Originally Posted by zohare (Post 861224)

Updates anyone?

Originally Posted by Shankenstein (Post 694501)

While we look forward to RobiSpec's analysis, I'll provide some brain food.

There are multiple systems interacting in a car suspension, with different natural frequencies and damping characteristics. The lowest decade (1-10Hz) is responsible for almost all system dynamics, but all of them should be mentioned. The system looka like dis:
http://ctms.engin.umich.edu/CTMS/Con...ures/susp1.png

1) Upper system (fix x_2 and w):
Sprung weight + suspension spring. This motion is damped by the suspension damper. These are very low frequencies (0.5-5 Hz).

f_nat1 = constant * sqrt(spring rate / sprung mass)
b_1 = damper constant / sqrt(spring rate / sprung mass)

2) Middle system (fix x_1 and w):
Unsprung weight + suspension + tires. This motion is damped by both the suspension damper and tire damping. These are generally much higher frequencies.

f_nat2 = constant * sqrt([spring rate + tire rate] / unsprung mass)
b_2 = damper constant / sqrt([spring rate + tire rate] / unsprung mass)

3) Lower system (fix x_1 and x_2)
If we assume that all of the car's weight is sent to the ground, the parts involved are the sprung weight + unsprung weight + tires. This motion is damped by the tire, which is generally a very low damping factor (tires bounce).

f_nat3 = constant * sqrt(tire rate / [sprung mass + unsprung mass])
b_3 = tire damping constant / sqrt(tire rate / [sprung mass + unsprung mass])

Due to the low damping capabilities of tires, it's best to let the dampers handle vibration control. For tire dynamics to minimally affect suspension dynamics, a decade of frequency separation should be sufficient.

F_tire > 10 * F_susp
sqrt(tire rate / unsprung mass) > 10 * sqrt(spring rate / sprung mass)
If both values are more than one,
tire rate / unsprung mass > 100 * spring rate / sprung mass
tire rate / spring rate > 100 * unsprung mass / sprung mass

for our example:
6500 / 131 > 100 * 83 / 618
49.6 > 13.43 --> sufficiently separated

I guess I should amend the above statement. Thanks for pointing it out!

Continuing this thought:
If we calculate the max spring rate that can be used without being affected by tire dynamics (at stock pressures):
max front wheel rate = 484 lbs/in
max front spring rate = 526 lbs/in
max rear wheel rate = 422 lbs/in
max rear spring rate is = 548 lbs/in

At autox pressures, max spring rates would be 809 (front) and 843 (rear). In metric, that's 14.2k and 14.8k. Interesting, not that anyone would want to run them that stiff anyways.

Originally Posted by EarlQHan (Post 905941)

Since tire damping is so low and so so very hard to quantify, you can use this simplified model for the transfer function:

http://i1304.photobucket.com/albums/...ps2fae98f8.jpg

NOTE: Should say MASS not WEIGHT

Originally Posted by plucas (Post 906005)

This is basically what I did for my capstone. However it was damping a chassis (no suspension, only chassis and tires for the spring). I used Matlab for the transfer functions, and I used the root locus method to design the desired damping ratio and frequency of the system.

Originally Posted by EarlQHan (Post 905941)

Since tire damping is so low and so so very hard to quantify, you can use this simplified model for the transfer function:

http://i1304.photobucket.com/albums/...ps2fae98f8.jpg

NOTE: Should say MASS not WEIGHT

Originally Posted by Shankenstein (Post 906212)

Everything checks out, to my eyes. That's the traditional generalization about suspensions... all masses are point masses, all forces are 1D, all spring rates are constant.

If you want to trick it up, you can do:
- progressive spring rate = f(x-x_0)
- linear damping = k * (x-x_0)'
- digressive damping = f((x-x_0)')
- damper hysteresis = nasty equations)
- pressure-sensitive tire rate = k_sidewall + k_air * pressure (absolute)
- temperature-sensitive tire rate = k_sidewall + k_air * n*R/V * temperature (absolute)
- tire temperature estimation = T_atm + k * log (T_tread - T_air_in_tire)
- tire tread temperature = T_atm + k * (heat generated - heat dissipated)
... lots of ways to complicate the problem.

Originally Posted by EarlQHan (Post 906250)

Too many deltas! :barf: I was thinking state-space might be a better way to model the suspension so you can do transient analysis. This, including modeling the driver-vehicle feedback loop as the base block diagram is what I want to do my masters (or possibly doctorate) research and thesis on. But that's just too much math and I'm going to say EF IT for now lol.

Originally Posted by robispec (Post 898068)

new products

STREET no sheetmetal triming
Adds 2" rear travel

http://i240.photobucket.com/albums/f...psb9beb778.jpg

RACE requires rear sheetmetal trimming
Adds 3" rear travel

http://i240.photobucket.com/albums/f...pse6631b0e.jpg
Last edited by robispec; Today at 10:50 PM.

Originally Posted by Shankenstein (Post 906529)

This IS state-space. People like to use that term to indicate magic.

Variables take specific states, which interact based on a set of differential equations (some complex some simple).

What are your states? You can consider either the ground or the car body to be fixed... it's just perspective (although it matters that you pick one and stick with it). We care about tire deflection (x) and shock displacement (y). Thus the states are:
Q =
[ x ]
[ y ]
[ x' ]
[ y' ]
[ x'' ]
[ y'' ]

Your state space matrix will have diagonal elements to define the derivatives:
Q' =
[ 0 0 1 0 0 0 ] * Q
[ 0 0 0 1 0 0 ]
[ 0 0 0 0 1 0 ]
[ 0 0 0 0 0 1 ]
[ 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 ]

You can fill in the rest of the elements using the force balance equations in any level of complication you desire... but stiffness and damping components will appear, scaled by mass.

Solving the state space version is the same as solving the diff-eq version is the same as solving the numerical version. I'm sure you know all this, but it's good to lay it out there for the forum to glance over.

Good luck with the Master's btw. Where are you planning to go to school (or are already there)?

Originally Posted by SubieNate (Post 906766)

@Shankenstein @EarlQHan @plucas

I have a copy of Matlab and I'm a relatively decent (if rusty) coder. If we want to collaboratively use it as a tool to model our suspension mathematically I'd be more than happy to help.

Cheers
Nathan

Originally Posted by SubieNate (Post 906766)

@Shankenstein @EarlQHan @plucas

I have a copy of Matlab and I'm a relatively decent (if rusty) coder. If we want to collaboratively use it as a tool to model our suspension mathematically I'd be more than happy to help.

Cheers
Nathan