A small-ratio harmonic reducer with a new profile wave generator

Abstract

The present application belongs to the field of harmonic reducer design, and provides a small transmission ratio harmonic reducer with a new profile wave generator. The number of the flexible gear cycle wave is set to 2, and the gear difference between the rigid gear and the flexible gear is set to 2n. In order to solve the problem of the decrease of the meshing depth and the increase of the tooth profile pressure angle caused by the decrease of the flexible gear deformation, a new profile wave generator suitable for the small transmission ratio harmonic reducer is proposed. This kind of harmonic reducer can meet the demand of the application market of the reducer with a transmission ratio of 20-60. Due to the application of the new profile wave generator and the optimization of the tooth profile, the small transmission ratio harmonic reducer has the advantages of small flexible gear deformation and secondary conjugate meshing. In addition, the involute fitting theory tooth profile can be used, which is convenient for batch production of the harmonic reducer through mature technology, thereby reducing the cost and accelerating the application.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of harmonic reducer design, and particularly relates to a small transmission ratio harmonic reducer with a new profile wave generator. BACKGROUND

[0002] Harmonic reducer is widely used due to its high transmission accuracy, small volume, light weight and a series of advantages. However, the transmission ratio is usually not less than 60. According to market research, more than 60% of the reducers have a transmission ratio less than 60. This means that the large transmission ratio limits the application of the harmonic reducer in the market of small transmission ratio (20-60) reducer. When designing a small transmission ratio harmonic reducer, the problem of large deformation of the flexspline is faced. Generally, the deformation of the flexspline is related to the meshing depth and the pressure angle of the tooth profile of the harmonic reducer. The smaller the deformation of the flexspline, the smaller the meshing depth and the larger the pressure angle of the tooth profile. How to reduce the deformation of the flexspline while meeting the transmission requirements of the meshing depth and the pressure angle is an important problem in the design of the small transmission ratio harmonic reducer. SUMMARY

[0003] To solve the above problems, the present application provides a small transmission ratio harmonic reducer with a new profile wave generator.

[0004] The technical scheme of the present application is as follows:

[0005] A small transmission ratio harmonic reducer with a new profile wave generator, comprising a rigid gear, a flexspline and a wave generator; the rigid gear is a rigid internal gear; the tooth profile curve of the rigid gear is obtained according to formula 8); the flexspline is a cup-shaped cylindrical straight-tooth external gear; the circular arc of the meshing tooth profile of the flexspline is obtained according to formula 16); the difference between the number of teeth of the rigid gear and the number of teeth of the flexspline is equal to 2n, wherein n is a positive integer greater than 1; compared with the traditional harmonic reducer, the harmonic reducer has a smaller transmission ratio; in order to solve the problems of increasing the tooth difference, increasing the deformation of the flexspline, reducing the meshing depth and possibly not existing the conjugate tooth profile, the wave generator with a new profile is proposed, which comprises a cam and a flexible bearing; the profile of the cam of the wave generator is determined according to formula 2); under the action of the wave generator, the deformation of the flexspline can be obviously reduced, the meshing depth can be increased, and the conjugate tooth profile that meets the meshing principle can be designed;

[0006] Under the action of the new profile wave generator, the center line equation of the flexspline is:

[0007]

[0008] Wherein, a and b represent the semi-major axis and semi-minor axis of the center line of the flexspline, and m and n represent the undetermined coefficients. represents the centrifugal angle.

[0009] The equation of the cam profile is represented as:

[0010]

[0011] Where ε represents the parameter, and h represents the normal distance between the convex profile and the centerline of the flexible wheel;

[0012] Divide the midline of the flexible wheel into e equal parts, and the length of the Kth arc is expressed as:

[0013]

[0014] Substituting equation 3) into equation 1), we get:

[0015]

[0016] Equation 4) represents the form of a point on the center line of the flexible wheel represented by K; given K, the coordinates of the point on the center line of the flexible wheel are obtained according to Equation 4).

[0017] By multiplying equation 4) by the coordinate transformation matrix, we obtain the equation of motion of the point on the midline relative to the rigid wheel, which is expressed as follows:

[0018]

[0019] Where φ represents the angle of rotation of the flexible wheel relative to the rigid wheel;

[0020] Based on Equation 5), the theoretical tooth profile of the rigid wheel is derived; the trajectory of the point is offset, and the equation of the offset curve is obtained as follows:

[0021]

[0022] Where d represents the offset distance; Φ represents the tilt angle, obtained by the following formula:

[0023]

[0024] By equidistantly aligning the offset curves, the theoretical tooth profile of the rigid wheel is obtained as follows:

[0025]

[0026] Where R represents the equidistant distance; θ represents the inclination angle of the tangent line to the offset curve, the value of which is obtained according to the following formula:

[0027]

[0028] in, and Represent x1 and y1 respectively The first derivative;

[0029] Since x1 and y1 contain the variable φ, a pair of φ appears when calculating equation 9). The derivative of the harmonic reducer is obtained from the following formula according to the geometric kinematics of the harmonic reducer:

[0030]

[0031] wherein z1 represents the number of pinion teeth, z2 represents the number of gear teeth, and z2-z1=4; r m represents the radius before the deformation of the center line;

[0032] The involute parameter equation is utilized

[0033]

[0034] The coordinates (X Ci ,Y Ci )(i=1,2,3,…,m1) of the gear tooth profile obtained according to the formula 8) are unilaterally approximated, so as to complete the fitting; wherein R C represents the radius of the gear pitch circle, δ i represents the parameter of the i-th point on the involute, θ1 represents one-half of the central angle of the tooth space width on the gear base circle, and m1 represents a positive integer;

[0035] In order to make the involute unilaterally approximate the gear tooth profile and not intersect, the following conditions must be met:

[0036] ΔX Ci =X eCi -X Ci ≥012)

[0037] Define M C as the arithmetic mean of the distance D(x MC ,δ i ) between the involute and the corresponding point on the gear tooth profile; then the fitting of the gear tooth profile by the involute can be expressed as:

[0038]

[0039] wherein x MC represents the modification coefficient of the gear;

[0040] The conditional extreme value of the above formula is solved by the following process:

[0041] (1) Assign an initial value x MC to x In order to prevent the influence of human factors on the calculation results, the pseudo-random numbers (0,1) with uniform distribution are used to generate

[0042] (2) Determine θ1; according to the number of gear teeth and the number of the gear shaping cutter with the modification coefficient of 0 z, θ1 is obtained, and the expression is as follows:

[0043]

[0044] where m g represents the module of the rigid wheel, and a represents the pressure angle of the rigid wheel tooth profile;

[0045] (3) Calculate δ i ; take the line connecting any point I(X Ci , Y Ci ) on the initial tooth profile with the coordinate origin O as the radius to draw a circle, which intersects the involute at point I e (X eCi , Y eCi ); then, the point I e corresponding parameter δ i is obtained according to the following formula:

[0046]

[0047] (4) Substitute θ1 and δ i into formula 11) to calculate I e (X eCi , Y eCi );

[0048] (5) Check formula 12); when ΔX Ci ≥ 0, calculate M C ; when ΔX Ci < 0, change the Δx generated in the first step by one and then recalculate from the second step in turn;

[0049] (6) Determine M C ; calculate the points (X Ci , Y Ci ) (i = 1, 2, 3,..., m1) on the involute corresponding to all coordinates (X eCi , Y eCi ) (i = 1, 2, 3,..., m1) of the given rigid wheel tooth profile; in order to make M C minimum, take a Δx MC , such that where n1 represents a positive integer; under the condition of satisfying formula 11), repeatedly steps (2) to (6); when formula 12) is not satisfied, take and then let Δx MC ' = Δx MC / 2, substitute it into , and repeat the calculation until Δx MC ' < 0.00000001; at this time, the minimum value of M C is obtained, and the x MC corresponding to it is the displacement coefficient of the involute rigid wheel; thus, the involute tooth profile of the rigid wheel is obtained;

[0050] The tooth profile of the flexspline is composed of an engagement tooth profile and a transition tooth profile; the engagement tooth profile is a circular arc, and its equation is:

[0051]

[0052] Wherein, u represents a variable; the transition tooth profile which is smoothly connected with the engagement tooth profile is designed as a straight line;

[0053] The present application provides a small transmission ratio harmonic reducer with a new profile wave generator. This harmonic reducer can meet the market demand for the reducer with a transmission ratio of 20-60. Due to the application of the new profile wave generator and the optimization of the tooth profile, this small transmission ratio harmonic reducer has the advantages of small flexspline deformation and secondary conjugate engagement. In addition, the involute can be used to fit the rigid wheel tooth profile, which facilitates batch production of the harmonic reducer through mature technology, thereby reducing the cost and accelerating the application. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 is a schematic diagram of the rigid wheel tooth profile generation of the present application.

[0055] Figure 2 is the fitting of the rigid wheel tooth profile of the present application.

[0056] Figure 3 is a schematic diagram of the flexspline tooth profile generation of the present application.

[0057] Figure 4 is a small transmission ratio harmonic reducer with a new profile wave generator of the present application.

[0058] In the figure: 1, rigid wheel tooth profile curve; 2, overlapping area; 3, rigid wheel theoretical tooth profile; 4, addendum; 5, involute tooth profile; 6, circular arc; 7, boundary point; 8, transition tooth profile; 9, flexspline center line. DETAILED DESCRIPTION

[0059] In order to facilitate the understanding of the technical means realized by the present application, the technical solutions provided by the present application are described in detail below in combination with the drawings and examples.

[0060] The present application provides a small transmission ratio harmonic reducer with a new profile wave generator. In this example, the number of flexspline teeth z1=80, the number of rigid wheel teeth z2=84, the transmission ratio is 20, the semi-major axis a=50.8197 / 2 mm, the semi-minor axis b=48.3386 / 2 mm, the offset distance d=0.89 mm, the equidistant distance R=0.25 mm, and the undetermined coefficients m and n are 0 and 1.945 respectively.

[0061] First step: substitute the corresponding parameters into equation 1) to obtain the flexspline center line 9; then calculate the wave generator with a new profile according to the flexspline center line 9 and equation 2).

[0062] Step 2: Based on the centerline 9 of the flexible wheel, obtain the tooth profile curve 1 of the rigid wheel using equation 8), as follows. Figure 1 As shown; since there is an overlapping region 2 between two adjacent tooth profile curves 1, the theoretical tooth profile 3 of the rigid wheel can only be composed of curves from non-overlapping regions. Because the teeth composed of curves from non-overlapping regions are very sharp, therefore, according to the gear tooth tip thickness 4, it is not less than 0.25m. g Or the thickness of the surface-hardened gear tooth tip shall not be less than 0.4 μm. g The top is cut according to the principle.

[0063] Step 3: Compile a fitting program and run it in MATLAB. Import the coordinates of the theoretical tooth profile 3 of the rigid wheel into the program and perform calculations to obtain the involute tooth profile 5, such as... Figure 2 As shown.

[0064] Step 4: Substitute the parameters related to the flexible gear tooth profile into Equation 16) to obtain the arc 6 corresponding to the meshing tooth profile of the flexible gear. The boundary point 7 on the arc 6, i.e., the end of the meshing tooth profile, can be calculated based on the principle that the point on the theoretical tooth profile 3 of the rigid gear with the maximum inclination angle θ meshes with the boundary point 7. Design the transition tooth profile 9 as a straight line, and obtain the flexible gear tooth profile through the smooth connection of the straight line and the boundary point 7, as shown below. Figure 3 As shown.

[0065] Finally, a small-ratio harmonic reducer with a new profile wave generator was obtained, as shown in the following results. Figure 4 As shown.

[0066] The above description is only used to illustrate the technical solution of the present invention and not to limit the technical solution. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention, as long as they do not depart from the spirit and scope of the technical solution of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A low-ratio harmonic reducer with a novel profile wave generator, characterized in that, The low-ratio harmonic reducer with a new profile wave generator includes a rigid wheel, a flexible wheel, and a wave generator; the rigid wheel is a rigid internal gear; the tooth profile curve of the rigid wheel is calculated according to Equation 8); the flexible wheel is a cup-shaped cylindrical spur gear; the arc of the meshing tooth profile of the flexible wheel is calculated according to Equation 11); the difference between the number of teeth of the rigid wheel and the number of teeth of the flexible wheel is equal to 2n, where n is a positive integer greater than 1; the wave generator with the new profile includes a cam and a flexible bearing, and the profile of the cam of the wave generator is determined according to Equation 2); Under the action of the wave generator, the equation of the flexural centerline in the rectangular coordinate system is: Where a and b represent the semi-major axis and semi-minor axis of the flexural wheel centerline, and m and n represent undetermined coefficients; Indicates the eccentric angle; The equation for the new profile of the cam in the first quadrant is: Where ε represents the parameter, and h represents the normal distance between the convex profile and the centerline of the flexible wheel; The midline of the flexible wheel is divided into e equal parts, and the length of the Kth arc is expressed as: Where S represents the arc length of the center line of the flexible wheel. This represents the centrifugal angle corresponding to the Kth arc length; Substituting equation 3) into equation 1), we get: Equation 4) represents the form in which a point on the center line of the flexible wheel is represented by K; when K is given, the coordinate values ​​of the point on the center line of the flexible wheel are obtained according to Equation 4). Multiplying equation 4) by the following coordinate transformation matrix yields the equation of motion of the point on the centerline of the flexible wheel relative to the rigid wheel: Where φ represents the angle of rotation of the flexible wheel relative to the rigid wheel; By offsetting the trajectory of the point represented by Equation 5), the equation of the offset curve is obtained as follows: Where d represents the offset distance; Φ represents the tilt angle, obtained by the following formula: By equidistantly aligning the offset curves, the tooth profile curve of the rigid wheel is obtained as follows: Among them, X C and Y C The x and y coordinates represent the profile curve of the rigid gear; R represents the equidistant distance; θ represents the inclination angle of the tangent to the offset curve, which is obtained according to the following formula: in, and Represent x1 and y1 respectively The first derivative; Since x1 and y1 contain the variable φ, a pair of φ appears when calculating equation 9). The derivative of φ; according to the geometric kinematics of the harmonic reducer, φ with respect to The derivative is obtained by the following formula: Where z1 represents the number of teeth on the flexible gear, z2 represents the number of teeth on the rigid gear, and z2-z1=4; r m This represents the radius of the flexible wheel's centerline before deformation; According to Equation 8), the non-overlapping region of the rigid wheel tooth profile curve is the theoretical tooth profile of the rigid wheel. The tooth profile of a flexible gear includes a meshing tooth profile and a transition tooth profile; the transition tooth profile is a straight line that smoothly connects with the meshing tooth profile; the meshing tooth profile is a circular arc, and its equation is: Where u represents a parameter.

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