Harmonic gear meshing pair with cycloid tooth profile and design method of harmonic gear meshing pair

Abstract

The invention relates to a harmonic gear meshing pair with a cycloid tooth profile and a design method of the harmonic gear meshing pair, and belongs to the technical field of mechanical transmission. The tooth profile of the harmonic gear meshing pair is mainly composed of a flexible gear profile, a rigid gear profile and a wave generator profile. Wherein the end face tooth profile or the normal face tooth profile of the flexible gear is a cycloid tooth profile, the cycloid tooth profile is formed by combining a cycloid curve section and an arc curve section, and the tooth profiles at the two ends are in smooth connection; the rigid gear is a thin-wall internal gear, and the tooth profile is an arc tooth profile or is obtained through enveloping calculation of the tooth profile of the deformed flexible gear; the contour of the wave generator is an elliptic curve. According to the harmonic gear meshing pair, the multi-tooth meshing characteristic is brought into full play in the meshing process, meanwhile, the number of meshed teeth accounts for 50% or above of the total tooth number, and the transmission precision and the bearing capacity of harmonic gears can be effectively improved.

Description

Technical Field

[0001] The invention relates to a harmonic gear meshing pair with a cycloid tooth profile and a design method thereof, belonging to the technical field of mechanical transmission. Background Art

[0002] Harmonic gear reducers are widely used in precision industries such as robotics, aerospace, etc. due to their advantages of high reduction ratio, small size, light weight, high precision, small tooth gap, high efficiency and low noise. The meshing pair of harmonic gears mainly relies on the thin-walled flexible wheel to produce continuous and controllable elastic deformation under the action of the wave generator to achieve meshing with the rigid wheel tooth profile, thereby completing the transmission of speed and torque. In order to achieve or improve the meshing performance of gear teeth in harmonic transmission, involute, circular arc and double circular arc tooth profiles are all applied to harmonic gear tooth profiles in the prior art. For example, 1) Chinese patent, publication number CN102959275B, patent name "wave gear device with three-dimensional contact involute positive offset tooth shape", its tapered flexible wheel teeth move the main section tooth profile along the tapered tooth line offset to achieve the line contact state between the flexible wheel teeth and the rigid wheel teeth in some areas along the tooth width direction. 2) Chinese patent, publication number: CN104074948B, the patent name is "A cup-type harmonic gear with a tangent-type double-arc tooth profile and its tooth profile design method". This patent comprehensively considers the multiple sets of conjugate points formed by the flexwheel tooth profile in different cross-sectional trajectories at the front, middle and rear, and designs a rigid wheel tooth profile that satisfies continuous conjugation and does not produce interference. In this solution, the flexwheel and the rigid wheel tooth surfaces are in point contact, and there is still a lot of room for improvement in the conjugate meshing range and the number of meshing teeth. 3) Chinese patent, publication number: CN110020509A, the patent name is "A harmonic gear with a variable coefficient cycloid tooth profile". The rigid wheel and the flexwheel with a variable coefficient cycloid tooth profile have line contact in the tooth surface contact during the meshing process. 4) U.S. Patent, Publication No.: US5458023, Patent Name: "Flexing contact type gear drive of non-profile-shifted two-circular-arc composite tooth profile", This patent proposes a combined double arc tooth profile from the perspective of easy processing, taking into account the taper characteristics of the flex spline deformation, and using a linear mapping with a 1 / 2 reduction ratio to obtain the flex spline tooth profile by double arc fitting on the basis of the s-tooth shape. The rigid gear tooth profile is obtained by connecting the motion trajectory of the flex spline near the rear section and the approximate motion trajectory envelope of the machined flex spline rack, which can achieve continuous meshing transmission.

[0003] The above patent 1) "wave gear device with three-dimensional contact involute positive offset tooth profile" mainly solves the contact problem of the involute tooth profile in the tooth width direction, that is, the axial line contact problem; patent 2) "a cup-type harmonic gear with a common tangent type double arc tooth profile and its tooth profile design method" needs further improvement to solve the axial line contact problem; the cycloid in patent 3) "a harmonic gear with a variable coefficient cycloid tooth profile" is also called a cycloid or a circular roller line, and the entire tooth profile is composed of two cycloids in the upper and lower parts; patent 4) "flexing contact type gear drive of non-profile-shiftedtwo-circular-arc composite tooth profile" is based on the mapping principle and takes processing issues into consideration. The tooth profile of the harmonic drive mainly meets the meshing transmission from two aspects, one is the meshing transmission in the end face, and the other is the line contact caused by axial deformation that puts higher requirements on the tooth profile. The tooth profile has a significant impact on the meshing performance and transmission accuracy of the harmonic gear meshing pair. Therefore, this technical field urgently needs to solve the technical problem of how to design a more reasonable and effective meshing pair tooth profile. Summary of the invention

[0004] The purpose of the present invention is to solve the technical problem of how to design a more reasonable and effective meshing pair tooth profile. In order to achieve the purpose of solving this technical problem, the technical solution adopted by the present invention is to provide a harmonic gear meshing pair with a cycloid tooth profile with a variable cross-section. The meshing pair can be an approximate meshing pair or a meshing pair that accurately satisfies the meshing transmission, and can solve the line contact problem after axial deformation as needed.

[0005] The present invention provides a harmonic gear meshing pair with a variable cross-section, wherein the harmonic gear meshing pair comprises a cam, a flexible bearing, a neutral layer, a flexible wheel and a rigid wheel from the inside to the outside; the cam, the flexible bearing and the neutral layer constitute a wave generator;

[0006] The flexible wheel is a spur gear with a thin-walled cup-shaped or top-hat-shaped structure, and the flexible wheel tooth profile is a cycloid tooth profile with a variable cross-section. The rigid wheel is a spur cylindrical internal gear. In general approximate transmission, the rigid wheel tooth profile is a circular arc tooth profile with a variable circular cross-section; in precision transmission, the rigid wheel tooth profile is a spatial tooth profile that strictly satisfies the meshing transmission and is enveloping the cycloid tooth profile of the flexible wheel with a variable cross-section. The rigid wheel and the flexible wheel have the same module, and the rigid wheel has more teeth, and two-tooth difference meshing occurs under the action of the wave generator. The wave generator is mainly composed of a flexible bearing and a cam, and the cam profile is an elliptical equidistant curve.

[0007] The present invention provides a design method for a harmonic gear meshing cycloid tooth profile with a variable cross-section, the design method comprising the following steps:

[0008] Step 1: Determine the basic cycloid tooth profile of the main section of the flexspline according to the geometric parameters of the harmonic drive;

[0009] Step 2: Based on the axial deformation in the harmonic meshing pair, the radial deformation curve of the flex spline tooth root along the axial direction is fitted;

[0010] Step 3: Determine the variable cross-section arc tooth profile of the rigid wheel under approximate meshing;

[0011] Step 4: Based on the variable cross-section arc tooth profile of the lower meshing rigid wheel, the variable cross-section tooth profile of the flexible wheel is formed according to the cycloid forming principle;

[0012] Step 5: Based on the variable cross-section tooth profile of the flexible wheel and the envelope principle of harmonic transmission, a variable cross-section tooth profile of the rigid wheel under precise meshing is formed.

[0013] Preferably, the design method of the basic cycloid tooth profile of the main cross section of the flexspline in the above step 1 is as follows:

[0014] Step 1.1: Determine the modulus m and the number of teeth z of the designed harmonic gear g 、Number of flexspline teeth z r , tooth height and radial deformation w0, the cycloid tooth profile of the main section of the flexspline is given as formula (1):

[0015]

[0016] Among them, R is the radius of the needle tooth distribution circle, which is numerically larger than the root circle radius R of the steel wheel tooth. f2 ; r0 is the initial needle tooth radius for generating the cycloid, which is 1-2 times the module m; is the cycloid parameter; K1 is the short amplitude coefficient; w0 is the radial deformation; m is the modulus of the harmonic gear; z g 、z r are the number of teeth on the rigid wheel and the flexible wheel respectively; x 1f ,y 1f is the cycloid tooth profile coordinate of the main section of the flexspline.

[0017] Step 1.2: As shown in the attached figure of the specification, the preliminarily determined flexspline tooth profile D1M1 is a section of the cycloid c drawn by formula (1), the tooth tip transition tooth profile C1M1 is a transition arc, and the transition tooth profile C1M1 is tangent to the flexspline tooth tip circle and the tooth profile D1M1 at the same time, and the center of the circle O d On the symmetrical center line S1-S1 of the flexspline teeth, it forms an angle a101 with the symmetrical center line S2-S2 of the flexspline tooth grooves. The value of angle a101 is π / z r , complete the design of the cycloidal tooth profile of the flexible wheel main section on the main section BB.

[0018] Preferably, the radial deformation curve in the above step 2 is obtained by finite element analysis or numerical analysis, specifically: as shown in the accompanying drawings of the specification, based on the radial deformation curve bb obtained by the cycloid tooth profile design method of the main section of the flexible wheel on the axial section AA of the gear, the meshing curve f(z) is obtained by coordinate change and numerical fitting, expressed in the coordinate system {Y r ,O r ,Z r}, the origin of the coordinate system is O r , the distance between the outer end face of the rigid wheel and the center of the rigid wheel is r ma +h, Y r The axis coincides with the long axis of the neutral layer, Z r The axis is parallel to the central axis OO of the rigid wheel; the magnitude of its value reflects the change in the cup body affected by the warping of the wave generator relative to the given radial deformation w0, so that the radius r of the variable cross-section arc generated by the cycloid of each cross section of the rigid wheel in formula (2) can be determined;

[0019] The variable cross-section arc tooth profile of the rigid wheel is as follows:

[0020]

[0021] Where R is the radius of the pin tooth distribution circle; r0 is the initial pin tooth radius of the generated cycloid; r is the radius of the variable cross-section arc of the generated cycloid; θ is the arc parameter; f(z) is the radial deformation fitting curve of the flexspline tooth root along the axial direction; x 2a ,y 2a are the coordinates of the variable cross-section circular arc tooth profile of the rigid wheel.

[0022] Preferably, the design method of the variable cross-section circular arc tooth profile of the rigid wheel under approximate meshing in step 3 is as follows:

[0023] Step 3.1: Determine the module m and the number of teeth z of the designed harmonic gear g , tooth root radius R f2 , and give the parameters R and r in formula (2);

[0024] Step 3.2: As shown in the attached figure of the specification, the tooth profile C2M2 of each cross-section of the preliminarily determined rigid wheel is a section of the arc drawn by formula (2), the tooth root transition tooth profile D2M2 is a transition arc, and the transition tooth profile D2M2 is tangent to the rigid wheel tooth root circle and the tooth profile C2M2 at the same time, and the center of the circle O d 'On the symmetric center line S4-S4 of the steel wheel tooth groove, the angle a102 between it and the symmetric center line S3-S3 of the steel wheel tooth is π / z g , complete the design of the variable cross-section circular arc tooth profile of the rigid wheel under approximate meshing.

[0025] Preferably, the design method of the variable cross-section tooth profile of the flexspline in step 4 is as follows:

[0026] Replace the fixed arc radius r0 in equation (1) with the variable section arc radius r, and give equation (3). According to the cycloid formation principle, the design of the flexspline variable section cycloid tooth profile under approximate meshing is completed.

[0027]

[0028] Among them, R is the radius of the needle tooth distribution circle; r is the radius of the variable cross-section arc that generates the cycloid; is the cycloid parameter; K1 is the short amplitude coefficient; w0 is the radial deformation; m is the modulus of the harmonic gear; z g 、z r are the number of teeth on the rigid wheel and the flexible wheel respectively; x 1f ',y 1f 'Coordinates of the flexspline variable cross-section cycloid tooth profile under approximate meshing.

[0029] Preferably, the variable cross-section tooth profile of the rigid wheel under precision meshing in step 5 and the design method thereof are as follows:

[0030] As shown in the attached drawings of the specification, the flexspline tooth profile D1M1 is transformed from the flexspline coordinate system {X t ,O t ,Y t} is transformed to the rigid wheel coordinate system {X2, O2, Y2}, and the tooth profile equation (5) of the flexible wheel variable cross-section tooth profile in the rigid wheel coordinate system {X2, O2, Y2} is obtained. Then, through the meshing equation (6), the envelope solution is performed in the meshing area to obtain the discrete point coordinates of the rigid wheel tooth profile C2M2 in the precise meshing conjugate with the flexible wheel tooth profile D1M1. The tooth profile discrete points are fitted, and the complete rigid wheel tooth profile C2D2 is obtained through the arc D2M2 transition, completing the design of the rigid wheel variable cross-section precise meshing tooth profile.

[0031]

[0032] Among them, β is the angle between the rigid wheel moving coordinate system and the flexible wheel moving coordinate system; ρ is the radius vector of the flexible wheel moving coordinate system relative to the rigid wheel moving coordinate system; γ is the angle between the rigid wheel moving coordinate system and the radius vector ρ.

[0033]

[0034] Where β is the angle between the rigid wheel moving coordinate system and the flexible wheel moving coordinate system; ρ is the radius vector of the flexible wheel moving coordinate system relative to the rigid wheel moving coordinate system; γ is the angle between the rigid wheel moving coordinate system and the radius vector ρ; x 1f ',y 1f ' is the coordinate of the cycloid tooth profile of the flexible spline with variable cross-section under approximate meshing; x2 and y2 are the coordinates of the cycloid tooth profile of the flexible spline with variable cross-section converted to the rigid wheel coordinate system.

[0035] E cosμ+F sinμ=M

[0036]

[0037] Wherein, ρ is the radius vector of the flexible wheel moving coordinate system relative to the rigid wheel moving coordinate system; μ is the angle between the flexible wheel moving coordinate system and the radius vector ρ; They are β, ρ, and γ The derivative of α t is the pressure angle; x2 and y2 are the coordinates of the cycloid tooth profile of the flexible wheel with variable cross-section converted to the rigid wheel coordinate system; E, F, and M are intermediate parameters.

[0038] The flexspline tooth profile with variable cross-section is expressed in the coordinate system {X t ,O t ,Y t}, the origin of the coordinate system is O t , on the neutral layer of the flexspline gear ring, at the thickness of h / 2, h is the wall thickness from the flexspline tooth root to the flexspline inner wall; Y t The axis and the flexspline teeth symmetric center line S1-S1 coincide, X t The axis is tangent to the neutral layer;

[0039] The variable cross-section tooth profile of the rigid wheel is expressed in the coordinate system {X2, O2, Y2}, where the origin O2 of the coordinate system is on the central axis OO of the rigid wheel and coincides with the central axis of the cam, and the Y2 axis coincides with the symmetric midline S4-S4 of the rigid wheel tooth groove.

[0040] The present invention provides a harmonic gear meshing pair with a variable cross-section, wherein the harmonic gear meshing pair comprises a cam, a wave generator, a flexible bearing, a neutral layer, a flexible wheel and a rigid wheel from the inside to the outside; the design method of the cycloid tooth profile of the harmonic gear meshing pair is obtained according to the above method.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The present invention uses the cycloid tooth profile as the basic tooth profile of the flexible wheel. According to the actual deformation of the flexible wheel, the generation principle of the cycloid and the meshing characteristics of the two-tooth difference of the harmonic drive, the variable cross-section tooth profile considering the axial deformation can be approximately obtained, which can solve the three-dimensional design of the tooth profile of the harmonic meshing pair under approximate meshing. At the same time, further according to the conjugate motion of the harmonic drive, the variable cross-section precise rigid wheel conjugate space tooth profile obtained can meet the precise meshing requirements of the harmonic drive, and can solve the contact problem caused by the axial deformation of the flexible wheel, thereby effectively reducing the occurrence of tooth surface wear and effectively increasing the transmission accuracy and load-bearing capacity of the harmonic gear. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1It is a front view of a harmonic gear meshing pair with a cycloid tooth profile according to the present invention.

[0044] Figure 2 yes Figure 1 The cross-sectional view on the AA section is a schematic diagram of the deformation of a cup-type or top-hat-type harmonic reducer that undergoes axial warping after deformation.

[0045] Figure 3A is the main cross section of the flexspline ( Figure 2 Schematic diagram of the basic tooth structure of the cycloid tooth profile (section BB).

[0046] Figure 3B is the main cross section of the rigid wheel ( Figure 2 Schematic diagram of the basic tooth structure of the arc tooth profile (BB section).

[0047] Figure 4 It is the design principle diagram of the variable cross-section tooth profile of the rigid wheel.

[0048] Figure 5A is the flexspline coordinate system.

[0049] Figure 5B It is the rigid wheel coordinate system.

[0050] Figure 6 This is the principle diagram of the harmonic meshing pair.

[0051] Figure numerals: 1. Flexspline; 2. Rigid wheel; 3. Cam; 4. Flexible bearing; 5. Neutral layer; 10. Flexspline tooth profile; 11. Cycloid tooth profile; 20. Rigid wheel tooth profile; 21. Rigid wheel main section tooth profile; 22. Rigid wheel front section tooth profile; 23. Rigid wheel rear section tooth profile. DETAILED DESCRIPTION

[0052] In order to make the present invention more clearly understood, a preferred embodiment is described in detail with reference to the accompanying drawings as follows:

[0053] like Figure 1-6 As shown, the present invention provides a harmonic gear meshing pair with a cycloid tooth profile, which is composed of a flexible wheel 1, a rigid wheel 2, and a wave generator. It includes the flexible wheel 1, the rigid wheel 2, a cam 3, a flexible bearing 4, a flexible wheel tooth profile 10 with a variable cross-section cycloid tooth profile, a flexible wheel main cross-section tooth profile 11, a rigid wheel tooth profile 20 with a circular arc tooth profile with a variable circular cross-section, a rigid wheel main cross-section tooth profile 21, a rigid wheel front cross-section tooth profile 22, and a rigid wheel rear cross-section tooth profile 23;

[0054] The flexible wheel 1 is a spur gear with a thin-walled cup-shaped or top-hat-shaped structure, and the flexible wheel tooth profile 10 is a cycloidal tooth profile with a variable cross-section. The rigid wheel 2 is a spur cylindrical internal gear. In general approximate transmission, the rigid wheel tooth profile 20 is a circular arc tooth profile with a variable circular cross-section; in precision transmission, the rigid wheel tooth profile 20 is a spatial tooth profile that is enveloped by the flexible wheel tooth profile 10 and strictly satisfies the meshing transmission. The rigid wheel 2 and the flexible wheel 1 have the same module m, and the number of teeth of the rigid wheel 2 is 2 more than the number of teeth of the flexible wheel 1, and two-tooth difference meshing occurs under the action of the wave generator. The wave generator is mainly composed of a flexible bearing 4 and a cam 3. Under the action of the wave generator, the flexible wheel 1 undergoes elastic deformation, and its neutral layer 5 is elliptical, and the major semi-axis of the ellipse is r. ma , the minor semi-axis is r mb The profile of the cam 3 is also an ellipse, and is an equidistant curve of the ellipse curve after the neutral layer 5 is deformed.

[0055] The design steps of the variable cross-section cycloid tooth profile of the harmonic gear meshing pair are as follows:

[0056] 1. Determine the basic flexspline cycloid tooth profile 11 of the flexspline main section according to the geometric parameters of the harmonic drive;

[0057] 2. Based on the axial deformation in the harmonic meshing pair, the radial deformation curve f(z) of the flexspline 1 tooth root D1 along the axial direction is fitted;

[0058] 3. According to the arc radius r of the cycloid generated by each cross section of the rigid wheel 2, the variable cross section rigid wheel tooth profile 20 under approximate meshing is determined;

[0059] 4. Based on the variable cross-section rigid wheel tooth profile 20 of the approximately meshing lower rigid wheel 2, the variable cross-section flexible wheel tooth profile 10 is formed according to the cycloid forming principle;

[0060] 5. Based on the variable cross-section flexible wheel tooth profile 10 and the envelope principle of harmonic drive, a variable cross-section rigid wheel tooth profile 20 under precise meshing is formed.

[0061] The main cross-section cycloid tooth profile 11 of the flexible wheel 1 and its design method are as follows:

[0062] Determine the module m and the number of teeth z of the designed harmonic gear g 、Number of flexspline teeth z r , tooth height and radial deformation w0, giving the parameters R and r0 in formula (1).

[0063]

[0064] Where R is the radius of the pinion tooth distribution circle (slightly larger than the root circle radius R of the steel wheel tooth). f2), r0 is the initial pin tooth radius of the generated cycloid (valued at about 1-2 times the modulus m). The preliminarily determined tooth profile D1M1 of the flexspline 1 is a section of the cycloid c drawn by formula (1), the tooth top transition tooth profile C1M1 is a transition arc, and the transition tooth profile C1M1 is tangent to the flexspline tooth top circle and tooth profile D1M1 at the same time, and the center of the circle O d On the symmetrical center line S1-S1 of the flexspline teeth, it forms an angle a101 with the symmetrical center line S2-S2 of the flexspline tooth grooves. The value of angle a101 is π / z r , and complete the design of the flexspline main section cycloid tooth profile 11 on the main section BB.

[0065] The radial deformation curve f(z) of the flexspline tooth root D1 along the axial direction can be obtained by finite element analysis or numerical analysis, specifically, the radial deformation curve bb obtained by the design method of the flexspline main section cycloid tooth profile 11 on the section AA, and the meshing curve f(z) can be obtained by coordinate change and numerical fitting, which is expressed in the coordinate system {Y r ,O r ,Z r}, the origin of the coordinate system is O r , the distance between the outer end face of the rigid wheel and the center of the rigid wheel is r ma +h, Y r The axis coincides with the long axis of the neutral layer 5, Z r The axis is parallel to the central axis OO of the rigid wheel 2. The value of the value reflects the change in the cup body affected by the warping of the wave generator relative to the given radial deformation w0, so that the arc radius r of the cycloid generated by each cross section of the rigid wheel 2 in formula (2) can be determined.

[0066]

[0067] The variable cross-section steel wheel tooth profile 20 of the steel wheel 2 under the approximate meshing and the design method thereof are as follows:

[0068] Determine the module m and the number of teeth z of the designed harmonic gear g , tooth root radius R f2 , and give the parameters R and r in formula (2). The tooth profile C2M2 of each section of the rigid wheel 2 is initially determined to be a section of the arc drawn by formula (2), and the tooth root transition tooth profile D2M2 is a transition arc, and the transition tooth profile D2M2 is tangent to the rigid wheel tooth root circle and the tooth profile C2M2 at the same time, and the center O d 'On the symmetric center line S4-S4 of the steel wheel tooth groove, the angle a102 between it and the symmetric center line S3-S3 of the steel wheel tooth is π / z g , and complete the design of the variable cross-section circular arc tooth profile of the rigid wheel 20.

[0069] The variable cross-section tooth profile of the flexible wheel 1 and the design method thereof are as follows:

[0070] The fixed arc radius r0 in equation (1) is replaced by the variable cross-section arc radius r, and equation (3) is given. According to the cycloid formation principle, the design of the variable cross-section cycloid tooth profile 10 of the flexible wheel 1 under approximate meshing is completed.

[0071]

[0072] The variable cross-section tooth profile of the rigid wheel 2 under the precision meshing and the design method thereof are as follows:

[0073] The flexspline tooth profile D1M1 obtained by the design method of the flexspline tooth profile 10 with variable cross-section tooth profile of the flexspline 1 is converted from the flexspline coordinate system {X t ,O t ,Y t} is converted to the rigid wheel coordinate system {X2, O2, Y2}, and the tooth profile equation (5) of the flexible wheel 1 variable cross-section tooth profile flexible wheel tooth profile 10 in the rigid wheel coordinate system {X2, O2, Y2} is obtained. Then, through the meshing equation (6), the envelope solution is performed in the meshing area to obtain the discrete point coordinates of the rigid wheel 2 tooth profile C2M2 in precise meshing that is conjugate with the flexible wheel 1 tooth profile D1M1. The tooth profile discrete points are fitted, and the complete rigid wheel tooth profile C2D2 is obtained through the arc D2M2 transition, completing the design of the rigid wheel tooth profile 20 with variable cross-section precision meshing tooth profile of the rigid wheel 2.

[0074]

[0075] E cosμ+F sinμ=M

[0076]

[0077] The variable cross-section tooth profile of the flexible wheel 1 is expressed in the coordinate system {X t ,O t ,Y t}, the origin of the coordinate system is O t , on the neutral layer 5 of the gear ring of the flexspline 1 (at a thickness of about h / 2, where h is the thickness from the flexspline tooth root to the inner wall of the flexspline), Y t The axis and the flexspline teeth symmetric center line S1-S1 coincide, X t The axis is tangent to the neutral layer 5. The variable cross-section tooth profile of the rigid wheel 2 is expressed in the coordinate system {X2, O2, Y2}, the origin O2 of the coordinate system is on the central axis OO of the rigid wheel 2 and coincides with the central axis of the cam 3, and the Y2 axis coincides with the symmetric center line S4-S4 of the tooth groove of the rigid wheel 2.

[0078] As can be seen from the attached figure, the cycloid tooth profile of the variable cross-section harmonic gear meshing pair adopts the cycloid tooth profile as the basic tooth profile of the flexible wheel. The flexible wheel and the rigid wheel can approximately obtain the variable cross-section tooth profile considering the axial deformation according to the actual deformation of the flexible wheel, the generation principle of the cycloid and the two-tooth difference meshing characteristics of the harmonic transmission. Different tooth profiles are provided in each section to achieve the maximum range of conjugate meshing motion, which effectively solves the three-dimensional design of the tooth profile of the harmonic meshing pair under approximate meshing. Further modifying the tooth profile, the tooth profile of each section of the flexible wheel maintains continuous conjugate meshing with the rigid wheel tooth profile in the meshing area (φ=-45°~45°), which can meet the precise meshing requirements of the harmonic transmission and solve the contact problem caused by the axial deformation of the flexible wheel, thereby effectively reducing the occurrence of tooth surface wear and effectively increasing the transmission accuracy and load-bearing capacity of the harmonic gear. When processing the rigid wheel tooth profile, no special equipment is required, and the CNC machine tool can be used for processing. Two degrees of freedom are added to the development motion of the ordinary gear, and high processing accuracy and processing efficiency can be obtained while ensuring that the tool has sufficient straightness.

[0079] The present invention discloses a harmonic gear meshing pair with a cycloid tooth profile, which is mainly composed of a flexible wheel tooth profile, a rigid wheel tooth profile and a wave generator profile. The flexible wheel end face tooth profile or normal face tooth profile is a cycloid tooth profile, which is composed of a cycloid curve segment and a circular arc curve segment, and the tooth profiles at both ends are smoothly connected; the rigid wheel is a thin-walled internal gear, and the tooth profile is a circular arc tooth profile or calculated by the envelope of the deformed flexible wheel tooth profile; the wave generator profile is an elliptical curve. The harmonic gear meshing pair provided by the present invention can give full play to the multi-tooth meshing characteristics during the meshing process, and the number of meshing teeth accounts for more than 50% of the total number of teeth, which can effectively increase the transmission accuracy and load-bearing capacity of the harmonic gear.

[0080] The above is only a preferred embodiment of the present invention, and is not any formal or substantial limitation of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and supplements without departing from the present invention, and these improvements and supplements should also be regarded as the protection scope of the present invention. Any technician familiar with this profession, without departing from the spirit and scope of the present invention, can make some changes, modifications and equivalent changes made by using the technical content disclosed above, which are equivalent embodiments of the present invention; at the same time, any changes, modifications and evolutions of any equivalent changes made to the above embodiments based on the essential technology of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A design method for a cycloid tooth profile of a harmonic gear meshing pair with a variable cross-section, wherein the harmonic gear meshing pair comprises a cam, a flexible bearing, a neutral layer, a flexible wheel and a rigid wheel from the inside to the outside; the cam, the flexible bearing and the neutral layer constitute a wave generator; characterized in that: The design method comprises the following steps: Step 1: Determine the basic cycloid tooth profile of the main section of the flexspline according to the geometric parameters of the harmonic drive; Step 2: Based on the axial deformation in the harmonic meshing pair, the radial deformation curve of the flex spline tooth root along the axial direction is fitted; Step 3: Determine the variable cross-section arc tooth profile of the rigid wheel under approximate meshing; Step 4: Based on the variable cross-section arc tooth profile of the lower meshing rigid wheel, the variable cross-section tooth profile of the flexible wheel is formed according to the cycloid forming principle; Step 5: Based on the variable cross-section tooth profile of the flexible wheel and the envelope principle of harmonic transmission, a variable cross-section tooth profile of the rigid wheel under precise meshing is formed.

2. The design method of a harmonic gear meshing cycloid tooth profile with a variable cross-section according to claim 1, characterized in that: The design method of the basic cycloid tooth profile of the main cross section of the flexspline in step 1 is as follows: Step 1.1: Determine the modulus m and the number of teeth z of the designed harmonic gear g 、Number of flexspline teeth z r , tooth height and radial deformation w0, giving the parameters R and r0 in formula (1). Among them, R is the radius of the needle tooth distribution circle, which is numerically larger than the root circle radius R of the steel wheel tooth. f2 ; r0 is the initial needle tooth radius for generating the cycloid, which is 1-2 times the module m; is the cycloid parameter; K1 is the short amplitude coefficient; w0 is the radial deformation; m is the modulus of the harmonic gear; z g 、z r are the number of teeth on the rigid wheel and the flexible wheel respectively; x 1f ,y 1f is the cycloid tooth profile coordinate of the main section of the flexspline; Step 1.2: As shown in the attached figure of the specification, the preliminarily determined flexspline tooth profile D1M1 is a section of the cycloid c drawn by formula (1), the tooth tip transition tooth profile C1M1 is a transition arc, and the transition tooth profile C1M1 is tangent to the flexspline tooth tip circle and the tooth profile D1M1 at the same time, and the center of the circle O d On the symmetrical center line S1-S1 of the flexspline teeth, it forms an angle a101 with the symmetrical center line S2-S2 of the flexspline tooth grooves. The value of angle a101 is π / z r , complete the design of the cycloidal tooth profile of the flexible wheel main section on the main section BB.

3. The design method of the meshing secondary cycloid tooth profile of a harmonic gear with a variable cross-section according to claim 2, characterized in that: The radial deformation curve in step 2 is obtained by finite element analysis or numerical analysis, specifically: as shown in the accompanying drawings of the specification, based on the radial deformation curve bb obtained by the cycloid tooth profile design method of the main section of the flexible wheel on the axial section AA of the gear, the meshing curve f(z) is obtained by coordinate change and numerical fitting, expressed in the coordinate system {Y r ,O r ,Z r }, the origin of the coordinate system is O r , the distance between the outer end face of the rigid wheel and the center of the rigid wheel is r ma +h, Y r The axis coincides with the long axis of the neutral layer, Z r The axis is parallel to the central axis OO of the rigid wheel; the value of the value reflects the change in the cup body affected by the warping of the wave generator relative to the given radial deformation w0, so that the arc radius r of the cycloid generated by each section of the rigid wheel in formula (2) can be determined; the variable section arc tooth profile of the rigid wheel is formula (2): Where R is the radius of the pin tooth distribution circle; r0 is the initial pin tooth radius of the generated cycloid; r is the radius of the variable cross-section arc of the generated cycloid; θ is the arc parameter; f(z) is the radial deformation fitting curve of the flexspline tooth root along the axial direction; x 2a ,y 2a are the coordinates of the variable cross-section circular arc tooth profile of the rigid wheel.

4. The design method of the meshing secondary cycloid tooth profile of a harmonic gear with a variable cross-section according to claim 3, characterized in that: The design method of the variable cross-section circular arc tooth profile of the rigid wheel under approximate meshing in step 3 is as follows: Step 3.1: Determine the modulus m and the number of teeth z of the designed harmonic gear g , tooth root radius R f2 , and give the parameters R and r in formula (2); Step 3.2: As shown in the attached figure of the specification, the tooth profile C2M2 of each cross-section of the preliminarily determined rigid wheel is a section of the arc drawn by formula (2), the tooth root transition tooth profile D2M2 is a transition arc, and the transition tooth profile D2M2 is tangent to the rigid wheel tooth root circle and the tooth profile C2M2 at the same time, and the center of the circle O d 'On the symmetric center line S4-S4 of the steel wheel tooth groove, it has an angle a102 with the symmetric center line S3-S3 of the steel wheel tooth. The value of angle a102 is π / z g , complete the design of the variable cross-section circular arc tooth profile of the rigid wheel.

5. The design method of the meshing secondary cycloid tooth profile of a harmonic gear with a variable cross-section according to claim 4, characterized in that: The design method of the variable cross-section tooth profile of the flexspline in step 4 is as follows: Replace the fixed arc radius r0 in equation (1) with the variable section arc radius r, and give equation (3). According to the cycloid formation principle, the design of the flexspline variable section cycloid tooth profile under approximate meshing is completed. Among them, R is the radius of the needle tooth distribution circle; r is the radius of the variable cross-section arc that generates the cycloid; is the cycloid parameter; K1 is the short amplitude coefficient; w0 is the radial deformation; m is the modulus of the harmonic gear; z g 、z r are the number of teeth on the rigid wheel and the flexible wheel respectively; x 1f ',y 1f 'Coordinates of the flexspline variable cross-section cycloid tooth profile under approximate meshing.

6. The design method of the harmonic gear meshing secondary cycloid tooth profile with variable cross-section according to claim 5, characterized in that: The variable cross-section tooth profile of the rigid wheel under precision meshing in step 5 and the design method thereof are as follows: As shown in the attached drawings of the specification, the flexspline tooth profile D1M1 is transformed from the flexspline coordinate system {X t ,O t ,Y t } is transformed to the rigid wheel coordinate system {X2, O2, Y2}, and the tooth profile equation (5) of the flexible wheel variable cross-section tooth profile in the rigid wheel coordinate system {X2, O2, Y2} is obtained. Then, through the meshing equation (6), the envelope solution is performed in the meshing area to obtain the discrete point coordinates of the rigid wheel tooth profile C2M2 in the precise meshing conjugate with the flexible wheel tooth profile D1M1. The tooth profile discrete points are fitted, and the complete rigid wheel tooth profile C2D2 is obtained through the arc D2M2 transition, completing the design of the rigid wheel variable cross-section precise meshing tooth profile. Among them, β is the angle between the rigid wheel moving coordinate system and the flexible wheel moving coordinate system; ρ is the radius vector of the flexible wheel moving coordinate system relative to the rigid wheel moving coordinate system; γ is the angle between the rigid wheel moving coordinate system and the radius vector ρ; Where β is the angle between the rigid wheel moving coordinate system and the flexible wheel moving coordinate system; ρ is the radius vector of the flexible wheel moving coordinate system relative to the rigid wheel moving coordinate system; γ is the angle between the rigid wheel moving coordinate system and the radius vector ρ; x 1f ',y 1f ' is the coordinate of the flexspline variable cross-section cycloid tooth profile under approximate meshing; x2 and y2 are the coordinates of the flexspline variable cross-section cycloid tooth profile converted to the rigid wheel coordinate system; Ecosμ+Fsinμ=M Where ρ is the radius vector of the flexible wheel moving coordinate system relative to the rigid wheel moving coordinate system; μ is the angle between the flexible wheel moving coordinate system and the radius vector ρ; They are β, ρ, and γ Derived; α t is the pressure angle; x2 and y2 are the coordinates of the flexspline variable cross-section cycloid tooth profile converted to the rigid wheel coordinate system; E, F, and M are intermediate parameters; The flexspline tooth profile with variable cross-section is expressed in the coordinate system {X t ,O t ,Y t }, the origin of the coordinate system is O t , on the neutral layer of the flexspline gear ring, at the thickness of h / 2, h is the wall thickness from the flexspline tooth root to the flexspline inner wall; Y t The axis and the flexspline teeth symmetric center line S1-S1 coincide, X t The axis is tangent to the neutral layer; The variable cross-section tooth profile of the rigid wheel is expressed in the coordinate system {X2, O2, Y2}, where the origin O2 is on the center axis OO of the rigid wheel and coincides with the center axis of the cam, and the Y2 axis coincides with the symmetric center line S4-S4 of the rigid wheel tooth groove.

7. A harmonic gear meshing pair with a variable cross-section, the harmonic gear meshing pair comprising a cam, a wave generator, a flexible bearing, a neutral layer, a flexible wheel and a rigid wheel from the inside to the outside; characterized in that: The design method of the harmonic gear meshing sub-cycloid tooth profile is obtained according to the method described in any one of claims 1 to 6 above.

Images