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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.

**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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