The disc spring has a small axial dimension, a large bearing capacity, and a non-linear characteristic with variable stiffness, and thus has been widely used in the introduction of equipment, especially in recent years, in the main clutch of the introduction of the vehicle, the disc spring is increasingly used. In order to achieve the separation and combination of power transmission, therefore, the advantages and disadvantages of the disc spring design directly affect the vehicle's performance. To this end, this paper discusses the working characteristics, optimization design and CAD method of the disc spring. At the same time, the practical disc spring optimization software was developed. According to the optimization results, CAD design was carried out, and various disc spring load and deformation characteristic curves, stress and deformation curves and disc spring parts working diagrams were drawn. In order to facilitate the user's use, the software adopts the combination of Chinese and Western styles, and designs a two-level color interface menu, thus forming a disc spring optimization and CAD software system. This is of great significance for the integrated design of the disc spring and the localization of the introduction of the vehicle clutch.
Deformation characteristics of disc spring
Figure 1 is a deformation characteristic curve of a disc spring. Point b is the operating point of the clutch friction plate in the engaged state when it is not worn. This point should ensure that the disc spring has sufficient pressing force and has an appropriate reserve factor. Point P is the operating point when the disc spring is flattened, so point b should be selected between the curves SP. When the friction plate wears Δλ, the working point of the disc spring is moved from b to point a. At this time, the pressing force Pa should be close to Pb to ensure that the clutch reserve coefficient is basically unchanged. The d point is the working point of the disc spring after the clutch is completely separated. In order to ensure the small pedal force during the operation, the separation point d should be close to the minimum point c of the load.
Formula for calculation of disc spring characteristics
The relation between the load P and the deformation λ and the maximum stress appearing at the upper edge of the inner circumference of the disc spring are
(1)
(2)
figure 1
In the formula:
E——the modulus of elasticity of the material;
μ - material Poisson ratio;
H - the truncated cone is high inside the disc spring portion;
H——the thickness of the disc spring;
Re——the outer radius of the disc spring;
Ri - the inner radius of the disc spring portion;
Re1 - the radius of contact between the disc spring and the platen;
Ri1 - the average radius of the support ring;
Rf——the separation radius of the bearing;
β2——The root width coefficient of the separation claw.
The disc spring must ensure that the maximum torque of the engine is reliably transmitted when the clutch is engaged, and the working load is
Pb=βMemax/(fRcZc) (3)
Where: β - clutch reserve factor;
Memax - the maximum output torque of the engine;
F——friction coefficient;
Rc——the average radius of the friction plate;
Zc——The total number of working faces of the friction plate.
figure 2
Disc spring optimization mathematical model and method
3.1 Design variables and objective functions
The inner cone height H, the thickness h of the disc spring and the inner radius Ri of the disc spring have a significant influence on the working performance. In addition, the separation point and compression point deformation λD and λb are also the main factors affecting performance. Therefore, considering the structure and working parameters, the design variables are determined as H, h, Ri, λb, λf, ie X=[x1, x2, X3, x4, x5] = [H, h, Ri, λb, λf].
For the vehicle clutch, the friction plate is worn due to frequent engagement and separation, causing a pressure drop, which causes the transmitted torque to be unstable. In order to ensure the reserve coefficient of the clutch and its working reliability, the working load change of the disc spring (|Pa-Pb|) before and after the friction plate wear is taken as an objective function. Another important feature of the clutch is the portability of the operation, so the pedal force cannot be too large when separating, and the disc spring separation force also serves as an objective function.
In the formula:
Δs - the maximum amount of wear allowed per friction plate;
λD=λb+λf
Δ1, δ2 - weighting factor.
3.2 Constraints
(1) The height-thickness ratio H/h of the disc spring has the greatest influence on its characteristics, and it has a negative stiffness only when it is controlled within a certain range. Therefore
Therefore
(2) The life of the friction plate requires that the pressure should not be too high and must be lower than the allowable stress [q]
(3) The deformation of the disc spring under the action of the load Pb should be in accordance with λs < λb < λp, λp = H, and λs is the deformation at the maximum load of the disc spring. Obtained by formula (1)
(4) When the clutch is completely separated, the working point d of the disc spring should be close to point c, ie λd-λc
(5) Disc spring strength requirements
Here, the intensity condition is treated as a fuzzy problem. The amplification coefficient β (β=1.05～1.30) is now introduced, and the fuzzy intensity condition is calculated as: σmax(λD)<β[σ]-80λ*, λ* is the most Excellent level cuts.
G7(X)=β[σ]-80λ-σmax(λD)>0
(6) Disc spring structure and process requirements
1.2
0.15
G8(X)=Re/x3-1.2>0
G9(X)=1.8-Re/x3>0;
G10(X)=x1/(Re-x3)-0.15>0
G11(X)=0.28-x1/(Re-x3)>0
(7) Disc spring deformation limit
1.8<λb<13 1.0<λf<11
G12(X)=x4-1.8>0
G13(X)=13-x4>0
G14(X)=x5-1.0>0
G15(X)=11-x5>0
(8) Boundary condition requirements
Tgα=H/(Re-Ri); 5°<α<11°;5
G16(X)～g23(X)
(9) Disc spring working load meets clutch requirements
P(λb)=Pb
H1(X)=Pb-P(x4)=0
3.3 Optimization method
In summary, a mathematical model of five-dimensional nonlinear optimization consisting of 23 inequality constraints, one equality constraint, and two objective functions is established.
(5)
Here, the hybrid penalty function method is used for optimization, and its expression is
Through the above method, the optimization software is completed, and the result can be obtained through calculation.
Disc spring CAD
Through the above optimization, the H, h, Ri, λb and λf of the disc spring can be obtained, so that all the structural parameters and performance parameters can be calculated, and the disc springs of different specifications can be obtained by changing the ratio of the inner and outer diameters to form a full series. design. On this basis, the working characteristic curve, stress deformation curve and part working diagram of the disc spring can be drawn, and the optimization results are output in the form of drawings and data. In addition, the CAD software also designed a two-level user interface menu with a three-dimensional stereo display for users to choose. The above CAD program software is written in Turbo C language and runs under the Turbo C 2.0 integrated development environment to complete the process of reviewing the source program, modifying the original data, running the optimization program, consulting the running results, and drawing the characteristic graph and the part drawing. All processes form an optimization and CAD software system.
Case analysis and discussion
The relevant parameters of a vehicle clutch and disc spring are: N=14.7kW; n=2000r/min; β=1.7; f=0.25; Zc=2; Δs=1.0mm; e=0.2, μ=0.3; [q]= 7 MPa; [σ] = 1570 MPa; E = 2.06 × 105 MPa. The results obtained by optimization and CAD analysis are shown in Table 1 and Figures 3 to 5.
Figure 3 disc spring load deformation diagram
It can be seen that when the clutch transmission torque is the same, the optimized structural dimensions of the disc spring are basically the same, and do not change with the change of m=Re/Ri, but the pressure, deformation, stress and the outer diameter of the disc spring vary with m. When m is increased, the pressures Pb and Pa also increase, and the outer diameters of the disc springs De=2Re and Ri become smaller. This is because when the outer diameter is reduced, only Ri decreases, and sufficient friction area is obtained. In order to meet the requirements of transmitting the same torque, of course, the pressure must be increased, that is to say, when the structure size is large, it is preferable to select a small m value, and when the structure size is small, it is preferable to use a larger m, so that the disc spring pressure is good. The change ΔP is small and the separation force is also small, as shown in Table 1 for m=1.2 and 1.4 optimization results. When the m=1.7, the disc spring pressure change reaches 23.92%. This result is not preferable, so it is recommended that the value of m be between 1.2 and 1.6. Therefore, the selection principle of the disc spring can be carried out as follows: for a high-power vehicle clutch having a large structural size, the disc spring should be selected to have a small m value, and for a clutch having a small power structure size, the disc spring should be selected to have a larger m value. .
Figure 4 Disc spring stress deformation diagram
Figure 5 Working part of the disc spring part
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