CN111853158B - Conical internal meshing line gear mechanism, construction method thereof and simulation verification method - Google Patents

Conical internal meshing line gear mechanism, construction method thereof and simulation verification method Download PDF

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CN111853158B
CN111853158B CN202010676919.8A CN202010676919A CN111853158B CN 111853158 B CN111853158 B CN 111853158B CN 202010676919 A CN202010676919 A CN 202010676919A CN 111853158 B CN111853158 B CN 111853158B
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conical
gear
cylindrical pinion
line
tooth profile
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CN111853158A (en
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何恩义
何迪
叶喜葱
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China Three Gorges University CTGU
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/02—Toothed gearings for conveying rotary motion without gears having orbital motion
    • F16H1/04—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members
    • F16H1/12—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes
    • F16H1/125—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes comprising spiral gears
    • 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
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0853—Skewed-shaft arrangement of the toothed members
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/20—Design optimisation, verification or simulation

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Abstract

The invention provides a conical inner meshing line gear mechanism which comprises a cylindrical pinion and a conical gear ring, wherein the cylindrical pinion and the conical gear ring form a gear pair, the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees. Meanwhile, a construction method of the conical inner engaged line gear mechanism is also provided, and comprises the following steps: step one, establishing a gear coordinate system; step two, establishing a contact line between the cylindrical pinion and the conical gear ring; step three, selecting the radius of the tooth profile of the cylindrical pinionρ 1 Radius of tooth profile of conical gear ringρ 2 And contact angleφ(ii) a And step four, sweeping the tooth profile of the cylindrical pinion along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the tooth profile of the conical spiral line along the conical spiral line to obtain spiral concave teeth. The mechanism can realize the 0 degree included angle of the transmission shaft<θ<90 degrees, and provides an inner meshing linear gear mechanism which has a simple structure and small volume and can realize forward and reverse continuous stable transmission.

Description

Conical internal meshing line gear mechanism, construction method thereof and simulation verification method
Technical Field
The invention belongs to the field of gear transmission, and particularly relates to a conical internal meshing line gear mechanism, a construction method thereof and an analog simulation verification method.
Background
Gears are important basic elements in mechanical transmission, and have been widely applied to the fields of aerospace vehicles, new energy equipment, high-speed rails, ships and the like. At present, gear mechanisms based on the conjugate curved surface meshing theory have been widely used, such as spur gears, helical gears, worm gears, herringbone gears, and the like. The gear can realize high power, large transmission ratio, high-power movement and power transmission. With the rapid development of industrial production in the current society, micro-electromechanical products are sought by consumers. The miniature electromechanical product puts forward the requirements of small occupied space, light weight, stable transmission and the like on the transmission mechanism, and the development of the gear meshing theory is promoted.
In recent years, scholars at home and abroad have studied a novel gear mechanism suitable for a micromachine. For example, chinese patent application No. 200810029646.0 discloses "a space curve meshing transmission mechanism", application No. 201110009692.2 discloses "a parallel multi-output shaft micro transmission", patent No. 201210449290.9 discloses "a space staggered shaft gear mechanism". The gear mechanisms are all linear gear mechanisms based on the space curve meshing theory and mainly comprise a driving wheel and a driven wheel, hook rods are uniformly distributed on the driving wheel and the driven wheel, and stable transmission is realized by means of the engagement of the hook rods.
Although the line gear mechanism can realize continuous and stable transmission in a small space, the gear teeth are hook rods in convex contact, so that the tooth surface contact strength is low and the lubrication is difficult; in addition, the hook rod and the gear matrix form a cantilever beam structure, so that the hook rod of the linear gear pair is easy to deform in the meshing process, and even the hook rod is easy to break. These drawbacks result in a limited range of applications for the line gear mechanism, mostly for light load conditions.
Disclosure of Invention
The invention aims to solve the technical problem of providing a conical inner meshing line gear mechanism, a construction method and an analog simulation verification method thereof, which can realize the transmission of intersecting shafts at any angle of a transmission shaft included angle of 0 degree < theta <90 degrees, and provide the inner meshing line gear mechanism which has a simple structure and small volume and can realize forward and reverse continuous and stable transmission.
In order to solve the technical problem, the technical scheme adopted by the invention is that the conical internal meshing line gear mechanism comprises a cylindrical pinion and a conical gear ring which form a gear pair, wherein the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees.
In a preferred scheme, spiral convex teeth and spiral concave teeth are respectively distributed on the cylindrical pinion and the conical gear ring, the convex teeth and the concave teeth are meshed, a contact line of the convex teeth is a cylindrical spiral line, and a contact line on the concave teeth is a conical spiral line.
In a further scheme, the convex tooth profile of the cylindrical pinion is formed by a section of circular arc, and the concave tooth profile of the conical gear ring is formed by two symmetrical circular arcs and respectively used as a forward rotation working tooth profile and a reverse rotation working tooth profile.
The invention also provides a construction method of the conical internal meshing line gear mechanism, which comprises the following steps:
step one, establishing a gear coordinate system;
step two, establishing a contact line between the cylindrical pinion and the conical gear ring;
step three, selecting the radius rho of the tooth profile of the cylindrical pinion 1 Tooth profile radius rho of conical gear ring 2 And contact angle
Figure BDA0002584383910000023
And step four, sweeping the tooth profile of the cylindrical pinion along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the tooth profile of the conical gear ring along the conical spiral line to obtain spiral concave teeth.
In a preferred embodiment, in the first step, o-xyz and o-x p y p z p Is a fixed coordinate system, o-x 1 y 1 z 1 And o-x 2 y 2 z 2 Is a coordinate system fixedly connected with the cylindrical pinion and the conical gear ring respectively, xoz and x p o p z p Coplanar; z-axis and z p The axis coinciding with the axes of rotation of the pinion and the ring gear, respectively, the z-axis and the z-axis p The included angle of the axes being theta (0 DEG)<θ<90 degrees is adopted; at the initial moment of engagement, o-xyz and o-x p y p z p Are each independently of o-x 1 y 1 z 1 And o-x 2 y 2 z 2 Overlapping; the cylindrical pinion and the conical ring gear each having an angular velocity ω 1 、ω 1 Around z 0 、z p The shaft rotates at a constant speed, the steering is the same, and the rotating angle is theta after t steps 1 And theta 2 (ii) a The components of the center-to-center distance in the x-axis and z-axis are a, b.
In a preferred embodiment, the contact line parameter equation on the tooth surface of the cylindrical pinion is:
Figure BDA0002584383910000021
calculating a contact line equation of the tooth surface of the conical gear ring according to a space curve meshing equation as follows:
Figure BDA0002584383910000022
in the formula: m-the spiral radius of the cylindrical pinion contact line;
p is the pitch coefficient;
t is the parameter of the helix;
i 1 ,j 1 ,k 1 coordinate system o-x 1 y 1 z 1 The base vector of (2);
i 2 ,j 2 ,k 2 coordinate system o-x 2 y 2 z 2 The base vector of (2);
i 12 -a transmission ratio;
a. b-the components of the center-to-center distances in the x-axis and z-axis;
theta is the angle between the input shaft and the output shaft;
t S 、t E the corresponding values of the contact lines entering and exiting mesh.
In a preferred scheme, the tooth profile radius rho of the convex tooth in the third step 1 Should be less than the tooth profile radius ρ of the concave teeth 2 。
The invention also provides a simulation and verification method of the conical internal meshing line gear mechanism, which guides the assembled conical internal meshing line gear mechanism into a motion simulation module of NX software for performing kinematic simulation and comprises the following steps:
the method comprises the following steps: the cylindrical pinion and the conical gear ring are respectively arranged to be rigid connecting rods L001 and L002;
step two: the kinematic pairs of the cylindrical pinion and the conical gear ring are respectively defined as revolute pairs J001 and J002;
step three: setting a contact mode of the cylindrical pinion and the conical gear ring to be 3D contact;
step four: applying driving force to cylindrical pinion gear with given angular speed of omega 1 ；
Step five: setting a solving scheme to solve, and recording the angular velocity omega of the conical gear ring in the motion process 2 Obtaining an instantaneous angular velocity curve chart;
step six: calculating formula i = ω by transmission ratio 1 /ω 2 The instantaneous transmission ratio during movement is obtained.
The conical internal meshing line gear mechanism and the construction method thereof provided by the invention have the following advantages:
1. the conical internal meshing line gear mechanism has the advantages of compact structure, small volume and light weight, and can realize stable transmission of forward and reverse rotation.
2. The minimum tooth number of the small gear of the conical inner meshing linear gear mechanism can be 1, and the conical inner meshing linear gear mechanism has larger transmission ratio and coincidence ratio compared with the existing inner meshing straight gears and helical gears.
3. Compared with the line gear taking the hook rod as the gear tooth in the early period, the conical internal meshing line gear mechanism has higher tooth surface contact strength and transmission precision and can bear larger load.
4. The invention relates to a conical inner meshing line gear mechanism, wherein a pinion can be used for conical inner meshing line gear pairs with different transmission ratios.
5. The conical inner meshing line gear mechanism has the advantages of simple structure, convenience in manufacturing, good economical efficiency and manufacturability, and can be produced to be used as a micro mechanical transmission mechanism.
Drawings
The invention is further illustrated with reference to the accompanying drawings and examples:
FIG. 1 is a schematic structural view of a tapered internal meshing linear gear mechanism of the present invention;
FIG. 2 is a solid model of a cylindrical pinion;
FIG. 3 is a top view of a solid model of a cylindrical pinion;
FIG. 4 is a front view of a solid model of a cylindrical pinion;
FIG. 5 is a solid model of a bevel ring gear.
FIG. 6 is a phantom elevation view of a bevel ring gear.
FIG. 7 is a cylindrical contact line on a cylindrical pinion and a conical contact line on a conical ring gear;
FIG. 8 is a schematic diagram of a space curve engagement coordinate system in an embodiment;
FIG. 9 is a schematic illustration of the normal profile meshing of a cylindrical pinion gear and a bevel ring gear;
FIG. 10 is a graph of instantaneous angular velocity of a bevel ring gear;
in the figure: the device comprises a driver 1, an input shaft 2, a cylindrical pinion 3, convex teeth 4, concave teeth 5, a conical gear ring 6, a coupling sleeve 7, an output shaft 8, a cylindrical contact line 9 and a conical contact line 10.
Detailed Description
As shown in fig. 1 to 6, a conical inner meshing line gear mechanism includes a cylindrical pinion and a conical ring gear constituting a gear pair, the axis of the cylindrical pinion intersects with the axis of the conical ring gear at an angle of 0 ° to 90 °.
Spiral convex teeth and concave teeth are respectively distributed on the cylindrical pinion and the conical gear ring, the convex teeth and the concave teeth are meshed, contact lines of the convex teeth are cylindrical spiral lines, and contact lines of the concave teeth are conical spiral lines. When one or more pairs of teeth are meshed but not completely disengaged, adjacent teeth are meshed, so that continuous stable transmission of the conical internal meshing linear tooth mechanism in a spatial intersecting axis is realized. The main elements participating in the meshing are the contact lines on the tooth flanks.
The driver is connected with the input shaft, the cylindrical pinion is sleeved on the input shaft, the driver rotates to drive the cylindrical pinion to rotate, the conical gear ring is driven to rotate by the meshing of the convex teeth and the concave teeth, and the conical gear ring drives the output shaft to rotate through the connecting sleeve, so that the stable transmission of the spatial intersecting shafts is realized.
The spiral convex teeth are uniformly distributed on the outer part of the cylindrical base body of the cylindrical pinion, and the tooth width is as follows: b = p Δ t, i.e. B = p (t) E -t S ) The tooth width of the convex tooth is determined by the parameters of the cylindrical contact line, and when the cylindrical contact line is determined, the tooth width of the convex tooth is also determined.
The conical gear ring is uniformly distributed with spiral concave teeth in the conical base body, and the tooth width of the conical gear ring is the same as that of the cylindrical pinion.
The tooth profile shapes of the convex teeth of the cylindrical pinion and the concave teeth of the conical gear ring gear are shown in FIG. 9, and the tooth profile of the convex teeth is that the radius is rho 1 A section of circular arc is cut on the circle of the gear, and the tooth profile of the concave tooth is formed by the radius rho 2 Wherein AB is a positive rotation working tooth profile, CD is a reverse rotation working tooth profile,and vice versa. The positive and negative rotating mesh points are respectively M 1 ，M 2 Contact angle
Figure BDA0002584383910000041
And determining the position of the meshing point on the tooth profile.
Tooth profile radius ρ of convex tooth 1 Should be smaller than the tooth profile radius ρ of the concave teeth 2 。
A construction method of a conical inner engaged line gear mechanism comprises the following steps:
step one, establishing a gear coordinate system, as shown in FIG. 8, o-xyz and o-x p y p z p Is a fixed coordinate system, o-x 1 y 1 z 1 And o-x 2 y 2 z 2 Is a coordinate system fixedly connected with the cylindrical pinion and the conical gear ring respectively, xoz and x p o p z p Coplanar; z axis and z p The axis coinciding with the axis of rotation of the pinion and the bevel gear, respectively, and the z-axis p The included angle of the axes being theta (0 DEG)<θ<90 degrees); at the initial moment of engagement, o-xyz and o-x p y p z p Are each independently of o-x 1 y 1 z 1 And o-x 2 y 2 z 2 Overlapping; the cylindrical pinion and the conical ring gear each having an angular velocity ω 1 、ω 1 Around z 0 、z p The shaft rotates at a constant speed, the steering is the same, and the rotating angle is theta after t steps 1 And theta 2 (ii) a The components of the center-to-center distance in the x-axis and z-axis are a, b.
Step two, establishing a contact line between the cylindrical pinion and the conical gear ring, wherein a contact line parameter equation on the tooth surface of the cylindrical pinion is as follows:
Figure BDA0002584383910000051
calculating a contact line equation of the tooth surface of the conical gear ring according to a space curve meshing equation as follows:
Figure BDA0002584383910000052
in the formula: m-helical radius of the cylindrical pinion contact line;
p-pitch coefficient;
t is the parameter of the helix;
i 1 ,j 1 ,k 1 coordinate system o-x 1 y 1 z 1 The base vector of (2);
i 2 ,j 2 ,k 2 coordinate system o-x 2 y 2 z 2 The base vector of (2);
i 12 -a transmission ratio;
a. b-the components of the center-to-center distances in the x-axis and z-axis;
theta is the angle between the input shaft and the output shaft;
t S 、t E -the respective values of the contact lines entering and exiting the mesh.
When determining the parameters a, b, theta, t S 、t E 、i 12 And m and n rear cylindrical spiral contact lines and conical spiral contact lines can be determined.
Step three, selecting the radius rho of the tooth profile of the cylindrical pinion 1 Tooth profile radius rho of conical gear ring 2 And contact angle
Figure BDA0002584383910000053
When determining the normal profile radius ρ 1 、ρ 2 And contact angle
Figure BDA0002584383910000054
The normal tooth profile shapes of the pinion 3 and the ring gear 6 are also determined.
And step four, sweeping the cylindrical pinion gear tooth profile along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the conical gear tooth profile along the conical spiral line to obtain spiral concave teeth.
According to the transmission ratio i 12 The contact ratio and the actual load determine the number of teeth.
In this embodiment, the values of the relevant parameters are set as follows: θ =30 °, a =12.8mm, b =12mm, m =8mm, p =4mm, ρ 1 ＝1mm，ρ 2 ＝2mm，
Figure BDA0002584383910000055
i 12 ＝3，t S ＝-π/4,t E The gear tooth number is 6, and the contact ratio is 1.5;
substituting equation (1) results in the equation for the line of cylinder contact:
Figure BDA0002584383910000061
substituting equation (2) results in the conic contact line equation:
Figure BDA0002584383910000062
in the same way, different shapes of convex teeth and concave teeth can be obtained by selecting other parameters, wherein the cylindrical pinion is used for the bevel gear pair with the internal meshing line of the bevel gear rings with different transmission ratios.
A simulation and verification method for a conical inner meshing line gear mechanism guides an assembled conical inner meshing line gear mechanism into a motion simulation module of NX software for kinematic simulation, and comprises the following steps:
the method comprises the following steps: the cylindrical pinion and the conical gear ring are respectively arranged to be rigid connecting rods L001 and L002;
step two: the kinematic pairs of the cylindrical pinion and the conical gear ring are respectively defined as revolute pairs J001 and J002;
step three: setting a contact mode of the cylindrical pinion and the gear ring to be 3D contact;
step four: applying a driving force to the cylindrical pinion gear with a given angular velocity of ω 1 In the present embodiment, the angular velocity is 900 °/s;
step five: setting a solving scheme to solve, and recording the angular velocity omega of the conical gear ring in the motion process 2 Obtaining a graph of instantaneous angular velocity, as shown in fig. 10;
step six: calculating formula i = ω by gear ratio 1 /ω 2 The instantaneous transmission ratio during the movement is obtained.
By recording the angular velocity of the bevel ring gear during the movement, an instantaneous velocity change value can be obtained, as shown in table 1,
TABLE 1 angular velocity data
Figure BDA0002584383910000063
Figure BDA0002584383910000071
Angular velocity of cylindrical pinion gear 900 0 The gear ratio of the gear pair is 3, and the angular speed of the conical gear ring should be 300 theoretically 0 And s. As can be seen from fig. 10, the rotation speed of the bevel ring gear is stable, and the angular velocity of the bevel ring gear is always stable at 300 during the movement 0 Around/s. From Table 1, it can be seen that the maximum angular velocity of the bevel ring gear is 302.840 0 S, minimum angular velocity 299.046 0 S, calculating formula i = ω by transmission ratio 1 /ω 2 The instantaneous transmission ratio fluctuates at 2.972-3.010 in the movement process, the change of the transmission ratio of the gear pair is very small, the transmission error is only 0.013, the transmission requirement of the fixed transmission ratio can be met, and the stable transmission of the conical internal meshing line gear mechanism can be realized through simulation experiments.

Claims (6)

1. A construction method of a conical inner meshing line gear mechanism is characterized in that the conical inner meshing line gear mechanism comprises a cylindrical pinion and a conical gear ring which form a gear pair, the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees; the construction method comprises the following steps:
step one, establishing a gear coordinate system;
step two, establishing a contact line between the cylindrical pinion and the conical gear ring, wherein a contact line parameter equation on the tooth surface of the cylindrical pinion is as follows:
Figure FDA0003807352130000011
calculating a contact line equation of the tooth surface of the conical gear ring according to a space curve meshing equation as follows:
Figure FDA0003807352130000012
in the formula: m-the spiral radius of the cylindrical pinion contact line;
p-pitch coefficient;
t is the parameter of the helix;
i 1 ,j 1 ,k 1 coordinate system o-x 1 y 1 z 1 The base vector of (2);
i 2 ,j 2 ,k 2 coordinate system o-x 2 y 2 z 2 The base vector of (2);
i 12 -a transmission ratio;
a. b-the components of the center-to-center distances in the x-axis and z-axis;
theta is the angle between the input shaft and the output shaft;
t S 、t E -the contact lines enter into engagement and exit from engagement with corresponding values;
step three, selecting the radius rho of the tooth profile of the cylindrical pinion 1 Tooth profile radius rho of conical gear ring 2 And a contact angle phi;
and step four, sweeping the cylindrical pinion gear tooth profile along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the conical gear tooth profile along the conical spiral line to obtain spiral concave teeth.
2. The method of claim 1 for constructing a conical internal gear-line gear mechanism, wherein: in the first step, o-xyz and o-x p y p z p Is a fixed coordinate system, o-x 1 y 1 z 1 And o-x 2 y 2 z 2 Is a coordinate system fixedly connected with the cylindrical pinion and the conical gear ring respectively, xoz and x p o p z p Coplanar; z axisAnd z p The axis coincides with the axis of rotation of the cylindrical pinion and the conical ring gear, respectively, the z-axis and the z-axis p The included angle of the axes being theta (0 DEG)<θ<90 degrees is adopted; at the initial moment of engagement, o-xyz and o-x p y p z p Are each independently of o-x 1 y 1 z 1 And o-x 2 y 2 z 2 Overlapping; the cylindrical pinion and the conical ring gear each having an angular velocity ω 1 、ω 1 Around z 0 、z p The shaft rotates at a constant speed, the steering is the same, and the rotating angle is theta after t steps 1 And theta 2 (ii) a The components of the center-to-center distances in the x-axis and z-axis are a, b.
3. The method for constructing a conical internal engaged wire gear mechanism according to claim 1, wherein in the second step, helical convex teeth and helical concave teeth are uniformly distributed on the cylindrical pinion and the conical gear ring respectively, the convex teeth and the concave teeth are engaged, the contact line of the convex teeth is a cylindrical spiral line, and the contact line of the concave teeth is a conical spiral line.
4. The method for constructing a tapered internal-meshing-line gear mechanism according to claim 3, wherein the convex tooth profile of the cylindrical pinion is formed by a section of circular arc, and the concave tooth profile of the tapered ring gear is formed by two symmetrical circular arcs and is respectively used as a forward rotation working tooth profile and a reverse rotation working tooth profile.
5. The method of claim 1 wherein the tooth profile radius p of the raised teeth of step three is 1 Should be less than the tooth profile radius ρ of the concave teeth 2 。
6. A simulation and verification method for a conical internal meshing line gear mechanism is characterized in that the conical internal meshing line gear mechanism constructed according to the construction method of the conical internal meshing line gear mechanism of any one of claims 1 to 5 is led into a motion simulation module of NX software to carry out kinematic simulation, and comprises the following steps:
the method comprises the following steps: the cylindrical pinion and the conical gear ring are respectively arranged to be rigid connecting rods L001 and L002;
step two: the kinematic pairs of the cylindrical pinion and the conical gear ring are respectively defined as revolute pairs J001 and J002;
step three: setting a contact mode of the cylindrical pinion and the conical gear ring to be 3D contact;
step four: applying driving force to cylindrical pinion gear with given angular speed of omega 1 ；
Step five: setting a solving scheme to solve, and recording the angular velocity omega of the conical gear ring in the motion process 2 Obtaining an instantaneous angular velocity curve chart;
step six: calculating formula i = ω by gear ratio 1 /ω 2 The instantaneous transmission ratio during movement is obtained.
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CN101372100A (en) * 2007-08-24 2009-02-25 曹伟明 Gear type power transmission of three-head rotating shaver
RU2592032C1 (en) * 2015-03-31 2016-07-20 Закрытое акционерное общество "МНИТИ" (ЗАО "МНИТИ") Radial conical gear
CN105202152B (en) * 2015-09-11 2019-04-02 重庆大学 Multi-contact conical gear Meshing Pair based on conjugate curves
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