When the shape memory alloy wire with initial residual deformation is completely confined, the relationship between the recovery stress and temperature changes is as shown. In the OA segment and BC segment, the SMA recovery stress changes linearly with temperature, but in the AB segment, the change in the recovery stress is no longer nonlinear. In this case, the recovery stress is not only a function of temperature but also the elastic modulus of the material. The tensor is related to the expansion coefficient, and the recovery stress of this segment increases sharply with the increase of temperature. Compared with the OA segment and the BC segment, the corresponding time is faster, which is very favorable for controlling the stiffness variation of the suspension.
Restoration Stress and Suspension Stiffness After adding the shape memory alloy, the stiffness k of the spring is regarded as having two parts. The stiffness of the ks. spring produced by the kb produced by the matrix and the shape memory is equivalent to the parallel effect of the two. :k=kb+ks(7) According to the σr-T curve shown, we can definitely find the mapping of σr to ks, that is, there is a one-to-one relationship between σr and ks. Let us assume that: ks=f(σr) is Ks is a function of σr recovery stress. From equation (7): k=kb+f(σr)(8) and: σr=f(T)(9) is known from equation (3), equation (8), and equation (9), and the car with shape memory alloy is added. Suspension natural frequency ω = f (T), that is, adjusting the temperature can change the natural frequency of the suspension to reach the goal set by the active control.
LQG controller design evaluation The main indicators of suspension performance are: tire dynamic load D, suspension stroke H and vertical acceleration I. The performance indicator J in the controller design is the weighted sum of squares of D, I, and H. The integral in the time domain T is expressed by the following formula: J=limT→∞1T0" (q1D2+q2H2+q3I2)dt(10)q1, q2, and q3—weighting coefficients for tire movement, suspension travel, and body vertical acceleration. It can be obtained through experience or relevant data.The optimal control feedback gain matrix can be obtained by the Riccati equation: K=BTP+NT;the optimal control force is: Ua=-KX(t), the optimal control temperature is: Ta=φ -1(Ua).
Conclusions and prospects This article analyzed in detail the influencing factors of the car suspension performance, put forward the idea of ​​introducing shape memory alloy into the active suspension, and proved its feasibility in theory, in order to give full play to the special performance of shape memory alloys, part 3 The application of the optimal control theory to the suspension with SMA is introduced. Through theoretical analysis, the optimal control temperature is obtained. As the suspension system of the composite material adjusts the rigidity, it has a very attractive development prospect and development space, and is a very ideal suspension system. Can achieve higher control performance and better economic benefits, with a wide range of application value.
This thesis only qualitatively analyzes the suspension system with SMA. In the actual design of the automobile suspension, it should be calculated and calculated according to the objective factors such as actual material selection and environment, so as to achieve the optimal design. Although the research of SMA smart composite structure has made a series of progress recently and it has gradually entered the stage of engineering application, because many of the theoretical and technical problems have not yet been broken, there is still a certain gap from the practical goal. In addition, SMA has a certain lag on temperature conduction, and the development of advanced heat transfer methods is the first problem to be solved.
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