Question

ть KŽ Uc F 1 Forces on the wheel and suspension F, = K, (x– x,,) F, = K (x, -x)+C(, x;) mw кр F, Equations of motion muž, = F, - F, mä= F, The two-mass mechanical system represents a simplified model of one quarter of a car. Your task is to "tune” the suspension components of the spring Ks, and the damper, Cs, to give the best ride comfort. The ride comfort can be measured by how much the acceleration of the car body (čo) reacts to road inputs (e.g. a step input), but it is also important to keep the relative movement of the suspension low. The transfer function between the input (the road surface displacement, xg) and the body displacement (xb) is defined, and the frequency and (time domain) step response needs to be determined. Check these responses. Initially you can begin with Ks=10000 and Cs=125. (You may keep Kp=, 120000 since this is determine by the tyre pressure and mo=250, mw=50). In both the frequency and time domain you should be able to observe two different oscillations. The high frequency one is due to the tyre, while the lower frequency one is due to the body mass. Obviously, the parameters given do not result in good suspension system. Your task is to try and obtain a better system by altering the suspension parameters K, and Cs. Firstly derive:- a) The transfer function between the road surface displacement and the acceleration of the car body. b) The transfer function between the road surface displacement and the relative movement between the car body and the tyre (Xb - Xw) (called the suspension deflection).

Please explain and describe in details by step step how the transfer function between the road surface displacement and the acceleration of the car body is derived and how the transfer function between the road surface displacement and the relative movement between the car body and the tyre is derived.

Answer 1

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