A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline

Abstract

The present invention relates to a harmonic tooth profile design method for simultaneously generating the tooth profiles of a flexible gear and a rigid gear. Based on the elastic deformation law of the flexible gear, the steps are as follows: First, determine the parameters such as the specifications, module, reduction ratio, and original curve equation required for the tooth profile design of the harmonic reducer; then establish a global fixed coordinate system, a local coordinate system for the flexible gear and the rigid gear; secondly, select the initial meshing position in the global coordinate system, and obtain the corresponding coordinates in the local coordinate systems of the flexible gear and the rigid gear through the transformation matrix; according to the deformation law of the flexible gear, obtain each meshing point in turn through matrix transformation; after determining the number of meshing points and adjusting the meshing range, simultaneously obtain the meshing curves of the flexible gear and the rigid gear. Finally, add the tooth root curve and the transition curve to obtain the complete tooth profile curves of the flexible gear and the rigid gear. The present invention is applicable to the tooth profile design of harmonic reducers, and has the characteristics of convenient adjustment of the meshing range, continuous meshing range of the tooth profile, and small backlash, which helps to expand the application scenarios of harmonic reducers, improve the load-bearing capacity, transmission accuracy, and stability of harmonic reducers.

Description

Technical Field

[0001] The present invention relates to a harmonic tooth profile design method in the field of mechanical transmission, and more particularly to a harmonic tooth profile design method that can generate the tooth profiles of both the flexspline and the rigid spline simultaneously based on the elastic deformation law of the flexspline. Background Art

[0002] As a precision speed reducer, the harmonic speed reducer has been widely used in recent years in fields such as satellites, radars, and especially the end effectors of robots. It has the characteristics of small volume, large transmission ratio, high transmission accuracy, and long service life. Harmonic tooth profile design is an important part of the design of harmonic speed reducers, and the tooth profile directly affects the load-carrying capacity, transmission accuracy, and transmission smoothness of harmonic speed reducers. Experts at home and abroad have studied the tooth profile. Musser first proposed the concept of a harmonic speed reducer and applied for a patent (Patent No.: US Patent US 2906143), which used a straight tooth profile with a relatively small meshing range. Currently, commonly used tooth profiles include involute, double circular arc, and S-shaped tooth profiles, etc. The involute tooth profile is easy to machine, but there is edge contact, which is not conducive to the formation of an oil film. There are currently a large number of related patents for the double circular arc tooth profile (Patent Nos.: Chinese Patent CN200610112756.0, CN201410309903.8, CN201710436032.X, CN201710647236.8). This tooth profile improves the stress condition of the flexspline tooth root and the meshing quality of the transmission, and increases the load-carrying capacity and torsional stiffness. The double circular arc tooth profile design often uses conjugate methods, such as the envelope method, the instantaneous center method, etc. Given the known flexspline tooth profile, the matching rigid spline tooth profile is derived according to the conjugate theory. The S-shaped tooth profile (Patent No.: US Patent US 3415143) uses the rack approximation method. The approximate motion trajectory of the flexspline tooth profile relative to the rack of the rigid spline pitch circle is mapped proportionally to obtain the tooth profiles of both the flexspline and the rigid spline simultaneously. The above tooth profiles and design methods have certain limitations. First, during the tooth profile generation process, the meshing range is difficult to adjust and can only be calculated after the tooth profiles of the flexspline and the rigid spline are determined. Second, the tooth profile meshing interval is discontinuous. For example, there is a discontinuous interval of 5 to 10 degrees between the two circular arcs of the double circular arc. Third, the backlash is relatively large. For example, the involute tooth side backlash is generally dozens of micrometers. The difficulty in adjusting the meshing range restricts the application scenarios of harmonic speed reducers and the load-carrying capacity of the transmission. The discontinuous tooth profile meshing interval and the relatively large backlash restrict the transmission accuracy and stability of harmonic speed reducers.

[0003] With the increasing requirements for the performance of harmonic speed reducers, it is necessary to design a tooth profile with more convenient meshing range adjustment, continuous meshing range, and small backlash, so as to make the application scenarios of harmonic speed reducers wider and further improve the load-carrying capacity, transmission accuracy, and stability. Summary of the Invention

[0004] Objective of the Invention: To solve the problems existing in the prior art, the objective of the present invention is to propose a harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, automatically generating the tooth profile curve, with an adjustable meshing range, continuous meshing and zero backlash harmonic tooth profile, which helps to expand the application scenarios of the harmonic reducer, and improve the load-carrying capacity, transmission accuracy and stability of the harmonic reducer.

[0005] Technical Solution: To achieve the above objective, the technical solution provided by the present invention is as follows:

[0006] A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, based on the elastic deformation law of the flexspline, comprises the following steps:

[0007] First, determine the parameters such as the specifications, module, reduction ratio and original curve equation required for the tooth profile design of the harmonic reducer;

[0008] Then, establish a global fixed coordinate system, a local coordinate system of the flexspline and a local coordinate system of the rigid spline;

[0009] Secondly, select the initial meshing position in the global coordinate system, and obtain the corresponding coordinates in the local coordinate systems of the flexspline and the rigid spline through the transformation matrix; according to the deformation law of the flexspline, obtain each meshing point in turn through matrix transformation; after determining the number of meshing points and adjusting the meshing range, obtain the meshing curves of the flexspline and the rigid spline simultaneously.

[0010] Finally, add the tooth root curve and the transition curve to obtain the complete tooth profile curves of the flexspline and the rigid spline.

[0011] Specifically, the content is as follows:

[0012] A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, the harmonic tooth profile including the flexspline tooth profile and the rigid spline tooth profile, comprises the following steps:

[0013] (1) Determine the specifications of the harmonic reducer, module m, reduction ratio i and the original curve equation of the designed harmonic tooth profile, that is, the neutral layer curve of the flexspline, and calculate the number of teeth of the flexspline, the number of teeth of the rigid spline and the rigid spline pitch circle equation;

[0014] (2) Establish a global fixed coordinate system, a local coordinate system of the flexspline and a local coordinate system of the rigid spline;

[0015] The global fixed coordinate system S w (O w ; X w , Y w ) is fixedly connected to the wave generator, where the point O w is the center of the wave generator, the X w axis coincides with the minor axis, and the Y w axis coincides with the major axis;

[0016] The local coordinate system S' of the flexsplinef (O′ f ; X′ f , Y′ f ) of O′ f point is the equal division point of the flexspline neutral layer curve, the X′ f axis coincides with the tangent vector of the O′ f point, and the Y′ f axis coincides with the normal vector of the O′ f point; specifically, the flexspline neutral layer curve is equally divided by arc length, and the number of equal divisions N f is a multiple of the flexspline tooth number z f ; local coordinate systems of the flexspline are successively established at each equal division point of the flexspline neutral layer curve. The coordinate system at the i-th equal arc length position is S′ fi (O′ fi ; X′ fi , Y′ fi ), the O′ fi point is located at the i-th equal division point, the X′ fi axis coincides with the tangent vector of this point, and the Y′ fi axis coincides with the normal vector of this point;

[0017] The O′ c (O′ c ; X′ c , Y′ c ) of the rigid spline local coordinate system S′ c point is the equal division point of the rigid spline pitch circle, the X′ c axis coincides with the tangent vector of the O′ c point, and the Y′ c axis coincides with the normal vector of the O′ c point; specifically, the rigid spline pitch circle curve is equally divided by arc length, and the number of equal divisions N c is a multiple of the rigid spline tooth number z c ; local coordinate systems of the rigid spline are successively established at each equal division point. The coordinate system at the i-th equal arc length position is S′ ci (O′ ci ; X′ ci , Y′ ci ), the O′ ci point is located at the i-th equal division point, the X′ ci axis coincides with the tangent vector of the O′ ci point, and the Y′ ci axis coincides with the normal vector of the O′ ci point;

[0018] (3) Select the initial meshing position in the global fixed coordinate system, and obtain the corresponding coordinates in the local coordinate systems of the flexspline and the rigid spline through the transformation matrix; specifically, in the global fixed coordinate system S wIn the flexspline local coordinate system S′, select the initial meshing point, which is marked as point A1 with coordinates (X1, Y1). f1 A′ 11 Point, coordinates (X′ f11 ,Y′ f11 ), A′ 11 The relationship between point A1 is as follows:

[0019] (X′ f11 ,Y′ f11 )=M wf11 (X1,Y1);

[0020] Where M wf11 For S w to S′ f1 The transformation matrix of

[0021] Point A1 is in the local coordinate system S′ of the rigid wheel c1 Denoted as B′ 11 Point, coordinates (X′ c11 ,Y′ c11 ); B′ 11 The relationship between point A1 and point A2 is as follows:

[0022] (X′ c11 ,Y′ c11 )=M wc11 (X1,Y1);

[0023] Where M wc11 For S w to S′ c1 The transformation matrix of

[0024] (4) According to the deformation law of the flexible wheel, each meshing point is obtained in sequence through matrix transformation;

[0025] Specifically, according to the motion relationship between the coordinates of the points on the neutral layer curve of the flexspline and the corresponding points on the pitch circle coordinates of the rigid pulley, after coordinate transformation, a point is generated in both the local coordinate system of the flexspline and the local coordinate system of the rigid pulley from the previous meshing point. Then, these two points are transformed into the global fixed coordinate system, and a new meshing point is taken between these two points. The meshing points of each equally divided angle are derived in sequence.

[0026] (5) Determine the number of meshing points j and adjust the meshing range ε j , ε j ∈(0,1), the flexspline meshing curve and the rigid wheel meshing curve are obtained at the same time; after fitting the meshing points, the flexspline meshing curve and the rigid wheel meshing curve are obtained at the same time; when i=j, the flexspline coordinate system S′ corresponding to the i-th meshing point fi In the figure, the meshing arc length of the flexspline is from point A′ i,j , A′ i,j-1…A′ i,2 and A′ i,1 constitute. After fitting the meshing points, they are used as the tooth profile curve of the flexspline; where A′ i,j-1 corresponds to the i-th meshing point and is obtained from the coordinate transformation of A′ fi-1 in the S′ i-1,j-1 coordinates; at the same time, in the corresponding rigid spline coordinate system S′ ci , the meshing arc length of the rigid spline is composed of points B′ i,j , B′ i,j-1 …B′ i,2 , B′ i,1 constitute. After fitting the meshing points, they are used as the tooth profile curve of the rigid spline; where B′ i,j-1 corresponds to the i-th meshing point and is obtained from the coordinate transformation of B′ ci-1 in the S′ i-1,j-1 coordinates;

[0027] (6) Add the tooth root curve and the tooth tip and tooth root transition curves to obtain the complete flexspline tooth profile curve and rigid spline tooth profile curve; the specific steps are: use the flexspline meshing curve and the rigid spline meshing curve obtained by fitting in step (5) as the tooth tip curve, and add the tooth root curve. The tooth root curve is an arbitrary smooth curve, but it needs to meet the condition of not interfering with the rigid spline tooth profile; after adding the tooth tip and tooth root transition arc curves, the complete flexspline tooth profile curve and the complete rigid spline tooth profile curve

[0028] For the above harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, in the global fixed coordinate system S w (O w ; X w , Y w ), the original curve is an ellipse, and the equation is as follows:

[0029] Ellipse equation:

[0030] where a is the major semi-axis of the ellipse and b is the minor semi-axis of the ellipse.

[0031] For the above harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, in the global fixed coordinate system S w (O w ; X w , Y w ), the original curve is a cosine curve, and the equation is as follows:

[0032] Cosine curve equation:

[0033] where ρ is the polar radius of the neutral layer after the flexspline is deformed, R f is the radius of the neutral layer of the flexspline before deformation, and ω0 is the maximum deformation of the semi-axis of the flexspline, is the flexspline rotation angle.

[0034] In the above harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, the tooth thickness is determined by the abscissa X1 of the initial meshing point A1, and its value satisfies the approximate equation X1≈π / 4·m, where m is the module.

[0035] The ordinate Y1 of the initial meshing point A1 is selected near the rigid spline pitch circle radius R c and satisfies |R c -Y1|<0.15mm.

[0036] In the above harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, in step (4), the specific process of deriving the second meshing point from the initial meshing point is as follows:

[0037] Transform the A′ 11 point from the local coordinate system S′ of the flexspline f1 to the local coordinate system S′ of the flexspline f2 and denote it as the A′ 21 point with coordinates (X′ f21 ,Y′ f21 ), as shown in the formula:

[0038] (X′ f21 ,Y′ f21 )=M ff21 (X′ f11 ,Y′ f11 );

[0039] In the formula, M ff21 is the transformation matrix from S′ f1 to S′ f2 ;

[0040] The A′ 21 point is denoted as the A w point in S 21 with coordinates (X f21 ,Y f21 ). The relationship between the A 21 point and the A′ 21 point is as follows:

[0041] (X f21 ,Y f21 )=M′ ff21 (X′ f21 ,Y′ f21 );

[0042] In the formula, M′ ff21 is the transformation matrix from S′ f1 to S w ;

[0043] Then, the B′11 The point is transformed from the local coordinate system S' of the flexspline c1 to the local coordinate system S' of the flexspline c2 and is denoted as B' 21 The point has coordinates (X' c21 , Y' c21 ); B' 21 The point is denoted as B in S w and has coordinates (X 21 , Y c21 , Y c21 );

[0044] Select a second meshing point on or near the line connecting points A 21 and B 21 In S, it is denoted as point A2 with coordinates (X2, Y2); The positional relationship between point A2 and points A w and B 21 and B 21 is as follows:

[0045] (X2, Y2) = [K x1 (X f21 +X c21 ), K y1 (Y f21 +Y c21 )];

[0046] Where K x1 , K y1 is the proportionality coefficient, K x1 , K y1 ∈(0, 1);

[0047] Then the coordinates of point A2 are:

[0048]

[0049] In the above harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, in step (4), the i-th meshing point is derived from the (i - 1)-th meshing point:

[0050]

[0051] The coordinates of each meshing point are:

[0052]

[0053] Where K x1 , K x2 …K x(i-1) , K y1 , K y2 …K y(i-1) are the proportionality coefficients, and the value range is (0, 1), M wfiiis the coordinate system S w To coordinate system S′ fi The transformation matrix, M wcii is the coordinate system S w to S′ ci The transformation matrix, M ffi+1,i is the coordinate system S′ fi to S′ fi+1 The transformation matrix, M′ ffi+1,i is the coordinate system S′ fi+1 to S w The transformation matrix, M cci+1,i is the coordinate system S′ ci to S′ ci+1 The transformation matrix, M′ cci+1,i is the coordinate system S′ ci+1 to S w The transformation matrix.

[0054] The above harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexible spline and the rigid spline, the number of meshing points determines the meshing range, and the meshing range ε is adjusted by changing the number of meshing points j. j , j = ε j ·N f , N f is the number of equal divisions of the flexspline neutral layer curve; when N f When it is a constant value, the more the number of meshing points j is, the longer the contact arc length is, the larger the meshing range is, and the higher the overlap is.

[0055] The harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline is as follows: the maximum radial deformation of the major semi-axis of the original curve satisfies the inequality |ω0-m|<0.1mm, where ω0 is the maximum deformation of the major axis of the flexspline and m is the modulus.

[0056] The harmonic tooth profile design method for generating the tooth profiles of the flexspline and the rigid wheel at the same time, the semi-long axis a of the neutral layer curve of the flexspline and the pitch circle radius R of the rigid wheel c Satisfying inequality 4·m>R c -a>0.

[0057] Beneficial Effects: Based on the elastic deformation laws of the flexspline, this invention provides a new harmonic tooth profile design method. The resulting tooth profile features easy adjustment of the meshing range, a continuous meshing range, and minimal backlash. Compared to traditional harmonic tooth profile design methods, this invention has a wider range of applications and can significantly improve the load-bearing capacity, transmission accuracy, and stability of harmonic reducer transmission processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] FIG1 is a general flow chart of tooth profile design according to the present invention;

[0059] Figure 2 Schematic diagram of three types of coordinates in Example 1 of the present invention;

[0060] Figure 3 Derivation flowchart of the i-th meshing point in Embodiment 1 of the present invention;

[0061] Figure 4 Flexspline tooth profile diagram of Embodiment 1 of the present invention;

[0062] Figure 5 Circular spline tooth profile diagram of Embodiment 1 of the present invention;

[0063] Figure 6 Meshing state diagram of the first quadrant of the harmonic gear in Embodiment 1 of the present invention;

[0064] Figure 7 Meshing range diagram of Embodiment 1 of the present invention;

[0065] Figure 8 Backlash distribution diagram of Embodiment 1 of the present invention. Detailed implementation manners

[0066] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with 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. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0067] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs; the terms used in the description of the present invention in this specification are only for the purpose of describing specific embodiments, and are not intended to limit the present invention; the term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0068] Embodiment 1

[0069] A harmonic tooth profile design method for simultaneously generating the tooth profiles of a flexspline and a circular spline. According to the specifications of a specific harmonic reducer (in this embodiment, type 40, reduction ratio of 100, and module of 0.508 mm), it is mainly applied to the end effector of a robot, and the meshing range is required to be greater than 30%. Using an elliptical cam wave generator, the meshing range is determined, and at the same time, the tooth profiles of the engaged parts of the flexspline and the circular spline are obtained, and then the complete tooth profiles are obtained. The overall design process is as Figure 1 shown. The specific steps are as follows:

[0070] Step 1: Determine the basic parameters

[0071] Harmonic reducer model 40, reduction ratio of 100, module of 0.508 mm, number of teeth of the flexspline zf = 200, the number of teeth of the rigid gear \(z\) c = 202, the pitch circle of the flexible gear \(R\) f = 50.8 mm, the pitch circle of the rigid gear \(R\) c = 51.308 mm.

[0072] In the fixed coordinate system \(S\) w , the original curve of the flexible gear (i.e., the neutral layer deformation curve) is a standard ellipse, and the equation is:

[0073]

[0074] In this embodiment, the major axis of the original curve \(a = 49.808\) mm, and the minor axis of the original curve \(b = 48.673\) mm.

[0075] The initial engagement point \(X1 = 0.41\) mm, and the initial engagement point \(Y1 = 51.408\) mm.

[0076] The radial deformation of the major axis \(\omega = 0.566\).

[0077] The proportionality coefficient \(K\) x1 , \(K\) y1 Both are taken as 0.5. The engagement range is set to 33%, that is, a total of 68 pairs of teeth are engaged simultaneously.

[0078] Step 2: Establish three types of coordinate systems, namely the global fixed coordinate system, the local coordinate systems of the flexible gear and the rigid gear. As Figure 2 shown, 1 in the figure is the global fixed coordinate system \(S\) w , 2 is the coordinate system of the flexible gear \(S'\) fi , 3 is the coordinate system of the rigid gear \(S''\) ci , 4 is the pitch circle curve of the rigid gear, and 5 is the original curve of the flexible gear.

[0079] The global fixed coordinate system \(S\) w (\(O\) w ; \(X\) w , \(Y\) w ) is fixedly connected to the wave generator, and the point \(O\) w is the center of the wave generator. The \(X\) w axis coincides with the minor axis, and the \(Y\) w axis coincides with the major axis.

[0080] The local coordinate system of the flexible gear \(S'\) f (\(O'\) f ; \(X'\) f , \(Y'\) f ), \(O'\) f is located at the equal division point of the neutral layer curve of the flexible gear. The \(X'\) f axis coincides with the tangent vector at this point, and the \(Y'\) f axis coincides with the normal vector at this point. The neutral layer curve of the flexible gear is equally divided by arc length, and the number of equal divisions \(N\)f is 200. Coordinate systems are successively established at each equal division point. For example, the coordinate system S' at the i-th equal arc length position fi (O' fi ; X' fi , Y' fi ). The point O' fi is located at the i-th equal division point. The X' fi axis coincides with the tangent vector at this point, and the Y' fi axis coincides with the normal vector at this point.

[0081] The local coordinate system S' of the rigid gear c (O' c ; X' c , Y' c ). O' c is located at the equal division point of the pitch circle of the flexible gear. The X' c axis coincides with the tangent vector at this point, and the Y' c axis coincides with the normal vector at this point. The pitch circle curve of the rigid gear is equally divided by arc length, and the number of equal divisions N c is 202. Coordinate systems are successively established at each equal division point. For example, the coordinate system S' at the i-th equal arc length position ci (O' ci ; X' ci , Y' ci ). The point O' ci is located at the i-th equal division point. The X' ci axis coincides with the tangent vector at this point, and the Y' ci axis coincides with the normal vector at this point.

[0082] Step 3: Select the initial meshing position in the global coordinate system and obtain the corresponding coordinates in the local coordinate systems of the flexible gear and the rigid gear through the transformation matrix. In this example, in the fixed coordinate system S w , the initial meshing point is point A1, with coordinates (X1, Y1), where X1 = 0.41 mm and Y1 = 51.408 mm. In the coordinate system S' of the rigid gear c1 it is denoted as point B' 11 , with coordinates (X' c11 , Y' c11 ). The relationship between A' 11 and point A1 is as follows:

[0083] (X' f11 , Y' f11 ) = M wf11 (X1, Y1),

[0084] where M wf11 is the transformation matrix from S w to S' f1 .

[0085] B'11 The relationship between point and point A1 is as follows:

[0086] (X′ c11 , Y′ c11 ) = M wc11 (X1, Y1),

[0087] where M wc11 is the transformation matrix from S w to S′ c1 .

[0088] Step 4: According to the deformation law of the flexspline, each meshing point is obtained sequentially through matrix transformation.

[0089] Transform point A 11 from the flexspline coordinate system S′ f1 to the flexspline coordinate system S′ f2 , denoted as point A′ 21 with coordinates (X′ f21 , Y′ f21 ), as shown in the formula:

[0090] (X′ f21 , Y′ f21 ) = M ff21 (X′ f11 , Y′ f11 ),

[0091] where M ff21 is the transformation matrix from coordinate system S′ f1 to S′ f2 .

[0092] Point A′ 21 is denoted as point A w in S 21 with coordinates (X f21 , Y f21 ). The relationship between point A 21 and point A′ 21 is as shown in the formula:

[0093] (X f21 , Y f21 ) = M′ ff21 (X′ f21 , Y′ f21 ),

[0094] where M′ ff21 is the transformation matrix from coordinate system S′ f1 to S w .

[0095] Then, transform point B 11 from the rigid spline coordinate system S′ c1 to S′c2 In it, it is denoted as B'. 21 Point, with coordinates (X' c21 , Y' c21 ). B' 21 The point is denoted as B in S w Point, with coordinates (X 21 , Y c21 , Y c21 ).

[0096] Select a second meshing point on the line connecting points A 21 and B 21 . In S w , it is denoted as point A2, with coordinates (X2, Y2). The positional relationship between point A2 and A 21 and B 21 is as follows:

[0097] (X2, Y2) = (K x1 (X f21 + X c21 ), K y1 (Y f21 + Y c21 ))

[0098] wherein, K x1 , K y1 is the proportionality coefficient, K x1 , K y1 ∈(0, 1). In this example, the proportionality coefficients K x1 , K y1 are both taken as 0.5.

[0099] Then the coordinates of point A2 are:

[0100]

[0101] In this embodiment, X2 = 0.41 mm, Y2 = 51.409 mm.

[0102] The i-th meshing point can be derived from the (i - 1)-th meshing point, and the flowchart is as Figure 3 shown:

[0103]

[0104] The coordinates of the i-th meshing point are:

[0105]

[0106] Step 5: Determine the number of meshing points j and adjust the meshing range ε j, while obtaining the meshing curves of the flexspline and the rigid spline. The larger the number of meshing points, the larger the meshing range. However, an overly large meshing range is likely to cause interference. In this embodiment, the number of meshing points j in the first quadrant is 34, and the meshing range ε j is set to 33%. Transform the 34 meshing points into the same flexspline coordinate system. In this embodiment, first transform each point to the flexspline coordinate system S′ f1 and the rigid spline coordinate system S′ c1 , and then transform it to the global fixed coordinate system S w . Then, the meshing point coordinates of the flexspline and the rigid spline can be obtained:

[0107] Table 1 Meshing Point Coordinates of Flexspline and Rigid Spline

[0108]

[0109]

[0110] In the global fixed coordinate system S w , fit the meshing points of the flexspline and the rigid spline.

[0111] Step 6: Add the tooth root curve and the transition curve to obtain the complete tooth profile curves of the flexspline and the rigid spline and Take the meshing curves of the flexspline and the rigid spline obtained by fitting in step (5) as the tooth tip curves, and add the tooth root curves. The tooth root curves can be smooth curves as long as the non-interference condition is satisfied. After adding the tooth tip and tooth root transition arc curves, the complete tooth profile of the flexspline and the rigid spline are obtained. As shown in Figure 4 , Figure 5, it is composed of four parts: the tooth tip curve, the tooth root curve, and the tooth tip and tooth root transition arc curves.

[0112] In this embodiment, the total number of teeth of the flexspline is 200. By setting the number of meshing points j in the first quadrant of the fixed coordinate system to 34 and adjusting the meshing range to 33%, the actual meshing range is 32.77%, and the contact ratio is 65.54. The meshing state range in the first quadrant is as shown in Figure 6 . In the figure, 1 is the flexspline, 2 is the rigid spline, 3 is the 0-degree position, at which time the flexspline and the rigid spline are fully meshed; 4 is the 59.44-degree position, at which time the flexspline just disengages; 5 is the 90-degree position, at which time the flexspline and the rigid spline are completely disengaged, verifying that the design method of this embodiment has the characteristic of convenient adjustment of the meshing range. In the entire meshing range [0.46°, 59.44°], the meshing of the flexspline and the rigid spline is continuous. The corresponding relationship between the meshing arc length and the angle of the flexspline is as shown in Figure 7 , verifying that the tooth profile designed by this design method has the characteristic of continuous meshing range. In the meshing interval, the side clearance is stable at 5×10 -3 μm in the range of 0.46° to 59.44°, as shown in Figure 8As shown, compared with the involute tooth backlash which is generally dozens of micrometers, the meshing backlash is more evenly distributed and the maximum meshing backlash is smaller, verifying that the tooth profile designed by this design method has the characteristic of small backlash.

[0113] Example 2

[0114] The harmonic reducer model is 40, the reduction ratio is 100, the module is 0.508 mm, the number of teeth of the flexspline is z f = 200, the number of teeth of the rigid spline is z c = 202, the pitch circle of the flexspline is R f = 50.8 mm, the pitch circle of the rigid spline is R c = 51.308 mm.

[0115] In the fixed coordinate system S w , the original curve of the flexspline (i.e., the neutral layer deformation curve) is a cosine curve, and the equation is:

[0116]

[0117] In this embodiment, R f = 50.8 mm, ω0 = 0.566 mm.

[0118] The initial meshing point X1 = 0.41 mm, the initial meshing point Y1 = 51.408 mm.

[0119] The proportionality coefficient K x1 , K y1 Both are taken as 0.5. The meshing range is set to 33%, that is, a total of 68 pairs of teeth are meshing simultaneously.

[0120] Using the same steps as in Example 1, the meshing point coordinates of the flexspline and the rigid spline can be obtained:

[0121] Table 2 Meshing point coordinates of the flexspline and the rigid spline

[0122]

[0123]

[0124] Furthermore, the tooth tip curves of the flexspline and the rigid spline are fitted, and the tooth root curves and the transition curves between the tooth tip and the tooth root are added to obtain the complete tooth profile curves of the flexspline and the rigid spline.

[0125] The above-described embodiments only represent certain implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the patent of the present invention; it should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline, where the harmonic tooth profile includes the flexspline tooth profile and the rigid spline tooth profile. First, determine the parameters such as the specifications, module, reduction ratio, and original curve equation required for the tooth profile design of the harmonic reducer. Then, establish a global fixed coordinate system, local coordinate systems for the flexspline and the rigid spline. Next, select the initial meshing position in the global coordinate system and obtain the corresponding coordinates in the local coordinate systems of the flexspline and the rigid spline through transformation matrices. According to the deformation law of the flexspline, obtain each meshing point in turn through matrix transformation. After determining the number of meshing points and adjusting the meshing range, obtain the meshing curves of the flexspline and the rigid spline simultaneously. Finally, add the tooth root curve and the transition curve to obtain the complete tooth profile curves of the flexspline and the rigid spline. It is characterized in that The specific steps are as follows: (1) Determine the specifications of the harmonic reducer, module m, reduction ratio i of the designed harmonic tooth profile, and the neutral layer curve of the flexspline, and calculate the number of teeth of the flexspline, the number of teeth of the rigid spline, and the equation of the pitch circle of the rigid spline. (2) Establish a global fixed coordinate system, a local coordinate system for the flexspline, and a local coordinate system for the rigid spline. The global fixed coordinate system S w (O w ; X w , Y w ) is fixedly connected to the wave generator, where O w is the center of the wave generator, the X w axis coincides with the minor axis, and the Y w axis coincides with the major axis; The local coordinate system S' of the flexspline f (O' f ; X' f , Y' f ) The point O' f is the equal division point of the flexspline neutral layer curve, the X' f axis coincides with the tangent vector of the O' f point, and the Y' f axis coincides with the normal vector of the O' f point; specifically, the flexspline neutral layer curve is equally divided by arc length, and the number of equal divisions N f is a multiple of the number of teeth z f of the flexspline; local coordinate systems of the flexspline are successively established at each equal division point of the flexspline neutral layer curve, and the coordinate system at the i-th equal arc length position is S' fi (O' fi ; X' fi , Y' fi ), the O' fi point is located at the i-th equal division point, the X' fi axis coincides with the tangent vector of this point, and the Y' fi axis coincides with the normal vector of this point; The local coordinate system S' of the rigid gear c (O' c ; X' c , Y' c ) The point O' c is the equally divided point of the rigid gear pitch circle. The X' c axis coincides with the tangent vector of the O' c point, and the Y' c axis coincides with the normal vector of the O' c point; Specifically, the rigid gear pitch circle curve is equally divided by arc length, and the number of equal divisions N c is a multiple of the number of teeth z c of the rigid gear; The local coordinate system of the rigid gear is established successively at each equally divided point. The coordinate system S' ci (O' ci ; X' ci , Y' ci ) at the i-th equal arc length position, the O' ci point is located at the i-th equally divided point, the X' ci axis coincides with the tangent vector of the O' ci point, and the Y' ci axis coincides with the normal vector of the O' ci point; (3) Select the initial meshing position in the global fixed coordinate system and obtain the corresponding coordinates in the local coordinate systems of the flexspline and the rigid spline through transformation matrices. Specifically, in the global fixed coordinate system S w , an initial meshing point is selected, denoted as point A1, with coordinates (X1, Y1); point A1 is denoted as A′ f1 in the local coordinate system S′ 11 of the flexspline, with coordinates (X′ f11 , Y′ f11 ). The relationship between A′ 11 and point A1 is as follows: (X′ f11 ,Y′ f11 ) = M wf11 (X1, Y1); where M wf11 is the transformation matrix from S w to S′ f1 ; Point A1 is denoted as point B' in the local coordinate system S' of the rigid gear c1 and its coordinates are (X' 11 , Y' c11 ); The relationship between point B' c11 and point A1 is as follows: 11 ​ (X′ c11 ,Y′ c11 ) = M wc11 (X1, Y1); where M wc11 is the transformation matrix from S w to S′ c1 ; (4) According to the deformation law of the flexspline, obtain each meshing point in turn through matrix transformation. Specifically, according to the motion relationship between the points on the neutral layer curve coordinates of the flexspline and the corresponding points on the pitch circle coordinates of the rigid spline, through coordinate transformation, one point is generated simultaneously in the local coordinate systems of the flexspline and the rigid spline from the previous meshing point, and then these two points are transformed to the global fixed coordinate system. A new meshing point is taken between these two points, and the meshing points at each equal division angle are deduced in turn. (5) Determine the number of meshing points j and adjust the meshing range ε j , ε j ∈(0,1), and simultaneously obtain the flexspline meshing curve and the rigid spline meshing curve; after fitting the meshing points, simultaneously obtain the flexspline meshing curve and the rigid spline meshing curve; When \(i = j\), in the flexspline coordinate system \(S'\) corresponding to the \(i\)-th meshing point fi the flexspline meshing arc length is composed of points \(A'\) i,j , \(A'\) i,j-1 … \(A'\) i,2 , \(A'\) i,1 After fitting the meshing points, it is used as the tooth profile curve of the flexspline; where \(A'\) i,j-1 corresponds to the \(i\)-th meshing point and is obtained from the coordinate change of \(A'\) fi-1 in the \(S'\) i-1,j-1 coordinates; at the same time, in the corresponding rigid spline coordinate system \(S'\) ci the rigid spline meshing arc length is composed of points \(B'\) i,j , \(B'\) i,j-1 … \(B'\) i,2 , \(B'\) i,1 After fitting the meshing points, it is used as the tooth profile curve of the rigid spline; where \(B'\) i,j-1 corresponds to the \(i\)-th meshing point and is obtained from the coordinate change of \(B'\) ci-1 in the \(S'\) i-1,j-1 coordinates; (6) Add the tooth root curve and the tooth tip and tooth root transition curves to obtain the complete flexspline tooth profile curve and the rigid spline tooth profile curve. The specific steps are as follows: Use the flexspline meshing curve and the rigid spline meshing curve obtained by fitting in step (5) as the tooth tip curve, and add the tooth root curve. The tooth root curve is an arbitrary smooth curve, but it needs to meet the condition of not interfering with the rigid spline tooth profile. After adding the tooth tip and tooth root transition arc curves, the complete flexspline tooth profile curve is obtained. and the complete rigid spline tooth profile curve The complete tooth profile curve consists of four parts: the tooth tip curve, the tooth root curve, and the tooth tip and tooth root transition arc curves.

2. A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 1, characterized in that: In the global fixed coordinate system S w (O w ; X w , Y w ), the original curve is an ellipse, and the equation is as follows: Elliptic equation: Where a is the major semi - axis of the ellipse and b is the minor semi - axis of the ellipse.

3. A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 1, characterized in that: In the global fixed coordinate system S w (O w ; X w , Y w ), the original curve is a cosine curve, and the equation is as follows: Cosine curve equation: where ρ is the polar radius of the neutral layer after the deformation of the flexspline, R f is the radius of the neutral layer before the deformation of the flexspline, ω0 is the maximum deformation of the flexspline semi-axis, and is the rotation angle of the flexspline.

4. The harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 1, characterized in that: The tooth thickness of the harmonic tooth profile is determined by the abscissa X1 of the initial meshing point A1 in step (3), and its value satisfies the approximate equation X1≈π / 4·m, where m is the module.

5. The harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 1, characterized in that: In the said step (3), the ordinate Y1 of the initial meshing point A1 is selected near the rigid gear pitch circle radius R c such that |R c - Y1| < 0.15 mm.

6. The harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 1, wherein: In step (4), the specific process of deriving the second meshing point from the initial meshing point is as follows: Transform A' 11 from the local coordinate system S' of the flexspline f1 to the local coordinate system S' of the flexspline f2 , denoted as point A' 21 with coordinates (X' f21 , Y' f21 ), as shown in the formula: (X′ f21 ,Y′ f21 ) = M ff21 (X′ f11 ,Y′ f11 ); where M ff21 is the transformation matrix from S′ f1 to S′ f2 ; A′ 21 The point in S w is denoted as A 21 The point, with coordinates (X f21 , Y f21 ). The relationship between point A 21 and point A′ 21 is as follows: (X f21 , Y f21 ) = M′ ff21 (X′ f21 , Y′ f21 ); where M' ff21 is the transformation matrix from S' f1 to S w ; Then, point B′ 11 is transformed from the local coordinate system S′ c1 of the rigid gear to the local coordinate system S′ c2 of the rigid gear, denoted as point B′ 21 with coordinates (X′ c21 , Y′ c21 ); Point B′ 21 is denoted as point B w in S 21 with coordinates (X c21 , Y c21 ). At A 21 and B 21 Select the second meshing point on the line connecting points A and B or in the area near the line. Denote it as point A2 in S w with coordinates (X2, Y2). The position relationship between point A2 and points A 21 and B 21 is as follows: (X2, Y2) = [K x1 (X f21 + X c21 ), K y1 (Y f21 + Y c21 )]; Among them, K x1 , K y1 is a proportionality coefficient, K x1 , K y1 ∈(0, 1); Then the coordinates of point A2 are:

7. The harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 6, characterized in that: In step (4), the i - th meshing point is derived from the (i - 1) - th meshing point: The coordinates of each meshing point are: Among them, K x1 , K x2 …K x(i-1) , K y1 , K y2 …K y(i-1) are proportionality coefficients, and the value range is (0, 1). M wfii is the transformation matrix from coordinate system S w to coordinate system S′ fi . M wcii is the transformation matrix from coordinate system S w to S′ ci . M ffi+1,i is the transformation matrix from coordinate system S′ fi to S′ fi+1 . M′ ffi+1,i is the transformation matrix from coordinate system S′ fi+1 to S w . M cci+1,i is the transformation matrix from coordinate system S′ ci to S′ ci+1 . M′ cci+1,i is the transformation matrix from coordinate system S′ ci+1 to S w .

8. A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the circular spline according to claim 1, characterized in that: In step (5), the number of meshing points determines the meshing range, and the meshing range ε is adjusted by changing the number of meshing points j. j , j = ε j ·N f , N f is the number of equal divisions of the flexspline neutral layer curve; when N f When it is a constant value, the more the number of meshing points j is, the longer the contact arc length is, the larger the meshing range is, and the higher the overlap is.

9. A harmonic tooth profile design method for simultaneously generating the tooth profiles of the flexspline and the rigid spline according to claim 1, characterized in that: The maximum radial deformation of the major semi - axis of the neutral layer curve of the flexspline satisfies the inequality |ω0 - m|<0.1mm, where ω0 is the maximum deformation of the major axis of the flexspline and m is the module. The semi-major axis a of the neutral layer curve of the flexspline and the pitch circle radius R of the rigid spline c satisfy the inequality 4·m>R c -a>0.

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