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Dyno data –And what it tells us about how to tune a shim stack and control the shape of the damping force curve

Clicked when you say 30% equals 10 face shims ,that's a huge amount of extra shims , I had no idea it took that many face shims on this stack to make a 30% stiffness change

Could the same change be achieved by going from .10 thickness shims to .11 thickness shims, all else being equal? Approx 30% change in stiffness with that change in thickness on an individual level.

Clicked when you say 30% equals 10 face shims ,that's a huge amount of extra shims , I had no idea it took that many face shims on this stack to make a 30% stiffness change

For that shim factor plot above missing a setup by ten face shims is a lot....

That MXScandinavai stack has 14 face shims. To make the face shims 30% stiffer you would have to add about 5 more shims. The tapered section in that stack turns out to have about the same stiffness as the face shims. To make the tapered section 30% stiffer you have to add another 5 face shims.

Add that up an you get 10 shims. For that stack anyway, would not take that as a universal rule.

Could the same change be achieved by going from .10 thickness shims to .11 thickness shims, all else being equal? Approx 30% change in stiffness with that change in thickness on an individual level.

Thinking of that in terms of thickness cubed that would work out. If you used a kyb shim at 0.114 versus a showa shim at 0.10 the stack would be (0.114/0.1)^3= 1.48, 48% stiffer.

For the MXScandinavia stack most of the shims are 0.20 mm. To make those 30% stiffer you would have to find some 0.218 mm shims.

**Shim Stiffness Theory**

Talk to your average “hands on engineer” about structural stiffness and there are two basic theories in engineering:

Thickness cubed “beam theory”

Non-linear “Belleville washer” spring theory

The wave shaped deflection of shim stacks partially relieves internal stress in the shim. That makes the stiffness of shim stacks softer than non-linear theory of Belleville springs.

The alternative theory from basic engineering is the linear thickness cubed relationships of “beam theory”. The wave shaped stack deflection relieves stress, but only partially. That makes shim stacks stiffer then the simple linear thickness cubed relationships of beam theory. Shim stacks are their own thing somewhere in between the basic structural stiffness theories of Belleville springs and linear beam theory.

MXScandinavia shows the actual behavior of shim stacks gets even more complex. Not only is the stiffness of a shim stack non-linear, the non-linear stiffness behavior of the 4x40.3 shim stack was different then the 14x40.2 stack. The 14x40.2 stack got stiffer faster. That resulted in a 20% difference in stack stiffness at high lift for these two shim factor equivalent stacks. Creating a shim factor relationship that works for all of those configurations will probably end up with a more complex expression then the typical back of the envelope “hands on engineer” calculation.

So far we have only looked at four dyno tests:

The two MXScandinavia shim factor scaled stacks

A backer limit test from MXScandinavia

A backer limit test from Valving Logic

There are a bunch more dyno tests scattered through the suspension forms of TT. We need to start looking at some of that data over a wider range of shim stack configurations to see if some better form of the shim factor equation can be developed through comparison with data.

**Edited by Clicked**

**Stack Taper Tuning**

The MXScandinavia shim factor test replacing face shims did not work out. The stacks were supposed to be matched. Turns out the 14x40.2 stack was 8% stiffer at 40 in/sec on the dyno and 20% stiffer at high speed on the finger press. That was for replacing face shims on the stack. What about the tapered section of a stack, do shim factors work better there?

MXScandinavia ran a second series of dyno tests to see how shim factors worked out for tuning the tapered section of the shim stack. From thickness cubed theory a pair of 0.15 mm shims should be 19% softer than a single 0.2 mm shim.

To test that theory MXScandinavia replaced all of the 0.2 mm shims in the stack taper with a pair of 0.15 mm shims. Those changes are in the “high speed” stack so the stack using the softer shim pairs should end up producing less high speed damping.

The other thing going on here, from Kawamaha's theory (linky), is thicker 0.2 mm shims should produce a more progressive high speed damping profile compared to the thinner shims used in the modified stack.

There are a couple of theories for the dyno to work out in this test:

If you replace a 0.2 mm shim with a pair of 0.15mm shims is the stack 19% softer?

Webology: If you soften the high speed stack does the high speed damping get softer?

Webology: Is a short stack of thick shims more progressive than a tall stack of thin shims?

**Shim Factor Theory**

From shim factor theory, sum up the tapered section and the baseline stack of 0.2 mm shims has a shim factor of 119. The replacement stack using 0.15 mm shim pairs has a shim factor of 106. So the high speed stack should be 11% softer. That value is different than thickness cubed theory because MXScandinavia also replaced the 38.25 and 36.25 shims at the start of the stack tapper with a softer pair of 0.2 mm shims. Sum all of those up and the modified stack should be 11% softer instead of 19% expected from thickness cubed theory.

Sum up the entire stack, including the face shims, gives a tsf of 238 for the baseline stack of 0.2 mm shims. The thinner shim pairs in the modified stack reduce the tapered shim factor to 225. So the modified stack should be 5% softer.

There is a wide range of results here depending on how you apply shim factors:

Thickness Cubed Theory: Tapered section should be 19% softer

Shim Factor Theory: Tapered section should be 11% softer

Tapered Shim Factor Theory: Overall stack should be 5% softer

And there are some shim stack tuning webology points being tested:

Webology: A softer high speed stack produces less high speed damping

Webology: A short stack of thick shims is more progressive than a tall stack of thin shims

Either way, shim stiffness theory says the modified stack using replacement shim pairs should be softer. Add to that the webology theory and the shorter stack of thick shims should get progressively stiffer as the stack is deflected.

That's the arm chair theory anyway, what does the dyno say?

Any ideas on how the dyno test for these two stacks is going to turn out?

**MXScandinavia Dyno Data**

The dyno data shows the actual stack stiffness is opposite of the stiffness difference expected by shim factors. The theoretically softer stack using the replacement shim pairs produces more damping force. The data shows no difference in high or low speed damping. The theoretically softer stack is just stiffer and it is stiffer everywhere. There is no difference in high speed or low speed damping and no stiffness progression expected by webology for the short stack of thick shims.

**Shim Factor Theory: **

The stack using pairs of the thinner 0.15mm shims should have been 5% softer based on shim factor theory. The dyno shows the stack was about 3% stiffer. Shim factors missed the change in damping force by 8%. The bigger problem is shim factors got the direction wrong. The stack was supposed to be softer, turns out the stack was stiffer. The dyno data and FEA calculations both show that stack was stiffer.

**Webology:**

From the webology of shim stack tuning, the softer 0.15 mm shim pairs was supposed to soften high speed damping somewhere between 11% to 19%. That's a bunch. The dyno shows no difference in high speed damping. The theoretically softer stack was stiffer and it was stiffer everywhere through the velocity range.

Webololgy also asserted the thicker 0.2 mm shims were supposed to be more progressive at high speed. The dyno shows no progression at all. The 0.2 mm stack starts out softer and remains softer over the entire velocity range.

This dyno test was supposed to be a simple example demonstrating effects of tuning the high speed stack. Shim factory theory and the basic webology principles of high speed stack tuning just aren't working out. We need some better theories.....

Digging around I've found four different theories trying to explain why these two stacks give results opposite of the effect expected by shim factors.

- The clamp fulcrum effect
Non-linear shim stiffness

Shim Friction

The stacked bowl theory

We need to look at each of those theories and see if any of them make any sense compared to the dyno data and the performance differences the dyno measured for these two stacks.

**Fulcrum Effect**

Each shim added to the stack increases the clamp effective “fulcrum” diameter. Project the clamp fulcrum all the way through the stack to the face shim and the effective “fulcrum” diameter becomes larger making the face shims stiffer than expected. Jake Z describes the theory here.

mog expands on the theory here (linky), and DaveJ introduces the idea the fulcrum diameter shifts with stack deflection here (linky).

The “fulcrum” idea is each shim added to the stack tapered section adds more support to the pivot shim. That support makes the pivot shim effective “fulcrum” diameter larger. Project the clamp fulcrum all the way through the stack to the face shim and the face shims become stiffer then expected due to the larger projected clamp “fulcrum” diameter. Tall stacks are stiffer because the clamp “fulcrum” is projected through a longer distance.

Replacing nine 0.20 mm shims with a theoretically softer pair of 0.15 mm shims made the stack 50% taller. That gives the taller stack a larger projected clamp “fulcrum” diameter making the tall stack stiffer. Bushmechanic points out (linky) this same effect also comes into play when using thicker shims in a stack as well.

An oddity I am not sure about is how the projected clamp fulcrum diameter changes with stack lift. If the fulcrum moves inward the stack would become softer as lift increases. That would make the stiffness digressive and opposite of the MXScandinavia finger press data.

**Internal Shim Strain**

The Almen and Laszlo Belleville spring equations were discussed a bit at the top of this thread. One of the parameters in that equation is the ratio of shim edge lift (h) to shim thickness (t). That ratio of h/t is used in the Belleville spring equations to estimate the increase in internal strain in the shim material and its effect on stiffness. The effect is a function of shim thickness.

A stack of 0.2 mm shims with an edge lift of 0.2 mm has a h/t strain ratio of 1.0

A stack of 0.1 mm shims at the same edge lift of 0.2 mm has a h/t strain ratio of 2.0

From Almen and Laszlo, a tall stack of thin shims is going to be stiffer than a short stack of thick shims because the edge lift h/t ratio, and internal strain, is larger for thin shims. MXScandinavia mentions that effect in his thread here.

**Shim Friction**

The modified stack used pairs of 0.15 mm shims to replace the 0.2 mm shims in the stack taper. The replacement shim pairs doubles the number of shims in the tapered section, doubles the shim surface area and increases effects from shim friction.

Professor Darling at the University of Bath, The Aerospace Corp and the Schnorr handbook all show shim friction can increase the stiffness of a stack of Belleville springs by 15 to 30%.

Replacing the 0.2 mm shims with pairs of 0.15 mm shims was supposed to make the stack 19% softer based on shim factor theory. But, doubling the number of shims in the stack taper increases the shim surface area and shim friction making friction one of the factors that may have swung the actual stiffness of the modified stack back the other way to end up being stiffer. That is what the data shows.

It goes to show how theory can get it very wrong and how a dyno would show actual results

If shim factors work for anything you'd think it would be these simple stack mods MXScandinavia is making. The test here put softer shims in the stack taper, that should have made the high speed stack 11% to 19% softer. Seemed pretty straight forward. Instead the stack dyno tested 3% stiffer. FEA showed the same thing, stiffer stack.

Other stuff seems to be going on in the stack that are not accounted for by shim factors. Shim friction, non-linear stiffness and the fulcrum theory are possible explanations.

Here's another theory why shim factors got it wrong:

**Stacked Bowl Theory**

Stack up a set of kitchen bowls, all with the same diameter, and the bowls don't fit. To make the bowls fit, each bowl has to have a diameter slightly smaller than the bowl below it.

In terms of shims stacks the “stacked bowl theory” asserts shims at the top of the stack are forced to bend around a sharper radius to fit into the shim below it. Forcing shims to bend around a smaller radius obviously requires more force and that makes shims at the top of the stack stiffer then expected by shim factor theory. The stacked bowl theory is consistent with Mog's theory (linky) that a tall stack of thin shims gives more damping then a short stack of thick shims.

The stacked bowl theory also gives some insight into why shim stacks become progressively stiffer at high lift. At low deflection the bend radius is large so all of the shims are bent about the same. As the deflection increases the shims at the top of the stack are forced to bend around a progressively sharper radius making the stack progressively stiffer as lift increases.

**Edited by Clicked**

Wow that's a great old thread

Some good stuff there, trying to dig out the dyno data from those old threads and compare it with shim stack tuning theories to see if any of those theories make any sense. There are four theories on why tall stacks are stiffer. Each theory is a little different.

From the Belleville spring equation the stiffness of shims increase with deflection due to the build up of internal strain within the shim material. At the same edge lift thin shims create larger internal strains making thin shims stiffer.

From the stacked bowl theory, the stack structure becomes stiffer due to the forced sharper bend radius at the top of the stack. The stiffness of the individual shims remains the same.

The fulcrum theory shows the face shims become stiffer due to the larger projected clamp diameter through a tall stack.

In that respect the fulcrum theory is opposite of the stacked bowl theory. The stacked bowl theory asserts the sharper bend radius at the top of the stack makes the top of the stack stiffer. The fulcrum theory asserts the larger projected clamp diameter makes the face shim stiffer. Either way, tall stacks are stiffer but for opposite reasons.

Both of those theories are based on things going on in the stack structure that make the structure stiffer then the sum of the individual shims assumed by shim factors. The Belleville spring theory asserts thin shims are just flat stiffer regardless of the stack structure.

Which ever theory you chose, the MXScandinavia dyno data shows there are things going on in the shim stack that cause the stiffness of the structure to be different than the sum of the individual shim stiffness. The projected clamp fulcrum and stacked bowl effect caused shim factors to under estimated the stiffness of thin face shims, over estimate thick shims and get the change in stiffness direction wrong for the stacks dyno tested here.

- Shim stack stiffness depends on two things:
- The stiffness of the shims
- The stiffnesss of the stack structure.

When the stack structure interacts with the stiffness of the individual shims it makes it hard to figure out the actual stiffness of a shim stack using shim factors. The MXScandinavia dyno data has shown examples of that.

**Webology: A tall stack of thin shims is stiffer than a short stack of thick shims**

True. The fulcrum theory, internal shim strain, shim friction, stacked bowl theory and the MXScandinavia dyno data all show a tall stack of thin shims is stiffer than a short stack of thick shims. Differences in stack surface area, non-linear shim stiffness and the way forces are transferred through the shim stack structure alter the shim bend profile and the effective stiffness of shims making tall stacks stiffer. Those effects are not included in shim factor theory.

**Webology: A short stack of thick shims is more progressive than a tall stack of thin shims**

False. The stacked bowl theory and the fulcrum theory both claim a tall stack of thin shims is stiffer. The stacked bowl theory also asserts shims at the top of the stack are forced to bend around a sharper bend radius as lift increases. That makes tall stacks become progressively stiffer as lift increases.

That theory is backed up by the MXScandinavia dyno data and finger press data. Both show a tall stack of thin shims is stiffer than a theoretically equivalent short stack of thick shims scaled by shim factors. The finger press data also shows shim stacks become progressively stiffer as lift increases backing up the progressive stiffness increase expected by the stacked bowl theory.

Sounds interesting.

Would you say the stock (EU) shock stack it's n ot as stiff as it seems to be?

Stock.

23.3

24.2

26.2

28.2

30.2

32.2

34.2

36.2

38.2

40.2

42.2

44.25 7x

So this stack would be ~ 20% stiffer with 14 44.20 faceshims?

I don't think the stiffness difference would be 20% for those stacks.

The stacks MXScandinavia dyno tested replaced a stack of 14x40.2 face shims with a shorter stack of 4x40.3 thicker shims. That reduced the face shim stack height by 57%. Based on the thickness cubed rule the replacement stack was supposed to be 4% softer. The dyno data, finger press data and FEA analysis all showed the stiffness difference was larger than that. At high lift (7 h/t) that difference was 20% stiffer. Shim factors and the thickness cubed rule both messed up the stiffness estimates for those two stacks.

For the stacks you're showing, replacing 7x44.25 face shims with a taller stack of 14x44.2 shims gives a 2% stiffer stack based on the thickness cubed rule. That mod increases the face shim stack height by 38% compared to 57% for the MXScandinavia case.

If you buy the “tall stacks are stiffer” webology deal then the 14x44.2 stack is going to be stiffer than estimated by the thickness cubed rule or shim factor theory because it is taller. Simple enough. The stacks MXScandinavia dyno tested had a 57% difference in face shim stack height compared to 38% for the EU stack you are showing. Since the stack height difference is less I would expect the stiffness difference would be less as well, but by how much?

**Tall Stacks Are Stiffer**

The first two dyno test series from MXScandinavia checked out the use of shim factors for tuning a stack. The first test modified the face shims and the second test modified the stack taper. Results of those tests demonstrated an important point: Simple changes to a shim stack do not produce a simple result. The actual stiffness of a shim stack structure is different than a simple sum of the individual shim stiffness.

Now that we know a little more about the influence of a shim stack structure on the overall stiffness of a shim stack based on the fulcrum and stacked bowl theory we need to go back and look at the test data from the first MXScandinavia dyno test again.

Based on shim factors those two stacks were setup to be theoretically equivalent. The dyno test data, finger press and FEA analysis all showed the SF14 stack was stiffer with a difference in the 20% range at high lift. Review of that test data was focus on verifying the MXScandinavia dyno data against the Ohlins factory data and verifying both of those data sources against the finger press measurements. Data from each of those tests provided an independent validation of the other giving some confidence in the measurements and the result. All of that test data and the FEA results showed the SF14 stack was stiffer then expected by shim factor theory. The “why” of that difference and the “why” of shim factors mucking up the stack stiffness estimate was left hanging.

Now that we know a little more about shim stack theory we can go back and look at those two stacks and understand the SF14 stack was stiffer because it was taller. That difference is a result of the fulcrum theory, stacked bowl theory, non-linear shim stiffness, shim friction or some combination of all four effects. The bottom line is tall stacks are stiffer. The dyno data from that first test series is a second example demonstrating that point and a second example demonstrating the structural stiffness of a shim stack is different than a simple sum of the individual shim stiffness. That difference was 20% at high lift, so it is an important effect.

The other important thing to point out here is data from the first MXScandinavia test demonstrated a tall stack of face shims is stiffer than a short stack. Dyno data from the second test series demonstrated a tall tapered section of the stack is stiffer than a short one. It makes no difference what section of the stack is taller. Tall stacks are just flat stiffer.

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Shim FactorsThe dyno data we have looked at so far shows shim factors can be off by +/- 30%. What does a 30% error mean in terms of shim stack tuning? Like, how many face shims would you have to add to a stack to be off by 30%?

For the MXScandinavia's baseline 14x40.2 shim stack you would have to add 10 face shims to increase the stiffness by 30%. That means using shim factors to scale one shim stack to another you could end up being off by 10 face shims. Missing your setup by 10 face shims just isn't much help for suspension tuning.

For suspension tuning we need a better shim factor equation.