CN113969968A - E-shaped tooth speed reducer, generalized tooth form generation method and tooth form design method - Google Patents

E-shaped tooth speed reducer, generalized tooth form generation method and tooth form design method Download PDF

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CN113969968A
CN113969968A CN202111205214.9A CN202111205214A CN113969968A CN 113969968 A CN113969968 A CN 113969968A CN 202111205214 A CN202111205214 A CN 202111205214A CN 113969968 A CN113969968 A CN 113969968A
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tooth
theta
tooth form
formula
flexible
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CN113969968B (en
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杨荣刚
杨涛
鲍肖剑
徐贤广
王乃格
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Wenzhou University
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Wenzhou University
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Priority to CN202310970376.4A priority patent/CN116733932A/en
Priority to CN202310970375.XA priority patent/CN116906531A/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
    • F16H55/08—Profiling
    • 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
    • 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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  • General Engineering & Computer Science (AREA)
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  • Gears, Cams (AREA)

Abstract

The invention discloses an E-shaped reducer, a generalized tooth form generation method and a tooth form design method. 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 shape and the like, and all teeth can be engaged by designing the specific flexible gear tooth profile by the design method provided by the invention, so that the bearing capacity of the flexible gear is stronger. Generalized tooth profile generation methods generalized tooth profile designs include generic formulas for different cam outer surface shapes. And discloses a tooth profile design method for obtaining a specific tooth profile by calculation according to the shape of the outer surface of the cam. So that different tooth forms can be obtained according to different cams, and the change law of the pressure angle is different. The smaller the pressure angle, the stronger the load bearing capacity.

Description

E-shaped tooth speed reducer, generalized tooth form generation method and tooth form design method
Technical Field
The invention relates to the field of speed reducers, in particular to an E-shaped tooth speed reducer, a generalized tooth form generating method and a tooth form design method.
Background
The reducer is an important component in the mechanical industry, and the transmission performance of the reducer directly influences the production efficiency, the working performance and the product quality of the machine. However, because the bearing capacity of the modern high-precision transmission mechanism is limited, the precision life is short, the transmission performance is inevitably influenced, and the requirements on the precision life and the bearing capacity in industrial production cannot be met simultaneously. The harmonic gear drive speed reducer (harmonic speed reducer) is a new 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 flexible gear produce radial deformation.
The transmission is essentially different from the ordinary gear transmission, and has particularity in the aspects of meshing theory, collective calculation and structural design. The harmonic gear reducer has the advantages of high precision, high bearing capacity and the like, and compared with a common reducer, the volume and the weight of the harmonic gear reducer are reduced by at least 1/3 due to the fact that 50% less materials are used. The specific techniques can be found in [1] Wangjia preface, Yuan Pan, Lijunyang, etc. Research on harmonic drive tooth profiles based on different meshing principles [ J ]. university of China university of science (Nature science edition), 2017(45):58-64 ] and [2] Yangyong, Wangjiaji, Zhouyanhua, and the like.
In practice, it can be found that abrasion is easily generated in the meshing process of the flexible gear teeth and the steel gear teeth of the conventional harmonic reducer, so that the transmission precision of the reducer is reduced, and the precision service life of the reducer is influenced. And the harmonic reducer can not realize that all teeth participate in meshing, influences bearing capacity.
Disclosure of Invention
In order to solve the above problems, the present invention provides an E-tooth reducer that can realize engagement of all teeth and has a strong bearing capacity. Secondly, the purpose is to provide a tooth form design and structure capable of reducing friction force and abrasion loss and an E-shaped tooth form speed reducer applied by the tooth form design and structure.
In order to achieve the purpose, the invention provides an E-shaped tooth speed reducer, a generalized tooth shape generating method and a tooth shape designing method. The rolling body can be a roller, a steel ball and the like, and the outer surface of the cam can be in an oval shape, an arc shape, a logarithmic spiral shape and the like. The invention can realize that all the teeth participate in the meshing, so the bearing capacity is stronger. Generalized tooth profile generation methods generalized tooth profile designs include generic formulas for different cam outer surface shapes. And discloses a tooth profile design method for obtaining a specific tooth profile by calculation according to the shape of the outer surface of the cam. So that different tooth forms can be obtained according to different cams, and the change law of the pressure angle is different. The smaller the pressure angle, the stronger the load bearing capacity.
The outer surface of the cam of the invention can be in an elliptical shape, a circular arc shape, a logarithmic spiral shape and the like. Different tooth forms can be obtained according to different cams, and the pressure angle change law is also different. The smaller the pressure angle, the stronger the load bearing capacity.
The invention has the beneficial effects that the invention discloses a generalized tooth profile generation method and a structure obtained according to the method; disclosed is an E-tooth type speed reducer in which a rolling body is mounted on a steel wheel and then is brought into rolling contact with a flexible gear tooth by means of the rolling body.
By means of the technical scheme, the tooth form of the steel wheel is designed to be concave arc-shaped, the rolling bodies (the roller, the steel ball and the like) are arranged in the arc, and are meshed with the tooth form of the flexible wheel and roll purely, so that the friction force is reduced, and the abrasion loss is reduced. The invention can realize that all the teeth participate in the meshing, so the bearing capacity is stronger. In addition, the outer surface of the cam can be in an elliptical shape, an arc shape, a logarithmic spiral shape and the like. Different tooth forms can be obtained according to different cams, the pressure angle change rule is different, and the smaller the pressure angle is, the stronger the bearing capacity is.
Drawings
FIG. 1 is a schematic diagram of tooth profile generation;
FIG. 2 is a logarithmic spiral shock wave schematic diagram of an E-tooth reducer according to the present invention;
FIG. 3 is a logarithmic spiral;
FIG. 4 is a schematic side sectional view of an E-tooth form of the present invention;
FIG. 5 is a front view of an E-tooth form of the present invention;
FIG. 6 is a schematic diagram of a flexspline of an E-tooth reducer of the present invention;
FIG. 7 is a schematic view of the end face of the casing of the E-tooth reducer of the present invention;
FIG. 8 is an elliptical shock wave diagram of an E-tooth reducer according to the present invention;
FIGS. 9a-f are schematic views of the elliptical shock profiles of the E-shaped tooth form reducer according to the present invention;
FIG. 10 is a schematic diagram of a circular shock wave of an E-tooth reducer according to the present invention;
FIGS. 11a-E are schematic views of the circular shock profile of an E-profile reducer of the present invention;
FIGS. 12a-E are schematic diagrams of logarithmic spiral shock profiles of an E-profile reducer according to the present invention;
FIGS. 13a-E are schematic views of the cycloid tooth profile of an E-tooth reducer of the present invention;
FIG. 14 is a schematic view of an embodiment of a reducer with an E-tooth-shaped steel wheel;
wherein:
the flexible roller comprises a positioning shaft 1, a flexible gear 2, a bolt 3, a crossed bearing 4, a screw 5, a shell 6, a retaining ring 7, a rolling needle 8, a flexible bearing 9, an input shaft 10, a retaining ring 11, a retaining plate 12, an input shaft 13 II, a steel gear 14 II, a flexible gear 15 II and a flexible bearing 16 II.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
In view of the defects of the conventional harmonic reducer when the flexible gear teeth are meshed with the steel gear teeth, the invention designs the steel gear teeth into an inwards concave arc shape, installs rolling bodies (rollers, steel balls and the like) in the arc, and then changes the combined motion into pure rolling by means of the meshing of the rolling bodies and the flexible gear teeth, thereby reducing the friction force and reducing the abrasion loss.
In order to enable all the teeth to participate in meshing, the tooth form of the flexible gear teeth needs to be specially designed, and therefore the invention further discloses a tooth form generation method and a tooth form design method of the structure.
In the structure, the outer surface of the cam can be in an elliptical shape, an arc shape, a logarithmic spiral shape and the like, different tooth shapes can be obtained according to different cams, and the pressure angle change rule is different. Therefore, the invention discloses a generalized tooth profile generation method and a specific tooth profile design method of an E-shaped tooth profile speed reducer aiming at different cam outer surfaces. In the tooth profile generation method, the derivation overall route is designed according to the generalized tooth profile, and the cams (input shafts 10) adopt different outer surface shapes, so that the appearance expressions are different, the specific derivation process is different, and different design methods are required. The steel wheel, the flexible wheel and the cam are in one-to-one correspondence, and the cam rotates to push the upper teeth of the flexible wheel to be meshed with the upper roller needles of the steel wheel, so that the speed reduction rotation of the speed reducer is realized.
1. Generalized tooth profile generation method
Fig. 1 is a schematic diagram of tooth profile generation, and the theoretical tooth profile of the outer surface of the flexible gear is as follows:
Figure RE-GDA0003429821360000041
wherein rho (theta) is the sagittal diameter of the tooth profile, epsilon is the angle rotated by the sagittal diameter, and theta is the angle rotated by the sagittal diameter relative to the input shaft. Theta is solved according to the following formula
Figure RE-GDA0003429821360000042
Wherein phi is the rotating angle of the output end relative to the input shaft,Scis the distance point B moves along the outer surface of the cam.
The formula of curvature is
Figure RE-GDA0003429821360000051
Derivation of theoretical tooth form coordinate
Figure RE-GDA0003429821360000052
Figure RE-GDA0003429821360000053
The actual tooth profile equation is
Figure RE-GDA0003429821360000054
Wherein r is an offset distance,
Figure RE-GDA0003429821360000055
the actual tooth profile is an E-tooth profile.
The pressure angle is the included angle between the common normal line of the points on the actual tooth profile curve and the circumferential direction, and the pressure angle formula is as follows
Figure RE-GDA0003429821360000056
Wherein, l ═ x2+y2)0.5X and y are coordinates of points on the theoretical tooth profile curve,
Figure RE-GDA0003429821360000057
xs、 ysthe 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, to which the process is applied, are intended to illustrate the invention, but are not intended to limit the scope of the invention.
2. The invention relates to a tooth profile design of an E-shaped tooth profile speed reducer
When the outer cylindrical surface of the cam (input shaft 10) is a logarithmic spiral, the schematic diagram is shown in fig. 2 and 3.
Is a number of spiral shock waves, and the theoretical tooth form equation is
Figure RE-GDA0003429821360000061
When theta isdWhen 0, the coordinate point is (x)1、y1) (ii) a When theta isdWhen pi/2, the coordinate point is (x)2、y2). The intersection point of the common normal lines at the two points is (x)0、y0)。
ρL(θd) As shown below
Figure RE-GDA0003429821360000062
Wherein R isaLength parameter, k-index parameter.
θdThe relationship with β is as follows
Figure RE-GDA0003429821360000063
Wherein R is the radius of a circle with the same length as the log-spiral on the shock wave device.
For rhoL(θd) Derivation of middle beta to obtain
Figure RE-GDA0003429821360000064
To thetadThe first derivative and the second derivative of beta are calculated to obtain
Figure RE-GDA0003429821360000065
Wherein,
Figure RE-GDA0003429821360000066
theta and thetadThe relationship between
Figure RE-GDA0003429821360000067
Wherein l1＝[(x1-x0)2+(y1-y0)2]0.5，
Figure RE-GDA0003429821360000068
Figure RE-GDA0003429821360000069
Xd1＝xd-x1，Yd1＝yd-y1H ═ flo (2 θ/π), flo denotes the largest integer no greater than 2 θ/π, H ═ 1+ flo (θ/π -0.5).
Vector rho (theta) of
ρ(θ)＝((xd-x0)2+(yd-y0)2)0.5
First and second derivatives of beta with respect to theta
Figure RE-GDA0003429821360000071
Wherein,
Figure RE-GDA0003429821360000072
Figure RE-GDA0003429821360000073
ρL(θd) Derivative to beta is
Figure RE-GDA0003429821360000074
Figure RE-GDA0003429821360000075
The derivative of ρ (θ) with respect to β is
Figure RE-GDA0003429821360000076
Wherein x isd0＝xd-x0，yd0＝yd-y0。
The curvature, actual tooth profile and pressure angle of the tooth profile can be obtained according to the formula.
3. The invention relates to a structural design of an E-shaped reducer
As shown in fig. 4 to 7, the E-tooth reducer of the present invention includes a positioning shaft 1, a flexible gear 2, a bolt 3, a crossed bearing 4, a screw 5, a housing 6, a retainer 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 crossed bearing 4 is fixed on the end surface of the shell 6 through a screw 5, the flexible gear 2 is fixed on the end surface of the crossed bearing 4 through a bolt 3, and the coaxiality of the flexible gear 2 and the crossed 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 rolling needles 8 are 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 reference circles being logarithmic spiral lines are processed 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 surface; the baffle plate 12 limits the axial movement of the roller pin 8, and the retaining ring 7 limits the radial and axial movement of the roller pin 8.
Wherein, the cylindrical surface of the inner surface of the shell 6 is processed with Z1Has a diameter of d1Said circle ofArc groove teeth, Z1The arc groove teeth are uniformly distributed on a circle with the radius of R, and the arc groove is internally provided with a circle with the diameter of drAnd the needle roller 8, and dr<d1，dr/2>r。
Wherein, a cylindrical surface of the outer surface of the flexible gear 2 is processed with Z2Each of the E-shaped teeth satisfies Z1>Z2Or Z1＝Z2Or Z1<Z2；
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 roller pin 8, the roller pin 8 reacts on the flexible gear 2, the flexible gear 2 rotates at a low speed under the pushing action of the input shaft 10 and the limiting action of the roller pin 8, the roller pin 8 rolls in the arc groove in a sliding mode, the flexible gear 2 drives the inner ring of the crossed bearing 4 to rotate, and the power of an output shaft realizes the speed reduction movement of the speed reducer.
Transmission ratio
Figure RE-GDA0003429821360000081
Referring to fig. 12, it is a schematic diagram of logarithmic spiral shock wave tooth profile of the E-shaped tooth reducer according to the present invention.
4. Specific application example of the invention
Index k is arccot93 DEG, needle number Z1Number of teeth Z equal to 100298, base circle of logarithmic spiral Ra＝31.284mm。
The cylindrical surface of the inner surface of the shell 6 is provided 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 roller pin 8 with the diameter of 1.32 mm;
the cylindrical surface of the outer surface of the flexible gear 2 is provided with 98E-shaped teeth, and the E-shaped teeth are obtained according to a derived formula.
The transmission ratio i is-49.
The tooth profile is as shown in fig. 12 a. The pressure angle is as in fig. 12b, with the minimum value of the pressure angle being less than 20 deg., less than the minimum pressure angle in a cycloid tooth profile (fig. 13b), and significantly less than the pressure angle of a tooth profile with an elliptical shock wave (fig. 11 b). Therefore, the E-tooth reducer using the logarithmic spiral shock wave has excellent performance.
5. The invention relates to a tooth profile design of an E-shaped tooth speed reducer by adopting elliptical shock waves
Referring to fig. 1, the theoretical tooth profile of the outer surface of the flexspline using the elliptical shock wave is:
Figure RE-GDA0003429821360000091
wherein,
Figure RE-GDA0003429821360000092
ε＝θ-φ，
Figure RE-GDA0003429821360000093
a is a major semi-axis of the ellipse, b is a minor semi-axis of the ellipse, and the transmission ratio i is equal to Z1/(Z1-Z2) θ is solved according to
Figure RE-GDA0003429821360000094
Wherein,
Figure RE-GDA0003429821360000095
φ∈[0,Z1π)。
the formula of curvature is
Figure RE-GDA0003429821360000096
By taking the derivative of equation (2), the derivative of theta to phi can be obtained
Figure RE-GDA0003429821360000097
Figure RE-GDA0003429821360000101
Wherein, A is (rho (theta))2+(ρd(θ))2
The derivative of ρ (θ) with respect to φ is
Figure RE-GDA0003429821360000102
Figure RE-GDA0003429821360000103
ρdThe derivative of (theta) with respect to phi is
Figure RE-GDA0003429821360000104
Derivation of phi in equation (1)
Figure RE-GDA0003429821360000105
Figure RE-GDA0003429821360000106
Figure RE-GDA0003429821360000107
Figure RE-GDA0003429821360000108
Substituting the formula (4) to the formula (12) into the formula (3) to obtain a tooth-shaped curvature formula;
the actual tooth profile equation is
Figure RE-GDA0003429821360000109
Wherein,
Figure RE-GDA00034298213600001010
angle of pressure
Figure RE-GDA00034298213600001011
Wherein, l ═ x2+y2)0.5，
Figure RE-GDA0003429821360000111
r is the offset distance.
Z1＝100、Z1＝98、e＝0.5、S2＝0.5、r＝0.5、R1The tooth profile and the like are shown in fig. 9 at 30.
6. The invention relates to a tooth profile design of an E-shaped tooth speed reducer by adopting circular shock waves
When the outer cylindrical surface of the cam is round, the schematic diagram is shown in fig. 10.
Figure RE-GDA0003429821360000112
Where ∈ θ - Φ, ρ (θ) is the pole diameter. Transmission ratio i ═ Z1/(Z1-Z2) ρ (θ) is as follows
Figure RE-GDA0003429821360000113
Wherein e is eccentricity, h is half width, R1Is the radius of the arc. Theta is as follows
Figure RE-GDA0003429821360000114
Wherein S is1Is composed of
Figure RE-GDA0003429821360000115
S2Is BC, h is OC,
Figure RE-GDA0003429821360000116
φ∈[0,Z1π)。
the formula of curvature is
Figure RE-GDA0003429821360000117
By taking the derivative of equation (3), the derivative of theta to phi can be obtained
Figure RE-GDA0003429821360000121
Wherein,
Figure RE-GDA0003429821360000122
Figure RE-GDA0003429821360000123
Sh＝S1+S2，
Figure RE-GDA0003429821360000124
Figure RE-GDA0003429821360000125
the derivative of ρ (θ) with respect to φ is
Figure RE-GDA0003429821360000126
Derivation of phi in equation (1)
Figure RE-GDA0003429821360000127
Figure RE-GDA0003429821360000128
Figure RE-GDA0003429821360000129
Figure RE-GDA0003429821360000131
Substituting the equations (4) to (12) into the equation (3) can obtain the tooth profile curvature equation. The actual tooth profile equation is
Figure RE-GDA0003429821360000132
Wherein,
Figure RE-GDA0003429821360000133
angle of pressure
Figure RE-GDA0003429821360000134
Wherein, l ═ x2+y2)0.5，
Figure RE-GDA0003429821360000135
r is the offset distance.
Z1＝100、Z1＝98、e＝0.5、S2＝0.5、r＝0.5、R1The tooth profile and the like are shown in fig. 11 at 30.
Wherein,
Figure RE-GDA0003429821360000136
angle of pressure
Figure RE-GDA0003429821360000137
Wherein, l ═ x2+y2)0.5，
Figure RE-GDA0003429821360000138
r is the offset distance.
The tooth profile is as shown in fig. 11 a. Pressure angle as in fig. 11b, the minimum pressure angle is significantly smaller than the pressure angle of the E-tooth profile using elliptical shock waves (fig. 11 b). Therefore, the E-tooth reducer using the circular shock wave has excellent performance.
7. The invention relates to a structural design of an E-shaped tooth speed reducer adopting a steel wheel with logarithmic spiral shock waves as an E-shaped tooth
The tooth form of the steel wheel II 14 of the harmonic reducer is E tooth form, the tooth form of the flexible wheel is a convex circular arc curve, and the E tooth form tooth of the steel wheel is meshed with the circular arc tooth of the flexible wheel. The structure is shown in fig. 14.
The outer surface of the input shaft II 13 is a logarithmic spiral curve surface.
Wherein, a cylindrical surface on the inner surface of the steel wheel II 14 is processed with Z3Each E tooth-shaped tooth, flexible gear II 15 plus Z4And the circular arc teeth are meshed with the E-shaped teeth, and all the teeth participate in meshing.
The number of teeth satisfies Z3>Z4Or Z3＝Z4Or Z3<Z4。
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 action of the input shaft II 13 and the limiting action of the E-shaped teeth, and the output shaft rotates to realize the speed reduction motion of the speed reducer.
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 various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention.

Claims (10)

1. A generalized tooth form generation method of an E-shaped tooth form speed reducer is characterized in that a tooth form generation theoretical tooth form of a flexible gear is as follows:
Figure FDA0003306614130000011
wherein rho (theta) is the sagittal diameter of the tooth profile, epsilon is the angle rotated by the sagittal diameter, and theta is the angle rotated by the sagittal diameter relative to the input shaft; theta is solved according to the following formula
Figure FDA0003306614130000012
Phi is the rotating angle of the output end relative to the input shaft, and Sc is the moving distance of the point B along the outer surface of the cam;
the formula of curvature is
Figure FDA0003306614130000013
Derivation of theoretical tooth form coordinate
Figure FDA0003306614130000014
Figure FDA0003306614130000015
The actual tooth profile equation is
Figure FDA0003306614130000016
Wherein r is an offset distance,
Figure FDA0003306614130000017
the actual tooth form is an E tooth form;
the pressure angle is the included angle between the common normal line of the points on the actual tooth profile curve and the circumferential direction, and the pressure angle formula is as follows
Figure FDA0003306614130000018
Wherein, l ═ x2+y2)0.5X and y are coordinates of points on the theoretical tooth profile curve,
Figure FDA0003306614130000019
xs、ysthe coordinates of the points on the actual profile curve.
2. A tooth form design method of an E-shaped tooth form speed reducer is characterized in that,
when the E-shaped tooth-shaped speed reducer adopts logarithmic spiral line laser, the theoretical tooth-shaped equation is
Figure FDA0003306614130000021
When theta isdWhen 0, the coordinate point is (x)1、y1) (ii) a When theta isdWhen pi/2, the coordinate point is (x)2、y2)；
The intersection point of the common normal lines at the two points is (x)0、y0)；
ρL(θd) As shown below
Figure FDA0003306614130000022
Wherein R isaLength parameter, k-index parameter;
θdthe relationship with β is as follows
Figure FDA0003306614130000023
Wherein R is the radius of a circle with the same length as the log spiral on the shock wave device;
for rhoL(θd) Derivation of middle beta to obtain
Figure FDA0003306614130000024
To thetadThe first derivative and the second derivative of beta are calculated to obtain
Figure FDA0003306614130000025
Wherein,
Figure FDA0003306614130000026
theta and thetadThe relationship between
Figure FDA0003306614130000031
Wherein l1＝[(x1-x0)2+(y1-y0)2]0.5，
Figure FDA0003306614130000032
Figure FDA0003306614130000033
Xd1＝xd-x1，Yd1＝yd-y1H ═ flo (2 θ/pi), flo denotes the largest integer no greater than 2 θ/pi, H ═ 1+ flo (θ/pi-0.5);
vector rho (theta) of
ρ(θ)＝((xd-x0)2+(yd-y0)2)0.5
First and second derivatives of beta with respect to theta
Figure FDA0003306614130000034
Wherein,
Figure FDA0003306614130000035
Figure FDA0003306614130000036
ρL(θd) Derivative to beta is
Figure FDA0003306614130000037
Figure FDA0003306614130000038
The derivative of ρ (θ) with respect to β is
Figure FDA0003306614130000039
Wherein x isd0＝xd-x0，yd0＝yd-y0；
And obtaining the curvature and the pressure angle of the flexible gear tooth form according to the formula, wherein the actual tooth form obtained according to the formula is an E tooth form.
3. The design method of the E-shaped tooth reducer according to claim 2, characterized by comprising the following steps:
the tooth form of the steel wheel tooth of the harmonic reducer is E tooth form, the flexible wheel tooth is a convex circular arc curve, and the E tooth form tooth of the steel wheel is meshed with the circular arc tooth of the flexible wheel.
4. A tooth form design method of an E-shaped tooth form speed reducer is characterized in that when the E-shaped tooth form speed reducer adopts an elliptic laser, the theoretical tooth form of the outer surface of a flexible gear is as follows:
Figure FDA0003306614130000041
wherein,
Figure FDA0003306614130000042
a is a major semi-axis of the ellipse, b is a minor semi-axis of the ellipse, and the transmission ratio i is equal to Z1/(Z1-Z2) θ is solved according to
Figure FDA0003306614130000043
Wherein,
Figure FDA0003306614130000044
φ∈[0,Z1π)；
the formula of curvature is
Figure FDA0003306614130000045
By taking the derivative of equation (2), the derivative of theta to phi can be obtained
Figure FDA0003306614130000046
Figure FDA0003306614130000051
Wherein, A is (rho (theta))2+(ρd(θ))2
The derivative of ρ (θ) with respect to φ is
Figure FDA0003306614130000052
Figure FDA0003306614130000053
ρdThe derivative of (theta) with respect to phi is
Figure FDA0003306614130000054
Derivation of phi in equation (1)
Figure FDA0003306614130000055
Figure FDA0003306614130000056
Figure FDA0003306614130000057
Figure FDA0003306614130000058
Substituting the formula into the formula (3) to obtain a tooth-shaped curvature formula;
the actual tooth profile equation is
Figure FDA0003306614130000059
Wherein,
Figure FDA00033066141300000510
the actual tooth profile obtained according to the formula is an E tooth profile;
pressure angle:
Figure FDA0003306614130000061
wherein, l ═ x2+y2)0.5，
Figure FDA0003306614130000062
r is the offset distance.
5. A tooth form design method of an E-shaped tooth form speed reducer is characterized in that when the E-shaped tooth form speed reducer adopts circular laser, the outer cylindrical surface of a cam is a circle, and the theoretical tooth form equation is
Figure FDA0003306614130000063
Where ∈ θ - Φ, ρ (θ) is the pole diameter. Transmission ratio i ═ Z1/(Z1-Z2) ρ (θ) is as follows
Figure FDA0003306614130000064
Wherein e is eccentricity, h is half width, R1Is the radius of a circular arc; theta is as follows
Figure FDA0003306614130000065
Wherein S is1Is composed of
Figure FDA0003306614130000066
S2Is BC, h is OC,
Figure FDA0003306614130000067
φ∈[0,Z1π)；
the formula of curvature is
Figure FDA0003306614130000068
Derivative of theta to phi can be obtained by differentiating theta
Figure FDA0003306614130000071
Wherein,
Figure FDA0003306614130000072
Figure FDA0003306614130000073
Sh＝S1+S2，
Figure FDA0003306614130000074
Figure FDA0003306614130000075
the derivative of ρ (θ) with respect to φ is
Figure FDA0003306614130000076
Derivation of phi in theoretical tooth profile equation
Figure FDA0003306614130000077
Figure FDA0003306614130000078
Figure FDA0003306614130000079
Figure FDA0003306614130000081
Substituting the above into the curvature formula can obtain the tooth-shaped curvature formula. The actual tooth profile equation is
Figure FDA0003306614130000082
Wherein,
Figure FDA0003306614130000083
the actual tooth profile obtained according to the formula is an E tooth profile;
pressure angle:
Figure FDA0003306614130000084
wherein, l ═ x2+y2)0.5，
Figure FDA0003306614130000085
r is the offset distance.
6. The utility model provides a E profile of tooth reduction gear, is the harmonic reduction gear, the steel wheel tooth profile of harmonic reduction gear is indent arc to install the rolling element in the circular arc of steel wheel tooth, the rolling element meshes with the flexbile gear profile of tooth, makes the flexbile gear teeth and steel teeth of a cogwheel pass through the rolling element becomes pure rolling meshing, its characterized in that, the tooth of flexbile gear adopts following method setting:
the theoretical tooth profile generated by the shape is as follows:
Figure FDA0003306614130000086
wherein rho (theta) is the sagittal diameter of the tooth profile, epsilon is the angle rotated by the sagittal diameter, and theta is the angle rotated by the sagittal diameter relative to the input shaft; theta is solved according to the following formula
Figure FDA0003306614130000087
Phi is the rotating angle of the output end relative to the input shaft, and Sc is the moving distance of the point B along the outer surface of the cam;
the formula of curvature is
Figure FDA0003306614130000091
Derivation of theoretical tooth form coordinate
Figure FDA0003306614130000092
Figure FDA0003306614130000093
The actual tooth profile equation is
Figure FDA0003306614130000094
Wherein r is an offset distance,
Figure FDA0003306614130000095
the pressure angle is the included angle between the common normal line of the points on the actual tooth profile curve and the circumferential direction, and the pressure angle formula is as follows
Figure FDA0003306614130000096
Wherein, l ═ x2+y2)0.5X and y are coordinates of points on the theoretical tooth profile curve,
Figure FDA0003306614130000097
xs、ysthe coordinates of the points on the actual profile curve.
7. An E-tooth reducer according to claim 1, including:
the flexible roller bearing comprises a positioning shaft (1), a flexible gear (2), a bolt (3), a cross bearing (4), a shell (6), a roller pin (8), a flexible bearing (9) and an input shaft (10);
the flexible gear comprises a flexible bearing (9), a cross bearing (4), a flexible gear (2), a positioning shaft (1), a flexible gear (2), a cylindrical surface, a plurality of circular arc groove teeth, rolling bodies, a cylindrical surface, a plurality of teeth with reference circles being elliptic, and a plurality of teeth meshed with the teeth on the flexible gear (2), wherein the flexible bearing (9) is arranged on the outer surface of an input shaft (10), the cross bearing (4) is fixed on the end surface of a shell (6), the flexible gear (2) is fixed on the end surface of the cross bearing (4), and the coaxiality of the flexible gear (2) and the cross bearing (4) is ensured by the positioning shaft (1);
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 body, the rolling body reacts on the flexible gear (2), the flexible gear (2) rotates at a low speed under the pushing action of the input shaft (10) and the limiting action of the rolling body, the rolling body rolls in the arc groove in a sliding mode, the flexible gear (2) drives the inner ring of the crossed bearing (4) to rotate, power is output, and the speed reduction motion of the speed reducer is achieved.
8. An E-tooth reducer as claimed in claim 2 in which the rolling bodies are rigid needles or balls.
9. The E-shaped tooth reducer according to claim 2, characterized in that the E-shaped tooth reducer further comprises a retainer ring (11), a baffle plate (12), a screw (5), a bolt (3) and a retainer ring (7), wherein the cross bearing (4) is fixed on the end face of the shell (6) through the screw (5); the flexible gear (2) is fixed on the end surface of the crossed bearing (4) through a bolt (3); the baffle (12) limits the axial movement of the rolling body, and the baffle ring (7) limits the radial and axial movement of the rolling body.
10. An E-tooth reducer as set forth in claim 1 in which: the cylindrical surface of the inner surface of the shell (6) is processed with Z1Has a diameter of d1The circular arc groove teeth, Z1The arc groove teeth are uniformly distributed on a circle with the radius of R, and the rolling bodies arranged in the arc grooves have the diameter of drAnd a needle roller (8) ofr<d1。，dr/2>r，
Wherein, a cylindrical surface of the outer surface of the flexible gear (2) is processed with Z2Each of the teeth, and satisfies Z1>Z2Or Z1＝Z2Or Z1<Z2；
Transmission ratio
Figure FDA0003306614130000101
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