CN113503353B - Logarithmic spiral conjugate tooth profile harmonic speed reducer - Google Patents
Logarithmic spiral conjugate tooth profile harmonic speed reducer Download PDFInfo
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- CN113503353B CN113503353B CN202110930198.3A CN202110930198A CN113503353B CN 113503353 B CN113503353 B CN 113503353B CN 202110930198 A CN202110930198 A CN 202110930198A CN 113503353 B CN113503353 B CN 113503353B
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- gear
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- tooth profile
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- logarithmic spiral
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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
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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
- F16H57/00—General details of gearing
- F16H57/02—Gearboxes; Mounting gearing therein
- F16H57/021—Shaft support structures, e.g. partition walls, bearing eyes, casing walls or covers with bearings
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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
- F16H57/00—General details of gearing
- F16H57/02—Gearboxes; Mounting gearing therein
- F16H57/023—Mounting or installation of gears or shafts in the gearboxes, e.g. methods or means for assembly
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
- Y02P70/10—Greenhouse gas [GHG] capture, material saving, heat recovery or other energy efficient measures, e.g. motor control, characterised by manufacturing processes, e.g. for rolling metal or metal working
Abstract
The invention discloses a logarithmic spiral conjugate tooth profile harmonic reducer which comprises a rigid gear, a flexible gear, a wave generator and a flexible bearing. The tooth profiles of the rigid gear and the flexible gear in a meshing state are respectively designed by adopting two sections of curves in different intervals on the same logarithmic spiral, the origin of the logarithmic spiral is superposed with the rotation center of the flexible gear, and complete conjugation is realized in the meshing transmission process. Wherein, the minimum curvature radius of the rigid gear tooth profile curve is larger than the maximum curvature radius of the flexible gear tooth profile curve. In a meshing state, a tapered wedge-shaped side gap is formed between tooth profiles of the rigid gear and the flexible gear, and the conjugate tooth profiles are in approximate surface contact when in load; and the smaller the difference of the curvature radiuses of the tooth profile curves of the rigid wheel and the flexible wheel is, the smaller the backlash between conjugate tooth profiles is, and the higher the contact degree of the approximate surface is. The logarithmic spiral conjugate tooth profile harmonic reducer has the characteristics of high bearing capacity, impact resistance, high precision, small return difference, low slip rate, high efficiency and the like.
Description
Technical Field
The invention relates to the field of precision gear transmission, in particular to the field of harmonic transmission, and particularly relates to a logarithmic spiral conjugate tooth profile harmonic reducer.
Background
In recent years, with the development of production and the advancement of science and technology, higher requirements are put forward on speed reducers in the fields of aerospace, national defense, medical treatment, robots, precision machine tools and the like. In particular, a precision speed reducer applied to special fields such as national defense and weaponry often has more rigorous performance requirements such as small volume, high bearing capacity and impact resistance.
The harmonic gear transmission has the outstanding advantages of compact structure, large speed ratio, small volume, light weight, large bearing capacity, small back clearance, high transmission precision and the like, and becomes the first choice of engineering application. In the harmonic gear transmission, the flexible gear generates complex elastic deformation along with the shape of the wave generator, so that the novel tooth profile in the field of harmonic transmission has larger design space and becomes a research hotspot of gear transmission.
In a review of the development history of harmonic drive, american scholars c.w. musser in 1955 firstly proposed the basic concept of elliptical wave generator linear tooth profile harmonic drive, but did not consider the tangential displacement of the point on the neutral line of the flexspline and the swinging of the flexspline teeth caused by elastic deformation, so that the linear tooth profile meshing performance was not good and was not the ideal tooth profile of harmonic drive. In order to improve the meshing performance of the tooth profile, a great deal of research is carried out by related scholars on optimization and innovation of the tooth profile. The involute tooth profile is used for replacing a linear tooth profile of a flexible gear for a long time due to mature manufacturability, but the involute tooth profile has the problems of tooth top interference and edge meshing in a load state, and an Indian scholars R.Maiti proposes that the shape of a wave generator cam adopts an arc in a long-axis meshing section, adopts an elliptic curve to be tangent to the arc in a disengagement meshing section, and can realize the theoretical complete conjugate meshing of the involute tooth profile.
The present widely used harmonic gear tooth form also has a double-circular-arc tooth form, which is composed of two circular arcs and a straight line tangent to the two circular arcs, so that the problem of too few meshing teeth in an unloaded state is solved, and the number of the meshing teeth is greatly increased. However, in the study of the double-circular-arc tooth profile, the flexible gear tooth profile is designed, the complex rigid gear tooth profile is solved by using the meshing equation, and then the approximation fitting is performed by using a simple curve so as to meet the processing requirement. The method can cause deviation between the meshing state of the actually processed tooth profile and a theoretical analysis result, reduce the performance of the tooth profile, and is difficult to adjust the tooth profile parameters according to the performance so as to realize forward design.
Disclosure of Invention
Aiming at the prior art, the invention provides a novel high-performance logarithmic spiral conjugate tooth profile harmonic reducer with a theoretical design basis.
In order to solve the technical problem, the logarithmic spiral conjugate tooth profile harmonic reducer provided by the invention comprises a rigid gear, a flexible gear, a wave generator and a flexible bearing, wherein the flexible bearing is arranged between the flexible gear and the wave generator; the tooth profiles of the rigid wheel and the flexible wheel in a meshing state are respectively designed by adopting two sections of curves in different intervals on the same logarithmic spiral line, and the origin of the logarithmic spiral line is superposed with the rotation center of the flexible wheel; the tooth profiles of the rigid gear and the flexible gear are completely conjugated in the meshing transmission process, and the minimum curvature radius of the tooth profile curve of the rigid gear is larger than the maximum curvature radius of the tooth profile curve of the flexible gear.
Further, the invention relates to a logarithmic spiral conjugate tooth profile harmonic reducer, wherein:
in a meshing state, a tapered wedge-shaped backlash is formed between conjugate tooth profiles of the rigid gear and the flexible gear, and the smaller the difference of curvature radiuses of tooth profile curves of the rigid gear and the flexible gear is, the smaller the wedge-shaped backlash between the conjugate tooth profiles is.
The wave generator's profile is the interior equidistance curve of the neutral layer of flexspline, the profile about the major axis and the minor axis of wave generator are symmetrical respectively, the profile includes: two long axis transition sections, two short axis transition sections and four working sections respectively positioned between the long axis transition section and the short axis transition section of each section; and the connection point of the long shaft transition section and the working section and the connection point of the short shaft transition section and the working section are in smooth connection.
Compared with the prior art, the invention has the beneficial effects that:
according to the logarithmic spiral conjugate tooth profile harmonic reducer, the curvature radius of the tooth profile curve of the rigid wheel is larger than that of the tooth profile curve of the flexible wheel, so that the gear teeth are prevented from interference in the meshing transmission process.
In a meshing state, a tapered wedge-shaped side gap is formed between conjugate tooth profiles of the rigid gear and the flexible gear, so that a lubricating oil film is favorably formed, and when the difference of curvature radiuses of tooth profile curves of the rigid gear and the flexible gear is smaller, the side gap between the conjugate tooth profiles is smaller, the contact degree of an approximate surface is higher, and the conjugate tooth profiles achieve approximate surface contact in a load process, so that the bearing capacity is favorably improved.
Under the states of engagement and disengagement, when the flexible gear teeth are in transmission loading, the central line deviates from the engaging side and the disengaging side by a small angle respectively, which is beneficial to prepressing and eliminating return difference.
In conclusion, the logarithmic spiral conjugate tooth profile harmonic reducer has the characteristics of high bearing capacity, impact resistance, high precision, small return difference, low slip rate, high efficiency and the like.
Drawings
The features, objects, and advantages of the present invention will become more apparent upon reading the following drawings:
FIG. 1 is a schematic diagram of a logarithmic spiral tooth profile harmonic reducer of the present invention;
FIG. 2 is a schematic view of the tooth profiles of the rigid gear and the flexible gear shown in FIG. 1 in a meshing state;
FIG. 3 is a schematic illustration of the neutral layer line of the flexspline of FIG. 1;
FIG. 4 is a schematic view of the wave generator profile shown in FIG. 1;
in the figure:
1-rigid wheel, 2-flexible wheel, 3-wave generator, 4-flexible bearing, 5-wave generator profile, 6-neutral layer, 7-long axis transition section, 8-short axis transition section and 9-working section.
Detailed Description
The design concept of the invention is as follows: tooth profiles of a rigid gear and a flexible gear in the harmonic drive reducer in a meshing state are respectively designed by adopting two sections of curves with different intervals on the same logarithmic spiral, and the origin of the logarithmic spiral is superposed with the rotation center of the flexible gear, so that complete conjugation is realized in the meshing drive process. The minimum curvature radius of the tooth profile curve of the rigid wheel is larger than the maximum curvature radius of the tooth profile curve of the flexible wheel, so that the gear teeth are not interfered in the meshing transmission process; in a meshing state, a tapered wedge-shaped side gap is formed between tooth profiles of the rigid gear and the flexible gear, and the conjugate tooth profiles are in approximate surface contact when in load; and the smaller the difference of the curvature radiuses of the tooth profile curves of the rigid gear and the flexible gear is, the smaller the backlash between conjugate tooth profiles is, and the higher the contact degree of the approximate surface is, so that the bearing capacity is favorably improved.
The features and objects of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings and examples, it being understood that the specific embodiments described herein are illustrative of the invention and are not limiting. It should be noted that, for convenience of description, only the portions related to the invention are shown in the drawings. In addition, it is to be emphasized that: in the present application, the embodiments and features of the embodiments may be combined with each other without conflict.
As shown in fig. 1, the logarithmic spiral conjugate tooth profile harmonic reducer provided by the invention comprises a rigid gear 1, a flexible gear 2, a wave generator 3 and a flexible bearing 4, wherein the flexible bearing 4 is arranged between the flexible gear 2 and the wave generator 3.
As shown in fig. 2, the tooth profiles of the rigid gear 1 and the flexible gear 2 in a meshing state are respectively designed by two sections of curves in different intervals on the same logarithmic spiral, the origin of the logarithmic spiral is coincident with the rotation center of the flexible gear, and the tooth profiles of the rigid gear 1 and the flexible gear 2 are completely conjugated in the meshing transmission process. In order to ensure that the gear teeth do not interfere in the meshing transmission process, the minimum curvature radius of the tooth profile curve of the rigid gear 1 is larger than the maximum curvature radius of the tooth profile curve of the flexible gear 2.
For example, after the neutral layer is deformed, the tooth profile equations of the rigid gear 1 and the flexible gear 2 can be expressed as follows in a rectangular coordinate system:
in the formula, R is the initial pole diameter of the logarithmic spiral, beta is the spiral angle, and theta is the curve angle parameter. A. The 1 、B 1 Addendum and dedendum points, A, of the profile of the rigid gear, respectively 2 、B 2 Respectively the addendum point and the dedendum point of the flexible gear tooth profile. Theta a1 、θ b1 、θ a2 、θ b2 Are respectively A 1 、B 1 、A 2 、B 2 The corresponding central angle, as shown in fig. 2.
In a meshing state, a tapered wedge-shaped backlash is formed between conjugate tooth profiles of the rigid gear 1 and the flexible gear 2, and the conjugate tooth profiles are in approximate surface contact when in load; and the smaller the difference of the curvature radiuses of the tooth profile curves of the rigid wheel 1 and the flexible wheel 2 is, the smaller the wedge-shaped backlash between conjugate tooth profiles is, and the higher the contact degree of the approximate surface is.
As shown in fig. 3 and 4, the profile of the wave generator 3 is an inner equidistant curve of the neutral layer 6 of the flexspline 2, the profile 5 is symmetrical with respect to the major axis and the minor axis of the wave generator 3, respectively, and the wave generator profile 5 includes: two long axis transition sections 7, two short axis transition sections 8 and four working sections 9 respectively positioned between each long axis transition section 7 and each short axis transition section 8; wherein, the connection point of the long axis transition section 7 and the working section 9 and the connection point of the short axis transition section 8 and the working section 9 are all connected smoothly.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the invention herein disclosed is not limited to the particular combination of features described above, but also encompasses other arrangements in which any combination of the above features or their equivalents is incorporated without departing from the spirit of the invention. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.
Claims (3)
1. A logarithmic spiral conjugate tooth profile harmonic reducer comprises a rigid gear (1), a flexible gear (2), a wave generator (3) and a flexible bearing (4), wherein the flexible bearing (4) is arranged between the flexible gear (2) and the wave generator (3); the method is characterized in that:
the tooth profiles of the rigid wheel (1) and the flexible wheel (2) in a meshing state are respectively designed by adopting two sections of curves in different intervals on the same logarithmic spiral line, and the origin of the logarithmic spiral line is superposed with the rotation center of the flexible wheel;
the tooth profiles of the rigid wheel (1) and the flexible wheel (2) are completely conjugated in the meshing transmission process, and the minimum curvature radius of the tooth profile curve of the rigid wheel (1) is larger than the maximum curvature radius of the tooth profile curve of the flexible wheel (2);
after the neutral layer (6) of the flexible gear (2) is deformed, tooth profile equations of the rigid gear (1) and the flexible gear (2) are respectively expressed as follows under a rectangular coordinate system:
wherein R is the initial pole diameter of the logarithmic spiral, beta is the spiral angle, theta is the curve angle parameter, A 1 、B 1 Addendum and dedendum points, A, of the profile of the rigid wheel 2 、B 2 Addendum and dedendum points, θ, of the flexspline tooth profile, respectively a1 、θ b1 、θ a2 、θ b2 Are respectively A 1 、B 1 、A 2 、B 2 The corresponding central angle.
2. The logarithmic spiral conjugate tooth profile harmonic reducer of claim 1, wherein: in a meshing state, a tapered wedge-shaped backlash is formed between conjugate tooth profiles of the rigid gear (1) and the flexible gear (2), and the smaller the difference between the curvature radiuses of tooth profile curves of the rigid gear (1) and the flexible gear (2), the smaller the wedge-shaped backlash between the conjugate tooth profiles.
3. The logarithmic spiral conjugate tooth profile harmonic reducer of claim 1, wherein: the profile (5) of the wave generator (3) is the inner equidistant curve of the neutral layer (6) of the flexspline (2), the profile (5) is respectively symmetrical about the long axis and the short axis of the wave generator (3), the profile (5) comprises: two long axis transition sections (7), two short axis transition sections (8) and four working sections (9) respectively positioned between each long axis transition section (7) and each short axis transition section (8); the connection point of the long shaft transition section (7) and the working section (9) and the connection point of the short shaft transition section (8) and the working section (9) are connected smoothly.
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| CN202110930198.3A CN113503353B (en) | 2021-08-13 | 2021-08-13 | Logarithmic spiral conjugate tooth profile harmonic speed reducer |
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| CN202110930198.3A CN113503353B (en) | 2021-08-13 | 2021-08-13 | Logarithmic spiral conjugate tooth profile harmonic speed reducer |
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| CN113503353B true CN113503353B (en) | 2023-02-24 |
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Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| GB1269056A (en) * | 1968-07-03 | 1972-03-29 | Henry Edward Merritt | Gear type pumps |
| CN101135357B (en) * | 2006-08-31 | 2010-09-08 | 北京工商大学 | Harmonic gear power transmission with double circular arc tooth outline |
| DE102007011175A1 (en) * | 2007-03-06 | 2008-09-11 | Wittenstein Ag | coaxial |
| DE102009040453A1 (en) * | 2009-08-28 | 2011-03-03 | Keiper Gmbh & Co. Kg | Fitting for a vehicle seat |
| CN106402327A (en) * | 2016-12-09 | 2017-02-15 | 东华大学 | Robot joint precision transmission gear structure |
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