CN109190214B - Planetary gear transmission mechanism and design method thereof - Google Patents

Planetary gear transmission mechanism and design method thereof Download PDF

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CN109190214B
CN109190214B CN201810947830.3A CN201810947830A CN109190214B CN 109190214 B CN109190214 B CN 109190214B CN 201810947830 A CN201810947830 A CN 201810947830A CN 109190214 B CN109190214 B CN 109190214B
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gear
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planetary gear
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sun
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刘金武
洪汉池
易子超
陈阿龙
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Xiamen University of Technology
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Abstract

The invention relates to a design method of a planetary gear transmission mechanism, which comprises the following steps: s1: constructing a model of a planetary wheel mechanism, the planetary wheel mechanism comprising: a housing having an internal gear formed on an inner peripheral wall thereof, a planet carrier, a sun gear, and at least one planetary gear set disposed on the planet carrier; the planetary gear set comprises a first planetary gear and a second planetary gear which are coaxially arranged, the first planetary gear is meshed with the sun gear, and the second planetary gear is meshed with the inner gear; when the sun gear rotates, the planet carrier can be driven to rotate through the planetary gear set; s2: adjusting the number of gears of the sun gear, the first planet gear, the second planet gear and the inner gear, so that the angular speed ratio of the sun gear to the planet carrier calculated according to a first formula meets a preset target value, wherein the first formula is as follows:
Figure DDA0001770694340000011
the planet wheel design method can ensure that the designed transmission ratio of the planet wheel mechanism has higher accuracy. The present application further provides a planetary gear transmission.

Description

Planetary gear transmission mechanism and design method thereof
Technical Field
The invention relates to the technology of a planetary gear mechanism, in particular to a planetary gear transmission mechanism and a design method thereof.
Background
At present, when the transmission ratio is calculated in the transmission design of the gourd planetary gear, the calculation is usually carried out according to a formula provided by a mechanical design theory. The method has poor logicality, the scientific meaning of formula expression is difficult to understand and use, only a hard-set formula is used, the transmission precision of the planetary wheel mechanism designed based on the existing scheme is poor, and the design efficiency is low. In view of this, the present application is specifically proposed.
Disclosure of Invention
The invention aims to solve the technical problem of providing a design method of a planetary gear transmission mechanism so as to solve the problems of poor definition and low design efficiency of the existing design method of the planetary gear mechanism.
In order to solve the above technical problem, the present invention provides a design method of a planetary gear mechanism, comprising the following steps: s1: constructing a model of a planetary wheel mechanism, the planetary wheel mechanism comprising: a housing 5 having an internal gear 4 formed on an inner peripheral wall thereof, a planet carrier, a sun gear, and at least one planetary gear set disposed on the planet carrier; the planetary gear set comprises a first planetary gear and a second planetary gear which are coaxially arranged, the first planetary gear is meshed with the sun gear, and the second planetary gear is meshed with the inner gear; when the sun gear rotates, the planet carrier can be driven to rotate through the planetary gear set; s2: adjusting the number of gears of the sun gear, the first planet gear, the second planet gear and the inner gear, so that the angular speed ratio of the sun gear to the planet carrier calculated according to a first formula meets a preset target value, wherein the first formula is as follows:
Figure BDA0001770694320000011
obtaining the linear velocity of the meshing point at the reference circle of the gear according to the motion relation of equal linear velocity; where ω 1 is an angular velocity of rotation of the sun gear 1, ω 7 is an angular velocity of rotation of the carrier 7, and Z1, Z2, Z3, and Z4 are the numbers of gears of the sun gear 1, the first planetary gear 2, the second planetary gear 3, and the ring gear 4, respectively.
By adopting the technical scheme, the invention can obtain the following technical effects: the design method of the planet gear can ensure that the number of teeth of the gear of the planetary gear transmission system and the required transmission ratio are obtained through design, and the process is clear, the efficiency is high, and the quality is high.
The application further provides a planetary gear drive mechanism, comprising: an inner peripheral wall is formed with an innerThe planetary gear set comprises a shell of a gear, a planet carrier, a sun gear and at least one planetary gear set arranged on the planet carrier; the planetary gear set comprises a first planetary gear and a second planetary gear which are coaxially arranged, the first planetary gear is meshed with the sun gear, and the second planetary gear is meshed with the inner gear; when the sun gear rotates, the planet carrier can be driven to rotate by the planetary gear set; the angular speed ratio of the sun gear and the planet carrier meets a formula I; the first formula is as follows:
Figure BDA0001770694320000021
wherein, ω 1 is the angular speed of the sun gear (1), ω 7 is the angular speed of the planet carrier, and Z1, Z2, Z3 and Z4 are the gear numbers of the sun gear, the first planet gear, the second planet gear and the internal gear respectively.
Drawings
FIG. 1 is a schematic diagram of a planetary gear mechanism according to an embodiment of the present application;
FIG. 2 illustrates a schematic diagram of a planetary gear mechanism according to an embodiment of the present application;
FIG. 3 depicts a view corresponding to the direction B-B of FIG. 2;
FIG. 4 shows a view corresponding to the direction A-A of FIG. 2;
fig. 5 and 6 each show a schematic illustration of a planetary gear mechanism based on the schematic illustration of fig. 2 from a different perspective.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings of the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention.
Referring to fig. 1, in one embodiment, the design method of the planetary gear transmission mechanism of the present application substantially comprises the following steps: 1. constructing a planet wheel mechanism model; 2. establishing a linear velocity relation model; 3. establishing a known condition model; 4. solving; 5. and (6) ending.
With reference to fig. 2 to 6, the model of the planetary gear mechanism constructed in the present embodiment includes: a housing 5 with an internal gear 4 formed on the inner peripheral wall, a planet carrier 7, a sun gear 1, two planetary gear sets 9 arranged on the planet carrier 7; the planetary gear set 9 comprises a first planetary gear 2 and a second planetary gear 3 which are coaxially arranged (namely, the rotating shafts of the first planetary gear 2 and the second planetary gear 3 are overlapped and can synchronously rotate), the first planetary gear 2 is meshed with the sun gear 1, and the second planetary gear 3 is meshed with the inner gear 4; when the sun gear 1 rotates, the planet carrier 7 can be driven to rotate by the planetary gear set 9. In the actual product, the housing 5 may also be formed with a hook 6, and the sun gear may be driven by a power input wheel 8, as shown in fig. 2, and fig. 5 and 6 do not show the hook 6 and the power input wheel 8. O1 denotes the rotation center line of the sun gear 1 and the power input wheel 8, O2 denotes the rotation center line of the first planetary gear 2, O3 denotes the rotation center line of the second planetary gear 3, O2O3 denotes the rotation axis line of the first planetary gear 2 and the second planetary gear 3, and O7 denotes the rotation center line of the carrier 7. A-A and B-B are symbols for drawing cross-sectional views. The power input by the power input wheel 8 is engaged with the first planet wheel 2 through the sun wheel 1 to transmit power to the first planet wheel 2, the first planet wheel 2 is engaged with the inner gear 4 through the second planet wheel 3 to transmit power, and simultaneously, the planet wheel carrier 7 is driven through the inner hole of the first planet wheel to output power. Note that fig. 5 and 6 do not show the tooth portions on the respective gear members.
Fig. 3 shows the transmission relationship of the sun gear 1, the first planet gear 2 and the planet carrier 7 at the position B-B. In fig. 3, the sun gear 1, the first planet gear 2, the carrier 7, O1, O2 are as before. V1 represents the linear speed (m/s) of the mesh point at the pitch circle of the sun wheel 1, V2 represents the linear speed (m/s) of the mesh point at the pitch circle of the first planet wheel 2, and V7 represents the linear speed (m/s) of O2O3 around O7. ω 1 represents the angular speed of engagement (°/s) at the pitch circle of the sun wheel 1, ω 2 represents the angular speed of engagement (°/s) at the pitch circle of the first planet 2, and ω 7 represents the angular speed (°/s) of O2O3 around O7. The velocity and angular velocity are positive as shown in the figure.
According to the mechanical theory and the kinematic theory, the linear velocity relation model of the sun gear 1, the first planet gear 2 and the planet carrier 7 is established as shown in equation (1).
V1＝V7+V2(1) In equation (1), V1, V2 and V7 are as before.
Fig. 4 shows the section a-a of the second planetary gear 3, the internal gear 4 and the planetary carrier 7 in transmission relation. In fig. 4, the second planet gears 3, the internal gear 4, the planet carrier 7, V7, ω 7, O3, and O7 are the same as above. V3 represents the linear velocity (m/s) of the mesh point at the pitch circle of the second planetary gear 3, V4 represents the linear velocity (m/s) of the mesh point at the pitch circle of the internal gear 4, ω 3 represents the angular velocity (°/s) of the mesh point at the pitch circle of the second planetary gear 3, and ω 4 represents the angular velocity (°/s) of the mesh point at the pitch circle of the internal gear 4. The velocity and angular velocity are positive as shown in the figure. According to the graph of fig. 4, the mechanical theory and the kinematic theory, a linear velocity relation model of the second planet gears 3, the internal gear 4 and the planet carrier 7 is established as shown in the equation (2).
V4＝V7-V3(2) V3, V4 and V7 are as before in equation (2).
From the transmission principle shown in fig. 2, the mechanical design theory and the kinematics theory, the calculation formulas of the known conditions of the sun gear 1, the first planet gear 2 and the second planet gear 3 are established as shown in equation (3), equation (4) and equation (5).
V1＝ω1×m×Z1/2 (3)。
V2＝ω2×m×Z2/2 (4)。
V3＝ω2×m×Z3/2 (5)
In equations (2) to (5), V1, V2, ω 1, ω 2, ω 3, and V3 are as above, m is a gear module (mm), Z1, Z2, and Z3 are the numbers of teeth of the sun gear 1, the first planetary gear 2, and the second planetary gear 3, respectively, and ω 2 is ω 3.
From the transmission principle shown in fig. 2, the mechanical design theory and the kinematics theory, a calculation formula of known conditions of the internal gear 4 is established as equation (6).
V4＝ω4×m×Z4/2＝0 (6)。
In equation (6), V4 and ω 4 are the same, m is the gear module (mm), and Z4 is the number of teeth of the internal gear 4. According to the transmission principle, the mechanical design theory and the kinematics theory shown in fig. 2, a known conditional calculation formula of the planet carrier 7 is established as equation (7).
V7＝ω7×m×(Z4-Z3)/2 (7)。
In equation (7), V7 and ω 7 are as before, m is the gear module (mm), and Z4 and Z3 are as before.
By combining equations (1) and (2) in conjunction with the known conditional solutions of equations (3) to (7), a calculation formula for the planetary gear ratio such as equation (8) can be obtained.
Figure BDA0001770694320000041
In equation (8), Z1, Z2, Z3 and Z4 are as before.
Selecting Z1, Z2, Z3 and Z4, calculating a transmission ratio according to equation (8), comparing whether the transmission ratio is in accordance with the use requirement (namely a preset target value), if so, finishing the transmission design, and then checking the service life strength, drawing an engineering drawing and the like. Otherwise, the number of transmission gear teeth is reselected, again calculated and analyzed according to equation (8).
The application has the advantages that: 1. a design method of planet gear structure transmission is provided, a planet gear transmission principle model, a linear velocity model and a known condition model are established, and an equation of the expression model is solved to obtain key parameters of a transmission system; 2. a modeling method for establishing a linear velocity model according to a kinematic relationship that the linear velocities of meshing points at the gear reference circle are equal is provided. The method for establishing the kinematic model is adopted to design the transmission system, so that the logic, the intuition, the accuracy and the efficiency of design can be improved. 3. The planet wheel design method can ensure that the designed planet wheel mechanism has higher accuracy. Because the planet wheel structure is a common mechanical structure, such as an automobile, the design method can be applied to the field of ultra-precise creative transmission.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. A design method of a planetary gear transmission mechanism is characterized by comprising the following steps:
s1: constructing a model of a planetary wheel mechanism, the planetary wheel mechanism comprising: a housing (5) with an internal gear (4) formed on the inner peripheral wall, a planet carrier (7), a sun gear (1), at least one planetary gear set (9) arranged on the planet carrier (7); the planetary gear set (9) comprises a first planetary gear (2) and a second planetary gear (3) which are coaxially arranged, the first planetary gear (2) is meshed with the sun gear (1), and the second planetary gear (3) is meshed with the inner gear (4); when the sun gear (1) rotates, the planet carrier (7) can be driven to rotate through the planetary gear set (9); wherein, the first and the second end of the pipe are connected with each other,
establishing a linear velocity relation model of the sun wheel (1), the first planet wheel (2) and the planet carrier (7): v1＝V7+V2；
Establishing a second planet wheel (3), an internal gear (4) and a planet carrier (7) linear velocity relation model: v4＝V7-V3；
Establishing a known conditional calculation formula of the sun wheel (1), the first planet wheel (2) and the second planet wheel (3): v1＝ω1×m×Z1/2；V2＝ω2×m×Z2/2；V3＝ω3×m×Z3/2；
Establishing a known condition calculation formula of the internal gear (4): v4＝ω4×m×Z4/2＝0；
Establishing a known condition calculation formula of the planet carrier (7): v7＝ω7×m×(Z4-Z3)/2；
S2: the gear numbers of the sun gear (1), the first planet gear (2), the second planet gear (3) and the internal gear (4) are adjusted, so that the angular speed ratio of the sun gear (1) and the planet carrier (7) is calculated according to a formula IThe target value is in accordance with a preset target value; the first formula is as follows:
Figure FDA0003640288110000011
wherein, ω is1 Angular velocity, omega, of rotation of the sun gear (1)7 Is the angular velocity, Z, of the rotation of the planet carrier (7)1 、Z2 、Z3 And Z4 The gear numbers of the sun gear (1), the first planet gear (2), the second planet gear (3) and the internal gear (4) are respectively; wherein, V1 Is the linear velocity V of the meshing point at the reference circle of the sun wheel (1)2 Is the linear speed of the meshing point at the reference circle of the first planet wheel (2), V7 Is a linear velocity, V, about the centre line of rotation of the planet carrier (7)3 Is the linear velocity V of the meshing point at the reference circle of the second planet wheel (3)4 The linear speed of the meshing point at the reference circle of the internal gear (4); omega2 Angular velocity, omega, for rotation of the first planet wheel (2)3 Is the angular velocity, omega, of the rotation of the second planet wheel (3)4 The angular speed of the rotation of the internal gear (4); m is the gear module.
2. A planetary gear transmission, comprising: a housing (5) with an internal gear (4) formed on the inner peripheral wall, a planet carrier (7), a sun gear (1), at least one planetary gear set (9) arranged on the planet carrier (7); the planetary gear set (9) comprises a first planetary gear (2) and a second planetary gear (3) which are coaxially arranged, the first planetary gear (2) is meshed with the sun gear (1), and the second planetary gear (3) is meshed with the inner gear (4); when the sun gear (1) rotates, the planet carrier (7) can be driven to rotate through the planetary gear set (9); wherein the content of the first and second substances,
sun gear (1), first planet wheel (2), planet carrier (7) linear velocity relation model is: v1＝V7+V2(ii) a The second planet wheel (3), internal gear (4), planet carrier (7) linear velocity relation model are: v4＝V7-V3(ii) a The known conditional calculation formula of the sun wheel (1), the first planet wheel (2) and the second planet wheel (3) is as follows: v1＝ω1×m×Z1/2；V2＝ω2×m×Z2/2；V3＝ω3×m×Z32; the known conditional calculation formula of the internal gear (4) is: v4＝ω4×m×Z40 is defined as/2; the known condition calculation formula of the planet carrier (7) is as follows: v7＝ω7×m×(Z4-Z3)/2；
The angular speed ratio of the sun gear (1) and the planet carrier (7) meets a formula I; the first formula is as follows:
Figure FDA0003640288110000021
wherein, ω is1 Angular velocity, omega, of rotation of the sun gear (1)7 Is the angular velocity, Z, of the rotation of the planet carrier (7)1 、Z2 、Z3 And Z4 The gear numbers of the sun gear (1), the first planet gear (2), the second planet gear (3) and the internal gear (4) are respectively; wherein, V1 Is the linear velocity V of the meshing point at the reference circle of the sun wheel (1)2 Is the linear speed of the meshing point at the reference circle of the first planet wheel (2), V7 Is a linear velocity, V, about the centre line of rotation of the planet carrier (7)3 Is the linear velocity V of the meshing point at the reference circle of the second planet wheel (3)4 The linear speed of the meshing point at the reference circle of the inner gear (4); omega2 Angular velocity, omega, for rotation of the first planet wheel (2)3 Is the angular velocity, omega, of the rotation of the second planet wheel (3)4 The angular speed of the rotation of the internal gear (4); m is the gear module.
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