CN112392935A - Harmonic speed reducer - Google Patents

Harmonic speed reducer Download PDF

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CN112392935A
CN112392935A CN202011255147.7A CN202011255147A CN112392935A CN 112392935 A CN112392935 A CN 112392935A CN 202011255147 A CN202011255147 A CN 202011255147A CN 112392935 A CN112392935 A CN 112392935A
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parabola
flexible
point
gear
wave generator
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CN112392935B (en
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李国斌
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H49/00—Other gearings
    • F16H49/001—Wave gearings, e.g. harmonic drive transmissions
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0833—Flexible toothed member, e.g. harmonic drive
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/17—Toothed wheels
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H2057/0087—Computer aided design [CAD] specially adapted for gearing features ; Analysis of gear systems

Abstract

The utility model provides a harmonic speed reducer device, 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 flexible bearing hole, cam cross section outer contour line is formed by the tangent connection of four sections eccentric circular arcs in the same order in the looks, whole class ellipse that is central symmetry roughly, in two sections adjacent eccentric circular arcs, the centre of curvature of one section eccentric circular arc is located the minor axis, the centre of curvature of another section eccentric circular arc is located the major axis, 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 four sections eccentric circular arcs in the same order in the looks tangent connection. 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.

Description

Harmonic speed reducer
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 traditional elliptical wave generator makes the design and manufacture of the transmission device complex and difficult, and in products which are often manufactured, when the elliptical wave generator props up the flexible gear, the tooth shape of the propped flexible gear can not meet the requirement that the tooth shape of the flexible gear is consistent with the tooth shape which is designed in advance by the flexible gear; that is to say, the present harmonic reducer structure makes the manufacturing difficulty and the processing difficulty relatively large, and is difficult to achieve the expected manufacturing precision, so a harmonic reducer structure suitable for manufacturing a high-precision harmonic reducer is needed.
Disclosure of Invention
In order to solve the above technical problem, the present invention provides a harmonic reduction gear.
The technical scheme adopted by the invention to solve the technical problems is as follows: the utility model provides a harmonic speed reducer device, including the rigid wheel that has the internal tooth, have flexible wheel and a wave generator of external tooth, the flexible wheel sets up inside the rigid wheel, wave generator set up inside the flexible wheel, wave generator be two wave generator, wave generator includes a flexible bearing and the cam of suit in flexible bearing hole, thereby wave generator rotates under drive arrangement's drive and makes the flexible wheel produce elastic deformation to mesh with the rigid wheel mutually with transmission motion and power, cam cross section outer contour line form in the same direction as inscription tangent connection mutually by four sections eccentric circular arcs, whole is roughly the class ellipse of central symmetry, in two sections adjacent eccentric circular arcs, the centre of curvature of one section eccentric circular arc is located the minor axis, the centre of curvature of another section eccentric circular arc is located the major axis, the cam is installed behind the flexible bearing hole, outer contour line after the flexible bearing outer lane warp also corresponds to be four sections eccentric circular arcs in the same direction as inscription tangent connection mutually for four sections and forms in the same direction as the And (5) structure.
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;
2) selecting a value in a range between 0< R1 ≦ e as the eccentric distance R1 of the center of curvature of the eccentric arc on the major axis;
3) selecting the numerical value of the central angle 2 gamma of the eccentric circular arc on the minor axis, wherein gamma is more than 0 and less than or equal to pi/9;
4) determining the numerical value of the central angle 2 theta of the eccentric arc on the major axis according to a formula theta pi/2-gamma;
5) determining according to the eccentric distance R1 of the curvature center of the eccentric arc on the major axis and the eccentric arc center angle 2 gamma on the minor axis: the values of the major semiaxis R2, the radius R5 of the eccentric arc on the major axis, the radius R8 of the eccentric arc on the minor axis, and the minor semiaxis R9;
R2＝R6+R1(πsinγ-2γ)/(πsinγ)；
R5＝(πR6sinγ-2γR2)/(πsinγ-2γ)；
R8＝R5+R1/sinγ；
R9＝R5+R1/sinγ-R1/tgγ；
then, the relation is adopted: verifying that R2-R9 ≦ e, if the relation is not satisfied, reselecting R1 and repeating the steps until the finally obtained major semiaxis R2 and minor semiaxis R9 satisfy the relation;
then, the flexible bearing thickness R69 is subtracted from the sizes of the eccentric arc radius R5 on the major axis, the eccentric arc radius R8 on the minor axis, the major axis R2 and the minor axis R9 determined above, respectively, to obtain the curvature radius size of each eccentric arc corresponding to the normal direction of the cam 3.
Furthermore, 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.
Furthermore, the external tooth profile of the flexible gear is a cylindrical double-parabolic tooth profile, and the internal tooth profile of the rigid gear is a conjugate meshing envelope trajectory line of the flexible gear.
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)
Closure point C2(x2,y2) Satisfies the following conditions: r7＜x2＜R7+h；
Figure BDA0002772577290000031
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 ofFrom C2 C1The calculation is as follows;
Figure BDA0002772577290000032
vertical point C1Distance O C from gear center O1The calculation is as follows:
Figure BDA0002772577290000033
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)；
Figure BDA0002772577290000034
Figure BDA0002772577290000035
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/n①；
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 with
Figure BDA0002772577290000041
Within the range;
focal length p of parabola 22Must be satisfied in absolute value
Figure BDA0002772577290000042
Within 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 of
Figure BDA0002772577290000043
A nearby value; focal length p of parabola 22Has an absolute value of
Figure BDA0002772577290000044
A nearby value; x is the number of2Is (2R)7+ h)/2.
Has the advantages that:
according to the invention, the cam in the wave generator is formed by connecting four sections of circular arcs in an inscribed tangent and smooth manner, so that the wave generator is easy to achieve the expected manufacturing precision, the flexible rotation can be ensured, and the tooth-shaped meshing between the rigid wheel and the flexible wheel is stable.
Furthermore, the tooth form of the flexible gear adopts a double-parabola tooth form, and the tooth form of the internal tooth of the rigid gear is a conjugate meshing envelope trajectory line of the flexible gear, so that the external tooth of the flexible gear and the internal tooth of the rigid gear are meshed smoothly, the meshing rate is greatly improved to be more than 30% (the meshing rate of triangular teeth or involute teeth adopted in the prior art is 10% -15%), the heat productivity and the abrasion caused by friction can be reduced, the temperature rise of the speed reducer is reduced, the transmission precision of the harmonic speed reducer can be further improved by matching with the motion rule of the wave generator, the capacity of transmission torque is improved, and the service life of the harmonic speed reducer is prolonged.
The invention is expected to break the long-term technical monopoly abroad, improve the core competitiveness of China in the aspect of precision speed reducers and promote the development of the precision speed reducers and the robot industry of China.
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).
In the figure, 1, a rigid wheel, 101, internal teeth, 2, a flexible wheel, 201, external teeth, 3, a cam, 4, a flexible bearing, 401, a flexible bearing inner ring, 402, a rolling body, 403, a flexible bearing outer ring, 5, an outer ring mounting bolt, 6, an inner ring mounting bolt, 7, an inner ring, 8 and an outer ring.
Detailed Description
As shown in fig. 1 to 3, a harmonic speed 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 4 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 outer contour line of the cross section of the cam is formed by four eccentric circular arcs which are connected in an inscribed tangent mode in sequence, the whole cam is roughly in a centrosymmetric ellipse shape, the curvature center of one eccentric circular arc is located on a short axis line and the curvature center of the other eccentric circular arc is located on a long axis line in two adjacent eccentric circular arcs, the cam is installed in an inner hole of a flexible bearing, the outer contour line after the outer ring of the flexible bearing deforms is correspondingly of a structure formed by four eccentric circular arcs which are connected in an inscribed tangent mode in sequence, and namely the outer contour line of the wave generator is also in a four-segment circular arc structure. .
The wave generator of the present invention can be called a two-wave four-segment arc wave generator because the wave number of the wave generator of the present invention is 2 (in the transmission process, the cycle number of the wave generator rotating one circle, and the deformation of a certain point on the flexible gear is called the wave number) and the outer contour line of the wave generator is a four-segment arc. The double-wave four-band 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 double-wave four-band arc wave generator to force the flexible gear 2 to be meshed with the inner 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. In practice, the flexspline 2 may also be hat-shaped or cylindrical.
The working process of the harmonic speed 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. 6 and 7, 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 double-wave four-band arc wave generator as a coordinate origin, the long axis of the double-wave four-band arc wave generator is positioned on the x axis, the short axis of the double-wave four-band arc wave generator is positioned on the y axis (so the x axis can be called as a long axis, and the y axis can be called as a short axis)), the double-wave four-band 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 shape of each quadrant is completely symmetrical.
Fig. 6 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 cam 3 supports the outer contour of the flexible bearing outer ring 403 into a four-segment arc structure, the whole is in a centrosymmetric ellipse-like shape, and the four-segment arc is sequentially an arc B1B, arc BB3Arc B3B2And arc B2 B1And the sum of the arc lengths of the four sections of arcs is equal to the outer circumference of the outer ring of the flexible bearing. The four sections of circular arcs are all arranged deviating from the center of the flexible bearing (coinciding with the center of the cam) and are eccentric circular arcs. And arc B therein1The curvature centers of B and the arc B3B2 are positioned on the short axis and are called eccentric arcs on the short axis; the centers of curvature of arc BB3 and arc B2B1 lie on the major axis, which is referred to as the off-center arcs on the major axis.
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) determining the outer circle radius R6 of the flexible bearing outer ring and the maximum deformation of the flexible bearing as e, wherein the maximum deformation is the difference e between the long half shaft OC (or 0F) and the short half shaft OA (or OG) of the outer contour line (namely the maximum deformation of the wave generator, which is equal to the difference between the long half shaft length and the short half shaft length after the flexible bearing is deformed). The maximum deformation e of the compliant bearing is obtained from the parameters of the compliant bearing purchased according to the design volume of the reduction gear.
2) And selecting a value in a range between 0< R1 ≦ e as the decentering distance R1 of the center of curvature of the decentered circular arc on the major axis. In fig. 7, the distance from the center point H of curvature of the eccentric arc on the major axis to the center point O of the compliant bearing is R1.
3) Selecting the numerical value of the central angle 2 gamma of the eccentric circular arc on the minor axis, preferably, 0< gamma ≦ pi/9;
the central angle 2 γ of the eccentric arc on the minor axis refers to an included angle formed by connecting two ends of the eccentric arc and the curvature center of the eccentric arc, as shown in fig. 7, the curvature center of the eccentric arc B1B on the minor axis is located at point E on the y axis, the eccentric arc B1B on the minor axis intersects with the y axis at point a, and the included angle between the EA connecting line and the EB connecting line is γ. The length of EA or EB is equal to the eccentric arc radius R8 on the minor axis.
4) Determining the numerical value of the central angle 2 theta of the eccentric arc on the major axis according to a formula theta pi/2-gamma;
the central angle 2 theta of the eccentric arc on the major axis refers to the included angle formed by the connection line of the two ends of the eccentric arc and the curvature center of the eccentric arc. In fig. 7, the eccentric arc BB3 on the major axis intersects the x axis at point C, and the angle between the HB line and the HC line is θ. HB or HC is equal to the major axis eccentric arc radius R5. The arc radius herein refers to a radius of curvature corresponding to the respective arc.
5) Determining according to the eccentric distance R1 of the curvature center of the eccentric arc on the major axis and the eccentric arc center angle 2 gamma on the minor axis: the values of the major semiaxis R2, the radius R5 of the eccentric arc on the major axis, the radius R8 of the eccentric arc on the minor axis, and the minor semiaxis R9;
R2＝R6+R1(πsinγ-2γ)/(πsinγ)；
R5＝(πR6sinγ-2γR2)/(πsinγ-2γ)；
R8＝R5+R1/sinγ；
R9＝R5+R1/sinγ-R1/tgγ；
then, the relation is adopted: and verifying that R2-R9 ≦ e, if the relation is not satisfied, reselecting R1 and repeating the steps until the finally obtained major semiaxis R2 and minor semiaxis R9 satisfy the relation.
Wherein R6 is the outer circle radius of the outer ring when the flexible bearing is not deformed, and R6 is L1/2 pi; l1 is the outer circumference of the flexible bearing outer race.
Then, the flexible bearing thickness R69(R69 — R6-R99, and R99 is the inner hole radius of the flexible bearing inner race) is subtracted from the above-determined dimensions of the eccentric arc radius R5 on the major axis, the eccentric arc radius R8 on the minor axis, the major axis R2, and the minor axis R9, respectively, to obtain respective dimensions corresponding to 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 speed reducer are improved, the transmission precision and the transmission torque of the harmonic speed reducer are improved, the vibration noise is reduced, the heat is reduced, and the service life of the harmonic speed reducer is prolonged.
In order to further improve the manufacturing accuracy and the transmission accuracy of the harmonic speed reducer, it is preferable that the external tooth profile of the flexspline 2 is in a cylindrical double-parabolic (including a root parabola and a tip parabola, which are collectively called double parabolas) structure, and the internal tooth of the rigid spline is in a profile that is in conjugate engagement with the external tooth 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 speed 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 is too thin, the tooth tops are too sharp, and the strength of the external teeth is reduced; if the number of teeth 2 of the cylindrical double parabolic external teeth 201 is too small, the internal tooth pitch 4 (p) is caused1-p2) When the size of the gear is less than or equal to P, the intermediate distance between adjacent internal teeth on the rigid wheel is too large under the condition of unchanged volume, and the transmission ratio of the harmonic speed reducer is reduced; 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 reduction gear having a high reduction ratio and a higher natural frequency can be configured.
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；
Figure BDA0002772577290000091
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;
Figure BDA0002772577290000092
vertical point C1Distance O C from gear center O1The calculation is as follows:
Figure BDA0002772577290000093
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, 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)；
Figure BDA0002772577290000101
Figure BDA0002772577290000102
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 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 with
Figure BDA0002772577290000103
Within the range, it is preferable
Figure BDA0002772577290000104
A nearby value;
focal length p of parabola 22Must be satisfied in absolute value
Figure BDA0002772577290000105
Within the range, it is preferable
Figure BDA0002772577290000106
A 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.

Claims (6)

1. The utility model provides a harmonic speed reducer device, 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 cam cross section outer contour line is formed by four eccentric circular arcs which are connected in an inscribed tangent mode in sequence, the whole cam cross section outer contour line is roughly in a centrosymmetric ellipse shape, in two adjacent eccentric circular arcs, the curvature center of one eccentric circular arc is located on a short axis, the curvature center of the other eccentric circular arc is located on a long axis, the cam is installed in an inner hole of the flexible bearing, and the outer contour line after the outer ring of the flexible bearing deforms is correspondingly of a structure formed by four eccentric circular arcs which are connected in an inscribed tangent mode in sequence.
2. A harmonic speed reduction device as in claim 1, wherein: 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;
2) selecting a value in a range between 0< R1 ≦ e as the eccentric distance R1 of the center of curvature of the eccentric arc on the major axis;
3) selecting the numerical value of the central angle 2 gamma of the eccentric circular arc on the minor axis, wherein gamma is more than 0 and less than or equal to pi/9;
4) determining the numerical value of the central angle 2 theta of the eccentric arc on the major axis according to a formula theta pi/2-gamma;
5) determining according to the eccentric distance R1 of the curvature center of the eccentric arc on the major axis and the eccentric arc center angle 2 gamma on the minor axis: the values of the major semiaxis R2, the radius R5 of the eccentric arc on the major axis, the radius R8 of the eccentric arc on the minor axis, and the minor semiaxis R9;
R2＝R6+R1(πsinγ-2γ)/(πsinγ)；；
R5＝(πR6sinγ-2γR2)/(πsinγ-2γ)；
R8＝R5+R1/sinγ；
R9＝R5+R1/sinγ-R1/tgγ；
wherein R6 is the outer circle radius of the outer ring when the flexible bearing is not deformed;
then, the relation is adopted: verifying that R2-R9 ≦ e, if the relation is not satisfied, reselecting R1 and repeating the steps until the finally obtained major semiaxis R2 and minor semiaxis R9 satisfy the relation;
then, the flexible bearing thickness R69 is subtracted from the sizes of the eccentric arc radius R5 on the major axis, the eccentric arc radius R8 on the minor axis, the major axis R2 and the minor axis R9 determined above, respectively, to obtain the curvature radius size of each eccentric arc corresponding to the normal direction of the cam 3.
3. A harmonic speed reduction device as in claim 1, wherein: 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 speed reduction device as claimed in any one of claims 1 to 3, wherein: 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.
5. A harmonic speed reduction device as in claim 4, wherein: 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)；
Closure point C2(x2,y2) Satisfies the following conditions: r7＜x2＜R7+h；
Figure FDA0002772577280000021
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;
Figure FDA0002772577280000022
vertical point C1Distance O C from gear center O1The calculation is as follows:
Figure FDA0002772577280000023
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)；
Figure FDA0002772577280000024
Figure FDA0002772577280000025
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 K1Phase weightThe 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 with
Figure FDA0002772577280000031
Within the range;
focal length p of parabola 22Must be satisfied in absolute value
Figure FDA0002772577280000032
Within the range of p2The actual value of (a) is negative; x is the number of2Need to satisfy R7＜x2＜R7+h。
6. A harmonic speed reduction device as in claim 5 wherein:
focal length p of parabola 11Is composed of
Figure FDA0002772577280000033
A nearby value; focal length p of parabola 22Has an absolute value of
Figure FDA0002772577280000034
A nearby value; x is the number of2Is (2R)7+ h)/2.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113309842A (en) * 2021-05-24 2021-08-27 温州大学 Cycloidal pin gear harmonic speed reducer
CN113898712A (en) * 2021-10-08 2022-01-07 吴松涛 Harmonic speed reducer
CN113931990A (en) * 2021-08-31 2022-01-14 北京精密机电控制设备研究所 Harmonic drive cam

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10137230C1 (en) * 2001-07-30 2003-04-24 Jens Falkenstein Electrically driven harmonic drive gearbox has flexible unit magnetic flux guidance region with sufficient cross-sectional area to guide fluxes causing magnetic forces acting on flexible unit
CN107882949A (en) * 2017-10-27 2018-04-06 哈尔滨工业大学 A kind of heavily loaded monophasic waveform generator harmonic speed reducer of ultrashort projected life
US20180347679A1 (en) * 2017-06-05 2018-12-06 Harmonic Drive Systems Inc. Strain wave gearing with full separation of two stresses
CN110822055A (en) * 2019-11-15 2020-02-21 珠海格力电器股份有限公司 Harmonic speed reducer
CN111120622A (en) * 2020-01-14 2020-05-08 湖北科峰传动设备有限公司 Modified wave cam and design method thereof, wave generator and wave reducer

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10137230C1 (en) * 2001-07-30 2003-04-24 Jens Falkenstein Electrically driven harmonic drive gearbox has flexible unit magnetic flux guidance region with sufficient cross-sectional area to guide fluxes causing magnetic forces acting on flexible unit
US20180347679A1 (en) * 2017-06-05 2018-12-06 Harmonic Drive Systems Inc. Strain wave gearing with full separation of two stresses
CN107882949A (en) * 2017-10-27 2018-04-06 哈尔滨工业大学 A kind of heavily loaded monophasic waveform generator harmonic speed reducer of ultrashort projected life
CN110822055A (en) * 2019-11-15 2020-02-21 珠海格力电器股份有限公司 Harmonic speed reducer
CN111120622A (en) * 2020-01-14 2020-05-08 湖北科峰传动设备有限公司 Modified wave cam and design method thereof, wave generator and wave reducer

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
黄维等: "不同齿形谐波传动柔轮齿廓设计及有限元分析", 《机械传动》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113309842A (en) * 2021-05-24 2021-08-27 温州大学 Cycloidal pin gear harmonic speed reducer
CN113931990A (en) * 2021-08-31 2022-01-14 北京精密机电控制设备研究所 Harmonic drive cam
CN113898712A (en) * 2021-10-08 2022-01-07 吴松涛 Harmonic speed reducer

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