The main objective of the project was to optimise the suspension setup for maximum mechanical grip.
Back to Basics
Going back to basics, what actually is the purpose of the suspension in a race car? All breaking, accelerating and cornering forces are transmitted through the contact patches of the 4 tyres and, simply, the maximum amount of force they can produces is F = μN where μ = the dynamic coefficient of friction & N = the normal force i.e one of the 4 vertical corner weights. The aim is to increase F as much as we can and improve the traction circle that is available at any time throughout the race. Larger, stickier slick tyres have more "grip" and therefore increase μ. The only way to increase N - the amount of "weight" pushing down on the tyre - without adding mass to the car (which would actually slow it down!) is through aerodynamic downforce. This has a significant effect on the tyre's grip, especially as speeds increase due to the square law mentioned previously.
The above seems simple enough, however, μ & N are constantly changing throughout the race and at all 4 corners of the car! Changes in N are known as variations to the contact patch load (CPL). Unlike in a road car, we don't really care about the comfort of the driver and it's therefore the job of the suspension system to control the changes in CPL (dynamics) as well as changes in the camber, castor, toe geometry etc etc (kinematics). We'll look just at the basics of the suspension's dynamics at the moment.
Soft or Hard?
Choosing soft or hard spring rates depends a lot on what we want to achieve with the suspension set-up. Consider a single tyre going over a bump in the track. Very stiff springs will cause the tyre to "hop" and lose contact with the road surface all together. If there's no N, it doesn't matter how grippy your tyres are- they're not going to transmit any forces, meaning they'll spin, lock-up or skid! A softly sprung wheel however, will continue to contact the road surface with a more constant CPL, compared with the stiffly sprung wheel, giving a more predictably handling car.
So why bother with stiff springs in a race car then?
As with everything, this of course comes at a cost. Softer springs will result in more rolling and pitching of the car through the corners and under braking/acceleration- changing the kinematics (which reduces grip) and more importantly, the car's aero performance. The aero sensitivity of a high-downforce car must be minimised by reducing the body movements and accelerations of the car, partly achieved via stiffer springs- at the expense of increasing CPL variations. Although the CPL variations are more with a stiff car, the increase in N offered by a car with large amounts of downforce is significantly more at medium and high speeds than a soft car and is therefore more important- think F1! A stiff car will feel very "skittish" at low speeds, but as soon as speeds increase, downforce increases and the car settles down.
This is basically the difference between mechanical and aerodynamic grip and at this stage, we need to decide which direction to take with the car. A stiff aero car or a soft and predictable car? Or somewhere in between? This then determines whether to tune the suspension for minimised CPL variations (mechanical grip) or minimised body movements (aero grip).
Above Images Courteous of Oxford Brookes University
The plan basically now is; buy the softest springs we can practically run, adjust the dampers to suit; remove as much body-roll as possible with very stiff front & rear anti-roll bars! Looks like all the initial CFD work isn't needed anymore. Gutted.
The plan for Won's MSc. dissertation project was to:
- Build a simulation model of the standard Z3 car.
- Validate the model against real 4-Post rig test data.
- Test the new Gaz race spring & dampers over their setting range and incorporate them into the model.
- Find the optimised setting which will maximise the grip available from the tyres.
The criteria for maximising the grip was to minimise the RMS value of the CPL variation over an input frequency range representing a typical tarmac surface. Furthermore, the optimisation was expanded to include a simplified kerb strike scenario.
Hand Calcs - Quarter-Car Model
As a starting point, simple hand calculations were performed using the equations of vibration of sprung masses shown.
The values for the sprung / unsprung masses were measured on the car, while published values for the spring and damping coefficients were used. Each corner of the car was simplified into a “quarter-car model” consisting of a basic 2 degree-of-freedom sprung mass system shown.
First it was assumed that:
Tyre spring coeff >> Suspension spring coeff
Suspension damping coeff >> Tyre damping coeff
Body mass >> Hub mass
Depending on the frequency and amplitude of the input (road surface roughness) the system can be simplified further. The following tables show the combined coefficients for each vibration mode.
While the quarter-car model doesn't take into account the movement of the body mass that ties all four corners together, it gives a reasonably good approximation of what to expect in the further testing and simulation in terms of characteristic frequencies.
The front and rear frequencies were then calculated, assuming left-to-right symmetry.
4-Post Rig Test (4PR)
The Z3 was tested on the Oxford Brookes' 4PR with the standard factory suspension components installed. Most of the body panels were removed and ballast was used to approximate the target weight and distribution of the race car. Using the standard suspension was acceptable, since the stock simulation model was then validated with the 4PR test data and can easily be adjusted to incorporate the upgraded suspension parameters.
Each corner of the car was fitted with an accelerometer on the chassis, another one on the wheel and a string pot between the two.
Furthermore, the pads on the hydraulic posts were fitted with load cells to measure the contact patch loads and encoders to accurately track the displacement of the pads.
The standard input for the baseline tests was a frequency sweep from low to high as shown. There a 4 different input tests of interest:
By sweeping through a frequency range in a variety of 4 different input movements, all likely road surface inputs that could be seen on track are represented and the resulting output contact patch load variations recorded for analysis.
For example, the results of the heave run contact patch load variations of the baseline car with standard suspension are shown opposite and a slow-motion recording below. Also shown below is the warp run. Note the movement between the windscreen and the rollcage. I'll have to weld in some A-pillar gussets to stiffen this up!
Write up to be continued......