Spring Damper Calculations

[Garre88e]

Hello all,

Ive been trying to figure out the spring calculations for some time now and have been running into problems. Most of the equations I got out of the Milliken book and my OptimumG binder, but some I came up with myself.

Here is the process I used:

We have 43mm of shock travel(additional 7mm of bump rubber), and require 50mm of wheel travel, therefore our installation ratio would be 0.86.
<span class="ev_code_RED">IR=Shock Travel/Wheel Travel</span>

If we have 54.25kg of sprung mass per wheel and design for a natural frequency of 3Hz, then our wheel rate would be 19.25N/mm
<span class="ev_code_RED">WR=4*f^2*SM*Pi^2</span>

Then, the necessary spring rate would be 26.1 N/mm
<span class="ev_code_RED">Ks=WR/IR^2</span>

Finally, to achieve 70% critical damping, the damping coefficient should be 1.66 N/mm/s
<span class="ev_code_RED">c=2*sqrt(Ks/SM)*0.7</span>

This all seems well, however, statically, the spring will compress 24mm and a 3G bump will compress it 71mm, obviously bottoming out our 43mm shock.
<span class="ev_code_RED">static compression=((SM*9.8)/IR)/Ks
3g compression=((SM*9.8*3)/IR)/Ks</span>

Forcing the shock to have 75% bump travel results in a required spring preload of 333N. However, still a 3g bump will compress the spring to 56mm, bottoming it out.
<span class="ev_code_RED">preload=((SM*9.8)/IR)-(43*(1-.75)*Ks)
3g compression=((SM*9.8*3-preload)/IR)/Ks</span>

Even using 100% of the travel for bump, the shock is about 0.5mm away from bottoming out.

Please, can someone tell me if there is an error in my logic or calculations. The only solution I see is either increasing the natural frequency (undesired),or increasing the wheel travel(difficult)

[Pennyman]

At first glance your calcs look good. I haven't taken the time to double check them for you however.

Remember that a 3g bump will most likely take place in a very short amount of time (enough to consider it a dynamic load rather than a static load) this means that the compression setting in the damper is also going to have a large effect on the amount that the spring is compressed.

I think using 3g as a starting point for stress analysis and worst-case loading is good for loading in the z direction, but may not be as useful for analyzing spring and damper compression in a steady-state scenario.

[Thomas MuWe]

I agree with pennyman. At first glance it looks alright.
It seems that you have been new to that issue and you look at it from the theory. At the test track all that changes IMO.
But some input from my side:
- Is your IR or Motion Ration constant during wheel / damper travel? (I don't think so)
- What is your damper doing in high speed / low speed? (same coefficient?)
- What is your wheel rate and natural frequency if you hit the bump rubber? (for what do you use the bump rubber?)
- How many times do you have a 3g bump on the track? (Germany - mope often, Michigan - i don't think so, Silverstone - never, Hybrid - no plan)
- What is the resulting anti roll torque from your springs?

Just a few questions to think about.....

[Bobby Doyle]

I think using 3g as a starting point for stress analysis and worst-case loading is good for loading in the z direction, but may not be as useful for analyzing spring and damper compression in a steady-state scenario.

+1


I would suggest calculating your wheel loads at a certain lateral acceleration. I think this strategy will give you the numbers you are looking for.

[murpia]

Although the rules only require 50mm wheel travel, limiting yourself to that amount in practice means you need to be very, very precise when setting up the car and very careful when making changes not to hit the damper end stops.

To put it another way, 50mm is probably about right for total wheel travel around a lap, but to match that 50mm exactly to the 50mm available is not trivial.

If you go with that solution I would suggest you add some simple datalogging to ensure you aren't driving on the bump rubbers and / or droop stops for half the lap...

Regards, Ian

[BilletB]

Finally, to achieve 70% critical damping, the damping coefficient should be 1.66 N/mm/s
c=2*sqrt(Ks/SM)*0.7

Equation here isn't right. You can't use the sprung mass with the spring's rate. You need to use the wheel rate and the sprung mass or the spring's rate and a 'virtual' mass. Basically you need the mass and rate modified or not modified according to your IR.

3g is a dynamic case. Damper rates come into play as well as the impulse nature of the excitation. You will NOT see 3*car weight sustained on the wheel. Least, I hope not. Do a dynamic simulation/analysis not a static approach.

[Garre88e]

Thanks for the replies guys! They were definitely helpful.

I'm not sure why I didn't realize that the 3g bump would be dynamic. It totally makes sense now as to why it would.

[murpia]

Originally posted by BilletB:
3g is a dynamic case. Damper rates come into play as well as the impulse nature of the excitation. You will NOT see 3*car weight sustained on the wheel. Least, I hope not.
It is very common to simplify dynamic loads as static ones. 3g bump is normally interpreted to mean 3g as measured by an accelerometer on the sprung mass at the axle line. You can then simplify the wheel load in Newtons to (total axle mass in kg) * 3 * 9.81 i.e. F=ma. Physically this is interpreted as a single bump input to one wheel performing the sprung mass acceleration and neglecting any rotation of the sprung mass about a pitch axis.

It's usual to put together a composite load case for the suspension consisting of cornering + braking / acceleration + bump input + aero (if you have it) to determine how strong to make it all.

It's also usual for Design Judges to ask how you developed your load cases at competition.

Regards, Ian

[Dan B]

2 words. Bump Stops

To be more specific Micro-Cellular Urethane (MCU). Carroll Smith talks about them in "Tune to Win" as well as "Engineer to Win" IIRC. You have read both of those books right?

[BilletB]

Originally posted by murpia:
It is very common to simplify dynamic loads as static ones. 3g bump is normally interpreted to mean 3g as measured by an accelerometer on the sprung mass at the axle line. You can then simplify the wheel load in Newtons to (total axle mass in kg) * 3 * 9.81 i.e. F=ma. Physically this is interpreted as a single bump input to one wheel performing the sprung mass acceleration and neglecting any rotation of the sprung mass about a pitch axis.

It's usual to put together a composite load case for the suspension consisting of cornering + braking / acceleration + bump input + aero (if you have it) to determine how strong to make it all.

It's also usual for Design Judges to ask how you developed your load cases at competition.

Regards, Ian

Because it's common doesn't make it right. Initially we weren't exactly talking about suspension loading calculations. We all do some cases where dynamic cases are simplified as static ones and in fact we here at VT have traditionally used a 5g bump analysis. However, the question is the simplification and I questioned its validity depending on the analysis method. How much does that simplification neglect and what effects may it be missing? Is it okay to assume the static simplification of the case and then call it done? I won't answer those questions because it depends on what you want to do with your analysis and where you are as a team.

And remember, this discussion started by the original poster's application of sustained 3g*sprung mass modeled statically to check shock/spring travel. For shock travel this is not applicable and the dynamic nature and impulse of the excitation are very important for accurate analysis. So a static simplification in this scenario used to check travel is a bad, bad idea.

[Yunlong Xu]

Originally posted by BilletB:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by murpia:
It is very common to simplify dynamic loads as static ones. 3g bump is normally interpreted to mean 3g as measured by an accelerometer on the sprung mass at the axle line. You can then simplify the wheel load in Newtons to (total axle mass in kg) * 3 * 9.81 i.e. F=ma. Physically this is interpreted as a single bump input to one wheel performing the sprung mass acceleration and neglecting any rotation of the sprung mass about a pitch axis.

It's usual to put together a composite load case for the suspension consisting of cornering + braking / acceleration + bump input + aero (if you have it) to determine how strong to make it all.

It's also usual for Design Judges to ask how you developed your load cases at competition.

Regards, Ian

Because it's common doesn't make it right. Initially we weren't exactly talking about suspension loading calculations. We all do some cases where dynamic cases are simplified as static ones and in fact we here at VT have traditionally used a 5g bump analysis. However, the question is the simplification and I questioned its validity depending on the analysis method. How much does that simplification neglect and what effects may it be missing? Is it okay to assume the static simplification of the case and then call it done? I won't answer those questions because it depends on what you want to do with your analysis and where you are as a team.

And remember, this discussion started by the original poster's application of sustained 3g*sprung mass modeled statically to check shock/spring travel. For shock travel this is not applicable and the dynamic nature and impulse of the excitation are very important for accurate analysis. So a static simplification in this scenario used to check travel is a bad, bad idea. </div></BLOCKQUOTE>

+1


Looking at a 3g static case is like finding the final value of the STEP RESPONSE of your spring-damper system. While the real world bump scenario is probably more like the IMPULSE RESPONSE of the system since it happens with very large force in very short time.

So I think what I will do if faced with this quesion is probably starting with finding the transfer function of the spring-damper system (of course modified by installation ratio, etc). And then see what the system transient response is to inputs such as an impulse, or probably less radical inputs such as a rectangular/triangular pulse with large magnitude and small duration

[murpia]

Originally posted by Yunlong Xu:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by BilletB:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by murpia:
It is very common to simplify dynamic loads as static ones. 3g bump is normally interpreted to mean 3g as measured by an accelerometer on the sprung mass at the axle line. You can then simplify the wheel load in Newtons to (total axle mass in kg) * 3 * 9.81 i.e. F=ma. Physically this is interpreted as a single bump input to one wheel performing the sprung mass acceleration and neglecting any rotation of the sprung mass about a pitch axis.

It's usual to put together a composite load case for the suspension consisting of cornering + braking / acceleration + bump input + aero (if you have it) to determine how strong to make it all.

It's also usual for Design Judges to ask how you developed your load cases at competition.

Regards, Ian

Because it's common doesn't make it right. Initially we weren't exactly talking about suspension loading calculations. We all do some cases where dynamic cases are simplified as static ones and in fact we here at VT have traditionally used a 5g bump analysis. However, the question is the simplification and I questioned its validity depending on the analysis method. How much does that simplification neglect and what effects may it be missing? Is it okay to assume the static simplification of the case and then call it done? I won't answer those questions because it depends on what you want to do with your analysis and where you are as a team.

And remember, this discussion started by the original poster's application of sustained 3g*sprung mass modeled statically to check shock/spring travel. For shock travel this is not applicable and the dynamic nature and impulse of the excitation are very important for accurate analysis. So a static simplification in this scenario used to check travel is a bad, bad idea. </div></BLOCKQUOTE>

+1


Looking at a 3g static case is like finding the final value of the STEP RESPONSE of your spring-damper system. While the real world bump scenario is probably more like the IMPULSE RESPONSE of the system since it happens with very large force in very short time.

So I think what I will do if faced with this quesion is probably starting with finding the transfer function of the spring-damper system (of course modified by installation ratio, etc). And then see what the system transient response is to inputs such as an impulse, or probably less radical inputs such as a rectangular/triangular pulse with large magnitude and small duration </div></BLOCKQUOTE>
Performing a true dynamic analysis is of course better than a static simplification. It's also probably 10x as time consuming to do and 10x as expensive to validate. Hence the common simplification approach...

Regards, Ian

[Pennyman]

Originally posted by murpia:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Yunlong Xu:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by BilletB:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by murpia:
It is very common to simplify dynamic loads as static ones. 3g bump is normally interpreted to mean 3g as measured by an accelerometer on the sprung mass at the axle line. You can then simplify the wheel load in Newtons to (total axle mass in kg) * 3 * 9.81 i.e. F=ma. Physically this is interpreted as a single bump input to one wheel performing the sprung mass acceleration and neglecting any rotation of the sprung mass about a pitch axis.

It's usual to put together a composite load case for the suspension consisting of cornering + braking / acceleration + bump input + aero (if you have it) to determine how strong to make it all.

It's also usual for Design Judges to ask how you developed your load cases at competition.

Regards, Ian

Because it's common doesn't make it right. Initially we weren't exactly talking about suspension loading calculations. We all do some cases where dynamic cases are simplified as static ones and in fact we here at VT have traditionally used a 5g bump analysis. However, the question is the simplification and I questioned its validity depending on the analysis method. How much does that simplification neglect and what effects may it be missing? Is it okay to assume the static simplification of the case and then call it done? I won't answer those questions because it depends on what you want to do with your analysis and where you are as a team.

And remember, this discussion started by the original poster's application of sustained 3g*sprung mass modeled statically to check shock/spring travel. For shock travel this is not applicable and the dynamic nature and impulse of the excitation are very important for accurate analysis. So a static simplification in this scenario used to check travel is a bad, bad idea. </div></BLOCKQUOTE>

+1


Looking at a 3g static case is like finding the final value of the STEP RESPONSE of your spring-damper system. While the real world bump scenario is probably more like the IMPULSE RESPONSE of the system since it happens with very large force in very short time.

So I think what I will do if faced with this quesion is probably starting with finding the transfer function of the spring-damper system (of course modified by installation ratio, etc). And then see what the system transient response is to inputs such as an impulse, or probably less radical inputs such as a rectangular/triangular pulse with large magnitude and small duration </div></BLOCKQUOTE>
Performing a true dynamic analysis is of course better than a static simplification. It's also probably 10x as time consuming to do and 10x as expensive to validate. Hence the common simplification approach...

Regards, Ian </div></BLOCKQUOTE>

+1

I know what I'd rather spend my time doing...