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CN102486226A - Cycloid gear with high-speed transmission, heavy load and low abrasion - Google Patents

Cycloid gear with high-speed transmission, heavy load and low abrasion Download PDF

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Publication number
CN102486226A
CN102486226A CN2010105846225A CN201010584622A CN102486226A CN 102486226 A CN102486226 A CN 102486226A CN 2010105846225 A CN2010105846225 A CN 2010105846225A CN 201010584622 A CN201010584622 A CN 201010584622A CN 102486226 A CN102486226 A CN 102486226A
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general
theta
gear
lambda
cycloid
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李远庆
李睿
李景
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Abstract

The invention provides a cycloid gear with high-speed transmission, heavy load and low abrasion, comprising a hypocycloid gear, an epicycloid gear and a flat cycloid rack which can be combined to form transmission pairs including an outer engagement, an inner engagement, a gear and rack engagement and the like. The cycloid gear completely complies with natural laws, has no interferences and does not need correction; compared with an involute gear, the engagement sliding rate of the cycloid gear is only about 20%, the thickness of a tooth root is much thicker and the loading capability is improved by more than one time; the anti-agglutination capability is strong, the cycloid gear is not easy to abrade, the noise is small and the temperature rise is low; the cycloid gear is particularly suitable for high-speed and heavy-load transmission; the cycloid gear is machined by gear hobbing and gear shaping and the minimum teeth number reaches six teeth without undercutting; under the conditions of same output power and an approximate transmission ratio, the modulus can be decreased and the gear ratio is decreased to corresponding fewer teeth, so that the volume of a transmission system is reduced by about 30%; and the service life is improved by more than 3 times.

Description

The general cycloidal gear of high speed transmission, heavy load, low wearing and tearing
The present invention relates to a kind of general cycloidal gear that adapts to high speed transmission, heavy load, low wearing and tearing.The notion of general cycloid is: the equidistant curve on hypocycloid, epicycloid, flat cycloid and the short width of cloth, prolate cycloid and their both sides, derivation curve etc. are referred to as general cycloid; Hypocycloid, epicycloid, flat cycloid and the short width of cloth thereof, prolate cycloid are the special cases of general cycloid.The general cycloidal gear that is formed by the equidistant curve of the definite hypocycloid of the long coefficient lambda of the width of cloth, epicycloid, flat cycloid, the complete honor of tooth curve need not be revised according to mathematical model, meets natural general cycloid rule fully.
Involute gear, circular tooth gear, cycloidal-pin wheel or the like are arranged in gear transmission, use general be involute gear, minimum teeth number generally is 17 teeth; In involute gear, in the engagement, exist involute and interfere, profile overlap interference, radial interference, transition curve is interfered, and need reach steady transmission through tooth-shape angle, modification coefficient, the high many-sided correction of tooth top, tip relief; Circular tooth gear is a helical gear of doing flank profil with the concave, convex circular arc, and is higher 1.5~2 times than the bearing capacity of involute gear, but noise is big with vibration, minimum teeth number 11 teeth; The cycloidal-pin wheel transmission; Its cycloid wheel is the inboard equidistant curve flank profil and the engagement of pin tooth of curtate epicycloid, and in fact cycloid wheel can not adopt standard tooth form, exists the monodentate top and interferes; Interfere on the bidentate top, all must be modified to the compound tooth-shaped purpose that just can reach steady transmission.
The purpose of this invention is to provide the general cycloidal gear transmission of a kind of high speed transmission, heavy load, low wearing and tearing.General cycloidal gear shaping law is: half general cycloid is left out the beginning and the end, do flank profil with the line segment on basic circle both sides, the general cycloidal gear that is meshed all is the basic circle pure rolling, and rule fully complies with the nature; Load-carrying ability is an involute gear more than 2 times, and the engagement sliding ratio has only about 20% of involute, is the extremely low friction driving near pure rolling, is adapted to the high speed transmission especially.The thickness at root of tooth of general cycloidal gear is big more a lot of than involute, does not have undercut, does not need tip relief, and interior engagement does not have interference, and antiscuffing capacity is strong, and not easy to wear, noise is little, and temperature rise is low, is adapted to heavy load especially; Adopt gear hobbing, Gear Shaping, general epicycloid minimum teeth number can reach 6 teeth, general hypocycloid minimum teeth number can reach 7 teeth does not have undercut; Under the identical situation of output power, because thickness at root of tooth is big more a lot of than involute, load-carrying ability is big; Can dwindle the gear pair modulus is corresponding; Under the approaching situation of velocity ratio, can the gear ratio of gear pair be reduced to rational minimum teeth number, therefore; The volume ratio involute of general cycloidal gear transmission system reduces more than 30% at least, and be more than 3 times of involute gear working life.
The object of the invention is realized through following scheme: owing to found the normal characteristics of motion of general cycloid; Deduce hypocycloid, epicycloid, the flat mutual conjugation of cycloid three; Derive normal, the equidistant curve of general cycloidal profile, the mathematical models such as path of action of gear pair, find high speed, heavy load, the low general cycloidal gear that weares and teares; The equidistant curve of definite hypocycloid, epicycloid, flat cycloid by the long coefficient lambda of the width of cloth and the general cycloidal profile that forms, the flank profil of general hypocycloid flank profil, general epicycloid flank profil, general flat cycloid tooth bar is described respectively with three equations:
General hypocycloid flank profil by X = ( R - r ) Cos θ + Rλ Cos ( Uθ - θ ) + C Cos θ - λ Cos ( Uθ - θ ) 1 + λ 2 - 2 λ Cos Uθ Y = ( R - r ) Sin θ - Rλ Sin ( Uθ - θ ) + C Sin θ - λ Sin ( Uθ - θ ) 1 + λ 2 - 2 λ Cos Uθ y - - - ( 1 )
General epicycloid flank profil by X = ( R + r ) Cos θ - Rλ Cos ( Uθ + θ ) - C Cos θ - λ Cos ( Uθ + θ ) 1 + λ 2 - 2 λ Cos Uθ Y = ( R + r ) Sin θ - Rλ Sin ( Uθ + θ ) - C Sin θ - λ Sin ( Uθ + θ ) 1 + λ 2 - 2 λ Cos Uθ - - - ( 2 )
General flat cycloid rack tooth profile by X = Rθ - Rλ Sin θ + C λ Sin θ 1 + λ 2 - 2 λ Cos θ Y = r - Rλ Cos θ + C λ Cos θ - 1 1 + λ 2 - 2 λ Cos θ - - - ( 3 )
Above in three equations: the general cycloid basic circle of R-; The general cycloid of r-is justified; The long coefficient of λ-width of cloth, 0.75≤λ<1; U-basic circle and the ratio that circle takes place, u=R/r; C-equidistance value; The corner at θ-relative basic circle center, generation circle center is a variable.
When modulus m is identical, five kinds of general cycloidal gear engagement pair capable of being combined:
1, the general cycloid tooth wheel set of outer gearing; By the engagement pair that general inner cycloidal gear and general epicycloidal gear conjugation constitute, profile geometry is described by (1), (2) two equations;
2, the general hypocycloidal tooth wheel set of interior engagement; Constitute internal meshing pair by general inner cycloidal gear and general hypocycloid internal gear conjugation, profile geometry is described by (1) formula;
3, the general epicycloidal tooth wheel set of interior engagement; Constitute internal meshing pair by general epicycloidal gear and general epicycloid internal gear conjugation, profile geometry is described by (2) formula;
4, general inner cycloidal gear and general flat cycloid tooth bar engagement pair; Constitute the gear rack engagement pair by general inner cycloidal gear and general flat cycloid tooth bar conjugation, profile geometry is described by (1), (3) two equations;
5, general epicycloidal gear and general flat cycloid tooth bar engagement pair; Constitute the gear rack engagement pair by general epicycloidal gear and general flat cycloid tooth bar conjugation, profile geometry is described by (2), (3) two equations.
Above-mentioned five kinds of engagement pair can be two types of general cycloidal gear engagement pair of straight-tooth and helical tooth (helical teeth).
The invention has the beneficial effects as follows: the engagement sliding ratio of general cycloidal gear does not have only about 20% of involute gear, and is easy to wear in engagement driving, antiscuffing capacity is strong, and the life-span of general cycloidal gear is more than 3 times of involute gear; Noise and temperature rise simultaneously descends, and efficient is significantly improved with respect to involute gear; Because the thickness at root of tooth of general cycloidal gear is big more a lot of than involute, load-carrying ability is more than the twice of involute gear; The no undercut of generate processing of the few number of teeth of general cycloidal gear can dwindle the gear pair modulus is corresponding, under the approaching situation of velocity ratio, can the gear ratio of gear pair be reduced to rational minimum teeth number; Under the situation with power, corresponding can the reduction more than at least 30% of volume of general cycloidal gear system makes transmission system weight saving, saves material, reduces energy consumption.Can be used for the gear transmission in the transmission system of space flight, transportation, lathe, mine, metallurgy, petrochemical industry, weaving, light industry, food or the like various machineries.
With reference to the accompanying drawings with embodiment to the detailed description of the invention:
Fig. 1 is a general cycloid spur gear planetary transmission of the present invention photo in kind.
Fig. 2 is general cycloid spiral of the present invention (tiltedly) gear planetary transmission schematic representation.
Fig. 3 is that the flank profil of general cycloidal gear of the present invention forms principle schematic.
Fig. 4 is the sliding ratio of general cycloid tooth wheel set of the present invention and Involute Gear Pair, area, the contact ratio contrast schematic representation that sliding ratio surrounds.
Fig. 5 be general cycloidal profile of the present invention and involute profile the intensity contrast schematic representation.
Fig. 6 is the master gear and the modified gear schematic representation of general cycloid of the present invention.
Fig. 7 does not have undercut gear hobbing, Gear Shaping and envelope sketch map for general cycloid gear minimum teeth number of the present invention.
Fig. 8 is general cycloid gear Gear Shaping of the present invention and envelope sketch map.
Fig. 9 is general cycloid internal gear Gear Shaping of the present invention and envelope sketch map.
As shown in Figure 1, the sun gear of the planetary transmission of general cycloid spur gear is 9 teeth, and 3 planet wheels all are 12 teeth, and gear ring is 33 teeth; Sun gear and 3 planet wheels are outer gearings, and planet wheel and gear ring are interior engagements;
As shown in Figure 2, compared to Figure 1 the planetary transmission of general cycloid spiral (tiltedly) gear is to have strengthened contact ratio ε.
As shown in Figure 3; Tooth form factor ψ confirms the distribution of general cycloidal profile on basic circle R, and a point of the starting point of half general cycloid on the ox axle intersects at the s point with basic circle R; ∠ soa=θ; Ab, the cd section of general cycloid are removed, and the b-s-c line segment that keeps s two edge points is done flank profil, and the span of the ψ of tooth form factor is 0≤ψ<1; Get ψ=0.5, flank profil line 0.5 θ that turns clockwise is arrived s ' point, just formed general cycloidal profile.Whether the general cycloid tooth wheel set of a pair of outer gearing stable drive, and contact ratio ε is crucial, ε>1, then stable drive; Vibrations and noise must appear in ε<1; ε=1, then trend vibrations and noise.Contact ratio ε and the tooth form factor of general cycloidal gear in engagement is closely related.This is the formation principle of general cycloidal profile.
As shown in Figure 4, be the contrast of general cycloid tooth wheel set and Involute Gear Pair, their modulus all is m=2; The number of teeth all is z 1=11, z 2=15; The reference radius of involute gear equates with the Base radius of general cycloidal gear, i.e. R 1=11, R 2=15; The line of contact A-P-C of involute gear is a straight line, and the actual line of action A-P-C of general cycloidal gear is a curve; Formula according to the gear engagement sliding ratio:
σ 1 = l ( 1 / R 1 + 1 / R 2 ) / ( l / R 1 + 1 ) σ 2 = l ( 1 / R 1 + 1 / R 2 ) / ( l / R 2 - 1 ) - - - ( 4 )
(4) in the formula, σ 1, σ 2-be respectively the sliding ratio of two phase gears;
R 1, R 2-be two general cycloidal gear Base radius, be reference radius for involute gear;
L-is the calculated value of sliding ratio.
The l of two maximums of general cycloid tooth wheel set 1=4.775, l 2=4.7146; The l of Involute Gear Pair 1=12.78691, l 2=12.05069.
Two maximum sliding ratio: σ of general cycloid tooth wheel set 1=0.5247 and 0.52; σ 2=-1.1038 and-1.0834.
Two maximum sliding ratio: σ of Involute Gear Pair 1=0.9318 and 0.9062; σ 2=-13.6567 and-9.6577.
The sliding ratio area of general cycloid tooth wheel set: 6.2054mm 2
The sliding ratio area of Involute Gear Pair: 27.60439mm 2
General cycloid compares with the sliding ratio area of Involute Gear Pair: 6.2054/27.60439=21.93%.
Contact ratio ε=1.265 of general cycloid tooth wheel set; Contact ratio ε=1.244 of Involute Gear Pair; The contact ratio of general cycloid is slightly larger than involute.
Contrast thus, demonstrate the superiority of general cycloidal gear.
As shown in Figure 5, be the identical flank profil contrast of two kinds of numbers of teeth, modulus: dotted line a-d e is an involute profile, and solid line b-d-f is general cycloidal profile, and they intersect at the d point; The basic circle R of general cycloidal gear overlaps with the standard pitch circle of involute gear; Dotted line below the involute basic circle r is not participated in engagement; From figure, can find out that the thickness at root of tooth of general cycloid is much larger than involute tooth root thickness; Therefore the load-carrying ability of general cycloidal profile is much larger than involute profile, so the general cycloidal profile load-carrying ability of figure (a) is more than 1.5 times of involute; The thickness at root of tooth of figure (b) is bigger than involute, and load-carrying ability is more than 2.5 times of involute, because the sliding ratio of general cycloidal gear is extremely low, and the sliding ratio of figure (b) also will be lower than figure (a); Stable drive, the circular tooth gear of complete alternative heavy load.Because general cycloid thickness at root of tooth is big more a lot of than involute, load-carrying ability is big, can the modulus of general cycloidal gear system be reduced with respect to involute, thereby reduces the volume of transmission system.
As shown in Figure 6, the left side is the general cycloid tooth wheel set of standard, and the right is the general cycloid tooth wheel set of displacement: Z 2Tooth top and Z 1The a point of tooth root on line of contact begin to get into engagement, Z 1Counterclockwise to drive Z 2Turn clockwise, the contact points of gear pair is just moved to the p-c point along path of action by a point, when contact points arrives the c point, and Z 1The t point just with Z 2The s point overlap at the c point, this is the engagement process of a flank profil.
Z 1=6 teeth are minimum teeth numbers of general epicycloidal gear, Z 2=7 teeth are minimum teeth numbers of general inner cycloidal gear; Can obviously find out: the flank profil Z after the general cycloidal gear displacement 1Z than master gear flank profil 1Greatly, the flank profil Z after the displacement 2Flank profil Z than standard 2Little.
When needs lack number of teeth transmission,, can improve the thickness of tooth root through displacement if the density of load needs; Because the tooth root of general cycloidal gear is more a lot of greatly than involute tooth root, when tooth number Z=more than 9 teeth, generally do not need displacement, when the big load of gear pair needs relative equilibrium also can displacement.
Because minimum 6 teeth that reach of the general cycloid number of teeth under the approaching situation of velocity ratio, can reduce to the number of teeth of gear pair rational gear ratio, the volume ratio involute of general cycloidal gear transmission system reduces more than 30% at least.
As shown in Figure 7, the left side is general epicycloidal gear hobboing cutter Machining of Gear, and perhaps wheel and rack engagement and envelope also are general epicycloid pinion cutter manufacturing gear strips simultaneously.The right is general hypocycloid hobboing cutter Machining of Gear, and perhaps wheel and rack engagement and envelope also are general hypocycloid pinion cutter manufacturing gear strips simultaneously.Involute gear has undercut below 15 teeth in gear hobbing or Gear Shaping; General epicycloidal gear carries out gear hobbing at minimum 6 teeth does not have undercut, and general inner cycloidal gear carries out gear hobbing at minimum 7 teeth does not have undercut.
As shown in Figure 8, the left side is that general hypocycloid gear shaper cutter (15 tooth) is processed general epicycloidal gear (11 tooth); The right is that general epicycloid gear shaper cutter (15 tooth) is processed general inner cycloidal gear; Certainly, the general hypocycloid gear shaper cutter of 15 teeth can be processed the general epicycloidal gear of any number of teeth more than 6 teeth, and the general epicycloid gear shaper cutter of 15 teeth can be processed the general inner cycloidal gear of any number of teeth more than 7 teeth; Because outer gearing must be general epicycloid and general hypocycloidal tooth wheel set, gear pair Z 1With Z 2Number of teeth difference can be 1~n, and their path of action overlaps fully, do not have undercut, also do not have any interference that has, and do not need to revise, tip relief.
As shown in Figure 9, the left side is general epicycloid gear shaper cutter, processes general epicycloid internal gear; The right is general hypocycloid gear shaper cutter, processes general hypocycloid internal gear.Two kinds of general cycloid gear shaper cutter numbers of teeth all are Z D=9, the internal gear minimum teeth number of being processed all is 14 teeth, and promptly processing more than 14 teeth general cycloid internal gear of any number of teeth all is not have to interfere.Form the engaging tooth wheel set because interior engagement is general epicycloid and general epicycloid, general hypocycloid and general hypocycloid form engaging tooth wheel set, internal gear engagement pair Z 1With Z 2Number of teeth difference can be to be equal to or greater than any number of 5, like the interior engagement of planet wheel and the gear ring of Fig. 1, Fig. 2, the outer gearing of planet wheel and sun gear; Their path of action overlaps fully, does not have undercut, also has no interference; Need not revise the complete natural law according to general cycloid.

Claims (8)

1. one kind is left out the beginning and the end general cycloid and does profile of tooth, adapts to the general cycloidal gear of high speed transmission, heavy load, low friction; Select and the equidistant curve of the hypocycloid confirmed, epicycloid, flat cycloid and the general cycloidal profile that forms is described general hypocycloid flank profil, general epicycloid flank profil, general flat cycloid rack tooth profile respectively with three equations by the long coefficient lambda of the width of cloth;
General hypocycloid flank profil: X = ( R - r ) Cos θ + Rλ Cos ( Uθ - θ ) + C Cos θ - λ Cos ( Uθ - θ ) 1 + λ 2 - 2 λ Cos Uθ Y = ( R - r ) Sin θ - Rλ Sin ( Uθ - θ ) + C Sin θ - λ Sin ( Uθ - θ ) 1 + λ 2 - 2 λ Cos Uθ y - - - ( 1 )
General epicycloid flank profil: X = ( R + r ) Cos θ - Rλ Cos ( Uθ + θ ) - C Cos θ - λ Cos ( Uθ + θ ) 1 + λ 2 - 2 λ Cos Uθ Y = ( R + r ) Sin θ - Rλ Sin ( Uθ + θ ) - C Sin θ - λ Sin ( Uθ + θ ) 1 + λ 2 - 2 λ Cos Uθ - - - ( 2 )
General flat cycloid rack tooth profile: X = Rθ - Rλ Sin θ + C λ Sin θ 1 + λ 2 - 2 λ Cos θ Y = r - Rλ Cos θ + C λ Cos θ - 1 1 + λ 2 - 2 λ Cos θ - - - ( 3 )
In three equations: the general cycloid basic circle of R-; The general cycloid of r-is justified; The long coefficient of λ-width of cloth, 0.75≤λ<1; U-basic circle and the ratio that circle takes place, u=R/r; C-equidistance value; The corner at θ-relative basic circle center, generation circle center is a variable.
2. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by identical general inner cycloidal gear of modulus and the outer gearing of general epicycloidal gear conjugation.
3. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by engagement in identical general inner cycloidal gear of modulus and the general hypocycloid internal gear conjugation.
4. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by engagement in identical general epicycloidal gear of modulus and the general epicycloid internal gear conjugation.
5. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by identical general inner cycloidal gear of modulus and general flat cycloid tooth bar conjugation engagement.
6. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by identical general epicycloidal gear of modulus and general flat cycloid tooth bar conjugation engagement.
7. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by the general cycloid tooth wheel set that the identical general cycloidal gear of modulus can be a straight-tooth, can be the general cycloid tooth wheel set of spiral (tiltedly) tooth.
8. according to claims 1 described high speed transmission, heavy load, the low general cycloidal gear that rubs; It is characterized by the general cycloid tooth wheel set that the identical general cycloidal gear of modulus can be a standard, can be the general cycloid tooth wheel set of displacement.
CN2010105846225A 2010-12-02 2010-12-02 Cycloid gear with high-speed transmission, heavy load and low abrasion Pending CN102486226A (en)

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105221704A (en) * 2015-10-23 2016-01-06 中国人民解放军军事交通学院 The raising method of the contact ratio of outer gearing cycloidal gear
CN106640629A (en) * 2016-08-30 2017-05-10 重庆红宇精密工业有限责任公司 Oil pump rotor
CN110069799A (en) * 2018-09-18 2019-07-30 中车戚墅堰机车车辆工艺研究所有限公司 A kind of strength calculation method of cycloid gear
CN110630720A (en) * 2019-09-20 2019-12-31 厦门理工学院 Cycloidal gear and cycloidal gear reducer
CN111173894A (en) * 2020-01-06 2020-05-19 河南烛龙高科技术有限公司 Two-stage nested closed type undercut cycloid oscillating tooth transmission unit

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105221704A (en) * 2015-10-23 2016-01-06 中国人民解放军军事交通学院 The raising method of the contact ratio of outer gearing cycloidal gear
CN106640629A (en) * 2016-08-30 2017-05-10 重庆红宇精密工业有限责任公司 Oil pump rotor
CN110069799A (en) * 2018-09-18 2019-07-30 中车戚墅堰机车车辆工艺研究所有限公司 A kind of strength calculation method of cycloid gear
CN110069799B (en) * 2018-09-18 2023-02-24 中车戚墅堰机车车辆工艺研究所有限公司 Method for calculating strength of cycloid gear
CN110630720A (en) * 2019-09-20 2019-12-31 厦门理工学院 Cycloidal gear and cycloidal gear reducer
CN110630720B (en) * 2019-09-20 2020-11-03 厦门理工学院 A kind of cycloid gear reducer
CN111173894A (en) * 2020-01-06 2020-05-19 河南烛龙高科技术有限公司 Two-stage nested closed type undercut cycloid oscillating tooth transmission unit
CN111173894B (en) * 2020-01-06 2021-05-04 河南烛龙高科技术有限公司 Two-stage nested closed type undercut cycloid oscillating tooth transmission unit

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Application publication date: 20120606