Modeling of McPherson System

The McPherson strut suspension is a very popular mechanism for independent

front suspension of street cars and was invented by Earl McPherson in the 1940 . It was first introduced on the 1949 Ford Vedette, and also adopted in the 1951 Ford Consul, and then

become one of the dominating suspension systems because it’s compactness

and has a low cost.

Let's learn to model this system as an inverted slider mechanism.

This image represents the kinematics model of McPherson suspension system.

Let's assume

length of link 1 = a

length of link 2 = b

length of link 3 = c

length of link NB = d

Considering M = (0,0) we can find out the other co-ordinates

A= (b cosθ2, b sinθ2)

N= (a,0)

B= (a + d cosθ4, d sinθ4)

Coordinates of A in terms of link 3 (c) = (a + d cosθ4 -c sinθ4 ,d sinθ4-c cosθ4)

b cosθ2 = a + d cosθ4 -c sinθ4

b sinθ2 = d sinθ4-c cosθ4

These two equations can be solved easily.

Active Vibration Control

Yesterday while solving a problem of cramster.com,I successfully modeled a quarter car suspension which can control the vibration actively.Refer below diagram.

m1 = Sprung mass

k1 = spring constant of spring attached between sprung and unsprung mass

d1 = damping co-eff of damper attached between sprung and unsprung mass

q1 = displacement of sprung mass

m2 = Unsprung mass

k2 = spring constant of tire

d2 = damping co-eff of tire

q2 = displacement of unsprung mass

z = displacement of tire

Writing an equation of motion for sprung mass m1, we get

m1 * d^2/dt^2 *q1 + k1 ( q1 - q2) + d1 *d/dt ( q1 - q2) = u

Similarly writing an equation of motion for unsprung mass m2, we get

m2 * d^2/dt^2 *q2+ k1(- q1 + q2) + d1 *d/dt(- q1 + q2)+ k2 ( q2 -z) + d2 *d/dt ( q2 - z ) + u=0

These two equations can easily be solved using MATLAB.

The active control is generated here with non-negligible time lag by using a pneumatic actuator.An active suspension systems offer the possibility to vary the damper characteristics along with the road profile and thus far better than passive suspension.