WO2021248761A1

WO2021248761A1 - Bevel gear planetary transmission mechanism

Info

Publication number: WO2021248761A1
Application number: PCT/CN2020/120744
Authority: WO
Inventors: 李轩; 孙立宁
Original assignee: 苏州大学
Priority date: 2020-06-12
Filing date: 2020-10-14
Publication date: 2021-12-16
Also published as: CN111637200A; CN111637200B

Abstract

Disclosed is a bevel gear planetary transmission mechanism, comprising a sun gear (1), a planet gear (2) and an internal gear (3). The sun gear (1) and the internal gear (3) are both meshed with the planet gear (2); the sun gear (1), the planet gear (2) and the internal gear (3) are all bevel gears; and a normal tooth profile curve of the sun gear (1) is an arc curve, a normal tooth profile curve of the planet gear (2) is a cycloid curve, and a normal tooth profile curve and a cycloid curve of the internal gear (3) are conjugate curves, such that the tooth root bending strength and the tooth surface bearing capacity of a transmission gear are improved, root cutting is less prone to occurring, a large transmission ratio can be obtained under the condition of the same center distance and volume, sliding abrasion of gear teeth is greatly reduced, and the gear transmission requirements of a high speed, a heavy load and a high power can be successfully met.

Description

Helical gear planetary transmission mechanism

Technical field

The invention relates to the technical field of gear transmission, in particular to a helical gear planetary transmission mechanism.

Background technique

Gear is a basic component that transmits motion and power through tooth surface meshing. Among various gear meshing pairs, involute gears are widely used because of their convenience in processing and manufacturing, and the separability of center distances. However, the teeth of involute gears are thin and tall, with poor root bending strength and low tooth surface load-bearing capacity. In order to prevent undercutting during processing of involute gears, the number of teeth is at least 17 teeth. In the case of the same center distance and volume, the existing involute gear transmission mechanism cannot achieve a large transmission ratio; at the same time, the relative sliding speed between the meshing tooth surfaces near the tooth root near the pitch circle is too high, resulting in this area It is prone to severe wear and can not meet the requirements of high-speed, heavy-duty and high-power gear transmission.

Summary of the invention

The technical problem to be solved by the present invention is to provide a helical gear planetary transmission mechanism, which can improve the tooth root bending strength and tooth surface bearing capacity of the transmission gear, and is not prone to undercutting, and can obtain better results under the same center distance and volume. The large transmission ratio is beneficial to reduce the sliding wear of the gear teeth, which can better meet the requirements of high-speed, heavy-duty, and high-power gear transmission.

In order to solve the above technical problems, the technical solutions provided by the present invention are as follows:

A helical gear planetary transmission mechanism, comprising a sun gear, a planetary gear and an internal gear. The sun gear and the internal gear mesh with the planetary gear. The sun gear, the planetary gear and the internal gear are all helical gears. The normal tooth profile curve of the sun gear is a circular arc curve, the normal tooth profile curve of the planetary gear is a cycloid curve, and the normal tooth profile curve of the internal gear and the cycloid curve are conjugate curves.

In one of the embodiments, the cycloid curve is formed by the envelope motion of the circular arc curve, and the normal tooth profile curve of the internal gear is formed by the cycloid curve as the envelope motion.

In one of the embodiments, the tooth surface equation of the sun gear is:

Among them, x ₁ , y ₁ , z ₁ represent the coordinates of the sun gear tooth surface in the x, y and z directions, e is the radius of the distribution circle of the sun gear normal tooth profile, and ρ is the arc of the sun gear normal tooth profile Radius, n ₁ is the number of sun gear teeth, φ ₁ = 2π/n ₁ is the angle between adjacent gear teeth of the sun gear, k = ±1, γ is the deflection angle between the center of the arc and the center of the sun gear, p ₁ ＝R ₁ tanβ is the pitch coefficient of the sun gear, R ₁ ＝a/(i ₁₂ +1) is the base circle radius of the sun gear, a is the center distance between the sun gear and the planetary gear, i ₁₂ ＝n ₂ /n ₁ is the planet The gear ratio of the wheel to the sun gear, n ₂ is the number of planetary gear teeth, β is the helix angle,

Is the variable of the spiral angle of the sun wheel,

Is the maximum helix angle of the sun gear, B is the gear width, θ ₁ ∈[θ _1o ,θ _1t ] is the sun gear tooth profile angle parameter, θ _1o is the sun gear tooth profile angle parameter minimum, θ _1t is the sun gear tooth profile The maximum value of the angle parameter.

In one of the embodiments, the tooth surface equation of the planetary gear is:

Among them, x ₂ , y ₂ , and z ₂ represent the coordinates in the x, y, and z directions of the planetary gear tooth surface, respectively, and a is the center distance between the sun gear and the planetary gear,

Is the angle between the adjacent teeth of the planetary gear, α ₁ represents the rotation angle of the sun gear, α ₂ represents the rotation angle of the planetary gear during the formation of the normal tooth profile curve of the planetary gear, p ₂ =-R ₂ tanβ is the planet Wheel pitch coefficient, R ₂ =ai ₁₂ /(i ₁₂ +1) is the radius of the planetary wheel base circle,

Is the variable of the spiral angle of the planetary gear,

Θ ₂ ∈ [θ _2o ,θ _2t ] is the planetary gear tooth profile angle parameter, θ _2o is the planet gear tooth profile angle parameter minimum, θ _2t is the planet gear tooth profile angle parameter maximum.

In one of the embodiments, the tooth surface equation of the internal gear is:

Among them, x ₃ , y ₃ , and z ₃ represent the coordinates in the x, y, and z directions of the internal gear tooth surface, respectively, n ₃ is the number of internal gear teeth, and φ ₃ =2π/n ₃ is the distance between adjacent teeth of the internal gear The included angle, β ₂ represents the rotation angle of the planetary gear during the formation of the normal tooth profile curve of the _{internal gear, β 3} represents the rotation angle of the internal gear, i ₂₃ =n ₃ /n ₂ is the gear ratio of the internal gear to the planetary gear, p ₃ = -R ₃ tanβ is the internal gear pitch coefficient, R ₃ =2R ₂ +R ₁ is the internal gear base circle radius,

Is the variable of the spiral angle of the internal gear,

Θ ₃ ∈ [θ _3o , θ _3t ] is the internal gear tooth profile angle parameter, θ _3o is the internal gear tooth profile angle parameter minimum, θ _3t is the internal gear tooth profile angle parameter maximum.

In one of the embodiments, the number of teeth of the internal gear n ₃ =n ₁ +2n ₂ .

In one of the embodiments, the number of the planetary gears is N, and let W=2(n ₁ +n ₂ )/N, then W is an integer.

In one of the embodiments, the sun gear, planetary gears and internal gears all adopt herringbone gears.

The present invention has the following beneficial effects: In the helical gear planetary transmission mechanism of the present invention, the normal tooth profile curve of the sun gear is a circular arc curve, the normal tooth profile curve of the planetary gear is a cycloid curve, and the normal tooth profile of the internal gear The curve and cycloid curve are conjugate curves, thus forming a conjugate gear pair composed of normal arc, cycloid and cycloid conjugate curve, which realizes spiral meshing transmission. The transmission mechanism has a small slip rate. It can effectively avoid gear failure due to sliding wear; and is not prone to undercutting, the minimum number of teeth of the sun gear can reach 1, which can obtain a larger transmission ratio under the same center distance and volume; the gear tooth height of the gear meshing pair is small , The tooth root is wide, with good tooth root bending strength and tooth surface contact strength, the tooth surface bearing capacity is large and the gear volume is small, which can better meet the transmission requirements of high speed, heavy load and high power.

Description of the drawings

Figure 1 is a schematic diagram of the three-dimensional structure of the helical gear planetary transmission mechanism of the present invention;

Fig. 2 is a front view of the helical gear planetary transmission mechanism shown in Fig. 1;

Fig. 3 is a schematic diagram of the normal tooth profile meshing of the helical gear planetary transmission mechanism shown in Fig. 1;

Fig. 4 is a schematic diagram of the formation of the normal tooth profile curve of the sun gear and the planetary gear shown in Fig. 1;

Fig. 5 is a schematic diagram of the formation of the normal tooth profile curve of the planetary gear and the internal gear shown in Fig. 1;

Fig. 6 is a schematic diagram of the three-dimensional structure of the sun gear shown in Fig. 1;

Fig. 7 is a schematic diagram of the three-dimensional structure of the planetary gear shown in Fig. 1;

Fig. 8 is a schematic diagram of the three-dimensional structure of the internal gear shown in Fig. 1;

Fig. 9 is a structural schematic diagram of the internal meshing helical gear pair composed of planetary gears and internal gears shown in Fig. 1;

Fig. 10 is a schematic structural diagram of the external meshing helical gear pair composed of the sun gear and the planetary gear shown in Fig. 1;

In the picture: 1. Sun gear, 2. Planetary gear, 3. Internal gear.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention, but the examples given are not intended to limit the present invention.

As shown in Figures 1 to 3, this embodiment discloses a helical gear planetary transmission mechanism, which includes a sun gear 1, a planet gear 2 and an internal gear 3. The sun gear 1 and the internal gear 3 both mesh with the planet gear 2 in conjugate. , The sun gear 1, the planet gear 2 and the internal gear 3 are all helical gears, the normal tooth profile curve of the sun gear 1 is a circular arc curve, the normal tooth profile curve of the planet gear 2 is a cycloid curve, the normal tooth profile of the internal gear 3 Tooth profile curve and cycloid curve are conjugate curves.

Further, the cycloid curve is formed by a circular arc curve doing an enveloping motion, and the normal tooth profile curve of the internal gear 3 is formed by a cycloid curve doing an enveloping motion.

As shown in Figure 4, the normal tooth profile curve of the sun gear 1 is a circular arc curve 1a, the radius of the circular arc curve 1a is ρ, and the production circle (radius ρ) 1b where the circular arc curve 1a is located is based on relative motion The relationship forms an envelope motion to form a cycloid curve 2b, and the normal tooth profile curve 2a of the planetary gear 2 is a part of the cycloid curve 2b;

As shown in FIG. 5, the cycloid curve 2b performs an envelope motion according to the relative motion relationship to form a conjugate curve 3b, and the normal tooth profile curve 3a of the internal gear 3 is a part of the conjugate curve 3b.

In one of the embodiments, the structure of the sun gear 1 is shown in Fig. 6, and the tooth surface equation of the sun gear 1 is:

Among them, x ₁ , y ₁ , and z ₁ represent the coordinates of the sun gear 1 tooth surface in the x, y, and z directions, e is the radius of the distribution circle of the sun gear 1 normal tooth profile, and ρ is the sun gear 1 normal tooth profile The arc radius of, n ₁ is the number of teeth of sun gear 1, φ ₁ = 2π/n ₁ is the angle between adjacent gear teeth of sun gear 1, k = ±1, k = 1 represents the tooth surface equation Corresponds to the left tooth surface of the gear tooth, k = -1 means that the tooth surface equation corresponds to the right tooth surface of the corresponding gear tooth, γ is the deflection angle of the line connecting the _{arc center and the sun gear center O 1,} p ₁ ＝R ₁ tanβ is the pitch coefficient of the sun gear 1, R ₁ ＝a/(i ₁₂ +1) is the radius of the base circle of the sun gear 1, a is the center distance between the sun gear 1 and the planetary gear 2, and β is the spiral Angle, i ₁₂ =n ₂ /n ₁ is the gear ratio of the planetary gear 2 to the sun gear 1, and n ₂ is the tooth number of the planetary gear 2,

Is the helix angle variable of sun wheel 1,

Is the maximum helix angle of sun gear 1, B is gear width, θ ₁ ∈[θ _1o ,θ _1t ] is the tooth profile angle parameter _{of sun gear 1, θ 1o} is the minimum tooth profile angle parameter of sun gear 1, θ _1t is the maximum value of the tooth profile angle parameter of the sun gear 1.

Among them, the helix angle β of the sun gear 1, the planetary gear 2 and the internal gear 3 are the same, and the gear width B is also the same.

Further, the structure of the planetary wheel 2 is shown in Fig. 7. The tooth surface equation of the planetary wheel 2 is:

Among them, x ₂ , y ₂ , and z ₂ represent the coordinates of the tooth surface of the planetary gear 2 in the x, y, and z directions, a is the center distance between the sun gear 1 and the planetary gear 2, and φ ₂ ＝2π/n ₂ is the planetary gear 2 The angle between adjacent gear teeth, α ₁ represents the rotation angle of the sun gear 1, and α ₂ represents the rotation angle of the planet wheel 2 during the formation of the normal tooth profile curve of the planet gear, that is, when it is made by the arc curve The enveloping motion forms the rotation angle of the planetary wheel 2 in the enveloping motion of the cycloid curve;

p ₂ =-R ₂ tanβ is the pitch coefficient of the planetary wheel 2, R ₂ =ai ₁₂ /(i ₁₂ +1) is the base circle radius of the planetary wheel 2,

Is the variable of the helix angle of planet wheel 2,

Is the maximum value of the helical rotation angle of the planetary wheel 2, θ ₂ ∈[θ _2o ,θ _2t ] is the tooth profile angle parameter _{of the planetary wheel 2, θ 2o} is the minimum tooth profile angle parameter of the planetary wheel 2 _{, and θ 2t is the planetary wheel 2} The maximum value of the tooth profile angle parameter.

Further, refer to Fig. 8 for the structure of the internal gear 3, and the tooth surface equation of the internal gear 3 is:

Among them, x ₃ , y ₃ , and z ₃ represent the coordinates in the x, y, and z directions of the tooth surface of the internal gear 3, n ₃ is the number of teeth of the internal gear 3, and φ ₃ = 2π/n ₃ is the adjacent wheel of the internal gear 3 The angle between the teeth, β ₃ represents the rotation angle of the internal gear 3, β ₂ represents the rotation angle of the planetary gear 2 during the formation of the normal tooth profile curve of the internal gear, which is formed by the enveloping motion of the cycloid curve The rotation angle of the planetary gear 2 in the enveloping motion of the normal tooth profile curve of the internal gear;

i ₂₃ =n ₃ /n ₂ is the gear ratio of the internal gear 3 to the planetary gear 2, p ₃ =-R ₃ tanβ is the pitch coefficient of the internal gear 3, R ₃ ＝2R ₂ +R ₁ is the base circle of the internal gear 3 radius,

Is the variable of the spiral angle of the internal gear 3,

Is the maximum value of the spiral angle of the internal gear 3, θ ₃ ∈[θ _3o ,θ _3t ] is the tooth profile angle parameter _{of the internal gear 3, θ 3o} is the minimum tooth profile angle parameter _{of the internal gear 3, and θ 3t} is the internal gear 3. The maximum value of the tooth profile angle parameter.

The number of teeth of the internal gear 3 is n ₃ , and n ₃ =n ₁ +2n ₂ .

Further, the number of the planetary wheels 2 is N, and W=2(n ₁ +n ₂ )/N, then W is an integer. That is, the number N of _{planetary gears 2 arranged is determined by whether the calculation result of 2(n 1} +n ₂ )/N is an integer. If the calculation result W is an integer, it means that N planetary gears 2 can be arranged in the planetary transmission mechanism. , When N planet gears 2 are arranged, the planetary transmission mechanism can operate normally. If the calculation result W is not an integer, the arrangement number N does not meet the transmission requirements.

In one of the embodiments, sun gear 1, planetary gear 2 and internal gear 3 can all adopt herringbone gears, that is, the tooth surfaces of sun gear 1, planetary gear 2 and internal gear 3 can all be designed to be axially symmetrical and spiral. The herringbone structure with the opposite direction can better eliminate the lateral force of the gear on the central axis.

It is understandable that, as shown in FIG. 10, in practical applications, the internal gear 3 in the planetary transmission mechanism can be removed, and the external meshing helical gear transmission mechanism composed of the sun gear 1 and the planetary gear 2 can be directly used.

Similarly, as shown in FIG. 9, the sun gear 1 in the planetary transmission mechanism can also be removed, and the planetary gear 2 and the internal gear 3 can be directly used to form an internal meshing helical gear transmission mechanism.

In the helical gear planetary transmission mechanism of this embodiment, the normal tooth profile curve of the sun gear 1 is a circular arc curve, the normal tooth profile curve of the planetary gear 2 is a cycloid curve, and the normal tooth profile curve and the pendulum curve of the internal gear 3 The line curve is a conjugate curve, thus forming a conjugate gear pair composed of a normal arc, cycloid and cycloid conjugate curve, which realizes spiral meshing transmission. The transmission mechanism has a small slip rate and can effectively avoid The gear fails due to sliding wear; it is not prone to undercutting and is easy to process. The minimum number of teeth of the sun gear can reach 1. Under the same volume and center distance conditions, the design requirements of small number of teeth and large transmission can be achieved; the gear teeth of this gear meshing pair The tooth height is small, the tooth root is wide, and the modulus is large. It has good tooth root bending strength and tooth surface contact strength. The tooth surface load capacity is large and the gear volume is small, which can better meet high speed, heavy load and high power. Transmission requirements.

The above-mentioned embodiments are only preferred embodiments for fully explaining the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or alterations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims

A helical gear planetary transmission mechanism, comprising a sun gear, a planetary gear and an internal gear. The sun gear and the internal gear mesh with the planetary gear. The feature is that the sun gear, the planetary gear and the internal gear are all Helical gear, the normal tooth profile curve of the sun gear is a circular arc curve, the normal tooth profile curve of the planetary gear is a cycloid curve, the normal tooth profile curve of the internal gear and the cycloid curve are Conjugate curve.
The helical gear planetary transmission mechanism according to claim 1, wherein the cycloid curve is formed by the circular arc curve making an enveloping motion, and the normal tooth profile curve of the internal gear is formed by the cycloid curve. Do the enveloping movement to form.
The helical gear planetary transmission mechanism of claim 2, wherein the tooth surface equation of the sun gear is:

Among them, x 1 , y 1 , z 1 represent the coordinates of the sun gear tooth surface in the x, y and z directions, e is the radius of the distribution circle of the sun gear normal tooth profile, and ρ is the arc of the sun gear normal tooth profile Radius, n 1 is the number of sun gear teeth, φ 1 = 2π/n 1 is the angle between adjacent gear teeth of the sun gear, k = ±1, γ is the deflection angle between the center of the arc and the center of the sun gear, p 1 ＝R 1 tanβ is the pitch coefficient of the sun gear, R 1 ＝a/(i 12 +1) is the base circle radius of the sun gear, a is the center distance between the sun gear and the planetary gear, i 12 ＝n 2 /n 1 is the planet The gear ratio of the wheel to the sun gear, n 2 is the number of planetary gear teeth, β is the helix angle,
Is the variable of the spiral angle of the sun wheel,
Is the maximum helix angle of the sun gear, B is the gear width, θ 1 ∈[θ 1o ,θ 1t ] is the sun gear tooth profile angle parameter, θ 1o is the sun gear tooth profile angle parameter minimum, θ 1t is the sun gear tooth profile The maximum value of the angle parameter.
The helical gear planetary transmission mechanism of claim 3, wherein the tooth surface equation of the planetary gear is:

Among them, x 2 , y 2 , z 2 represent the coordinates of the planetary gear tooth surface in the x, y, and z directions, a is the center distance between the sun gear and the planetary gear, and φ 2 ＝2π/n 2 is the adjacent gear tooth of the planetary gear The angle between, α 1 represents the rotation angle of the sun gear, α 2 represents the rotation angle of the planetary gear during the formation of the normal tooth profile curve of the planetary gear, p 2 =-R 2 tan β is the planetary gear pitch coefficient, R 2 ＝ ai 12 /(i 12 +1) is the radius of the planetary wheel base circle,
Is the variable of the spiral angle of the planetary gear,
Θ 2 ∈ [θ 2o ,θ 2t ] is the planetary gear tooth profile angle parameter, θ 2o is the planet gear tooth profile angle parameter minimum, θ 2t is the planet gear tooth profile angle parameter maximum.
The helical gear planetary transmission mechanism of claim 4, wherein the tooth surface equation of the internal gear is:

Among them, x 3 , y 3 , and z 3 represent the coordinates in the x, y, and z directions of the internal gear tooth surface, respectively, n 3 is the number of internal gear teeth, and φ 3 =2π/n 3 is the distance between adjacent teeth of the internal gear The included angle, β 2 represents the rotation angle of the planetary gear during the formation of the normal tooth profile curve of the internal gear, β 3 represents the rotation angle of the internal gear, i 23 =n 3 /n 2 is the gear ratio of the internal gear to the planetary gear, p 3 = -R 3 tanβ is the internal gear pitch coefficient, R 3 =2R 2 +R 1 is the internal gear base circle radius,
Is the variable of the spiral angle of the internal gear,
Θ 3 ∈ [θ 3o , θ 3t ] is the internal gear tooth profile angle parameter, θ 3o is the internal gear tooth profile angle parameter minimum, θ 3t is the internal gear tooth profile angle parameter maximum.
The helical gear planetary transmission mechanism of claim 5, wherein the number of teeth of the internal gear is n 3 =n 1 +2n 2 .
The helical gear planetary transmission mechanism of claim 5, wherein the number of the planetary gears is N, and if W=2(n 1 +n 2 )/N, then W is an integer.
The helical gear planetary transmission mechanism of claim 1, wherein the sun gear, planetary gear and internal gear all adopt herringbone gears.