A half-car model of an automobile suspension system is shown below. You are to design its suspension systems (values of spring constants and damping constants). Generally, for ride comfort, it is desired to have the bounce motion at low frequency and the pitch motion at

Question

relatively higher frequency for handling and control.Assuming the mass of the half-car is 0.8 metric ton, the moment of inertia about
the center of mass being 260 kg-m2, and the wheel base of 2 meters, design the suspension system such that the predominantly bouncing mode (or approximate bouncing) occurs at a frequency between 1.5 Hz and 2.2 Hz and the predominantly pitching mode (or approximate pitching) between 2.5 to 3.0 Hz. The center of mass of the car does not have to be at the geometrical center. Also, for each quarter car system, the damping ratio should be between 0.5 and 0.6. The damping ratio for each quarter car is defined as :
£ii=bi/2m wni where i=1 is for the
rear quarter car and i=2 is for the front quarter car, and £sn is the natural frequency for the quarter car.

Answer 1

Estimate and discuss the maximum bouncing and pitching generated by your
design when the car travels at 40 km/hr over a rugged terrain roughly modeled by a sine wave
with 0.10 meter amplitude and 4.0 meter period. (This one does not have to be an accurate
calculation. State all your assumptions for this estimation.) Be as detailed in your discussion as
possible!