CN115199727A - Small tooth difference planetary reduction mechanism and tooth profile design method thereof - Google Patents

Small tooth difference planetary reduction mechanism and tooth profile design method thereof Download PDF

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Publication number
CN115199727A
CN115199727A CN202211125777.1A CN202211125777A CN115199727A CN 115199727 A CN115199727 A CN 115199727A CN 202211125777 A CN202211125777 A CN 202211125777A CN 115199727 A CN115199727 A CN 115199727A
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gear
tooth
teeth
planetary
elastic
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金正已
胡牧原
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Rouhao Precision Technology Suzhou Co ltd
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Rouhao Precision Technology Suzhou Co ltd
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Priority to CN202211125777.1A priority Critical patent/CN115199727A/en
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Priority to CN202310998604.9A priority patent/CN116989101A/en
Priority to PCT/CN2023/118024 priority patent/WO2024055933A1/en
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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
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • 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
    • F16H55/14—Construction providing resilience or vibration-damping
    • 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
    • F16H55/18—Special devices for taking up backlash
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H57/02—Gearboxes; Mounting gearing therein
    • F16H57/028—Gearboxes; Mounting gearing therein characterised by means for reducing vibration or noise
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H57/08—General details of gearing of gearings with members having orbital motion
    • F16H57/082—Planet carriers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H57/12—Arrangements for adjusting or for taking-up backlash not provided for elsewhere
    • 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
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • F16H2001/327—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear with orbital gear sets comprising an internally toothed ring gear
    • 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
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • F16H2001/328—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear comprising balancing means
    • 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
    • F16H2055/176—Ring gears with inner teeth
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H57/12—Arrangements for adjusting or for taking-up backlash not provided for elsewhere
    • F16H2057/126—Self-adjusting during operation, e.g. by a spring

Abstract

The invention discloses a small-tooth-difference planetary reduction mechanism and a tooth profile design method thereof. The tooth profile design method comprises the following steps: constructing a small-tooth-difference planetary reduction mechanism which comprises a planetary gear, an elastic gear ring and a limit gear carrier, wherein the elastic gear ring is provided with first internal teeth capable of being meshed with first external teeth of the planetary gear and second external teeth capable of being meshed with second internal teeth of the limit gear carrier, and the planetary gear is driven by an eccentric shaft and is eccentrically arranged relative to the limit gear carrier, so that the elastic gear ring and the planetary gear deform after being meshed; enabling the small-tooth-difference planetary reduction mechanism to satisfy a relational expression, and enabling the first external teeth to form a motion trail M without sharp points; and obtaining a tooth profile function of the first internal teeth according to the motion trail M. The tooth shape design method can improve the transmission precision and rated transmission torque of the planetary speed reducing mechanism with small tooth difference.

Description

Small tooth difference planetary reduction mechanism and tooth profile design method thereof
Technical Field
The invention relates to a small-tooth-difference planetary reduction mechanism and a tooth profile design method thereof, in particular to a small-tooth-difference planetary reduction mechanism adopting an elastic gear ring and a tooth profile design method of the inner tooth of the elastic gear ring.
Background
The gear transmission has the characteristics of high efficiency, accurate transmission ratio, compact structure and the like, and is used as one of the transmission mechanisms which are most widely applied in mechanical transmission. Most of the existing gear transmission theories are based on rigid engagement, namely when a conjugate curve (such as an involute and a cycloid) corresponding to a meshing pair is calculated, the meshing pair is regarded as a rigid body, and the movement of the meshing pair is regarded as known rigid body displacement without considering the magnitude of transmission torque and deformation generated by a meshing tooth surface.
The rigid meshing theory can enable the meshing pair to roll purely, and theoretically, the optimal gear transmission efficiency can be realized. However, there are objective tolerances in the manufacture of any meshing pair and clearances required to account for lubrication or temperature effects. Gears based on the theory of positive engagement have some backlash that would otherwise render the manufactured mechanism unassemblable or unusable. The rigid drive theory is unable to overcome the backlash problem.
The backlash size directly affects the transmission accuracy of the gear train. When the gear train reverses, the driving wheel reverses first, the driven gear reverses according to the sequence, and an angle error is output, so that equipment is inaccurate. If the output is high power, the backlash can cause the vibration of the whole gear train, generate noise and damage the gear teeth and other parts in serious conditions. Therefore, the gear train designed based on the rigid meshing theory can only reduce the adverse effects by continuously improving the precision of the gear train mechanism in gear machining and assembling precision.
According to the gear train designed based on the rigid meshing theory, the meshing number of teeth is determined by the geometric design of the teeth, and the problem that the loaded teeth are independently damaged to cause tooth system failure is easily caused by a large torque load.
Generally, a gear designed based on a rigid meshing theory mainly has the following problems if the requirements of industrial development on future transmission precision and transmission energy density are met: the side clearance exists, the precision requirement is high, and the processing difficulty is large; the meshing teeth are few, fixed and prone to partial failure under high torque load.
The motion trail of teeth on a planetary gear in a planetary transmission mechanism with small tooth difference in the industry is mainly based on a theoretical frame corresponding to the configuration of the corresponding planetary gear mechanism. Track sharp points exist in theoretical frames of the RV reducer and the harmonic reducer; the motion track is shown in fig. 1a, and a sharp point in the motion track is enlarged as shown in fig. 1 b. The sharp point means that the meshing state of the gears at this point must be "completely accurate" and must reach a theoretical position to achieve a theoretical meshing effect. It is clear that this is not possible in practice, that there are objective errors in the manufacture of any meshing pair and that the clearances required for lubrication or temperature effects need to be taken into account. Otherwise the manufactured mechanism cannot be assembled or used.
The cycloid tooth profile of the RV reducer is based on pitch circle division, the change of the pitch circle means the change of the pitch circle, and the tooth profile does not accord with the principle of generating a pure rolling cycloid by single node meshing, so that the tooth profile is not a conjugate curve. Theoretically, nearly half of the needles in the transmission direction can be meshed simultaneously, and the bearing capacity is certain. However, due to the existence of the meshing gaps, the gaps are not uniformly distributed at all the teeth, so that the meshing of the teeth number is not guaranteed, although multiple teeth can be meshed due to the elastic deformation of the needle teeth, the meshing teeth number is uncertain, and the reliable bearing capacity can only be designed according to the meshing of single teeth. The designed mechanism has large size and small nominal bearing capacity.
In the harmonic reducer, the deformation coefficient of the wave generator can be adjusted
Figure 439221DEST_PATH_IMAGE001
The sharp point can be eliminated, but such adjustment results in increased backlash between the flexspline and reduced accuracy.
Therefore, a series of schemes are researched in the industry and aim at trimming the tooth form, so that the teeth of the harmonic reducer or the RV reducer can still maintain partial precision in the meshing state of reaching the theoretical track point, or the damage to the gear caused by the non-theoretical ideal meshing state is reduced, and the service life of the gear is prolonged. But there is no way in the industry to overcome the adverse effects of sharp points on the trajectory.
Disclosure of Invention
In view of the above problems, it is an object of the present invention to provide a tooth profile design method for a planetary reduction mechanism with small tooth difference, which improves transmission accuracy and rated transmission torque.
Another object of the present invention is to provide a planetary reduction mechanism with small tooth difference, which has high transmission accuracy and rated transmission torque.
According to one aspect of the invention, a tooth form design method of a small tooth difference planetary reduction mechanism comprises the following steps:
(1) Constructing a small tooth difference planetary reduction mechanism including a planetary gear, an elastic ring gear and a limit carrier, the elastic ring gear being elastically deformable and being located between the planetary gear and the limit carrier, the elastic ring gear having first internal teeth engageable with first external teeth of the planetary gear and second external teeth engageable with second internal teeth of the limit carrier, the planetary gear being driven by an eccentric shaft and being eccentrically disposed with respect to the limit carrier so that the elastic ring gear and the planetary gear are deformed after engagement, the deformed elastic ring gear having a long axis and a short axis perpendicular to each other;
(2) Enabling the small tooth difference planetary reduction mechanism to satisfy the following relational expressions (a) to (c), and enabling the first external teeth to form a motion trail M without a sharp point represented by the following parameter equation (d);
Figure 887519DEST_PATH_IMAGE002
（a）
Figure 198415DEST_PATH_IMAGE003
（b）
Figure 875515DEST_PATH_IMAGE004
（c）
Figure 221046DEST_PATH_IMAGE005
（d）
in the above formula:
Figure 840246DEST_PATH_IMAGE006
the distance between the circle center of the elastic gear ring and the circle center of the planetary gear is obtained;
Figure 654749DEST_PATH_IMAGE007
、
Figure 650387DEST_PATH_IMAGE008
the pitch circle radius of the first external teeth and the pitch circle radius of the first internal teeth,
Figure 850424DEST_PATH_IMAGE009
respectively the equivalent pitch circle radius of the meshing of the planet gear and the elastic gear ring after the elastic gear ring is deformed, and
Figure 374947DEST_PATH_IMAGE010
，
Figure 411167DEST_PATH_IMAGE011
；
Figure 944916DEST_PATH_IMAGE012
the transmission ratio of the planet gear and the elastic gear ring;
Figure 733881DEST_PATH_IMAGE013
the length of the minor axis of the ellipse formed after the elastic gear ring is deformed;
Figure 694884DEST_PATH_IMAGE014
is the number of teeth of the first internal teeth,
Figure 481050DEST_PATH_IMAGE015
is the modulus of the first internal teeth;
Figure 287332DEST_PATH_IMAGE016
、
Figure 461961DEST_PATH_IMAGE017
respectively is the intersection point of the first external tooth pitch circle of the planetary gear and the tooth center line
Figure 79018DEST_PATH_IMAGE018
In that
Figure 604677DEST_PATH_IMAGE019
Coordinates in a coordinate system of
Figure 214650DEST_PATH_IMAGE019
The coordinate system takes the center of the limit gear carrier as an origin, and takes the short axis and the long axis of the deformed elastic gear ring which form an approximate ellipse as the origin respectivelyxA shaft,yA shaft;
Figure 243786DEST_PATH_IMAGE020
the angle of rotation of the eccentric shaft;
(3) And obtaining a tooth profile function of the first internal teeth according to the motion trail M.
In a preferred embodiment, in relation (a),
Figure 297324DEST_PATH_IMAGE021
wherein, the first and the second end of the pipe are connected with each other,
Figure 513542DEST_PATH_IMAGE022
is the modulus of the first outer tooth,
Figure 927206DEST_PATH_IMAGE023
is the number of teeth of the first outer teeth.
In a preferred embodiment, in step (2),
Figure 810848DEST_PATH_IMAGE024
wherein, the first and the second end of the pipe are connected with each other,
Figure 35287DEST_PATH_IMAGE023
is the number of teeth of the first external teeth.
In a preferred embodiment, in step (2), the step
Figure 4380DEST_PATH_IMAGE025
A modulus approximately equal to the first internal teeth after the elastic gear ring is deformed
Figure 956156DEST_PATH_IMAGE026
。
In a preferred embodiment, in step (3), an envelope equation of the first internal tooth is obtained according to the motion trajectory M, which is as follows:
Figure 959884DEST_PATH_IMAGE027
wherein, the first and the second end of the pipe are connected with each other,
Figure 352294DEST_PATH_IMAGE028
is the first external tooth at
Figure 808683DEST_PATH_IMAGE019
The function of the tooth shape in the coordinate system,
Figure 298571DEST_PATH_IMAGE029
is composed of
Figure 891226DEST_PATH_IMAGE028
Rotating about an eccentric axis formed by movement along the path MAngle of rotation
Figure 706735DEST_PATH_IMAGE020
Is a family of curves of parameters.
In a preferred embodiment, in step (3), an envelope function numerical solution of the first external teeth is generated by using a trajectory function according to the motion trajectory M, and a tooth profile function of the first internal teeth of the elastic ring gear is obtained by fitting.
In a preferred embodiment, the deformed part of the elastic ring gear adjacent to the long shaft is engaged with the planetary gear, and the long shaft
Figure 135574DEST_PATH_IMAGE030
。
In a preferred embodiment, the meshing of the elastic ring gear and the planet gear forms a radius equivalent to a pitch circle
Figure 960310DEST_PATH_IMAGE009
Modulus of elasticity, modulus of elasticity
Figure 673051DEST_PATH_IMAGE026
The engaged state of (1).
In a preferred embodiment, the deformed part of the elastic ring gear adjacent to one end of the long shaft is meshed with one planetary gear, the deformed part of the elastic ring gear adjacent to the other end of the long shaft is meshed with the other planetary gear, and the two planetary gears are eccentrically arranged and have the same first external teeth.
In a preferred embodiment, the tooth profile design method further comprises the steps of:
(4) Make the engagement of the first external teeth of the planetary gear contain the angle
Figure 393883DEST_PATH_IMAGE031
Satisfies the following formula (e)
Figure 575596DEST_PATH_IMAGE032
（e）。
The tooth form of the first internal tooth of the elastic gear ring and the meshing internal and external teeth of the first external tooth of the planetary gear have side clearances, and the mechanism cannot be jammed in the meshing process. Angle of engagement
Figure 938445DEST_PATH_IMAGE031
The meshing range of the first external teeth of the planetary gear is theoretically over 90 stars. Adjusting eccentricity of planetary geardThe locus M can be controlled, so that the tooth form of the first inner teeth and the meshing side gap of the first outer teeth of the planetary gear are adjusted, the multi-tooth meshing range is controlled, the side gap can be eliminated in the overall transmission effect by designing the multi-tooth meshing state and range, and precise transmission is realized.
According to a second aspect of the present invention, there is provided a small teeth difference planetary reduction mechanism comprising a planetary gear, an elastic ring gear and a limit carrier, the elastic ring gear being elastically deformable and being located between the planetary gear and the limit carrier, the elastic ring gear having first internal teeth capable of meshing with the first external teeth of the planetary gear and second external teeth capable of meshing with the second internal teeth of the limit carrier, the planetary gear being driven by an eccentric shaft and being eccentrically disposed with respect to the limit carrier so that the elastic ring gear and the planetary gear are meshed and deformed, the elastic ring gear after the deformation having a major axis and a minor axis perpendicular to each other, the first internal teeth having a tooth shape formed by the above-described tooth shape designing method.
In a preferred embodiment, the small tooth difference planetary reduction mechanism includes two planetary gears which are eccentrically arranged and have the same first external teeth, and the two planetary gears are connected by the eccentric shaft.
In a preferred embodiment, two of the planet gears are respectively engaged with portions of the deformed elastic ring gear adjacent to both ends of the long shaft.
Compared with the prior art, the invention has the following advantages by adopting the scheme:
according to the planetary reduction mechanism with the small tooth difference, the constructed planetary reduction mechanism with the small tooth difference comprises the elastic gear ring, so that the meshing state is related to the load bearing state, the elastic gear ring is extruded and deformed at the meshing position through the tooth shape design of the first inner teeth of the elastic gear ring and the like, the motion path of any point on the first outer teeth of the planetary gear has no sharp point, the overall backlash of a gear train can be eliminated, and the transmission precision is improved; the elastic gear ring deforms to absorb vibration, so that noise in the transmission process is reduced; the number of meshing teeth is increased, and the rated transmission torque is improved; when the input torque of the planetary gear is increased, the elastic gear ring is deformed by the axial load, the meshing state is changed, the number of meshing teeth is passively increased along with the input torque, the limit transmission torque is improved, and the impact load resistance of the tooth form is improved.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1a shows the movement locus of the teeth on the planetary gear in the conventional planetary transmission mechanism with small teeth difference.
Fig. 1b is a partial enlarged view of fig. 1 a.
Fig. 2 is a partial sectional view of a planetary reduction mechanism with small teeth difference according to an embodiment of the present invention.
Fig. 3 is a partially enlarged view of a portion a in fig. 2.
Fig. 4 is a sectional view of a small tooth difference planetary reduction mechanism according to an embodiment of the present invention, taken along an axial direction.
Fig. 5 is a schematic view of the engagement of the planetary gears and the elastic ring gear according to the embodiment of the present invention.
Fig. 6 is a movement trace of any point on the first external teeth of the planetary gear according to the embodiment of the present invention.
Fig. 7 is a partial enlarged view of fig. 5 at B.
Fig. 8 is a schematic diagram of the tooth profile and the motion trajectory of the first internal teeth.
Reference numerals:
1. a planetary gear; 11. a first external tooth;
2. an elastic gear ring; 21. a first internal tooth; 22. a second outer tooth;
3. a limit gear carrier; 31. a second internal tooth;
4. an eccentric shaft.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the invention may be more readily understood by those skilled in the art. It should be noted that the description of the embodiments is provided to help understanding of the present invention, and is not intended to limit the present invention.
The embodiment provides a planetary speed reducing mechanism with small tooth difference, in particular to an internal gear output mechanism with small tooth difference of 2K-H. Referring to fig. 2 to 4, the small teeth difference planetary reduction mechanism includes a planetary gear 1, an elastic ring gear 2, and a carrier 3, the planetary gear 1 and the carrier 3 are rigid members, and the elastic ring gear 2 is an elastic member capable of elastic deformation. Wherein, the planet gear 1 is connected with an eccentric shaft 4 as a power input element; the limit gear carrier 3 outputs the power transmitted by small tooth difference, for example, the power can be connected through an output flange connected with the limit gear carrier; the elastic ring gear 2 is arranged between the planet gears 1 and the limit carrier 3. The planetary gear 1 has first external teeth 11, the elastic ring gear 2 has first internal teeth 21 and second external teeth 22, the limit carrier 3 has second internal teeth 31, the first external teeth 11 of the planetary gear 1 and the first internal teeth 21 of the elastic ring gear 2 can be engaged with each other, and the second external teeth 22 of the elastic ring gear 2 and the second internal teeth 31 of the limit carrier 3 can be engaged with each other. The planet gear 1 is eccentrically arranged relative to the limit gear carrier 3, the elastic gear ring 2 is meshed with the planet gear 1 and then deforms, and the deformed elastic gear ring 2 has a long shaft and a short shaft which are perpendicular to each other.
Further, as shown in fig. 4 and 5, the number of the planetary gears 1 is two, two planetary gears 1 have the same first external teeth 11, and the two planetary gears 1 are connected by one above-mentioned eccentric shaft 4, which eccentric shaft 4 is embodied as a crankshaft. After the planetary gears 1 and the elastic ring gear 2 are engaged, the two planetary gears 1 respectively apply outward extrusion forces to opposite side portions of the elastic ring gear 2, so that opposite side portions (e.g., upper and lower side portions in fig. 5) of the elastic ring gear are deformed outward, and the elastic ring gear 2 is deformed into a shape similar to an ellipse, and further has the above-mentioned long axis and short axis perpendicular to each other, and the long axis passes through the centers of the two planetary gears 1, and the short axis passes through the center of the limit gear carrier 3. The two planetary gears 1 are respectively engaged with portions of the deformed elastic ring gear 2 adjacent to both ends of the long shaft.
The limiting gear rack 3 and the elastic gear ring 2 are combined to form a loaded gear; the planetary gear 1 is matched with a non-limiting side tooth (namely a first internal tooth 21) of the elastic gear ring 2, a radial load is applied along the direction of the center distance between the loaded gear and the planetary gear 1, the limiting tooth (namely a second external tooth 22) of the elastic gear ring 2 is pressed into the meshing range of the limiting gear carrier 3 by the planetary gear 1 to form a limiting flexible meshing pair, and the elastic gear ring 2 is deformed to wrap the planetary gear 1 to form a loading flexible meshing pair. The material of the elastic gear ring 2 can be selected from high-toughness alloy steel or other materials with better fatigue performance, the tooth modulus is recommended to be between 0.2 and 2, and the width of the elastic gear ring is recommended to be less than 20 percent of the diameter of the planetary gear. The shape of the first external teeth 11 is specifically designed, as explained below.
The embodiment also provides a tooth profile design method of the small tooth difference planetary reduction mechanism, which comprises the following steps:
s100, constructing the small-tooth-difference planetary reduction mechanism;
s101, allowing the small teeth difference planetary reduction mechanism to satisfy the following relational expressions (a) to (c) so that the first external teeth 11 form a motion locus M without cusp, as shown in fig. 6 and 7;
Figure 505692DEST_PATH_IMAGE002
（a）
Figure 397425DEST_PATH_IMAGE003
（b）
Figure 66435DEST_PATH_IMAGE004
（c）
wherein the parametric equation of the trajectory M is shown in the following formula (d):
Figure 967395DEST_PATH_IMAGE005
（d）
in the above formula:
Figure 123569DEST_PATH_IMAGE016
、
Figure 451783DEST_PATH_IMAGE017
respectively, any point on the first external teeth 11 of the planetary gear 1
Figure 363017DEST_PATH_IMAGE018
In that
Figure 67668DEST_PATH_IMAGE019
Coordinates in a coordinate system of
Figure 609508DEST_PATH_IMAGE019
The coordinate system takes the circle center of the limit gear carrier 3 as the origin and takes the short axis and the long axis of the deformed elastic gear ring 2 as the short axis and the long axis respectivelyxA shaft,yA shaft;
Figure 843043DEST_PATH_IMAGE007
、
Figure 470333DEST_PATH_IMAGE008
the pitch circle radius of the first external teeth 11 and the pitch circle radius of the first internal teeth 21,
Figure 463828DEST_PATH_IMAGE033
、
Figure 125754DEST_PATH_IMAGE034
respectively the equivalent pitch circle radius of the meshing teeth of the planet gear 1 and the elastic gear ring 2 after the elastic gear ring 2 is deformed, and
Figure 61349DEST_PATH_IMAGE010
，
Figure 926668DEST_PATH_IMAGE011
；
Figure 441963DEST_PATH_IMAGE020
the angle of rotation of the eccentric shaft 4;
Figure 958395DEST_PATH_IMAGE012
the transmission ratio of the planet gear 1 and the elastic gear ring 2 is shown;
Figure 799312DEST_PATH_IMAGE013
the length of the minor axis of the ellipse formed after the deformation of the elastic ring gear 2;
Figure 151927DEST_PATH_IMAGE014
the number of teeth of the first internal teeth 21,
Figure 736492DEST_PATH_IMAGE015
the modulus of the first internal teeth 21;
and S102, obtaining a tooth profile function of the first internal teeth 21 according to the motion trail M.
In step S101, in the relation (b),
Figure 841851DEST_PATH_IMAGE021
wherein the content of the first and second substances,
Figure 853670DEST_PATH_IMAGE022
is the modulus of the first outer tooth 11,
Figure 677269DEST_PATH_IMAGE023
the number of teeth of the first external teeth 11.
The transmission ratio is calculated by the following formula,
Figure 813328DEST_PATH_IMAGE024
wherein the content of the first and second substances,
Figure 773194DEST_PATH_IMAGE023
the number of teeth of the first external teeth 11.
The meshing part of the elastic gear ring 2 and the planet gear 1 forms a radius equivalent to a pitch circle
Figure 955913DEST_PATH_IMAGE009
Modulus of
Figure 532388DEST_PATH_IMAGE026
The engaged state of (1). The deformed part of the elastic ring gear 2 adjacent to the long shaft is engaged with the planetary gear 1, and the long shaft
Figure 193177DEST_PATH_IMAGE035
。
Figure 289440DEST_PATH_IMAGE025
Approximately equal to the modulus of the first internal teeth 21 after deformation of the elastic ring gear 2
Figure 908640DEST_PATH_IMAGE026
。
In step S102, an envelope equation of the first internal teeth 21 may be obtained from the motion trajectory M, as shown in fig. 8. The method comprises the following specific steps:
Figure 706832DEST_PATH_IMAGE027
wherein the content of the first and second substances,
Figure 171311DEST_PATH_IMAGE028
is the first external tooth 11
Figure 856501DEST_PATH_IMAGE019
The function of the tooth shape in the coordinate system,
Figure 646603DEST_PATH_IMAGE036
is composed of
Figure 932091DEST_PATH_IMAGE028
Formed by movement along the locus M and rotated by an angle of the eccentric shaft 4
Figure 200261DEST_PATH_IMAGE020
Is a family of curves of parameters.
In step S102, an envelope function numerical solution of the first external teeth 11 may also be generated by using a trajectory function according to the motion trajectory M, and a tooth profile function of the first internal teeth 21 of the elastic ring gear 2 is obtained by fitting.
The tooth profile design method also comprises the following steps:
s103, making the meshing containing angle of the first external teeth 11 of the planet gear 1
Figure 739958DEST_PATH_IMAGE037
Satisfies the following formula (e)
Figure 700961DEST_PATH_IMAGE032
（e）。
The tooth form of the first internal tooth 21 of the elastic gear ring 2 is meshed with the internal and external teeth of the first external tooth 11 of the planet gear 1, so that backlash exists, and the mechanism cannot be locked in the meshing process. Angle of engagementθThe meshing range of the first external teeth 11 of the planetary gear 1 is theoretically over 90. Adjusting the eccentricity of the planetary gear 1dThe locus M can be controlled, so that the meshing side gap between the tooth form of the first inner tooth 21 and the first outer tooth 11 of the planetary gear 1 is adjusted, the multi-tooth meshing range is controlled, the side gap can be eliminated in the overall transmission effect by designing the multi-tooth meshing state and range, and the precise transmission is realized.
The principle of the present embodiment is described in detail below.
As shown in figure 5 of the drawings,
Figure 208165DEST_PATH_IMAGE038
is the pitch circle radius of the first internal teeth 21,
Figure 280026DEST_PATH_IMAGE009
are respectively provided withIs the equivalent pitch circle radius of the meshing of the planetary gear 1 and the elastic ring gear 2 after the elastic ring gear 2 is deformed,dc1 is the distance between the circle center of the planet gear 1 and the circle center of the elastic gear ring 2, and C2 is a theoretical gear ring which meets the modulus of the planet gear 1, and an equivalent gear ring after the elastic gear ring 2 is denatured. Wherein the content of the first and second substances,
Figure 202459DEST_PATH_IMAGE039
the transmission ratio of the planetary reduction mechanism with small tooth difference
Figure 68783DEST_PATH_IMAGE012
Is composed of
Figure 63284DEST_PATH_IMAGE040
Figure 673257DEST_PATH_IMAGE041
Wherein, if the normal meshing of the conventional gear mechanism is realized, the requirements are met
Figure 702393DEST_PATH_IMAGE042
，
Figure 490352DEST_PATH_IMAGE043
Theoretically, one point on the planetary gear 1 of the conventional gear mechanism
Figure 237728DEST_PATH_IMAGE018
The trajectory has sharp points as shown in fig. 1a and 1 b.
In order to eliminate the sharp point of the track, the following design scheme can be adopted, the number of teeth of each gear is kept, the transmission ratio of the mechanism is unchanged, the center distance of the gears is adjusted, so that the elastic gear ring is deformed,
Figure 651392DEST_PATH_IMAGE044
modulus of the first internal teeth 21 of the elastic ring gear 2
Figure 269455DEST_PATH_IMAGE025
Slightly larger than
Figure 493894DEST_PATH_IMAGE045
Modulus of the elastic gear ring 2 after deformation
Figure 462987DEST_PATH_IMAGE046
The number of teeth of the first internal teeth 21 is
Figure 414762DEST_PATH_IMAGE047
(ii) a Modulus of the planetary gear 1
Figure 418490DEST_PATH_IMAGE048
I.e. by
Figure 548252DEST_PATH_IMAGE049
，
Figure 4641DEST_PATH_IMAGE050
The number of first external teeth 11 is
Figure 760107DEST_PATH_IMAGE023
，
Figure 352762DEST_PATH_IMAGE018
The motion track is
Figure 168272DEST_PATH_IMAGE051
When:
Figure 859760DEST_PATH_IMAGE052
one point on the planetary gear 1 can be realized
Figure 153338DEST_PATH_IMAGE018
The trajectories are shown in fig. 7 and 8, eliminating sharp points in the original path. In the present embodiment, the elastic ring gear 2 is used to realize this special meshing state, the planet gear 1 is used as a loading wheel to apply pressure to the elastic ring gear 2 along the radial direction, so that the elastic ring gear 2 is deformed, and the internal teeth of the elastic ring gear 2 within the deformation tolerance range are meshed with the external teeth of the loading wheel, as shown in fig. 5.
The deformation of the elastic gear ring 2 is approximate to ellipse and the major axis
Figure 866079DEST_PATH_IMAGE053
The major axis meshing part has a radius equivalent to the pitch circle
Figure 852489DEST_PATH_IMAGE009
A modulus of
Figure 768624DEST_PATH_IMAGE026
The engaged state of (c). The elliptic internal gear has a modulus of
Figure 865893DEST_PATH_IMAGE025
The number of internal teeth is
Figure 433140DEST_PATH_IMAGE047
The elastic gear ring 2 is formed and has smaller actual deformation amount and perimeter
Figure 590452DEST_PATH_IMAGE054
Considered as invariant. The minor axis of the ellipse has a length of
Figure 259462DEST_PATH_IMAGE013
The following relationship should be satisfied:
Figure 894843DEST_PATH_IMAGE055
satisfying the above relationship, a single-tooth motion locus M satisfying no cusp can be formed, as shown in the following equation:
Figure 582176DEST_PATH_IMAGE056
then, the tooth profile function of the first external teeth 11 of the planetary gear 1 is given
Figure 910389DEST_PATH_IMAGE057
The tooth-shaped function image forms a function curve family along the track M of
Figure 801116DEST_PATH_IMAGE058
The envelope, i.e. the tooth form of the first internal teeth 21 of the elastic toothed ring 2, should satisfy:
Figure 505767DEST_PATH_IMAGE059
the tooth function of the first internal teeth 21 of the elastic ring gear 2 can be determined. Or generating a numerical solution of the motion envelope function of the planetary gear 1 by using a track function, and fitting an internal tooth profile function of the elastic gear ring 2. Solving the tooth shape according to the motion trajectory of the tooth is not the invention point of the present invention, and a conventional solving method can be adopted, which is not described herein.
The flexible gear device is based on a flexible meshing pair theory, the meshing state and the loaded state of the flexible gear device are related through the structures of the limiting gear carrier, the elastic gear ring and the like, the elastic gear ring can deform through the geometric design of the meshing surfaces of the limiting gear carrier and the elastic gear ring and the combination of the geometric design of the meshing surfaces of the limiting gear carrier and the elastic gear ring, the radial pressure between gear trains enables the elastic gear ring to deform, the overall backlash of the gear train can be eliminated, and the transmission precision is improved; the elastic gear ring deforms to absorb vibration, so that noise in the transmission process is reduced; the number of meshing teeth is increased, and the rated transmission torque is improved; when the input torque of the gear train is increased, the elastic gear ring is deformed by the axial load, the meshing state is changed, the number of meshing teeth is passively increased along with the input torque, the limit transmission torque is improved, and the impact load resistance of the tooth shape is improved.
The small tooth difference planetary reduction mechanism of the embodiment includes a larger number of meshing teeth than a rigid theoretical meshing state. Therefore, the driving torque can be distributed to more teeth to transmit machining and assembly errors of parts to be shared by more teeth uniformly, and the abrasion of each tooth surface is more uniform, so that the structure can realize larger torque transmission, higher driving precision and longer structural service life.
The profile of the loading teeth of the elastic gear ring is determined by the envelope of the relative motion of the teeth matched with the loading gear and the elastic gear ring on the loading gear; the profile of the limit teeth of the limit gear carrier is determined by an envelope formed by the movement and deformation of the elastic ring gear relative to the limit gear carrier. Through proper control envelope curve and the clearance of corresponding cooperation tooth, can guarantee that the poor planetary reduction mechanism of few tooth of this embodiment moves and can not block to death, and elastic ring gear radial deformation in advance is stable controllable, and spacing tooth and loading tooth are stable when getting into engaged state or breaking away from the engaged state and do not have the collision.
The embodiment is a state that rigid engagement and flexible engagement are combined, and the elastic gear ring can be controlled not to generate uncontrolled (such as buckling instability and other states) deformation through the limitation of the geometric boundary of the limiting gear carrier; the torsional rigidity of the whole mechanism can be adjusted by controlling the thickness of the elastic gear ring; the radial loading amount of the loading gear is controlled, and the prestress loading state of the mechanism can be controlled, so that the structure can be balanced between the precision and the stress state of the elastic gear ring.
The embodiment does not depend on the radius relation between the loading gears or the elastic gear rings, and transmission mechanisms with different sizes and different accuracies can be obtained by designing different motion tracks of the loading gears.
In summary, the embodiment can realize 0 side clearance, and greatly improve the transmission precision; the number of the meshing teeth can be increased greatly, and larger torque can be transmitted; the vibration generated by rigid meshing can be reduced, and the running noise of the gear is reduced; the large number of teeth are meshed, so that machining errors can be shared uniformly, and the requirement of a confidential transmission mechanism on the machining precision grade is lowered.
As used in this specification and the appended claims, the terms "comprises" and "comprising" are intended to cover only the explicitly recited steps or elements as not constituting an exclusive list and that the method or apparatus may include other steps or elements. As used herein, the term "and/or" includes any combination of one or more of the associated listed items.
It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to the other feature or indirectly fixed or connected to the other feature. In addition, the descriptions of the upper, lower, left, right, etc. used in the present invention are only relative to the mutual positional relationship of the components of the present invention in the drawings, and reference may be made to fig. 5.
It is further understood that the use of "a plurality" in this disclosure means two or more, as other terms are analogous. "and/or" describes the association relationship of the associated object, indicating that there may be three relationships, for example, a and/or B, which may indicate: a exists alone, A and B exist simultaneously, and B exists alone.
It will be further understood that the terms "first," "second," and the like are used to describe various information and that such information should not be limited by these terms. These terms are only used to distinguish one type of information from another and do not denote a particular order or importance. Indeed, the terms "first," "second," etc. are used interchangeably throughout. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present disclosure.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and are preferred embodiments, which are intended to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the scope of the present invention. All equivalent changes and modifications made according to the principles of the present invention should be covered within the scope of the present invention.

Claims (13)

1. A tooth form design method of a small tooth difference planetary reduction mechanism is characterized by comprising the following steps:
(1) Constructing a small tooth difference planetary reduction mechanism including a planetary gear, an elastic ring gear, and a limit carrier, the elastic ring gear being elastically deformable and being located between the planetary gear and the limit carrier, the elastic ring gear having first internal teeth engageable with first external teeth of the planetary gear and second external teeth engageable with second internal teeth of the limit carrier, the planetary gear being driven by an eccentric shaft and being eccentrically disposed with respect to the limit carrier such that the elastic ring gear and the planetary gear are deformed after being engaged, the deformed elastic ring gear having a long axis and a short axis perpendicular to each other;
(2) Enabling the small tooth difference planetary reduction mechanism to satisfy the following relational expressions (a) to (c), and enabling the first external teeth to form a motion trail M without a sharp point represented by the following parameter equation (d);
Figure DEST_PATH_IMAGE001
（a）
Figure 691799DEST_PATH_IMAGE002
（b）
Figure DEST_PATH_IMAGE003
（c）
Figure 281044DEST_PATH_IMAGE004
（d）
in the above formula:
Figure DEST_PATH_IMAGE005
the distance between the circle center of the elastic gear ring and the circle center of the planetary gear is set;
Figure 654256DEST_PATH_IMAGE006
、
Figure DEST_PATH_IMAGE007
the pitch circle radius of the first external teeth and the pitch circle radius of the first internal teeth,
Figure 269039DEST_PATH_IMAGE008
、
Figure DEST_PATH_IMAGE009
respectively the equivalent pitch circle radius of the elastic gear ring and the meshing teeth of the planetary gear after the elastic gear ring is deformed, and
Figure 473625DEST_PATH_IMAGE010
，
Figure DEST_PATH_IMAGE011
；
Figure 968191DEST_PATH_IMAGE012
the transmission ratio of the planet gear and the elastic gear ring;
Figure DEST_PATH_IMAGE013
the length of a minor axis of an approximate ellipse formed after the elastic gear ring is deformed;
Figure 327235DEST_PATH_IMAGE014
is the number of teeth of the first internal teeth,
Figure DEST_PATH_IMAGE015
is the modulus of the first internal teeth;
Figure 713086DEST_PATH_IMAGE016
、
Figure DEST_PATH_IMAGE017
respectively is the intersection point of the first external tooth pitch circle of the planetary gear and the tooth center line
Figure 116385DEST_PATH_IMAGE018
In that
Figure DEST_PATH_IMAGE019
Coordinates in a coordinate system, the
Figure 939110DEST_PATH_IMAGE019
The coordinate system takes the center of the limit gear carrier as an origin, and takes the short axis and the long axis of the deformed elastic gear ring which form an approximate ellipse as the origin respectivelyxA shaft,yA shaft;
Figure 145969DEST_PATH_IMAGE020
the angle of rotation of the eccentric shaft;
(3) And obtaining a tooth profile function of the first internal teeth according to the motion trail M.
2. The method for designing a tooth profile of a small teeth difference planetary reduction gear according to claim 1, wherein in the relation (a),
Figure DEST_PATH_IMAGE021
wherein the content of the first and second substances,
Figure 555085DEST_PATH_IMAGE022
is the modulus of the first outer tooth,
Figure DEST_PATH_IMAGE023
is the number of teeth of the first external teeth.
3. The tooth form design method of a small tooth difference planetary reduction mechanism according to claim 1, wherein in the step (2),
Figure 318552DEST_PATH_IMAGE024
wherein the content of the first and second substances,
Figure 686079DEST_PATH_IMAGE023
is the number of teeth of the first external teeth.
4. The method for designing a tooth profile of a small tooth difference planetary reduction mechanism according to claim 1, wherein in the step (2), the tooth profile is designed
Figure DEST_PATH_IMAGE025
Is approximately equal to the modulus of the first internal teeth after the elastic gear ring is deformed
Figure 786759DEST_PATH_IMAGE026
。
5. The method for designing the tooth profile of the small tooth difference planetary reduction mechanism according to claim 1, wherein in the step (3), an envelope equation of the first internal tooth is obtained according to the motion locus M, and specifically, the envelope equation is as follows:
Figure DEST_PATH_IMAGE027
wherein the content of the first and second substances,
Figure 484719DEST_PATH_IMAGE028
is the first external tooth at
Figure 331453DEST_PATH_IMAGE019
The function of the tooth shape in the coordinate system,
Figure DEST_PATH_IMAGE029
is composed of
Figure 587990DEST_PATH_IMAGE028
Formed by movement along the locus M and rotated by an eccentric axis
Figure 520174DEST_PATH_IMAGE020
Is a family of curves of parameters.
6. The tooth form design method of the small tooth difference planetary reduction mechanism according to claim 1, characterized in that in step (3), an envelope function numerical solution of the first external teeth is generated by using a trajectory function according to the motion trajectory M, and a tooth form function of the first internal teeth of the elastic ring gear is obtained by fitting.
7. The method as claimed in claim 1, wherein the deformed portion of the elastic ring gear adjacent to the long axis engages with the planetary gear, and the long axis is engaged with the planetary gear
Figure 130147DEST_PATH_IMAGE030
。
8. The method as claimed in claim 7, wherein the meshing point between the elastic ring gear and the planetary gear is formed to be equivalent to a pitch circle radius
Figure 313610DEST_PATH_IMAGE008
Modulus of
Figure 226203DEST_PATH_IMAGE026
The engaged state of (c).
9. The method of designing a tooth profile of a small tooth difference planetary reduction mechanism according to claim 7, wherein a portion of the deformed elastic ring gear adjacent to one end of the long axis is engaged with one planetary gear, a portion of the deformed elastic ring gear adjacent to the other end of the long axis is engaged with the other planetary gear, and both planetary gears are eccentrically disposed and have the same first external teeth.
10. The tooth profile design method of a small tooth difference planetary reduction mechanism according to claim 1, characterized by further comprising the steps of:
(4) Make the engagement of the first external teeth of the planetary gear contain the angle
Figure DEST_PATH_IMAGE031
Satisfies the following formula (e)
Figure 160530DEST_PATH_IMAGE032
（e）。
11. A small teeth difference planetary reduction mechanism comprising a planetary gear, an elastic ring gear and a limit carrier, the elastic ring gear being elastically deformable and being located between the planetary gear and the limit carrier, the elastic ring gear having first internal teeth engageable with the first external teeth of the planetary gear and second external teeth engageable with the second internal teeth of the limit carrier, the planetary gear being driven by an eccentric shaft and being eccentrically disposed with respect to the limit carrier so that the elastic ring gear is deformed after engagement with the planetary gear, the elastic ring gear after the deformation having a long axis and a short axis perpendicular to each other, the first internal teeth having a tooth form formed by the tooth form design method of any one of claims 1 to 10.
12. The mechanism of claim 11, comprising two of the planetary gears eccentrically disposed and having the same first external teeth, the two planetary gears being connected by the eccentric shaft.
13. The small teeth difference planetary reduction mechanism according to claim 12, wherein two of said planetary gears are respectively engaged with portions of said elastic ring gear after being deformed, which portions are adjacent to both ends of the long shaft.
CN202211125777.1A 2022-09-16 2022-09-16 Small tooth difference planetary reduction mechanism and tooth profile design method thereof Pending CN115199727A (en)

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WO2024055933A1 (en) * 2022-09-16 2024-03-21 柔昊精密科技(苏州)有限公司 Small-tooth-difference planetary speed-reduction mechanism and tooth shape design method therefor

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CN202674185U (en) * 2012-07-20 2013-01-16 浙江顺天减速机制造有限公司 Small-tooth-difference engagement type gear speed reducer
CN103032525A (en) * 2013-01-18 2013-04-10 王榕生 Zero-tooth-difference internal gear pair transmission mechanism with planetary gear elastic deformation ring
CN209370407U (en) * 2018-10-03 2019-09-10 爱磁科技（深圳）有限公司 Double flexbile gear harmonic wave speed reducing machines
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CN115199727A (en) * 2022-09-16 2022-10-18 柔昊精密科技(苏州)有限公司 Small tooth difference planetary reduction mechanism and tooth profile design method thereof

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US20220136588A1 (en) * 2020-11-02 2022-05-05 Toyota Jidosha Kabushiki Kaisha Gear mechanism and gear
WO2024055933A1 (en) * 2022-09-16 2024-03-21 柔昊精密科技(苏州)有限公司 Small-tooth-difference planetary speed-reduction mechanism and tooth shape design method therefor

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