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View Full Version : Vehicle dynamics theory- unsprung weight bias vs. Oversteer?



formula
03-26-2010, 07:18 AM
Ok, so unrelated to my formie I'm working on another project. I'm considering using in-hub electric motors for the car, but wince it will be a rwd vehicle, this will most likely lead to a large difference in unsprung weight between the axles. This car is NOT designed to be ultra-high performance, primary operation mode will be city speeds, 30-50 mph. I'm trying to think through all of the pros and cons of having this additional unsprung mass at the rear.

One thing the guys who are working on this with me have brought forward is their belief that this high unsprung mass may lead to oversteer issues. I'm trying to think this through.

First angle of attack: the higher unsprung mass will generate a higher moment of inertia about the vehicle axis of rotation, leading to greater oversteer.

Second angle of attack: the higher rear unsprung mass will have a higher inertia itself, causing the rear wheels to be less likely to be upset by road undulations, leading to better tire contact, improved rear grip, and less oversteer.

What else do I need to think through on this? Please keep the operating range of the vehicle in mind- oversteer- inducing scenarios would generally be panic/accident avoidance maneuvers.

Thanks boyos!

LSx_88_Ciera
03-26-2010, 07:44 AM
Second angle of attack: the higher rear unsprung mass will have a higher inertia itself, causing the rear wheels to be less likely to be upset by road undulations, leading to better tire contact, improved rear grip, and less oversteer.

Actually it is the opposite with the higher unsprung weight it is harder for the shocks to control the movement. The only way for the weight to reduce the response from undulations is if it were heavy enough to make the undulation respond to it and I am pretty sure you aren't building a steam roller.
Excuse my abstract sense of humor.

formula
03-26-2010, 10:23 AM
I feel like that's ignoring the natural spring rate of the tires, though. Yes, for low frequency high amplitude undulations the energy will transfer to the suspension, but under a short burst- the kind of thing that would suddnly upset a low-unsprung mass system easily, might the additional mass of the higher- mass system act as an "energy sink" of sorts, producing a temporary decoupling effect that would cause greater tire compression but help dampen transmission through to the chassis

sik68
03-26-2010, 12:17 PM
I am not an expert here, but I am guessing that tire rates are several times higher than the spring rates resolved to the wheel (for a tire I'm guessing ~600lbs/inch for an order of magnitude). I don't think they can be expected to be a reliable isolater in the way you are describing. I could be wrong though...staying tuned.

My line of reasoning is: Even a harshly sprung car with under-inflated tires still rides like a harshly sprung car...just a little less so.

formula
03-26-2010, 12:50 PM
No you're definitely right. My point is, if your unsprung mass is greater, that tire would have to exert a lot more force upward to cause the same motion on a very heavy wheel to accelerate it upward at a given rate than it would with a very light wheel, since force is mass times acceleration. For a given upward force, the more mass being accelerated, the less acceleration, and thus the less velocity, less position change, less final change in the suspension that must be compensated for.

j-rho
03-26-2010, 01:36 PM
No you're definitely right. My point is, if your unsprung mass is greater, that tire would have to exert a lot more force upward to cause the same motion on a very heavy wheel to accelerate it upward at a given rate than it would with a very light wheel, since force is mass times acceleration. For a given upward force, the more mass being accelerated, the less acceleration, and thus the less velocity, less position change, less final change in the suspension that must be compensated for.
Yep, and it does exert a lot more upward force. It has to, because the accleration is the same for the heavier wheel/tire unit going over the bump in the same amount of time - you can't go "through" the bump, you have to go over it, which means you have to displace the wheel/tire vertically a given distance, in a given amount of time, dictated by vehicle speed. Ignoring the tire's springing effect, for simplicity. F=MA. More M for a given A, means more F.

There are a TON more variables at play - spring rate, damper tuning, sprung weight on the corner, etc. In general, lower unsprung mass gives rise to increased roadholding with everything else equal. To that extent, increasing unsprung mass will decrease road-holding over uneven surfaces, which, at the rear, would tend to shift the balance to oversteer. But this isn't to say that such a thing couldn't be compensated for in any one of many ways - softer rear bars/springs, softer rear shocks, wider rear wheels/tires, etc.

formula
03-26-2010, 04:05 PM
Yes theoretically that would be true. But I'm talking about if you don't hold everything constant, and if you do consider the fact that you can compress the tire at different rates.

LSx_88_Ciera
03-26-2010, 04:32 PM
Something I am not sure you are considering is that the effect of unsprung weight on ride and handling characteristics is proportional to unsprung weight vs sprung weight so in order to maintain undulation effect you have to increase sprung weight proportionally. Regardless of how good your shocks and springs are setup it is still the sprung weight that is controlling unsprung weight and the closer unsprung gets to sprung the larger the impact.
Hope this give a little different prospective to help explain why your angle 2 thought is flawed.

LSx_88_Ciera
03-26-2010, 04:40 PM
If I were designing an electric vehicle I would use a chain/belt drive system that utilized a suspension travel based tensioner system instead of a hub mounted motor so I could keep unsprung weight low.

David Pozzi
03-28-2010, 09:37 AM
Go drive a flat bed truck, or a dual wheel pickup. The rear hopps around when you hit bumps, there isn't enough sprung weight for the springs and shocks to resist the high unsprung weight. Tire spring rates are usually around 1000 lbs maybe a little less with a smaller tire.

There are plenty of ways to reduce unsprung weight, why not consider them?

Norm Peterson
03-31-2010, 04:19 AM
For a given upward force, the more mass being accelerated, the less acceleration, and thus the less velocity, less position change, less final change in the suspension that must be compensated for.
I think you're looking at the wrong parameter being the independent variable here. Road roughness is basically a displacement input rather than some sort of force input.

You can't lump what you then do to cope with the response to displacement input (through suspension and tire tuning) into changing the definition of the initial displacement input from the road contour. The bump is still the same bump.


Norm

funcars
03-31-2010, 01:37 PM
Another way to look at it is the lower the relative percentage of unsprung mass to sprung, the less effect the unsprung mass will have on the sprung mass when you see a bump. A lighter mass relative to the sprung component is easier to control and isolate than a heavy one. You still need a certain minimum natural frequency so the spring rates get higher with heavier parts (everything else being the same). So one way to get a smooth ride with heavy wheels, tires and suspension parts is to have a very heavy sprung mass - think old Lincoln or Caddy.

mikedc
04-03-2010, 10:19 PM
Forgive me for suggesting something so basic, but why do you want the electric motors mounted on the axle so badly?


The common solid axle or IRS setup seems adaptable enough to electric motors.

Even if you're trying to separate the motor drive action by wheel, I would think you could do a pair of smaller axleshafts leading to chassis-mounted motors.

exwestracer
05-22-2010, 04:52 PM
I feel like that's ignoring the natural spring rate of the tires, though. Yes, for low frequency high amplitude undulations the energy will transfer to the suspension, but under a short burst- the kind of thing that would suddnly upset a low-unsprung mass system easily, might the additional mass of the higher- mass system act as an "energy sink" of sorts, producing a temporary decoupling effect that would cause greater tire compression but help dampen transmission through to the chassis

Yes, it does act like an energy sink...for awhile, BUT the energy was still imparted into the system by the bump in the first place...Where did it go?? Newton says it still has to be around here somewhere....:candle:...

You'll find that energy in the sidewall (as you stated), but for the system to regain equilibrium it has to be released. Being made of rubber, the sidewall will snap back to and beyond it's normal height. Now the energy is transferred into the unsprung mass without any damping (no shocks inside the tires). Low amplitude-high frequency "stutter bumps" will cause these undamped releases to get "out of phase" with the sprung mass. David Pozzi's comments about driving an unladen truck are spot on concerning the results...