Harmonic reducer space meshing tooth surface design method

Abstract

The invention relates to a method for designing a space meshing tooth surface of a harmonic reducer, which comprises the following steps of: bringing the influence of space deformation of a flexible gear cup body on a motion law of a harmonic gear into a consideration range for calculating the space tooth surface of the harmonic gear, and establishing a given straight line gamma1 on a fixed tooth surface and a conjugate curve gamma2, a meshing equation and a conjugate curve equation of the given straight line gamma1; and on the basis, correctly meshed rigid and flexible gear tooth surfaces are constructed. According to the harmonic gear designed and calculated through the method, inter-tooth interference is reduced, the number of meshing pairs is increased, the contact stress is reduced, and the service life is prolonged.

Description

Technical Field

[0001] The present invention relates to the technical field of harmonic reducers, and particularly to a method for designing the spatial meshing tooth surface of a harmonic reducer. Background Art

[0002] Harmonic gear transmission has many advantages such as simple structure, convenient installation, strong load capacity, high transmission efficiency, long service life, high transmission accuracy, low vibration and noise, etc., and is widely used in high-precision control fields such as aerospace vehicles, industrial robotic arms, humanoid robots, and medical devices. However, during the harmonic gear transmission process, due to the action of the wave generator, the spatial rotation angle generated by the spatial deformation of the flexspline cup causes the contact law between the rigid and flexspline to become difficult to solve. Currently, most scholars design the tooth profile of the harmonic gear by simplifying it into a planar conjugate tooth profile to replace the spatial tooth profile, or discretize the spatial tooth profile into multiple cross-sections for design. However, these design methods do not fundamentally consider the influence of the spatial deformation of the flexspline cup on the motion law of the harmonic gear. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for designing the spatial meshing tooth surface of a harmonic reducer to solve the problems existing in the above-mentioned prior art. The present invention incorporates the influence of the spatial deformation of the flexspline cup on the motion law of the harmonic gear into the consideration range of calculating the spatial tooth surface of the harmonic gear, solves the conjugate curve Γ2 of a given straight line Γ1 on a given tooth surface through numerical calculation, and constructs the required gear tooth surface by continuously varying the tooth profile of the required normal section along the curve Γ2 and intercepting it with the root cylinder and the tip cylinder. It reduces tooth interference, increases the number of meshing pairs, reduces the contact stress, and improves the service life.

[0004] To achieve the above purpose, the present invention provides the following solution:

[0005] A method for designing the spatial meshing tooth surface of a harmonic reducer includes:

[0006] Construct a spatial coordinate system and an auxiliary coordinate system for harmonic gear transmission; wherein, the spatial coordinate system for harmonic gear transmission is used to describe the relative motion between the flexspline, the rigid gear, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral surface of the flexspline; the auxiliary coordinate system is used to describe the position movement and the change of the coordinate axis orientation during the process of the conical deformation of the middle surface of the flexspline;

[0007] Based on the auxiliary coordinate system, assist the spatial coordinate system for harmonic gear transmission to construct a straight-tooth involute tooth surface equation;

[0008] Select a straight line Γ1 in the straight-tooth involute tooth surface equation;

[0009] Solve and obtain the conjugate curve Γ2 by the straight line Γ1 through the meshing equation and coordinate transformation;

[0010] Continuously construct a normal-consistent sectional tooth profile along the curve Γ2, and intercept to form the rigid gear tooth surface.

[0011] Optionally, the space coordinate system of the harmonic gear drive is as follows:

[0012] Establish a space coordinate system for the harmonic gear drive to describe the relative motion between the flexspline, the rigid spline, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral surface of the flexspline. Among them, S{O,X,Y,Z} is a moving coordinate system of the wave generator established with the rotation center O of the wave generator as the origin, and X is the major axis of the wave generator; S1{O1,X1,Y1,Z1} is a moving coordinate system of the flexspline teeth, the X1 axis is the symmetry line of the flexspline teeth, and the origin O1 is the intersection of the X1 axis and the neutral layer of the flexspline; S2{O2,X2,Y2,Z2} is a fixed coordinate system established with the rotation center O2 of the rigid spline as the origin.

[0013] The auxiliary coordinate system is as follows:

[0014] Establish an auxiliary coordinate system to describe the position movement and the change of the coordinate axis orientation during the taper deformation of the middle surface of the flexspline. Among them, (a) is that the deformation of the flexspline causes the origin O1 of the flexspline coordinate system to generate a radial displacement and a tangential displacement, moving from the Figure 1 point O1 in ′ to the point O1, that is, the auxiliary coordinate system S c , the X c axis is along the direction of OO1, and the Z c axis is parallel to the rotation axis Z axis of the wave generator; (b) is that the radial displacement ω causes the auxiliary coordinate system S c to rotate by an angle θ around the Y c axis to obtain the auxiliary coordinate system S b ; (c) is that the tangential displacement v causes the auxiliary coordinate system S b to rotate by an angle ξ around the X c axis of the coordinate system S c to obtain the auxiliary coordinate system S a ; (d) is that the normal rotation angle μ generated by the deformation of the flexspline causes the auxiliary coordinate system S a to rotate to the coordinate system S1.

[0015] Optionally, the straight-tooth involute tooth surface equation is:

[0016]

[0017] where u k is the rotation angle when the tool rolls without slipping along the pitch circle of the gear to be cut, θ k is half of the central line angle corresponding to the tooth thickness of the gear pitch circle, α0 is the reference tooth profile angle, x is the coordinate value on the x-axis, y is the coordinate value on the y-axis, and r is the radius of the neutral layer of the flexspline.

[0018] Optionally, the straight line Γ1 is:

[0019]

[0020] Among them, z is the coordinate value on the z-axis, and k0 is a constant.

[0021] Optionally, obtaining the conjugate curve Γ2 by solving the meshing equation and coordinate transformation for the straight line Γ1 includes:

[0022] Substitute the straight line Γ1 into the meshing equation, and obtain a conjugate curve Γ2 conjugate to the straight line Γ1 through coordinate transformation, and maintain point contact during the meshing process.

[0023] Optionally, the meshing equation is:

[0024]

[0025] Γ i (2) = M 21 · Γ i (1)

[0026] Among them, n i and are respectively the unit normal vector and the relative motion velocity vector at the contact point of the two conjugate surfaces. i is 1 or 2, Γ i (2) is the conjugate curve to be obtained, M 21 is the coordinate transformation matrix, and Γ i (1) is the given curve.

[0027] Optionally, continuously constructing a normal-consistent sectional tooth profile along the curve Γ2 and intercepting to form the rigid gear tooth surface includes:

[0028] On the normal plane of each point on the curve Γ2, construct a sectional tooth profile curve Γ c , and make the sectional tooth profile curve Γ c pass through this point and the principal normal vector direction at this point is consistent with the unit normal vector n i at the contact point. Intercept the tooth surface of the gear teeth through the addendum cylindrical surface and the dedendum cylindrical surface to finally form the rigid gear tooth surface.

[0029] Optionally, the output part is of a cup-shaped structure, and at this time the entire harmonic reducer is a cup-shaped harmonic reducer;

[0030] The output part is of a top hat-shaped structure, and at this time the entire harmonic reducer is a top hat-shaped harmonic reducer.

[0031] The beneficial effects of the present invention are:

[0032] The present invention first constructs a spatial coordinate system and an auxiliary coordinate system for harmonic gear transmission; secondly, based on the auxiliary coordinate system, it assists the spatial coordinate system of the harmonic gear transmission to construct a straight-tooth involute tooth surface equation; then, a straight line Γ1 is selected in the straight-tooth involute tooth surface equation; then, the conjugate curve Γ2 of the straight line Γ1 is obtained through the meshing equation and coordinate transformation; finally, a normal-consistent cross-sectional tooth profile is continuously constructed along the curve Γ2, and the rigid gear tooth surface is intercepted. The harmonic gear designed and calculated by the present invention reduces tooth interference, increases the number of meshing pairs, reduces the contact stress, and improves the service life.

[0033] Under the same parameters and working conditions, the number of meshing pairs is more, reduced from 17 pairs to 18 pairs of teeth, the contact position changes from the tooth tip R corner to the tooth side, which is more reasonable, the contact stress is smaller, reduced from 128 Mpa to 119 MPa, and the equivalent stress of the flexspline is lower, reduced from 464.57 Mpa to 421.39 MPa. Brief Description of the Drawings

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0035] Figure 1 Schematic diagram of the harmonic drive coordinate system for the embodiment of the present invention;

[0036] Figure 2 Schematic diagram of the harmonic drive auxiliary coordinate system for the embodiment of the present invention;

[0037] Figure 3 Schematic diagram of the straight line selection on the flexspline for the embodiment of the present invention;

[0038] Figure 4 Schematic diagram of the spatial curve solution for the embodiment of the present invention;

[0039] Figure 5 Schematic diagram of the tooth surface forming for the embodiment of the present invention;

[0040] Figure 6 Three-dimensional model established for the embodiment of the present invention;

[0041] Figure 7 Meshing state diagram of the flexspline and rigid gear at different rotation angles for the embodiment of the present invention;

[0042] Figure 8 Tooth surface contact stress comparison diagram for the embodiment of the present invention;

[0043] Figure 9The equivalent stress comparison diagram of the flexspline in the embodiment of the present invention. Detailed implementation manners

[0044] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0045] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0046] This embodiment proposes a method for designing the spatial meshing tooth surface of a harmonic reducer, including:

[0047] Construct a spatial coordinate system for harmonic gear transmission and an auxiliary coordinate system; wherein, the spatial coordinate system for harmonic gear transmission is used to describe the relative motion between the flexspline, the rigid gear, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral plane of the flexspline; the auxiliary coordinate system is used to describe the position movement and the change of the coordinate axis orientation during the taper deformation of the middle surface of the flexspline;

[0048] Based on the auxiliary coordinate system to assist the spatial coordinate system for harmonic gear transmission, construct a straight-tooth involute tooth surface equation;

[0049] Select a straight line Γ1 in the straight-tooth involute tooth surface equation;

[0050] Solve and obtain its conjugate curve Γ2 by the meshing equation and coordinate transformation for the straight line Γ1;

[0051] Continuously construct a normal-consistent sectional tooth profile along the curve Γ2, and intercept to form a line-surface meshing tooth surface.

[0052] Specifically, in this embodiment, a spatial coordinate system for harmonic gear transmission is established to describe the relative motion between the flexspline, the rigid gear, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral plane of the flexspline;

[0053] An auxiliary coordinate system is established to describe the position movement and the change of the coordinate axis orientation during the taper deformation of the middle surface of the flexspline;

[0054] Select a straight line Γ1 on the tooth surface of the flexspline, and its shape and parameters are determined by the surface parameter u k The selection method is diverse, and countless straight lines can be selected on the tooth surface of the flexspline;

[0055] Solve the curve conjugate to the straight line Γ1 by the meshing equation and obtain the conjugate curve Γ2 through coordinate transformation;

[0056] On the normal plane at each point of the curve Γ2 to be obtained, construct another curve Γ c As the cross-sectional tooth profile, the curve Γ c Passes through this point and the principal normal vector direction at this point is the same as the unit normal vector n at the contact point i When the curve Γ c Changes continuously along the curve Γ2, a continuous surface can be constructed. By intercepting with the addendum cylindrical surface and the dedendum cylindrical surface, it serves as the rigid gear tooth surface meshing with the given flexible gear tooth surface.

[0057] The present invention takes into account the spatial rotation angle generated by the spatial deformation of the flexible gear cup body in the design of the spatial tooth profile of the harmonic gear. On this basis, the correct meshing rigid and flexible gear tooth surfaces are constructed. And through the finite element analysis of this embodiment, it is proved that the harmonic gear designed and calculated by this method reduces the tooth interference, increases the number of meshing pairs, reduces the contact stress, and improves the service life.

[0058] Further, obtaining its conjugate curve Γ2 by solving the straight line Γ1 through the meshing equation and coordinate transformation includes:

[0059] Substitute the straight line Γ1 into the meshing equation, and through coordinate transformation, obtain a conjugate curve Γ2 conjugate to the straight line Γ1, and always maintain point contact during the meshing process.

[0060] Further, continuously constructing the normal-consistent cross-sectional tooth profile along the curve Γ2 and intercepting to form the rigid gear tooth surface includes:

[0061] On the normal plane at each point of the curve Γ2, construct the cross-sectional tooth profile curve Γ c , and make the cross-sectional tooth profile curve Γ c Pass through this point and the principal normal vector direction at this point is the same as the unit normal vector n at the contact point i Consistent. Intercept the tooth surface of the gear by the addendum cylindrical surface and the dedendum cylindrical surface, and finally form the rigid gear tooth surface.

[0062] This embodiment takes the involute harmonic gear drive with a wave generator as a standard elliptical cam as an example, and designs the rigid gear tooth surface through the given flexible gear tooth surface. The specific main parameters are as follows: module m = 0.4043 mm, number of teeth of the flexible gear z r = 100, number of teeth of the rigid gear z g = 102, radial deformation coefficient k = 0.8, total tooth height h = 1.1m, addendum height h a = 0.55m, dedendum height h f = 0.55m, the distance from the mouth to the bottom of the flexible gear cup is l = 26.5 mm, and the torque applied to the rigid gear is T = 44 N·m.

[0063] A spatial coordinate system of the harmonic gear drive is established to describe the relative motion among the flexspline, the rigid spline, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral surface of the flexspline. As Figure 1 shown, where S{O,X,Y,Z} is the moving coordinate system of the wave generator established with the rotation center O of the wave generator as the origin, and X is the major axis of the wave generator; S1{O1,X1,Y1,Z1} is the moving coordinate system of the flexspline teeth, the X1 axis is the symmetry line of the flexspline teeth, and the origin O1 is the intersection point of the X1 axis and the neutral layer of the flexspline; S2{O2,X2,Y2,Z2} is the fixed coordinate system established with the rotation center O2 of the rigid spline as the origin.

[0064] An auxiliary coordinate system is established to describe the position movement and the change of the coordinate axis orientation during the process of the taper deformation of the flexspline middle surface. As Figure 2 shown, where Figure 2 (a) is that the deformation of the flexspline causes the origin O1 of the flexspline coordinate system to generate a radial displacement and a tangential displacement, moving from the Figure 1 O1 ′ point in c to the O1 point, that is, the auxiliary coordinate system S c , the X c axis is along the OO1 direction, and the Z Figure 2 (b) is that the radial displacement ω causes the auxiliary coordinate system S c to rotate by an angle θ around the Y c axis to obtain the auxiliary coordinate system S b ; Figure 2 (c) is that the tangential displacement v causes the auxiliary coordinate system S b to rotate by an angle ξ around the X c axis of the coordinate system S c to obtain the auxiliary coordinate system S a ; Figure 2 (d) is that the normal rotation angle μ generated by the flexspline deformation causes the auxiliary coordinate system S a to rotate to the coordinate system S1.

[0065] In the Figure 1 shown flexspline coordinate system, the straight-tooth involute tooth surface equation is constructed:

[0066]

[0067] In the formula, u k is the rotation angle when the cutting tool rolls without slipping along the pitch circle of the gear to be cut, α0 is the reference tooth profile angle, and θ k is half of the central line angle corresponding to the tooth thickness of the gear pitch circle.

[0068] On this surface, a straight line Γ1 can be selected, and its shape and parameters are all determined by the surface parameter u k , as Figure 3 shown. This straight line Γ1 can be expressed as:

[0069]

[0070] In the formula, k0 is a constant;

[0071] Substitute the selected straight line Γ1 of the flexspline into the following meshing equation, and through coordinate transformation, a conjugate curve Γ2 conjugate to the straight line Γ1 is obtained, and point contact is always maintained during the meshing process, as Figure 4 shown;

[0072]

[0073] Γ i (2) = M 21 ·Γ i (1)

[0074] In the formula: n i and are respectively the unit normal vector and the relative motion velocity vector at the contact point of the two conjugate surfaces;

[0075]

[0076] On the normal plane of each point on the curve Γ2, construct the cross-sectional tooth profile curve Γ c , and make the curve Γ c pass through this point and the principal normal vector direction at this point is consistent with the unit normal vector n i at the contact point. The tooth surface of the rigid gear is finally formed by intercepting the tooth surface of the gear tooth through the addendum cylinder surface and the dedendum cylinder surface, as Figure 5 shown.

[0077] Through the above tooth surface construction method, a three-dimensional model of the harmonic gear is established, as Figure 6 shown.

[0078] Analyze the fitting state of the two constructed tooth surfaces at different rotation angles, as Figure 7 shown, where from left to right are the meshing states at the engaging position, any position, and the disengaging position. It can be clearly seen that the tooth surface of the flexspline meshes with the rigid gear along the contact trace from engaging to disengaging, and the contact point always moves on the contact trace.

[0079] In this embodiment, the output part is of cup-shaped structure, and at this time the whole harmonic reducer is a cup-shaped harmonic reducer; the output part is of top-hat-shaped structure, and at this time the whole harmonic reducer is a top-hat-shaped harmonic reducer.

[0080] Establish a finite element analysis model of the above harmonic reducer in ANSYS, and the analysis results are as Figure 8 and Figure 9As shown, compared with the harmonic gear obtained by the traditional design method, the harmonic gear in this embodiment has more meshing pairs, smaller contact stress, and lower equivalent stress of the flexspline under the same parameters and working conditions. It is proved that the harmonic gear designed by the tooth surface design method of the present invention has better mechanical properties.

[0081] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for designing the spatial meshing tooth surface of a harmonic reducer, characterized in that, Including: Construct a spatial coordinate system and an auxiliary coordinate system for the harmonic gear drive; wherein, the spatial coordinate system for the harmonic gear drive is used to describe the relative motion between the flexspline, the rigid spline, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral surface of the flexspline; the auxiliary coordinate system is used to describe the position movement and the change of the coordinate axis orientation during the taper deformation of the flexspline middle surface; Based on the auxiliary coordinate system to assist the spatial coordinate system of the harmonic gear drive, construct a straight-tooth involute tooth surface equation; Select a straight line Γ1 in the straight-tooth involute tooth surface equation; Solve the straight line Γ1 through the meshing equation and coordinate transformation to obtain the conjugate curve Γ2; Continuously construct a normal-consistent sectional tooth profile along the curve Γ2 to form a surface, and intercept it with the addendum cylindrical surface and the dedendum cylindrical surface to form the rigid spline tooth surface.

2. The spatial meshing tooth surface design method of the harmonic reducer according to claim 1, characterized in that, The spatial coordinate system for the harmonic gear drive is used to describe the relative motion between the flexspline, the rigid spline, and the wave generator, as well as the displacement and spatial rotation angle of a selected point on the neutral surface of the flexspline; the spatial coordinate system for the harmonic gear drive includes: a wave generator moving coordinate system S{O,X,Y,Z} established with the rotation center O of the wave generator as the origin, X being the long axis of the wave generator, and a flexspline tooth moving coordinate system S1{O1,X1,Y1,Z1}, the X1 axis being the symmetry line of the flexspline tooth, the origin O1 being the intersection of the X1 axis and the neutral layer of the flexspline, and a fixed coordinate system S2{O2,X2,Y2,Z2} with the rotation center O2 of the rigid spline as the origin; The auxiliary coordinate system is used to describe the position movement and the change of the coordinate axis orientation during the taper deformation of the flexspline middle surface.

3. The design method of the spatial meshing tooth surface of the harmonic reducer according to claim 1, characterized in that, The straight-tooth involute tooth surface equation is: where u k is the rotation angle when the cutting tool rolls without slipping along the pitch circle of the gear to be cut, θ k is half of the central line angle corresponding to the tooth thickness of the gear pitch circle, α0 is the reference tooth profile angle, x is the coordinate value on the x coordinate, y is the coordinate value on the y coordinate, and r is the radius of the neutral layer of the flexspline.

4. The spatial meshing tooth surface design method of the harmonic reducer according to claim 3, characterized in that The straight line Γ1 is: Wherein, z is the coordinate value on the z-axis, and k0 is a constant.

5. The spatial meshing tooth surface design method of the harmonic reducer according to claim 1, characterized in that, Solving the straight line Γ1 through the meshing equation and coordinate transformation to obtain the curve Γ2 includes: Substitute the straight line Γ1 into the meshing equation, and through coordinate transformation, obtain a conjugate curve Γ2 conjugate to the straight line Γ1, and always maintain point contact during the meshing process.

6. The spatial meshing tooth surface design method of the harmonic reducer according to claim 1, characterized in that The meshing equation is: Γ i (2) = M 21 ·Γ i (1) where n i and are respectively the unit common normal vector and the relative motion velocity vector of the two conjugate surfaces at the contact point, i is 1 or 2, Γ i (2) is the conjugate curve to be obtained, M 21 is the coordinate transformation matrix, Γ i (1) is the given curve.

7. The design method of the spatial meshing tooth surface of the harmonic reducer according to claim 1, characterized in that Continuously constructing a normal-consistent sectional tooth profile along the curve Γ2 and intercepting to form the rigid spline tooth surface includes: On the normal plane of each point on the curve Γ2, a cross-sectional tooth profile curve Γ is constructed. c and make the cross-sectional tooth profile curve Γ c The principal normal vector direction passing through the point and at the point is the unit common normal vector n at the contact point i The tooth surface is cut through the top cylindrical surface and the root cylindrical surface to form the tooth surface.

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