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The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simplified model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car's speed. a) Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function.

The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simplified model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car's speed. a) Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Task 1): The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simplified model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car's speed. a) Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. Body m 1 Suspension Road k Datum level Figure 1 Dynamic Analysis and Control If assume: m=250 kg k=10000, 30000, 50000 N/m c=1000, 2000, 3000 N.s/m b) Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). c) Use the derived transfer function to model the system and plot the step response for the system by Matlab or Simulink. 10100101010 101010101 133374
Transcribed Image Text:Task 1): The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simplified model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car's speed. a) Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. Body m 1 Suspension Road k Datum level Figure 1 Dynamic Analysis and Control If assume: m=250 kg k=10000, 30000, 50000 N/m c=1000, 2000, 3000 N.s/m b) Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). c) Use the derived transfer function to model the system and plot the step response for the system by Matlab or Simulink. 10100101010 101010101 133374
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