CN110020509B - Harmonic gear with variable coefficient cycloid tooth profile - Google Patents
Harmonic gear with variable coefficient cycloid tooth profile Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
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Abstract
The invention discloses a harmonic gear with a variable coefficient cycloid tooth profile, which mainly comprises a wave generator, a rigid gear and a flexible gear, wherein the rigid gear is a straight-tooth cylindrical inner gear with the variable coefficient cycloid tooth profile, the flexible gear is a thin-wall straight-tooth outer gear, the tooth profile of each section of the flexible gear tooth is calculated by the rigid gear tooth profile in an enveloping way and is the variable coefficient cycloid tooth profile with different coefficients; the variable coefficient cycloid tooth profile mainly comprises an addendum cycloid and a dedendum cycloid, and the two tooth profiles are connected by a common tangent; the tooth surface contact of the rigid gear and the flexible gear with the variable-coefficient cycloid tooth profile is line contact in the meshing process, the tooth surface abrasion can be effectively reduced, the continuous conjugate meshing interval is larger than 90 degrees, the number of meshing teeth accounts for more than 50 percent of the total number of teeth, and the transmission precision and the bearing capacity of the harmonic gear can be effectively improved.
Description
Technical Field
The invention relates to a harmonic gear, in particular to a harmonic gear with a variable coefficient cycloid tooth profile.
Background
The harmonic gear mainly depends on the fact that the thin-wall flexible gear and the rigid gear form small tooth difference meshing after elastic deformation is generated under the action of the wave generator, and therefore transmission of rotating speed and torque is achieved. The tooth profile has obvious influence on the meshing performance, the transmission precision and the like of the harmonic gear. The involute tooth profile machining process is mature and can be applied to harmonic gear transmission at the earliest time, but when the number of teeth is large (about 200 teeth), the tooth profile is close to a straight line, the conjugate existing interval is small in harmonic gear transmission, most teeth are in a sharp point meshing state in a load state, and the transmission precision and the load capacity are low. Patent document 1 proposes a wave gear device having a three-dimensional contact involute positive-displacement tooth profile that provides a tapered flexible gear tooth that displaces a main-section tooth profile along a tapered tooth line to achieve a line contact state of the flexible gear tooth and the rigid gear tooth in a partial region in the tooth width direction.
According to the motion trail of the flexible gear teeth of the harmonic gear, the ideal tooth profile of the harmonic gear is a curve with convex tooth profiles at the tooth tops of the rigid gear and the flexible gear. In order to improve the gear tooth meshing state in the harmonic gear, the circular arc tooth profile and the double circular arc tooth profile are applied to the harmonic gear, the double circular arc tooth profile has the convex tooth characteristic at the tooth tops of the rigid gear and the flexible gear, the conjugate existence interval of the harmonic gear can be effectively improved, the continuous conjugate meshing of the rigid gear and the flexible gear is realized in a larger range, the transmission precision and the load capacity are improved, and the meshing characteristic superior to the involute tooth profile is realized in the harmonic gear transmission. Patent document 2 proposes a harmonic gear drive with a double circular arc tooth profile, giving some ranges of selection of circular arc parameters. The scheme does not consider the taper deformation characteristic of the cup-shaped or silk-hat-shaped flexible gear, and the tooth profile interference occurs in the front and rear sections if no correction is carried out.
The cup-shaped and hat-shaped flexible gears have taper characteristics when deformed, the motion tracks of the gear teeth of the flexible gears on different sections are different, the conjugate tooth profiles of the rigid gears are obtained by considering the taper deformation of the cup-shaped or hat-shaped flexible gears and needing conjugate solution on different sections for eliminating interference and realizing continuous conjugate meshing, a cup-shaped harmonic gear with a common tangent type double circular arc tooth profile and a tooth profile design method thereof are provided in patent document 3, and a rigid gear tooth profile which meets continuous conjugation and does not generate interference is designed by comprehensively considering a plurality of groups of conjugate points formed by the tracks of different sections of the flexible gear tooth profiles in the front, middle and rear. In the scheme, the tooth surfaces of the flexible gear and the rigid gear are in point contact, and a great lifting space is reserved between the conjugate meshing interval and the meshing tooth pair number. Patent document 4 proposes a composite double circular arc tooth profile for harmonic gear transmission, which is obtained by fitting 1/2 reduction mapping according to the motion trajectories of the flexspline on different cross sections based on a rack approximation method, and which can realize continuous meshing in a wide range. The scheme uses the rack to make approximation, the deflection angle change of the gear teeth is not considered in the motion track, and the formed tooth profile is not in an accurate conjugate state in harmonic gear transmission.
Generally, the rigid wheel is an internal gear, and the rigid wheel tooth profile designed by taking the flexible wheel tooth profile as the basic tooth profile has space three-dimensional characteristics, so that the process is complex, the processing difficulty is high, and the assembly is inconvenient. Therefore, designing a tooth profile which can realize line contact conjugate meshing of tooth surfaces in a full meshing interval, is easier to realize in process and is convenient to assemble becomes one of the key problems of harmonic gear design. According to the fact that the shape of the motion track of the flexible gear is similar to a cycloid, the curve with cycloid characteristics is suitable to be used as the tooth profile of the harmonic gear, and the cycloid is properly designed, so that the motion characteristics of harmonic gear transmission can be utilized to the maximum extent, continuous conjugate meshing transmission in a wider range is achieved, and the transmission precision and the bearing capacity of the harmonic gear are improved.
Patent documents:
patent document 1: chinese patent publication No. CN102959275A
Patent document 2: chinese patent publication No. CN101135357A
Patent document 3: chinese patent publication No. CN104074948B
Patent document 4: U.S. patent publication No. US005458023A
Disclosure of Invention
The present invention has been made to solve the above problems, and an object of the present invention is to provide a harmonic gear having a variable-coefficient cycloid tooth profile.
In order to achieve the purpose, the invention provides the following technical scheme:
a harmonic gear with a variable coefficient cycloid tooth profile is characterized in that a rigid gear is a straight-tooth cylindrical inner gear with a variable coefficient cycloid tooth profile, a flexible gear is a thin-wall straight-tooth outer gear, the tooth profile of each section of the flexible gear is calculated by the rigid gear tooth profile in an enveloping mode, and the flexible gear is the variable coefficient cycloid tooth profile with different coefficients.
The design method comprises the following steps:
1) rigid wheel variable coefficient cycloid tooth profile design
Firstly, determining parameters such as a module, a tooth number, a tooth height, a tooth thickness and the like of required harmonic transmission, giving a rigid gear tooth crest variable coefficient cycloid tooth profile formula (1), fitting a rigid gear tooth root variable coefficient cycloid tooth profile formula (2) according to a flexible gear main section tooth crest tooth profile enveloping result after completing flexible gear main section variable coefficient cycloid tooth profile design, and completing rigid gear variable coefficient cycloid tooth profile design by making a common tangent line between a rigid gear tooth crest line and a tooth root profile line;
the tooth profile expression (1) of the rigid wheel tooth crest:
tooth profile expression (2) of the rigid gear dedendum:
2) flexible gear variable coefficient cycloid tooth profile design
On the premise that the tooth profile of the rigid gear tooth along the tooth width direction is kept unchanged, the flexible gear tooth has variable coefficient cycloid tooth profiles with different coefficients on different sections; the flexible gear is subjected to fitting design by an enveloping result of the rigid gear tooth top tooth profile (1) in a meshing area in the tooth top tooth profile (3) and the tooth root tooth profile (4) of the main section and the rear section (close to the bottom end of the flexible gear cup), the flexible gear is subjected to fitting design by an enveloping result of the rigid gear tooth root profile (2) in a meshing area in the tooth top tooth profile (5) of the front section (close to the cup mouth end of the flexible gear), and the flexible gear is subjected to fitting design by an enveloping result of the rigid gear tooth top tooth profile (1) in the meshing area in the tooth root tooth profile (3) of the front section.
The tooth profile expression (3) of the flexible gear tooth against the main section and the rear section is as follows:
expression (4) of flexspline dedendum profile:
the tooth profile expression (5) of the flexible gear tooth crest on the front section:
in the formulae (1) to (5), rtIs the radius of the cycloid generating circle, u is the cycloid parameter, e2Width of the reference circle tooth groove of the rigid wheel s1Is the reference circle tooth thickness of the flexible gear Ra2Radius of addendum circle of a rigid gear Rf2Is the radius of the root circle of the rigid wheel, rmaIs the radius of the long axis of the neutral layer r after the flexible gear is deformedmbIs the minor axis radius of the neutral layer after the flexspline is deformed. A. the1，A2Is the x-direction cycloid magnification factor, B1，B2Generating a circular radius amplification factor, C, for the cycloid1，C2Is composed ofxCoefficient of cycloid correction, D1，D2Is composed ofyAnd (4) enlarging the coefficient to a cycloid curve.
The method comprises the following specific steps:
step 1: determining parameters such as modulus, tooth number, tooth height, tooth thickness and the like of the designed harmonic gear, and giving a parameter A in the formula (1)2，B2，C2And D2. And (4) preliminarily determining the tooth top profile of the rigid wheel.
Step 2: expressing the tooth profile formula (1) of the rigid wheel tooth top in a flexible wheel tooth profile coordinate system through a main section coordinate conversion relation, substituting the expression into an envelope equation, carrying out envelope solution in a meshing area, obtaining the main section tooth profile discrete point coordinate conjugated with the rigid wheel tooth top profile, and dividing the tooth profile discrete point into a convex tooth profile and a concave tooth profile.
And step 3: performing unilateral approximation fitting on the discrete points of the convex tooth profile by taking the formula (3) as a target curve, and determining a parameter A in the formula (3)1，B1，C1And D1. Preliminary determination of flexsplineA tooth crest profile at the main section. Carrying out unilateral approximation fitting on the concave tooth profile discrete points by taking the formula (4) as a target curve, and determining a parameter A in the formula (4)2，B2，C2And D2. The tooth profile of the flexible gear tooth root at the main section is preliminarily determined. Calculating the common tangent of the two variable coefficient cycloids determined by the formula (3) and the formula (4), determining the main section profile angle of the flexible gear, and finishing the design of the main section variable coefficient cycloid tooth profile of the flexible gear.
And 4, step 4: expressing the obtained flexible gear main section tooth top tooth profile formula (3) in a rigid gear tooth profile coordinate system through a main section coordinate conversion relation, substituting the expression into an envelope equation, carrying out envelope solution in a meshing area to obtain tooth profile discrete point coordinates conjugated with a flexible gear main section tooth top profile line, carrying out unilateral approximation fitting on convex tooth portion discrete points by taking the formula (2) as a target curve, and determining a parameter A in the formula (2)1，B1，C1And D1And preliminarily determining the tooth root profile of the rigid wheel. And (3) calculating the common tangent of the two variable coefficient cycloids determined by the formula (1) and the formula (2), determining the tooth profile angle of the rigid wheel, and finishing the design of the variable coefficient cycloid tooth profile of the rigid wheel.
And 5: expressing the tooth profile formula (1) of the rigid gear tooth top in a flexible gear tooth profile coordinate system through a rear section coordinate conversion relation, substituting the expression into an envelope equation, and carrying out envelope solution in a meshing area to obtain tooth profile discrete point coordinates of a rear section conjugated with the rigid gear tooth top profile. And (5) repeating the step (3) to complete the design of the variable coefficient cycloid tooth profile of the rear section of the flexible gear.
The tooth profile of the rigid wheel forms a quartic envelope on the front section, wherein the tooth profile of the tooth top of the rigid wheel forms a quadratic envelope in a meshing area, and the rigid wheel interferes with a conjugate point generated by the quadratic envelope in a subsequent meshing process, so that the quadratic envelope is not available. Forming a third envelope on the tooth top profile of the rigid gear in a meshing area to generate conjugate discrete points of the tooth root profile of the front section of the flexible gear; and the tooth root tooth profile of the rigid gear forms a fourth envelope in a meshing area to generate conjugate discrete points of the tooth top tooth profile of the front section of the flexible gear.
Step 6: expressing the rigid gear tooth top profile formula (1) in a flexible gear tooth profile coordinate system through a front section coordinate conversion relation, substituting the flexible gear tooth profile coordinate system into an envelope equation, carrying out envelope solution in a meshing area, and obtaining a front conjugate with the rigid gear tooth top profileAnd (4) coordinates of discrete points of the concave profile of the cross section. Performing unilateral approximation fitting on the concave tooth profile discrete points by taking the formula (4) as a target curve, and determining a parameter A in the formula (4)2，B2，C2And D2And preliminarily determining the tooth profile of the flexible gear tooth root at the front section.
And 7: expressing the rigid gear tooth root tooth profile formula (2) in a flexible gear tooth profile coordinate system through a front section coordinate conversion relation, substituting the flexible gear tooth profile coordinate system into an envelope equation, and carrying out envelope solution in a meshing area to obtain the coordinates of the front section convex tooth profile discrete points conjugated with the rigid gear tooth root profile. Performing unilateral approximation fitting on the discrete points of the convex tooth profile by taking the formula (5) as a target curve, and determining a parameter A in the formula (5)1，B1，C1And D1. And preliminarily determining the tooth profile of the flexible gear tooth top in the front section. Calculating the common tangent of the two variable coefficient cycloids determined by the formula (5) and the formula (3), determining the front section tooth profile angle of the flexible gear, and finishing the design of the front section variable coefficient cycloid tooth profile of the flexible gear.
The invention has the beneficial effects that:
in the invention, the tooth profile of the rigid gear is used as a basic tooth profile, and the conjugate tooth profiles of the flexible gears with different sections are designed according to the conjugate motion of the gear teeth of the rigid gear relative to the gear teeth of the flexible gears, so that the method is easy to realize in process. The designed rigid gear and the flexible gear with the variable-coefficient cycloid tooth profiles are in a linear contact state in the meshing process, the tooth surface abrasion can be effectively reduced, the continuous conjugate meshing interval is larger than 90 degrees, the number of the meshed teeth accounts for more than 50% of the total number of the teeth, and the transmission precision and the bearing capacity of the harmonic gear can be effectively improved. The larger the taper deformation characteristic of the flexible gear is, the larger the envelope range of the front section tooth profile in the meshing area is, the larger the total interval of conjugate meshing is, and the more the total tooth number of the conjugate meshing is.
Drawings
Fig. 1 is a front view of an example of a harmonic gear device having a variable ratio cycloid tooth profile to which the present invention is applied.
Fig. 2 is a schematic left side sectional view of an example harmonic gear device having a variable ratio cycloid tooth profile to which the present invention is applied.
Fig. 3A is a schematic diagram of a variable coefficient cycloid tooth profile structure of a flexible gear in the invention.
Fig. 3B is a schematic diagram of a variable coefficient cycloid tooth profile structure of the rigid wheel in the invention.
Fig. 4 is a geometrical relationship diagram of a flexspline tooth profile coordinate system and a rigid spline tooth profile coordinate system in a deformed state.
Fig. 5A is a movement diagram of an example of the rigid gear tooth profile relative to the flexible gear main-section tooth profile.
Fig. 5B is a movement diagram of an example of the rigid gear tooth profile relative to the flexible gear rear section tooth profile.
Fig. 5C is a movement diagram of an example of the rigid gear tooth profile relative to the flexible gear front section tooth profile.
Fig. 6 shows the profiles of the flexspline in front section, main section and rear section.
Fig. 7 shows a conjugate meshing interval between a rigid gear and a flexible gear in a harmonic gear having a variable-ratio cycloid tooth profile to which the present invention is applied.
In the figure: the gear comprises a flexible gear 1, a rigid gear 2, a flexible bearing 3, a cam 4, a rigid gear tooth profile T2, a flexible gear main section tooth profile T1m, a flexible gear rear section tooth profile T1r and a flexible gear front section tooth profile T1 f.
Detailed Description
In order to make the technical means for implementing the present invention easily understood, the technical solutions provided by the present invention will be described in detail below with reference to the accompanying drawings and embodiments.
Example (b):
the invention provides a harmonic gear with a variable coefficient cycloid tooth profile. In this example, the designed harmonic gear module is 0.5mm, the tooth height is 1mm, the tooth number of the flexible gear is 200, the tooth number of the rigid gear is 202, the tooth top height of the rigid gear is 0.5mm, rt0.25mm, the tooth thickness of flexible gear and the tooth groove width of rigid gear are s1＝e2＝0.785mm。
Fig. 1 is a front view of a harmonic gear to which the present invention is applied. As shown in fig. 1, the harmonic gear mainly comprises a wave generator, a rigid gear and a flexible gear, wherein the rigid gear 2 is a straight-tooth cylindrical internal gear with a variable coefficient cycloid tooth profile, the flexible gear 1 is a thin-wall straight-tooth external gear, and the wave generator is composed of a flexible bearing 3 and a cam 4. Under the action of wave generator, the flexible gear is elastically deformed, and the size of the polar diameter of the neutral layer at the long axis is rmaAt the minor axisHas a size of rmb。
Fig. 2 is a schematic left side sectional view of an example harmonic gear device having a variable ratio cycloid tooth profile to which the present invention is applied.
Fig. 3A is a variable coefficient cycloid tooth profile of a main section of a flexspline in an embodiment of the present invention. The tooth profile of which is expressed in a coordinate system { X1，O1，Y1In the coordinate system, the origin of coordinates O1On the neutral layer (about h/2 thickness, h is the wall thickness of the flexible gear ring gear part) of the flexible gear ring gear, Y1The axis coincides with the symmetry line of the flexible gear teeth, X1The axis is tangent to the neutral layer. In the figure, Ra1Radius of addendum circle of flexspline (undeformed)f1Radius of root circle of flexible gear R1Is the reference circle radius of the flexible gear rmIs the radius of the circle where the neutral layer of the gear ring is located in the undeformed state of the flexible gear.
Fig. 3B is a variable coefficient cycloid tooth profile of a rigid wheel in an embodiment of the present invention. The tooth profile of which is expressed in a coordinate system { X2，O，Y2In the above, the origin of coordinates O of the coordinate system is on the central axis of the rigid wheel, Y2The shaft is superposed with the symmetry line of the tooth socket of the rigid wheel. In the figure, Ra2Radius of addendum circle of a rigid gear, Rf2Is the radius of the root circle of the rigid wheel, R2Is the reference circle radius of the rigid wheel, ha2Is the tooth crest height of the rigid wheel hnIs the full tooth height of the rigid wheel.
Fig. 4 is a geometrical relationship diagram of a rigid gear tooth profile and a flexible gear tooth profile in an embodiment of the invention. As shown in FIG. 4, the rigid gear tooth profile A2D2From the coordinate system { X2，O，Y2Converting to coordinate system X1，O1，Y1The transformation matrix of is:
flexspline tooth profile A1D1From the coordinate system { X1，O1，Y1Converting to coordinate system X2，O，Y2The transformation matrix of is:
step 1: determining parameters such as modulus, tooth number, tooth height, tooth thickness and the like of the designed harmonic gear, and giving a parameter A in the formula (1)2＝1，B2＝1，C 20 and D 21. Preliminary determination of tooth top profile F of rigid wheel2H2(FIG. 3B).
Step 2: the tooth profile formula (1) of the addendum of the rigid wheel is determined from a coordinate system { X2，O，Y2Converting to coordinate system X1，O1，Y1Get in the previous step:
then, x is21，y21Substitution into the envelope equation:
and carrying out envelope solution in the meshing area to obtain the discrete point coordinates of the flexible gear main section tooth profile conjugated with the tooth crest profile of the rigid gear, and dividing the tooth profile discrete points into a convex tooth profile and a concave tooth profile.
And step 3: performing unilateral approximation fitting on the discrete points of the convex tooth profile by taking the formula (3) as a target curve, and determining a parameter A in the formula (3)1，B1，C1And D1. Preliminary determination of tooth profile E of flexible gear teeth against main section1G1(FIG. 3A). Carrying out unilateral approximation fitting on the concave tooth profile discrete points by taking the formula (4) as a target curve, and determining a parameter A in the formula (4)2，B2，C2And D2. Preliminary determination of the tooth profile F of the flexible gear root in the main section1H1. Calculating the common tangent G of two variable coefficient cycloids in formula (3) and formula (4)1H1The common tangent line simultaneously determines the tooth profile angle alpha of the main section tooth profile of the flexible gear1. And finishing the design of the variable coefficient cycloid tooth profile of the main section of the flexible gear.
Step 4: the obtained flexspline main section tooth crest tooth profile form (3) is driven from a coordinate system { X1，O1，Y1Converting to coordinate system X2，O，Y2Get in
Then, x is12，y12Substitution into the envelope equation:
enveloping and solving in a meshing area to obtain tooth profile discrete point coordinates conjugated with the tooth top profile of the main section of the flexible gear, performing unilateral approximation fitting by taking the convex tooth part discrete points in the tooth profile discrete point coordinates and taking the formula (2) as a target curve, and determining a parameter A in the formula (2)1，B1，C1And D1Preliminary determination of the profile E of the dedendum of a rigid gear2G2. Calculating the common tangent G of the two coefficient-variable cycloids determined by the equations (1) and (2)2H2And determining the profile angle alpha of the rigid wheel2And finishing the design of the variable coefficient cycloid tooth profile of the rigid wheel.
FIG. 5A is a kinematic diagram of a rigid wheel profile T2 relative to a flexible wheel major section profile T1m in an embodiment of the present invention. The figure shows the engaging and disengaging process of the rigid gear teeth relative to the flexible gear teeth on the main section, and the tooth tops of the rigid gear teeth continuously form a secondary envelope with the tooth tops and the tooth bottoms of the main section of the flexible gear during the engaging process.
And 5: expressing the tooth profile formula (1) of the rigid gear tooth top in a flexible gear tooth profile coordinate system through a rear section coordinate conversion relation, substituting the expression into an envelope equation, and carrying out envelope solution in a meshing area to obtain tooth profile discrete point coordinates of a rear section conjugated with the rigid gear tooth top profile. And (5) repeating the step (3) to complete the design of the variable coefficient cycloid tooth profile of the rear section of the flexible gear.
FIG. 5B is a movement diagram of a rigid gear profile T2 relative to a flexible gear rear section profile T1r in an embodiment of the present invention. The figure shows the engaging and disengaging process of the rigid gear teeth relative to the flexible gear teeth on the rear section, and the tooth tops of the rigid gear teeth continuously form a secondary envelope with the tooth tops and the tooth bottoms of the rear section of the flexible gear during the engaging process.
Step 6: expressing the rigid gear tooth top profile formula (1) in a flexible gear tooth profile coordinate system through a front section coordinate conversion relation, substituting the flexible gear tooth profile coordinate system into an envelope equation, and carrying out envelope solution in a meshing area to obtain the coordinates of discrete points of the front section concave tooth profile conjugated with the rigid gear tooth top profile. Performing unilateral approximation fitting on the concave tooth profile discrete points by taking the formula (4) as a target curve, and determining a parameter A in the formula (4)2，B2，C2And D2And preliminarily determining the tooth profile of the flexible gear tooth root at the front section.
And 7: expressing the rigid gear tooth root tooth profile formula (2) in a flexible gear tooth profile coordinate system through a front section coordinate conversion relation, substituting the flexible gear tooth profile coordinate system into an envelope equation, and carrying out envelope solution in a meshing area to obtain the coordinates of the front section convex tooth profile discrete points conjugated with the rigid gear tooth root profile. Performing unilateral approximation fitting on the discrete points of the convex tooth profile by taking the formula (5) as a target curve, and determining a parameter A in the formula (5)1，B1，C1And D1. And preliminarily determining the tooth profile of the flexible gear tooth top in the front section. Calculating the common tangent of the two variable coefficient cycloids determined by the formula (5) and the formula (3), determining the front section tooth profile angle of the flexible gear, and finishing the design of the front section variable coefficient cycloid tooth profile of the flexible gear.
FIG. 5C is a kinematic diagram of a rigid wheel profile T2 relative to a flexible wheel front section profile T1f in an embodiment of the present invention. The figure shows the engagement and disengagement process of the rigid gear teeth relative to the flexible gear teeth in the front section, the rigid gear does not contact with the flexible gear front section teeth in the engagement process, and the secondary envelope formed in the stage is not available; in the meshing process, the tooth top of the rigid gear and the tooth root of the front section of the flexible gear form a third envelope, and the tooth root of the rigid gear and the tooth top of the front section of the flexible gear form a fourth envelope.
Fig. 6 shows a flexspline forward section profile T1f, a main section profile T1m, and a rear section profile T1r in an embodiment of the present invention.
Fig. 7 is a fourth-order envelope interval of a rigid-wheel variable-coefficient cycloid tooth profile in an embodiment of the present invention. The figure shows the location of the tip of the rigid gear and the tip of the flexible gear at the main section
A primary envelope e3 is formed between the tooth top of the rigid gear and the tooth bottom of the flexible gear
Form a quadratic envelope e 4; at the position of the rear section, the tooth top of the rigid gear is located at the tooth top of the flexible gear
A primary envelope e5 is formed between the tooth top of the rigid gear and the tooth bottom of the flexible gear
Form a quadratic envelope e 6; at the front section position, the addendum of the rigid gear and the dedendum of the flexible gear are at
Forming a cubic envelope e1 between-5 and 0 DEG, the gear root of the rigid gear and the gear tip of the flexible gear
The fourth envelope e2 is formed between about-4 DEG and 0 deg. The continuous conjugate meshing total interval on the front section, the main section and the rear section is about 95 degrees, which means that the number of teeth of the rigid gear and the flexible gear which are simultaneously in conjugate meshing accounts for more than 50 percent of the total number of teeth.
It can be known from these drawings that the tooth profiles of the rigid gears in the variable coefficient cycloid tooth profile harmonic gear are consistent along the tooth width direction, the internal gear machining process is easy to realize, the flexible gears have different tooth profiles on the front, main and rear sections to realize the maximum range of conjugate meshing motion, and two degrees of freedom motion is required to be added on the basis of the generating motion of the common gear when the flexible gear tooth profile machining is carried out. Tooth profiles of main and rear sections of flexible gear in engaging zone
Continuously conjugate meshing with the tooth profile of the rigid wheel; the tooth profile of the front section of the flexible gear and the tooth profile of the rigid gear do not participate in meshing in the meshing area, so that the tooth profile interference is avoided, and small-range conjugate meshing is performed in the meshing area. Harmonic tooth with variable coefficient cycloid tooth profileThe wheel obviously increases the conjugate meshing range of harmonic transmission, can improve the transmission precision and improve the transmission load capacity.
The above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the technical solutions, and those skilled in the art should understand that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and shall be covered by the claims of the present invention.
Claims (2)
1. A harmonic gear having a variable coefficient cycloidal tooth profile, characterized by: the rigid gear of the harmonic gear is a straight-tooth cylindrical inner gear with a variable coefficient cycloid tooth profile, the flexible gear is a thin-wall straight-tooth outer gear, and the flexible gear has variable coefficient cycloid tooth profiles with different coefficients on each section, and the design method is as follows:
1) rigid wheel variable coefficient cycloid tooth profile design
Firstly, determining parameters of a module, a tooth number, a tooth height and a tooth thickness of required harmonic transmission, giving a rigid gear tooth crest variable coefficient cycloid tooth profile formula (1), fitting a rigid gear tooth root variable coefficient cycloid tooth profile formula (2) according to a flexible gear main section tooth crest tooth profile enveloping result after completing flexible gear main section variable coefficient cycloid tooth profile design, and making a common tangent line between a rigid gear tooth crest line and a tooth root profile line to complete rigid gear variable coefficient cycloid tooth profile design;
the tooth profile expression (1) of the rigid wheel tooth crest:
tooth profile expression (2) of the rigid gear dedendum:
2) flexible gear variable coefficient cycloid tooth profile design
On the premise that the tooth profile of the rigid gear tooth along the tooth width direction is kept unchanged, the flexible gear tooth has variable coefficient cycloid tooth profiles with different coefficients on different sections; wherein, the tooth top tooth profile formula (3) and the tooth bottom tooth profile formula (4) of the flexible gear on the main section and the rear section are designed by the enveloping result of the tooth top tooth profile formula (1) of the rigid gear in the mesh-in area in a fitting manner, the tooth top tooth profile formula (5) of the flexible gear on the front section is designed by the enveloping result of the tooth bottom tooth profile formula (2) of the rigid gear in the mesh-out area in a fitting manner, the tooth profile formula (3) of the flexible gear on the front section is designed by the enveloping result of the tooth top tooth profile formula (1) of the rigid gear in the mesh-out area in a fitting manner,
the tooth profile expression (3) of the flexible gear tooth against the main section and the rear section is as follows:
expression (4) of flexspline dedendum profile:
the tooth profile expression (5) of the flexible gear tooth crest on the front section:
in the formulae (1) to (5), rtIs the radius of the cycloid generating circle, u is the cycloid parameter, e2Width of the reference circle tooth groove of the rigid wheel s1Is the reference circle tooth thickness of the flexible gear Ra2Radius of addendum circle of a rigid gear Rf2Is the radius of the root circle of the rigid wheel, rmaIs the radius of the long axis of the neutral layer r after the flexible gear is deformedmbIs the minor axis radius of the neutral layer after deformation of the flexspline, A1，A2Is the x-direction cycloid magnification factor, B1，B2Generating a circular radius amplification factor, C, for the cycloid1，C2Is a x-direction cycloid correction coefficient, D1，D2Is the y-direction cycloid amplification factor.
2. A device according to claim 1 having a variationHarmonic gear of coefficient cycloid flank profile, its characterized in that: wherein the radius r of the cycloidal generating circletIs half of the design value of the tooth crest height of the rigid wheel.
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| CN110688614B (en) * | 2019-09-18 | 2022-10-28 | 北京工业大学 | Multi-tooth meshing composite stress solving method for cup-shaped flexible wheel of harmonic reducer |
| CN110909430B (en) * | 2019-11-26 | 2024-03-08 | 北京工业大学 | Design method for cycloidal tooth profile of flexible gear of harmonic reducer |
| CN113032923B (en) * | 2021-03-23 | 2022-10-28 | 武汉理工大学 | Flexible gear, tooth shape design method thereof and harmonic reducer |
| CN113446377B (en) * | 2021-08-13 | 2023-03-10 | 天津大学 | Conjugate cycloid tooth profile harmonic speed reducer |
| CN113931991B (en) * | 2021-08-31 | 2023-07-14 | 北京精密机电控制设备研究所 | Method for determining tooth form of harmonic transmission with small reduction ratio |
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