CN112483625A - Harmonic gear shaping method and harmonic reducer - Google Patents
Harmonic gear shaping method and harmonic reducer Download PDFInfo
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- CN112483625A CN112483625A CN202011428804.3A CN202011428804A CN112483625A CN 112483625 A CN112483625 A CN 112483625A CN 202011428804 A CN202011428804 A CN 202011428804A CN 112483625 A CN112483625 A CN 112483625A
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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
- 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
- F16H55/088—Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
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Abstract
The invention discloses a harmonic gear shape modification method and a harmonic reducer, comprising the following steps of (1) calculating a gear module of a flexible gear through a formula; (2) drawing an original involute tooth profile of the flexible gear according to basic tooth profile elements of the flexible gear; (3) correcting the shape of the original involute tooth profile of the flexible gear, and correcting an involute section df close to an addendum circle; (4) and determining a tooth direction correction parameter according to the tooth width of the flexible gear and a constraint condition that tooth crest interference does not occur instantaneously when the flexible gear is meshed in or out, and correcting the tooth shape of the flexible gear in the tooth direction to finish the final design of the tooth shape of the flexible gear. According to the invention, aiming at the condition that the tooth number Z of the flexible gear is less than or equal to 130, the tooth top part of the harmonic gear is shaped, so that the tooth top interference is avoided, the stress concentration of the tooth root is reduced, the meshing condition of the whole tooth part is improved, and the bearing capacity, the efficiency and the service life of the whole harmonic reducer are improved.
Description
Technical Field
The invention is used in the field of harmonic reducers, and particularly relates to a harmonic gear shaping method and a harmonic reducer.
Background
As shown in fig. 1 and 2, the harmonic reducer is mainly composed of a harmonic gear and a wave generator 3, wherein the harmonic gear comprises a rigid gear 1 and a flexible gear 2, and the working principle of the harmonic reducer is that the wave generator 3 enables the flexible gear 2 to generate controllable elastic deformation waves, and the transmission device realizes motion and power transmission through interaction with the rigid gear 1.
Generally, the flexspline 2 is designed as external teeth, the ring gear 1 is designed as internal teeth, and the ring gear 1 has 2 more teeth than the flexspline 2. The wave generator 3 is composed of a cam 31 and a flexible bearing 32, wherein the contour of the cam 31 is an ellipse or a curve similar to the ellipse, the flexible bearing 32 is arranged on the outer surface of the ellipse of the cam 31, and the inner ring and the outer ring form an ellipse curve under the action of the cam 31. The outer surface of the wave generator 3 is the outer ring of the flexible bearing 32, and is an elliptic curve, and has a long axis and a short axis. The wave generator 3 is mounted in the internal bore of the open end 21 of the flexspline (i.e. the end remote from the mounting flange 22) to force the internal bore to ovalize. The opening end 21 of the flexible gear is simultaneously designed with a tooth part, so that the flexible gear 2 with external teeth and the rigid gear 1 with internal teeth are in a meshed state within a certain range of a long shaft of the wave generator 3, if the rigid gear 1 is fixed, the flexible gear 2 rotates in the opposite direction by an angle of 2 teeth because the flexible gear 2 is less than the rigid gear 1 by 2 teeth every time the wave generator 3 rotates for one circle, and the effects of speed reduction and power transmission are realized.
In the design of harmonic gears, the design of tooth profiles is one of the key technologies. The flexible gear 2 and the rigid gear 1 adopt linear tooth profiles at the earliest, and involute tooth profiles are generally adopted later for the convenience of manufacture and the capability of improving performance. At present, the harmonic reducer with low requirements on performance, volume and weight still adopts an involute tooth form.
As the harmonic speed reducer advances to a higher speed, the reduction ratio i is required to be smaller and smaller, and accordingly, the number of teeth Z is required to be smaller and smaller. When the number of the flexible gear teeth Z is less than or equal to 130, the requirement on the meshing quality of the harmonic gear is very high. The existing harmonic reducer has the following defects:
(1) the involute tooth profile parameters are not properly selected or the modification is not reasonable, so that the phenomenon of easy interference exists;
(2) although the meshing condition of the tooth profile of the harmonic gear can be improved, the problems of difficult tooth profile processing, high cost and the like exist.
(3) Good meshing effect cannot be obtained over the entire length of the teeth.
Disclosure of Invention
The invention aims to solve at least one of the technical problems in the prior art, and provides a harmonic gear shaping method and a harmonic reducer, aiming at the condition that the tooth number Z of a flexible gear is less than or equal to 130, avoiding tooth top interference and reducing tooth root stress concentration, improving the meshing condition of the whole tooth part, and improving the bearing capacity, efficiency and service life of the whole harmonic reducer.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for modifying the shape of a harmonic gear, which comprises a flexible gear, comprises a flexible gear modifying step, and the flexible gear modifying step comprises the following steps:
(1) calculating the gear module m of the flexible gear by the following formular,
mr＝(drn+2δr)/[Zr-2(hra+cr)],
Wherein Z isrNumber of teeth of flexible gear, hraIs the coefficient of crest height of the flexspline crIs the coefficient of the head clearance of the flexspline, drnIs the diameter of the inner hole of the flexible gear deltarThe tooth root wall thickness of the flexible gear;
(2) determining the value range of basic elements of the flexible gear tooth form to obtain a solution set which accords with the value range; the flexible gear tooth form basic elements comprise:
pressure angle alpha of flexsplinerWhen 90 < ZrWhen the alpha is less than or equal to 130, alphar25-30 DEG, when ZrWhen the value is less than or equal to 90, alphar＝30°～35°；
Root wall thickness delta of flexspliner＝(0.007～0.012)drn；
Reference circle diameter d of flexible gearr＝mr×Zr；
Crest height factor h of flexsplinera；
Addendum circle diameter d of the flexsplinera＝dr+2mr×hra；
Coefficient of backlash c of flexspliner；
Root diameter d of flexsplinerf＝drn+2δrOr dr–2mr(hra+cr)；
Pitch p of flexspliner＝πmr；
Tooth thickness s of flexsplinerWhen 90 < ZrWhen s is less than or equal to 130, sr＝(0.35～0.40)prWhen Z isrWhen s is less than or equal to 90, sr＝(0.3～0.35)pr；
Drawing an original involute tooth profile of the flexible gear according to basic tooth profile elements of the flexible gear, wherein a left tooth surface involute tooth profile curve before the flexible gear is not modified comprises an arc ab, an arc bc, involutes cd, de, ef and an arc fg;
wherein, the point d is the starting point of the modification, the height coefficient of the point d is hrsThe diameter of the circle is as follows: drs＝dr+2mr×hrs；
The point e is a shape modification control point, and the height coefficient of the point e is hrkThe diameter of the circle is as follows: drk＝dr+2mr×hrk；
(3) Modifying the shape of an original involute tooth profile of the flexible gear, modifying an involute section df close to an addendum circle, replacing an involute section df with a section of curve df ', wherein the curve df ' consists of one or more sections of circular arcs, the curve df ' is smoothly connected with the involute section cd at a point d, intersects with a circle where the point e is located at a point e ', intersects with an addendum circular arc fg at a point f ', and a shape-modified tooth profile curve of the left tooth surface of the flexible gear is a new curve comprising an arc ab, an arc bc, the involute cd, the curve df ' and an addendum circular arc f ' g;
the right tooth surface tooth profile curve and the left tooth surface tooth profile curve are symmetrical around the central axis of the tooth profile;
(4) and determining a tooth direction correction parameter according to the tooth width of the flexible gear and a constraint condition that tooth crest interference does not occur instantaneously when the flexible gear is meshed in or out, and correcting the tooth shape of the flexible gear in the tooth direction to finish the final design of the tooth shape of the flexible gear.
With reference to the first aspect, in certain implementations of the first aspect, the flexible gearTooth crest height coefficient hra0.5 to 0.6, coefficient of backlash of flexspline cr0.1 ~ 0.2, flexible wheel profile of tooth basic element still includes:
root arc ρrWhen 90 < ZrAt 130 or less, rhor＝(0.6～0.8)mrWhen Z isrAt 90 ℃ or less, rhor＝(0.8～1.0)mr。
With reference to the first aspect and the foregoing implementations, in some implementations of the first aspect, the height coefficient of the point d is hrs0.15 to 0.2, and the height coefficient of the e point is hrk＝0.4。
With reference to the first aspect and the foregoing implementation manners, in some implementation manners of the first aspect, the distance between the points e and e' is defined as a modification control point modification amount ΔrkIt satisfies the inequality: 0.02mr≤Δrk≤0.04mr。
With reference to the first aspect and the foregoing implementation manners, in some implementation manners of the first aspect, the constraint condition that tooth crest interference does not occur at the moment when the flexible gears mesh in or mesh out includes:
the tooth top and the tooth bottom of a section of tooth part close to the opening end of the flexible gear are inclined towards the axis to form a taper beta1(ii) a The length of the section of tooth part is L1It satisfies the inequality: 0.25Lr≤L1≤0.35LrWherein L isrIs the tooth width; taper beta1Satisfies the inequality: beta is not less than 0.5 degree1≤1.5°；
The middle tooth part has no taper with the axis and has a length L2It satisfies the inequality: 0.3Lr≤L2≤0.4Lr；
The tooth top and the tooth bottom of a section of tooth part close to the flange end of the flexible gear are inclined towards the axis to form a taper beta3It satisfies the inequality: beta is not less than 0.5 degree3≤1.5°。
With reference to the first aspect and the foregoing implementations, in certain implementations of the first aspect, the harmonic gear includes a rigid wheel, and the rigid wheel shaping step includes:
(1) determining the value range of the basic tooth profile elements of the rigid wheel to obtain a solution set which accords with the value range; the flexible gear tooth form basic elements comprise:
number of teeth Z of rigid gearg＝Zr+2；
Modulus m of rigid wheelgWhen 92 < ZgWhen m is less than or equal to 132, mr[Zg-(0.2～0.4)]/ZgWhen Z isgWhen m is less than or equal to 92, mr[Zg-(0.5～0.8)]/Zg；
Pressure angle alpha of rigid wheelgWhen 92 < ZgWhen the value is less than or equal to 132, alphag25-30 DEG, when ZgWhen the value is less than or equal to 92, alphag＝30°～35°；
Tooth crest height coefficient h of rigid wheelga＝0.5～0.6；
Head clearance coefficient c of rigid wheelg＝0.1～0.2；
Reference circle diameter d of rigid wheelg＝mg×Zg；
Addendum circle diameter d of a rigid gearga＝dg-2hga mg；
Root diameter d of rigid wheelgf＝dg+2(hga+cg)mg；
Pitch p of rigid wheelg＝πmg；
Width e of tooth space of rigid wheelgWhen 92 < ZgWhen the temperature is less than or equal to 132, eg＝(0.35～0.40)pgWhen Z isgWhen the temperature is less than or equal to 92, eg＝(0.30～0.35)pg；
Drawing an original involute tooth profile of the rigid gear according to basic tooth profile elements of the rigid gear, wherein a left tooth surface involute tooth profile curve before the rigid gear is not modified comprises an arc AB, an arc BC, an involute CD, DE, EF and an arc FG;
wherein, the D point is a starting point of the modification, and the height coefficient of the D point is hgsThe diameter of the circle is as follows: dgs＝dg+2mg×hgs；
The point E is a shape modification control point, and the height coefficient of the point E is hgkThe diameter of the circle is as follows: dgk＝dg+2mg×hgk；
(3) The method comprises the following steps of modifying the shape of an original involute tooth profile of a rigid wheel, modifying an involute section DF close to an addendum circle, replacing an involute section DF with a section of curve DF ', wherein the curve DF' consists of one or more sections of circular arcs, is smoothly connected with the involute section CD at a point D, intersects with a circle where the point E is located at a point E ', intersects with an addendum circular arc FG at a point F', and is a new curve comprising an arc AB, an arc BC, an involute CD, a curve DF 'and an addendum circular arc F' G after being modified in shape;
and the right tooth surface tooth profile curve and the left tooth surface tooth profile curve are axisymmetric with respect to the center line of the tooth profile, and the final design of the rigid wheel tooth profile is completed.
With reference to the first aspect and the foregoing implementations, in some implementations of the first aspect, the height coefficient of the point D is hgs0.3 to 0.35, and the height coefficient of the E point is hgk＝0.45。
With reference to the first aspect and the foregoing implementation manners, in some implementation manners of the first aspect, the distance between the points E and E' is defined as a modification control point modification amount ΔgkIt satisfies the inequality: 0.02mg≤Δgk≤0.03mg。
In a second aspect, a harmonic reducer comprises a harmonic gear, wherein the harmonic gear is obtained according to the method for modifying the harmonic gear in any one of the implementation manners of the first aspect.
One of the above technical solutions has at least one of the following advantages or beneficial effects: aiming at the condition that the tooth number Z of the flexible gear is less than or equal to 130, the tooth top part of the harmonic gear (comprising the flexible gear and the rigid gear) is modified, and the tooth direction of the flexible gear is modified, so that the interference of the gears in the meshing motion is avoided, and the meshing quality is improved. Meanwhile, the stress condition of the flexible gear tooth root is improved by reducing the tooth thickness coefficient of the flexible gear tooth and increasing the tooth root circular arc.
1) Compared with the prior art, the bearing capacity of the whole harmonic reducer can be improved by more than 50%, and meanwhile, the transmission efficiency is also greatly improved.
2) Compared with the prior art, the transmission precision life and the rigidity life of the whole harmonic reducer are obviously prolonged.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram of a prior art harmonic reducer;
FIG. 2 is a cross-sectional view of a prior art harmonic reducer construction;
FIG. 3 is a schematic diagram of a flexible gear tooth profile modification according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a flexible gear tooth profile modification according to another embodiment of the present invention;
FIG. 5 is a schematic cross-sectional view of a flexspline of the present invention;
FIG. 6 is an enlarged view of a portion of FIG. 5 at I;
FIG. 7 is a schematic comparison of the accuracy life of the harmonic gear of the present invention versus a prior art transmission;
FIG. 8 is a graphical illustration of a stiffness life comparison of a harmonic gear of the present invention with a prior art.
Detailed Description
The embodiment of the invention provides a harmonic gear shaping method, wherein the harmonic gear comprises a flexible gear 2 and a rigid gear 1, the harmonic gear comprises a flexible gear 2 shaping step and a rigid gear correcting step, and the flexible gear shaping step comprises the following steps:
(1) the gear module m of the flexible gear is calculated by the following formular,
mr＝(drn+2δr)/[Zr-2(hra+cr)],
Wherein Z isrNumber of teeth of flexible gear, hraIs the coefficient of crest height of the flexspline crIs the coefficient of the head clearance of the flexspline, drnIs the diameter of the inner hole of the flexible gear deltarThe tooth root wall thickness of the flexible gear;
(2) determining the value range of basic elements of the flexible gear tooth form to obtain a solution set which accords with the value range; the flexible gear tooth form basic elements comprise:
pressure angle alpha of flexsplinerWhen 90 < ZrWhen the alpha is less than or equal to 130, alphar25-30 DEG, when ZrWhen the value is less than or equal to 90, alphar＝30°～35°；
Root wall thickness delta of flexspliner＝(0.007～0.012)drn；
Reference circle diameter d of flexible gearr＝mr×Zr；
Crest height factor h of flexsplinera；
Addendum circle diameter d of the flexsplinera＝dr+2m×hra；
Coefficient of backlash c of flexspliner；
Root diameter d of flexsplinerf＝drn+2δrOr dr–2mr(hra+cr)；
Pitch p of flexspliner＝πmr；
Tooth thickness s of flexsplinerWhen 90 < ZrWhen s is less than or equal to 130, sr＝(0.35～0.40)prWhen Z isrWhen s is less than or equal to 90, sr＝(0.3～0.35)pr；
Referring to fig. 3 and 4, according to basic tooth profile elements of the flexible gear, drawing an original involute tooth profile of the flexible gear, wherein an involute tooth profile curve of a left tooth surface before the flexible gear is subjected to shape modification comprises an arc ab, an arc bc, involutes cd, de, ef and an arc fg;
wherein, the point d is the starting point of the modification, the height coefficient of the point d is hrsThe diameter of the circle is as follows: drs＝dr+2mr×hrs；
The point e is a shape modification control point, and the height coefficient of the point e is hrkThe diameter of the circle is as follows: drk＝dr+2mr×hrk；
(3) Referring to fig. 3 and 4, the original involute tooth profile of the flexible gear is modified in shape, an involute section df close to an addendum circle is modified, a gradual-opening line section df is replaced by a section of curve df ', the curve df' consists of one or more sections of circular arcs, the curve df 'is smoothly connected with the involute section cd at a point d, intersects with a circle at a point e' and intersects with an addendum circular arc fg at a point f ', the shape-modified tooth profile curve of the left tooth surface of the flexible gear is a new curve including an arc ab, an arc bc, an involute cd, a curve df' and an addendum circular arc f 'g, and the point f' can even coincide with an addendum central point g;
the right tooth surface tooth profile curve and the left tooth surface tooth profile curve are symmetrical around the central axis of the tooth profile;
(4) and determining a tooth direction correction parameter according to the tooth width of the flexible gear and a constraint condition that tooth crest interference does not occur instantaneously when the flexible gear is meshed in or out, and correcting the tooth shape of the flexible gear in the tooth direction to finish the final design of the tooth shape of the flexible gear.
Furthermore, the crest height coefficient h of the flexible gearra0.5 to 0.6, coefficient of backlash of flexspline cr0.1 ~ 0.2, flexspline profile of tooth basic element still includes:
root arc ρrWhen 90 < ZrAt 130 or less, rhor＝(0.6～0.8)mrWhen Z isrAt 90 ℃ or less, rhor＝(0.8～1.0)mr。
With reference to the first aspect and the foregoing implementations, in some implementations of the first aspect, the height coefficient of the point d is hrs0.15 to 0.2, and the height coefficient of the e point is hrk＝0.4。
With reference to the first aspect and the foregoing implementation manners, in some implementation manners of the first aspect, the distance between the points e and e' is defined as a modification control point modification amount ΔrkIt satisfies the inequality: 0.02mr≤Δrk≤0.04mr。
Further, the constraint condition that the tooth crest interference does not occur at the moment of meshing or meshing of the flexspline includes:
referring to fig. 5 and 6, the tooth crest and the tooth bottom of a section of the tooth part close to the opening end of the flexible gear are inclined to the axial line to form a taper beta1(ii) a The length of the section of tooth part is L1It satisfies the inequality: 0.25Lr≤L1≤0.35LrWherein L isrIs the tooth width; taper beta1Satisfies the inequality: beta is not less than 0.5 degree1≤1.5°；
The middle tooth part has no taper with the axis and has a length L2It satisfies the inequality: 0.3Lr≤L2≤0.4Lr；
The tooth top and the tooth bottom of a section of tooth part close to the flange end of the flexible gear are inclined towards the axis to form a taper beta3It satisfies the inequality: beta is not less than 0.5 degree3≤1.5°。
Further, the harmonic gear comprises a rigid gear, the tooth profile modification method of the rigid gear is similar to that of the flexible gear, and specifically, the rigid gear modification step comprises the following steps:
(1) determining the value range of the basic tooth profile elements of the rigid wheel to obtain a solution set which accords with the value range; the flexible gear tooth form basic elements comprise:
number of teeth Z of rigid gearg＝Zr+2；
Modulus m of rigid wheelgWhen 92 < ZgWhen m is less than or equal to 132, mr[Zg-(0.2～0.4)]/ZgWhen Z isgWhen m is less than or equal to 92, mr[Zg-(0.5～0.8)]/Zg；
Pressure angle alpha of rigid wheelgWhen 92 < ZgWhen the value is less than or equal to 132, alphag25-30 DEG, when ZgWhen the value is less than or equal to 92, alphag＝30°～35°；
Tooth crest height coefficient h of rigid wheelga＝0.5～0.6；
Head clearance coefficient c of rigid wheelg＝0.1～0.2；
Reference circle diameter d of rigid wheelg＝mg×Zg；
Addendum circle diameter d of a rigid gearga＝dg-2hga mg；
Root diameter d of rigid wheelgf＝dg+2(hga+cg)mg；
Pitch p of rigid wheelg＝πmg；
Width e of tooth space of rigid wheelgWhen 92 < ZgWhen the temperature is less than or equal to 132, eg＝(0.35～0.40)pgWhen Z isgWhen the temperature is less than or equal to 92, eg＝(0.30～0.35)pg；
Drawing an original involute tooth profile of the rigid gear according to basic tooth profile elements of the rigid gear, wherein a left tooth surface involute tooth profile curve before the rigid gear is not modified comprises an arc AB, an arc BC, an involute CD, DE, EF and an arc FG;
wherein, the D point is a starting point of the modification, and the height coefficient of the D point is hgsThe diameter of the circle is as follows: dgs＝dg+2mg×hgs；
The point E is a shape modification control point, and the height coefficient of the point E is hgkThe diameter of the circle is as follows: dgk＝dg+2mg×hgk；
(3) The method comprises the following steps of modifying the shape of an original involute tooth profile of a rigid wheel, modifying an involute section DF close to an addendum circle, replacing an involute section DF with a section of curve DF ', wherein the curve DF' consists of one or more sections of circular arcs, is smoothly connected with the involute section CD at a point D, intersects with a circle where the point E is located at a point E ', intersects with an addendum circular arc FG at a point F', and is a new curve comprising an arc AB, an arc BC, an involute CD, a curve DF 'and an addendum circular arc F' G after being modified in shape;
and the right tooth surface tooth profile curve and the left tooth surface tooth profile curve are axisymmetric about the center line of the tooth profile, and the final design of the rigid wheel tooth profile is completed.
Further, the height coefficient of the point D is hgs0.3 to 0.35, and the height coefficient of the E point is hgk＝0.45。
With reference to the first aspect and the foregoing implementation manners, in some implementation manners of the first aspect, the distance between the points E and E' is defined as a modification control point modification amount ΔgkIt satisfies the inequality: 0.02mg≤Δgk≤0.03mg。
A harmonic reducer comprises a harmonic gear, wherein the harmonic gear is obtained according to the modification method of the harmonic gear.
Specifically, the tooth profile design process of the flexible gear is as follows:
firstly, the model of a flexible bearing is selected before the harmonic gear is designed, the diameter of an inner hole of the flexible gear is determined according to the diameter of an outer ring of the flexible bearing, and then a plurality of given parts are combinedThe modulus m is calculated from the parametersr. The recommended values or design calculation formulas of the basic tooth form elements of the flexible gear are shown in table 1.
The original involute tooth profile is drawn according to the tooth profile basic elements of the gear shown in the table 1.
TABLE 1 basic elements of flexible gear tooth form and recommended values or design calculation formulas thereof
According to the tooth profile shape correction parameters shown in table 2, one or more sections of smooth curves are used to correct the tooth crest portion of the original involute tooth profile.
TABLE 2 shape correction parameters of flexspline tooth profile
Finally, according to the tooth direction correction parameters shown in table 3, the tooth profile is corrected in the tooth direction, and the final design of the tooth profile is completed.
| Serial number | Name (R) | Symbol | Recommended value or |
| 1 | Width of tooth | Lr | Given before |
| 2 | Corrected tooth length of open end | L1 | (0.25～0.35) |
| 3 | Open end tooth direction correction angle | β1 | 0.5°～1.5° |
| 4 | Mid-section length | L2 | (0.3～0.4)Lr |
| 5 | Flange end tooth direction correction angle | β3 | 0.5°～1.5° |
The tooth profile design of the rigid wheel is relatively simple, only the shape of the tooth top part needs to be corrected, and correction in the tooth direction is not needed. The process is as follows:
first, the original involute tooth profile is drawn based on the tooth profile basic elements of the gears shown in table 4.
Secondly, according to the tooth profile shape correction parameters shown in table 5, one or more sections of smooth curves are used for correcting the tooth crest part of the original involute tooth profile, and then the final design of the tooth profile can be completed.
TABLE 4 basic elements of the tooth profile of a rigid wheel and its recommended values or design calculation formulas
TABLE 5 shape correction parameters for the profile of the steel wheel
1) Compared with the prior art, the bearing capacity of the whole harmonic reducer can be improved by more than 50%, and meanwhile, the transmission efficiency is also greatly improved.
2) Compared with the prior art, referring to the figures 7 and 8, the transmission precision life and the rigidity life of the whole harmonic reducer are obviously prolonged,
in the description herein, references to the description of the term "example," "an embodiment," or "some embodiments," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The invention is not limited to the above embodiments, and those skilled in the art can make equivalent modifications or substitutions without departing from the spirit of the invention, and such equivalent modifications or substitutions are included in the scope of the claims of the present application.
Claims (9)
1. A method for modifying the shape of a harmonic gear, wherein the harmonic gear comprises a flexible gear, is characterized by comprising a flexible gear modifying step, and the flexible gear modifying step comprises the following steps:
(1) calculating the gear module m of the flexible gear by the following formular,
mr＝(drn+2δr)/[Zr-2(hra+cr)],
Wherein Z isrNumber of teeth of flexible gear, hraIs the coefficient of crest height of the flexspline crIs the coefficient of the head clearance of the flexspline, drnIs the diameter of the inner hole of the flexible gear deltarThe tooth root wall thickness of the flexible gear;
(2) determining the value range of basic elements of the flexible gear tooth form to obtain a solution set which accords with the value range; the flexible gear tooth form basic elements comprise:
pressure angle alpha of flexsplinerWhen 90 < ZrWhen the alpha is less than or equal to 130, alphar25-30 DEG, when ZrWhen the value is less than or equal to 90, alphar＝30°～35°；
Root wall thickness delta of flexspliner＝(0.007～0.012)drn；
Reference circle diameter d of flexible gearr＝mr×Zr；
Crest height factor h of flexsplinera；
Addendum circle diameter d of the flexsplinera＝dr+2mr×hra；
Coefficient of backlash c of flexspliner；
Root diameter d of flexsplinerf＝drn+2δrOr dr–2mr(hra+cr)；
Pitch p of flexspliner＝πmr；
Tooth thickness s of flexsplinerWhen 90 < ZrWhen s is less than or equal to 130, sr＝(0.35～0.40)prWhen Z isrWhen s is less than or equal to 90, sr＝(0.3～0.35)pr；
Drawing an original involute tooth profile of the flexible gear according to basic tooth profile elements of the flexible gear, wherein a left tooth surface involute tooth profile curve before the flexible gear is not modified comprises an arc ab, an arc bc, involutes cd, de, ef and an arc fg;
wherein, the point d is the starting point of the modification, the height coefficient of the point d is hrsThe diameter of the circle is as follows: drs＝dr+2mr×hrs；
The point e is a shape modification control point, and the height coefficient of the point e is hrkThe diameter of the circle is as follows: drk＝dr+2mr×hrk；
(3) Modifying the shape of an original involute tooth profile of the flexible gear, modifying an involute section df close to an addendum circle, replacing an involute section df with a section of curve df ', wherein the curve df ' consists of one or more sections of circular arcs, the curve df ' is smoothly connected with the involute section cd at a point d, intersects with a circle where the point e is located at a point e ', intersects with an addendum circular arc fg at a point f ', and a shape-modified tooth profile curve of the left tooth surface of the flexible gear is a new curve comprising an arc ab, an arc bc, the involute cd, the curve df ' and an addendum circular arc f ' g;
the right tooth surface tooth profile curve and the left tooth surface tooth profile curve are symmetrical around the central axis of the tooth profile;
(4) and determining a tooth direction correction parameter according to the tooth width of the flexible gear and a constraint condition that tooth crest interference does not occur instantaneously when the flexible gear is meshed in or out, and correcting the tooth shape of the flexible gear in the tooth direction to finish the final design of the tooth shape of the flexible gear.
2. The method of modifying a harmonic gear according to claim 1, wherein the addendum coefficient h of the flexsplinera0.5 to 0.6, coefficient of backlash of flexspline cr0.1 ~ 0.2, flexible wheel profile of tooth basic element still includes:
root arc ρrWhen 90 < ZrAt 130 or less, rhor＝(0.6～0.8)mrWhen Z isrAt 90 ℃ or less, rhor＝(0.8～1.0)mr。
3. The method of claim 1, wherein the height factor of the point d is hrs0.15 to 0.2, and the height coefficient of the e point is hrk＝0.4。
4. The method of claim 1, wherein the distance between e and e' is defined as a modification control point modification amount ΔrkIt satisfies the inequality: 0.02mr≤Δrk≤0.04mr。
5. The method for modifying a harmonic gear according to claim 1, wherein the constraint condition that tooth crest interference does not occur at the moment when the flexible gears mesh in or mesh out includes:
the tooth top and the tooth bottom of a section of tooth part close to the opening end of the flexible gear are inclined towards the axis to form a taper beta1(ii) a The length of the section of tooth part is L1It satisfies the inequality: 0.25Lr≤L1≤0.35LrWherein L isrIs the tooth width; taper beta1Satisfies the inequality: beta is not less than 0.5 degree1≤1.5°；
The middle tooth part has no taper with the axis and has a length L2It satisfies the inequality: 0.3Lr≤L2≤0.4Lr；
The tooth top and the tooth bottom of a section of tooth part close to the flange end of the flexible gear are inclined towards the axis to form a taper beta3It satisfies the inequality: beta is not less than 0.5 degree3≤1.5°。
6. The method of modifying a harmonic gear of claim 1, wherein the harmonic gear comprises a rigid wheel, and the rigid wheel modifying step comprises:
(1) determining the value range of the basic tooth profile elements of the rigid wheel to obtain a solution set which accords with the value range; the flexible gear tooth form basic elements comprise:
number of teeth Z of rigid gearg＝Zr+2；
Modulus m of rigid wheelgWhen 92 < ZgWhen m is less than or equal to 132, mr[Zg-(0.2～0.4)]/ZgWhen Z isgWhen m is less than or equal to 92, mr[Zg-(0.5～0.8)]/Zg；
Pressure angle alpha of rigid wheelgWhen 92 < ZgWhen the value is less than or equal to 132, alphag25-30 DEG, when ZgWhen the value is less than or equal to 92, alphag＝30°～35°；
Tooth crest height coefficient h of rigid wheelga＝0.5～0.6；
Head clearance coefficient c of rigid wheelg＝0.1～0.2；
Reference circle diameter d of rigid wheelg＝mg×Zg；
Addendum circle diameter d of a rigid gearga＝dg-2hga mg；
Root diameter d of rigid wheelgf＝dg+2(hga+cg)mg；
Pitch p of rigid wheelg＝πmg；
Width e of tooth space of rigid wheelgWhen 92 < ZgWhen the temperature is less than or equal to 132, eg＝(0.35～0.40)pgWhen Z isgWhen the temperature is less than or equal to 92, eg＝(0.30～0.35)pg；
Drawing an original involute tooth profile of the rigid gear according to basic tooth profile elements of the rigid gear, wherein a left tooth surface involute tooth profile curve before the rigid gear is not modified comprises an arc AB, an arc BC, an involute CD, DE, EF and an arc FG;
wherein, the D point is a starting point of the modification, and the height coefficient of the D point is hgsThe diameter of the circle is as follows: dgs＝dg+2mg×hgs；
The point E is a shape modification control point, and the height coefficient of the point E is hgkThe diameter of the circle is as follows: dgk＝dg+2mg×hgk；
(3) The method comprises the following steps of modifying the shape of an original involute tooth profile of a rigid wheel, modifying an involute section DF close to an addendum circle, replacing an involute section DF with a section of curve DF ', wherein the curve DF' consists of one or more sections of circular arcs, is smoothly connected with the involute section CD at a point D, intersects with a circle where the point E is located at a point E ', intersects with an addendum circular arc FG at a point F', and is a new curve comprising an arc AB, an arc BC, an involute CD, a curve DF 'and an addendum circular arc F' G after being modified in shape;
and the right tooth surface tooth profile curve and the left tooth surface tooth profile curve are axisymmetric with respect to the center line of the tooth profile, and the final design of the rigid wheel tooth profile is completed.
7. The method of claim 6, wherein the height factor of point D is hgs0.3 to 0.35, and the height coefficient of the E point is hgk＝0.45。
8. The method of claim 6, wherein the distance between E and E' is defined as the modification control point modification amount ΔgkIt satisfies the inequality: 0.02mg≤Δgk≤0.03mg。
9. A harmonic reducer comprising a harmonic gear obtained by the method of modifying a harmonic gear according to any one of claims 1 to 8.
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