The quarter-car model of a vehicle suspension and its free body diagram is 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.
- Draw a free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function.
k=10000, 30000, 50000 N/m
c=1000, 2000, 3000 N.s/m
- 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).
- Use the derived transfer function to model the system and plot the step response for the system by Matlab or Simulink.
A common example of base excitation is caused by a vehicle moving along a bumpy road surface as shown in Figure 2. This motion produces a displacement input to the suspension system via the wheels. The second task is to calculate and draw a displacement transmissibility ratio diagram for a quarter car with 250 kg, the spring constant is 10000 N/m, but varying damping constant to be 1000, 2000, 3000, 5000, and 10000 N.s/m. If the vehicle driver wishes to reduce the vehicle’s body displacement, what suggestion you could make for the driver and why?
Are You Looking for Answer of This Assignment or Essay
The post NHA2414: Draw a free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function: Dynamic Analysis and Control Assignment, UOH, UK appeared first on Students Assignment Help UK.