CN104819267B - Harmonic gear device adopting non-interference and wide range meshing tooth profile - Google Patents
Harmonic gear device adopting non-interference and wide range meshing tooth profile Download PDFInfo
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- CN104819267B CN104819267B CN201510244297.0A CN201510244297A CN104819267B CN 104819267 B CN104819267 B CN 104819267B CN 201510244297 A CN201510244297 A CN 201510244297A CN 104819267 B CN104819267 B CN 104819267B
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- 230000002452 interceptive effect Effects 0.000 claims description 3
- 229910000831 Steel Inorganic materials 0.000 abstract description 3
- 239000010959 steel Substances 0.000 abstract description 3
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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
- F16H55/0833—Flexible toothed member, e.g. harmonic drive
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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
- F16H55/17—Toothed wheels
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Abstract
The invention discloses a harmonic gear device adopting a non-interference and wide range meshing tooth profile. The harmonic gear device adopting the non-interference and wide range meshing tooth profile comprises a steel wheel having internal tooth, a flexible gear arranged in the steel wheel and having external tooth, and a wave generator mounted in the flexible gear; the internal tooth is meshed with the external tooth, the tooth profile of the internal tooth and the external tooth can be obtained by following formula: the formula is as shown in specification; the harmonic gear device adopting the non-interference and wide range meshing tooth profile has more reasonable tooth profile and can meet better tooth profile meshing performance.
Description
Technical Field
The invention relates to a harmonic gear device, in particular to a harmonic gear device adopting a non-interference and large-range meshing tooth profile.
Background
Harmonic gear transmission is a transmission that relies on the elastic deformation of compliant gears to transmit force and motion. The typical harmonic reducer consists of three elements, namely a flexible gear, a rigid gear and a wave generator. In general, the rigid gear is fixed, the wave generator is an elliptical component and is arranged in the flexible gear, so that the flexible gear is forced to generate radial deformation at the long axis end according to a certain rule to form an elliptical shape. When the wave generator is driven to rotate, the flexible gear is forced to deform continuously, and the flexible gear teeth gradually enter the space between the rigid gear teeth in the deformation process, are meshed with the rigid gear teeth, and then gradually exit until the flexible gear teeth are completely separated. Therefore, the wave generator continuously rotates, the flexible gear teeth and the rigid gear teeth continuously and repeatedly carry out the cyclic mutual staggered tooth movement of meshing, meshing and disengaging, and the staggered tooth movement converts the input of the wave generator into the output of the flexible gear to realize speed reduction transmission.
In order to ensure high-quality transmission performance, the harmonic gear needs to have excellent performances in the aspects of angle transmission precision, strength, rigidity and the like, and the performances are in the same relation with the selection of tooth profiles.
The harmonic gear adopts a straight triangular tooth profile at the earliest, such as the tooth profile shape disclosed in U.S. patent document 1 with the patent number of US2906143, and adopts an involute tooth profile at the later time, and the harmonic gear used in China still mainly adopts the involute tooth profile because the involute tooth profile is developed most perfectly in the process. However, in order to further improve the transmission performance of the harmonic gear, japanese proposes an IH tooth profile based on a curve (curved surface) geometric mapping theory, such as the tooth profile shape disclosed in U.S. patent document 2 of patent No. US4823638, which is currently used in high-performance harmonic gears in japan. However, the tooth profile is an approximate design under the condition that the flexible gear and the rigid gear are assumed to be racks, and the condition that the tooth profile of the flexible gear inclines during the relative movement of the flexible gear and the rigid gear is not considered, so that the tooth profile interference phenomenon exists in the transmission. In view of this drawback, U.S. patent document 3 of patent No. US5456139 discloses an improvement method, but it considers only the tilting phenomenon of the flexspline tooth profile and does not consider the case where the movement locus of a point on the tooth profile neutral line changes, and therefore, U.S. patent document 4 of patent No. US5918508 makes a further improvement.
According to patent document 4, based on the geometric mapping theory based on the curve (curved surface) of patent document 2, the flexible gear and the rigid gear are assumed to be racks, and then the approximately designed tooth profile is obtained according to the motion track of the flexible gear relative to the rigid gear. Then, considering the inclination phenomenon of the tooth profile of the flexible gear and the change of the motion track, the tooth profile of the approximate design is further corrected to obtain the tooth profile with more ideal meshing condition. The tooth profile keeps continuous correct contact when in a meshing state and a meshing state in the harmonic gear transmission process, and does not generate tooth profile interference, so that the number of teeth participating in meshing is increased, and the meshing range is large. Therefore, the transmission performance of the gear, such as transmission precision, strength, rigidity, service life and the like, is greatly improved.
However, patent document 4 still has a disadvantage that it does not distinguish the modulus on the neutral line (circle) of the flexible gear from the modulus on the pitch circle, which affects the motion trajectory of the flexible gear with respect to the rigid gear, and also affects the phenomenon of inclination of the tooth profile, thereby having a significant effect on the acquisition of the final tooth profile and the transmission performance of the gear.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a harmonic gear device adopting a non-interference and large-range meshing tooth profile, which has a more reasonable tooth profile and realizes better tooth profile meshing performance.
The purpose of the invention is realized by adopting the following technical scheme:
a harmonic gear device employing a non-interfering and large-range meshing tooth profile, comprising a rigid gear having internal teeth, a flexible gear provided in the rigid gear and having external teeth, and a wave generator mounted in the flexible gear, the internal teeth and the external teeth meshing, the tooth profiles of the internal teeth and the external teeth being obtained by:
x＝mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)-0.5(g1-g2) (1)
y＝0.5·m·[1-cos2θ](2)
wherein,
rn＝m·ZF/2
mg＝(2rn+t)/[ZF-2(ha*+c*)]
g1＝h·Φ
g2＝{0.5·m·[2θ-sin2θ]-xN}+0.5·tanθ·{yN-m[1-cos2θ]}
h＝0.5·t+mg·(ha*+c*)+f
f＝0.5·m·[1-cos2θ]-0.5·tanθ·{mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)}
Φ＝γ+μ
μ＝arctan{2·m·sin2θ/(rn+m·cos2θ)}
xN＝[rn+m·cos2θ]·sinγ
yN＝(rn+m)-(rn+m·cos2θ)·cosγ
in the formula, the origin of a coordinate system is arranged at the intersection point of the tooth profile central line and a reference circle, the X axis of the coordinate system is tangent to the reference circle, and the Y axis of the coordinate system is superposed with the tooth profile central line; m, mg, ZF, ha, c, rn, theta and t are respectively the neutral line (circle) modulus, reference circle modulus, tooth number, tooth root height coefficient, top clearance coefficient, neutral line (circle) radius, corner of non-deformation end and rim thickness of the flexible gear in sequence; ZC is the number of teeth of the rigid wheel; tau is a tooth thickness variation coefficient, plus or minus in the formula (1) is positive when the tooth thickness of the flexible gear is reduced, and minus or plus in the formula (1) is negative when the tooth thickness of the rigid gear is increased; g1 is the correction term of the tooth profile tilting phenomenon, and g2 is the correction term of the motion trajectory change.
Preferably, the number of teeth of the external teeth is two less than the number of teeth of the internal teeth.
Compared with the prior art, the invention has the beneficial effects that:
(1) the tooth profiles adopted by the flexible gear and the steel gear are calculated by the formulas (1) and (2), the inclination phenomenon and the track change condition of the tooth profile of the flexible gear in the motion process are combined, the modulus on the neutral line (circle) of the flexible gear is combined with the difference between the modulus on the reference circle, so that the tooth profiles are more reasonable, and the acquisition of the final tooth profile and the transmission performance of the gear are prevented from being influenced by distinguishing the modulus on the neutral line (circle) of the flexible gear from the modulus on the reference circle;
(2) the tooth profile obtained by calculation through the formula (1) and the formula (2) is used, and the tooth profile of the flexible gear is continuously and correctly contacted with the tooth profile of the rigid gear in the processes of meshing in and meshing out, so that the meshing tooth number is increased, the meshing range is enlarged, the number of engaged teeth is large, various performances of the harmonic gear transmission device are greatly improved on the premise of not generating interference, and the performances such as bearing capacity, transmission precision, strength, rigidity, service life and the like are improved.
Drawings
FIG. 1 is a schematic front view of a harmonic gear device according to the present invention;
FIG. 2 is a graph of the angular position of the inner tooth profile centerline and the outer tooth profile centerline of the present invention;
FIG. 3 is a schematic diagram of a method for obtaining a tooth profile pitch correction term g1 and a motion trajectory correction term g2 according to the present invention;
FIG. 4 is a schematic view of an external tooth profile of the flexspline of the present invention;
FIG. 5 is a schematic diagram of tooth profile of the outer teeth of the flexible gear meshing with the inner teeth of the rigid gear.
In the figure: 1. a harmonic gear device; 2. a rigid wheel; 2a, internal teeth; 3. a flexible gear; 3a, external teeth; 4. a wave generator; 4a, a long axis; 4b, minor axis.
Detailed Description
The invention will be further described with reference to the accompanying drawings and the detailed description below:
a harmonic gear device 1 employing a non-interfering and large-range meshing tooth profile as shown in fig. 1 includes a rigid gear 2 having internal teeth 2a, a flexible gear 3 provided in the rigid gear 2 and having external teeth 3a, and a wave generator 4 mounted in the flexible gear 3, the internal teeth 2a and the external teeth 3a being meshed, the tooth profiles of the internal teeth 2a and the external teeth 3a being obtained by the following formula:
x＝mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)-0.5(g1-g2) (1)
y＝0.5·m·[1-cos2θ](2)
wherein,
rn＝m·ZF/2
mg＝(2rn+t)/[ZF-2(ha*+c*)]
g1＝h·Φ
g2＝{0.5·m·[2θ-sin2θ]-xN}+0.5·tanθ·{yN-m[1-cos2θ]}
h＝0.5·t+mg·(ha*+c*)+f
f＝0.5·m·[1-cos2θ]-0.5·tanθ·{mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)}
Φ＝γ+μ
μ＝arctan{2·m·sin2θ/(rn+m·cos2θ)}
xN＝[rn+m·cos2θ]·sinγ
yN＝(rn+m)-(rn+m·cos2θ)·cosγ
in the formula, the origin of a coordinate system is arranged at the intersection point of the tooth profile central line and a reference circle, the X axis of the coordinate system is tangent to the reference circle, and the Y axis of the coordinate system is superposed with the tooth profile central line; m, mg, ZF, ha, c, rn, theta and t are sequentially and respectively the neutral line (circle) modulus, the reference circle modulus, the tooth number, the tooth root height coefficient, the top clearance coefficient, the neutral line (circle) radius, the corner of a non-deformation end and the rim thickness of the flexible gear 3; ZC is the number of teeth of the rigid wheel 2; tau is a tooth thickness variation coefficient, plus or minus in the formula (1) is taken as positive when the tooth thickness of the flexible gear 3 is reduced, and minus or plus in the formula (1) is taken as negative when the tooth thickness of the rigid gear 2 is increased; g1 is the correction term of the tooth profile tilting phenomenon, and g2 is the correction term of the motion trajectory change.
The working principle of the harmonic gear device 1 of the present invention is as follows:
as shown in fig. 1, the number of teeth of the external teeth 3a of the flexible gear 3 is 2 less than that of the internal teeth of the rigid gear to form double wave transmission, so that the stress of the flexible gear 3 is small, the structure is simpler, and a large transmission ratio is easily obtained. The outer contour of the wave generator 4 is elliptical.
Normally, the rigid wheel 2 is stationary. The flexspline 3 is disposed in the ring gear 2 and is connected to an output shaft (not shown). The wave generator 4 is arranged in an inner hole of the flexible gear 3, the outer contour of the wave generator 4 is tightly attached to the inner hole wall of the flexible gear 3, and the flexible gear 3 is bent into an oval shape, so that the inner teeth 2a and the outer teeth 3a in the direction of the major axis 4a enter a meshing state, and the inner teeth 2a and the outer teeth 3a in the direction of the minor axis 4b are mutually separated; meanwhile, the wave generator 4 is connected to an input shaft (not shown in the figure). When the input shaft drives the wave generator 4 to rotate, the meshing position of the flexible gear 3 and the rigid gear 2 moves in the circumferential direction, and the flexible gear 3 and the rigid gear 2 generate speed reduction relative movement, wherein the speed reduction ratio is related to the tooth number and the tooth number difference of the flexible gear 3 and the rigid gear 2; for example, when the wave generator 4 rotates clockwise one turn, the flexspline 3 rotates counterclockwise two teeth, and the reduction ratio is: 2/number of teeth of the flexspline 3; finally, the power or motion is transmitted to the output shaft via the flexspline 3.
The principle of calculating the tooth profiles of the outer teeth 3 of the flexible gear 3 and the inner teeth 2a of the rigid gear 2 is as follows:
the motion law of points on the neutral line of the flexible gear 3 is as follows:
υ＝-0.5m·sin2θ；
ω＝m·cos2θ；
where ω is the radial displacement and υ is the circumferential displacement.
Assuming that the flexible gear 3 and the rigid gear 2 are both racks, the motion track of a point on the neutral line of the flexible gear 3 relative to the rigid gear 2 is as follows:
x1＝0.5m·(2θ-sin2θ)
y1＝m·(1-cos2θ)
according to the curve (curved surface) geometric mapping theory and through proper coordinate conversion, the upper tooth surface tooth profile which is approximately designed is obtained, and the equation is as follows:
x0＝mg[0.25π-(±τ)]-0.25m·(2θ-sin2θ) (3)
y0＝0.5m·(1-cos2θ) (4)
it has been considered in equation (3) that the modulus corresponding to the neutral line (circle) of the flexspline 3 is different from the modulus corresponding to the reference circle.
The following analyzes how the final tooth profile is obtained by correcting equations (3) and (4).
The angular position relationship between the tooth profile center line of the inner teeth 2a and the tooth profile center line of the outer teeth 3a is shown in fig. 2, which is the basis for correcting the tooth profile lean phenomenon. The meaning of the parameters in fig. 2 is as follows: phi is a rotation angle of the tooth profile central line of the inner teeth 2a relative to the tooth profile central line of the outer teeth 3a, namely the total inclination angle of the tooth profile of the flexible gear; ρ represents the radial direction of a point on the neutral line;the included angle between the tooth profile central line of the inner teeth 2a and the long axis 4a of the wave generator;the included angle between the tooth profile central line of the external teeth 3a and the long axis 4a of the wave generator; gamma is an included angle between rho and the tooth profile central line of the internal teeth 2 a; mu is an included angle between rho and the tooth profile center of the external tooth 3a, namely a rotating angle of a normal line of a point on a neutral line of the flexible gear 3. The values of the angles in fig. 2 can be calculated by the following equations.
μ＝arctan{2·m·sin2θ/(rn+m·cos2θ)}
Φ＝γ+μ
Fig. 3 shows a method for calculating the tooth profile inclination correction term g1 and the motion trajectory correction term g2, which is more reasonable to distinguish the modulus corresponding to the neutral line (circle) of the flexspline 3 from the modulus corresponding to the reference circle.
In fig. 3, a point P, a point M, and a straight line e are respectively a tooth profile meshing point, a point on the neutral line, and a tooth profile center line of the external tooth 3a at the time of approximate design, a straight line n is a tooth profile normal line at the point P, and a point F is an intersection of the straight line n and the straight line e.
When the tooth profile is inclined, the point F rotates clockwise around the point M by the angle phi to reach the point A, the line segment PB is equal to and parallel to the line segment FA, and PB is the inclination correction term g 1. The following equation is obtained:
g1＝h·Φ
h＝0.5·t+mg·(ha*+c*)+f
f＝0.5·m·[1-cos2θ]-0.5·tanθ·{mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)}
in addition, when the tooth profile is inclined, the motion trail of a point on the neutral line of the flexible gear 3 is changed, in the figure, a curve i is the original motion trail, a curve j is the changed motion trail, and a point M on the curve i reaches a point N on the curve j after the track is changed. The line BQ is equal to the line ML, and BQ is the motion trajectory change correction term g 2. The following equation is thus obtained:
g2＝{0.5·m·[2θ-sin2θ]-xN}+0.5·tanθ·{yN-m[1-cos2θ]}
xN＝[rn+m·cos2θ]·sinγ
yN＝(rn+m)-(rn+m·cos2θ)·cosγ
finally, the midpoint R of the line PQ is obtained, i.e. the point on the final tooth profile.
From the above, by combining formula (3), formula (4), the tilt correction term g1, the trajectory change correction term g2, and the midpoint R, the final equation of the tooth profile of the internal teeth and the external teeth can be obtained:
x＝mg[0.25π-(±τ)]-0.25m·(2θ-sin2θ)-0.5(g1-g2)
y＝0.5m·(1-cos2θ)
the tooth profile of the flexspline 3 obtained is shown in fig. 4. Fig. 5 shows the process of engagement of the external teeth 3a of the flexspline 3 with the internal teeth 2a of the rigid spline 2, and it can be seen that no interference occurs and continuous contact is maintained throughout the engagement process.
Various other modifications and changes may be made by those skilled in the art based on the above-described technical solutions and concepts, and all such modifications and changes should fall within the scope of the claims of the present invention.
Claims (2)
1. A harmonic gear device adopting non-interference and large-range meshing tooth profile comprises a rigid gear with internal teeth, a flexible gear arranged in the rigid gear and provided with external teeth, and a wave generator installed in the flexible gear, wherein the internal teeth and the external teeth are meshed, and the harmonic gear device is characterized in that: the tooth profiles of the internal and external teeth are obtained by the following formula:
x＝mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)-0.5(g1-g2) (1)
y＝0.5·m·[1-cos2θ](2)
wherein,
rn＝m·ZF/2
mg＝(2rn+t)/[ZF-2(ha*+c*)]
g1＝h·Φ
g2＝{0.5·m·[2θ-sin2θ]-xN}+0.5·tanθ·{yN-m[1-cos2θ]}
h＝0.5·t+mg·(ha*+c*)+f
f＝0.5·m·[1-cos2θ]-0.5·tanθ·{mg·[0.25π-(±τ)]-0.25m·(2θ-sin2θ)}
Φ＝γ+μ
μ＝arctan{2·m·sin2θ/(rn+m·cos2θ)}
xN＝[rn+m·cos2θ]·sinγ
yN＝(rn+m)-(rn+m·cos2θ)·cosγ
in the formula, the origin of a coordinate system is arranged at the intersection point of the tooth profile central line and a reference circle, the X axis of the coordinate system is tangent to the reference circle, and the Y axis of the coordinate system is superposed with the tooth profile central line; m, mg, ZF, ha, c, rn, theta and t are respectively the neutral line modulus, reference circle modulus, tooth number, tooth root height coefficient, top clearance coefficient, neutral line radius, corner of a non-deformation end and rim thickness of the flexible gear in sequence; ZC is the number of teeth of the rigid wheel; tau is a tooth thickness variation coefficient, plus or minus in the formula (1) is positive when the tooth thickness of the flexible gear is reduced, and minus or plus in the formula (1) is negative when the tooth thickness of the rigid gear is increased; g1 is the correction term of the tooth profile tilting phenomenon, and g2 is the correction term of the motion trajectory change.
2. The harmonic gear device with non-interfering and large range of meshing tooth profiles of claim 1 wherein: the number of teeth of the outer teeth is two less than the number of teeth of the inner teeth.
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| CN106090185B (en) * | 2016-06-16 | 2018-11-30 | 南通慧幸智能科技有限公司 | The flute profile design method of three-dimensional high rigidity harmonic speed reducer |
| US20210364077A1 (en) * | 2018-05-14 | 2021-11-25 | Harmonic Drive Systems Inc. | Strain wave gearing |
| CN109099115B (en) * | 2018-10-25 | 2021-04-20 | 北京工商大学 | Harmonic gear transmission device with flexible gear having automatic positioning function |
| CN109695694B (en) * | 2018-12-10 | 2021-04-30 | 广州市昊志机电股份有限公司 | Involute harmonic gear shaping method and harmonic reducer |
| CN113361031B (en) * | 2021-06-03 | 2023-03-17 | 重庆大学 | Three-dimensional tooth shape design method for flexible gear of harmonic reducer |
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| US2906143A (en) * | 1955-03-21 | 1959-09-29 | United Shoe Machinery Corp | Strain wave gearing |
| US4823638A (en) * | 1986-11-05 | 1989-04-25 | Harmonic Drive Systems Inc. | Tooth profile of spline of strain wave gearing |
| US5429556A (en) * | 1992-06-03 | 1995-07-04 | Sumimoto Heavy Industries, Ltd. | Internally meshing planetary gear structure and flexible meshing type gear meshing structure |
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