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Brief summary of calculation process for spring rate and anti roll bar rate:
Table of known or assumed parameters:
In the first step we have to calculate ride rate and roll rate. But they are dependent on each other; you can not find their value separately. The best way is to assume one of them and calculate for the other and use that value to determine the other again, reiterate until reaching final values which are the actual ride rate and roll rate of the car.
The front usually has a higher ride frequency so some adjustment is needed. 120 cpm is chosen for the new front ride frequency. It is also important to keep the ride frequency below 2 Hz since it will cause too much discomfort and instability.
These roll rates are then going back to step 1 and repeat until they converge into the real roll rates and ride rates of the car.
Another importance parameter is roll gradient. This value describes how much degree the car rolls when it encounters lateral acceleration. For a race car, it has a typical value of 1.5 deg/g. It is defined by:
Meaning we lack a total of 1860 kg.m/rad of roll stiffness in order to achieve 1.5 deg/g which will be address in the installation of anti roll bar but we have to allocate how much the front and the rear get. Considering the weight transfer, the inner wheels are almost lifted off the ground which is the perfect spot in this scenario. We want to keep that so the new roll stiffness will also retain the same front-rear ratio.
To this point, we have not consider the effect of tire spring rate yet. In order to determine the anti roll bar stiffness, wheel center rate must be evaluated first by using the following equation.
Then we can calculate the effect of anti roll bar on total car's roll rate.
But this is not actually the anti roll bar stiffness. For that, we have to use the following equation to convert into the actual anti roll bar stiffness.
Lastly, we need to determine the diameter of the anti roll bar.
That concludes the anti roll bar we have to install. Next is the spring we can achieve easily using the geometry of the bell-crank in push rod system.
In this case, we assumed that geometric rate (the first term) is not used in the calculation but it will be contributing to 10% of the spring rate instead.
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