CN112507481B - Profile design method of three-wave and four-wave generator of cam of harmonic reducer - Google Patents
Profile design method of three-wave and four-wave generator of cam of harmonic reducer Download PDFInfo
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- CN112507481B CN112507481B CN202011342593.1A CN202011342593A CN112507481B CN 112507481 B CN112507481 B CN 112507481B CN 202011342593 A CN202011342593 A CN 202011342593A CN 112507481 B CN112507481 B CN 112507481B
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Abstract
The invention discloses a method for designing the profile of a cam three-wave and four-wave generator of a harmonic speed reducer. The invention directly deduces the plane cam profile equation. Compared with a double wave cam generator, the harmonic reducer has larger meshing area, faster starting speed and stronger impact load bearing capacity during operation, and meanwhile, the range of the meshing area can be changed by changing the central angle of the protruding circular arcs of design parameters, and the position of the meshing area can be changed by changing the included angle between the protruding circular arcs. The technical scheme adopted is also applicable to other wave number generators and specific cam profile curves.
Description
Technical Field
The invention relates to the technical field of design and manufacture of harmonic reducers, in particular to a three-wave and four-wave cam design method of a wave generator which is a main component of a harmonic reducer.
Background
The harmonic gear transmission device is a gear transmission device proposed by a American scholars Musser in 1955 based on a thin-shell elastic deformation theory, mainly comprises a flexible gear, a rigid gear and a wave generator 3, and is widely applied to a plurality of fields such as industry, medical treatment, aerospace, nuclear power and the like. The wave generator is a component for enabling the flexible gear to generate continuous deformation waves, the type of the wave generator not only determines the shape of the original curve of the harmonic gear transmission, but also has important influence on the meshing performance of the transmission and the strength of the flexible gear. As the wave generator most widely used, the mechanical wave generator generally has five types of contact type wave generator, planetary wave generator, disc type wave generator, multi-roller type wave generator and cam type wave generator, while the cam type wave generator has the advantage of more ideal meshing state of the flexspline and the rigid spline due to simple structure and is most applied in various fields. The cam type wave generator can be divided into a double wave generator, a three wave generator and a four wave generator according to the circulation times that the cam type wave generator rotates for one circle to deform a certain point of the flexible wheel.
Disclosure of Invention
The invention aims to deduce theoretical contour coordinate equations of three-wave and four-wave cam generators, and convert the theoretical contour coordinate equations into functions of specific design parameters by solving the angular geometric relationship and the length geometric relationship of the wave generators.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: a method for designing the profile of a cam three-wave and four-wave generator of a harmonic reducer includes the following implementation procedures:
s1, neglecting a flexible bearing, and assuming that a wave generator is directly assembled with a flexible gear to generate elastic deformation, the design of the wave generator needs to meet two points: firstly, the contour circumference is ensured to be equal to the circumference of the inner wall of the flexible gear, and the contour circumference and the circumference of the inner wall of the flexible gear can be tightly attached after being assembled, so that the circumference of the inner wall of the flexible gear and the circumference of the neutral layer cannot be changed due to deformation of the flexible gear. Secondly, the wave generation convex part area enables the flexible gear to generate maximum radial deformation, and the rest part areas enable the radial deformation quantity of the flexible gear to be smaller than the maximum radial deformation.
S2, determining the central angle of the protruding circular arcs of the three-wave generator and the four-wave generator and the included angle between the protruding circular arcs.
And S3, smoothly connecting all sections of cam arcs by using connecting arcs with the radius different from the radius of the protruding arc.
S4, listing the geometrical relation of the angle of the wave generator and the geometrical relation equation of the length.
S5, setting the parameter values of the control through the S2, and solving the other parameter values according to an equation.
And S6, calculating a coordinate equation expression of each arc relative to the origin of coordinates according to each parameter.
S7, checking whether the design cam meets the requirement.
The step S6 specifically further comprises the following steps:
calculating the center coordinates of the first section of convex arc, calculating the coordinate expression of the contour of the first section of convex arc relative to the center point, and converting the expression into the coordinate expression relative to the origin of coordinates. Rotating the convex arc around the origin, and obtaining the outline coordinate expression of the rest convex arcs by using a rotating shaft formula; and obtaining the outline coordinate expression of the connecting circular arcs.
The radius of the inner wall of the flexible wheel is 24.1mm, and the maximum radial deformation provided by the wave generator to the flexible wheel is 0.27mm.
Compared with the prior art, the invention has the beneficial effects that:
the design method of the three-wave and four-wave cam generator provided by the invention directly deduces the plane cam profile equation. Compared with a double wave cam generator, the harmonic reducer has larger meshing area, faster starting speed and stronger impact load bearing capacity during operation, and meanwhile, the range of the meshing area can be changed by changing the central angle of the protruding circular arcs of design parameters, and the position of the meshing area can be changed by changing the included angle between the protruding circular arcs. The technical scheme adopted is also applicable to other wave number generators and specific cam profile curves.
Drawings
Fig. 1 is a schematic plan view of a three-wave cam generator, in which three convex arcs with radius R are used to spread the flexspline for deformation when assembled with the flexspline, and a connecting arc R is used to sequentially and smoothly connect the three convex arcs.
Fig. 2 is a schematic plan view of a four-wave cam generator, in which four arcs with radius R are located in four quadrants of the coordinate axis, respectively, and a connecting arc R1 and a connecting arc R2 are sequentially and smoothly connected to the four arcs R.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
1) As shown in fig. 1: phi represents the central angle of the convex arc, phi 1 represents the central angle of the connecting arc (for convenience of calculation, all angles are represented by radians hereinafter), R represents the radius of the convex arc, R represents the radius of the connecting arc, e represents the distance between the centers of the three convex arcs, and the three convex arcs are uniformly distributed along the circumferential direction. The geometric relationship of the three-wave cam generator is as follows:
from phi 1>0, it can be determined that the value range of phi is (0, 2/3 pi), and if the value of phi is a, phi 1=b, r=q, r=v, e=m is obtained by the above geometric relationship.
The center coordinates of the convex circular arcs r positioned in the first and the fourth quadrants are as follows:
rotating the first protruding arc around the original point by 2/3 pi to obtain a second protruding arc, rotating by 2/3 pi to obtain a third protruding arc, wherein phi' represents the variation of phi angle in the interval [ -a/2, a/2], so that the three protruding arcs are obtained by a rotating shaft formula, and the contour coordinate relation of r is as follows:
the center coordinates of the connecting circle R positioned in the first quadrant are as follows:
phi 1' indicates that the phi 1 angle varies over the interval [0, b ], so that the three connecting circles R have the following profile coordinate relationship:
2) As shown in fig. 2: phi represents the central angle of a convex arc, phi 1 represents the central angle of a connecting arc, phi 2 represents the included angle between two convex arcs, phi 3 represents the central angle of the connecting arc, R represents the radius of the convex arc, R1 represents the radius of the connecting arc, R2 represents the radius of the connecting arc, e1 represents the central distance between the convex arcs in the first quadrant and the fourth quadrant, and e2 represents the central distance between the convex arcs in the first quadrant and the second quadrant. The geometric relationship of the four-wave cam generator is as follows:
the four-wave generator is designed to ensure that the effect is similar to a dual wave generator while the meshing area of the flexspline and the rigid spline is increased, so that the angle phi 2 is controlled within (0, 20 pi/180), and if phi 2 is c and phi is a, phi 1 = b, phi 3 = d, R = q, R1 = v, R2 = w, e1 = m, and e2 = n.
The center coordinates of the convex arc r in the fourth quadrant are as follows:
phi' represents that the phi angle changes in the interval [ -a/2, a/2], the contour coordinate relation of the four quadrant arc r is as follows:
the center coordinates of the arc R1 connecting the fourth quadrant and the first quadrant protruding arc are as follows:
phi 1' represents that the phi 1 angle changes in the interval [ -b/2, b/2], and then the profile coordinate relationship of the two sections of connecting arcs R1 is as follows:
the coordinates of the intersection point of the fourth quadrant arc R and the first quadrant connecting arc R1 are as follows:
the center coordinates of the arc R2 connecting the arcs of the first quadrant and the second quadrant are as follows:
phi 3' represents that the phi 3 angle changes in the interval [ -d/2, d/2], and then the profile coordinate relation of the two sections of connecting arcs R2 is as follows:
verifying that the maximum distance between the connecting arc and the origin coordinate is less than 24.37 by matlabMeets the requirements.
Claims (2)
1. A method for designing the profile of a three-wave and four-wave generator of a cam of a harmonic reducer is characterized by comprising the following steps: the implementation flow of the method is as follows:
s1, neglecting the flexible bearing, assuming that the wave generator is directly assembled with the flexible gear to generate elastic deformation,
s2, determining the central angle of the protruding circular arcs of the three-wave generator and the four-wave generator and the included angle between the protruding circular arcs;
s3, connecting all sections of cam arcs smoothly by using connecting arcs with the radius different from the radius of the protruding arc;
s4, listing an angular geometric relation and a length geometric relation equation of the wave generator;
s5, setting the magnitude of the controlled parameter value through the S2, and solving the magnitude of each other parameter according to an equation;
s6, calculating a coordinate equation expression of each arc relative to the origin of coordinates according to each parameter;
s7, checking whether the design cam meets the requirement;
the step S6 specifically further comprises the following steps:
calculating the center coordinates of the first section of cam arc, calculating the coordinate expression of the first section of cam arc outline relative to the center point, and converting the expression into the coordinate expression relative to the coordinate origin; rotating the cam arc around the origin, and obtaining outline coordinate expressions of the rest cam arcs by using a rotating shaft formula; and obtaining the outline coordinate expression of the connecting circular arcs.
2. The method for designing the profile of the three-wave and four-wave generator of the cam of the harmonic reducer according to claim 1, wherein the method comprises the following steps of: the wave generator design needs to meet two points: firstly, the contour circumference is ensured to be equal to the circumference of the inner wall of the flexible gear, and the contour circumference can be tightly attached to the circumference of the inner wall of the flexible gear after being assembled, so that the circumference of the inner wall of the flexible gear and the circumference of the neutral layer cannot be changed due to deformation of the flexible gear; secondly, the wave generation convex part area enables the flexible gear to generate maximum radial deformation, and the rest part areas enable the radial deformation quantity of the flexible gear to be smaller than the maximum radial deformation.
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| CN113623365A (en) * | 2021-08-16 | 2021-11-09 | 浙江环动机器人关节科技有限公司 | Ultra-flat three-wave harmonic speed reducer |
| CN114370486B (en) * | 2022-01-13 | 2023-08-11 | 珠海格力电器股份有限公司 | Three-wave cam wave generator on harmonic reducer and harmonic reducer |
Citations (4)
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|---|---|---|---|---|
| WO2007115510A1 (en) * | 2006-04-12 | 2007-10-18 | Beijing Kemei Harmonic Drive And Precision Machinery Co. | A harmonic drive device having three-dimensional modified involute tooth profile |
| CN106640958A (en) * | 2016-11-09 | 2017-05-10 | 上海斐赛轴承科技有限公司 | Novel flexible gear and wave generator assembly used for harmonic gear transmission device |
| CN110688716A (en) * | 2019-09-23 | 2020-01-14 | 大连理工大学 | Method for obtaining harmonic gear transmission conjugate profile based on rotation transformation |
| 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 |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007115510A1 (en) * | 2006-04-12 | 2007-10-18 | Beijing Kemei Harmonic Drive And Precision Machinery Co. | A harmonic drive device having three-dimensional modified involute tooth profile |
| CN106640958A (en) * | 2016-11-09 | 2017-05-10 | 上海斐赛轴承科技有限公司 | Novel flexible gear and wave generator assembly used for harmonic gear transmission device |
| CN110688716A (en) * | 2019-09-23 | 2020-01-14 | 大连理工大学 | Method for obtaining harmonic gear transmission conjugate profile based on rotation transformation |
| 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 (2)
| Title |
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| 谐波齿轮传动双波发生器凸轮的工艺研究;孙凤鸣;;电子机械工程(05);全文 * |
| 谐波齿轮传动重合度的计算方法研究;毛彬彬;张石平;;机械设计与制造(07);全文 * |
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