Sprung and unsprung weight natural frequencies

Posted on May 10th, 2015 in Suspension,testing by Julian Edgar

My major job – training people in business and government writing skills – takes me all over the country. Usually that involves lots of flights, but recently I chose to take the Greyhound bus between Coffs Harbour and Port Macquarie.

The bus travel was actually very pleasant – though I didn’t envy the driver threading his way through the dusk traffic on narrow roads constrained by constant roadworks.

When I was sitting in the bus, I started analysing its ride quality over the often poor road surfaces.

To cope with the large variation in possible load while still giving the best ride quality, long-distance buses typically use air suspension. (This also lets the bus ‘kneel’ as people get on and off.)

The air suspension stiffness is set to give a natural frequency of about 1Hz – the best frequency for ride quality.

And, in the bus, the ride felt about right for a 1Hz natural frequency – the absorption of large bumps was superb.

However, sitting back and admiring the flowing scenery outside the window, I thought I could feel another ride quality characteristic – and this one was not so pleasant.

Superimposed on the soft suspension movements was a higher frequency judder. It was like riding in a conventional car travelling on a road that had long wavelength bumps – but a corrugated surface.

Rather than guess any longer, I whipped out my iPhone and, using the ‘Vibration’ app, recorded the ride accelerations being experienced by the bus body. The seat next to me was empty and so I put the phone down on the cushion and gently held it in place.

Ten seconds later I had a record, and a moment after that I used the software to perform a Fourier analysis, giving the dominant frequencies in the waveform.

This showed a peak at 1Hz (the air springs) but also another peak at about 10Hz. The latter was the juddering “corrugations” I could also feel.

But what was causing this higher frequency of vibration?

The higher speed juddering was caused by the natural frequency of the unsprung mass – the weight of the suspension acting on the “springs” that comprise the tyres.

But it gets more complex. How do the 10Hz unsprung weight vibrations get through the 1Hz air spring isolation? With the forcing frequency (10Hz) so far from the natural frequency (1Hz), wouldn’t the transmission be almost zero?

I am not completely sure, but I think it has to do with the massiveness of the unsprung weight. Was that rapid shaking of the huge tyres and suspension arms feeding a vibration through the suspension mounts that I could feel?

Reflecting on this, I realised that I’d felt all this before – but to a lesser degree. In 4WD passenger cars using solid front and rear axles (ie a high unsprung:sprung mass ratio) you can feel something similar… it’s a bit like the car is being shaken by the suspension. So the soft main springing was being subverted in ride quality by the high unsprung weight bouncing on the tyres.

Here’s another point: dampers need to control suspension movement at both the suspension and tyre natural frequencies…. but the requirements for controlling each mode are quite different. One requires damping of large amplitude, low frequencies (the movement on the body springs) – and the other damping of high frequency, low amplitudes (the movement on the tyre springs).

It would be interesting to talk to a damper manufacturer about the decisions in damper design that they must be making.

4 Responses to 'Sprung and unsprung weight natural frequencies'

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  1. Ben Powell said,

    on May 11th, 2015 at 1:11 am

    I don’t see a problem with a 10hz vibration coming through?

    If you’re travelling along at 100km/h, it’s 25m/s. I’m going to assume that the bus tyre is around a meter in diameter, so has a circumference of 3.14m. This gives me a shade under 8 revolutions/sec (not too far from your 10hz, and would be closer to 10 if the wheels are smaller).

    If there was any imperfections at all in the tyre or wheel it would show up as the axle vibrating/shaking at that frequency, and the movement is at least slightly transferred to the body through the dampers (unless there is no damping whatsoever in the system, which seems unlikely).

    I don’t think natural frequency plays a part in the 10hz measurement, I think it just happens to be the revolutions/second of the tyre at that particular speed. If the tyre or wheel *did* have a natural frequency of around 10hz it would be too close to operating conditions for comfort and the forces involved would soon compound themselves and get out of hand.

    The feeling you describe is similar to when one of my car tyres was developing a bulge on a road trip. I thought it was the road initially but it slowly increased in intensity (but not frequency) regardless of where I positioned the car on the road. After finding a 1-2cm bulge in one of my rear tyres and changing the wheel the vibration vanished.

    It would have been interesting to graph the 10hz movement in different planes, to whether it went forwards and backwards as well as up and down, and which was greater. I would expect the forwards and backwards to be much greater as the axle is solidly located in that direction but allowed to float vertically…

    Some thoughts…


  2. Julian Edgar said,

    on May 11th, 2015 at 6:10 am

    I don’t think it was a wheel balance problem, as I could feel it mostly after the bus had passed over a sharp bump. I did measure accelerations in all planes and it appeared in pitch* as well as bump.

    Who wants to work out static tyre deflection with the bus weight and then calculate from this the natural frequency of the tyre spring?

    * but at a slightly higher frequency

  3. Ben Powell said,

    on May 12th, 2015 at 1:29 am

    Possibly the higher frequency was due to the weight (and tyre count) distribution front to rear giving different frequencies then? I imagine the verticals were dominated by the nearest axle group and pitch was controlled by both ends. I have a couple of bus depots near enough to me to take a tape measure to. Most companies would probably let me do that “for science”…

  4. Matt King said,

    on May 14th, 2015 at 12:51 pm

    Could the high frequency vibrations be from the bending/torsional vibration of the bus chassis? For a long, heavy structure like a bus I would guess that 10Hz is possible.