CN113969968B - E-tooth-shaped speed reducer, generalized tooth shape generation method and tooth shape design method - Google Patents
E-tooth-shaped speed reducer, generalized tooth shape generation method and tooth shape design method Download PDFInfo
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- CN113969968B CN113969968B CN202111205214.9A CN202111205214A CN113969968B CN 113969968 B CN113969968 B CN 113969968B CN 202111205214 A CN202111205214 A CN 202111205214A CN 113969968 B CN113969968 B CN 113969968B
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- 239000003638 chemical reducing agent Substances 0.000 title claims abstract description 48
- 238000000034 method Methods 0.000 title claims abstract description 31
- 229910000831 Steel Inorganic materials 0.000 claims abstract description 29
- 238000005096 rolling process Methods 0.000 claims abstract description 29
- 239000010959 steel Substances 0.000 claims abstract description 29
- 230000005540 biological transmission Effects 0.000 claims description 12
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- 230000033001 locomotion Effects 0.000 claims description 6
- 230000000670 limiting effect Effects 0.000 claims description 4
- 230000008859 change Effects 0.000 abstract description 5
- 230000035939 shock Effects 0.000 description 17
- 239000004973 liquid crystal related substance Substances 0.000 description 16
- 238000010586 diagram Methods 0.000 description 9
- 238000005299 abrasion Methods 0.000 description 4
- 230000007246 mechanism Effects 0.000 description 2
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- 230000009286 beneficial effect Effects 0.000 description 1
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Classifications
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H49/00—Other gearings
- F16H49/001—Wave gearings, e.g. harmonic drive transmissions
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
- Y02P70/10—Greenhouse gas [GHG] capture, material saving, heat recovery or other energy efficient measures, e.g. motor control, characterised by manufacturing processes, e.g. for rolling metal or metal working
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Abstract
The invention discloses an E-tooth type speed reducer, a generalized tooth form generating method and a tooth form designing method, wherein the tooth form of a steel tooth of the harmonic speed reducer is of an inward concave circular arc shape, rolling bodies are arranged in the circular arc of the steel tooth, and are in shape engagement with flexible gear teeth, so that the flexible gear teeth and the steel gear teeth are in pure rolling engagement through the rolling bodies. The rolling body can be a rigid member such as a roller, a steel ball and the like, the outer surface of the cam can be in an elliptical shape, an arc shape, a logarithmic spiral line shape and the like, and all teeth can be engaged by designing the tooth shape of the special flexible gear teeth through the design method provided by the invention, so that the bearing capacity of the special flexible gear teeth is stronger. Generalized tooth form generation method generalized tooth form design includes general formulas of external surface shapes of cams of different types. And discloses a tooth shape design method for calculating according to the shape of the outer surface of the cam to obtain a specific tooth shape. So that different tooth shapes can be obtained according to different cams, and the change rule of the pressure angle is also different. The smaller the pressure angle, the stronger the load carrying capacity.
Description
Technical Field
The invention relates to the field of speed reducers, in particular to an E-tooth-shaped speed reducer, a generalized tooth shape generating method and a tooth shape design method.
Background
The speed reducer is an important component in the mechanical industry, and the transmission performance of the speed reducer directly influences the production efficiency, the working performance and the product quality of the machine. However, the modern high-precision transmission mechanism has limited bearing capacity and low precision service life, so that the transmission performance of the transmission mechanism is inevitably influenced, and the requirements of the industrial production on the precision service life and the bearing capacity cannot be met at the same time. The harmonic gear drive speed reducer (harmonic speed reducer) is a new type speed reducer developed by utilizing planetary gear drive principle, and is formed from fixed internal tooth rigid gear, flexible gear and wave generator capable of making the flexible gear produce radial deformation.
This transmission is essentially different from the typical gear transmission, and has specificity in terms of meshing theory, set calculation, and structural design. Compared with the common speed reducer, the harmonic gear speed reducer has the advantages of high precision, high bearing capacity and the like, and the volume and the weight of the speed reducer are reduced by at least 1/3 due to the fact that the used materials are reduced by 50 percent. Specific techniques can be found in [1] Wang Guxu, yuan Pan, li Junyang, etc. Harmonic drive tooth profile research based on different meshing principles [ J ]. University of science and technology (natural science edition), 2017 (45): 58-64, and [2] Yang Yong, wang Guxu, zhou Qinghua, etc. the elliptic cam wave generator zero backlash harmonic drive conjugate tooth profile accurately solves [ J ]. University of south China (natural science edition), 2017.
In practice, it can be found that abrasion is easy to occur in the process of meshing the flexible gear teeth and the steel gear teeth of the existing harmonic speed reducer, so that the transmission precision of the speed reducer is reduced, and the precision life of the speed reducer is affected. And the harmonic reducer can not realize that all teeth participate in meshing, so that the bearing capacity is affected.
Disclosure of Invention
In order to solve the problems, the main purpose of the invention is to provide an E-tooth reducer which can realize that all teeth participate in meshing and has stronger bearing capacity. The second aim is to provide an E-tooth-shaped speed reducer which can reduce friction and abrasion loss and has tooth-shaped design and structure and application thereof.
In order to achieve the above purpose, the invention provides an E-tooth-shaped speed reducer, a generalized tooth shape generating method and a tooth shape designing method, wherein the tooth shape of a steel tooth of the harmonic speed reducer is in an inward concave circular arc shape, rolling bodies are arranged in the circular arc of the steel tooth, and the rolling bodies are in shape engagement with flexible gear teeth, so that the flexible gear teeth and the steel gear teeth are in pure rolling engagement through the rolling bodies. The rolling bodies can be rollers, steel balls and the like, and the outer surface of the cam can be elliptical, circular arc, logarithmic spiral and the like. The invention can realize that all teeth participate in meshing, so the bearing capacity is stronger. Generalized tooth form generation method generalized tooth form design includes general formulas of external surface shapes of cams of different types. And discloses a tooth shape design method for calculating according to the shape of the outer surface of the cam to obtain a specific tooth shape. So that different tooth shapes can be obtained according to different cams, and the change rule of the pressure angle is also different. The smaller the pressure angle, the stronger the load carrying capacity.
The outer surface of the cam in the invention can be elliptical, or can be arc, logarithmic spiral, etc. Different tooth shapes can be obtained according to different cams, and the change rule of the pressure angle is also different. The smaller the pressure angle, the stronger the load carrying capacity.
The invention has the beneficial effects that the invention discloses a generalized tooth form generating method and a structure obtained by the method; an E-tooth reduction gear is disclosed, in which rolling elements are mounted on a steel wheel and then in rolling contact with a flexspline tooth by means of the rolling elements.
By means of the technical scheme, the steel wheel tooth shape is designed into the concave arc shape, rolling bodies (rollers, steel balls and the like) are arranged in the arc shape, the rolling bodies are meshed with the flexible gear tooth shape, and the steel wheel tooth shape is purely rolling, so that friction force is reduced, and abrasion loss is reduced. The invention can realize that all teeth participate in meshing, so the bearing capacity is stronger. In addition, the outer surface of the cam can be elliptical, arc, logarithmic spiral and the like. Different tooth shapes can be obtained according to different cams, the change rule of the pressure angle is also different, and the smaller the pressure angle is, the stronger the bearing capacity is.
Drawings
FIG. 1 is a schematic diagram of tooth form generation;
FIG. 2 is a diagram of the logarithmic spiral shock wave principle of an E-tooth reducer of the invention;
FIG. 3 logarithmic spiral;
FIG. 4 is a schematic side cross-sectional view of an E-tooth reduction gear of the present invention;
FIG. 5 is a front view of an E-tooth reduction gear of the present invention;
FIG. 6 is a schematic view of a flexspline of an E-tooth reduction gear of the present invention;
FIG. 7 is a schematic end view of a housing of an E-tooth reduction gear of the present invention;
FIG. 8 is a schematic diagram of an elliptic shock wave of an E-tooth reducer of the present invention;
FIGS. 9a-f are schematic diagrams of an elliptical shock wave profile for an E-tooth speed reducer of the present invention;
FIG. 10 is a schematic diagram of a circular shock wave of an E-tooth speed reducer of the present invention;
FIGS. 11a-E are schematic illustrations of the circular shock tooth profile of an E-tooth speed reducer of the present invention;
FIGS. 12a-E are schematic diagrams of logarithmic spiral shock wave profiles of an E-tooth reduction gear of the present invention;
FIGS. 13a-E are cycloidal tooth profiles of an E-tooth reduction gear of the present invention;
FIG. 14 is a schematic view of an embodiment of an E-tooth reduction gear with a steel wheel;
wherein:
the device comprises a positioning shaft 1, a flexible gear 2, a bolt 3, a cross bearing 4, a screw 5, a shell 6, a baffle ring 7, a needle roller 8, a flexible bearing 9, an input shaft 10, a retainer ring 11, a baffle 12, an input shaft 13, a steel gear 14, a flexible gear 15 and a flexible bearing 16.
Detailed Description
The technical scheme of the invention is further specifically described below through examples and with reference to the accompanying drawings.
In view of the defect of the prior harmonic speed reducer when the flexible gear teeth are meshed with the steel gear teeth, the invention designs the steel gear teeth into an inward concave arc shape, installs rolling bodies (rollers, steel balls and the like) in the arc, and then makes the combined movement become pure rolling by virtue of the shape meshing of the rolling bodies and the flexible gear teeth, thereby reducing friction force and abrasion loss.
In order to enable all teeth to participate in meshing, special design is needed for the tooth shape of the flexible gear tooth, and the invention further discloses a tooth shape generating method and a tooth shape designing method of the structure.
In the structure, the outer surface of the cam can be elliptical, arc, logarithmic spiral and the like, and different tooth shapes can be obtained according to different cams, and the change rule of the pressure angle is also different. The invention discloses a generalized tooth form generating method and a specific tooth form design method of an E tooth form speed reducer aiming at different cam outer surfaces. The tooth profile generating method of the present invention derives the overall route according to the generalized tooth profile design, while the cam (input shaft 10) adopts different outer surface shapes, so that the external expressions are different, the specific deriving process is also different, and different design methods are required. The steel wheel, the flexible wheel and the cam have one-to-one correspondence, and the cam rotates to push the teeth on the flexible wheel to be meshed with the needle rollers on the steel wheel, so that the speed reducer can rotate in a decelerating way.
1. Generalized tooth form generating method
Fig. 1 is a schematic diagram of tooth form generation, and the theoretical tooth form of the outer surface of the flexspline is:
wherein ρ (θ) is the sagittal diameter of the tooth shape, ε is the angle through which the sagittal diameter rotates, and θ is the angle through which the sagittal diameter rotates relative to the input axis. θ is solved according to
Wherein phi is the angle of rotation of the output end relative to the input shaft, S c Is the distance that point B moves along the outer surface of the cam.
The curvature formula is
Deriving theoretical tooth form coordinates
The actual tooth form equation is
Wherein r is the offset distance,
the actual tooth form is an E tooth form.
The pressure angle is the included angle between the common normal line of the point on the actual tooth profile curve and the circumferential direction, and the pressure angle formula is as follows
Wherein, l= (x 2 +y 2 ) 0.5 X and y are coordinates of points on the theoretical tooth profile curve,x s 、y s is the coordinates of the points on the actual profile curve.
The present invention will be described in further detail with reference to the accompanying drawings. The following examples of application of the method are illustrative of the invention and are not intended to limit the scope of the invention.
2. The invention relates to a tooth shape design of an E tooth shape speed reducer
When the outer cylindrical surface of the cam (input shaft 10) is a logarithmic spiral, the schematic is shown in fig. 2 and 3.
A digital helix shock wave, and a theoretical tooth form equation is
When theta is as d When=0, the coordinate point is (x 1 、y 1 ) The method comprises the steps of carrying out a first treatment on the surface of the When theta is as d When =pi/2, the coordinate point is (x 2 、y 2 ). The intersection point of the common normal line at the two points is (x) 0 、y 0 )。
ρ L (θ d ) The following is shown
Wherein R is a Length parameter, k index parameter.
θ d The relation with beta is as follows
Wherein R is the radius of a circle of equal length to the logarithmic spiral on the shock wave device.
P L (θ d ) Middle beta derivation, get
For theta d The first derivative and the second derivative of beta are obtained
Wherein, the liquid crystal display device comprises a liquid crystal display device,
θ and θ d Relationship between
Wherein l 1 ＝[(x 1 -x 0 ) 2 +(y 1 -y 0 ) 2 ] 0.5 ， X d1 ＝x d -x 1 ，Y d1 ＝y d -y 1 H=flo (2θ/pi), flo represents a maximum integer not greater than 2θ/pi, and h=1+flo (θ/pi-0.5).
The sagittal ρ (θ) is
ρ(θ)＝((x d -x 0 ) 2 +(y d -y 0 ) 2 ) 0.5
First and second derivatives of θ to β
Wherein, the liquid crystal display device comprises a liquid crystal display device,
ρ L (θ d ) The derivative of beta is
The derivative of ρ (θ) to β is
Wherein x is d0 ＝x d -x 0 ，y d0 ＝y d -y 0 。
The curvature of the tooth form, the actual tooth form and the pressure angle can be obtained according to the formula.
3. The invention relates to a structural design of an E-shaped gear reducer
As shown in fig. 4 to 7, the E-shaped reducer of the present invention comprises a positioning shaft 1, a flexible gear 2, a bolt 3, a cross bearing 4, a screw 5, a housing 6, a baffle ring 7, a needle roller 8, a flexible bearing 9, an input shaft 10, a retainer ring 11 and a baffle 12;
the flexible bearing 9 is arranged on the outer surface of the input shaft 10, the flexible bearing 9 is arranged in the flexible gear 2, the cross bearing 4 is fixed on the end surface of the shell 6 through the screw 5, the flexible gear 2 is fixed on the end surface of the cross bearing 4 through the bolt 3, and the coaxiality of the flexible gear 2 and the cross bearing 4 is ensured through the positioning shaft 1; the inner surface of the shell 6 is provided with a cylindrical surface, a plurality of arc groove teeth (steel gear teeth) are processed on the inner cylindrical surface of the inner surface of the shell 6, and the needle roller 8 is arranged in the arc groove teeth; the outer surface of the flexible gear 2 is provided with a cylindrical surface, a plurality of E-shaped teeth with logarithmic spiral reference circles are machined on the cylindrical surface of the outer surface of the flexible gear 2, and the needle roller 8 is meshed with the teeth on the flexible gear 2; the outer surface of the input shaft 10 is a logarithmic spiral curve; the baffle 12 limits the axial movement of the needle roller 8, and the baffle ring 7 limits the radial and axial movement of the needle roller 8.
Wherein, the cylindrical surface of the inner surface of the shell 6 is processed with Z 1 A diameter d 1 The arc groove teeth Z 1 The circular arc groove teeth are uniformly distributed on a circle with the radius R, and the diameter d is arranged in the circular arc groove r And d is equal to r <d 1 ，d r /2>r。
Wherein, a Z is processed on the cylindrical surface of the outer surface of the flexible gear 2 2 The E tooth shape meets the requirement of Z 1 >Z 2 Or Z is 1 ＝Z 2 Or Z is 1 <Z 2 ；
The input shaft 10 rotates, the input shaft 10 pushes the flexible gear 2 to deform through the flexible bearing 9, the flexible gear 2 pushes the needle rollers 8, the needle rollers 8 react with the flexible gear 2, the flexible gear 2 rotates at a low speed under the pushing of the input shaft 10 and the limiting effect of the needle rollers 8, the needle rollers 8 slide in the arc grooves, the flexible gear 2 drives the inner ring of the cross bearing 4 to rotate, the power of the output shaft is outputted, and the speed reduction motion of the speed reducer is realized.
Ratio of transmission
Referring to fig. 12, a diagram of the logarithmic spiral shock wave tooth profile of an E-tooth type speed reducer according to the present invention is shown.
4. Specific application examples of the invention
Index k=arcot 93 °, needle count Z 1 Number of teeth Z =100 2 =98, logarithmic spiral base circle R a ＝31.284mm。
The cylindrical surface of the inner surface of the shell 6 is processed with 100 arc groove teeth with the diameter of 1.34mm, the 100 arc groove teeth are uniformly distributed on a circle with the radius of 32.653mm, and the arc groove is internally provided with a needle roller 8 with the diameter of 1.32 mm;
the cylindrical surface of the outer surface of the flexible gear 2 is processed with 98E-shaped teeth, and the E-shaped teeth are obtained according to a deduction formula.
The transmission ratio i= -49.
The tooth form is shown in fig. 12a. The pressure angle is as in fig. 12b, the pressure angle minimum is less than 20 °, less than the minimum pressure angle in cycloidal tooth form (fig. 13 b), and significantly less than the pressure angle of tooth form employing elliptical shock waves (fig. 11 b). Therefore, the E-tooth reducer adopting logarithmic spiral shock waves has excellent performance.
5. The E-shaped reducer adopts the tooth shape design of elliptical shock waves
Referring to fig. 1, the theoretical tooth profile of the outer surface of the flexspline using elliptical shock waves is:
wherein, the liquid crystal display device comprises a liquid crystal display device,ε＝θ-φ，/>a is an elliptic long half shaft, b is an elliptic short half shaft, and the transmission ratio i=z 1 /(Z 1 -Z 2 ) θ is solved according to
Wherein, the liquid crystal display device comprises a liquid crystal display device,φ∈[0,Z 1 π)。
the curvature formula is
Deriving equation (2) to obtain derivative of θ to φ
Wherein a= (ρ (θ)) 2 +(ρ d (θ)) 2
The derivative of ρ (θ) to φ is
ρ d The derivative of (θ) to φ is
Deriving phi in formula (1)
Bringing the formulas (4) to (12) into the formula (3) to obtain a tooth-shaped curvature formula;
the actual tooth form equation is
Wherein, the liquid crystal display device comprises a liquid crystal display device,
pressure angle
Wherein, l= (x 2 +y 2 ) 0.5 ，r is the offset distance.
Z 1 ＝100、Z 1 ＝98、e＝0.5、S 2 ＝0.5、r＝0.5、R 1 Tooth profile, etc. are shown in fig. 9 =30.
6. The E-shaped reducer adopts the tooth shape design of circular shock waves
When the outer cylindrical surface of the cam is round, the schematic diagram is shown in fig. 10.
Where ε=θ - φ, ρ (θ) is the polar diameter. Transmission ratio i=z 1 /(Z 1 -Z 2 ) ρ (θ) is as follows
Wherein e is the eccentricity, h is half-width, R 1 Is a circular arc radius. θ is as follows
Wherein S is 1 Is thatS 2 BC, h is OC, < >>φ∈[0,Z 1 π)。
The curvature formula is
Deriving equation (3) to obtain derivative of θ to φ
Wherein, the liquid crystal display device comprises a liquid crystal display device, S h ＝S 1 +S 2 ，/>
the derivative of ρ (θ) to φ is
Deriving phi in formula (1)
And (3) bringing the formula (4) to the formula (12) into the formula (3) to obtain a tooth-shaped curvature formula. The actual tooth form equation is
Wherein, the liquid crystal display device comprises a liquid crystal display device,
pressure angle
Wherein, l= (x 2 +y 2 ) 0.5 ，r is the offset distance.
Z 1 ＝100、Z 1 ＝98、e＝0.5、S 2 ＝0.5、r＝0.5、R 1 Tooth profile, etc. are shown in fig. 11 =30.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
pressure angle
Wherein, l= (x 2 +y 2 ) 0.5 ，r is the offset distance.
The tooth form is shown in fig. 11a. The pressure angle is shown in fig. 11b, where the pressure angle minimum is significantly smaller than the pressure angle of the E-profile using an elliptical shock wave (fig. 11 b). Therefore, the E-tooth-shaped speed reducer adopting the circular shock wave has better performance.
7. The invention relates to a structural design of an E-shaped reducer, which adopts a steel wheel with logarithmic spiral shock waves as E-shaped teeth
The tooth shape of the steel wheel II 14 of the harmonic speed reducer is an E tooth shape, the tooth shape of the flexible gear is a convex arc curve, and the tooth shape of the steel wheel E tooth shape is meshed with the arc tooth of the flexible gear. The structure is shown in fig. 14.
The outer surface of the input shaft II 13 is a logarithmic spiral curve.
Wherein, the cylindrical surface of the inner surface of the steel wheel II 14 is processed with Z 3 E tooth shape teeth, flexible gear II 15 and Z 4 And each arc tooth is meshed with the E-tooth-shaped tooth, and all the teeth participate in meshing.
The number of teeth satisfies Z 3 >Z 4 Or Z is 3 ＝Z 4 Or Z is 3 <Z 4 。
The input shaft II 13 rotates, the input shaft II 13 pushes the flexible gear II 15 to deform through the flexible bearing II 16, the circular arc teeth of the flexible gear II 15 act on the E-shaped teeth on the inner surface of the steel gear II 14, the flexible gear II 15 rotates at a low speed under the pushing of the input shaft II 13 and the limiting effect of the E-shaped teeth, and the output shaft rotates to realize the speed reduction motion of the speed reducer.
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made to the specific embodiments of the present invention without departing from the spirit and scope of the present invention, and all modifications and equivalents are intended to be included in the scope of the claims of the present invention.
Claims (4)
1. A generalized tooth form generating method of an E tooth form speed reducer is characterized in that the tooth form generating theory tooth form of a flexible gear is as follows:
wherein ρ (θ) is the sagittal diameter of the tooth, ε is the angle through which the sagittal diameter rotates, θ is the angle through which the sagittal diameter rotates relative to the input shaft; θ is solved according to
Wherein phi is the rotation angle of the output end relative to the input shaft, sc is the moving distance of the point B along the outer surface of the cam;
the curvature formula is
Deriving theoretical tooth form coordinates
The actual tooth form equation is
Wherein r is the offset distance,
the actual tooth form is an E tooth form;
the pressure angle is the included angle between the common normal line of the point on the actual tooth profile curve and the circumferential direction, and the pressure angle formula is as follows
Wherein, l= (x 2 +y 2 ) 0.5 X and y are coordinates of points on the theoretical tooth profile curve,x s 、y s is the coordinates of the points on the actual profile curve.
2. An E-tooth reduction gear as claimed in claim 1, comprising:
the device comprises a positioning shaft (1), a flexible gear (2), a bolt (3), a cross bearing (4), a shell (6), a needle roller (8), a flexible bearing (9) and an input shaft (10);
the flexible bearing (9) is arranged on the outer surface of the input shaft (10), the flexible bearing (9) is arranged in the flexible gear (2), the cross bearing (4) is fixed on the end surface of the shell (6), the flexible gear (2) is fixed on the end surface of the cross bearing (4), the coaxiality of the flexible gear (2) and the cross bearing (4) is ensured through the positioning shaft (1), the inner surface of the shell (6) is provided with a cylindrical surface, a plurality of circular arc groove teeth are processed on the inner cylindrical surface of the inner surface of the shell (6), rolling bodies are arranged in the circular arc groove teeth, the outer surface of the flexible gear (2) is provided with a cylindrical surface, a plurality of teeth with elliptical reference circles are processed on the cylindrical surface of the outer surface of the flexible gear (2), the rolling bodies are meshed with the teeth on the flexible gear (2), and the outer surface of the input shaft (10) is an elliptical curved surface;
when the input shaft (10) rotates, the input shaft (10) pushes the flexible gear (2) to deform through the flexible bearing (9), the flexible gear (2) pushes the rolling bodies, the rolling bodies react to the flexible gear (2), the flexible gear (2) rotates at a low speed under the pushing of the input shaft (10) and the limiting action of the rolling bodies, the rolling bodies slide and roll in the arc grooves, the flexible gear (2) drives the inner ring of the cross bearing (4) to rotate, and the power of the output shaft is utilized to realize the decelerating motion of the speed reducer.
3. An E-tooth reduction gear according to claim 1, wherein: the cylindrical surface of the inner surface of the shell (6) is processed with Z 1 A diameter d 1 Arc groove tooth Z of (2) 1 The circular arc groove teeth are uniformly distributed on a circle with the radius of R, and the diameter of the rolling body installed in the circular arc groove is d r And d is as follows r <d 1 ，d r /2>r，
Wherein, Z is processed on the cylindrical surface of the outer surface of the flexible gear (2) 2 Each said tooth and meets Z 1 >Z 2 Or Z is 1 ＝Z 2 Or Z is 1 <Z 2 ；
Ratio of transmission
4. An E tooth-shaped speed reducer is a harmonic speed reducer, the tooth shape of a steel gear of the harmonic speed reducer is a concave circular arc shape, rolling bodies are arranged in the circular arc of the steel gear, the rolling bodies are meshed with flexible gear teeth in a shape, and the flexible gear teeth and the steel gear teeth are in pure rolling meshing through the rolling bodies, and the E tooth-shaped speed reducer is characterized in that the teeth of the flexible gear are arranged by adopting the following method:
the shape generating theoretical tooth shape is as follows:
wherein ρ (θ) is the sagittal diameter of the tooth, ε is the angle through which the sagittal diameter rotates, θ is the angle through which the sagittal diameter rotates relative to the input shaft; θ is solved according to
Wherein phi is the rotation angle of the output end relative to the input shaft, sc is the moving distance of the point B along the outer surface of the cam;
the curvature formula is
Deriving theoretical tooth form coordinates
The actual tooth form equation is
Wherein r is the offset distance,
the pressure angle is the included angle between the common normal line of the point on the actual tooth profile curve and the circumferential direction, and the pressure angle formula is as follows
Wherein, l= (x 2 +y 2 ) 0.5 X and y are coordinates of points on the theoretical tooth profile curve,x s 、y s is the coordinates of the points on the actual profile curve.
Priority Applications (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111205214.9A CN113969968B (en) | 2021-10-15 | 2021-10-15 | E-tooth-shaped speed reducer, generalized tooth shape generation method and tooth shape design method |
| CN202310970375.XA CN116906531A (en) | 2021-10-15 | 2021-10-15 | Elliptic shock wave E-shaped tooth-shaped speed reducer and tooth shape design method thereof |
| CN202310970387.2A CN116989116A (en) | 2021-10-15 | 2021-10-15 | Tooth shape design method of logarithmic spiral shock wave E tooth shape speed reducer and speed reducer thereof |
| CN202310970376.4A CN116733932A (en) | 2021-10-15 | 2021-10-15 | Circular shock wave E-shaped tooth-shaped speed reducer and tooth shape design method thereof |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111205214.9A CN113969968B (en) | 2021-10-15 | 2021-10-15 | E-tooth-shaped speed reducer, generalized tooth shape generation method and tooth shape design method |
Related Child Applications (3)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310970387.2A Division CN116989116A (en) | 2021-10-15 | 2021-10-15 | Tooth shape design method of logarithmic spiral shock wave E tooth shape speed reducer and speed reducer thereof |
| CN202310970375.XA Division CN116906531A (en) | 2021-10-15 | 2021-10-15 | Elliptic shock wave E-shaped tooth-shaped speed reducer and tooth shape design method thereof |
| CN202310970376.4A Division CN116733932A (en) | 2021-10-15 | 2021-10-15 | Circular shock wave E-shaped tooth-shaped speed reducer and tooth shape design method thereof |
Publications (2)
| Publication Number | Publication Date |
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| CN113969968A CN113969968A (en) | 2022-01-25 |
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| CN202111205214.9A Active CN113969968B (en) | 2021-10-15 | 2021-10-15 | E-tooth-shaped speed reducer, generalized tooth shape generation method and tooth shape design method |
| CN202310970387.2A Pending CN116989116A (en) | 2021-10-15 | 2021-10-15 | Tooth shape design method of logarithmic spiral shock wave E tooth shape speed reducer and speed reducer thereof |
| CN202310970375.XA Pending CN116906531A (en) | 2021-10-15 | 2021-10-15 | Elliptic shock wave E-shaped tooth-shaped speed reducer and tooth shape design method thereof |
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| CN202310970375.XA Pending CN116906531A (en) | 2021-10-15 | 2021-10-15 | Elliptic shock wave E-shaped tooth-shaped speed reducer and tooth shape design method thereof |
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106641183A (en) * | 2016-12-28 | 2017-05-10 | 重庆大学 | Design method of harmonic drive rack approximation tooth profile |
| CN107588177A (en) * | 2017-09-28 | 2018-01-16 | 深圳市领略数控设备有限公司 | A kind of cycloidal-pin wheel harmonic drive |
| CN207261609U (en) * | 2017-09-28 | 2018-04-20 | 深圳市领略数控设备有限公司 | A kind of cycloidal-pin wheel harmonic drive |
| CN113374852A (en) * | 2021-05-24 | 2021-09-10 | 温州大学 | Movable tooth harmonic speed reducer |
-
2021
- 2021-10-15 CN CN202310970376.4A patent/CN116733932A/en active Pending
- 2021-10-15 CN CN202111205214.9A patent/CN113969968B/en active Active
- 2021-10-15 CN CN202310970387.2A patent/CN116989116A/en active Pending
- 2021-10-15 CN CN202310970375.XA patent/CN116906531A/en active Pending
Patent Citations (4)
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|---|---|---|---|---|
| CN106641183A (en) * | 2016-12-28 | 2017-05-10 | 重庆大学 | Design method of harmonic drive rack approximation tooth profile |
| CN107588177A (en) * | 2017-09-28 | 2018-01-16 | 深圳市领略数控设备有限公司 | A kind of cycloidal-pin wheel harmonic drive |
| CN207261609U (en) * | 2017-09-28 | 2018-04-20 | 深圳市领略数控设备有限公司 | A kind of cycloidal-pin wheel harmonic drive |
| CN113374852A (en) * | 2021-05-24 | 2021-09-10 | 温州大学 | Movable tooth harmonic speed reducer |
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| 渐开线谐波齿轮空间齿廓设计及优化分析;吴鸿雁;机械传动;全文 * |
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| CN116989116A (en) | 2023-11-03 |
| CN113969968A (en) | 2022-01-25 |
| CN116733932A (en) | 2023-09-12 |
| CN116906531A (en) | 2023-10-20 |
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Application publication date: 20220125 Assignee: ZHEJIANG ZHONGXING EQUIPMENT Co.,Ltd. Assignor: Wenzhou University Contract record no.: X2024330000006 Denomination of invention: An E-tooth reducer, generalized tooth generation method, and tooth design method Granted publication date: 20230829 License type: Common License Record date: 20240116 |