Wheel frequencies VS track surface

[Rustem 1988]

Thank you, Greg.

[Rustem 1988]

Rustem,

While we wait for someone who really knows what they're talking about to respond, you might consider the content of the text you'd quoted, and whether or not it makes sense to you. Particularly the last bit about the direction of spring and damper forces in compression and rebound.
One of the fundamental parameters affecting 'grip' is the normal load on the tire. As such, minimizing the variation of this load about some mean value would be a good thing, if our primary concern were optimizing grip (and we had a driver that could make use of it).
So you might wonder why it would advantageous to have a wheel (tire and rim assembly) working against a high damper force in rebound.

I think we need to know how the forces vary in different phases of 0-pi/2, pi/2-pi, pi-3pi/2, 3pi/2-2pi. Now if the displacement is determined through the cosine then the speed will be minus the sine. So the speed and displacement can have different signs.

[Rustem 1988]

Perhaps there is a difference when the road profile goes down or up.

[DaveW]

Rustem: It would be very helpful, and might elicit useful replies, if you could sometimes state the context of your postings.

So: "I read an article" should generally reference the article,
"speed and displacement can have different signs" should perhaps state what speed & what displacement,
"Perhaps there is a difference when the road profile goes down or up", the difference in what perhaps,
etc...

Many of your points are, at first sight, blindingly obvious.
Regards,

[Rustem 1988]

Rustem: It would be very helpful, and might elicit useful replies, if you could sometimes state the context of your postings.

Many of your points are, at first sight, blindingly obvious.
Regards,

I'm trying to figure out mathematical equations to find the wheel load at different damping levels when the road profile changes. Do I need to find a transmitting force in the suspension? What set of parameters do I need to know to predict the performance of the suspension? I want not so much to calculate a specific value, but to understand how the suspension works in a wide range of changing loads.

[DaveW]

I'm trying to figure out mathematical equations to find the wheel load at different damping levels when the road profile changes.

As Greg Locock has hinted there a several texts books that will help. There are also several other publcations that do the job & cost nothing (if cost is an issue). Alternatively, there are probably (I've not looked in detail) several computer "games" that might be made to work for you.

Most require work. That will be good for the soul - and will mean that you will be able to answer many of your questions (apologies).

[Rustem 1988]

I think about, so the load on the wheel W=Wst+ks(Xs-Xu)+Cs*(dXs/dt-dXu/dt)+kt(Xu-Xr)+Ct*(dXu/dt-dXr/dt), where Wst-static wheel load, ks-spring rate, kt-tyre rate, Cs-damping rate for spring, Ct-damping rate for tyre, Xs-sprung mass displacement, Xr-road profile displacement, Xu-unsprung mass displacement, dXs/dt, dXu/dt, dXr/dt-velocity for sprung, unsprung mass and road respectively.

I read some theory on physics and on this topic,but when I tried to apply it in one computer game, I realized that I still do not see in general how the suspension works.

[Rustem 1988]

Rustem,

While we wait for someone who really knows what they're talking about to respond, you might consider the content of the text you'd quoted, and whether or not it makes sense to you. Particularly the last bit about the direction of spring and damper forces in compression and rebound.
One of the fundamental parameters affecting 'grip' is the normal load on the tire. As such, minimizing the variation of this load about some mean value would be a good thing, if our primary concern were optimizing grip (and we had a driver that could make use of it).
So you might wonder why it would advantageous to have a wheel (tire and rim assembly) working against a high damper force in rebound.

I think that if we have a damping force too high, the hysteresis curve will be wide, so the load change in different phases will also be great. Probably, we should try to reduce the change in load. We also need a compromise between the rate of variation of the load and the magnitude of the variation of the load.

[Rustem 1988]

Rustem,
So you might wonder why it would advantageous to have a wheel (tire and rim assembly) working against a high damper force in rebound.

Maybe we have reduced the unsprung mass acceleration, and therefore the load is less changing?

[DaveW]

...the load on the wheel W=Wst+ks(Xs-Xu)+Cs*(dXs/dt-dXu/dt)+kt(Xu-Xr)+Ct*(dXu/dt-dXr/dt)

I believe you have forgotten the inertia force acting on the wheel. If I simply rewrite your equation:
Load on the wheel = Wst+(Ks+ Cs*D)*(Xs-Xu) + (Kt+Ct*D)*(Xu-Xr), where D is the operator d/dt.

Then dyamically, Mu*D*D(Xu) = (Ks+Cs*D)*(Xs-Xu) + (Kt+Ct*D)*(Xu-Xr). Here D*D(Xu) is the acceleration of the wheel, and Mu is the wheel (unsprung) mass. Wst disappears because it is balanced by static offsets of the springs. A similar equation can be written for the acceleration of the sprung mass, and the two can be solved together to compute the various responses of the vehicle per unit road input.

It is a little more than that, because the sprung mass connects the front & rear suspensions (so the sprung mass has "heave" & "pitch" inertias).

I hope this helps...

[DaveW]

I think that if we have a damping force too high, the hysteresis curve will be wide.

Damping force and hysteresis are two different properties. The properties can be related in some damper designs, but it doesn't have to be the case. A damper force can be modeled quite accurately by a spring installed in series with a pure damper, where the stiffness may be different in compression and rebound.

This suggests that damper hysteresis is mainly due to compliance of the damper fluid and damper structure. "Good" dampers tend to have a large cylinder size (and are therefore stiff), "Poor" dampers tend to be small (F1 please note...) Damper motion ratios away from unity are generally a bad idea. Flexible (&/or long) pipes are usually not good. Rotary dampers are particularly bad...

[Rustem 1988]

I think that if we have a damping force too high, the hysteresis curve will be wide.

Damping force and hysteresis are two different properties. The properties can be related in some damper designs, but it doesn't have to be the case. A damper force can be modeled quite accurately by a spring installed in series with a pure damper, where the stiffness may be different in compression and rebound.

Thank you for your comment. I meant a curve in the form elipsa for the damping force with spring force and the displacement or velocity.

[Rustem 1988]

I looked at the load for compression and rebound.

http://www.theoryinpracticeengineering. ... damper.pdf

Another contributing factor is the fact
that during compression the forces of the spring and damper are in the same direction
while during rebound the spring and damper forces act in opposite directions.

If we express the displacement of the shock absorber through cosine(x=x0*cos(w*t), where x0 -the amplitude of the displacement), then сompression can be during the phase from 0 to pi (or x0 to -x0). The velocity as derived from the displacement will be expressed through minus sine (v=-x0*w*sin(w*t)) and will be on the segment from 0 to pi negative, while the displacement on the segment 0-1/2 pi positive and negative on the segment 1/2 pi- pi. Since m*a = -k*x-c * v, where k*x - spring force, c*v-damping force, m * a is the force of inertia, the different signs at x and v spring force and damping force are also different signs. Therefore, the damping force and spring force will not always be in the same direction when the spring is compressed. (In this case, only on the segment 1/2 pi- pi.)

[DaveW]

Thank you for your comment. I meant a curve in the form elipsa for the damping force with spring force and the displacement or velocity.

.... So not damper hysteresis. That could be confusing (it was to me...)

However, looking up that reminded me that Jim Kasprzak has published in informative paper that might work for you. Here is the reference.

[Rustem 1988]

Thank you for your comment. I meant a curve in the form elipsa for the damping force with spring force and the displacement or velocity.

.... So not damper hysteresis.

Yes, not damper hysteresis.

I saw the graph on page 16 figure 2.19 of the article on the theory of oscillations and there was the word hysteresis. https://engfac.cooper.edu/pages/tzaveli ... Theory.pdf