CN112711821A - Design method of spring for clutch gear - Google Patents

Design method of spring for clutch gear Download PDF

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CN112711821A
CN112711821A CN202011593340.1A CN202011593340A CN112711821A CN 112711821 A CN112711821 A CN 112711821A CN 202011593340 A CN202011593340 A CN 202011593340A CN 112711821 A CN112711821 A CN 112711821A
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spring
clutch
turns
diameter
force
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CN112711821B (en
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胡波
周长江
刘辉华
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Hunan Desheng Intelligent Technology Co Ltd
Changsha University of Science and Technology
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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Abstract

The invention discloses a design method of a spring for a clutch gear. The invention adopts the finite element thought to disperse the contact surface of the clutch, thereby achieving high calculation precision and realizing the rapid design of the inner diameter and the outer diameter of the spring and the number of surrounding circles through the working range of the torque.

Description

Design method of spring for clutch gear
The technical field is as follows:
the invention belongs to the field of machinery, and particularly relates to a design method of a spring for a clutch gear.
Background art:
when the steering engine operates, overload bagging easily occurs, and damage occurs to a motor transmission shaft or a transmission gear and the like. The present company has therefore invented a clutch as shown in particular in figures 1 and 2. The clutch gear with sawteeth on the end face and the spring are adopted to realize transmission and overload protection. The spring is the key for ensuring that the clutch can normally work within the range of ensuring the rated torque and can carry out overload protection after the rated torque is exceeded.
However, the rated torque depends not only on the material of the spring but also on the frictional force between the saw-tooth end surfaces and the axial displacement distance of the saw-tooth end surfaces, but the saw-tooth has a curved surface shape, and the frictional force differs depending on the state. Therefore, when clutches with different specifications are manufactured, continuous trial and error are usually required, and when the spring material is replaced in different applicable environments, the trial and error are required again, so that the spring design is time-consuming and labor-consuming, and improvement is required.
The invention content is as follows:
the invention aims to provide a design method of a spring for a clutch gear, which disperses a contact surface of a clutch by adopting a finite element idea so as to achieve high calculation precision and realizes the rapid design of the inner diameter and the outer diameter of the spring and the number of surrounding circles through the working range of torque.
In order to solve the problems, the technical scheme of the invention is as follows:
5. a design method of a spring for a clutch gear is characterized by comprising the following steps:
step one, obtaining the number of sawteeth on a single clutch gear, namely the number N of contact surfaces between the clutch gears; then each contact surface is separated and dispersed into m units by finite element analysis, and then:
Figure BDA0002869267130000021
in the formula (1), T is the torque of the clutch shaft; n is the number of contact surfaces, m is the number of units of a single contact surface, alphaiIs the included angle between the normal line of the ith unit centroid and the clutch axis;
Figure BDA0002869267130000026
is the displacement vector from the centroid of the unit i to the clutch axis, mu is the coefficient of friction, FniFor the contact force of unit i, let fiIs the friction of cell i; ftiIs FniComponent along the gear face, ftiIs fiComponent along the gear face;
step two, let the contact force on the unit area of the contact surface be P, then the formula (1) is written as:
Figure BDA0002869267130000022
in the formula (2), siIs the area of cell i;
Figure BDA0002869267130000023
in the formula (3), gammaiFor projection and vector of contact force in xy plane, i.e. radial section of clutch shaft
Figure BDA0002869267130000027
The included angle therebetween;
step three, obtaining the elastic force F of the spring:
Figure BDA0002869267130000024
Fsiand fsiThe component force of the contact force and the friction force in the axial line direction of the clutch shaft respectively;
substituting the formula (3) into the formula (4) to obtain:
Figure BDA0002869267130000025
step four, the contact surface does not slide relatively under the rated torque, and the method comprises the following steps:
Figure BDA0002869267130000031
wherein, T0Representing the rated output torque of the gear shaft; f0Indicating the spring pre-tightening force when the rated torque is maintained;
at a defined maximum torque, the contact surfaces need to be disengaged from each other, then:
Figure BDA0002869267130000032
wherein, TeRepresenting a defined maximum torque; fsThe maximum elastic force of the spring indicating that the contact surfaces are separated from each other; m is1The number of the units of the topmost 1 line of the contact surface;
step five, according to the elastic force formula of the spring, the method comprises the following steps:
F0＝kΔl0 (8)
Δl0indicating spring preload of F0The precompression of the spring at time, k, represents the theoretical spring rate of the spring, and is further found to be:
Fs＝k(Δl0+h) (9)
wherein h is the height of the saw teeth on the clutch gear;
the combined type (8) and the formula (9) obtain:
Figure BDA0002869267130000033
Figure BDA0002869267130000034
step six, obtaining the diameter of the clutch shaft, namely the inner diameter D of the springiAdding a to the diameter of the clutch shaft; setting: d is the diameter of the spring wire; doIs the outer diameter of the spring;
the pitch diameter D of the spring is then expressed as:
Figure BDA0002869267130000041
calculating the theoretical effective number of turns n of the spring0Comprises the following steps:
Figure BDA0002869267130000042
wherein G represents the shear modulus of the spring material;
wherein for the springThe manufacture is convenient, the effective turns of the spring are standardized and serialized, and the theoretical effective turns n are selected according to the standardized series0The most similar standard effective number of turns n is obtained due to the standard effective number of turns n and the theoretical effective number of turns n0And (3) difference exists, after the standard effective number of turns n is taken, the actual elastic coefficient K of the spring is checked again as follows:
Figure BDA0002869267130000043
checking according to the actual elastic coefficient K of the spring: whether the springs can prevent the two gears under rated torque from sliding in the compression range of actual work when the springs are at the minimum elastic force and whether the two gears under the limited maximum torque can be separated when the springs are at the maximum elastic force is obtained; if yes, checking, and taking the number of standard effective turns as n; otherwise, adjusting the diameter d of the spring wire until the diameter d passes the verification;
and step seven, adding the additional number of the cold coil of the spring and the additional number of the hot coil of the spring to the effective number of the coils n of the spring to obtain the total number of the coils of the spring.
In a further improvement, m is 566.
In a further improvement, N is 6.
In a further improvement, a is 0.1-0.2 mm.
Further improvement, the wire diameter d of the spring wire is determined firstly, and then the effective number of turns n is calculated for the formula (13); checking whether the selected d is reasonable or not through the shearing strength of the formula (15), and if not, replacing the diameter d of the spring silk thread until the checking is passed;
spring shear strength formula:
Figure BDA0002869267130000051
wherein C is the surrounding ratio of the spring, D is the middle diameter of the spring, FmaxIs the maximum force to which the spring is subjected during operation.
The further improvement is that the number of additional turns of the cold coil is 2-2.5 turns, and the number of additional turns of the hot coil of the spring is 1.5-2 turns.
The invention has the advantages that:
the invention adopts the finite element thought to disperse the contact surface of the clutch, thereby achieving high calculation precision and realizing the rapid design of the inner diameter and the outer diameter of the spring and the number of surrounding circles through the working range of the torque.
Description of the drawings:
FIG. 1 is a schematic view of a connection structure of two clutch gears;
FIG. 2 is a schematic view of a saw tooth structure of the clutch gear;
FIG. 3 is a schematic view of a discrete contact surface of the clutch gear;
FIG. 4 is a schematic view of a force analysis of a unit plane i;
FIG. 5 is DiAnd DoA parameter diagram of (a);
FIG. 6 is a parameter diagram of d and l.
The specific implementation mode is as follows:
in order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
Example 1
In a steering engine, the clutch gear is used for overload protection, and the gear can normally work under the working condition of rated torque; when the load of the output shaft reaches the protection threshold, the sawtooth contact force of the end faces of the two clutch gears 1 is increased, so that the clutch springs 2 are compressed, and the end faces of the clutch gears are meshed and separated, so that the function of protecting the servo motor and the gear set is achieved, as shown in fig. 1. According to the structure of the steering engine, when the motor rotates forwards or backwards, the clutch gears are in contact with 6 curved surfaces, as shown in fig. 2.
Because the contact curved surface is complicated, the curvature and normal direction of each contact position are different. In order to calculate the contact force and the spring force under different load torques more accurately, the contact curved surface of the clutch gear is divided into 566 small units, as shown in fig. 3. Based on the finite element concept, each small unit can be regarded as a plane, and the contact of the clutch end faces can be regarded as plane contacts with 566 different areas and normal directions.
Contact force F of unit i assuming uniform force of end face contactniAnd a friction force fiCan be decomposed into force components in the axial direction and the circumferential direction of the gear as shown in fig. 4.
Figure BDA0002869267130000061
In the formula: t is the torque of the clutch shaft; n is the number of contact surfaces (6 in this example), m is the number of cells, αiIs the included angle between the normal line of the centroid of the unit i and the clutch axis;
Figure BDA0002869267130000062
and mu is a displacement vector from the centroid of the unit i to the clutch axis, and is a friction coefficient. Let the contact force per unit area be P, the above equation can be rewritten as:
Figure BDA0002869267130000071
sithe area of the unit i is determined by the shape of the end face contact curved surface of the clutch gear, and the area of each unit, the included angle between the normal direction and the axial direction of the centroid,
Figure BDA0002869267130000072
The length of the modulus (c) is known, and P:
Figure BDA0002869267130000073
wherein, γiFor the contact force in the xy-plane (see the coordinate system of fig. 3, i.e. the plane of the section of the clutch shaft, in this caseHorizontal plane) and vectors
Figure BDA0002869267130000074
The included angle therebetween. And further obtaining the overall spring force F:
Figure BDA0002869267130000075
f in formula (5.4)siAnd fsiThe component of the contact force and the friction force in the direction of the clutch axis. Substituting equation (5.3) into (5.4), the spring force calculation can be changed to:
Figure BDA0002869267130000076
5.2 calculation of Pre-pressure and maximum spring force of spring
In order to ensure the steering engine to normally work under rated torque, the clutch gear can be designed to keep T under the action of the pre-tightening force of the spring0An output torque of 30N · mm (i.e., a rated torque). The pre-pressure F of the spring can be calculated by substituting the torque into the formula (5.5)0：
Figure BDA0002869267130000077
The output torque of the clutch shaft reaches TeThe clutch needs to be realized at 110N · mm. Substituting the value into equation (5.5) to obtain the elastic force F when the spring is compressed maximally (the clutch teeth are disengaged)s：
Figure BDA0002869267130000081
5.3 spring rate and precompression calculation
Let the spring constant and precompression be k and Δ l, respectively0Then the pre-pressure can be expressed as:
F0＝kΔl0 (5.8)
the height of the clutch section according to the tooth is h 1.0mm, so the maximum elastic force can be expressed as:
Fs＝k(Δl0+h) (5.9)
the elastic coefficient and the precompression of the spring can be obtained by simultaneous equations (5.8) and (5.9):
Figure BDA0002869267130000082
Figure BDA0002869267130000083
the requirement of machining precision is reduced, wherein 1 digit after the decimal point is taken, namely the precompression quantity of the clutch spring can be 0.4mm, the precompression force is slightly larger than the needed precompression force under the rated output torque, and enough spring force can be provided to ensure the rated output torque.
5.4 spring parameter design
The structure of a general cylindrical coil spring is shown in fig. 5 and 6. Wherein DiAnd DoRespectively the inner diameter and the outer diameter of the spring, d the diameter of the spring wire and l the free length of the spring.
The pitch diameter of the spring is an important parameter of a cylindrical helical spring, which can be expressed as:
Figure BDA0002869267130000084
the diameter of the clutch shaft is 1.6mm, and the clutch shaft must penetrate through the inner hole of the spring, so the inner diameter of the spring is 1.7 mm. The diameter of the temporary spring wire is 0.65mm, and the effective number of turns of the spring is calculated as follows:
Figure BDA0002869267130000091
according to the common series of values of the effective turns of the cylindrical spring, the effective turns n is 4.75. The number of additional turns of the spring cold coil is 2-2.5 turns; the additional number of turns of the spring hot coil is 1.5-2 turns. Here an additional 2 turns are taken so that the total number of turns of the spring is 6.75 turns. When the number of effective turns is 4.75, the elastic coefficient of the spring is
Figure BDA0002869267130000092
The elastic coefficient is slightly smaller than the calculated elastic coefficient, so that the normal work of rated torque can be ensured, and the clutch protection can be realized before the gear reaches the limited maximum torque.
The parameters of the clutch spring are shown in table 5.1.
TABLE 5.1 design parameters of steering engine clutch spring
Figure BDA0002869267130000093
5.5 advantages of the method
1: the conventional method mostly adopts the method that the equivalent wedge is formed, the stress analysis and the parameter calculation of the spring parameter are carried out, although the method is simple and convenient, the error is very large, and the clutch can not be realized when the clutch protection threshold value is exceeded.
2: the ideal method is to derive the curved surface equation of the clutch tooth surface, and carry out the calculation of the stress of the spring and the parameter design through the calculus. The method has the highest calculation precision on the curved surface which can be expressed by a simple equation, but is difficult to operate on the complex curved surface.
3: the method provided by the invention adopts a finite element idea and can realize the calculation of any clutch tooth surface. The calculation precision is very high, and the curved surface equation of the clutch tooth surface does not need to be derived.
The above-mentioned embodiment is only a specific embodiment of the present invention, and is not meant to be a limitation of the present invention, and any simple modification and replacement thereof are within the scope of the present invention.

Claims (6)

1. A design method of a spring for a clutch gear is characterized by comprising the following steps:
step one, obtaining the number of sawteeth on a single clutch gear, namely the number N of contact surfaces between the clutch gears; based on the finite element idea, then each contact surface is discretized into m units, then:
Figure FDA0002869267120000011
in the formula (1), T is the torque of the clutch shaft; n is the number of contact surfaces, m is the number of units of a single contact surface, alphaiIs the included angle between the normal line of the ith unit centroid and the clutch axis;
Figure FDA0002869267120000012
is the displacement vector from the centroid of the unit i to the clutch axis, mu is the coefficient of friction between the contact surfaces, FniIs the contact force of unit i, fiIs the friction of cell i; ftiIs FniComponent along the gear face, ftiIs fiComponent along the gear face;
step two, let the contact force on the unit area of the contact surface be P, then the formula (1) is written as:
Figure FDA0002869267120000013
in the formula (2), siIs the area of cell i;
Figure FDA0002869267120000014
in the formula (3), gammaiFor projection and vector of contact force in xy plane, i.e. radial section of clutch shaft
Figure FDA0002869267120000016
The included angle therebetween;
step three, obtaining the elastic force F of the spring:
Figure FDA0002869267120000015
Fsiand fsiThe component force of the contact force and the friction force along the axial direction of the clutch shaft respectively;
substituting the formula (3) into the formula (4) to obtain:
Figure FDA0002869267120000021
step four, the contact surface does not slide relatively under the rated torque, and the method comprises the following steps:
Figure FDA0002869267120000022
wherein, T0Representing the rated output torque of the gear shaft; f0Indicating the spring pre-tightening force when the rated torque is maintained;
at a defined maximum torque, the contact surfaces need to be disengaged from each other, then:
Figure FDA0002869267120000023
wherein, TeRepresenting a defined maximum torque; fsThe maximum elastic force of the spring indicating that the contact surfaces are separated from each other; m is1The number of the units of the topmost 1 line of the contact surface;
step five, according to the elastic force formula of the spring, the method comprises the following steps:
F0＝kΔl0 (8)
Δl0indicating spring preload of F0The precompression of the spring at the time, k, represents the theoretical spring rate of the spring,
further obtaining:
Fs＝k(Δl0+h) (9)
wherein h is the height of the saw teeth on the clutch gear;
the combined type (8) and the formula (9) obtain:
Figure FDA0002869267120000031
Figure FDA0002869267120000032
step six, obtaining the diameter of the clutch shaft, namely the inner diameter D of the springiAdding a to the diameter of the clutch shaft; setting: d is the diameter of the spring wire; doIs the outer diameter of the spring;
the pitch diameter D of the spring is then expressed as:
Figure FDA0002869267120000033
calculating the theoretical effective number of turns n of the spring0Comprises the following steps:
Figure FDA0002869267120000034
wherein G represents the shear modulus of the spring material;
wherein, for the convenience of spring manufacture, the effective turns of the spring are standardized and serialized, and the theoretical effective turns n are selected according to the standardized series0The most similar standard effective number of turns n is obtained due to the standard effective number of turns n and the theoretical effective number of turns n0And (3) difference exists, after the standard effective number of turns n is taken, the actual elastic coefficient K of the spring is checked again as follows:
Figure FDA0002869267120000035
checking according to the actual elastic coefficient K of the spring: whether the springs can prevent the two gears under rated torque from sliding in the compression range of actual work when the springs are at the minimum elastic force and whether the two gears under the limited maximum torque can be separated when the springs are at the maximum elastic force is obtained; if yes, checking, and taking the number of standard effective turns as n; otherwise, adjusting the diameter d of the spring wire until the diameter d passes the verification;
and step seven, adding the additional number of the cold coil of the spring and the additional number of the hot coil of the spring to the effective number of the coils n of the spring to obtain the total number of the coils of the spring.
2. The spring design method for a clutch gear according to claim 1, wherein m is 566.
3. The spring design method for clutch gears according to claim 1, wherein N-6.
4. The spring design method for clutch gears according to claim 1, wherein a is 0.1-0.2 mm.
5. The spring design method for a clutch gear according to claim 1, wherein the diameter d of the spring wire is determined first, and then the effective number of turns n is calculated for equation (13); checking whether the selected d is reasonable or not through the shearing strength of the formula (15), and if not, replacing the diameter d of the spring silk thread until the checking is passed;
spring shear strength formula:
Figure FDA0002869267120000041
wherein C is the surrounding ratio of the spring, D is the middle diameter of the spring, FmaxIs the maximum force to which the spring is subjected during operation.
6. The method for designing a spring for a clutch gear according to claim 1, wherein the number of additional turns of the cold coil is 2 to 2.5 turns, and the number of additional turns of the hot coil of the spring is 1.5 to 2 turns.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2009259194A (en) * 2008-03-17 2009-11-05 Mitsubishi Fuso Truck & Bus Corp Design optimization method and device using the method
US20160040733A1 (en) * 2013-04-10 2016-02-11 Litens Automotive Partnership Clutch assembly
US20170045118A1 (en) * 2015-08-10 2017-02-16 Southwest Research Institute Two-stage hypocycloidal gear train
US20200274431A1 (en) * 2017-09-15 2020-08-27 University Of Utah Research Foundation Cogging-torque actuator
CN107605984A (en) * 2017-10-26 2018-01-19 十堰市常越机电科技有限公司 A kind of automobile diaphragm spring clutch Optimization Design

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石光林等: "基于赫兹理论的超越离合器力学模型适应性和接触特性研究", 《机械传动》 *
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