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Another Human Powered Vehicle! Part 10 - Rear Suspension

Stiff but light - not easy!

by Julian Edgar

Click on pics to view larger images

At a glance...

  • Suspension motion ratio
  • Vertical bending
  • Horizontal bending
  • Lateral bending
  • Torsional bending
  • Final design
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This article was first published in AutoSpeed.

So far in this series we’ve not even mentioned the rear suspension. In part that’s because there’s really only one design that can be used – a pair of parallel longitudinal trailing arms, forming a swing-arm. Of course, there are lots of variations on trailing rear arms, but the fundamental approach is pretty well fixed. Or is it?

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The aluminium trailing arm design that I used on my first HPV was very strong. It was also pretty light - but the new design needs to weigh a lot less. Another problem with the original design was its fairly high motion ratio – that is, the spring compressed much less than the vertical distance the wheel moved. With the selected Firestone airbag springs of the new design, taking a similar approach would cause problems.

In fact, let’s start off with motion ratios and possible designs.

Motion Ratios

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To give a motion ratio as close to 1:1 as possible, the spring needs to deflect as far as the wheel moves. One approach that achieves that is shown here – the green box is the spring and you can see that its base moves up and down just as far as the wheel. However, without the use of multiple rear suspension arms and at least four pivots, which are heavy, it’s hard to locate the wheel so it can move only up and down (and not through an arc).

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A more traditional motorcycle/bicycle/HPV approach is to locate the spring and pivot as shown here. However, this gives a very high motion ratio.

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It also doesn’t matter much if the suspension arm bends through 90 degrees and the spring is mounted horizontally – the motion ratio remains high.

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In fact, to get a 1:1 motion ratio without having the spring vertically above the wheel axle, the lever needs to be equally long either side of the suspension pivot. But as you can see, packaging then becomes difficult.

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In the end, this was the approach that was adopted. Long suspension arms were pivoted well forward, with the spring mounted vertically (or actually, near vertically) as close to the tyre tread as possible. While in this diagram the packaging doesn’t look any better than in the one above, this approach actually lends itself better to integration with the seat – the required vertical room is far back in the wheelbase, rather than being under the base of the seat.

Bending Forces

When I designed the rear suspension for my first HPV, I was most concerned with coping with the vertical loads – those caused by the weight of the rider and machine trying to bend the suspension arms in one direction, and the drag of rebound damping trying to bend the suspension arms in the other direction. Withstanding these loads remains very important - however, there are other loads which are also significant.

When cornering, the rear suspension tries to bend sideways. (This is completely unlike a bicycle where, because of the angle of lean of the bike, the sideways loads on the rear wheel are tiny.) But on a trike these lateral loads are not insignificant: they can be in the order of 20kg. Now, pull the rear wheel sideways with a force of 20kg and not only do you want the suspension to not fail, you also don’t want it to bend much at all, otherwise the chain alignment will alter.

Hmmm, so the rear suspension has to be stiff in both vertical and horizontal planes.

In addition, it also needs to keep the rear wheel pointing straight ahead, even though the pull of the chain is offset from the centreline of the wheel.

But one of the most challenging aspects is still to come. Again consider what happens when cornering hard. The cornering force is trying to bend the rear suspension sideways, but it’s doing more than this. Because the force is being developed at the tyre contact patch, but the suspension arms connect to the rear wheel’s axle, a twisting force (torsion or torque) is being applied to the rear suspension. In fact, if there’s 20kg sideways force at the tread, with a 20-inch nominal diameter wheel, a torque of 50Nm can be applied to the rear suspension. It’s like standig directly behind the vehicle, reaching forward to grasp the wheel, and then twisting it violently.

And it’s that last one that makes things really hard.

So the design goals become:

1) Provide suitable strength and rigidity to resist vertical bending due to loads caused by the weight of the machine and its rider

2) Provide suitable strength and rigidity to resists horizontal bending loads cause by lateral cornering forces

3) Provide suitable strength and rigidity to resist bending caused by the wheel attempting to steer with the pull of the chain

4) Provide suitable strength and rigidity to resist torsional (twisting) loads caused in cornering

Let’s tackle each in turn.

Vertical Bending

Vertical bending forces were accommodated by using a suitable tubing wall thickness and diameter. This was achieved with a pair of 22mm diameter chrome moly steel tubes, with a wall thickness of 1.2mm.

Horizontal Bending

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To better resist horizontal bending, the forward ends of the arms were positioned further apart than at the axle end. This diagram shows the idea. The view is looking straight down on the rear wheel, with the red line being the pivot axis. The further apart the leading end of the suspension arms are, the more that sideways motion of the rear wheel gets translated into compression and extension of the suspension arms. Since metal tube is stronger in compression and extension than it is in bending, this improves the lateral rigidity of the assembly. In addition, the further apart are the front pivot points, the lower the load on the bearings that is experienced when cornering.

Wheel ‘Steering’

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By placing the trailing arms on the same level as the rear axle, and locating the chain so it largely runs parallel with these arms, the ‘steering’ movement of the rear wheel caused by the pull of the chain is translated into compression and extension of the arms. As described above, tubes are strong in compression and extension so this force is well resisted.

Torsion

No here’s where is starts getting very interesting! If you have been mentally picturing the developing design, you’ll have in your mind a sort of ladder frame suspension, with the forward end splayed wider than the rear end. The assembly is wide and long, but has a height of only 22mm (the tube diameter). Now, if you get a ladder frame (eg a real ladder!), anchor one end and then twist the other, you’ll find it has very little resistance to torsion. Normally, to add torsional resistance you have to increase the height of the assembly, making it more box-like than flat. But even in the form so far described, the rear suspension was already borderline too heavy – certainly, no more material could be added.

So, how do you improve torsional rigidity while still keeping in place at least most of the existing design benefits?

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Ladder frames were once widely used in car chassis design. In fact, from the mid 1930s until the 1950s, nearly all cars used a steel ladder type of chassis. So how did they design them to withstand torsion? Amongst my collection of old automotive engineering books I have one that covers just this issue – and in quite some detail. In short, the addition of an X-member torsionally stiffens the frame. So how does this work? Let’s look at a simple parallel ladder frame.

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In this view, the longitudinals of the frame are shown in black and the cross-members in pink. The forces shown by the labels are being applied, causing the frame to twist as the joins between the cross-members and the longitudinals distort.

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Now we’ve added two extra members in the form of an X. It’s vitally important to note that, where they cross one another, they are joined.

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Let’s take it one step at a time. Pulling upwards as shown here causes each end of the arrowed member to also be pulled upwards. But the arrowed member is held fast in the middle by the other cross-member! As a result, the arrowed member is subjected to bending. As it resists being bent, it resists the ladder frame twisting.

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The same thing happens when we look at the other cross-member. Again, because it is held fast in the middle by the other cross-member, it is subject to bending and so resists torsional twist of the frame.

Now when you think about it, you’ll realise that, in terms of torsion, the black and purple members don’t even need to be there: most of the resistance to torsion will occur with just the X-frame in place. Furthermore, even if using just the ‘X’, resistance to vertical bending remains the same as the earlier design (because two tubes are still being used). However, lateral strength is lowered (because the spacing between the tubes is less – the crossover point of the X becomes a weakness in terms of sideways bending) and when resisting the chain pull, the tubes are no longer in direct compression (because they no longer run completely parallel with the chain).

Hmmmm.

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After making plenty of scale sketches to assess the weight of various design options, I decided on the following. The design integrates a (non-perfect) X-frame shape into the original ladder approach, maintaining the wider-spaced front mounting points. It trades off some lateral stiffness, and some stiffness in keeping the wheel pointing straight ahead, for an increase in torsional stiffness. The changes in tube direction, shown here as abrupt, are actually formed through bends in the tube. It’s obviously not a perfect X-frame (trace the bending forces that occur in torsion) but it looks to me like it will far better resist torsion than just a simple ladder frame.

More on X-Frames

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The book referred to above - Automobile Engineering, Volume 5 (Editor – H. Kerr Thomas) - has no publication date but is probably from the late 1930s. The description of X-frames also includes this fascinating diagram, showing how as the X-frame concept is altered by real world practicalities, torsional forces again start again being introduced. That makes the cross-pieces in the final version of the HPV rear suspension rather important – it’s being subject to lots of torsion.

Building the Suspension

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Using a hand tube bender and a long extension lever I was j-u-s-t able to bend the 22 x 1.2mm chrome moly tube. The two tubes, which needed to be (mostly) in mirror image to each other, were formed in shape and then two cross-pieces were brazed in. (Two cross-pieces were used, rather than the one of the original concept, to both further improve stiffness and also add a mount for the bump rubber.)

The front pivot points were formed by brazing two short sections of 32x 0.9mm tube at right angles to the leading ends of the tubes. A 30mm x 10mm sealed ball bearing was then mounted in each of these tubes. High tensile through-bolts were then used to mount the suspension pivots to the main frame.

(Incidentally, the rear suspension arm shown here isn’t finished – it’s just been quickly painted with a spray can to allow on-road testing without rust starting to occur. After testing any required modifications will be implemented and then the assembly will be sandblasted and powdercoated.)

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The wheel axle mounts ("drop-outs" in bike speak) were bought pre-cut from Greenspeed. Some material was removed from these heavy steel lugs before they were brazed to the ends of the steel suspension tubes, which were squashed a little with a press to better match the thickness of the lugs.

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A generator mount (again pre-formed and bought from Greenspeed) was also brazed into place.

The completed rear suspension arm, with bearings but minus through-bolts, has a mass of 1.5kg.

Conclusion

The trade-offs in trying to achieve appropriate stiffness together with a low weight and low motion ratio have never been clearer to me. By adding a few extra braces, lateral stiffness could be dramatically improved. By sticking with the original shape and adding an X-cross-member, torsional stiffness could be improved without a loss in other strengths. By using a spring location that allows a high motion ratio, the suspension arms could be made shorter and so overall weight could be much reduced.

They’re certainly not easy design decisions...

However, I think the final design is a good compromise of weight, strength and ease of fabrication.

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