CN111156306A - Undercut oscillating tooth transmission meshing pair and generation method thereof - Google Patents

Undercut oscillating tooth transmission meshing pair and generation method thereof Download PDF

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Publication number
CN111156306A
CN111156306A CN202010008305.2A CN202010008305A CN111156306A CN 111156306 A CN111156306 A CN 111156306A CN 202010008305 A CN202010008305 A CN 202010008305A CN 111156306 A CN111156306 A CN 111156306A
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tooth
undercut
meshing
curve
movable
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闫济东
邢鹏达
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Henan Zhulong High Tech Co Ltd
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Henan Zhulong High Tech Co Ltd
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Priority to CN202010008305.2A priority Critical patent/CN111156306A/en
Publication of CN111156306A publication Critical patent/CN111156306A/en
Priority to CN202180013709.3A priority patent/CN115066570A/en
Priority to PCT/CN2021/070226 priority patent/WO2021139636A1/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
    • 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
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/088—Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
    • 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
    • F16H55/12—Toothed members; Worms with body or rim assembled out of detachable parts
    • 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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  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)

Abstract

The invention provides an undercut oscillating tooth transmission meshing pair and a generation method thereof. On the basis of the movable tooth transmission configuration, large-size movable teeth are selected to meet the undercut condition, and a movable tooth meshing pair with the undercut characteristic is obtained by sweeping a movable tooth surface for a circle along a meshing curve, and is called as an undercut movable tooth meshing pair under the transmission type; the movable tooth transmission unit with the characteristics of an undercut movable tooth meshing pair is called an undercut movable tooth transmission unit; compared with the traditional movable tooth transmission unit with the same size and without undercut, the transmission ratio and the bearing capacity of the invention are both obviously increased, and the excellent comprehensive performance is more obvious.

Description

Undercut oscillating tooth transmission meshing pair and generation method thereof
Technical Field
The invention relates to the technical field of movable tooth transmission, in particular to an undercut movable tooth transmission meshing pair and a generation method thereof.
Background
In the traditional involute gear transmission, under some special conditions, designed gears can have undercut, although the transmission precision of the gears is not influenced, the root of a single tooth is thinned due to the undercut thickness, the bending resistance of the gears is reduced, the contact ratio is reduced, and the transmission stability is influenced, so that in the traditional design idea, the involute gears are designed to avoid undercut as much as possible. In the other conventional transmission form, the cycloidal pin gear transmission technology, the actual tooth profile of the cycloidal gear is strictly not allowed to be undercut, because the undercut distorts the transmission. With the development of the oscillating tooth transmission technology, various oscillating tooth transmission configurations are diversified, and the various oscillating tooth transmission configurations are provided with representatives such as push rod oscillating tooth transmission, roller (steel ball) oscillating tooth transmission, swing oscillating tooth transmission, sleeve oscillating tooth transmission, planar steel ball transmission and the like, and the roller (steel ball) oscillating tooth transmission is taken as an example, and two common configurations of cycloid steel ball oscillating tooth transmission and sine steel ball oscillating tooth transmission are provided; in any form of movable tooth transmission technology, the core and the essence of the movable tooth transmission technology are the movement of the movable tooth along the meshing curve thereof, and the space track curved surface obtained by the movement of the movable tooth along the meshing curve is the actual movable tooth meshing surface, and in the traditional movable tooth design, the actual movable tooth meshing surface is also not allowed to be undercut. For example, patent No. CN201721031991.5 proposes "a cycloidal steel ball speed reducer and its robot joint", and the specification clearly proposes conditions for avoiding undercut and avoiding undercut. The problems that the traditional movable-tooth speed reducer is low in power density, popular, large in size, relatively small in transmission ratio, insufficient in space utilization and poor in market competitiveness are solved. Aiming at the problems, a new method is developed, the traditional design thinking is broken through, and the method is carried out against the way, namely in the design of the movable tooth transmission, the undercut phenomenon is not avoided, and the undercut phenomenon is also utilized, so that the designed movable tooth meshing tooth profile is undercut, and the undercut movable tooth transmission technology is obtained. Compared with the traditional movable tooth transmission, the undercut movable tooth transmission has the advantages that under the same size, the number of movable teeth is more, the transmission ratio is larger, the whole-tooth whole-circumference meshing stress is basically achieved, and the comprehensive performance of the undercut movable tooth transmission is superior to that of the traditional movable tooth transmission structure.
Disclosure of Invention
Aiming at the problems, the invention provides an undercut oscillating tooth transmission meshing pair and a generation method thereof, on the basis of any oscillating tooth transmission configuration, large-size oscillating teeth are selected to meet the undercut condition, and an oscillating tooth meshing pair with undercut characteristics is obtained by sweeping a circle of an oscillating tooth surface along a meshing curve, and is called as the undercut oscillating tooth meshing pair under the transmission type; the movable tooth transmission unit with the characteristics of an undercut movable tooth meshing pair is called an undercut movable tooth transmission unit; compared with the traditional movable tooth transmission unit with the same size and without undercut, the transmission ratio and the bearing capacity of the invention are both obviously increased, and the excellent comprehensive performance is more obvious.
The technical scheme adopted by the invention is as follows: an undercut oscillating tooth transmission meshing pair comprises an oscillating tooth meshing tooth surface, an oscillating tooth meshing curve and an undercut oscillating tooth meshing tooth surface, wherein the oscillating tooth meshing tooth surface and the undercut oscillating tooth meshing tooth surface are meshed with each other, and the undercut oscillating tooth transmission meshing pair is formed.
Furthermore, the meshing curve of the movable teeth is cycloid or non-cycloid.
Furthermore, when the meshing curve of the movable teeth is cycloid, the curve is hypocycloid or epicycloid; when the meshing curve of the movable teeth is non-cycloid, the curve is a sine curve which is a plane sine curve or a space sine curve.
Furthermore, when the movable tooth meshing curve is a non-sinusoidal curve, the movable tooth meshing curve is a segmented meshing curve.
The method for generating the transmission meshing pair of the undercut oscillating teeth comprises the following steps: the movable tooth meshing tooth surface is a curved surface obtained by rotating a circle around a straight line which does not pass through a continuous curve in a plane; the meshing curve of the movable teeth is a space curve; the undercut oscillating tooth meshing tooth surface is an envelope surface of a curved track which is swept from head to tail on an oscillating tooth meshing curve by the geometric center of the oscillating tooth meshing tooth surface, and at least one side of the undercut oscillating tooth meshing tooth surface is undercut.
Furthermore, when the movable tooth meshing curve adopts a cycloid, the undercut movable tooth meshing tooth surface is an envelope surface of a curved surface track of which the geometric center of the movable tooth meshing tooth surface is swept from the head to the tail on the cycloid, and at least one side of the undercut movable tooth meshing tooth surface is undercut.
Furthermore, when the movable tooth meshing curve adopts a sine curve, the undercut movable tooth meshing tooth surface is an envelope surface of a curved track which is swept from head to tail on the sine curve by the geometric center of the movable tooth meshing tooth surface, and at least one side of the undercut movable tooth meshing tooth surface is undercut.
Furthermore, when the movable tooth meshing curve adopts a segmented meshing curve, the undercut movable tooth meshing tooth surface is an envelope surface of a curved track which is swept from head to tail on the segmented meshing curve by the geometric center of the movable tooth meshing tooth surface, and at least one side of the undercut movable tooth meshing tooth surface is undercut.
Further, the parameter equation of the movable tooth meshing curve is as follows:
Figure BSA0000199278870000031
when z is constant, the oscillating tooth meshing curve is a curve in the plane.
Further, when the meshing curve of the movable teeth is hypocycloid, the parameter equation is as follows:
Figure BSA0000199278870000032
when the meshing curve of the movable teeth is an epicycloid, the parameter equation is as follows:
Figure BSA0000199278870000033
when the meshing curve of the movable teeth is a plane sine curve, the parameter equation is as follows:
Figure BSA0000199278870000034
when the meshing curve of the movable teeth is a space sine curve, the parameter equation is as follows:
Figure BSA0000199278870000035
in the above formulas, the radial radius of the R-oscillating tooth meshing curve; a-the amplitude of the oscillating tooth meshing curve; zc-wave number of cycloid oscillating tooth engagement curves; zs-a sinusoidal oscillating tooth engagement curve wavenumber;
when the movable tooth meshing curve is a plane segmented meshing curve formed by continuously connecting i (i is 1, 2, …, n) segments of curves, the parameter equation of the i-th segment is as follows:
Figure BSA0000199278870000036
furthermore, the curvature radius rho of the movable tooth meshing curve is
Figure BSA0000199278870000041
Furthermore, the maximum distance from a point on the meshing surface of the movable tooth meshing curved surface to the axis of the movable tooth meshing curved surface is Dmax，DmaxSatisfy the relational expression that can make the raceway take place the undercut:
Dmax＞ρmin
in the formula, ρmin-minimum value of the radius of curvature p of the oscillating tooth engagement curve.
Due to the adoption of the technical scheme, the invention has the following advantages: (1) under the condition of the same size, compared with the traditional movable tooth transmission meshing pair, the meshing pair has more movable tooth numbers or larger movable tooth sizes, so that the meshing pair has larger speed reduction ratio and larger bearing capacity when being applied to a speed reducer; (2) when the undercut oscillating tooth meshing pair obtained by selecting a proper oscillating tooth meshing curve is applied to a speed reducer, the accuracy and the continuity of the whole transmission are not influenced by local undercut, all the oscillating teeth participate in meshing force transmission, and the impact resistance is strong. (3) The structure is simple and compact, and the processing, the manufacturing and the assembly are convenient.
Drawings
Fig. 1, fig. 2, fig. 3, fig. 4, and fig. 5 are schematic diagrams illustrating coordinate system setting and structure according to a first embodiment of the present invention.
Fig. 6 and 7 are schematic diagrams of generating a differential tangent profile according to a first embodiment of the present invention.
Fig. 8 and 9 are schematic views of the differential tangent plane undercut tooth profile structure according to the first embodiment of the present invention.
Fig. 10, 11, 12 and 13 are schematic diagrams illustrating coordinate system setting and structure according to a second embodiment of the invention.
Fig. 14 is a structural sectional view of a third embodiment of the present invention.
Fig. 15 and 16 are schematic exploded views of a third embodiment of the present invention.
Fig. 17 and 18 are schematic diagrams of the generation of a differential tangential profile according to the fourth embodiment of the present invention.
Reference numerals: 1-plane movable teeth; 2-a plane driving wheel I; 3-a plane driving wheel II; 201-plane undercut oscillating tooth engaging flank; 301-planar gullet; 4-space movable teeth; 5, a space transmission wheel I; 6-a space transmission wheel II; 7-space transmission wheel III; 501-space undercut oscillating tooth meshing tooth surface; 8-undercut hypocycloid; 9-steel ball oscillating tooth; 10-steel ball loose gear; 801-undercut hypocycloid raceway; 1001-steel ball movable tooth groove; 11-addendum curve; 12-flank curve; 13-root curve.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example (b): the meshing curve of the movable teeth is an arbitrary space curve, wherein two special conditions exist, the first is a closed curve in a plane, and the second is a closed curve on a cylindrical surface.
Fig. 1 to 9 show a first embodiment of the present invention, in which the oscillating tooth meshing curve is a plane closed curve C in a plane, and for the sake of illustration, a uniform coordinate system is first established for each element. As shown in fig. 1, a plurality of plane movable teeth are engaged between the first plane driving wheel and the second plane driving wheel to form an assembly body; a plane movable tooth is taken out separately and placed at the geometric center of the assembly body, and a space rectangular coordinate system is established by the geometric center as shown in figure 1; the first plane driving wheel is located in the area of the negative half shaft of the z axis, and the second plane driving wheel is located in the area of the positive half shaft of the z axis.
As shown in fig. 3, in the plane zoy, there is an arbitrary continuous curve y (f) (z) passing through the positive half axis of the y-axis but not the z-axis, i.e. a planar oscillating tooth generatrix. If a and b are any positive real numbers, the plane movable teeth are formed by rotating a closed graph formed by four lines of curves y ═ F (z), z ═ a, z ═ b and y ═ 0 around the z axis. When the meshing curve C of the movable teeth is determined, the section radius r of the movable teeth of the critical plane causing the undercut of the meshing tooth surface of the undercut movable teeth1Then, when z < 0, the maximum value of the curve y ═ F (z) is determined to be fmaxThen f ismaxNeed to satisfy the relation fmax＞r1。
As shown in FIG. 2, below the negative z-axis, xoy plane, there is a planar drive wheel I, whose upper planar undercut relieved tooth engaging flank is formed by the following principle: from the foregoing, the meshing curve equation C of the meshing tooth surface of the planar undercut oscillating tooth is expressed as a cylindrical surface infinitely extending to both sides of the z-axis in the spatial rectangular coordinate system. As shown in FIG. 5, the interval [ -a, 0 ] on the z-axis is divided by the differential concept]Equally dividing the section into n tiny sections, wherein n tends to be infinite, the length of each section is dz, the left end point of each section is taken as a reference point, n sections sigma parallel to the xoy plane can be made, and the ith section sigma is setiThe line of intersection with the cylindrical surface is CiThe function value at the intersection with the curve y ═ F (z) is fiThen the driving circle center is at CiUpper and radius fiAlong the circle CiThe envelope curve of all circles on the motion track forms the section sigmaiThe actual section profile of the engaging tooth surface of the plane undercut oscillating tooth is shown in fig. 6 and 7. Finally, all the sections sigmaiThe actual section tooth profile of the upper plane undercut oscillating tooth meshing tooth surface is in the range of [ -a, 0 []And integrating, namely superposing to obtain the plane undercut oscillating tooth meshing tooth surface. Fig. 8 and 9 are schematic diagrams of the structure of the plane undercut oscillating tooth meshing tooth surface, the undercut condition of the whole plane undercut oscillating tooth meshing tooth surface can be seen from fig. 8, fig. 9 is a partial enlargement of fig. 8, and it can be seen that the circle center is CiUpper and radius fiAlong the circle CiDuring motion, the envelope surface is actually the envelope curve of the scanning track endpoint of the diameter perpendicular to the meshing curve equation at the moment, the circle center moves in the section ab in the region ① without undercut, the circle center moves in the section bc in the region ② with undercut, and the circle center moves in the section cd in the region ③ without undercutAn undercut occurs, in the area ② where the undercut occurred, area a was swept only once, area B was swept twice, and area C was swept three times, so material in area B and area C was completely cut away, and an undercut occurred.
As shown in fig. 4, on the positive z-axis, xoy plane, there is a loose gear, on which the loose tooth slot is formed by the following principle: the section [0, b ] on the z-axis is divided by the idea of differentiation]Equally dividing the section into n tiny sections, wherein n tends to be infinite, the length of the section is dz, the right endpoint of each section is taken as a reference point, n sections a parallel to the xoy plane can be drawn, and the jth section a is setjThe function value at the intersection with curve y ═ F (z) is fjIn cross section ajThe radius is fjTo obtain a cross section ajThe actual tooth profile of the engaged tooth surface of the plane undercut active tooth is formed, and then all the sections ajThe actual tooth profile of the engaging tooth surface of the upper plane undercut oscillating tooth is in the interval [0, b]And integrating the two planes, namely superposing the two planes together to obtain the plane movable tooth slot.
Fig. 10 to 13 show a second embodiment of the present invention, in which the meshing curve of the movable teeth is a closed space curve S in the cylindrical surface, and for convenience of description, a uniform coordinate system is first established for each element. As shown in fig. 1, a plurality of space movable teeth are engaged among the empty driving wheel I, the space driving wheel II and the space driving wheel III to form an assembly body; a spatial movable tooth is taken out separately and placed at the geometric center of the assembly body, and a spatial rectangular coordinate system is established by the geometric center as shown in figure 10.
As shown in fig. 11, in the xoy plane, there is an arbitrary continuous curve y (f) (x) passing through the positive half axis of the y axis but not the x axis, which is a space oscillating tooth generatrix. If c and d are any positive real numbers, the spatial movable teeth are formed by rotating a closed graph formed by four lines of curves y ═ F (x), x ═ c, x ═ d and y ═ 0 around the x axis. When the meshing curve S of the movable teeth is determined, the section radius r of the movable teeth in the critical space causing the undercut of the meshing tooth surface of the undercut movable teeth2Then, when x is less than 0, the maximum value of the curve y ═ F (x) is determined to be fmaxThen f ismaxNeed to satisfy the relation fmax＞r2。
As shown in fig. 13, an upper space undercut oscillating tooth engaging flank of a space transmission wheel is formed by the following principle: from the foregoing, the projection of the meshing curve equation S of the meshing tooth surface of the space undercut oscillating tooth in the xoy plane is a circle. As shown in FIG. 14, the interval [ -c, 0 ] on the x-axis is divided by the differential concept]Equally dividing the two sections into n tiny sections, wherein n tends to be infinite, the length of each section is dr, taking the left end point of each section as a reference point, making a cylindrical section sigma with the same axis of n and the z axis, and setting the ith cylindrical section sigmaiThe equation of the meshing curve of (A) is SiThe function value of the intersection of the plane-c + idr and the curve y ═ f (x) is fiThe driving axis is at SiUpper and radius fiAlong the cylindrical surface of SiOne complete turn of movement, the axis always intersects with the z-axis and is parallel to the xoy plane, and the movement track has a cylindrical section sigmaiThe upper envelope, i.e. forming a cylindrical section ∑iThe space root of the tooth-engaging flank is cut off and the actual section tooth profile of the tooth-engaging flank is shown in fig. 12 and 13. Finally, all the cylinder sections are sigmaiThe actual section tooth profile of the upper space undercut oscillating tooth meshing tooth surface is in the interval [ r, r + c ] along the radial direction]And integrating, namely superposing to obtain the space undercut oscillating tooth meshing tooth surface.
Fig. 14 to 16 show a third embodiment of the present invention, which is a single-stage undercut hypocycloidal oscillating tooth transmission unit, wherein the meshing curve of the oscillating teeth is a hypocycloid in a plane. The plane rectangular coordinate parameter equation of the meshing curve of the undercut hypocycloid raceway is as follows:
Figure BSA0000199278870000071
in the above formulas, the R-steel ball oscillating tooth groove has a distributed circle radius, namely the distance from the axle center of the steel ball oscillating tooth groove to the axle center of the steel ball oscillating gear; a-the eccentricity of the undercut hypocycloid wheel and the steel ball loose gear, namely the distance between the axis of the undercut hypocycloid wheel and the axis of the steel ball loose gear; zcThe wave number of the undercut hypocycloidal raceway.
In the embodiment, the movable teeth adopt standardized standard balls which can be purchased in batches and are used as bearing balls, namely, the movable teeth of the steel balls are adopted, the corresponding movable tooth grooves of the steel balls are in a spherical bowl shape, the corresponding undercut hypocycloid raceways are spherical raceways, and the undercut tooth profile can be selected to be not blunted or blunted; the steel ball is used as the movable tooth, so that the processing and the manufacturing are convenient, and the service life of the whole transmission unit can reach the service life of the traditional deep groove ball bearing.
The transmission parameters of this preferred embodiment are shown in table 1:
TABLE 1 table of theoretical parameters of three structures of the examples
Figure BSA0000199278870000081
When the steel ball loose gear is fixed, the axis of the undercut hypocycloid wheel is driven to revolve around the axis of the steel ball loose gear, and because the relative positions of the steel ball loose teeth grooves where all the steel ball loose teeth are located in the steel ball loose gear are unchanged, and all the steel ball loose teeth are meshed with the undercut hypocycloid raceway of the undercut hypocycloid wheel, the steel ball loose teeth can drive the undercut hypocycloid wheel to rotate around the axis of the steel ball loose gear through the undercut hypocycloid raceway, namely, the undercut hypocycloid wheel rotates around the axis of the steel ball loose gear while revolving around the axis of the steel ball loose gear, the transmission rule is that the steel ball loose teeth just rotate along the axis of the undercut hypocycloid wheel every time the axis of the undercut hypocycloid wheel revolves around the axis of the steel ball loose gear, the rotation speed of the undercut hypocycloid wheel is output, and the speed reduction; similarly, when the undercut hypocycloid wheel is fixed, the axis of the steel ball loose gear is driven to revolve around the axis of the undercut hypocycloid wheel, and because all the steel ball loose teeth must move along the undercut hypocycloid wheel path, and the positions of the steel ball loose tooth grooves where all the steel ball loose teeth are located relative to the steel ball loose gear are unchanged, the steel ball loose teeth can drive the steel ball loose gear to rotate around the axis of the steel ball loose tooth groove, namely, the axis of the steel ball loose gear revolves around the axis of the undercut hypocycloid wheel and simultaneously can rotate around the axis of the steel ball loose gear, the transmission rule is that the rotation speed of the steel ball loose gear is output by just passing through one undercut hypocycloid wheel path along the axis of the steel ball loose gear every time the steel ball loose tooth groove revolves around the axis of the undercut hypocycloid wheel, and the purpose of.
Particularly, the undercut hypocycloid wheel and the steel ball loose gear are eccentrically arranged, when one part of the steel ball loose teeth in the eccentric direction transmits force through the outer side of the undercut hypocycloid raceway, the other side steel ball loose teeth in the opposite direction of the eccentric direction transmits force through the inner side of the undercut hypocycloid raceway, and therefore the effect of full-tooth meshing force transmission is achieved. Although the undercut exists between two adjacent waves at the inner side of the undercut hypocycloid raceway, the raceway transmission is completely accurate except for the undercut part; supposing that at a certain moment, one steel ball oscillating tooth is positioned at an undercut between two waves, and at the moment, the steel ball oscillating tooth needs the inner side of an undercut hypocycloid raceway to transfer force, obviously, because the steel ball oscillating tooth is not in contact with the inner side of the undercut hypocycloid raceway, the force cannot be transferred, but the steel ball oscillating tooth is in contact with the outer side of the undercut hypocycloid raceway at the moment, the steel ball oscillating tooth is taken away from the undercut at the outer side of the undercut hypocycloid raceway, and meanwhile, even if the steel ball oscillating tooth does not contribute to the force transfer, two adjacent steel ball oscillating teeth are positioned at the non-undercut at the inner side of the undercut hypocycloid raceway, and are accurately stressed in transmission. Because the undercut occupies only a small central angle, the non-force-transmission time of a single tooth in the above-mentioned case is very short, and with different tooth number conditions, in the transmission unit described in the embodiment, the tooth number in which the above-mentioned transient process occurs is either not present or very small, and the transmission fluctuation caused by the transient process is very small and can be ignored.
Fig. 17 and 18 show a fourth embodiment of the invention, which is a single-stage undercut segmented curve oscillating tooth transmission unit, in which the oscillating tooth meshing curve is a closed curve D in which segmented curves in one plane are all filled with one circle around the center of the circle. The tooth profile generation method is the same as that of the first embodiment, and the only difference is that the curve C is replaced by a segmented curve D, and the shape of the tooth profile envelope on a certain differential tangent plane is shown in figure 18. Specifically, the piecewise curve is a continuous curve formed by continuously connecting i (i ═ 1, 2, …, n) segments, and in the fourth embodiment, the piecewise curve is composed of three segments, namely, a tooth crest curve (mn segment), a tooth flank curve (np segment), and a tooth root curve (pq segment).
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (12)

1. The utility model provides an undercut oscillating tooth transmission meshing pair, includes oscillating tooth meshing flank, oscillating tooth meshing curve, undercut oscillating tooth meshing flank, its characterized in that: the movable tooth meshing tooth surface and the undercut movable tooth meshing tooth surface are meshed with each other, and the undercut movable tooth transmission meshing pair is formed.
2. An undercut oscillating tooth driving engagement pair as defined in claim 1, wherein: the movable tooth meshing curve is cycloid or non-cycloid.
3. An undercut oscillating tooth driving engagement pair as defined in claim 2, wherein: when the meshing curve of the movable teeth is cycloid, the curve is hypocycloid or epicycloid; when the meshing curve of the movable teeth is non-cycloid, the curve is a sine curve which is a plane sine curve or a space sine curve.
4. An undercut oscillating tooth driving engagement pair as defined in claim 3, wherein: when the movable tooth meshing curve is a non-sinusoidal curve, the movable tooth meshing curve is a segmented meshing curve.
5. A method of forming an undercut oscillating tooth drive mesh pair as claimed in claims 1 to 4, wherein: the movable tooth meshing tooth surface is a curved surface obtained by rotating a circle around a straight line which does not pass through a continuous curve in a plane; the meshing curve of the movable teeth is a space curve; the undercut oscillating tooth meshing tooth surface is an envelope surface of a curved track which is swept from head to tail on an oscillating tooth meshing curve by the geometric center of the oscillating tooth meshing tooth surface, and at least one side of the undercut oscillating tooth meshing tooth surface is undercut.
6. A method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: when the movable tooth meshing curve adopts a cycloid, the engaging tooth surface of the undercut movable tooth is an envelope surface of a curved surface track of which the geometric center of the engaging tooth surface of the movable tooth sweeps from the head to the tail on the cycloid, and at least one side of the engaging tooth surface of the undercut movable tooth is undercut.
7. A method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: when the movable tooth meshing curve adopts a sine curve, the undercut movable tooth meshing tooth surface is an envelope surface of a curved track which is swept from head to tail on the sine curve by the geometric center of the movable tooth meshing tooth surface, and at least one side of the undercut movable tooth meshing tooth surface is undercut.
8. A method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: when the movable tooth meshing curve adopts a segmented meshing curve, the undercut movable tooth meshing tooth surface is an envelope surface of a curved track which is swept from head to tail on the segmented meshing curve by the geometric center of the movable tooth meshing tooth surface, and at least one side of the undercut movable tooth meshing tooth surface is undercut.
9. A method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: the parameter equation of the meshing curve of the movable teeth is as follows:
Figure FSA0000199278860000011
when z is constant, the oscillating tooth meshing curve is a curve in the plane.
10. A method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: when the meshing curve of the movable teeth is hypocycloid, the parameter equation is as follows:
Figure FSA0000199278860000021
when the meshing curve of the movable teeth is an epicycloid, the parameter equation is as follows:
Figure FSA0000199278860000022
when the meshing curve of the movable teeth is a plane sine curve, the parameter equation is as follows:
Figure FSA0000199278860000023
when the meshing curve of the movable teeth is a space sine curve, the parameter equation is as follows:
Figure FSA0000199278860000024
in the above formulas, the radial radius of the R-oscillating tooth meshing curve; a-the amplitude of the oscillating tooth meshing curve; zc-wave number of cycloid oscillating tooth engagement curves; zs-a sinusoidal oscillating tooth engagement curve wavenumber;
when the movable tooth meshing curve is a plane segmented meshing curve formed by continuously connecting i (i is 1, 2, …, n) segments of curves, the parameter equation of the i-th segment is as follows:
Figure FSA0000199278860000025
11. a method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: the curvature radius rho of the meshing curve of the movable teeth is
Figure FSA0000199278860000026
12. A method of forming an undercut oscillating tooth drive mesh pair as defined in claim 5, wherein: the maximum distance from a point on the meshing surface of the movable tooth meshing curved surface to the axis of the movable tooth meshing curved surface is Dmax，DmaxSatisfy the relational expression that can make the raceway take place the undercut:
Dmax＞ρmin
in the formula, ρmin-minimum value of the radius of curvature p of the oscillating tooth engagement curve.
CN202010008305.2A 2020-01-06 2020-01-06 Undercut oscillating tooth transmission meshing pair and generation method thereof Pending CN111156306A (en)

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