Swift Sport Springs 2010/03/09Posted by Michael in my IS300.
I’ve read claims that stiffer springs installed in a vehicle can reduce the life of the shock strut. Argument being that a stiffer spring increases the rate of work that the shock strut is required to do.
In researching and preparing to install a set of Swift Springs I decided to analyze the problem. These springs are advertised as having a 25% stiffer spring rate than the stock IS300 springs.
An automotive suspension is easily approximated as a spring-mass-damper system. The motion equation for which is…
mx” + cx’ + kx = F(t)
m = mass
c = damping rate
k = spring force
t = time
x = displacement
x’ = first derivative (velocity)
x” = second derivative (acceleration)
For the analysis I made the following approximations/assumptions…
mass is = 1/4 vehicle curb weight = 340 kg
spring force k is constant = 43 N / mm (245 lbs/in) (front wheel)
damping rate c is constant
damping rate c for the IS300 is estimated at about 0.3 of critical damping which = 2300 Ns/m **
** Milliken (Race Car Vehicle Dynamics) apparently recommends 0.15 – 0.45 of critical for damping rates on road vehicles. I took a guess that the IS300 would be somewhere around 0.35. As this analysis is comparative the exact value will not be critical to the results.
My analysis is for a road disturbance = 0.10m to the front wheel, and an initial vertical velocity of the suspension = 0 (these initial conditions are used to solve for constants in the solution).
The motion equation (mx” + cx’ + kx = F(t)) is a second order linear differential. The general solution for an underdamped case is: x(t) = exp(-pt)(A cos(wt) + B sin(wt) . A thorough explanation is best left to a calculus textbook.
Solving for 2 scenarios…
1. Sport Design IS300 with stock springs
2. Sport Design IS300 with Swift springs (25% stiffer)
For each scenario I solved for suspension travel, suspension velocity, and suspension work vs. time. A brief discussion on each follows:
This is the interesting graph. The “Work” for a shock is the amount of energy it dissipates. After 1s the suspension with Stock springs dissipates 365 J of energy for the 10cm input. The Swift spring suspension dissipates 419 J of energy: 14.7% more.
The analysis suggests that installing 25% stiffer springs results in the shock strut performing 15% more work. All other things being equal, a shock might be considered to have a usable life proportional to the total work done. Thus 25% stiffer springs can be interpreted to result in an approximately 15% shorter life.
 Differential Equations and Boundary Value Problems 2nd Edition, Edwards, Penney.