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Source: Author: Shao Huangxinna Long Wu Keywords: clutch, CAD
Disc spring is widely used in imported equipment because of its nonlinear characteristics of small axial size, large bearing capacity and variable stiffness. Especially in recent years, more and more imported automobile main clutches use disc springs to realize the separation and combination of power transmission. Therefore, the quality of disc spring design directly affects the performance of vehicles.
Therefore, this paper discusses the working characteristics, optimal design and CAD method of disc spring. At the same time, the practical optimization software of disc spring is developed, and its CAD design is carried out according to the optimization results, and various load and deformation characteristic curves, stress and deformation curves and working drawings of disc spring parts are drawn. For the convenience of users, a two-level color interface menu is designed by combining Chinese and western languages in the software, thus forming a disc spring optimization and CAD software system. This is of great significance to the integrated design of disc springs and the localization of imported automobile clutches.
Deformation characteristics of disc spring
Figure 1 is the deformation characteristic curve of belleville spring. Point B is the working point when the clutch friction plate is not worn. This point should ensure that the disc spring has enough pressing force and suitable reserve coefficient. Point P is the working point when the belleville spring is compressed, so point B should be chosen between curves SP. When the friction plate wears Δ λ, the working point of the disc spring moves from B to A, and the pressing force Pa should be close to Pb at this time to ensure that the clutch reserve coefficient is basically unchanged. Point D is the working point of the disc spring after the clutch is completely separated. In order to ensure that the pedal force is small during operation, the separation point D should be close to the minimum load point C.
Related calculation formulas of disc spring characteristics
The relationship between the load p and the deformation λ and the maximum stress of the upper edge of the inner circumference of the belleville spring is as follows.
( 1)
(2)
Figure 1
Among them:
E—— elastic modulus of material;
μ —— Poisson's ratio of materials;
H—— the height of truncated cone in disc spring;
H—— thickness of belleville spring;
Re-determine the outer diameter of the disc spring;
Ri- inner diameter of belleville spring;
Re 1- contact radius between disc spring and pressure plate;
Ri 1- average radius of support ring;
RF-the action radius of the release bearing;
β2—— Width coefficient of separating claw root.
The disc spring must ensure that the maximum torque of the engine is reliably transmitted when the clutch is engaged, and its working load is
Pb=βMemax/(fRcZc) (3)
Where: β-clutch reserve coefficient;
Memax-the maximum output torque of the engine;
F- friction coefficient;
RC-average radius of friction plate;
Zc—— the total number of working faces of friction plates.
Figure 2
Mathematical model and method of disc spring optimization
3. 1 Design variables and objective functions
The height h and thickness h of the inner cone of the disc spring and the inner diameter ri of the disc spring have significant effects on its working performance. In addition, the deformation λD and λb of separation point and compaction point are also the main factors affecting the performance. Therefore, consideRing the structure and working parameters, the design vaRiables are determined as h, h, ri, λb, λf, that is, X=[x 1, x2, x3, x4, x5]=[H, h, ri, λb, λf].
For vehicle clutch, frequent engagement and disengagement will lead to friction plate wear, pressure drop and unstable transmission torque. In order to ensure the reserve coefficient of clutch and its working reliability, the working load change (|Pa-Pb|) of belleville spring before and after friction plate wear is taken as the objective function. Another important feature of the clutch is that it is easy to operate, so the pedal force should not be too large when separating, and the separation force of the disc spring is also taken as the objective function.
Among them:
δs—— the maximum allowable wear of each friction plate;
λD=λb+λf
δ 1, δ2- weighting factor.
3.2 Constraints
The height-thickness ratio H/h of (1) disc spring has the greatest influence on its characteristics, and it has negative stiffness only if it is controlled within a certain range. therefore
therefore
(2) The service life of the friction plate requires that the pressure should not be too high and must be lower than the allowable stress [Q].
(3) Under the action of load Pb, the deformation of the belleville spring should conform to λ s.
(4) When the clutch is completely disengaged, the working point D of λd-λc spring should be close to point C, namely λ D-λ C..
(5) disc spring strength requirements
In this paper, the strength condition is treated as a fuzzy problem, and the amplification factor β (β = 1.05 ~ 1.30) is introduced. Through calculation, the fuzzy strength condition is σ max (λ d)
G7(X)=βのσ?-80λ？ -σmax(λD)>0
(6) Structure and process requirements of disc spring
1.2
0. 15
G8(X)= Re/x3- 1.2 & gt； 0
g9(X)= 1.8-Re/x3 & gt； 0;
g 10(X)= X 1/(Re-x3)-0. 15 & gt； 0
g 1 1(X)= 0.28-X 1/(Re-x3)>0
(7) Deformation limit of belleville spring
1.8 & lt； λb & lt； 13 1.0 & lt； λf & lt； 1 1
g 12(X)= x4- 1.8 & gt； 0
g 13(X)= 13-x4 & gt； 0
g 14(X)= X5- 1.0 & gt； 0
g 15(X)= 1 1-X5 & gt； 0
(8) Boundary condition requirements
TGα= H/(Re-Ri)； 5 & ltα& lt； 1 1 ; five
g 16(X)~g23(X)
(9) The working load of the disc spring meets the requirements of the clutch.
P(λb)=Pb
h 1(X)=Pb-P(x4)=0
3.3 Optimization method
To sum up, a five-dimensional nonlinear optimization mathematical model consisting of 23 inequality constraints, 1 equality constraints and 2 objective functions is established, namely
(5)
In this paper, the mixed penalty function method is used for optimization, and its expression is
The optimization software is completed by the above method, and the results can be obtained by calculation.
Computer aided design of disc spring
Through the above optimization, H, H, Ri, λb and λf of the disc spring can be obtained, so that all structural parameters and performance parameters can be calculated. By changing the ratio of inner diameter to outer diameter, disc springs with different specifications can be obtained, forming a full series of designs. On this basis, the working characteristic curve, stress-deformation curve and working diagram of disc spring can be drawn, and the optimization results can be output in the form of graphics and data. In addition, a two-level user interface menu is designed in CAD software and displayed in three-dimensional characters for users to choose from. The above CAD program software is written in Turbo C language and runs in Turbo C 2.0 integrated development environment, thus completing the whole process from consulting the source program, modifying the original data, running the optimization program, consulting the running results, drawing the characteristic curve and part drawing, thus forming an optimization and CAD software system.
Example analysis and discussion
The relevant parameters of a vehicle clutch and disc spring are: n =14.7 kw; N = 2000r rpm; β= 1.7; f = 0.25ZC = 2； δs = 1.0mm； e=0.2，μ= 0.3； 〔q〕= 7 MPa； のσ?= 1570 MPa； E = 2.06× 105 MPa. Through optimization and CAD analysis, the results are shown in Table 1 and Figures 3 ~ 5.
Fig. 3 Load deformation diagram of belleville spring
It can be seen that when the clutch transmits the same torque, the optimized structural dimensions of the belleville spRing are basically the same, and do not change with the change of m=Re/Ri, but the pressure, deformation, stress and outer diameter of the belleville spring change with the change of m. When m increases, the pressures Pb and Pa also increase, while the outer diameters of the belleville spring De=2Re and ri decrease. This is because when the outer diameter decreases, only when Ri decreases can there be enough friction area to meet the requirement of transmitting the same torque. Of course, the pressure must be increased, that is to say, it is better to choose a small m value when the structural size is large and a large m value when the structural size is small, so that the pressure change δ P of the disc spring is small and the separation force is small. When m= 1.7, the pressure change of disc spring reaches 23.92%, which is not desirable. It is suggested that the value of m should be between 1.2 ~ 1.6. Therefore, the selection principle of disc spring can be carried out as follows: for high-power vehicle clutch with large structural size, the disc spring should choose a smaller M value, while for low-power clutch with small structural size, the disc spring should choose a larger M value.
Fig. 4 Stress-deformation diagram of belleville spring
Fig. 5 Working diagram of disc spring parts