CN113757310B - Light-weight parallel axis gear pair mechanism - Google Patents
Light-weight parallel axis gear pair mechanism Download PDFInfo
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- CN113757310B CN113757310B CN202110944242.6A CN202110944242A CN113757310B CN 113757310 B CN113757310 B CN 113757310B CN 202110944242 A CN202110944242 A CN 202110944242A CN 113757310 B CN113757310 B CN 113757310B
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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
- 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
- F16H1/06—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with parallel axes
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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
- F16H1/20—Toothed gearings for conveying rotary motion without gears having orbital motion involving more than two intermeshing members
- F16H1/206—Toothed gearings for conveying rotary motion without gears having orbital motion involving more than two intermeshing members characterised by the driving or driven member being composed of two or more gear wheels
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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
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/17—Toothed wheels
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- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Gear Transmission (AREA)
- Gears, Cams (AREA)
Abstract
The invention discloses a light-weight parallel axis gear pair mechanism. The mechanism consists of a pair of light-weight parallel axis gear pairs, wherein the line teeth of the driving wheel and the line teeth of the driven wheel of the light-weight parallel axis gear pairs are in point contact meshing transmission, and the contact line of the line teeth is designed according to the space conjugate curve meshing theory. In the mechanism, the spiral radius of the contact line of the driving line gear and the driven line gear is irrelevant to the transmission ratio of the gear pair, different line gear pairs with the same outer diameter size can have different transmission ratios, and the transmission with large transmission ratio can be realized in a limited space.
Description
Technical Field
The invention relates to the field of mechanical transmission, in particular to a light wire gear mechanism based on space conjugate curve meshing.
Background
In the industries of machinery, automobiles, toys and the like, the application of the speed changer is quite wide, and the main function of the speed changer is to change the transmission ratio and realize the functions of different speeds and torque transmission from an input shaft to an output shaft.
The gear transmission has the advantages of stable transmission, high transmission efficiency, good reliability, compact structure and the like, and is one of the most widely applied transmissions.
In a gear transmission, a gear pair is a core component of the gear transmission.
In the gear pair transmission, a large transmission ratio can be obtained in a limited space or the volume of the gear pair can be reduced under a given transmission ratio, and the gear pair belongs to a lightweight design of gears. The weight reduction of gears is one of the important development directions of gears.
The light gear pair is widely used for various gear reducers and is applied to various electromechanical products such as machinery, automobiles, toys, electric tools and the like.
The structure weight reduction is the main direction of the design of the gear weight reduction.
The structure of the gear is light and mainly comprises two development directions: on the one hand, the size and the volume of the gear are reduced; on the other hand, the speed reducer is designed as a specific drive train such as a small tooth difference planetary gear speed reducer, a harmonic gear speed reducer and the like. In addition, the design of the gear module and the deflection gear is reduced, and the involute gear with small size can be obtained.
The linear gear is a novel gear which uses space curve meshing theory to replace traditional space curve meshing theory, is mainly applied to the field of micro transmission, and has the advantages of small size, large transmission ratio, convenient manufacture and the like. Wire gears can be currently used for transmission on vertical shafts, intersecting shafts and staggered shafts, and research on design equations, coincidence degrees, strength criteria, micro-speed variators, manufacturing fields and the like of the wire gears have been perfected, and the minimum number of teeth of the wire gears can be 1.
In a small-sized reduction gear device, there is a demand for a lightweight design of a gear pair.
For the traditional involute gear, the transmission ratio of a single-stage involute gear pair is overlarge, and the size of a large gear is large; the number of parts is increased as the gear shift number of the multi-stage gear reducer is increased; the planetary gear reducer with small tooth difference and the harmonic gear reducer have complex structures and high internal gear processing difficulty.
Involute gear reducers composed of involute gears have some limitations in the process of lightweight design. The traditional involute gear reducer has the defects of large number of gears, large number of teeth of a single involute gear, large processing difficulty of a small-module gear and an internal gear, and limitation of light weight design of an involute gear pair.
Disclosure of Invention
The invention provides a design scheme of a light-weight parallel axis gear pair based on a linear gear theory, and the linear gear pair mechanism designed by the method can realize the transmission of a single-stage gear pair with a large transmission ratio in a limited space.
The technical scheme adopted by the invention is as follows.
The light parallel axis gear pair mechanism consists of a pair of light parallel axis gear pairs, wherein each light parallel axis gear pair consists of a driving wire gear and a driven wire gear, and each driving wire gear and each driven wire gear consist of a wire gear wheel body and wire teeth.
Further, the contact line of the line teeth of the light-weight parallel axis gear pair is in point contact engagement, and the contact line of the line teeth is designed according to the space conjugate curve engagement theory.
Further, the driving contact line and the driven contact line of the light-weight parallel axis gear pair are equal-pitch cylindrical spiral lines, and the transmission ratio of the line gear pair is equal to the pitch value of the driven contact line divided by the pitch value of the driving contact line.
Further, the spiral radius of the contact line of the driving line gear and the driven line gear of the light-weight parallel axis gear pair is irrelevant to the transmission ratio of the gear pair, and different line gear pairs with the same outer diameter size have different transmission ratios.
Further, the external diameter of the wire gear of the light-weight parallel axis gear pair can still be designed under the given condition, and the transmission ratio of the light-weight parallel axis gear pair can be realized in a limited space.
Further, the two contact lines of the light parallel axis gear pair are designed, and for a pair of line gear pairs with a given transmission ratio, the smaller the spiral angle of the designed driving contact line is, the larger the pressure angle of the line gear pair is, and when the pressure angle is larger than the maximum value of the pressure angle of the selected gear material, the gear pair can realize the self-locking function.
Furthermore, the thicknesses of the driving wire teeth and the driven wire teeth of the wire gear pair are designed, so that the function of no side gap in forward and reverse rotation of the wire gear pair is realized.
Further, the wire teeth of the light-weight parallel axis gear pair are distributed circumferentially around the gear axis, and the size of each wire tooth is consistent.
Further, the lightweight parallel axis gear pair can be designed in a given space; specifically, as shown in fig. 4 and fig. 5, under the condition that the outer diameter sizes of the driving wire gear and the driven wire gear are given, the contact lines on the driving wire gear and the driven wire gear can be designed, so that the functions of different transmission ratios are realized.
Further, the light-weight parallel axis gear pair forms a multi-stage gear pair, and is assembled into the light-weight parallel axis gear reducer.
Further, the light-weight parallel axis gear pair has a fixed slip ratio, which is beneficial to forming stable lubrication conditions.
Further, the driving wheel is connected with the driver to provide input, and one or more wire teeth on the driving wheel are distributed in a circumferential array; the wire teeth of the driving wheel are meshed with the wire teeth of the driven wheel through point contact; the driven wheel is connected with the output end to provide motion or force output, and the line teeth on the driven wheel are provided with a plurality of line teeth and are distributed in a circumferential array.
Further, in the light-weight parallel axis gear pair mechanism, the contact line for meshing on the line teeth of the driving wheel is a spatial constant-pitch cylindrical spiral line; the contact line for meshing on the line teeth of the driven wheel is a spatial constant-pitch cylindrical spiral line. The gear ratio of the light-weight parallel axis gear pair is equal to the pitch value of the driven contact line divided by the pitch value of the driving contact line.
Further, in the light-weight parallel axis gear pair mechanism, the wire teeth of the driving wheel are circumferentially distributed; the wire teeth of the driven wheel are circumferentially distributed.
Further, in the light-weight parallel axis gear pair mechanism, the transmission ratio of the line gear pair is equal to the number of line teeth of the driven wheels involved in meshing divided by the number of line teeth of the driving wheel.
Further, the spatial coordinates of the driving contact line and the driven contact line of the light-weight parallel axis gear pair mechanism are as follows.
In the light-weight parallel axis gear pair mechanism, o 0 -x 0 y 0 z 0 、o p -x p y p z p Is two space Cartesian coordinate systems, plane xoz and plane x p o p z p O in the same plane p Point to z 0 The distance of the axes is a, the space Cartesian coordinate system o 1 -x 1 y 1 z 1 Fixedly connected with the driving wheel and a space Cartesian coordinate system o 2 -x 2 y 2 z 2 And the driven wheel is fixedly connected with the driven wheel, the curve A is a driving contact line, and the curve B is a driven contact line. At any time, origin o 1 And o 0 Overlap, z 1 Axis and z 0 Axis coincidence, origin o 2 And o p Overlap, z 2 Axis and z p The axes coincide. After engagement is started, the main partThe driving wheel has uniform angular velocityAround z 0 The axis rotates, the angular velocity direction is z 0 The rotation angle of the driving wheel in the axial direction is +.>The driven wheel is at uniform angular velocity->Around z p The axis rotates, the angular velocity direction is z p The driven wheel rotates by an angle of +.>The transmission ratio of the linear gear pair rotating at constant speed is i, and the value of the linear gear pair is equal to +.>
In the light-weight parallel axis gear pair mechanism, the expression mode of the equation of the contact line of the driving line gear under the self coordinate system is as follows:
active contact line in coordinate system o 1 -x 1 y 1 z 1 The equation above is:
in the light-weight parallel axis gear pair mechanism, the expression mode of the equation of the contact line of the driven line gear under the self coordinate system is as follows:
the slave contact line is in the coordinate system o 2 -x 2 y 2 z 2 The equation above is:
in the light-weight parallel axis gear pair mechanism, in the equation expression of the driving contact line and the driven contact line, t is a parameter variable, a is a center distance of the line gear pair, m is a spiral radius of the driving contact line, n is a spiral pitch related parameter, and i is a transmission ratio of the line gear pair.
In the light-weight parallel axis gear pair mechanism, the spiral radius of the driving contact line is m, the spiral radius of the driven contact line is (a-m), and the center distance of the line gear pair is a.
In the light-weight parallel axis gear pair mechanism, the pitch value of the driving contact line is 2n pi, the pitch value of the driven contact line is 2n pi i, and the transmission ratio of the line gear pair is i.
The gear ratio of the light-weight parallel axis gear pair is directly related to the pitch value of the driving contact line and the pitch value of the driven contact line, and the gear ratio is equal to the pitch value of the driven contact line divided by the pitch value of the driving contact line.
The transmission ratio of the light-weight parallel axis gear pair is irrelevant to the spiral radius of the driving contact line and the spiral radius of the driven contact line.
The transmission ratio of the light-weight parallel axis gear pair is irrelevant to the outer diameter size of the driving wire gear and the outer diameter size of the driven wire gear.
The equations of the two contact lines of the light-weight parallel axis gear pair mechanism of the present invention are not limited to the above expression.
The two contact lines of the light-weight parallel axis gear pair mechanism can be designed, different pressure angles exist between different contact lines, and the self-locking function of the gear pair can be achieved.
The wire tooth part of the light-weight parallel axis gear pair mechanism has no specific shape, can be designed, and realizes the forward and reverse rotation transmission of the gear pair without side gaps.
According to the light-weight parallel axis gear pair mechanism, the driving contact line and the driven contact line are two equal-pitch space cylindrical spiral lines, and the light-weight parallel axis gear pair has fixed sliding rate, so that stable lubrication conditions can be formed.
The slip ratio of any spatially conjugate curve of the wire gear is analyzed as follows.
Let any pair of conjugate curve expressions be: Γ -shaped structure 1 :r (1) ＝r (1) (t)，Γ 2 :r (2) ＝r (2) (t) they are tangential to the point M at some instant. After a time Δt, curve Γ 1 M on 1 And curve Γ 2 M on 2 Tangential contact. Set the contact point at Γ 1 、Γ 2 The sliding arc lengths are s respectively 1 Sum s 2 Chord lengths are respectively |Deltar (1) |and |Δr (2) |。
Obviously, there are:
the slip ratio of a conjugate curve is defined as the limit value of the ratio of the relative arc length difference over which the two curves slip to the total arc length over which the curves slip.
If Γ is 1 For example, the slip ratio is denoted as sigma 1 ：
Similarly, curve Γ 2 Is sigma of 2 ：
Curve Γ 1 And Γ 2 Can be controlled by the sliding rate sigma 1 And slip ratio sigma 2 And (5) judging. For example, when sigma 1 At > 0, s 1 ＞s 2 Representing a curve Γ 2 Relative gamma 1 The direction of sliding being from M to M 2 I.e. at Γ with the point of contact 1 The upward movement direction is uniform; conversely, when sigma 1 When < 0, s 1 ＜s 2 Curve Γ 2 Relative gamma 1 The sliding direction is at gamma with the contact point 1 The direction of the upward movement is opposite.
The following equation incorporating the contact line of the lightweight parallel axis gear pair mechanism of the present invention analyzes the slip ratio problem of the lightweight parallel axis gear pair.
In the light-weight parallel axis gear pair mechanism, the expression mode of the equation of the contact line of the driving line gear under the self coordinate system is as follows:
active contact line in coordinate system o 1 -x 1 y 1 z 1 The equation above is:
in the light-weight parallel axis gear pair mechanism, the expression mode of the equation of the contact line of the driven line gear under the self coordinate system is as follows:
the slave contact line is in the coordinate system o 2 -x 2 y 2 z 2 The equation above is:
in the light-weight parallel axis gear pair mechanism, in the equation expression of the driving contact line and the driven contact line, t is a parameter variable, a is a center distance of the line gear pair, m is a spiral radius of the driving contact line, n is a spiral pitch related parameter, and i is a transmission ratio of the line gear pair.
When the wire gear rotates for one turn, the length of the contact line of the active contact line participating in the engagement is recorded as l 1 ：
Wherein p is 1 Represents the active contact line pitch, c 1 Representing the active contact line spiral circumference.
p 1 ＝2πn
c 1 ＝πd 1
Wherein d is 1 Representing the active contact line spiral diameter.
d 1 ＝2m
Similarly, the length of the contact line engaged with the driven contact line is denoted as l 2 ：
Wherein p is 2 Represents the active contact line pitch, c 2 Representing the active contact line spiral circumference.
p 2 ＝2πni
c 2 ＝πd 2
Wherein d is 1 Representing the active contact line spiral diameter.
d 2 ＝2(a-m)
The slip ratio of the active contact line is recorded as sigma 1 ：
Similarly, the slip rate of the driven contact line is sigma 2 ：
The slip ratio calculation formula is a slip ratio calculation formula of the light-weight parallel axis gear pair. The light-weight parallel axis gear pair has fixed slip rate, and is favorable for forming stable lubrication conditions.
The line gear set equations created in accordance with claim 3 can be used in a lightweight parallel axis gear set mechanism.
The wire teeth on the driving wheel and the driven wheel obtained by the mechanism are designed based on a constant-pitch cylindrical spiral line, and one or more wire teeth can be arranged; the wire teeth of the driving wheel are meshed with the wire teeth of the driven wheel through point contact; the driving wheel is connected with the input end, and the driven wheel is connected with the output end to provide motion or force output; the radius of the contact line on the driving wheel and the driven wheel is irrelevant to the gear pair transmission ratio, and the gear pair transmission ratio is equal to the pitch value of the driven contact line divided by the pitch value of the driving contact line and also equal to the number of the linear teeth of the driven wheel engaged by the number of the linear teeth of the driving wheel.
The principle of the invention is as follows: according to the meshing theory of the space conjugate curves of the line gears, the line tooth contact line equation of the outer diameter sizes of the driving wheel and the driven wheel which are irrelevant to the transmission ratio of the gear pair can be designed, so that the line tooth contact line equation is meshed stably, and the gear pair with a large transmission ratio can be designed in a limited space.
Compared with the prior art, the invention has the following advantages:
1. the outer diameter sizes of the driving wheel and the driven wheel are irrelevant to the gear pair transmission ratio, the gear pair with large transmission ratio and the speed reducer can be designed in a limited space, and the mass and the volume are smaller than those of the traditional involute gear, so that the device is suitable for microminiature electromechanical products.
2. The gear pair transmission ratio is equal to the pitch value of the driven contact line divided by the pitch value of the driving contact line, and the line gear pair with accurate transmission ratio can be obtained only by ensuring the accurate pitch value of the contact line, and the design is simple.
3. The least number of teeth of the gears is less, the least number of teeth of the gears is 1, the gears with less number of teeth of the gears can be obtained, the transmission ratio of a single gear pair is large, compared with the traditional involute gear pair, the number of teeth of the gears can be reduced, the number of the gears can be reduced, and the processing is convenient.
4. The driving contact line and the driven contact line of the gear pair can be designed to realize self-locking of the gear pair.
5. The driving contact line and the driven contact line of the gear pair are equal-pitch cylindrical spiral lines, and the gear pair has a fixed and unchanged sliding rate, so that stable lubrication conditions are formed.
The light-weight parallel axis gear pair mechanism can provide transmission with small volume and large transmission ratio, and is a gear pair with simple design and processing.
Drawings
FIG. 1 is a coordinate system of the mechanism of the present invention.
FIG. 2 is a schematic illustration of an embodiment of the present invention, a lightweight parallel axis gear pair with a ratio of 8, comprising a drive wheel and a driven wheel; wherein 1 is the driving wire gear wire teeth, 2 is the driving wire gear wheel body, 3 is the driven wire gear wire teeth, and 4 is the driven wire gear wheel body.
Fig. 3 shows an embodiment of the present invention, which is a lightweight parallel axis gear pair with a transmission ratio of 6, comprising a driving wheel and a driven wheel.
Fig. 4 shows an embodiment of the present invention, which is a lightweight parallel axis gear pair with a gear ratio of 2, comprising a driving wheel and a driven wheel.
Fig. 5 shows an embodiment of the present invention, which is a lightweight parallel axis gear pair with a transmission ratio of 1, comprising a driving wheel and a driven wheel.
Fig. 6 shows an embodiment of the present invention, which is a lightweight parallel axis gear reducer, comprising a two-stage lightweight parallel axis gear pair, a bearing, and a gearbox housing.
Fig. 7 is a method of generating a wire tooth entity according to the present invention.
Fig. 8 is a diagram for researching the slip ratio of a driving contact line and a driven contact line of a light-weight parallel axis gear pair.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, but the embodiments of the present invention are not limited thereto.
The light-weight parallel axis gear pair comprises a driving wheel and a driven wheel, wherein a coordinate system of the driving wheel and the driven wheel is shown in figure 1, and the coordinate system is used for establishing a line tooth contact line equation of a line gear. O as shown in FIG. 1 0 -x 0 y 0 z 0 、o p -x p y p z p Is two space Cartesian coordinate systems, plane xoz and plane x p o p z p O in the same plane p Point to z 0 The distance of the axes is a, the space Cartesian coordinate system o 1 -x 1 y 1 z 1 Fixedly connected with the driving wheel and a space Cartesian coordinate system o 2 -x 2 y 2 z 2 Is fixedly connected with a driven wheel, a curve A is a driving contact line, a curve B is a driven contact line, and the transmission is realizedThe driving wheel and the driven wheel respectively surround the z-axis and the z-axis p The shaft rotates.
The light parallel axis gear pair is shown in fig. 2, the left side is a driving wheel 1, the driving wheel is provided with driven wheel wire teeth 2, the right side is a driven wheel 3, and the driven wheel is provided with driven wheel wire teeth 4. The contact lines on the driving wheel and the driven wheel are equal-pitch cylindrical spiral lines, and the equations of the driving contact line and the driven contact line under the respective coordinate systems are as follows:
active contact line in coordinate system o 1 -x 1 y 1 z 1 The equation above is:
the slave contact line is in the coordinate system o 2 -x 2 y 2 z 2 The equation above is:
wherein t is a parameter variable, a is the center distance of the line gear pair, m is the spiral radius of the active contact line, n is a spiral pitch related parameter, and i is the transmission ratio of the line gear pair.
The equation of the contact lines on the driving wheel and the driven wheel is an expression mode of a constant-pitch cylindrical spiral line, but the embodiment of the invention is not limited to the equation.
The driving wheel and the driven wheel of the light parallel axis gear pair mechanism comprise a plurality of wire teeth, the wire tooth entity only needs to meet the strength requirement, and the wire tooth entity has no specific shape requirement. As shown in fig. 4, at each engagement point, a certain volume is extended outwards on one side of the contact direction of the driving and driven wire teeth, so as to generate the required wire teeth. The wheel body is used for fixedly connecting the wire teeth.
1. Example 1:
a lightweight parallel axis gear pair mechanism as shown in fig. 2 is one embodiment of the present invention.
Embodiment 1 is a light-weight parallel axis gear pair, wherein the number of teeth of a driving line gear is 2, the number of teeth of a driven line gear is 16, the normal tooth profile of the line teeth is a rounded equilateral triangle, the diameter of the rounded corner is 1mm, and the height of the triangle is 2.5mm.
Equations for the driving contact line and the driven contact line of example 1 in the respective coordinate systems are as follows, respectively.
The equation of the active contact line in its own coordinate system is:
the equation of the slave contact line under the self system is:
the gear ratio of example 1 was 8.
2. Example 2:
a lightweight parallel axis gear pair mechanism as shown in fig. 3 is one embodiment of the present invention.
Embodiment 2 is a light-weight parallel axis gear pair, wherein the number of teeth of a driving line gear is 2, the number of teeth of a driven line gear is 14, the normal tooth profile of the line teeth is a right triangle with a round angle diameter of 1mm, wherein the right angle of the triangle faces the outside of the gear, and the height of the triangle is 1.5mm.
Equations for the driving contact line and the driven contact line of example 2 in the respective coordinate systems are as follows, respectively.
The equation of the active contact line in its own coordinate system is:
the equation of the slave contact line under the self system is:
the gear ratio of example 2 is 7.
3. Example 3:
a lightweight parallel axis gear pair mechanism as shown in fig. 4 is one embodiment of the present invention.
Embodiment 3 is a light-weight parallel axis gear pair, wherein the number of teeth of a driving wire gear is 2, the number of teeth of a driven wire gear is 2, the normal tooth profile of the wire teeth is circular, and the diameter of the circle is 2mm. The number of teeth of the driving wire gear engaged simultaneously is 1, and the number of teeth of the driven wheel engaged simultaneously is 2.
Equations for the driving contact line and the driven contact line of example 3 in the respective coordinate systems are as follows, respectively.
The equation of the active contact line in its own coordinate system is:
the equation of the slave contact line under the self system is:
the gear ratio of example 3 is 2.
4. Example 4:
a lightweight parallel axis gear pair mechanism as shown in fig. 5 is one embodiment of the present invention.
Embodiment 4 is a light-weight parallel axis gear pair, wherein the number of teeth of a driving wire gear is 2, the number of teeth of a driven wire gear is 2, the normal tooth profile of the wire teeth is circular, and the diameter of the circle is 2mm. The number of teeth of the driving wire gear engaged simultaneously is 2, and the number of teeth of the driven wheel engaged simultaneously is 2.
Equations for the driving contact line and the driven contact line of example 4 in the respective coordinate systems are as follows, respectively.
The equation of the active contact line in its own coordinate system is:
the equation of the slave contact line under the self system is:
the gear ratio of example 4 is 1.
5. Example 5:
a lightweight parallel axis gear reducer, as shown in fig. 6, is an embodiment of the present invention.
Embodiment 5 is a lightweight parallel axis gear reducer comprising a two-stage lightweight parallel axis gear pair, wherein the two-stage lightweight parallel axis gear pair is identical. In each stage of light-weight parallel axis gear pair, the number of teeth of a driving line gear is 2, the number of teeth of a driven line gear is 16, the normal tooth profile of the line gear is a rounded equilateral triangle, the diameter of the rounded angle is 1mm, and the height of the triangle is 2.5mm.
The equations of the driving contact line and the driven contact line in each stage of the lightweight parallel axis gear pair under the respective coordinate systems are as follows.
The equation of the active contact line in its own coordinate system is:
the equation of the slave contact line under the self system is:
the gear ratio of example 5 is 64.
Embodiment 5 is a light-weight parallel axis gear reducer with a gear ratio of 64, and the light-weight parallel axis gear reducer consists of a two-stage light-weight parallel axis gear pair, a bearing and a gear box.
Claims (1)
1. A light-weight parallel axis gear pair mechanism is characterized in that: the mechanism consists of a pair of light-weight parallel axis gear pairs, wherein each light-weight parallel axis gear pair consists of a driving wire gear and a driven wire gear, and each driving wire gear and each driven wire gear consist of a wire gear wheel body and wire teeth;
the contact line of the line teeth of the light-weight parallel axis gear pair is in point contact engagement, and the contact line of the line teeth is designed according to the space conjugate curve engagement theory;
the driving contact line and the driven contact line of the light-weight parallel axis gear pair are equal-pitch cylindrical spiral lines, and the transmission ratio of the line gear pair is equal to the pitch value of the driven contact line divided by the pitch value of the driving contact line;
the equations of the driving contact line and the driven contact line of the light-weight parallel axis gear pair under the space Cartesian coordinate system are respectively as follows:
wherein t is a parameter variable, a is the center distance of the line gear pair, m is the spiral radius of the active contact line, n is a spiral pitch related parameter, and i is the transmission ratio of the line gear pair;
the spiral radius of the contact line of the driving line gear and the driven line gear of the light-weight parallel axis gear pair is irrelevant to the transmission ratio of the gear pair, and different line gear pairs with the same outer diameter size have different transmission ratios;
designing two contact lines of the light-weight parallel axis gear pair, for a pair of gear pairs with a given transmission ratio, the smaller the spiral angle of the designed driving contact line is, the larger the pressure angle of the gear pair is, and when the pressure angle is larger than the maximum value of the pressure angle of the selected gear material, the gear pair can realize the self-locking function;
the thicknesses of the driving wire teeth and the driven wire teeth of the wire gear pair are designed, so that the function of no side gap in forward and reverse rotation of the wire gear pair is realized;
the wire teeth of the light-weight parallel axis gear pair are distributed circumferentially around the axis of the gear, and the size of each wire tooth is consistent;
the light-weight parallel axis gear pair forms a multi-stage gear pair, and is assembled into a light-weight parallel axis gear reducer;
the light-weight parallel axis gear pair has fixed slip rate, and is favorable for forming stable lubrication conditions.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110944242.6A CN113757310B (en) | 2021-08-17 | 2021-08-17 | Light-weight parallel axis gear pair mechanism |
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| CN113757310B true CN113757310B (en) | 2024-04-02 |
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010156454A (en) * | 2008-12-05 | 2010-07-15 | Thk Co Ltd | Planetary type rotary-linear motion converting device |
| CN104455212A (en) * | 2014-10-24 | 2015-03-25 | 中国地质大学（武汉） | Hook rod gear mechanism for parallel shaft transmission |
| CN105114532A (en) * | 2015-09-08 | 2015-12-02 | 华南理工大学 | Convex-concave arc gear mechanism used for transmission of parallel shaft |
| CN111322374A (en) * | 2020-03-29 | 2020-06-23 | 华南理工大学 | Elastic variable transmission ratio line gear mechanism |
| CN112052535A (en) * | 2020-07-24 | 2020-12-08 | 重庆大学 | Backlash adjustable worm and helical gear transmission |
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2021
- 2021-08-17 CN CN202110944242.6A patent/CN113757310B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010156454A (en) * | 2008-12-05 | 2010-07-15 | Thk Co Ltd | Planetary type rotary-linear motion converting device |
| CN104455212A (en) * | 2014-10-24 | 2015-03-25 | 中国地质大学（武汉） | Hook rod gear mechanism for parallel shaft transmission |
| CN105114532A (en) * | 2015-09-08 | 2015-12-02 | 华南理工大学 | Convex-concave arc gear mechanism used for transmission of parallel shaft |
| CN111322374A (en) * | 2020-03-29 | 2020-06-23 | 华南理工大学 | Elastic variable transmission ratio line gear mechanism |
| CN112052535A (en) * | 2020-07-24 | 2020-12-08 | 重庆大学 | Backlash adjustable worm and helical gear transmission |
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| CN113757310A (en) | 2021-12-07 |
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