Continued
Enough chit chat....Lets continue. Again, I will keep this vague with as little mathematical derivation as possible. But, should you want to dive further I would definitely brush up on differential equations and basic physics.
I have found my interest lies within the damping aspect to determine my ride quality.
Relationship between spring and wheel rates
In general the relationship between spring deflections and wheel displacements in suspensions is non linear, which means that a desired wheel-rate (related to natural frequency) has to be interpreted into a spring-rate.
Suspension or motion ratio = Spring force/ Wheel force ******(Not the same as spring rates or wheel rates)
To find ANY motion ratio, jack the car up and let the suspension hang. Measure the spring length at this very moment. Then use the jack and deflect the wheel a given amount of inches. Once you do so record that and then measure spring length again. Use those numbers and relate it to this newly derived formula:
Motion ratio (R) = [Final spring length - Intial spring length] / Wheel deflection
Normally, you will know your spring rates. its as easy as searching on google. If you know your spring rates, then you can relate them to a spring energy formula....for the sake of no confusion I've derived it into its simplest form:
Wheel rate = Spring rate / [Motion ratio^2]
Motion ratio results from the same kinematic suspension analysis that gives camber gain and roll center. Note that R is usually greater than 1, so the wheel rate is less than the spring rate. R is not constant; it varies as a function of v. But on an front handling car, it will be close to the ride height value at both full bump and full droop. Once the desired kw is known, and R has been determined from a candidate suspension geometry, ks may be determined. Note that the spring’s own free length (i.e., under no load) corresponds to full droop and not to ride height.
Dampening and Natural Frequency
From Happian Smith:
Frequently called shock absorbers, dampers are the main energy dissipators in a vehicle suspension. They are required to dampen vibration after a wheel strikes a pothole and to provide a good compormise between low spring mass acceleration and adequate control of the unsprung mass to provide good road handling.
Might Wanna Look at Wiki too.....Click Me
Twin tube vs. Monotube
Good Read: Twin Tube vs. Monotube....CLICK ME
Basically Twin tube = comfort; Monotube = Performance
Back to the good stuff. While skipping the boring and tedious derivations, the undamped natural frequency is:
Nat. Frequency (omega) = Square root(wheel rate / sprung mass)
If the wheel rate is maintain constant, the natural freq decreases as the payload increases. It is possible to determine a variable wheel-rate which will ensure that the natural frequency ramains constant as the sprung mass increases. (More on that later)
Effective corner damping coefficients may be set by the damping ratio:
damping ratio (ζ) = effective wheel damping ratio / (2*omega*mass of the vehicle)
- Critical damping (ζ=1) is the boundary limiting oscillation after disturbance.
- Slightly overdamped (ζ=1.2) will keep the wheels hard-pressed to the ground.
- Slightly underdamped (ζ=0.6) will allow more rapid response to disturbance say rolling into a turn) without much oscillation.
- More underdamped (ζ=0.35) will allow rapid wheel deflection, such as necessary to follow a rough surface.
This part is hard because companies do not give these values. But you can calculate a critical damping ratio and go from there. You can see that there is A LOT of fine tuning that goes into this.
Look at this pic:
Normally you want to find that range of overshoot to not allow the car to go haywire when you hit a bump, but also you dont want to car to overshoot and bounce like a pogo stick when hitting a bump and returning on the rebound. Again, you can solve for which damping ratio you'd like and find a coefficient of damping and go from there. You might be able to ask companies for their values, but be warned, they might not give it to you.
Happian-Smith:
In dealing with road surface undulations in the bump direction (damper being compressed) relatively low levels of damping are required when compared with the rebound motion(damper being extended). This is because the damping force produced in bump tends to aid the acceleration of the spring mass, while in rebound an increased level of damping is required to dissipate the energy stored in the suspension spring.
What is the ultimate design? A controllable suspension (DCC) that electronically controls the adjustment forms of the basis of improving ride and handling. AKA Sport Standard and Comfort. Most companies design for the middle, but what the user wants to decide between tracking and daily driving? This system provails.
The biggest is when you chose a static spring and shock setup that has to balance the two: Comfort and Sport. Thats where multivariable input shocks such as Koni FSDs come into play. Basically just a valve that has high limits that soak up the major bumps in the road, but at slow compressions, such as during turns, they act as a performance shock. Still....when does the valve open? Thats left for some interpretation and subjective reasoning to deteremine "ride quality"
An objective approach to ride quality will be discussed further, when I can collaborate my notes a little better....Stay tuned.......