Measuring suspension natural frequencies

Text and pics: Julian Edgar

Let's say you want to compare the spring rates you are running in your car with someone else. You’re trying to sort out your suspension, and you are admiring a similar car where its handling and ride are excellent. You say to the owner: "What rate springs are you running?" He tells you what they are in pounds/inch and then adds: "But my car’s motion ratio is different to yours – and the motion ratio on my car actually varies through the wheel travel."

The motion ratio is how much the spring compresses for a given movement of the wheel. So you think: hmm, that means that the rate at the wheels is going to be (1) different to the rate at the spring, and (2) at any given suspension deflection, is likely to have a different wheel rate to your car.

And then it gets worse.

The owner of the other car then adds: “And of course my car's weight distribution is different to yours, what with this heavier engine and its slightly different location in the wheelbase. And don't forget I don’t care much about ride quality so my car’s springs are probably stiffer than you’ll want.”

You think: gosh, I thought comparing spring rates would be easy!

Well there is an approach that allows you to compare the suspension rates between different cars. It’s a technique that takes into account motion ratio, spring rate, and mass acting through the wheels. It’s called the suspension’s ‘natural frequency’ and it allows direct comparison of suspension stiffness of different cars. It’s why in all good suspension textbooks, spring rates are never referred to – just natural frequencies.

A stiff spring doesn’t necessarily mean stiff suspension – it depends on the motion ratio and the weight acting through the spring. Measuring the natural frequency of the suspension takes away this confusion.

So what is all this about – and then when we’ve got that sorted, how do we measure natural frequencies?

Natural frequencies

Let’s say we take a coil spring out of a car and mount it vertically on a surface. We then put a heavy weight on top of it and push down firmly on the weight. When released, the weight bounces up and down at (say) three times per second – so at a frequency of 3 Hertz (Hz). Now it doesn’t matter how far we push the weight down before releasing it, this combination of spring and weight “likes” bouncing at 3Hz. This is called the system’s natural or resonant frequency.

If we were to keep the spring the same but change the weight, the resonant frequency of the system would change. It would also change if we kept the mass the same but altered the spring characteristics. To put this another way, there is a direction relationship between mass (acting downwards through the spring in this case), spring stiffness and the resulting resonant frequency. So if we directly measure the resonant frequency of the suspension, we get a number that takes into account the spring stiffness, the motion ratio of the suspension, and the mass that is working through the spring.

The higher the natural frequency, the stiffer the suspension.

Sound hard to measure? It used to be, in fact needing lots of expensive gear. But these days, it takes less than a few minutes – you just use a cheap app and an iPhone or iPad. The app is produced by Diffraction Limited Design (see here) and is called Vibration. At the time of writing, it costs just US$5. (I’m told that similar apps also exist for other smartphone operating systems.)

The software takes advantage of the fact that the iPhone has an inbuilt 3-axis accelerometer. It can measure up to plus/minus 2.0g and has a sensitivity of about 0.02g. Those characteristics make it ideal for measuring suspension behaviour. The software can be set to sample at up to 100Hz (100 times a second) and the data can be displayed as graphs, or emailed as spreadsheets.

The first step is to download and then have a play with the Vibration app to see how it works. It’s pretty straightforward, but like a lot of things, much quicker to learn by exploring the software functions on the phone than through my writing about it here.

Set the logging so it occurs for 10 seconds at the highest sampling rate possible - 100Hz. You can also set the sensitivity to suit the accelerations – when statically bouncing the car (covered in a moment), start off with 0.2g per vertical division. Finally, you can put in a delay that will occur prior to sampling starting – this allows you to get the car bouncing well before the logging actually begins.

After you have the functionality sorted, place the phone on one end of the car – say across the front axle line. Bounce that end of the car up and down. The suspension will strongly resist being bounced at anything but its natural frequency, so you very soon get a feel for when to push. (This is just like with a child’s swing – it’s obvious when to do the pushing.) With a car having stiff damping and/or spring rates, you might need a helper.

Press the sample button on the software and start logging as the car is being bounced. You should end up with an up/down trace that looks something like the pic below. (It is the bottom yellow trace that shows vertical accelerations). This is the front suspension of a Honda Legend.

The measured front suspension behaviour of Honda Legend using the Vibration app and a smartphone. The bottom trace, that shows up/down movements, is the one we’re interested in. The next step is to switch the software to ‘frequency’ and do an analysis of this waveform to find the single dominant frequency.

Switch the app to ‘Frequency’ and place the cursor on the peak. If there are many peaks, look for the one in the range of 1-2.5Hz – that will be the suspension frequency. Make a note of the reading. You can then do the same at the other end of the car.

In the case of the Honda, the front suspension frequency was 1.4Hz and the rear was 1.8Hz. The higher the resonant frequency, the stiffer is the suspension. In order to reduce pitch, most – but not all - cars have a higher rear than front frequency.

Below are the results of testing a mid-Eighties W123 Mercedes 230, one equipped with hydraulic self-levelling suspension at the rear.

• Front: 1.3Hz
• Rear: 1.3Hz

Note that overall, the suspension of the Mercedes is quite a lot softer than that of the Honda.

There’s another thing to note as well. To be most representative of reality, during static testing, the car should be loaded as it normally is – e.g. with one or two people. Note that the Honda and Mercedes mentioned above were statically tested while unloaded.

Now if you’re thinking to yourself, ‘couldn’t the testing just be done by driving up and down the road?’, you’re right. When testing on the road, the ‘forcing frequencies’ that road bumps impart are much more complex and varied than is achieved by simple bouncing of the car, but you can still normally identify the peak on which to place the measuring cursor.

In addition to testing for bounce frequencies, this sort of testing can be easily carried out for roll frequencies (i.e. how stiff the car is in roll) and pitch frequencies (how stiff the car is in pitching – where when the back is up, the front is down, and vice versa). These are easiest to do statically by pushing on the car (to do pitch testing, you’ll need two people, one at each end of the car, working in a co-ordinated manner). The roll frequency will be typically higher than the bounce frequencies – that’s because of the additional spring of the anti-roll bars. However, that isn’t the case with the Honda Legend:

• Front: 1.4Hz
• Rear: 1.8Hz
•  Roll: 1.8Hz

The roll frequency of the Honda is the same as the rear frequency. This is presumably the case because the front springs are being stiffened enough by the anti-roll bar that in roll they are as stiff as the rear springs. (And the rear anti-roll bar is very soft – which it appears to be.) The pitch frequency of the Honda is 1.6Hz – as you’d expect, numerically between the front and rear frequencies.

The recorded accelerations of a Mercedes E500 equipped with OE air suspension, as measured on the road in Sports 1 suspension mode. Again, we’re interested in the bottom trace, that shows vertical accelerations.

The screen grab shows the frequency analysis of the Mercedes E500 vertical accelerations. The ellipse has been placed around the low frequency spike, indicative of the natural frequency of the suspension. Note the single big spike, which is at 1.9Hz.

In addition to comparing the effective suspension rates of different cars, what other use is this data? Most important is when you are making modifications. For example, if the rear springs are softer than the front, almost everyone will assume the rear suspension is also softer than the front. But that isn’t necessarily the case – if the rear weight is less than the front weight, the rear natural suspension frequency could be higher than the front! So when selecting new springs, ensure you know what the existing actual suspension stiffnesses are – otherwise you can start heading off in quite the wrong direction. (This isn’t an article on suspension modification, but for example in a front-wheel drive car, a car with existing high rear suspension stiffness that is made even stiffer can become dangerously unstable with quick changes of direction at high speed.) 

Another really important use for this data is when you can easily alter spring stiffness, as you can on a car with air springs. (This is achieved by plumbing extra volumes in series with the air springs. The bigger the connected volume, the softer the spring rate.) In order to assess what the extra volume is doing, you can do a quick natural suspension frequency measurement.  

Finally, in cars with variable rate springs, working out what the actual spring stiffness is (eg in pounds/inch) becomes quite problematic – it extends over a range and varies with compression. However, it’s easy to measure their effective stiffness with an in-car natural frequency measurement. 

This article is extracted from my book Optimising Car Performance Modifications