相对曲线l1绕中心轴线旋转角度Δθ1，基于坐标变换矩阵，可得圆柱螺旋线l2的曲线方程为
Figure PCTCN2016072279-appb-000035
同理，曲线l3相对曲线l1绕中心轴线旋转角度Δθ2，基于坐标变换矩阵，可得圆柱螺旋线l3的曲线方程为
Figure PCTCN2016072279-appb-000036
三个接触点在齿面上的运行轨迹分别为圆柱螺旋线l1、l2和l3，特别注意地是，应当满足三个接触点不在同一截面内，即呈异截面分布，该齿面主要包括三段曲面：
(1)已知圆柱螺旋线l1的表达式，基于啮合管齿面构建理论与方法，可得曲线l1成形的曲面Σ1方程为
Figure PCTCN2016072279-appb-000037
式中
其中符号“±”分别表示可成形凸、凹管状啮合齿面，h1表示所成形的啮合管齿面半径，nx1、ny1和nz1分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000039
和α1分别表示一般球面L1参数。
(2)已知圆柱螺旋线l2的表达式，基于啮合管齿面构建理论与方法，可得曲线l2成形的曲面Σ2方程为
Figure PCTCN2016072279-appb-000040
式中
Figure PCTCN2016072279-appb-000041
其中符号“±”分别表示可成形凸、凹管状啮合齿面，h2表示所成形的啮合管齿面半径，nx2、ny2和nz2分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000042
和α2分别表示一般球面L2参数。
(3)已知圆柱螺旋线l3的表达式，基于啮合管齿面构建理论与方法，可得曲线l3成形的曲面Σ3方程为
Figure PCTCN2016072279-appb-000043
式中
Figure PCTCN2016072279-appb-000044
其中符号“±”分别表示可成形凸、凹管状啮合齿面，h3表示所成形的啮合管齿面半径，nx3、ny3和nz3分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000045
和α3分别表示一般球面L3参数。
如图4、图5所示的另一个实施例中，在齿面局部异截面内选取三段齿廓曲线，前后两段齿廓曲线为圆弧曲线形式，中间齿廓曲线为二次抛物曲线形式，确定最优点接触压力角以实现局部四点对称接触。如图5所示，基于共轭曲线啮合理论构建的凸、凹管状啮合齿面形成配对啮合副，啮合副在轴向方向沿接触点轨迹运动，两者在齿面局部异截面内呈局部四点对称接触。
如图6、图7所示的另一个实施例中，在齿面沿齿宽方向的不同截面内选取不同段齿廓曲线，前后两段齿廓曲线为圆弧曲线形式，中间齿廓曲线为二次抛物曲线形式，确定最优点接触压力角以实现沿齿宽方向四点对称接触。如图7所示，基于共轭曲线啮合理论构建的凸、凹管状啮合齿面形成配对啮合副，啮合副在轴向方向沿接触点轨迹运动，两者在沿齿宽方向呈四点对称接触。
如图8所示，在轮齿齿面上选取三段齿廓曲线，其中前、后两段齿廓曲线为圆弧曲线形式，中间齿廓曲线为二次抛物曲线形式。啮合过程中，圆弧齿廓在各自截面区域内呈单点接触，抛物线齿廓在其截面区域内呈双点接触，啮合副构成四点接触状态。
(1)凸齿面
凸齿面全部采用圆弧齿廓形式，其齿面一般方程可参考啮合管齿面形成方法，进一步表示为
Figure PCTCN2016072279-appb-000046
式中
Figure PCTCN2016072279-appb-000047
其中rc表示圆柱螺旋线所在的圆柱半径，θc表示圆柱螺旋线的曲线参数，pc表示螺旋参数；h1c表示啮合管齿面半径，nx1c、ny1c和nz1c分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000048
和αc分别表示一般球面参数。
(2)凹齿面
凹齿面由三部分组成，包括圆弧齿廓c1段、抛物线齿廓c2段和圆弧齿廓c3段。
1)圆弧齿廓c1段齿面方程
假定圆弧齿廓c1表示为
Figure PCTCN2016072279-appb-000049
其中ρ表示圆弧齿廓半径；α表示齿形角，决定了接触点在圆弧中的位置；X，L分别表示圆弧中心距离坐标系y轴和x轴的距离。
采用齿轮啮合理论运动学方法推导齿面方程，法面圆弧齿廓c1做螺旋运动形成的齿面∑1方程为
Figure PCTCN2016072279-appb-000050
式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X为正，齿廓圆心位于齿轮节圆柱之内X为负；齿廓圆心位于齿形对称轴线的异侧L为正，同侧L为负。
2)二次抛物线齿廓c2段齿面方程
假定二次抛物线齿廓c2表示为
Figure PCTCN2016072279-appb-000051
式中t为自变量参数；A为抛物线参数，且为A＝ρcosα。
同理，二次抛物线齿廓做螺旋运动形成的齿面∑2方程为
Figure PCTCN2016072279-appb-000052
3)圆弧齿廓c3段齿面方程
圆弧齿廓c3段齿面方程与圆弧齿廓c1段齿面方程推导方法相同，假定圆弧齿廓c3表示为
Figure PCTCN2016072279-appb-000053
其中ρ'表示圆弧齿廓半径；α'表示齿形角，决定了接触点在圆弧中的位置；X’，L’分别表示圆弧中心距离坐标系y轴和x轴的距离。
采用齿轮啮合理论运动学方法推导齿面方程，法面圆弧齿廓c3做螺旋运动形成的齿面∑3方程为
Figure PCTCN2016072279-appb-000054
式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X’为正，齿廓圆心位于齿轮节圆柱之内X’为负；齿廓圆心位于齿形对称轴线的异侧L’为正，同侧L’为负。
综上，当两段圆弧齿廓与中部二次抛物线齿廓分布较紧密时可实现局部四点对称接触；当两段圆弧齿廓与中部二次抛物线齿廓分布沿全齿宽方向时可实现沿全齿宽方向四点对称接触。
如图9、10、11所示的实施例中，在齿面沿齿宽方向的不同截面内选取不同段齿廓曲线，前后两段齿廓曲线为二次抛物曲线形式，中间齿廓曲线为圆弧曲线形式，确定最优点接触压力角以实现沿齿宽方向的对称五点接触。如图10所示，基于共轭曲线啮合理论构建的凸、凹管状啮合齿面形成配对啮合副，啮合副在轴向方向沿接触点轨迹运动，两者在沿齿宽方向呈五点对称接触。
齿面方程：
在轮齿齿面上选取三段齿廓曲线，其中前后两段齿廓曲线为二次抛物曲线形式，中间齿廓曲线为圆弧曲线形式。啮合过程中，圆弧齿廓在各自截面区域内呈单点接触，抛物线齿廓在其截面区域内呈双点接触，啮合副构成五点接触状态。
(1)凸齿面
凸齿面仍全部采用圆弧齿廓形式，其齿面方程参考啮合管齿面成形方法，表示为
Figure PCTCN2016072279-appb-000055
式中
Figure PCTCN2016072279-appb-000056
其中rm表示圆柱螺旋线所在的圆柱半径，θm表示圆柱螺旋线的曲线参数，pm表示螺旋参数；h1m表示啮合管齿面半径，nx1m、ny1m和nz1m分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
Figure PCTCN2016072279-appb-000057
和αm分别表示一般球面参数。
(2)凹齿面
凹齿面由三部分组成，包括二次抛物线齿廓m1段、圆弧齿廓m2段和二次抛物线齿廓m3段。
1)二次抛物线齿廓m1段齿面方程
假定二次抛物线齿廓m1表示为
Figure PCTCN2016072279-appb-000058
式中t为自变量参数；A为抛物线参数，且为A＝ρcosα。
同理，二次抛物线齿廓做螺旋运动形成的齿面∑1方程为
Figure PCTCN2016072279-appb-000059
2)圆弧齿廓m2段齿面方程
假定圆弧齿廓m2表示为
Figure PCTCN2016072279-appb-000060
其中ρ表示圆弧齿廓半径；α表示齿形角，决定了接触点在圆弧中的位置；X，L分别表示圆弧中心距离坐标系y轴和x轴的距离。
采用齿轮啮合理论运动学方法推导齿面方程，法面圆弧齿廓c1做螺旋运动形成的齿面∑2方程为
Figure PCTCN2016072279-appb-000061
式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X为正，齿廓圆心位于齿轮节圆柱之内X为负；齿廓圆心位于齿形对称轴线的异侧L为正，同侧L为负。
3)二次抛物线齿廓m3段齿面方程
假定二次抛物线齿廓m3表示为
Figure PCTCN2016072279-appb-000062
式中t'为自变量参数；A'为抛物线参数，且为A'＝ρcosα。
同理，二次抛物线齿廓做螺旋运动形成的齿面∑3方程为
Figure PCTCN2016072279-appb-000063
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，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本发明技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。

Claims (8)

  1. 一种基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：包括相互点啮合的凸齿齿轮和凹齿齿轮且啮合点为多个，所述凸齿齿轮和凹齿齿轮的啮合曲面为管状曲面。
  2. 根据权利要求1所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮和凹齿齿轮的啮合点为3个且啮合点分布于其齿廓的不同截面上。
  3. 根据权利要求2所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮或凹齿齿轮的齿廓曲面上由啮合点构成的三条接触曲线分别为接触曲线l1、接触曲线l2和接触曲线l3；
    所述接触曲线l1的曲线方程为：
    Figure PCTCN2016072279-appb-100001
    其中r为圆柱螺旋线l1半径，θ1为圆柱螺旋线l1的曲线参数，其取值范围为θ1i≤θ1≤θ1o，p为圆柱螺旋线的螺旋参数；
    所述接触曲线l2的曲线方程为：
    Figure PCTCN2016072279-appb-100002
    其中r为圆柱螺旋线l1半径，θ1为圆柱螺旋线l1的曲线参数，其取值范围为θ1i≤θ1≤θ1o，p为圆柱螺旋线的螺旋参数；
    所述接触曲线l3的曲线方程为：
    Figure PCTCN2016072279-appb-100003
    其中r为圆柱螺旋线l1半径，θ1为圆柱螺旋线l1的曲线参数，其取值范围 为θ1i≤θ1≤θ1o，p为圆柱螺旋线的螺旋参数。
  4. 根据权利要求2所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮的齿廓曲面包括曲面Σ1、曲面Σ2和曲面Σ3；所述凹齿齿轮的齿廓曲面包括曲面Σ'1、曲面Σ'2和曲面Σ'3；
    所述曲面Σ1方程为：
    Figure PCTCN2016072279-appb-100004
    式中
    Figure PCTCN2016072279-appb-100005
    Figure PCTCN2016072279-appb-100006
    Figure PCTCN2016072279-appb-100007
    其中h1为所述齿廓曲面的半径，nx1、ny1和nz1分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100008
    和α1分别表示一般球面L1参数；
    所述曲面Σ2方程为：
    Figure PCTCN2016072279-appb-100009
    式中
    Figure PCTCN2016072279-appb-100010
    Figure PCTCN2016072279-appb-100011
    Figure PCTCN2016072279-appb-100012
    其中h2为所述齿廓曲面的半径，nx2、ny2和nz2分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100013
    和α2分别表示一般球面L2参数；
    所述曲面Σ3方程为：
    Figure PCTCN2016072279-appb-100014
    式中
    Figure PCTCN2016072279-appb-100015
    Figure PCTCN2016072279-appb-100016
    Figure PCTCN2016072279-appb-100017
    其中h3为所述齿廓曲面的半径，nx3、ny3和nz3分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100018
    和α3分别表示一般球面L3参数；
    所述曲面Σ'1方程为：
    Figure PCTCN2016072279-appb-100019
    式中
    Figure PCTCN2016072279-appb-100020
    Figure PCTCN2016072279-appb-100021
    Figure PCTCN2016072279-appb-100022
    其中h1为所述齿廓曲面的半径，nx1、ny1和nz1分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100023
    和α1分别表示一般球面L1参数；
    所述曲面Σ'2方程为：
    Figure PCTCN2016072279-appb-100024
    式中
    Figure PCTCN2016072279-appb-100025
    Figure PCTCN2016072279-appb-100026
    Figure PCTCN2016072279-appb-100027
    其中h2为所述齿廓曲面的半径，nx2、ny2和nz2分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100028
    和α2分别表示一般球面L2参数；
    所述曲面Σ'3方程为：
    Figure PCTCN2016072279-appb-100029
    式中
    Figure PCTCN2016072279-appb-100030
    Figure PCTCN2016072279-appb-100031
    Figure PCTCN2016072279-appb-100032
    其中h3为所述齿廓曲面的半径，nx3、ny3和nz3分别表示该段齿廓曲面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100033
    和α3分别表示一般球面L3参数。
  5. 根据权利要求1所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮和凹齿齿轮的啮合点为4个并分别为啮合点p1、啮合点p2、啮合点p3和啮合点p4；所述凸齿齿轮或凹齿齿轮的齿廓曲面上由啮合点构成的三条接触曲线分别为接触曲线l1、接触曲线l2和接触曲线l3；所述啮合点p1分布于接触曲线l1上，啮合点p2以及啮合点p3分布于接触曲线l2上，啮合点p4分布于接触曲线l3上；所述接触曲线l2为二次抛物曲线，接触曲线l1和接触曲线l3均为圆弧曲线并沿齿宽方向分列于接触曲线l2两侧。
  6. 根据权利要求5所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮的齿廓曲面包括曲面Σ1；所述凹齿齿轮的齿廓曲面包括 相互平滑过渡的曲面Σ'1、曲面Σ'2和曲面Σ'3；
    所述曲面Σ1的方程为：
    Figure PCTCN2016072279-appb-100034
    式中，
    Figure PCTCN2016072279-appb-100035
    Figure PCTCN2016072279-appb-100036
    Figure PCTCN2016072279-appb-100037
    其中rc表示圆柱螺旋线所在的圆柱半径，θc表示圆柱螺旋线的曲线参数，pc表示螺旋参数；h1c表示啮合管齿面半径，nx1c、ny1c和nz1c分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100038
    和αc分别表示一般球面参数；
    所述曲面Σ'1的方程为：
    Figure PCTCN2016072279-appb-100039
    式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X为正，齿廓圆心位于齿轮节圆柱之内X为负；齿廓圆心位于齿形对称轴线的异侧L为正，同侧L为负；
    所述曲面Σ'2的方程为：
    Figure PCTCN2016072279-appb-100040
    所述曲面Σ'3的方程为：
    Figure PCTCN2016072279-appb-100041
    式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X’为正，齿廓圆心位于齿轮节圆柱之内X’为负；齿廓圆心位于齿形对称轴线的异侧L’为正，同侧L’为负。
  7. 根据权利要求1所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮和凹齿齿轮的啮合点为5个并分别为啮合点p1、啮合点p2、啮合点p3啮合点p4以及啮合点p5；所述凸齿齿轮或凹齿齿轮的齿廓曲面上由啮合点构成的三条接触曲线分别为接触曲线l1、接触曲线l2和接触曲线l3；所述啮合点p1以及啮合点p2分布于接触曲线l1上，啮合点p3分布于接触曲线l2上，啮合点p4以及啮合点p5分布于接触曲线l3上；接触曲线l2为圆弧曲线，所述接触曲线l1以及接触曲线l3均为二次抛物曲线并沿齿宽方向分列于接触曲线l2两侧。
  8. 根据权利要求7所述的基于共轭曲线的多点接触圆柱齿轮啮合副，其特征在于：所述凸齿齿轮的齿廓曲面包括曲面Σ1；所述凹齿齿轮的齿廓曲面包括相互平滑过渡的曲面Σ'1、曲面Σ'2和曲面Σ'3；
    所述曲面Σ1的方程为：
    Figure PCTCN2016072279-appb-100042
    式中
    Figure PCTCN2016072279-appb-100043
    Figure PCTCN2016072279-appb-100044
    Figure PCTCN2016072279-appb-100045
    其中rm表示圆柱螺旋线所在的圆柱半径，θm表示圆柱螺旋线的曲线参数，pm表示螺旋参数；h1m表示啮合管齿面半径，nx1m、ny1m和nz1m分别表示该段啮合管齿面过接触点处的法矢量在各坐标轴方向上的分量，参数
    Figure PCTCN2016072279-appb-100046
    和αm分别表示一般球面参数；
    所述曲面Σ'1的方程为：
    Figure PCTCN2016072279-appb-100047
    所述曲面Σ'2的方程为：
    Figure PCTCN2016072279-appb-100048
    式中，φ1为齿轮旋转角度，r1为齿轮节圆柱半径，β为轮齿螺旋角。齿廓圆心位于齿轮节圆柱之外X为正，齿廓圆心位于齿轮节圆柱之内X为负；齿廓圆心位于齿形对称轴线的异侧L为正，同侧L为负；
    所述曲面Σ'3的方程为：
    Figure PCTCN2016072279-appb-100049
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