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# Dampers

## Damping theory basics

### by Julian Edgar

Click on pics to view larger images

At a glance...

• Bump input frequencies
• Spring natural frequencies
• Damping function
• Bump/rebound damping rates
• Friction (Coulomb) and velocity damping
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 This article was first published in 2007.

As we covered in Springs and Natural Frequencies, springs have a natural frequency – that is, a frequency that they will continue to bounce up and down at until the vibrations gradually die away. Car suspension systems have natural frequencies within the range of about 1 – 2.5 cycles per second (Hertz). If you have a car with stuffed dampers (shock absorbers), and you push up and down on a car’s body, the body will continue to bounce up and down at the suspension’s natural frequency for perhaps 5 or 6 bounces. In this case, the damping is being provided by mainly the friction in the bushes.

A car with little damping has suspension that can get so excited that the tyres actually bounce off the road. So the main purpose of dampers is to stop, within just a couple of bounces, the free oscillations of the suspension. In addition, dampers are used as dynamic springs that resist either slow or fast suspension movement, depending on the direction and speed of the movement.

That’s all pretty well known, but what of the detail?

### Input Frequencies

Road surfaces have differently sized and shaped bumps at different spacings. In addition to the height and spacing, the effect of these bumps on the car’s suspension system also depends on how fast the vehicle is travelling along the road. The faster the car goes, the shorter the apparent spacing between the bumps and the greater the vertical acceleration inputs into the suspension.

Imagine a series of house bricks placed on a road 1 metre apart. The vehicle is being driven over the bricks very slowly - the front wheels hit the bricks every 3 or 4 seconds. The speed of vertical movement will be slow and the frequency of bump input low compared with the suspension system’s natural frequency. Even with no damping, the wheels aren’t going to bounce around much.

But increase that forward speed and the bump input frequency will also rise. In fact, depending on the speed and the spacing of the bricks, the input bumps can reach the natural frequency of the suspension. That’s like making a child’s swing move further and further by pushing at just the right time. Here the ‘push’ is coming from the bump input of the bricks, and at this speed and with this brick spacing, the suspension will get more and more excited, until in fact the wheels are potentially bouncing right off the ground. Well they will if there aren’t any dampers present, anyway.

So dampers are particularly important in suppressing movement of the suspension around the system’s natural frequency – that’s the frequency of bouncing where the suspension will move furthest for a given input of bump energy. The greater the difference of bump input frequency from the suspension’s natural frequency, the less the suspension will tend to bounce.

However, suspension systems don’t comprise just the springs. The tyres also act as springs and have their own natural frequency. The natural frequency of tyres can be easily seen if you watch a front-end loader being driven down a road at 30 or 40 km/h. The vehicle has no suspension but for the tyres - and these are relatively poorly damped. If the driver is brave, sometimes you can see the vehicle developing more and more of a bounce at the tyres’ natural frequency.

So the dampers have to work particularly hard at both the suspension system’s natural frequency and the tyres’ natural frequency.

Also note that despite what you first think, most car damping doesn’t change the natural frequency of a suspension (or the tyres) by very much at all. It just stops the bouncing fairly quickly. But how much damping should be used? And should it be in the bump or rebound movements of the suspension?

### Damping

If the damping is too stiff, the suspension loses effectiveness at its primary function – absorbing bumps. Let’s look at that in more detail.

The suspension is said to have absorbed the bump if the vertical acceleration of the wheel is not passed onto the car’s body. So, when the bump is met, the wheel rises, the suspension compresses, but the body moves only little vertically – and when it does move vertically, it accelerates slowly. But damping which is stiff in bump will cause the suspension to pass more of the wheel’s vertical acceleration onto the body – so the ride will be hard. But if the bounces are to be brought under control within a few cycles, there’s not a lot of movement of the suspension in which to achieve this aim. And if you can’t use strong damping during bump, when can you?

The answer is in rebound. When the spring has compressed and then is extending again, that’s the time to apply most of the damping. So the ratio of rebound to bump damping can be something like 2:1, that is, the rebound damping is twice as firm as the bump damping. But in most cars, damping is still used on bump – it helps the car take a ‘set’ during cornering and also gives the dampers more opportunity to bring the suspension under control.

Earlier in this story we said that the deflection speed of the suspension will, for a given bump, depend on the speed with which the car is passing over it. So clearly speed of suspension movement is very important – it varies a huge amount. This brings us to the second characteristic of dampers which is important – how damping varies with suspension velocity.

If the bump damping is strong in low speed bump, but weak in high speed bump, it will make little difference to the ride – the ride won’t deteriorate much. That’s because the fast vertical accelerations of the suspension will be little damped, while the low speed bump (eg slow suspension deflection when the car is cornering or passing over long waves in the road) will still control suspension compression. Dampers achieve this softer high speed bump behaviour by using valves (called ‘blow off valves’) that open when the pressure rise within the damper is great. This allows the fluid to effectively bypass the more restrictive orifices which are normally at work during damper movement on bump.

### Taking Stock

Let’s summarise what we’ve covered so far.

• Both suspension systems and tyres have natural frequencies
• The closer the frequency of road roughness to these natural frequencies, the more excited will become the suspension and tyres
• Dampers are needed to control oscillations of the suspension and tyres, especially when the bump input frequency is near the suspension or tyre natural frequencies
• More damping occurs on rebound than bump
• Bump damping can be divided into high speed bump and low speed bump, with low speed bump much firmer than high speed bump

Let’s go back to our bricks on the road. Each time a wheel passes over a brick, the suspension compresses. Because these are relatively high speed bumps, the bump damping is low – much lower than the rebound damping. But if the bump damping is low and the rebound damping high, the spring will be quick to compress and slow to extend. So, if there are lots of bricks on the road one after the other, the suspension will compress further and further as each brick is met, until the suspension runs out of travel. Then when you hit the next brick, you get spat off the road...

From this example, you can see that the ratios of bump to rebound damping, and rates of high speed and low speed bump damping, need to be such that the springs will normally have time to extend back to their original position before the next bump is met. How quickly the springs re-extend will depend on their stiffness – so you can see that spring and damper behaviour need to be well matched.

### Conclusion

If you think about the ideas covered in this story – natural frequencies, bump input energy, and bump and rebound damping – you can often recognise examples of these ideas in action:

The bouncing of the front-end loader down the road

The creation of corrugations in dirt roads where the corrugations match the natural frequencies of the suspensions (or tyres) of trucks that have passed

The undamped feeling of a car that’s been fitting with stiffer springs but has retained the standard shock absorbers

In some cars, the over-strong rebound damping that gives greatest vertical accelerations as the top of the bump is reached and the wheel starts to descend the other side

Analysing what the suspension is doing means thinking about the ideas covered in this story and recognising when one or more aspects are not right.

### Fundamental Types of Damping

At its most basic, damping can be divided into two types: friction (sometimes called Coulomb) damping, and velocity damping. In both cases, the damping force opposes the free movement of the spring.

### Friction (Coulomb) Damping

If you look at a car from the 1920s you might notice that while the suspension has springs (invariably leaf springs), telescopic dampers aren’t present. Instead, most old cars use friction damping, often comprising an assembly on each wheel that uses stacked discs of leather and steel. During suspension motion, the discs twist against each other, providing a frictional resistance to suspension movement. The strength of the damping can be adjusted by a spring washer and bolt, the adjustment of which compresses the discs together. (Note that movement between the leaves of the spring also provided some damping.)

Friction damping provides a constant decrease in spring extension each cycle. For example, a certain frictional damping force might reduce the extension up and down of a bouncing spring by 1 inch each up/down movement. It doesn’t matter if the initial movement was very fast or relatively slow – this type of damping does not vary in strength with speed.

This diagram shows an extension spring on which a weight is hanging. (It doesn’t matter if the spring is in extension or compression; the same ideas apply.) As can be seen, the damping causes the up/down movements of the bouncing mass to get linearly smaller over time.

### Velocity Damping

All current car dampers use velocity damping, usually where oil is forced through small orifices within the damper. This type of damping is proportional to the speed of damper movement – the faster the suspension moves, the more the dampers resist that movement (unless variable internal valving is used, eg blow-off valves fitted to reduce the relative damping strength of high speed bumps).

With velocity damping, the up/down movements of the spring don’t die away in a linear progression. Instead, as the up/down movements get smaller, so does the effect of the damping. (Note how the dotted lines outlining the ‘envelope’ of spring oscillations don’t comprise straight lines, as they did with friction damping.)

### Comparison

The above might all seem irrelevant to car drivers – after all, no current cars use friction dampers. And it’s absolutely true that for most people, this material is simply an interesting technical diversion (which is why it’s in a breakout box!).

However, in a special class of vehicles (eg ultra light weight human-powered vehicles, and possibly also similar spec’d tiny cars), friction damping has some major advantages over velocity damping.

These advantages include light weight (no fluid); packaging (no space needed for long dampers), no requirement for high speed internal bump blow-off valves; and very simple construction, adjustment and rebuilding. In fact, this diagram shows the suspension of a Citroen 2CV. In addition to the very interesting spring arrangement, note that external dampers are not used. Sufficient damping is provided by the friction in the suspension pivots.

It would seem that the symmetrical bump/rebound damping associated with friction damping would be a major problem (because bumps would be felt more severely). However, this is ameliorated by the fact that with friction damping, the damping resistance does not increase with high speed bumps – so friction damping can be symmetrical in bump/rebound without a major loss in ride comfort.

Disadvantages of friction damping are primarily wear and heat build-up. Another disadvantage is stiction: the resistance to initial movement is higher than the resistance once movement is occurring, so potentially giving a jerky ride on relatively smooth surfaces.

### References:

Gillespie, T.D, Fundamentals of Vehicle Dynamics, 1992, ISBN 1-56091-199-9

Dixon, J.C., The Shock Absorber Handbook, 1999, ISBN 0-7680-0050-5

Coker, A.J. (Ed), Automobile Engineer’s Reference Book, 1959 (ISBN not available)

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