Goal: Understand the higher level functionality and purpose of suspension in a race vehicle

Notes from Race Car Vehicle Dynamics

General Notes

• There is no single best geometry, it depends on the rest of the characteristics of the car

• An independent suspension (suspension that allows each wheel to move independently of one another when subjected to an external load) is intended to control the wheel motion relative to the body of the car in only one path (up and down)

  Open

  

  knuckle (connects to wheel)

• The study of independent suspension geometries is to determine how to restrain the knuckle to limited motion in five directions.

Some Definitions

• 5 degrees of restraint (DOR) requires 5 tension-compression links

  • A-Arm = 2 links

  • McPherson strut = 2 links

    Open

    

• Solid axle (or beam axle) requires 2 degrees of freedom (up/down and roll) → 4 DOR

• Instant center (IC) - the projected imaginary pivot point of all the linkages at a specific position of the linkage

• Instant axis - the front view and side view instant centers connected by an axis

  • Independent suspensions have 2 instant center and 1 instant axis

  • Solid axles have 2 instant axes

• Sprung vs unsprung mass

  • Sprung mass is everything that is supported by springs from the suspension. This includes the chassis, motor, transmission, body, and passengers

  • Unsprung mass moves up and down with the wheels as they travel over bumps, potholes and other obstructions. This includes the wheels, tires, brake assemblies, differential, hub motors.

  • Semi-sprung parts are usually attached to both the wheel and to a sprung component. This includes shock absorbers and struts, control arms and other suspension parts and some steering components.

Independent Suspensions

Roll Center Height

• Roll center height is found by projecting a line from the center of the tire-ground contact to the front view instant center. This is done for both sides of the car. Where the two lines intersect is the roll center of the sprung mass of the car, relative to the ground.

• The roll center is does not necessarily have to be at the centerline of the car, especially with asymmetric suspension geometry or once the car assumes the roll angle in a turn.

• The roll center establishes the force coupling point between the unsprung and the sprung masses.

  • A force couple (aka. pure moment) is a system of forces with a resultant moment but no net force

Longer roll couple (distance between roll center and CG):

• More leverage centrifugal force acting on the suspension through the CG and the more the car will roll in a turn

• Slower response to steering input

• Resulting weight transfer from a long roll couple does not have that much an effect on overall weight transfer but it will increase the dynamic weight transfer

• When taking a corner, the centrifugal force at the CG is reacted by the tires

• The roll center height defines the trade off between the relative effects of the rolling and nonrolling moments

  • The higher the roll center the smaller the rolling moment about the roll center (which must be resisted by the springs) but the lateral force acting at the roll center is higher off the ground. The lateral force x the distance to the ground is called the nonrolling overturning moment.

• The horizontal-vertical coupling effect also affects the desired roll center height. The lateral force from the tire generates a moment about the instant center.

  • If the roll center is above ground level, the moment pushes the wheel down and lifts the sprung mass; this is called jacking.

  • If the roll center is below ground level (possible with SLA suspension) the moment will push the sprung mass down.

Motion Ratios and Suspension Frequency

Motion ratio

“The motion ratio of a mechanism is the ratio of the displacement of the point of interest to that of another point.” In suspension geometry, motion ratio refers to the ratio between the displacement of the wheel and the displacement of the spring (or shock). In industry, the motion ratio is usually WheelDisplacement/SpringDisplacement, however the inverse is also seen sometimes.

Suspension Frequency

In general, “natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force”. Suspension frequency is how fast the suspension travels up and then back down when you drive over a bump. Without shocks or dampers. the springs would continue to bounce up and down at this rate for some time.

Suspension frequency determines how soft or stiff the ride feels to the passenger.

How motion ratio and suspension frequency come together

This equation relates the suspension frequency (SF) and wheel rate (WR).

WR = SpringRate/(MotionRatio)^2

Using the suspension frequency in hertz and the chart above, the “softness” of the ride can be determined.

So based on the given spring rate of the shocks, the motion ratio can be adjusted to give a desired suspension frequency.

Note. MSXIV (and MSXV) uses shocks that have air springs which is quite hard to estimate the spring rate value for.