Vehicle Ride
1.The wheel center rate (Kw) is the rate of wheel displacement and the spring rate is the spring stiffness. They are related to each other by the installation ratio or the motion ratio.
Kw = Ks * (mr)^2.
Normally the wheel rate is always lesser than the spring rate in a double wishbone setup, because a 1:1 motion ratio is difficult to achieve due to packaging constraints.
However, the suspension can either have a rising rate (motion ratio increases with wheel travel) or falling rate ( motion ratio decreases with wheel travel)
2. The ride rate is the effective spring rate of the suspension stiffness and the tire stiffness, since they are connected in series. In essence, it is a series combination of the wheel rate and the tire rate. It is measured at the wheel center level.
Kr = (Kw*Kt)/(Kw+Kt).
In normal practice, the ride rate is slightly lesser than the wheel rate due to the series combination with the tires.
3. Damping required cannot be the same in all regions
1) At Low frequency - high damping ratio is preferred, to control the body bounce (sprung mass). More damping force.
At high frequency - low damping ratio is preferred, to control the wheel hop (unsprung mass). - Less damping force
2) Compression - lower damping rate is preferred, since the spring is compressing and the damping force is less.
Rebound - higher damping rate is preferred, since the spring is releasing the energy and we need high damping force.
Normally the rebound side is 2-3 times stiffer than the compression side.
4.When encountering a bump, the front suspension hits it a little earlier than the rear suspension. This time gap causes a pitching motion, if both the front and rear ride frequencies are the same. Therefore if the rear ride freqency is higher than the front, the rear will catch up with the front within 1-1.5 seconds. This is why rear ride frequency is normally higher (1.2 times) than the front ride frequency.
5. Vibration isolation
i) A lower unsprung mass is preferred in the wheel hop region for better vibration isolation
ii) A lower damping is preferred in the wheel hop ( high frequency) region for better vibration isolation.
6. Air suspensions are more compliant than steel suspensions, which means that they are less stiffer.
From a ride frequency standpoint, we know that fs = (1/2*pi)*sqrt(Kr/m) where Kr is the ride rate.
Therefore the lesser the stiffness, the lesser the ride rate and the lesser the ride frequency, which leads to a smoother ride.
7. M = 2000 kg
F:R = 50:50
Total Weight on each axle = 1000 kg.
Total Weight on each corner = 500 kg
Sprung mass_corner = Total weight on corner - Unsprung mass_corner
Sprung mass_corner = 500 - 50 = 450 kg
Spring stiffness Ks = 25 N/mm, tire stiffness Kt = 250 N/mm.
Wheel rate Kw = Ks * (MR)2.
Assuming MR of 1, Kw = Ks.
Kw = 25 N/mm.
Ride rate Kr = (Kw*Kt)/(Kw+Kt)
Kr = (25*250)/(25+250)
Kr = 22.72 N/mm or 22727.2 N/m.
Sprung mass natural frequency = (1/2*pi)*sqrt(Kr/m_s) =(1/2*pi)*sqrt(22727.2/450) = 1.13 Hz.
Unsprung mass natural frequency = (1/2*pi)*sqrt(Kw+Kt/m_us) = (1/2*pi)*sqrt((25000 + 250000) /50) = 11.80 Hz.
8. Time lag
i) Front ride frequency = 1.2 Hz. Time period (ts) = 1/1.2 = 0.833 s
Rear ride frequency = 0.8 Hz. Time period (ts) = 1/0.8 = 1.25 s
Time lag = 1.25 - 0.833 = 0.417s ( +ve sign because front faster than rear)
ii)Front ride frequency = 1.2 Hz. Time period (ts) = 1/1.2 = 0.833 s
Rear ride frequency = 1.45 Hz. Time period (ts) = 1/1.45 = 0.689 s
Time lag = 0.689 - 0.833 = - 0.143s (- ve sign because rear faster than front)
Wheelbase = 98.42 inches = 2.5 m
Speed = 37.42 mph = 16.72 m/s
Time lag = Wheelbase / Speed = 2.5/16.72 = 0.15 s
Due to the wheelbase, the time lag is 0.15 seconds, which means that the second set of frequency values (Front = 1.2 Hz, Rear = 1.45 Hz) would produce better results from a flat ride point of view, since the time lag for that case is 0.143 s which is within the time lag calculated due to the wheelbase.