First Principles
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. Here Mark answers your chassis setup and handling queries. If you have a question to put to him Email: [email protected] Tel: +1 7049338876 Write: Mark Ortiz 155 Wankel Drive, Kannapolis NC 280838200, USA
THIS MONTH: QHow much attention should be paid to preload on springs and Belleville stacks when setting up a monoshockequipped single seater? Plenty, and it is also important to understand why you might choose to have the stacks unequally preloaded on the shuttle, as it has a significant effect on this interconnective springing system
Monoamono a How do you go about sorting out ride and roll rates for a monoshockequipped Dallara F3 car and how much notice should be paid to preload on the springs and Belleville stacks?
Also, can you explain how one might go about calculating Belleville stack rates, wheel rates and load transfer distributions? My understanding is further muddied by the application of preload on ride springs and stacks, but I'm hoping to ignore these for now. Is this wise?
A Taking the last question first, no, we cannot ignore preload, especially on the washer stacks, though on the ride spring, it depends whether the spring is preloaded at static ride height or only at full droop.
If the ride spring is preloaded at static, the suspension is solid in ride (wheel rate approaching infinity, or undefined) until the preload is exceeded. If it is not preloaded at static, it provides a rate for the wheel pair that is equal to the spring rate times the square of the springtowheel motion ratio. This is the number of pounds of load change for the wheel pair, per inch of ride travel. It corresponds to the sum of the two individual wheel rates in ride in a conventional suspension so, if you have an equation that calls for individual wheel rate in ride, then you use half of that ride spring rate times the square of motion ratio quantity.
If the equation in question is for lateral load transfer, then you use zero for the ride spring rate. The ride spring in a monoshock suspension acts only in ride and does not contribute to roll resistance or elastic lateral load transfer at all. All the elastic roll resistance in a monoshock set up comes from the Belleville washer stacks. There is a stack on each side of the rocker where the shuttle passes through. Ordinarily, we use identical stacks on both sides of the rocker, which act in parallel so the rate of force change with respect to displacement at the shuttle is the sum of the rates of the individual stacks, if they are both active. However, they may or may not both be active and that's where preload comes in.
When both stacks are equally preloaded, there is a compressive load on each stack, and a reaction force from each stack trying to extend itself. Since these act on the shuttle in opposite directions, however, there is no net force trying to move the shuttle to either side.
Correspondingly, if there is an increase in extension force from one stack, and a decrease
^THE CONSULTANT
in extension force on the other, those force changes act additively, and the force trying to recentre the shuttle is the sum of the two.
That force acts on the wheels, through the pushrods and the rest of the suspension, at some motion ratio. The rate of force change with respect to displacement at the wheels is the rate at the shuttle times the square of the motion ratio.
Like an antiroll bar, the shuttle mechanism is an interconnective springing system. It generates force in response to a displacement difference between two wheels ie an oppositional displacement of the pair. To define a motion ratio for such a system, we need to resolve the question of what we call an inch (or mm) of motion: is it an inch at each wheel, meaning two inches difference between the two, or is it half an inch at each wheel, meaning one inch difference between the two? I prefer the former method, because it puts wheel rates for all modes, from all springing devices, in the same terms: force per unit of displacement per wheel. Using this method, the angular roll resistance is the wheel rate in roll times the square of the track times 0.5. That gives the angular rate in lb/in or N/mm per radian. To get lb/in or N/mm per degree, divide by 1 80/ti or 57.3.
Most books use the method above to calculate the component of angular roll resistance due to the ride springs (again, this is zero for a monoshock suspension), and use a different formula for the component due to the antiroll bar. The more common method for the bar component is as above, except the rate is taken as force per unit of displacement per wheel pair, and the angular rate from the bar is then as above, except with the multiplication by 0.5 omitted. Both methods work fine, and give the same answer for total angular rate, provided you use the method that goes with your expression of rate.
The angular roll displacement is then the sprung mass times the lateral acceleration times the moment arm of the sprung mass c of g about the roll axis, divided by the sum of the front and rear angular roll resistances. The front elastic lateral load transfer at that roll displacement is front angular roll resistance times angular roll displacement, divided by front track.
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