阅读说明：本技术 一种谐波减速器 (Harmonic speed reducer ) 是由 李国斌 于 2020-11-11 设计创作，主要内容包括：一种谐波减速器,包括具有内齿的刚轮、具有外齿的柔轮和一个波发生器,柔轮设置在所述刚轮内部,波发生器设置在柔轮内部,波发生器为双波发生器,波发生器包括一个柔性轴承和套装在柔性轴承内孔中的凸轮,凸轮横截面外轮廓线由八段偏心圆弧顺次相内接相切连接而成,整体大致呈中心对称的类椭圆形,凸轮安装在柔性轴承内孔后,柔性轴承外圈变形后的外轮廓线也对应为八段偏心圆弧顺次相内接相切连接而成的结构。从而使得波发生器易于达到理想制造精度,能够保证转动灵活,并且使得刚轮和柔轮间齿形啮合平稳。(The utility model provides a harmonic speed reducer ware, including the rigid wheel that has the internal tooth, have the flexbile gear and a wave generator of external tooth, the flexbile gear sets up inside the rigid wheel, wave generator sets up inside the flexbile gear, wave generator is dual-wave generator, wave generator includes a flexible bearing and the cam of suit in the flexible bearing hole, cam cross section outer contour line is formed by eight eccentric circular arcs inscription tangency connection in order, wholly roughly be centrosymmetric type ellipse, the cam is installed behind the flexible bearing hole, outer contour line after the flexible bearing outer lane warp also corresponds the structure that forms for eight eccentric circular arcs inscription connection in order mutually. Therefore, the wave generator is easy to achieve ideal manufacturing precision, can ensure flexible rotation, and enables the tooth-shaped meshing between the rigid gear and the flexible gear to be stable.)

1. The utility model provides a harmonic speed reducer ware, is including the rigid wheel that has the internal tooth, the flexbile gear and a wave generator that has the external tooth, the flexbile gear sets up inside the rigid wheel, wave generator set up inside the flexbile gear, wave generator be two wave generator, wave generator includes a flexible bearing and the cam of suit in the flexible bearing hole, thereby wave generator rotates under drive arrangement's drive and makes the flexbile gear produce elastic deformation to mesh with the rigid wheel with transmission motion and power, its characterized in that: the tooth form of the outer teeth of the flexible gear is a cylindrical double-parabolic tooth form, and the tooth form of the inner teeth of the rigid gear is a conjugate meshing envelope trajectory line of the flexible gear; the outer contour line of the cross section of the cam is formed by sequentially connecting eight eccentric circular arcs in an inscribed and tangent mode, the whole cam is approximately in a centrosymmetric ellipse-like shape, and the eight eccentric circular arcs comprise eccentric circular arcs on two short axis lines which are symmetrically arranged, eccentric circular arcs on two long axis lines which are symmetrically arranged and four eccentric circular arcs between axes which are symmetrically arranged between the eccentric circular arcs on the adjacent short axis lines and the eccentric circular arcs on the long axis lines; the cam is arranged in the inner hole of the flexible bearing, and the outer contour line of the deformed outer ring of the flexible bearing is correspondingly of a structure formed by sequentially internally connecting eight eccentric arcs in a tangent manner.

2. A harmonic reducer according to claim 1 in which: the method for determining the cam outer contour line comprises the following steps:

firstly, determining an outer contour line of a deformed flexible bearing outer ring, which comprises the following specific steps:

1) determining the outer circle radius R6 of the outer ring of the flexible bearing and the maximum deformation e of the flexible bearing; the maximum deformation e of the flexible bearing is obtained by the parameter of the flexible bearing purchased according to the design volume of the speed reducer;

2) determination of the eccentric arc center angle theta between the axes and the eccentric arc eccentric distance R1 between the axes: selecting a value in the range of 0< R1 ≦ e as the eccentric distance R1 of the curvature center of the eccentric arc between the axes, wherein the radius of the eccentric arc between the axes is equal to the outer ring peripheral radius R6 of the flexible bearing;

selecting the central angle theta of the eccentric circular arc between the axes: pi/10 < theta < pi/2;

the central angle of the eccentric arc among the axes refers to an included angle formed by connecting two ends of the eccentric arc among the axes and the curvature center of the eccentric arc;

3) and determining the central angle 2 gamma of the eccentric circular arc on the short axis:

determining the numerical value of the central angle 2 gamma of the eccentric circular arc on the short axis, wherein gamma is more than 0 and less than pi/18; wherein, the central angle 2 gamma of the eccentric arc on the minor axis means that the two ends of the eccentric arc form an included angle with the connecting line of the curvature centers of the eccentric arc;

radius of eccentric arc R8 on minor axis: r8 ═ R6+ R1sin α/sin γ;

eccentricity R19 of the eccentric arc on the minor axis: r19 ═ R1sin (pi- γ -a);

4) determining an acute angle alpha between a connecting line 0E between the eccentric arc curvature center point E between the axes and the wave generator center 0 and the y axis:

ɑ＝arctg(((π/2-θ-γ)sinγ)/(γcos(θ+γ)))

5) determination of the radius R8 of the eccentric circular arc on the minor axis: r8 ═ R6+ R1sin α/sin γ;

determination of the eccentricity R19 of the eccentric arc on the minor axis:

r19 ═ R1sin (pi- γ -a)/sin γ; 6) determining an eccentric arc on the major axis;

the central angle of the eccentric arc on the major axis is an included angle formed by connecting two ends of the eccentric arc and the curvature center of the eccentric arc, and half of the central angle of the eccentric arc on the major axis is pi/2-gamma-theta;

the radius of the eccentric arc on the major axis is R5, R5 ═ R6-R1 ═ cos alpha/cos (pi/2-gamma-theta);

the eccentric distance of the eccentric arc on the major axis is R3; r3 ═ R1sin α + R1cos α tg (γ + θ),

or R3 ═ R1sin α + (R6-R5) cos (pi/2- γ - θ);

7) determining a short half shaft and a long half shaft:

determining the long half shaft R2: r2 ═ R5+ R1 ═ sin α + (R6-R5) cos (pi/2- γ - θ);

determining a minor half axis R9; r9 ═ R8-R19.

8) Utilizing the relational expression: verifying by using R2-R9 ≦ e, and if the relation is not satisfied, reselecting R1 and repeating the steps until the relation is satisfied;

wherein, R6 is L1/2 pi;

then, the flexible bearing thickness R69 is subtracted from the dimensions of the eccentric arc radius R5 on the major axis, the eccentric arc radius R6 between axes, the eccentric arc radius R8 on the minor axis, the major axis R2, and the minor axis R9 among the above dimensions, to obtain the curvature radius dimension of each eccentric arc corresponding to the cam normal direction.

3. A harmonic reducer according to claim 1 in which: the same end of the rigid wheel and the flexible wheel is provided with a fixed bearing, the rigid wheel is connected with the outer ring of the fixed bearing, and the flexible wheel is connected with the inner ring of the fixed bearing.

4. A harmonic reducer according to claim 1 in which: the method for determining the external tooth profile of the flexible gear comprises the following steps:

1) establishing a plane rectangular coordinate system, firstly enabling the center O of the flexible gear to coincide with the origin of coordinates, and enabling a connecting line OG of the center O of the flexible gear and a tooth root point G of external teeth of the flexible gear to coincide with an x axis; an included angle between a connecting line OD of the center O of the flexible gear and the addendum point D of the external teeth of the flexible gear and the x axis is pi/n, wherein n is the number of teeth, and pi/n is half of a tooth distribution angle 2 pi/n;

let the root parabola where the root point G is located be called parabola 1, and the addendum parabola where the addendum point D is located be called parabola 2, then the equation of parabola 1 is:

y²＝2p₁(x-R₇)；

wherein p is₁Is the focal length of parabola 1，R₇The radius of the flexible gear tooth root circle;

the smooth tangency closure point of parabola 1 and parabola 2 is set as C₂(x₂,y₂) (ii) a Closure point C₂(x₂,y₂) The perpendicular point to the OD line is set to C₁(ii) a Parabola 1 at the point of closure C₂(x₂,y₂) The slope angle of the tangent line K is set to be beta,

then: parabola 1 at C₂(x₂,y₂) The tangent equation for the points is: y is₂y＝p₁(x+x₂-2R₇) (ii) a Closure point C₂(x₂,y₂) Satisfies the following conditions: r₇＜x₂＜R₇+h；Wherein h is the tooth height;

closure point C₂(x₂,y₂) The slope angle of the tangent K is β: beta is arctg [ p ]₁/y₂]；

Closure point C₂(x₂,y₂) To the vertical point C₁Distance C of₂ C₁The calculation is as follows;

vertical point C₁Distance O C from gear center O₁The calculation is as follows:

then, when the parabola 1 is rotated clockwise by pi/n angle, the junction C on the parabola 1₂After the cutting K rotates, the cutting K becomes K₁，K₁The slope angle of (d) is: beta-pi/n;

when the parabola 1 and the parabola 2 rotate by the same angle, the point of convergence C on the parabola 1₂With the point of merger C on parabola 2 "₂Always a coincidence point；

When parabola 2 is rotated clockwise by an angle of pi/n, the equation for parabola 2 is: y is²＝2p₂(x-R₇-h) wherein p₂Is the focal length of parabola 2, at which parabola 2 is at the point of closure C "₂(x"₂,y"₂) The tangent equation of (c) is: y'₂y＝p₂(x+x"₂-2R₇-2h)；

Point of merger C on parabola 2 "₂(x"₂,y"₂) Tangent line K₂The slope angle of (d) is: arctg (p)₂/y"₂)，K₂And K₁The two phases coincide, so that: arctg (p)₂/y"₂) β -pi/n, because β arctg [ p ═₁/y₂]Therefore, arctg (p)₂/y"₂)＝arctg(p₁/y₂)-π/n ①；

Then, p is selected₁,x₂,p₂Substituting any two values into equation to calculate another value, and finally obtaining p when the other value also meets the following conditions₁,x₂,p₂Substituting into parabola 1 and parabola 2 equation to obtain two parabolas and the coordinates of the closure point, and finishing the tooth shape design of the double parabolas:

focal length p of parabola 1₁Need to be satisfied withWithin the range;

focal length p of parabola 2₂Must be satisfied in absolute valueWithin the range of p₂The actual value of (a) is negative; x is the number of₂Need to satisfy R₇＜x₂＜R₇+h。

5. A harmonic reducer according to claim 4 in which:

focal length p of parabola 1₁Is composed ofA nearby value; focal length p of parabola 2₂Has an absolute value ofA nearby value; x is the number of₂Is (2R)₇+ h)/2.

Technical Field

The invention relates to the technical field of speed reducers, in particular to a harmonic speed reducer.

Background

The traditional Harmonic reducer (HD) is generally a transmission device that uses a pure elliptical wave generator to generate a controllable elastic deformation wave to realize motion and power transmission, and is widely applied to the fields of chip equipment, robots, manipulators, numerical control equipment, automation equipment, aerospace and the like at present because of the advantages of small volume, large torque, high positioning accuracy, small vibration, impact resistance and the like.

However, the tooth profile of the early harmonic reducer adopts a triangular tooth profile, so that the manufacturing difficulty is high, the transmission precision is low, although involute or s-shaped tooth profiles are mostly adopted in the market at present, the meshing rate is improved compared with the early triangular tooth profile, but the meshing rate can only reach 10% -20%, and the requirement of the high-precision harmonic reducer is still difficult to meet.

In addition, the harmonic reducer in the prior art usually adopts a traditional elliptical wave generator, which also makes the design and manufacture of the transmission device complicated and difficult, and in the often manufactured products, the elliptical wave generator cannot realize that the tooth shape of the supported flexible gear and the tooth shape designed in advance of the flexible gear reach the same requirement when the flexible gear is supported by the elliptical wave generator; that is, the current harmonic reducer structure makes it difficult for the manufactured finished product to achieve the desired manufacturing accuracy, and therefore, there is a need for a harmonic reducer structure suitable for manufacturing a high-accuracy harmonic reducer.

Disclosure of Invention

In order to solve the technical problem, the invention provides a harmonic reducer.

The technical scheme adopted by the invention to solve the technical problems is as follows: a harmonic reducer comprises a rigid gear with internal teeth, a flexible gear with external teeth and a wave generator, wherein the flexible gear is arranged in the rigid gear, the wave generator is arranged in the flexible gear, the wave generator is a double-wave generator and comprises a flexible bearing and a cam sleeved in an inner hole of the flexible bearing, the wave generator is driven by a driving device to rotate so as to enable the flexible gear to generate elastic deformation and be meshed with the rigid gear to transfer motion and power, the external tooth profile of the flexible gear is a cylindrical double-parabolic profile, and the internal tooth profile of the rigid gear is a conjugate meshing envelope track line of the flexible gear; the outer contour line of the cross section of the cam is formed by sequentially connecting eight eccentric circular arcs in an inscribed and tangent mode, the whole cam is approximately in a centrosymmetric ellipse-like shape, and the eight eccentric circular arcs comprise eccentric circular arcs on two short axis lines which are symmetrically arranged, eccentric circular arcs on two long axis lines which are symmetrically arranged and four eccentric circular arcs between axes which are symmetrically arranged between the eccentric circular arcs on the adjacent short axis lines and the eccentric circular arcs on the long axis lines; the cam is arranged in the inner hole of the flexible bearing, and the outer contour line of the deformed outer ring of the flexible bearing is correspondingly of a structure formed by sequentially internally connecting eight eccentric arcs in a tangent manner.

The method for determining the outer contour line of the cam comprises the following steps:

firstly, determining an outer contour line of a deformed flexible bearing outer ring, which comprises the following specific steps:

1) determining the outer circle radius R6 of the outer ring of the flexible bearing and the maximum deformation e of the flexible bearing; the maximum deformation e of the flexible bearing is obtained by the parameter of the flexible bearing purchased according to the design volume of the speed reducer;

2) determination of the eccentric arc center angle theta between the axes and the eccentric arc eccentric distance R1 between the axes:

selecting a value in a range between 0< R1 ≦ e as an eccentricity R1 of a center of curvature of the eccentric arc between the axes;

selecting the radius of the eccentric arc between the axes to be equal to the outer ring peripheral radius R6 of the flexible bearing;

selecting the central angle theta of the eccentric circular arc between the axes: pi/10 < theta < pi/2;

the central angle of the eccentric arc among the axes refers to an included angle formed by connecting two ends of the eccentric arc among the axes and the curvature center of the eccentric arc;

3) and determining the central angle 2 gamma of the eccentric circular arc on the short axis:

determining the numerical value of the central angle 2 gamma of the eccentric circular arc on the short axis, wherein gamma is more than 0 and less than pi/18; wherein, the central angle 2 gamma of the eccentric arc on the minor axis means that the two ends of the eccentric arc form an included angle with the connecting line of the curvature centers of the eccentric arc;

4) determining an acute angle alpha between a connecting line 0E between the eccentric arc curvature center point E between the axes and the wave generator center 0 and the y axis:

ɑ＝arctg(((π/2-θ-γ)sinγ)/(γcos(θ+γ)))

5) determination of the radius R8 of the eccentric circular arc on the minor axis: r8 ═ R6+ R1sin α/sin γ;

determination of the eccentricity R19 of the eccentric arc on the minor axis:

R19＝R1sin(π-γ-ɑ)/sinγ；

6) determining an eccentric arc on the major axis;

the central angle of the eccentric arc on the major axis is an included angle formed by connecting two ends of the eccentric arc and the curvature center of the eccentric arc, and half of the central angle of the eccentric arc on the major axis is pi/2-gamma-theta;

the radius of the eccentric arc on the major axis is R5, R5 ═ R6-R1 ═ cos alpha/cos (pi/2-gamma-theta);

the eccentric distance of the eccentric arc on the major axis is R3; r3 ═ R1sin α + R1cos α tg (γ + θ), or R3 ═ R1sin α + (R6-R5) cos (pi/2- γ - θ);

7) determining a short half shaft and a long half shaft:

determining the long half shaft R2: r2 ═ R5+ R1 ═ sin α + (R6-R5) cos (pi/2- γ - θ);

determining a minor half axis R9; r9 ═ R8-R19.

8) Utilizing the relational expression: verifying by using R2-R9 ≦ e, and if the relation is not satisfied, reselecting R1 and repeating the steps until the relation is satisfied;

wherein, R6 is L1/2 pi;

then, the flexible bearing thickness R69 is subtracted from the dimensions of the eccentric arc radius R5 on the major axis, the eccentric arc radius R6 between axes, the eccentric arc radius R8 on the minor axis, the major axis R2, and the minor axis R9 among the above dimensions, to obtain the curvature radius dimension of each eccentric arc corresponding to the cam normal direction.

And further, a fixed bearing is arranged at the same end of the rigid wheel and the flexible wheel, the rigid wheel is connected with the outer ring of the fixed bearing, and the flexible wheel is connected with the inner ring of the fixed bearing.

The method for determining the tooth profile of the external teeth of the gear comprises the following steps:

1) establishing a plane rectangular coordinate system, firstly enabling the center O of the flexible gear to coincide with the origin of coordinates, and enabling a connecting line OG of the center O of the flexible gear and a tooth root point G of external teeth of the flexible gear to coincide with an x axis; an included angle between a connecting line OD of the center O of the flexible gear and the addendum point D of the external teeth of the flexible gear and the x axis is pi/n, wherein n is the number of teeth, and pi/n is half of a tooth distribution angle 2 pi/n;

let the root parabola where the root point G is located be called parabola 1, and the addendum parabola where the addendum point D is located be called parabola 2, then the equation of parabola 1 is:

y²＝2p₁(x-R₇)；

wherein p is₁Is the focal length of parabola 1, R₇The radius of the flexible gear tooth root circle;

the smooth tangency closure point of parabola 1 and parabola 2 is set as C₂(x₂,y₂) (ii) a Closure point C₂(x₂,y₂) The perpendicular point to the OD line is set to C₁(ii) a Parabola 1 at the point of closure C₂(x₂,y₂) The slope angle of the tangent line K is set to be beta,

then: parabola 1 at C₂(x₂,y₂) The tangent equation for the points is: y is₂y＝p₁(x+x₂-2R₇)

Closure point C₂(x₂,y₂) Satisfies the following conditions: r₇＜x₂＜R₇+h；Wherein h is the tooth height;

closure point C₂(x₂,y₂) The slope angle of the tangent K is β: beta is arctg [ p ]₁/y₂]；

Closure point C₂(x₂,y₂) To the vertical point C₁Distance C of₂ C₁The calculation is as follows;

vertical point C₁Distance O C from gear center O₁The calculation is as follows:

then, when the parabola 1 is rotated clockwise by pi/n angle, the junction C on the parabola 1₂After the tangent line K rotates, the K becomes K₁，K₁The slope angle of (d) is: beta-pi/n;

when the parabola 1 and the parabola 2 rotate by the same angle, the point of convergence C on the parabola 1₂With the point of merger C on parabola 2 "₂Always a coincidence point;

when parabola 2 is rotated clockwise by an angle of pi/n, the equation for parabola 2 is: y is²＝2p₂(x-R₇-h) wherein p₂Is the focal length of parabola 2, at which parabola 2 is at the point of closure C "₂(x"₂,y"₂) The tangent equation of (c) is: y'₂y＝p₂(x+x"₂-2R₇-2h)；

Point of merger C on parabola 2 "₂(x"₂,y"₂) Tangent line K₂The slope angle of (d) is: arctg (p)₂/y"₂)，K₂And K₁The two phases coincide, so that: arctg (p)₂/y"₂) β -pi/n, because β arctg [ p ═₁/y₂]Therefore, arctg (p)₂/y"₂)＝arctg(p₁/y₂)-π/n ①；

Then, p is selected₁,x₂,p₂Substituting any two values into equation to calculate another value, and finally obtaining p when the other value also meets the following conditions₁,x₂,p₂Substituting into parabola 1 and parabola 2 equation to obtain two parabolas and the coordinates of the closure point, and finishing the tooth shape design of the double parabolas:

focal length p of parabola 1₁Need to be satisfied withWithin the range;

focal length p of parabola 2₂Must be satisfied in absolute valueWithin the range of p₂The actual value of (a) is negative; x is the number of₂Need to satisfy R₇＜x₂＜R₇+h。

Preferably, the focal length p of the parabola 1₁Is composed ofA nearby value; focal length p of parabola 2₂Has an absolute value ofA nearby value; x is the number of₂Is (2R)₇+ h)/2.

Has the advantages that:

according to the invention, the tooth form of the flexible gear adopts the double-parabola tooth form, and the tooth form of the internal tooth of the rigid gear is the conjugate meshing envelope trajectory of the flexible gear, so that the external tooth of the flexible gear and the internal tooth of the rigid gear are meshed smoothly, and the meshing rate is greatly improved and can reach more than 30%. The harmonic reducer can easily reach the expected manufacturing precision and transmission precision by matching with a wave generator formed by connecting eight sections of circular arcs in an inscribed tangent smooth bridging manner, can ensure flexible rotation, enables the tooth shape meshing between a rigid wheel and a flexible wheel to be more stable, improves the capacity of transmission torque, and prolongs the service life of the harmonic reducer.

The present invention will be described in further detail with reference to the drawings and specific examples. In this document, when referring to angles, they are values in radians (in rad, omitted).

Drawings

FIG. 1 is a schematic view of the structure of the present invention.

FIG. 2 is a schematic view A-A of FIG. 1.

FIG. 3 is a schematic diagram of a flexible gear tooth profile according to the present invention.

Fig. 4 is a schematic diagram of the flexspline of fig. 3 after rotation.

Fig. 5 is a schematic view of the state of the compliant bearing before deformation.

Fig. 6 is a diagram showing a deformed state of the compliant bearing after the cam is fitted into the inner race of the compliant bearing (which is also a schematic view of the wave generator).

Fig. 7 is a simplified schematic diagram of fig. 6 (only the outer contour of the flexible bearing outer race is shown in the figure).

Detailed Description

As shown in fig. 1 to 3, the harmonic reducer comprises a rigid gear 1 with internal teeth 101, a flexible gear 2 with external teeth 201, and a wave generator, wherein the flexible gear 2 is arranged inside the rigid gear 1, and the wave generator is arranged inside the flexible gear 2.

The wave generator is a double-wave generator and comprises a flexible bearing and a cam 3 sleeved in an inner hole of the flexible bearing, and the wave generator rotates under the driving of the driving device so as to enable the flexible gear 2 to generate elastic deformation, so that the external teeth 201 of the flexible gear 2 are in conjugate meshing with the internal teeth 101 of the rigid gear 1 to transmit motion and power.

The cam cross section outer contour line is formed by connecting eight eccentric circular arcs in an inscribed tangent mode in sequence, the whole cam cross section outer contour line is roughly in a centrosymmetric ellipse-like shape, the eight eccentric circular arcs comprise eccentric circular arcs on two short axis lines which are symmetrically arranged, eccentric circular arcs on two long axis lines which are symmetrically arranged and eccentric circular arcs between axes which are symmetrically arranged on the adjacent short axis lines and the eccentric circular arcs on the long axis lines, the curvature centers of the eccentric circular arcs on the short axis lines are located on the short axis lines, the curvature centers of the eccentric circular arcs on the long axis lines are located on the long axis lines, the curvature centers of the eccentric circular arcs between the axes are located near the intersection points of the long axis lines and the short axis lines, the curvature centers of the eccentric circular arcs between the axes are not located on the short axis lines or on the long axis lines, the curvature radii of the eccentric circular arcs between the axes are the same as the radii of inner holes of the flexible bearings, the cam is installed in the inner holes of the flexible bearings, and the outer contour line after the outer rings of the flexible bearings are deformed correspondingly connected in an inscribed tangent mode in sequence for the eight eccentric circular arcs to form the ellipse-like the tangent mode The structure of (1), namely the outer contour line of the wave generator is an eight-segment arc structure.

The wave generator of the present invention can be called a two-phase eight-segment arc wave generator because the phase number of the wave generator of the present invention is 2 (in the transmission process, the cycle number of the wave generator rotating for one circle and deforming a certain point on the flexible gear is called phase number or wave number), and the outer contour line of the wave generator is eight segments of arcs. The two-phase eight-section arc wave generator is arranged in the flexible gear 2 to support the flexible gear 2, and the flexible gear 2 is rolled, supported and pressed by the two-phase eight-section arc wave generator to force the flexible gear 2 to be meshed with the internal teeth 101 of the rigid gear 1; the thickness of the flexspline 2 is Q (the distance from the deepest portion of the root of the flexspline to the inner diameter of the flexspline), and the number s of the teeth of the internal teeth 101 of the rigid spline is 2 or an integer multiple of 2 greater than the number n of the teeth of the external teeth 201 of the flexspline 2.

In this embodiment, as shown in fig. 1, the flexible gear 2 is a thin-walled cup, a fixed bearing is disposed at the cup end of the flexible gear, the rigid gear 1 is connected with an outer ring 8 of the fixed bearing through an outer ring mounting bolt 5, and a cup bottom of the flexible gear 2 is connected with an inner ring 7 of the fixed bearing through an inner ring mounting bolt 6.

The working process of the harmonic reducer is as follows: the rigid wheel 1 is fixed (directly or indirectly fixedly installed on a relatively fixed component in an application device), the motor drives the input shaft to rotate so as to drive the cam 3 to rotate, the direction of the flexible wheel 2 actively rotating is opposite to that of the cam 3, and the expression of the rotation angular speed omega 1 of the flexible wheel 2 is as follows: ω 1 ═ - (s-n) ω/n; where ω is the rotational angular velocity of the cam 3, and the remaining parameters are explained in the above paragraph, and the ratio of- (s-n)/n in the expression can be defined as the reduction ratio. The cam 3 can be an annular structure, is sleeved on the input shaft and is fixedly connected with the input shaft (key connection and the like); the cam 3 may be formed integrally with the input shaft. The structure of the former is shown in the drawings of the present embodiment, and the input shaft is not shown in the drawings.

As shown in fig. 5 and 6, in order to facilitate the detailed description of the present invention, the wave generator is described as being placed in a planar rectangular coordinate system. A rectangular coordinate system is established by taking the center of the two-phase eight-section arc wave generator as a coordinate origin, the long axis (also called as the long axis) of the two-phase eight-section arc wave generator is positioned on the x axis, the short axis (also called as the short axis) is positioned on the y axis (therefore, the x axis can be called as the long axis, and the y axis can be called as the short axis)), the two-phase eight-section arc wave generator is divided into four quadrants (a first quadrant to a fourth quadrant) by the x axis and the y axis, and the outer contour shapes of the four quadrants are completely symmetrical.

Fig. 5 is a diagram showing a deformed state of the flexible bearing after the cam 3 is fitted into the inner race 401 of the flexible bearing in the present invention. At this time, the outer contour of the flexible bearing outer ring 403 is identical to the outer contour of the cam 3, and includes eight arcs, and the eight arcs are all disposed deviating from the center of the flexible bearing (coinciding with the center of the cam, also being the center of the wave generator), and thus are eight eccentric arcs. The whole body is in a centrosymmetric ellipse-like shape, and eight eccentric arcs are eccentric arcs A on a minor axis line in sequence₁A. Eccentric arc AB between axes and eccentric arc BB on major axis₃Eccentric arc B between axes₃A₃Eccentric arc A on minor axis₃A₂Eccentric arc A between axes₂B₂Eccentric arc B on major axis₂ B₁And the eccentric arc B between the axes₁A₁。

The cam cross section outer contour line is determined by the following method:

firstly, determining an outer contour line of a deformed flexible bearing outer ring, which comprises the following specific steps:

1) the difference e between the major axis OC and the minor axis OA (or OG) of the outer contour of the flexible bearing after deformation (i.e., the maximum deformation of the wave generator, which is also the maximum deformation of the flexible bearing — which is equal to the difference between the major axis and the minor axis when the deformation of the flexible bearing is the maximum) and the outer circumference L1 of the flexible bearing outer race 403 are determined on the basis that the inner circumference L of the flexible gear 2 is equal to the outer circumference L1 of the flexible bearing outer race 403.

2) Determination of the eccentric arc center angle theta between the axes and the eccentric arc eccentric distance R1 between the axes:

selecting a value within the range of 0< R1 ≦ E, and determining the value as an eccentric distance R1 between the axes according to experience or a summary formula by a person skilled in the art, wherein in FIG. 6, the distance from the center point E of the curvature of the eccentric arc between the axes to the center point O of the wave generator is R1;

selecting the radius of an eccentric circular arc between the axes to be equal to the outer ring peripheral radius R6 of the flexible bearing, wherein R6 is L1/2 pi;

selecting the central angle theta of the eccentric circular arc between the axes: preferably, π/10< θ < π/2;

the central angle of the eccentric arc between the axes means that the two ends of the eccentric arc between the axes form an included angle with the connection line of the curvature centers of the eccentric arc, and the included angle between the connection line of the EA and the connection line of the EB in fig. 6 is theta;

3) and determining the central angle 2 gamma of the eccentric circular arc on the short axis:

determining the value of the central angle 2 gamma of the eccentric circular arc on the short axis, preferably, 0< gamma < pi/18; the central angle 2 γ of the eccentric arc on the minor axis means that an included angle is formed between two ends of the eccentric arc and a connection line of the curvature centers of the eccentric arc and the minor axis, as shown in fig. 6, the curvature center of the eccentric arc A1A on the minor axis is located at a point M on the y axis, and an included angle between a MA connection line and a MA1 connection line is 2 γ; the eccentric arc A1A on the short axis intersects with the y axis at D, and the included angle between the MA connecting line and the MD connecting line is a gamma angle;

the length of MA1 or MD or MA is equal to the radius of the eccentric arc on the minor axis R8:

the distance from the point M to the center O of the wave generator, namely the eccentric distance of the eccentric arc on the minor axis is R19:

4) determining an acute angle alpha between a connecting line 0E between the eccentric arc curvature center point E between the axes and the wave generator center 0 and the y axis:

ɑ＝arctg(((π/2-θ-γ)sinγ)/(γcos(θ+γ)))

5) determination of the radius R8 of the eccentric circular arc on the minor axis: r8 ═ R6+ R1sin α/sin γ;

determination of the eccentricity R19 of the eccentric arc on the minor axis:

R19＝R1sin(π-γ-ɑ)/sinγ；

6) determining an eccentric arc on the major axis;

the central angle of the eccentric arc on the major axis is the included angle formed by the two ends of the eccentric arc and the connecting line of the curvature center of the eccentric arc. As shown in fig. 6, the eccentric arc BB3 on the major axis intersects the x axis at point C, point H is the center of curvature of the eccentric arc BB3 on the major axis, the included angle between the HB connection line and the HB3 connection line is the central angle of the eccentric arc on the major axis, and the included angle between HB and HC is pi/2- γ - θ;

HB or HC or HB3 is equal to the major axis eccentric arc radius R5 (the arc radius as used herein refers to the corresponding radius of curvature of the respective eccentric arc),

R5＝R6-R1*cosα/cos(π/2-γ-θ)；

the distance between the point H and the center O of the wave generator is R3, namely the eccentric distance of the eccentric arc on the major axis; r3 ═ R1sin α + R1cos α tg (γ + θ) or R3 ═ R1sin α + (R6-R5) cos (pi/2- γ - θ)

7) Determining a short half shaft and a long half shaft:

determining the long half shaft R2: r2 ═ R5+ R1 ═ sin α + (R6-R5) cos (pi/2- γ - θ);

the line connecting the center O and the point C of the wave generator in FIG. 6 is the minor semi-axis R₂。

Determining a minor half axis R9; r9 ═ R8-R19.

8) Utilizing the relational expression: and verifying by using R2-R9 ≦ e, and if the relation is not satisfied, reselecting R1 and repeating the steps until the relation is satisfied.

Then, of the above dimensions, the flexible bearing thickness R69(R69 is R6-R99, and R99 is the inner hole radius of the flexible bearing inner race) is subtracted from the dimensions of the eccentric arc radius R5 on the major axis, the eccentric arc radius R6 between axes, the eccentric arc radius R8 on the minor axis, the major axis R2, and the minor axis R9, respectively, to obtain the curvature radius dimension of each eccentric arc in the normal direction of the cam 3.

By adopting the invention, when the flexible gear 2 works on the same arc line of the double-wave four-segment arc wave generator, the external tooth shape of the flexible gear 2 is always in the same arc line state, namely, the flexible gear 2 is always in the same deformation condition, and the characteristic provides a new method and a new way for the tooth shape design and processing of the flexible gear 2 and the improvement of the transmission conjugate meshing precision; compared with the prior art that the deformation of the flexible gear tooth shape cannot be accurately determined, and only the deformation of the flexible gear tooth shape can be calculated or estimated according to experience and corrected through trial and error, the method only needs to consider the deformation of the flexible gear 2 on the corresponding section of the arc and the influence of the deformation of the tooth shape, so that the design is accurate, the tooth shape design and the machining precision of the flexible gear of the harmonic reducer are improved, the transmission precision and the transmission torque of the harmonic reducer are improved, the vibration noise is reduced, the heat is reduced, and the service life of the harmonic reducer is prolonged.

In order to further improve the manufacturing accuracy and the transmission accuracy of the harmonic reducer, the external tooth profile of the flexspline 2 in this embodiment preferably adopts a cylindrical double-parabolic (including a root parabola and a tip parabola, collectively called a double parabola) structure, and the internal teeth of the rigid spline are in conjugate meshing with the external teeth of the flexspline, as shown in fig. 3.

The outer teeth on the flexible gear are uniformly distributed along the periphery of the flexible gear according to the same pitch P, namely the circumference of a center point distribution circle of the tooth height of the outer teeth 201 of the flexible gear 2 is divided by the number n of teeth of the outer teeth 201 of the flexible gear 2 to form the pitch P.

The pitch P is preferably selected in the range of 2.4 (P)₁-p₂)≤P≤4(p₁-p₂) Within the range, the number of teeth n of the columnar double-parabolic external teeth 201 is selected from 30-500, wherein p₁、p₂Two focal lengths of the cylindrical double-parabolic outer teeth. The reason why this range is preferable is: if the number of teeth n is more than 500, the pitch P needs to be reduced under the premise of not considering the increase of the volume of the whole harmonic reducer (namely not considering the increase of the circumference of a midpoint distribution circle of the tooth height of the external tooth 201 of the flexible gear 2), and when the pitch is too small, the pitch P is less than or equal to 2.4(P₁-p₂) When the thickness of the external teeth of the steel wheel is too thin, the tooth tops are too sharp, and the strength of the external teeth is reduced; if it is notToo few teeth number 2 of the cylindrical double parabolic external teeth 201 causes the internal tooth pitch 4 (p)₁-p₂) When the distance between adjacent inner teeth on the rigid wheel is less than or equal to P, the transmission ratio of the harmonic reducer is reduced, and the miniaturization of the reducer is not facilitated; the outer teeth of the flexible gear are uniformly distributed, and the pitch p is 2.4 (p)₁-p₂)≤P≤4(p₁-p₂) Within this range, a high reduction ratio and high mechanical strength can be easily obtained, and a harmonic reducer having a high reduction ratio and a higher natural frequency can be formed.

The method for designing the external tooth double-parabolic tooth shape of the flexible gear comprises the following steps:

establishing a plane rectangular coordinate system, firstly enabling the center O of the flexible gear to coincide with the origin of coordinates, and enabling a connecting line OG of the center O of the flexible gear and a tooth root point G of external teeth of the flexible gear to coincide with an x axis; the included angle between the connecting line OD of the center O of the flexible gear and the external tooth crest point D of the flexible gear and the x axis is pi/n (n is the number of teeth, and the tooth distribution angle is 2 pi/n), as shown in FIG. 3.

Let the root parabola where the root point G is located be called parabola 1, and the addendum parabola where the addendum point D is located be called parabola 2, then the equation of parabola 1 is:

y²＝2p₁(x-R₇)；

wherein p is₁Is the focal length of parabola 1, R₇Is the root circle radius;

the smooth tangency closure point of parabola 1 and parabola 2 is set as C₂(x₂,y₂) (ii) a Closure point C₂(x₂,y₂) The perpendicular point to the OD line is set to C₁(ii) a Parabola 1 at the point of closure C₂(x₂,y₂) The slope angle of the tangent line K is set to be beta,

then: parabola 1 at C₂(x₂,y₂) The tangent equation for the points is: y is₂y＝p₁(x+x₂-2R₇)；

Closure point C₂(x₂,y₂) Satisfies the following conditions: r₇<x₂<R₇+h；Wherein h is the tooth height;

closure point C₂(x₂,y₂) Slope angle β of tangent line K: beta is arctg [ p ]₁/y₂]；

Closure point C₂(x₂,y₂) To the vertical point C₁Distance C of₂ C₁The calculation is as follows;

vertical point C₁Distance O C from gear center O₁The calculation is as follows:

when the parabola 1 is rotated clockwise by pi/n, the point of intersection C on the parabola 1 is shown in FIG. 4₂The tangent K at the position becomes the tangent K after rotating₁，K₁The slope angle is: beta-pi/n;

when the parabola 1 and the parabola 2 rotate by the same angle, the point of convergence C on the parabola 1₂With the point of merger C on parabola 2 "₂Always a coincidence point;

when parabola 2 is rotated clockwise by an angle of pi/n, the equation for parabola 2 is: y is²＝2p₂(x-R₇-h) wherein p₂Is the focal length of parabola 2, and at this time, parabola 2 is at the point of closure C₂”(x"₂,y"₂) The tangent equation of (c) is: y'₂y＝p₂(x+x"₂-2R₇-2h)；

Point of convergence C on parabola 2₂”(x"₂,y"₂) Tangent line K₂The slope angle of (d) is: arctg (p)₂/y"₂)，K₂And K₁Coincide with each other (K)₂Not shown in the figures),

therefore, the method comprises the following steps: arctg (p)₂/y"₂) β -pi/n, because β arctg [ p ═₁/y₂]Therefore, arctg (p)₂/y"₂)＝arctg(p₁/y₂)-π/n ①

Then, p is selected₁,x₂,p₂Substituting any two values into equation to calculate another value, and finally obtaining p when the other value also meets the following conditions₁,x₂,p₂Substituting into parabola 1 and parabola 2 equation to obtain two parabolas and the coordinates of the closure point, and finishing the tooth shape design of the double parabolas:

focal length p of parabola 1₁Need to be satisfied withWithin the range, it is preferableA nearby value;

focal length p of parabola 2₂Must be satisfied in absolute valueWithin the range, it is preferableA nearby value; p is a radical of₂Is negative.

x₂Need to satisfy R₇<x₂<R₇+ h, preferably (2R)₇A value of + h)/2 or so;

GC in FIG. 3₂And C₂D, synthesizing a double-parabola half-side tooth profile.

It should be noted that the above embodiments are only for illustrating the present invention, but the present invention is not limited to the above embodiments, and any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention fall within the protection scope of the present invention.