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THE SIZE/PERFORMANCE TRADEOFF IN DAMPERS

We have two somewhat related questions this month.

1. What are the pros and cons of using dual shocks, meaning two of them acting in parallel on a single wheel?

2. We are involved in designing a front and rear suspension for small formula vehicle. Both suspensions will be push or pull rod (still to be decided) with coil over spring/ shock absorber. The motion ratio wheel/spring will be higher than one. Due to some budget concerns, we have to use another shock absorber coming from a previous vehicle that was heavier; we have budget for new springs. Preliminary calculation shows that to keep these shocks, the new motion ratio will be around 1.4 to 1.5. This seems a little bit high based on similar vehicles, which are around 1.3. Apart from manufacturing tolerances – we know the higher the motion ratio the closer the tolerance has to be – we do not see any other drawback for this motion ratio. What do you think?

To take the simplest bit first, probably a change in motion ratio on the order of 10% isn’t going to dramatically hurt performance. That’s a fairly small change. Shocks are sometimes run with wheel/damper motion ratios of 2 or more (damper/wheel motion ratios of 0.5 or less).

There are both penalties and benefits when we do this. The main benefit is that the shock can be shorter. This will generally make it lighter and easier to package. It will also reduce shaft and piston accelerations, which could be good, bad, or largely inconsequential depending on the nature of the valving and the desired properties.

The penalties when we shrink dampers are considerable, however – at least if we shrink them a lot. The pressure required to get a given damping force at the wheel varies directly with the square of the wheel/damper motion ratio, or inversely with the square of the damper/wheel motion ratio. To

reduce the stroke by a factor of two, we have to quadruple the working pressures in the damper. To reduce the stroke by a factor of 1.10, we have to increase working pressures by a factor of 1.21.

This increases stresses on all the parts of the damper, particularly the seals. Not only is unintended bleeding past the piston more likely, but since piston velocity is lower, a given size bleed may have a greater effect on force produced.

Higher pressures and lower shaft velocities increase elastic effects in dampers. These effects have not been adequately researched, to my knowledge. In fact, these effects are so little recognized that the entire subject probably requires some introductory explanation.

A damper is intended to produce a force opposite in direction to shaft velocity, and dependent only on shaft velocity. However, actual damper behavior deviates from this, most noticeably near a reversal of motion, or the end of a stroke. Often, for a short period after piston motion reverses, the damper will actually exert a force on the piston in the same direction that it’s moving. While this is occurring, the damper isn’t damping at all. It is acting more like a spring.

This can be observed on a shock dyno, when doing the most common type of test, a sinusoidal test. When we measure the gas spring force at the top and bottom of the stroke, we will see a small spring rate. The gas force will be slightly greater at the top of the stroke than at the bottom, but only a little. Normally we will zero the dyno reading to subtract the gas force from the readout, most commonly at mid-stroke.

The most common form of shock dyno uses a scotch yoke mechanism to cycle the shock. We have choice of a few stroke lengths and rpm settings. The most common for car shocks is a 2” stroke at 100 rpm. This gives a peak velocity just under 10 in/sec.

When we cycle the shock through a 2” stroke at 100rpm, and plot force versus absolute velocity for the entire cycle, we get a trace that looks like two V’s lying on their sides. The V’s meet at their spread ends, at the right side of the graph. These are the points of maximum absolute velocity, at the midpoints of the upward and downward strokes. The points of the V’s are at the y axis, one higher than the other. These show the force at zero velocity: the points where the piston is instantaneously motionless at the top and bottom of the stroke. These points will be spread by a greater amount than when checking gas forces. This is due to other things than the gas reservoir acting like springs.

When the piston is moving down, the fluid below the piston compresses, and the body of the damper below the piston stretches a little. When the piston stops and begins moving upward, the body and fluid below the piston briefly act like an accumulator, and force fluid upward through the piston despite the fact that the piston is beginning to move upward. Until the piston has moved a bit and picked up some speed, the damper doesn’t damp. The graph shows the shock trying to hasten the motion of the suspension rather than retard it.

Suppose we built a dummy shock – no shims on the piston; essentially no damping effect – and put a spring on it and dynoed that. What sort of trace would we get? We’d get reversed V’s: big spread between the left points and very small spread between the right points.

Shock dynos typically also allow us to set the stroke at 1” and the rpm at 200. This gives us the same velocity range as a 2” stroke and 100rpm. This setting is often used for small dampers such as mountain bike shocks that don’t have two inches of stroke. These are often used on Formula SAE cars as well as bicycles. It is also possible to test full-sized car shocks this way, and compare the plots to tests at the more customary 2” @ 100rpm.

When we do that, we generally find that the points of the V’s, at the y axis, spread apart more at the higher rpm and shorter stroke. This means that for similar velocities, the shock is failing to damp over a larger percentage of the stroke when the frequency and acceleration are greater. This appears to be so even when peak velocities, and hence peak pressures, are similar. This could be explained by the fact that the pressure in the “accumulator” needs time to bleed off. The piston will therefore have to accelerate to a higher velocity after reversing direction before it will start to generate damping force.

This would agree well with popular thinking that it’s harder to make a shock damp small, fast suspension motions than large, slow ones.

We also see the points of the V’s, at the y axis, spread if we stiffen the valving. This is logical because we will see greater compliance when the pressures are greater.

All of this means that there are penalties in damping performance when we raise working pressures to try to shrink the dampers, and these cannot be entirely overcome by minimizing leakage inside the damper. The performance penalties will be particularly noticeable on chatter bumps.

But wait – if we make the damper bigger, doesn’t that by itself make the damper more compliant? If the body has more diameter or length, doesn’t it have less stiffness? If a column of fluid is longer, isn’t it more compliant? When we make a shock bigger to reduce the working pressures, are we tricking ourselves? Do we lose on the swings what we gained on the roundabouts?

Partly we do, but not entirely.

Consider what happens if we double the length of the damper, and adjust the motion ratio accordingly. The shock now only has to make half the force at given wheel velocity. When the velocity reverses, the pressure will be half as great, but the column of fluid will be twice as compliant, so it will deflect the same amount. However, the piston will accelerate away from its point of reversal twice as fast, so it will start damping sooner.

Suppose we leave the length and motion ratio alone, and double the piston area, meaning we increase the diameter by a factor of the square root of two. That also cuts the pressure in half, and does it without increasing the length of the fluid column. However, it does increase the surface area

of the body, and correspondingly its radial and circumferential compliance and the hoop stress acting on it. The hoop stress goes up by a factor of the square root of two, and the wall stretch per unit of hoop stress also goes up by a factor of two, so the diameter increase for a given rod force doesn’t change.

So, macht’s nicht?

Not quite. The changes in diameter and circumference are the same in absolute terms, but smaller in percentage terms, for the larger diameter. For identical small absolute values of diameter change, the larger diameter sees a smaller percentage area increase. For example, if a 1” cylinder grows to 1.01”, its cross-sectional area grows by a factor of 1.01 squared, or 1.0201. If a 1.4” cylinder grows to 1.41”, its cross-sectional area grows by a factor of 1.0143. So there is a little gain in terms of the effect of wall stretch, and a reduction of fluid compression by a factor of the square root of two.

Thus, we do reduce compliance effects in a damper by increasing its size, either by making it longer and adjusting the motion ratio to suit or by making it fatter.

Now, what about using two dampers? Other things held constant, we reduce working pressures by a factor of two, and we don’t increase fluid column length or reduce radial rigidity at all.

Then there’s the question of heat. Regardless of size, if the shocks are similarly effective they must generate similar amounts of heat, in calories per unit of time. This must be dissipated through the surface of the units. Other things being equal, greater surface area will translate to lower operating temperatures and improve damper performance in severe conditions. Using multiple dampers is best for this, followed closely by using longer dampers. Using fatter dampers also helps, but not as much.