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Potential Energy and Spring Rate

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motomadness

Potential Energy and Spring Rate
« on: September 02, 2004, 03:51:19 pm »
Anyone care to give me their opinions?

Many of us talk about preload and damping, but our suspensions aren't static devices, therefore, the combination of preload and damping relate to your suspensions potential and kinetic energy that is conserved not destroyed.

Hmmm!

I am starting this because SuperDave asked me during his VRU day at the last BHF round about how to explain some of the mechanical concepts.

Time for Dynamics 101 ...
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Zac

how much Re: Potential Energy and Spring Rate
« Reply #1 on: September 03, 2004, 09:27:35 am »
Preload only determines sag, which is both a measure of ride height (for this discussion "traditional" ride height adjustment such as fork height and shock length will be considered fixed) and the ratio of positive to negative suspension travel at the sag point.  On vehicles that don't have ture ride height adjustment such as certain classes of cars, ride height is adjusted using preload.

In other words preload does not have any effect on the potential energy stored in the spring.

As far as energy in the suspension system, the spring will store potential energy as the spring is compressed and release this energy as it extends.  The dampening converts kenetic energy (movement) into heat, thus removing the energy from the system.

We can start going into the differential equations which govern all of this, but suspension setup is still a black art.  I know the physics well, but that doesn't mean I can apply it.  It is very difficult to simulate motorcycle dynamics.  MotoGP has proven that the simulations can (sometimes) get in the ballpark, but Rossi is a much better developement tool.

-z.
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motomadness

Re: Potential Energy and Spring Rate
« Reply #2 on: September 03, 2004, 10:16:09 am »
Okay Zac,

I am glad you replied.  Preload does effect potential energy.  Thinking only in terms of ride height limits your understanding to only static equations.  When you think about the energy equation, you start looking at things dynamically, which is how we'll all increase our understand of the "art" of suspension movement - spring rate + damping effects.

For example, if you have a 6" spring preloaded to 12 mm, you have a PE = rate*(6"-(6"-12mm)).  If due to suspension movement, the spring further compresses 2", then your new PE = rate*(6"-(6"-12mm-2")), and the change in PE = rate*(2").    If you change the preload, you don't change the rate of the spring, but there's no guarantee that the change in potential energy will be maintained because it now takes more force to get the same change in PE.  If you knew how to account for the damping effect mathemetically, then you could estimate the kinetic energy part of the equation.  Therefore, it is theoretically possible in a viscous damping system to tune the damping with preload, of course due to the geometry effects, steering effects are coupled to the mathematics = the "art".  Furthermore, since nothing is absolute for all conditions choices are made to establish the best from what you've got.  

This approach begins to simplify the "art", not explaining it sufficiently, but allowing us to understand how changing a spring, for a different rate, can also allow us adjust the damping components to tune the spring effects.

This almost begs the question of whether just changing the spring on a stock shock would improve the damping performance of the shock because of where/how it changes the damping operating range.
« Last Edit: September 03, 2004, 01:29:52 pm by motomadness »
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motomadness

Re: Potential Energy and Spring Rate
« Reply #3 on: September 03, 2004, 10:18:42 am »
Also, heat isn't the only form of the energy in the suspension equation.  At some point, the fluid doesn't get hotter, the bike just moves differently in response to the damping changes.
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motomadness

Re: Potential Energy and Spring Rate
« Reply #4 on: September 03, 2004, 01:30:38 pm »
I rewrote the equations in my above message.
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Zac

Re: Potential Energy and Spring Rate
« Reply #5 on: September 03, 2004, 01:32:54 pm »
Quote
Okay Zac,

I am glad you replied.  Preload does effect potential energy.  Thinking only in terms of ride height limits your understanding to only static equations.  When you think about the energy equation, you start looking at things dynamically, which is how we'll all increase our understand of the "art" of suspension movement - spring rate + damping effects.

For example, if you have a 6" spring preloaded to 12 mm, you have a PE = rate*(6"-12mm).  If due to suspension movement, the spring further compresses 2", then your new PE = rate*(6"-12mm-2"), and the change in PE = rate*(2").    If you change the preload, you don't change the rate of the spring, but there's no guarantee that the change in potential energy will be maintained because it now takes more force to get the same change in PE.  If you then knew how to account for the damping effect mathemetically, then you could estimate the kinetic energy part of the equation.  Therefore in a viscous damping system it is possible to tune the damping with preload, of course due to the geometry effects, steering effects are coupled to the mathematics = the "art".


I will still have to disagree a little Sean.  We have to disregard the potential energy stored in the spring when the suspension is topped out.  There will be some amount of potential energy stored in the spring - rate*(free length-preloaded length), but this energy is not available to any work on the system.  

The spring will always compress to the same length when loaded with a static bike and rider.  Changing preload will change the shock length, but not the spring length.  In your case the PE in the spring would change with sag if the PE was defined as zero at the point where the suspension was topped out.  The PE in the spring would not change with sag if the PE was defined as zero when the spring was at full length.  

I think the best way to define the system is that the PE is zero when at the sag point, and PE is positive when the spring is compressed, and negative when the spring is extended.  This works because the system is comprised of both the PE in the spring AND the PE of the bike and riders mass, the equilbrium point (static sag) is defined as zero.  In this case, as long as the suspension is not  bottoming or topping out (statically or dynamically), the PE of the spring is independent of the preload.

Quote

Also, heat isn't the only form of the energy in the suspension equation.  At some point, the fluid doesn't get hotter, the bike just moves differently in response to the damping changes.


The damper can only dissipate energy, it cannot add energy back into the system (negleting the gas compressing in the shock).  Therefore, all the energy dissipated within the shock is converted to heat.  At some point the oil doesn't get any hotter, this is the steady state point where the energy is coming into the oil as heat at the same rate it is being transfered into the air outside the shock.  The shock will act different depending on the viscosity index of the fluid, but will still be dissipating the kinetic energy of the suspension movement.

This could become a fun discussion for us nerds  ;)

-z.
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motomadness

Re: Potential Energy and Spring Rate
« Reply #6 on: September 03, 2004, 09:31:08 pm »
Counter once more.  Any time the spring is compressed or extended beyond its free length, it will store energy.  The direction that energy acts along determines its effect.

I agree that the spring will always compress to the same length with the static bike and rider.  However, the spring length does change, it's just that the larger the preload, the more precompressed the spring becomes.  In my earlier example, the rider's PE changes with sag, although the overall PE will remain constant.  The rider will probably feel the RPE more than the overall PE.

Wait a minute.  I think I see where you are coming from.  I'll need to take a look at my shock to verify this. If sag were measured at the shock, I'm sure the difference in lengths will always be small.

Based on your comments, if more preload reduces your sag, and the spring length doesn't change with preload, then preload is merely a geometry adjustment.  Again, I will have to verify this on my bike.

KE -
The damper dissipates energy not through heat, but through a change in kinetic energy, or a change in velocity of the fluid, not heat.  I am confident that the heat produced is adiabatic.  If heat were the main damping mechanism your fluid would probably break down faster.  I think brake fluid would apply the heat mechanism damping effect - brake fade. Remember the dampers are flow control devices.

It may be a couple of days before I can reply, but don't let that hold up the discussion.
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Thingy

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Re: Potential Energy and Spring Rate
« Reply #7 on: September 04, 2004, 04:23:41 pm »
Quote


This could become a fun discussion for us nerds  ;)

-z.

It kind of makes my brain hurt, but I agree.

Aren't you guys both right about the PE stored with the preload?  Monsta is correct in real terms and Zac is correct in 'relative' terms?  I'm not an engineer.  I am just trying to follow along.  Maybe I should just sit back and watch...  :)
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Thingy

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Re: Potential Energy and Spring Rate
« Reply #8 on: September 04, 2004, 04:39:44 pm »
OK, I am still thinking about this.  I went back and read it again.  

I guess what I meant by this is that there IS PE stored in the spring with pre-load.  So, Monsta is right.

HOWEVER, Zac, are you saying that this PE is not used other than to change ride height?

If so, I think I agree with Sean.   ???  I say this under the assumption that the more you compress the spring, the more force that is needed to compress it.

Maybe this is not true.  I am not sure.  Even using a straight rate spring, it still requires more force to compress one with lots of preload, opposed to one with little preload, right?  (ie: it is storing more PE)

Since I am not an engineer, just tell me to shut up if I don't make any sense.  I will just watch from the sidelines.  It is fun to watch the discussion.
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tzracer

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Re: Potential Energy and Spring Rate
« Reply #9 on: September 05, 2004, 10:10:15 pm »
Some spring background (for the sake of people trying to follow this discussion).

Spring force = spring rate (k) * distance compressed or stretched (x). You will see a negative sign in this equation, it is because the spring force is opositely directed to the movement (displacement) of the spring (vectors).

Spring potential energy = 1/2 * k * x^2, with the displacement (x) measured from the equilibrium position - spring not loaded.

Example : k = 500lb/in, compress 2 inches,
PE = 1/2 * 500 * 2^2 = 1000 in-lb of energy. If I preload the spring 2 inches and compress it 3 more inches, the potential enegy released when the spring returns to the preloaded length will be
PE = 1/2 * 500 *(5^2 - 2^2) = 5250 in-lb ( 5 = 2 preload inches + 3 additional inches).

Measuring spring PE from a sag position does not make sense because of how the PE equation is derived, the zero position is the equilibrium length, and spring PE is always a positive number. You are not free to choose the zero position as you are with gravitational PE.

Damping is usually speed sensitive (usually linear for shocks). Damping is used to contol the speed at which the damper moves. Since the damper is slowing the spring (and all moving parts), it is dissipating energy. This energy is dissipated in the form of heat.

Changing preload will change the ride height of the bike and it will change how the bike reacts to smaller bumps. It does not change the spring rate, but it will make the suspension stiffer in the sense that it will take more force to compress the suspension the same amount with more preload.

example : k = 500 lbs/inch. preload 1 inch, move suspension 1 inch, spring moves a total of 2 inches = 500lb/in * 2 in = 1000 lbs of force. Increase preload to 2 inches, compress suspension 1 in, spring moves a total of 3 inches for a force of 1500 lbs. This is why adding preload can be used to reduce bottoming, but then becomes less sensitive to smaller bumps.

Changing the spring rate is different. Higher will make he suspension stiffer, lower will make the suspension softer. If you find yourself adding a large amount of preload to keep the suspension from bottoming (or when setting sag), you may want to try a stiffer spring. Similar, is you are using very little preload, or removing preload to use more travel (or setting sag), you may want to try a softer spring. The reason for measuring free (no rider) sag and rider sag is to get the proper (or at least in the ball park) spring rate.

Going to a higher rate spring usually requires less compression damping and more rebound. A lower rate spring, more compression and less rebound.

As far as energy, remember that the damper has to control the kinetic energy of all the unsprung parts (tires, wheels, some suspension parts). That is why changing to lighter wheels will cause your suspension settings to no longer work.

Suspension settings are very rider dependant, some like to use all/most of their suspension travel, others, such as Eddie Lawson do not (it slowed his ability to turn in rapidly waiting for the suspension to react). Different riders like different settings, this is why I think it is important to learn to set up your own bike (once your riding has gotten to the level where you are ready for this - you need to be able to ride consistant lap times to determine the affect of changes).
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motomadness

Re: Potential Energy and Spring Rate
« Reply #10 on: September 05, 2004, 10:38:30 pm »
Why is everyone referring to the energy dissipation in terms of heat.  It's not all about heat, it's about flow as well, probably more so.  At some point the suspension fluid will not heat up anymore and the suspension will respond with less variance in the presence of similar perturbations.  If heat was the only response, the system would continue to get hot and the suspension would fail. At least that's how I would envision a heat dissipating system.

Now preload vs ride height:
I haven't seen my bike yet, but I had about 600 miles of driving to St. Louis to think about this problem.  The reason why adjusting preload changes the ride height but not the spring length is because the collar on the shock is not the only thing that preloads the spring.  Think free sag.  If you were to take all of the support away from the swingarm - support the rear of the bike from under the foot pegs, the spring should extend.  If the spring does not extend, then any additional preload you add into the shock will compress the spring and take out ride height.  However, if the shock does extend, meaning you have some available free sag, then when the bike is being supported by its own weight, the bike's weight will preload the spring.  Then when you begin adding preload into the spring, for some amount of preload, the bike's ride height will change commensurate with the amount of preload the bike imparts on the suspension related to free sag.  In shorter terms - if you have free sag, you can change the ride height (+ height) without changing the length of the spring until you have no more free sag (-height).  

Furthermore the reason why your handling sucks when you don't have any free sag is because the suspension can only move in one direction, and is prone to topping out.  Not to mention the fact that the spring is storing lots of PE with the lack of free sag.  Increase the free sag, reduce the effective PE and your suspension will work better because you have more "ability" to control the movement.
« Last Edit: September 08, 2004, 01:32:25 pm by motomadness »
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motomadness

Re: Potential Energy and Spring Rate
« Reply #11 on: September 05, 2004, 10:50:07 pm »
More on the energy thang:

KE and PE are measured in terms of Joules, which is a unit os heat.  However in this example, KE and PE have length units, so energy dissipation must to focused more on displacement terms, not heat terms - thinking ideally.  In my mind the heating effects are more like correction terms.

If you still think it's heat dissipation, explain the mechanism and why.
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