CN116989101A - Planetary reduction mechanism with small tooth difference and tooth shape design method thereof - Google Patents
Planetary reduction mechanism with small tooth difference and tooth shape design method thereof Download PDFInfo
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- CN116989101A CN116989101A CN202310998604.9A CN202310998604A CN116989101A CN 116989101 A CN116989101 A CN 116989101A CN 202310998604 A CN202310998604 A CN 202310998604A CN 116989101 A CN116989101 A CN 116989101A
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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
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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
- F16H55/14—Construction providing resilience or vibration-damping
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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
- F16H55/18—Special devices for taking up backlash
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H57/00—General details of gearing
- F16H57/02—Gearboxes; Mounting gearing therein
- F16H57/028—Gearboxes; Mounting gearing therein characterised by means for reducing vibration or noise
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H57/00—General details of gearing
- F16H57/08—General details of gearing of gearings with members having orbital motion
- F16H57/082—Planet carriers
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H57/00—General details of gearing
- F16H57/12—Arrangements for adjusting or for taking-up backlash not provided for elsewhere
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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
- 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
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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
- 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
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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
- F16H2055/176—Ring gears with inner teeth
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H57/00—General details of gearing
- F16H57/12—Arrangements for adjusting or for taking-up backlash not provided for elsewhere
- F16H2057/126—Self-adjusting during operation, e.g. by a spring
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Abstract
The invention discloses a planetary reduction mechanism with small tooth difference and a tooth shape design method thereof, wherein the tooth shape design method comprises the following steps: the method comprises the steps of constructing a small-tooth-difference planetary reduction mechanism, wherein the small-tooth-difference planetary reduction mechanism comprises a planetary gear, an elastic gear ring and a limiting gear carrier, 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 limiting gear carrier, and the planetary gear is driven by an eccentric shaft and is eccentrically arranged relative to the limiting gear carrier, so that the elastic gear ring and the planetary gear are deformed after being meshed; the planetary reduction mechanism with small tooth difference meets a relational expression, so that the first external teeth form a movement track M without sharp points; and obtaining a tooth profile function of the first internal teeth according to the motion trail M. The meshing state of each tooth of the elastic gear ring is related to the loaded state, and the elastic gear ring is extruded and deformed at the meshing position through the tooth profile design of the first internal tooth, so that the movement path of any point on the first external tooth of the planetary gear has no sharp point, the overall side gap of the gear train can be eliminated, and the transmission precision is improved.
Description
Technical Field
The invention relates to a small-tooth-difference planetary reduction mechanism and a tooth shape design method thereof, in particular to a small-tooth-difference planetary reduction mechanism adopting an elastic gear ring and a tooth shape design method of inner teeth 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 one of the most widely applied transmission mechanisms in mechanical transmission. Most of the existing gear transmission theory is based on rigid engagement, namely when conjugate curves (such as involute and cycloid) corresponding to the engagement pairs are calculated, the engagement pairs are regarded as rigid bodies, the transmission torque and deformation generated by engagement tooth surfaces are not considered, and the movement of the engagement pairs is regarded as known rigid body displacement.
The rigid meshing theory can enable the meshing pair to roll purely, and the optimal gear transmission efficiency can be realized theoretically. However, any meshing pair is manufactured with objective errors and requires consideration of the clearances required for lubrication or temperature effects. Gears based on rigid meshing theory have certain backlash that would otherwise render the manufactured mechanism either unassembled or unusable. Thus the rigid transmission theory cannot overcome the backlash problem.
The size of the backlash directly affects the transmission accuracy of the gear train. When the gear train is reversed, the driving wheel is reversed first, the driven gear is reversed sequentially, and an angle error is output, so that the equipment is inaccurate. If the power is output at a high level, the backlash can cause the whole gear train to vibrate, noise is generated, and the teeth and other parts of the gear are damaged seriously. Therefore, the gear train designed based on the rigid meshing theory can only improve the precision of the gear train mechanism by continuously improving the machining and assembling precision of the gears, so that the adverse effects are reduced.
The gear train designed based on the rigid meshing theory has the meshing number of the teeth determined by the geometric design of the teeth, and is subjected to a large torque load, so that the problem that the loaded teeth are singly damaged to cause the failure of the gear train easily occurs.
In general, gears designed based on rigid meshing theory mainly have the following problems if the requirements of industrial development on future transmission precision and transmission energy density are to be met: the machining device has the advantages of side clearance, high precision requirement and high machining difficulty; the number of the meshing teeth is small, the fixed and high-torque load is easy to locally fail.
The motion track of the teeth on the planetary gears in the 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 points exist in theoretical frames of the RV reducer and the harmonic reducer; the motion trail is shown in fig. 1a, and one sharp point in the motion trail is enlarged as shown in fig. 1 b. The sharp point means that the gear mesh state at this point must be "perfectly accurate" and the theoretical position must be reached to achieve the theoretical meshing effect. Obviously, this is not possible in practical manufacturing trials, there are objective errors in the manufacture of any meshing pair, and the clearances required for lubrication or temperature effects need to be taken into account. Otherwise the manufactured mechanism cannot be assembled or used.
The cycloidal tooth profile of the RV speed reducer cannot avoid the needed meshing gap, the pitch circle diameter of the meshing pair is changed, but the deflection of the cycloidal pin gear meshing pair and the involute gear is completely different in nature, and from the analysis, the cycloidal tooth profile is based on pitch circle graduation, the change of pitch circle means the change of pitch circle, the tooth profile does not conform to the principle of generating a single-node meshing pure rolling cycloid, and therefore the tooth profile is not a conjugate curve. In theory, nearly half of the teeth needles can be meshed simultaneously in the transmission direction, and the bearing capacity is certain. However, because of the presence of the meshing gaps, the gaps are not uniformly distributed at each tooth, so that the meshing of so many teeth cannot be ensured, and although the meshing of multiple teeth may be caused due to elastic deformation of the needle teeth, the meshing number is not determined, and the reliable carrying capacity can be designed only according to single-tooth meshing. The designed mechanism has large size and small nominal bearing capacity.
Although the sharp point can be eliminated by adjusting the deformation coefficient of the wave generator in the harmonic reducer, the adjustment can cause the increase of the backlash between the rigid wheels of the flexible wheel and the reduction of the precision.
Therefore, a series of schemes are studied in the industry to trim the tooth form so that the teeth of the harmonic speed reducer or the RV speed reducer can still maintain partial precision in the meshing state reaching the theoretical track point, or damage to the gear caused by the non-theoretical ideal meshing state is reduced, and the service life of the gear is prolonged. There is always no way in the industry to overcome the adverse effects of the sharp points of the track.
Disclosure of Invention
The invention aims to provide a small-tooth-difference planetary reduction mechanism and a tooth shape design method thereof, which are used for solving the problems in the prior art, the constructed small-tooth-difference planetary reduction mechanism comprises an elastic gear ring with first inner teeth and second outer teeth, the meshing state of each tooth is related to the loaded state, and the elastic gear ring is extruded and deformed at the meshing position through the tooth shape design of the first inner teeth, so that the movement path of any point on the first outer teeth of a planetary gear is free of sharp points, the overall side gap of a gear train can be eliminated, and the transmission precision is improved.
In order to achieve the above object, the present invention provides the following solutions:
the invention provides a tooth shape design method of a planetary reduction mechanism with small tooth difference, which comprises the following steps:
(1) Constructing a small-tooth-difference planetary reduction mechanism, wherein the small-tooth-difference planetary reduction mechanism comprises an eccentric shaft with different eccentric sections, a planetary gear with first external teeth, an elastic gear ring with first internal teeth and second external teeth and a limiting gear carrier with second internal teeth, the elastic gear ring is sleeved between the outer diameter side of the planetary gear and the inner diameter side of the limiting gear carrier after being deformed, the first external teeth are meshed with the first internal teeth, the second external teeth are meshed with the second internal teeth, and the deformed elastic gear ring is provided with a long shaft and a short shaft which are perpendicular to each other;
(2) Enabling the small-tooth-difference planetary reduction mechanism to meet the following relational expressions (a) to (c), and enabling the first external teeth to form a movement track M without sharp points;
d＝r' f -r' h >r f -r h (a)
2πb+4(r' f -b)＝πZ f m' f (c)
by deformation yielding of the elastic gear ring, the meshing relationship between the planetary gear and the elastic gear ring is as follows:
the motion track of P meets the form of an internal rotation line equation, and the parameter equation of the track M is as follows:
in the above relation:
x 0 、y 0 the intersection point P (x) of the first external tooth pitch circle and the tooth center line of the planetary gear 0 ,y 0 ) The coordinates in an O-xy coordinate system take the center of the limiting gear frame as an origin, and the deformed elastic gear ring forms a short axis and a long axis which are approximate to ellipses as an x axis and a y axis respectively;
d is the distance between the circle center of the elastic gear ring and the circle center of the planetary gear;
r f 、r h the pitch radius of the first external teeth and the pitch radius of the first internal teeth are respectively r' f 、r' h The elastic gear rings are respectively after the elastic gear rings are deformedAn equivalent pitch radius of the planetary gear teeth, and r' f >r f ，r' h ＝r h ；
An angle through which the eccentric shaft rotates;
i p a gear ratio for the planetary gear and the elastic ring gear;
b is the length of the short axis of the approximate ellipse formed after the elastic gear ring is deformed;
Z f for the number of teeth of the first internal tooth, m' f Modulus for the first internal teeth;
Z h the number of teeth is the number of teeth of the first external teeth;
(3) And obtaining the tooth profile function of the first internal teeth according to the motion trail M.
Preferably, in the relation (a),
r' h ＝r h ＝Z h m' h /2
r' f >r f ＝Z f m' f /2
wherein m' h For the modulus of the first external tooth, Z h Is the number of teeth of the first external teeth.
Preferably, in step (2), the m' f About equal to the modulus m' of the first internal tooth after deformation of the elastic ring gear " f 。
Preferably, in step (3), an envelope equation of the first internal teeth is obtained according to the motion trajectory M, specifically as follows:
wherein F (x, y) is a tooth form function of the first external tooth in an O-xy coordinate system,is formed by F (x, y) moving along the track M and rotated by an eccentric shaftAngle->Is a family of curves for parameters.
Preferably, in the step (3), an envelope function numerical solution of the first external teeth is generated by using a track function according to the motion track M, and a tooth profile function of the first internal teeth of the elastic gear ring is obtained by fitting.
Preferably, the deformed portion of the elastic ring gear adjacent to the long axis is engaged with the planetary gear, and the long axis a=r '' f 。
Preferably, the engagement of the elastic gear ring and the planetary gear forms a position equivalent to the pitch circle radius r' f Modulus m' f Is engaged with the engagement state of the belt pulley.
Preferably, the deformed portion of the elastic ring gear adjacent to one end of the long shaft is engaged with one planetary gear, the deformed portion of the elastic ring gear adjacent to the other end of the long shaft is engaged with the other planetary gear, and the two planetary gears are eccentrically arranged and have the same first external teeth.
Preferably, the tooth profile design method further comprises the steps of:
(4) The meshing inclusion angle 2 theta of the first external teeth of the planetary gear is made to satisfy the following formula (d)
The invention also provides a small-tooth-difference planetary reduction mechanism, which comprises an eccentric shaft with different eccentric sections, a planetary gear with first external teeth, an elastic gear ring with first internal teeth and second external teeth and a limiting gear carrier with second internal teeth, wherein the elastic gear ring is sleeved between the outer diameter side of the planetary gear and the inner diameter side of the limiting gear carrier after being deformed, the first external teeth are meshed with the first internal teeth, the second external teeth are meshed with the second internal teeth, the elastic gear ring after being deformed is provided with a long shaft and a short shaft which are perpendicular to each other, and the first internal teeth are provided with tooth shapes formed by the tooth shape design method.
Preferably, the planetary gear comprises two planetary gears which are eccentrically arranged and have the same first external teeth, and the two planetary gears are connected through the eccentric shaft; the two planetary gears are respectively meshed with the deformed parts of the elastic gear ring adjacent to the two ends of the long shaft.
Compared with the prior art, the invention has the following technical effects:
1. the small-tooth-difference planetary reduction mechanism comprises the elastic gear ring with the first internal teeth and the second external teeth, the meshing state of each tooth is related to the loaded state, and the elastic gear ring is extruded and deformed at the meshing position through the tooth shape design of the first internal teeth, so that the movement path of any point on the first external 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;
2. according to the invention, the elastic gear ring is arranged, so that the deformation of the elastic gear ring can be utilized to absorb vibration, and the noise in the transmission process is reduced;
3. the deformed elastic gear ring has a long shaft and a short shaft which are perpendicular to each other, and the number of meshing teeth can be increased by utilizing the deformation of the elastic gear ring, so that rated transmission torque is improved;
4. when the input torque of the planetary gear is increased, the elastic gear ring is deformed by 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 tooth-shaped anti-impact load capacity is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1a shows the motion trace of the teeth on the planetary gear in the conventional small tooth difference planetary transmission mechanism.
Fig. 1b is an enlarged view of a portion of fig. 1 a.
Fig. 2 is a partial cross-sectional view of a small tooth difference planetary reduction mechanism according to an embodiment of the present invention.
Fig. 3 is a partial enlarged view at a in fig. 2.
Fig. 4 is a cross-sectional view of a small tooth difference planetary reduction mechanism according to an embodiment of the present invention in an axial direction.
Fig. 5 is a schematic view showing engagement of the planetary gear and the elastic ring gear according to the embodiment of the invention.
Fig. 6 is a motion trace of any point on the first external teeth of the planetary gear according to an embodiment of the present invention.
Fig. 7 is a partial enlarged view at B in fig. 6.
Fig. 8 is a schematic view of tooth shape and movement trace of the first internal tooth.
Wherein, 1, a planetary gear; 11. a first external tooth; 2. an elastic gear ring; 21. a first internal tooth; 22. a second external tooth; 3. a limit gear frame; 31. a second internal tooth; 4. and (3) an eccentric shaft.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a small-tooth-difference planetary reduction mechanism and a tooth shape design method thereof, which are used for solving the problems in the prior art, the constructed small-tooth-difference planetary reduction mechanism comprises an elastic gear ring with first inner teeth and second outer teeth, the meshing state of each tooth is related to the loaded state, and the elastic gear ring is extruded and deformed at the meshing position through the tooth shape design of the first inner teeth, so that the movement path of any point on the first outer teeth of a planetary gear is free of sharp points, the overall side gap of a gear train can be eliminated, and the transmission precision is improved.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 2 to 5, the present invention provides a small-tooth-difference planetary reduction mechanism, which may be specifically a small-tooth-difference 2K-H internal gear output mechanism, including an eccentric shaft 4 having different eccentric sections, a planetary gear 1 having first external teeth 11, an elastic ring gear 2 having first internal teeth 21 and second external teeth 22, which are elastically deformable, and a spacing carrier 3 having second internal teeth 31, wherein the planetary gear 1 and the spacing carrier 3 are rigid members, and the planetary gear 1 and the spacing carrier 3 remain unchanged in the case of deformation of the elastic ring gear 2. Different planetary gears 1 are sleeved on different eccentric sections of the eccentric shaft 4, so that the planetary gears 1 are eccentric relative to the limiting gear frame 3. The elastic gear ring 2 is sleeved between the outer diameter side of the planetary gear 1 and the inner diameter side of the limiting gear carrier 3 after being deformed, the first external teeth 11 of the planetary gear 1 can be meshed with the first internal teeth 21 of the elastic gear ring 2, the second external teeth 22 of the elastic gear ring 2 can be meshed with the second internal teeth 31 of the limiting gear carrier 3, and the deformed elastic gear ring 2 forms an elliptic-like structure which is provided with a long shaft and a short shaft which are perpendicular to each other. By adopting the planetary reduction mechanism with small tooth difference, pins can be arranged on the planetary gear 1 in a penetrating way, a movable gap is reserved between the pins and the planetary gear 1, the end parts of the pins are connected with an output flange, when the planetary reduction mechanism is in operation, the eccentric shaft 4 can be used as a power input element to be connected with parts such as an input motor or a motor, and the like, and the power is output by virtue of the output flange after being transmitted with small tooth difference through the fixed limit gear frame 3, or the power is output by virtue of the limit gear frame 3 after being transmitted with small tooth difference through the fixed output flange.
As shown in fig. 4 and 5, the number of the planetary gears 1 is two, the two planetary gears 1 have the same first external teeth 11, the two planetary gears 1 are connected through the same eccentric shaft 4, and the eccentric shafts 4 can be specifically crankshafts by respectively installing different eccentric sections on the eccentric shafts 4.
After the planetary gears 1 and the elastic ring gear 2 are meshed, the two planetary gears 1 apply outward extrusion forces to opposite side portions of the elastic ring gear 2, so that opposite sides (upper and lower side portions in fig. 5) of the elastic ring gear 2 are deformed outwards, and the elastic ring gear 2 is deformed into an elliptical-like shape, so that the elastic ring gear has the long axis and the short axis which are perpendicular to each other. The long axis passes through the circle centers of the two planetary gears 1 and the circle center of the limiting gear frame 3 at the same time, and the short axis is perpendicular to the long axis and only passes through the circle center of the limiting gear frame 3. The two planetary gears 1 are respectively meshed with portions of the deformed elastic ring gear 2 adjacent to both ends of the long axis.
As shown in fig. 4, which is merely a schematic structure of the present invention and does not conform to the actual size and the ratio, the outward pressing force applied by the two planetary gears 1 to the elastic ring gear 2 after the planetary gears 1 are engaged with the elastic ring gear 2 is not completely symmetrical, so that the left and right sides of the elastic ring gear 2 in fig. 4 may be unevenly stressed, the elastic ring gear 2 may be difficult to deform into an elliptical-like shape, and the stability of the operation of the planetary reduction mechanism with small tooth difference may be problematic due to the uneven stressing.
In the process of manufacturing products, the person skilled in the art has the ability to comprehensively consider the practical application problem and carry out adaptability adjustment, and when the elastic gear ring 2 is used in specific applications, the elastic gear ring can be manufactured by adopting high-toughness alloy steel, and in the current trial-manufactured successful products: the eccentric amount of the planetary gear 1 is about 1mm, the diameter is about 105mm, and the width is 10mm; the outer diameter of the elastic gear ring 2 is about 106mm, the width is 20mm, the thickness is 3mm, the deformation amount required by the elastic gear ring 2 is only about 0.2mm, and the effect of eliminating the return clearance of gear engagement is achieved. Through simulation calculation, the stress state of the elastic gear ring 2 in the state is about 300MPa (Von-Mises stress) when the mechanism is subjected to 500Nm torque load, the stress state of the elastic gear ring 2 is about 600MPa (Von-Mises stress), and the mechanical properties of the adopted high-toughness alloy steel can meet the stress state.
Although the elastic gear ring 2 can be slightly deformed into an elliptical structure on the whole, the elastic gear ring 2 still has larger rigidity in practice, and the small-tooth-difference planetary reduction mechanism can still stably output torque under a high torque load state. The force required for the elastic ring gear 2 to be pushed up by the planetary gear 1 is about 1.6kN in the sample with the above geometric dimensions, and the assembly process requires a special hydraulic clamp, so that the elastic ring gear 2 is difficult to deform only by manpower.
If the rigidity of the elastic gear ring 2 is insufficient, uneven stress may be caused, and it is difficult to ensure the running stability of the planetary reduction mechanism with small tooth difference. But this is a problem that can be expected by the person skilled in the art and therefore corresponding considerations will be made in the design. In the existing products which are successfully manufactured in trial, the rigidity of the elastic gear ring 2 needs to be ensured to be large enough, other dimensions can not be deformed obviously except radial deformation, the tooth profile configuration can still be kept in deformation, the influence on the meshing state is limited to the large stress of the meshing tooth surface of the elastic gear ring 2 and the limiting gear frame 3 on the meshing side (such as the upper left and the lower right in fig. 4), and the small stress of the meshing tooth surface of the elastic gear ring 2 and the limiting gear frame 3 on the free side (such as the lower left and the upper right in fig. 4). Since the first internal teeth 21 and the second external teeth 22 of the elastic ring gear 2 function like reinforcing ribs, the thickness of the elastic ring gear 2 can be ensured, and the elastic ring gear 2 can be basically ensured to be stably deformed.
In addition, the uneven stress of the elastic gear ring 2 can cause a torque, so that the elastic gear ring 2 deflects (deflects clockwise in fig. 4), in reasonable design, the eccentric amount and the tooth form can be controlled, the meshing state of the first internal tooth 21 and the second external tooth 22 of the elastic gear ring 2 when no load exists is controlled, enough friction force exists between the elastic gear ring 2 and the planetary gear 1 as well as between the elastic gear ring 2 and the limiting gear carrier 3 to overcome the deflection torque, and meanwhile, limiting mechanisms can be designed on two sides of the elastic gear ring 2 to prevent the elastic gear ring 2 from deflecting and falling out, so that the stable operation of the mechanism can be ensured.
The limiting gear frame 3 and the elastic gear ring 2 are combined to form a loaded gear; the planetary gear 1 is matched with the non-limiting side teeth (namely the first internal teeth 21) of the elastic gear ring 2, radial load is applied along the center distance direction between the loaded gear and the planetary gear 1, the planetary gear 1 presses the limiting teeth (namely the second external teeth 22) of the elastic gear ring 2 into the meshing range of the limiting gear carrier 3 to form a limiting flexible meshing pair, and the elastic gear ring 2 deforms 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 2 is recommended to be less than 20 percent of the diameter of the planetary gear 1. The design of the second external teeth 22 and the second internal teeth 31 may take the form of splines or involute teeth, etc., and the shape of the first internal teeth 21 and the first external teeth 11 is specifically designed for the present invention, as will be explained in detail below.
As shown in fig. 2 to 8, the present invention provides a tooth shape design method of a planetary reduction mechanism with small tooth difference, comprising the following steps:
s100, constructing the planetary reduction mechanism with small tooth difference;
s101, the planetary gears of the traditional planetary gear mechanism are meshed on the outer gear ring to form composite motion of rotating around the axis of the planetary gear mechanism and revolving around the axis of the planet carrier, the pitch circle radius of the outer gear ring is R and fixed, the pitch circle radius of the inner side rolling planetary gear is R, a rotating line obtained by tracking one point on the planetary gear ring is tracked, and the parameter equation of the inner rotating line is satisfied:
wherein the coordinate system is located in the center of the planetary gear mechanism,the angle formed by the connecting line of the center of the planet wheel and the center of the coordinate system and the coordinate axis in the horizontal forward direction is designed according to the conventional rigid meshing theory, and the following conditions must be met:
at this point, the motion trace of a point on the planet pitch will exhibit a typical epitrochoidal line with a sharp point.
The invention enables the planetary reduction mechanism with small tooth difference to satisfy the following relational expressions (a) to (c), and enables the first external teeth 11 to form a movement track M without sharp points (shown in fig. 6 and 7);
d＝r' f -r' h >r f -r h (a)
2πb+4(r' f -b)＝πZ f m' f (c)
by deformation yielding of the elastic gear ring 2, the meshing relationship between the planetary gear 1 and the elastic gear ring 2 can be satisfied:
the motion trail of a point P on the pitch circle of the planetary gear 1 still meets the form of an internal rotation line equation, and the parameter equation of the trail M is as follows:
in the above relation:
x 0 、y 0 the intersection point P (x) of the first external tooth pitch circle and the tooth center line of the planetary gear 1 0 ,y 0 ) The coordinates in the O-xy coordinate system, the O-xy coordinate system takes the center of the limiting gear frame 3 as an origin, and the deformed elastic gear ring 2 forms a short axis and a long axis which are approximate to ellipse as an x axis and a y axis respectively;
r f 、r h the pitch radius of the first external teeth 11, the pitch radius of the first internal teeth 21, r ', respectively' f 、r' h The equivalent pitch radii of the meshing teeth of the planetary gear 1 and the elastic gear ring 2 after the elastic gear ring 2 is deformed are respectively r' f >r f ，r' h ＝r h ；
d is the distance between the circle center of the elastic gear ring 2 and the circle center of the planetary gear 1;
for the angle through which the eccentric shaft 4 rotates, +.>Angle of rotation with the planetary gear 1>There is a proportional relationship of->
i p Is the transmission ratio of the planetary gear 1 and the elastic gear ring 2;
b is the length of the minor axis of the approximate ellipse formed after the elastic ring gear 2 is deformed;
Z f for the number of teeth of the first internal tooth 21, m' f A modulus of the first internal teeth 21;
Z h is the number of teeth of the first external teeth 11.
The track points of the track M in this scheme will disappear due to the change in the corresponding interline parameter relationship.
It should be noted that: for the parameter equation (corresponding to curve family) of the track M, if phi is defined differently, the starting position of the planetary gear 1 is different, and the coordinate system is defined differently, the formula form may be different, but the track M is a rotationally symmetrical graph, and the shape is only equal to r' h 、r' f 、i p In the following tooth form design method, the shape of the track M is only examined, and the track graph and the parameter equation thereof can be adjusted to a form convenient for calculation through simple rotation transformation for the tracks M with different phases. Therefore, no matter what form of the initial position the locus M is in, it does not affect the final result as an intermediate process, and the tooth profile function of the first internal teeth 21 to be obtained can be obtained finally. For a specific method of obtaining, see the description below.
For further illustration, examples are as follows:
in fact, the trajectory M belongs to an internal rotation line, which can be understood as a pitch circle radius r' h The planet gears 1 of (2) are dynamically deformed in the elastic gear ring 2 to form an equivalent meshing radius r' f Rolling (no sliding) on the pitch circle of (c). Row of linesThe circle center of the star gear 1 is at radius r' f -r' h At angular velocity omega on the circle of (2) 0 Revolution, and at the same time, the self-rotation is driven by the gear meshing and the eccentric shaft 4 to generate angular velocity ofSo that the locus of a point on the pitch radius can be described by an internal rotation axis. Considering the initial state position of the planetary reduction mechanism with small tooth difference, the motion root track of the point P can be expressed as:
in which x is 0 、y 0 The intersection point P (x) of the first external tooth pitch circle and the tooth center line of the planetary gear 1 0 ,y 0 ) In the O-xy coordinate system, the O-xy coordinate system and the limit gear frame 3 are relatively static, the center of the O-xy coordinate system is taken as an origin O, the elastic gear ring 2 is deformed to form a short axis and a long axis which are approximate to ellipse respectively in an initial state as an x axis and a y axis,is the angle through which the eccentric shaft 4 rotates.
When (when)When the eccentric shaft 4 corresponds to the highest point of the eccentric shaft 4 along the eccentric direction to be positioned on the y-axis, the planetary gear 1 should have a tooth with an outer pitch circle and a tooth center line intersection point P (x) 0 ,y 0 ) Located on the y-axis, corresponding to the coordinates (0, r' f ) Will->Substituting the formula of the locus of the P points,
x 0 ＝r’ h ·0+(r′ f -r′ h )·0＝0
y 0 ＝r’ h ·1+(r′ f -r′ h )·1＝r f
matching the coordinate position.
S102, obtaining a tooth profile function of the first internal teeth 21 according to the movement track M.
In step S101, in the relational expression (b),
r’ h ＝r h ＝Z h m’ h /2
r’ f >r f ＝Z f m’ f /2
wherein m' h Modulus Z of the first external teeth 11 h Is the number of teeth of the first external teeth 11.
The transmission ratio is calculated by the following formula,
wherein Z is h Is the number of teeth of the first external teeth 11.
The meshing position of the elastic gear ring 2 and the planetary gear 1 is equivalent to the pitch circle radius r' f Modulus m' f Is engaged with the engagement state of the belt pulley. The deformed portion of the elastic ring gear 2 adjacent to the long axis is engaged with the planetary gear 1, and the long axis a=r '' f 。，m' f Approximately equal to the modulus m "of the first internal teeth 21 after deformation of the elastic ring gear 2" f 。
In step S102, an envelope equation of the first internal teeth 21 may be obtained according to the movement locus M, as shown in fig. 8, which shows the tooth shape and movement locus of the first internal teeth 21, that is, shows the envelope of the first internal teeth 21. The method comprises the following steps:
wherein F (x, y) is a tooth profile function of the first external tooth 11 in an O-xy coordinate system,an angle of rotation +.f of the eccentric shaft 4 formed by the movement of F (x, y) along the trajectory M>Is a family of curves for parameters.
Namely, a first external tooth profile equation F (x, y) is known, a theoretical motion track M corresponding to a point P on a pitch circle of the planetary gear 1 is designed according to design indexes such as load, rotation precision and the like, and the pitch circle radius of the planetary gear 1 and the elastic gear ring 2 is determined; and meanwhile, the geometric shape of the track M is extracted, the phase is adjusted to a position convenient to calculate, and a first internal tooth 21 tooth form equation can be obtained by calculating a motion envelope formed by the tooth profile of the first external tooth 11 along the track M. The second external teeth 22 and the second internal teeth 31 are limiting structures of the elastic gear ring 2, and the second external teeth 22 in a partial area after the elastic gear ring 2 is deformed are meshed with the corresponding second internal teeth 31, so that the geometric dimension of the whole elastic gear ring 2 in the deformation yielding process is controlled within a theoretical constraint range.
In step S102, an envelope function value solution of the first external teeth 11 may be generated by a track function according to the motion track M, and a tooth profile function of the first internal teeth 21 of the elastic ring gear 2 may be obtained by fitting.
The tooth shape design method further comprises the following steps:
s103, the meshing inclusion angle 2 theta of the first external teeth 11 of the planetary gear 1 is set to satisfy the following formula (d)
The included angle refers to the included angle formed by the two outermost teeth and the center of the mechanism in the range of engaging the internal teeth after the elastic gear ring 2 is deformed, and can represent the proportion of the number of teeth engaged in force transmission to the number of the total internal teeth. As shown in fig. 5, the inclusion angle satisfies the corresponding geometric relationship, the size of the inclusion angle between the single-sided planetary gear 1 and the elastic ring gear 2 is 2θ, and in theory, the teeth of the elastic ring gear 2 within the range of the inclusion angle 2θ are equal to the teeth of the planetary gear 1, so that the teeth can be meshed, and the above formula (d) is satisfied according to the cosine theorem.
Elastic gear ring 2 modulus tooth pitch p f ＝m f Pi, pitch p of planet wheel 1 h ＝m h The tooth number of the elastic gear ring 2 and the tooth number of the planetary gear 1 within the range of the inclusion angle 2 theta are Z 0 If the engagement requirement is satisfiedThen
Z 0 p f -Z 0 p h ≤p f
I.e.
For example, when r f ＝60mm，r h Take Z =58 mm, d =2 mm f ＝162，Z h When=160, Z 0 ≤47.06
In theory, the maximum meshing tooth number of a single planetary gear 1 can reach 47 teeth, the total meshing tooth number of the elastic gear ring 2 and two symmetrical eccentric planetary gears 1 can reach 94 teeth, the total tooth number of the elastic gear ring and the two symmetrical eccentric planetary gears 1 accounts for 58% of the total tooth number, and 40-45% of the internal teeth of the elastic gear ring 2 can be easily met in a general design and are in a meshing state, so that the mechanism can output rated torque far exceeding that of a traditional mechanism with less tooth difference.
The principles of the present invention are described in detail below with reference to specific embodiments.
As shown in fig. 5, r h Is the pitch radius, r 'of the first internal tooth 21' f The pitch circle radii of the planetary gear 1 and the elastic gear ring 2 are respectively equivalent pitch circle radii of the planetary gear 1 and the elastic gear ring 2 after the elastic gear ring 2 is deformed, d is the distance between the circle center of the planetary gear 1 and the circle center of the elastic gear ring 2, C1 represents a theoretical gear ring meeting the modulus of the planetary gear 1, and C2 represents an equivalent gear ring after the elastic gear ring 2 is deformed. Wherein,,
r h ＝Z h m h /2
r f ＝z f m f /2
the transmission ratio i of the planetary reduction mechanism with small tooth difference p Is that
Wherein, if the conventional gear mechanism is normally meshed, m is satisfied f ＝m h ，
In theory, a point P (x 0 ,y 0 ) The track has sharp points as shown in fig. 1a and 1 b.
In order to eliminate the track sharp point, the following design scheme can be adopted, the gear number of each gear is kept, the transmission ratio of the planetary reduction mechanism with small tooth difference is unchanged, the center distance of the gears is adjusted, the elastic gear ring 2 is deformed,
d＝r’ f -r’ h >r f -r h
modulus m 'of the first internal teeth 21 of the elastic ring gear 2' f Slightly greater than m f Modulus m' after deformation of elastic gear ring 2 " f ≈m f The number of teeth of the first internal teeth 21 is Z f The method comprises the steps of carrying out a first treatment on the surface of the The modulus of the planetary gear 1 is m' h ＝m h I.e. r' h ＝r h ，
r’ h ＝r h ＝Z h m h /2
r’ f >r f ＝Z f m f /2
The number of teeth of the first external teeth 11 is Z h ，P(x 0 ,y 0 ) The motion trail is
When:
a point P (x) on the planetary gear 1 can be realized 0 ,y 0 ) The traces are shown in fig. 7 and 8, eliminating sharp points in the original path.
In the invention, the special meshing state is realized by the elastic gear ring 2, the planetary gear 1 is used as a loading wheel to apply pressure to the elastic gear ring 2 along the radial direction, so that the elastic gear ring 2 is deformed, and the inner teeth of the elastic gear ring 2 in the deformation containing range are meshed with the outer teeth of the loading wheel, as shown in fig. 5.
The elastic toothing 2 deforms approximately elliptical with the major axis a=r '' f The meshing position of the long shafts is equivalent to the radius r 'of the pitch circle' f Modulus of m' f Is engaged with the engagement state of the belt pulley. The elliptical internal gear is formed by a modulus of m' f The number of teeth of the internal tooth is Z f The elastic ring gear 2 of (2) is formed and the actual deformation is small, and the circumferential length L is regarded as invariable. The length of the minor axis of the ellipse is b, and the following relation should be satisfied:
L＝2πb+4(r′ f -b)＝πZ f m f
the single-tooth motion track M which can meet the no-sharp point can be formed by meeting the above relation
Thereafter, given the tooth profile function F (x, y) =0 of the first external tooth 11 of the planetary gear 1, the tooth profile function image forms a family of function curves along the locus M asThe external envelope, i.e. the profile of the first internal teeth 21 of the elastic ring gear 2, should satisfy:
the tooth profile function of the first internal teeth 21 of the elastic ring gear 2 can be determined. The trajectory function can also be used to generate a numerical solution of the motion envelope function of the planetary gear 1, fitting the tooth profile function of the internal teeth of the elastic ring gear 2. Solving the tooth shape according to the motion track of the tooth is not an invention point of the present invention, and a conventional solving method can be adopted, and a description thereof is omitted here.
Based on the flexible meshing pair theory, the flexible gear device with the meshing state related to the loaded state is realized through the structures of the limiting gear frame 3, the elastic gear ring 2 and the like, the elastic gear ring 2 can be deformed through the geometric design of the meshing surfaces of the limiting gear frame 3 and the elastic gear ring 2 and the radial pressure between gear trains, the total side gap of the gear trains can be eliminated, and the transmission precision is improved. The elastic gear ring 2 deforms to absorb vibration, so that noise in the transmission process can be reduced. By increasing the number of meshing teeth, the rated transmission torque can be increased. When the input torque of the gear train is increased, the elastic gear ring 2 is deformed by 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 tooth-shaped anti-impact load capacity is improved.
Compared with the meshing state of the rigidity theory, the planetary reduction mechanism with less tooth difference comprises more meshing teeth. Therefore, the driving torque can be distributed to more teeth to transfer machining and assembling errors of parts, the machining and assembling errors can be uniformly shared by more teeth, and meanwhile, the abrasion of each tooth surface is more uniform, so that the structure can realize larger torque transfer, higher driving precision and longer service life.
The profile of the loading teeth of the elastic ring gear 2 is determined by the envelope of the relative movement of the teeth of the loading gear cooperating therewith and the elastic ring gear 2. The outline of the limiting teeth of the limiting gear frame 3 is determined by an envelope formed by the combination of the movement and the deformation of the elastic gear ring 2 relative to the limiting gear frame 3. By properly controlling the clearance between the envelope line and the corresponding matched teeth, the small-tooth-difference planetary reduction mechanism can be ensured not to be blocked during operation, the elastic gear ring 2 is pre-radially deformed stably and controllably, and the limit teeth and the loading teeth are stable and collision-free when entering into or exiting from the meshing state.
The invention is in a state of combining rigid engagement and flexible engagement, and the elastic gear ring 2 can be controlled not to deform uncontrollably (such as buckling instability and the like) by limiting the geometric boundary of the limiting gear frame 3. By controlling the thickness of the elastic ring gear 2, the torsional rigidity of the small-tooth-difference planetary reduction mechanism can be adjusted. The radial loading amount of the loading gear is controlled, and the prestress loading state of the planetary reduction mechanism with small tooth difference can be controlled, so that balance can be achieved between the precision and the stress state of the elastic gear ring 2.
The invention does not depend on the radius relation between the loading gears or the elastic gear rings 2, and can obtain transmission mechanisms with different sizes and different accuracies by designing different motion tracks of the loading gears.
Summarizing, the invention can realize 0 side gap and greatly improve transmission precision; the number of the meshing teeth can be increased greatly, and larger moment is transmitted; vibration generated by rigid engagement can be reduced, and gear operation noise is reduced; by a large number of tooth meshing, the machining errors can be evenly shared, and the machining precision grade requirement of the confidential transmission mechanism is reduced.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (11)
1. The tooth shape design method of the planetary reduction mechanism with small tooth difference is characterized by comprising the following steps of:
(1) Constructing a small-tooth-difference planetary reduction mechanism, wherein the small-tooth-difference planetary reduction mechanism comprises an eccentric shaft with different eccentric sections, a planetary gear with first external teeth, an elastic gear ring with first internal teeth and second external teeth and a limiting gear carrier with second internal teeth, the elastic gear ring is sleeved between the outer diameter side of the planetary gear and the inner diameter side of the limiting gear carrier after being deformed, the first external teeth are meshed with the first internal teeth, the second external teeth are meshed with the second internal teeth, and the deformed elastic gear ring is provided with a long shaft and a short shaft which are perpendicular to each other;
(2) Enabling the small-tooth-difference planetary reduction mechanism to meet the following relational expressions (a) to (c), and enabling the first external teeth to form a movement track M without sharp points;
d＝r' f -r' h >r f -r h (a)
2πb+4(r' f -b)＝πZ r m' f (c)
by deformation yielding of the elastic gear ring, the meshing relationship between the planetary gear and the elastic gear ring is as follows:
the motion track of P meets the form of an internal rotation line equation, and the parameter equation of the track M is as follows:
in the above relation:
x 0 、y 0 the intersection point P (x) of the first external tooth pitch circle and the tooth center line of the planetary gear 0 ,y 0 ) The coordinates in an O-xy coordinate system take the center of the limiting gear frame as an origin, and the deformed elastic gear ring forms a short axis and a long axis which are approximate to ellipses as an x axis and a y axis respectively;
d is the distance between the circle center of the elastic gear ring and the circle center of the planetary gear;
r f 、r h the pitch radius of the first external teeth and the pitch radius of the first internal teeth are respectively r' f 、r' h Respectively equivalent pitch radii of the elastic gear ring and the planetary gear meshing teeth after the elastic gear ring is deformed, and r' f >r f ，r' h ＝r h ；
An angle through which the eccentric shaft rotates;
i p a gear ratio for the planetary gear and the elastic ring gear;
b is the length of the short axis of the approximate ellipse formed after the elastic gear ring is deformed;
Z f for the number of teeth of the first internal tooth, m' f Modulus for the first internal teeth;
Z h the number of teeth is the number of teeth of the first external teeth;
(3) And obtaining the tooth profile function of the first internal teeth according to the motion trail M.
2. The tooth profile design method for a small tooth difference planetary reduction mechanism according to claim 1, wherein, in the relational expression (a),
r′ h ＝r h ＝Z h m′ h /2
r′ f >r f ＝Z f m′ f /2
wherein m' h For the modulus of the first external tooth, Z h Is the number of teeth of the first external teeth.
3. The tooth profile design method for small tooth difference planetary reduction mechanism according to claim 1, wherein in step (2), the m' f About equal to the modulus m' of the first internal teeth after deformation of the elastic ring gear f 。
4. The tooth profile design method of a 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 trajectory M, specifically as follows:
wherein F (x, y) is a tooth form function of the first external tooth in an O-xy coordinate system,an eccentric shaft rotation angle +.>Is a family of curves for parameters.
5. The tooth profile design method of a small tooth difference planetary reduction mechanism according to claim 1, wherein in the step (3), an envelope function numerical solution of the first external teeth is generated by 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.
6. The tooth profile design method for a small tooth difference planetary reduction mechanism according to claim 1, wherein a deformed portion of the elastic ring gear adjacent to a long axis is engaged with the planetary gear, and the long axis a = r' f 。
7. The tooth profile design method for a small tooth difference planetary reduction mechanism according to claim 6, wherein the engagement of the elastic ring gear and the planetary gear forms a tooth profile equivalent to a pitch radius r' f Modulus m f Is engaged with the engagement state of the belt pulley.
8. The tooth profile design method for a small tooth difference planetary reduction mechanism according to claim 6, wherein a portion of the deformed elastic ring gear adjacent to one end of the long shaft is meshed with one planetary gear, a portion of the deformed 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.
9. The tooth profile design method for a small tooth difference planetary reduction mechanism according to claim 1, characterized in that the tooth profile design method further comprises the steps of:
(4) The meshing inclusion angle 2 theta of the first external teeth of the planetary gear is made to satisfy the following formula (d)
10. A small-tooth-difference planetary reduction mechanism, characterized by comprising an eccentric shaft having different eccentric sections, a planetary gear having first external teeth, an elastic ring gear having first internal teeth and second external teeth capable of elastic deformation, and a spacing gear frame having second internal teeth, different planetary gears being fitted between different eccentric sections, the elastic ring gear being deformed to be fitted between an outer diameter side of the planetary gear and an inner diameter side of the spacing gear frame, the first external teeth meshing with the first internal teeth, the second external teeth meshing with the second internal teeth, the deformed elastic ring gear having long and short axes perpendicular to each other, the first internal teeth having tooth shapes formed by the tooth shape design method according to any one of claims 1 to 9.
11. The small tooth difference planetary reduction mechanism according to claim 10, comprising two of the planetary gears which are eccentrically disposed and have the same first external teeth, the two planetary gears being connected by the eccentric shaft; the two planetary gears are respectively meshed with the deformed parts of the elastic gear ring adjacent to the two ends of the long shaft.
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| 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 |
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