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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

Crushing a conical Belleville spring flat is different then bending a flat washer into a cone shape. One is the reverse of the other, but the physical process is completely different.

Belleville springs start with a conical shape and are crushed flat. When the conical spring is crushed the outside edge of the cone is forced to stretch to progressively larger and larger diameters. At some point the outside edge gets sick of that and “snaps” over itself back into something closer to its original diameter. When the outside edge snaps over the washer distorts into an “S” shape. Almen and Laszlo call that oil canning. A remarkable feature of the Almen and Laszlo equations is they actually predict the combination of inside diameter, outside diameter, wall thickness, cone height and deflection that cause Belleville springs to oil can.

The important thing here is the outside diameter of Belleville springs are stretched when the original conical shape is crushed flat. Stretching steal to a larger diameter requires a whole bunch of force.

**Edited by Clicked**

**Shim Stack Deflection**

The Almen and Laszlo equations can be applied in the reverse direction of bending a flat washer into a cone shape. But there's a catch. If you start with a flat washer and bend it into a cone, the outside diameter of the shim has to become smaller. Shims hate that!

When a flat disk gets bent into a cone the outside edge wrinkles. The wrinkles allow the perimeter of the original flat disk to fold itself into the progressively smaller diameter of a cone. A coffee filter is an example of edge wrinkling. Fold a flat disk into a cone shape and the edge wrinkles, it is a simple conversation of perimeter length idea.

Edge wrinkling is entirely different from the problem Almen and Laszlo were solving for Belleville washers. For Belleville washers the perimeter gets stretched as the washer is crushed. Edge wrinkling never happens in that process so the effect is not included in the Belleville spring equations.

The Almen and Laszlo Belliville washer equations are not wrong, they were simply solving a different problem.

Instead, shims deflect into a wave shape. The photo of the MXScandinavia finger press shows that wave shape for a deflected stack. The wave is like the pleats of a coffee filter and allows the shim to preserve the original flat disk perimeter length. That relieves edge stress and results in shim stacks producing a nearly linear stiffness profile out to edge lifts out to 7 h/t (NastyR1 mentioned that effect earlier). That fact was verified by the MXScandinavia finger press data.

**Shim Stack Tuning Webology: **

**Shim stiffness increases at edge lifts greater than one shim thickness. FALSE****Shim stiffness becomes non-linear at high lift. FALSE**

MXScandinavia shows four data sources dispelling that myth:

Finger press data at edge lifts up to 7 h/t

MXScandinavia dyno data at edge lifts of 1.5 h/t

Ohlins factory dyno data at edge lifts of 2.8 h/t

FEA stack deflection calculations up to edge lifts of 7 h/t

The data shows shim stacks have a slightly progressive stiffness profile. The stiffness progression is far less than the Belleville washer equations predict with no evidence of a sharp stiffness increase at edge lifts greater than one shim thickness as is commonly thought.

The finger press data from MXScandinavia at edge lifts of 7 h/t is equivalent to a suspension velocity of 1500 in/sec. That is like hitting a four inch bump at 200 mph. That is some true high speed data and shows no significant non-linearity in the stiffness of shim stacks. The assertion of webology that you have to go to even higher suspension velocities to see the non-linear effects is kind of silly.

There is an exception. Shim stacks on compression adjuster valves are pressurized all the way around the perimeter. Other than the forces from the port jets, there is no force causing those shims to wrinkle into a wave shape. That could make compression adjuster stacks become stiffer at high lift. On the other hand, the fluid flow through compression adjusters is very small creating stack lifts well below the level where non-linear effects are expected to begin. Some data is needed to see what happens there.

Interesting data, thanks for sharing that.

I remember asking you some time ago if it would be possible to add a feature into Restackor that would allow the program to calculate how many/what type of shims could be added to a shim stack to make it increase in stiffness by a percentage. In other words if I felt that my shock compression was too stiff Restackor could calculate how many more face shims would be required to reduce the stack stiffness by 25% if I felt that was the direction I wanted to go. The same would be true if I wanted to increase the stack stiffness by the same amount or any other amount I wanted to try.

Given that a shim stack follows the same characteristics that a linear rate spring does this should be something that could be calculated. Or maybe, the feature is already there it just needs to be presented differently (force vs edge lift) ?

It would be interesting to see in terms of percentage what was required to get my 450 working the way it does now as it took many revalves to finalize the settings. Through trial and error I've found that you have to balance hydraulic pressure with coil spring pressure to get things working - could compare that with the percentage increase in stiffness I had to go with my fork and shock springs (assumiing all other factors - oil height, nitrogen pressure, spring preload - remain the same).

You just look at the scale and adjust the stacks ?doesn't take long

I do it the same way. Just start adding face shims until I get a 25% change.

The usual problem is that comes down to something like adding five face shims, but I only have three. So that starts a process of hacking around looking at other things like increasing the crossover shim diameter or taking a shim off the top of the stack to increase the clamp. Hacking around on those I can usually find something that works without having to wait around for a new set of shims to arrive.

Things get trickier when you try and change the shape of the damping force curve. Like increasing low speed by 20% and high speed by only 10%,. Like a spring rate change. That almost always requires order a handful of new shims to get the right shape of the damping force curve.

We will look at some of those tuning tricks latter when we start evaluating some of the dyno runs on TT that change the shape of the damping force curve.

Right now we are doing something more simple. Looking a shim factors compared to some shim stack configurations to get a feel how shim factors work and what the shape of the stack stiffness profile is supposed to look like.

**Edited by Clicked**

**Linear Thickness Cubed “Beam Theory” of Shim Factors**

Shim stacks do not show the strong non-linear stiffness increase of Belleville springs. On the other hand shim stacks are not exactly linear either. The MXScandinavia finger press data shows shim stacks have a slightly progressive stiffness profile. At low lift the stiffness of shim stacks, Belleville springs and shim factor theory more or less line up. The plot below forces all of those theories to line up at a port edge lift of one shim thickness (h/t). As shims start to bend the stack gets progressively stiffer with increasing edge lift. For the MXScandinavia stacks that progressive stiffness increase resulted in an 8% difference in stiffness for these two shim factor scaled stacks. Based on the linear thickness cubed “beam theory” of shim factors that stiffness increase and stiffness difference between the two stacks was unexpected.

The progressive stiffness increase makes shim stacks stiffer than expected by the linear thickness cubed *“beam theory”* of shim factors but less progressive then expected by Belliville spring washer theory. Shim stacks are their own deal and don't behave like either one of those basic “hands on” engineering theories.

The other interesting thing the data shows is the stiffness progression between the 14x40.2 and 4x40.3 stacks was different. The 14x40.2 stack got stiffer faster. That made the 14x40.2 stack 8% stiffer at a port edge lift of one shim thickness and 20% stiffer at a port edge lift of seven. The assumption of linear stiffness used in the thickness cubed *“beam theory”* of shim factors just doesn't work for scaling of practical shim stack configurations. We need a better theory.

**Finger Press Stack Deflection Data**

MXScandinavia is not the only guy using a finger press to measure the stiffness of shim stacks. Valving Logic used one for years developing the Shim Program. The Aerospace Corp has used on as well.

It's not easy relating finger press data to suspension performance. The finger press applies a point load to the stack. That mechanical point load has to be converted into an equivalent fluid pressure applied over the valve pocket area. Stack lifts measured at the finger press contact point have to be extrapolated to the valve port edge to estimate the stack fluid flow area, flow resistance and ultimately the relationship of finger press stack deflections to the damping force of a shock.

Professor Darling at the University of Bath, used a Kawamaha style hydraulic dyno to help perfect the suspension systems of British military tanks. The dyno was used for anchoring of 3D CFD fluid calculations and relate the computed damping force to the actual performance of the shock. From those tests, Darling noted two important things about the behavior of shim stacks:

Stack stiffness measured during lifting the stack was stiffer than forces measured when the stack was lowered

Darling's data shows the stiffness difference between opening and closing the stack was around 17%

The Aerospace Corp using a finger press showed the same thing. The stiffness of a Belleville washer stack is stiffer when lifted compared to lowering.

**Shim Lift From Backer Limit Dyno Data**

Getting good shim stack stiffness measurements out of a finger press and figuring out how to relate those measurements to the damping force of a shock is tricky. The mechanical point load of a finger press is different then floating the stack on the hydraulic fluid pressure jetting out from the valve port. Shim friction values from the more or less dry finger press measurements are going to be different than the friction values when the stack is flooded with oil in a shock. Those differences create questions and uncertainty in the accuracy of finger press data in comparison to the actual stiffness of a shim stack installed in a shock.

Due to those uncertainties dyno tuners have worked out other ways to measure shim stack lift. A simple way is put a backer on the top of the stack and use dyno measurements to figure out when the shim stack hits the backer. That provides an actual in-situ measurement of the true stack deflection of a shim stack installed in a shock.

Simple, no assumptions.

The dyno data on TT shows a couple of examples using backer limit tests to measure shim stack deflections directly from the results of a dyno test. We will look at those results next and compare the stack deflections estimated by shim factors and the finger press data to see how the data lines up in terms of shim stack stiffness.

**Backer Limit Dyno Testing**

MXScanindavia used a backer shim on an Ohlins three port valve to figure out how far the shim stack deflects during a dyno test:

In the dyno test the stack with the thinner 0.2 mm clamp (ct2025) hit the backer at a suspension velocity between 30 and 35 in/sec. The second stack with the thicker 0.3 mm clamp (ct3025) did not.

Backer limit tests give a way to figure out when events occur like closing a crossover gap. The tests deflect the shim stack in a natural way using the shock fluid pressure instead of the point load applied by a finger press. That avoids the uncertainties involved in interpreting finger press data, but backer limit tests only gives you info at low stack lifts – like a shim height or two.

Valving Logic has used this same dyno testing approachto measure shim stack lift. We will look at some of the Valving Logic dyno data posted on TT next to get some more stack stiffness measurements to compare with the shim factor equation.

**Valving Logic Backer Limit Dyno Data**

Valving Logic has used that same approach to measured stack lift in a thread here (linky) for one of Mog's stacks. The Valving Logic dyno has more power then the dyno MXScandinavia was using and can go to shaft velocities that are about 50% higher. That gives max shaft speeds in the 60 in/sec range.

The rmz250 test was run on a kyb 46mm shock valve.

The FEA calculations show the stack hit the backer at a shaft velocity around 53 in/sec. The PVP dyno data from Valving Logic only collects data at discrete points. So we have data at 50 in/sec and 60 in/sec. The stack hit the backer somewhere between those two data points, but not as hard as the FEA calculations predicted.

So far this thread has looked at dyno data of four shim stack configurations. For those shim stacks the stack deflection was measured four different ways:

Dyno measurements on 4 shim stacks

FEA analysis of 4 shim stacks

Finger press measurements on 2 shim stacks

Backer limits on 2 stacks

That gives 12 measurements of shim stack deflection for those 4 shim stack configurations run on three different valve port geometries.

The big question MXScandinavia was after, and the reason he went out and collected all of the data, was to try and figure out how well shim factors compare to these basic shim stack deflection measurements. We will compare those measurements next.

**Edited by Clicked**

**Shim Factors Compared to Dyno Data**

The thickness cubed relationship used to create shim factors is basically an estimate of the stack spring constant. To figure out the actual value of the spring constant is we need some measurement of the force required to deflect the stack some specified distance. The MXScandinavia finger press data gives those measurements.

For the 14x40.2 stack the finger press used a maximum force of 520 lbf and produced a maximum shim stack lift of 7 h/t. Those measurements are after correction for fluid torque and referencing the finger press lift to the valve port edge. The data works out to a stack spring constant of 9,500 lbf/in. Base on the finger press measurements multiplying the tapered stack shim factor by 40 gives a pretty good estimate of the stack spring constant. The finger press data shows the 4x40.3 tested softer than expected by shim factors. For that stack the spring constant works out to be 35. The equation below uses 40 because that centers the data better.

The above equation uses shim thickness and diameters in mm and computes the tsf spring constant in lbf/in. So it's mixed units.

**Shim Factors Compared to Measured Shim Stack Lift**

To estimate the shim stack spring constant multiply the tapered shim factor by 40. Divide the spring constant into the force applied to the stack and you get an estimate of shim stack lift. The plot below compares stack lift estimated by shim factors to the measured data for these four shim stack configurations. Shim factor estimates are off by +/- 30%.

The above comparison only looks at four shim stack configurations. Two of those stacks were tapered the other two were straight stacks. The data scatter for those four stacks is in the +/- 30% range.

What if you only looked at tapered stacks? If you only compared stacks with more similar shim stack structures would shim factors work better?

**More Dyno Data**

From the dyno tests we have looked at so far there is more data out there we can use to test the shim factor equation. The MXScandinavia thread shows dyno data for seventeen different shim stack configurations from the Ohlins factory testing. Those configurations all use a tapered shim stack with a similar stack structure. To get stack stiffness out of that dyno data we need to run the FEA calculations on each shim stack and compare the results to the dyno data to make sure the FEA calculations got the stack stiffness right.

Here is the factory data for the compression shim stack configurations:

**Rebound Dyno Data**

On the rebound side there are five more shim stack configurations.

Adding those 5 rebound shim stack configurations and the 12 compression stacks gives 17 more dyno runs to compare against the shim factor equation to test it's accuracy.

**Shim Factors Compared To Dyno Data**

Adding the additional 17 dyno runs to the shim factor comparison only fills in the +/- 30% error band comparing measured shim stack deflections to values predicted using shim factors. There isn't any obvious trend where the shim factors are too high or too low. Shim factors are just off and the error randomly floats over the +/- 30% range.

The fact that shim factors are off is not a big surprise, shim factors are just a rough approximation, everyone knows that. I am surprised the error is +/- 30%. I expected something more in the 15 or 20%, but have never seen a comparison of shim factors to the measured stack stiffness before.

The comparison shows there are some problems with shim factors. That does not mean shim factors are worthless. Shim factors are derived from the pretty sound basic theory of linear springs. Comparing shim factors to the actual stack stiffness determined from dyno testing makes some sense in terms of developing an understanding of why one shim stack structure behaves differently than another. For that reason you will see a lot of comparisons in this thread of shim factors and dyno data. Not because there is a “surprise” that shim factors don't work, that is widely known. The comparisons simply emphasizes the difference between basic linear spring theory and the actual behavior of shim stacks. That gives some insight into the magnitude of the difference and starts discussion of the why one shim stack structure is softer or stiffer than another and why dyno testing shows results that are opposite of the basic expectation of linear spring theory used in shim factors.

Clicked would you look at this thread

http://www.thumpertalk.com/index.php?/topic/1113476-KYB-SSS-fork-reb-stack-tuning-principles

Looks like numroe has a bunch of questions on how different crossover gap configurations behave.

TT has a bunch of dyno data evaluating behavior of crossover gaps. We'll look at some of those dyno test latter.

For that dyno comparision above why are shim factors so far off from the dyno data?

There are probably a bunch of reasons, here are a couple:

**Clamp:** The clamp diameter sets the location where the stack starts to bend. Tall stiff stacks don't change much with clamp diameter since they are already stiff. But a stiff clamp on a soft stack creates a large change creating what some call nonlinear effects.

**Stack Structure:** The shim factor equation makes the assumption the stack stiffness is simply the sum of the stiffness of each shim. A simple sum does not provide any way to account for local changes in the shim bend profile due to the stack structure. Accounting for stack structure effects requires some way to parses up the stack into separately analyzed sections and account for soft and stiff sections of the stack. The Valving Logic shim program does that. For shim factors there is no easy way to do that using a simple equation.

**Shim Friction:** For the MXScandinavia finger press data, shim factors expected the 14x40.2 stack to have the same stiffness as the shim factor scaled 4x40.3 stack. If shim factors are going to match anything it should have been this simple case of replacing face shims.

But, the finger press data shows the 14x40.2 stack was 20% stiffer than the 4x40.3 stack. Professor Darling's observation of shim friction increasing stack stiffness by 17% is a potential explanation. The 14x40.2 stack has more shims, more surface area and potentially more shim friction. Shim factors don't account for that effect. But what about the other 18 shim stack configurations?

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The Webology Of Shim Stack TuningThere is a lot of information out there, scattered through suspension forums, on how to tune a shim stack and the general webology of suspension tuning. Some of it is true and some myth. This first dyno test from MXScandinavia dispels two common myths in the webology of shim stack tuning.

Shim stacks become stiffer at high liftDig around in suspension forums and the usual statement is: “Shims become stiffer at edge lifts greater than one shim thickness”, sometimes worded as “shim stiffness is nonlinear at high lift”.

The webology is based on the Almen and Laszlo Belleville spring equations. Belleville springs become stiffer at high lift, that is a fact. Flat shims used in suspension systems do not. That is a fact demonstrated by the MXScandinavia finger press data.

Why are Belleville spring washers so much different from the flat shims used in suspension systems?

Edited by Clicked