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Swift Sport Springs 2010/03/09

Posted by Michael in my IS300.
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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)

where…
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) [1]. 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:

Travel
The Suspension Travel graph shows that all three suspension setups oscillate for approximately the same duration. The oscillation frequency is higher with stiffer springs (expected).

Velocity
The Suspension Velocity has higher velocity peaks for the suspension with stiffer springs only.

Work
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.
IS300 Suspension Work

Discussion
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.

[1] Differential Equations and Boundary Value Problems 2nd Edition, Edwards, Penney.

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