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Chalky, Part 5

The rear suspension

by Julian Edgar

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At a glance...

  • Designing and building a human-powered vehicle
  • The rear suspension arm
  • Design criteria
  • Designing a space frame
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After the complexities of the steering system (see Part 4), the simplicity of the rear suspension is a breath of clean, fresh air!

Design

The rear suspension comprises a trailing arm. This is the lightest suspension approach and works well in recumbent trikes. The pivot point has been placed relatively high so as to decrease suspension extension under rear braking (the rear wheel is fitted with a hydraulic disc) and to allow the chain to be kept high while still giving active anti-squat. (The latter means that the rearwards weight transfer – and so rear suspension compression – is actively resisted by the chain pull-line, which tries to extend the rear suspension.) The spring has been placed close to the wheel so that the motion ratio is kept low.

Click for larger image

On my previous Air 150 trike (and its Air 130 prototype) I had problems with the rear suspension. The problems on the Air 130 were tracked down to the pictured rear suspension torsionally winding-up and unwinding, so causing the rear wheel to skip in high-speed, bumpy cornering. The rear suspension design was changed so that it was stiffened in torsion and the problem disappeared.

Click for larger image

However, on the later model Air 150, that used the pictured single, large diameter tubular rear arm, the trike became twitchy in steering when carrying a full load of camping gear (about 30kg). In fact, it felt like the rear wheel was steering. Again, I think the problem could have been because the rear suspension was twisting, allowing the rear wheel to adopt camber angles and so steer.

A further problem with the Air 150 rear suspension arm, and one that probably contributed to the above problem, was that for packaging reasons, the damper was mounted off-axis. This meant that it tended to twist the rear suspension arm on rebound (the damper is a lot stiffer in rebound than bump) and over time, appeared to cause a permanent ‘set’ in the rear suspension arm. (The rear suspension twisted slightly – the only reason I can put it down to is the offset damper.)

Therefore, when compared with the Air 150 design, the rear suspension arm for Chalky needed to be stiffer in torsion, and mount the air spring and damper along the centreline of the arm. Rather than use a single large diameter tube, I chose to build a space frame design from smaller tubes.

The spring (a Firestone 4001 rolling lip airbag) and the damper (a modified Yamaha R1 steering damper) were the same as used on the previous designs.

Modelling Different Designs

By far the best way for non-engineers to develop a space frame design is to build a model of the proposed design and test it.

So how does the technique work? In short, you build a replica of the structure by soldering together copper wire, using a normal electronics soldering iron. You then input the forces in the direction that they occur in real life, and watch what fails.

The copper wire is most easily taken as single strands from heavy-duty electrical wiring of the sort used in houses and commercial premises. A few offcuts are usually easily sourced at zero cost. The insulation is stripped, then the thick strands removed individually. One end of the strand is placed in a vice and a pair of pliers is used to stretch the strand a little. This gives a relatively stiff, straight piece of copper wire that solders easily.

Making a copper wire model is a truly brilliant way of assessing different space frame designs. By closely watching the failure mode (eg Close to a join? In the middle of an unsupported length of ‘tube’? In compression? In bending? Failure by a gentle radius bend or sharp kink?) you can very quickly optimise and refine designs.

Complex, multi-tube designs can be modelled in a short time – in some case, in minutes.

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The modelling can be in two dimensions or in three. You can apply compression, extension, torsional and bending loads. You can model the affect of differing diameter (or wall thickness) tubes by altering the thickness of the wire, or by doubling or tripling the wire.

By photographing a full size mock-up, and then importing that pic into a PC and printing it out at much reduced size, you can model tube angles and lengths directly from the print-out. In many cases, I actually build the model by laying the wire on the 2D print-out and soldering it in place in situ.

Forces can be applied by pliers with the model held appropriately by a vice or simple jig.

To see what you thought would be a strong design fail with the greatest of ease is an amazing wake-up call. To then make some (relatively) simple changes and develop a model that you physically can’t distort with the pliers is quite awesome, especially when you grab a piece of the bare wire and can bend it easily with just your fingers.

By juggling wire thickness and length, you can optimise the required strength of the individual tubes: they need be only as strong as required.

By weighing the model (or measuring the length of its individual ‘tubes’ and working out how much it would weigh if built for real) it’s possible to quickly assess if weight is going up more quickly than tested strength. Alternatively, by setting yourself a weight limitation, you can to develop the strongest design possible for that weight.

Click for larger image

For Chalky’s rear arm design I built five different copper wire models. In the pictured model the rear axle (blue) and front frame mount (green) are modelled by tripled wire (ie three twisted strands). The spring mount (purple arrow) also uses this stronger (3 wrap) wire. The other parts of the model are made from single strand and double strand wires. The single wire represents 12.7 x 0.9mm chrome moly tube and the doubled wire represents 19 x 0.9mm tube.

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An example of a failed model can be seen here – when the model was subjected to bending loads, the single strand wire (indicative of the thinner tube) failed in compression.

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The final model is very simple. (Simple = light = good!) It is very strong in bending, and quite stiff in torsion. As part of the modelling I added braces that improved torsional rigidity even further – this allowed me to see what improvements are available if they later prove to be necessary on the full-size construction.

In the Metal

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The rear suspension arm was simple to make - but not as simple as the front suspension. The upper parts of the arm were constructed from 19 x 0.9mm chrome moly steel tube, while the lower horizontals (that are primarily in tension) use smaller 12.7 x 0.9mm tube.

The rear drop-outs (the bits the wheels bolt to) were sourced from recumbent trike manufacturers Greenspeed and are laser-cut steel. Short sections of heavier wall thickness 25 x 1.6mm tube are used to space the suspension arm longitudinals outside the chain path, to locate the hydraulic discs rear calliper mount, and to extend fowards a little the drop-outs.

The suspension pivots comprise 30 x 10mm sealed ball bearings with 10mm high tensile through-bolts.

Click for larger image

The air spring mount is located at the apex of the pentahedron and comprises a short length of vertical tube. The mount for the damper is made from 19 x 0.9mm tube (the cross-piece) and 1.6mm chrome moly steel sheet (the lugs the damper bolts to).

The motion ratio of the rear suspension is 0.5:1. That is, the spring moves half as far as the wheel. Since the Firestone 4001 air spring is rated to a maximum of 180kg at peak inflation pressure, the maximum vertical load that can be fed through the rear suspension is 90kg. This is in excess of what would be ever expected to occur, allowing conservative air pressures to be used in the spring (eg 35 psi with just a single person load).

The damper stroke is the limiting factor on rear suspension travel – located as shown, there is a rear suspension travel of 180mm.

The rear chain path is positioned just under the pivot point of the suspension – thus slight suspension extension occurs on pedal strokes (ie offsetting the squat that would otherwise occur through weight transfer). Note that, on pedalling, the rear suspension arm is subjected to longitudinal compression. This puts the smaller diameter tube under buckling loads – these tubes could be stiffened by additional bracing, but at the cost of greater weight.

Including its bearings, the mass of the rear suspension arm is 1.3kg. The spring and damper add another 800g.

Development Testing

To properly test the rear suspension, the machine needs to be almost finished. That is, the chain drive needs to be working, the seat installed, the frame structurally complete - and so on. So again, initial testing was by necessity incomplete.

However, the testing that was carried out showed that the ride quality was excellent, and as far as could be ascertained at low speeds and with low loads, the torsional performance of the arm was also fine.

Conclusion

Because the rear suspension of a tadpole trike takes both bending and torsional loads, it needs to be stiff in these directions, as well as light. A three-dimensional space-frame design is the lightest way of achieving this stiffness. As is the case with Chalky, such a structure also lends itself to further stiffening, should more extensive testing later show that this is necessary.

Next week – the seat and frame

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