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This article was first published in AutoSpeed.
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Another Human Powered Vehicle!
Yes, it’s on again. In part because of the very
high popularity of the series Building a Human Powered Vehicle, I’ve decided to
again cover the machine I am making. Yep, I am doing another....
So what was wrong with the old machine, one I
agonised and laboured over for so long? Head and shoulders above anything else
on the deficiencies list is its weight. At about 40kg when wearing its carrier,
it’s around twice as heavy as it should be. When up to speed on the flat, the
extra weight doesn’t make a lot of difference, but in accelerating to that speed
and in climbing hills (especially in climbing hills!) the weight is a
killer. Other deficiencies? Despite tweaking the castor angle and having
trialled so many steering systems, I don’t think the steering is as good as it
should be. Primarily that’s because it has some stiction in it – the result of
so many balljoints and the high steering loads caused by running lots of castor.
However, it’s not all doom and gloom – I think
that in some respects, I got it right. Take the suspension travel and the wheel
rates. Data-logging (both vertical accelerations and travel) has shown that the
spring stiffness and wheel travel are damn-near perfect. The roll stiffness is
good and the front and rear damping excellent. As a result, the ride quality is
probably the best of any Human Powered Vehicle in the world. Handling is also
very good – my wife is now a Greenspeed dealer and so I get to ride the
different Greenspeed demonstrator recumbent trikes. On a skidpan, my trike
outperforms even the sportiest of the mainstream Greenspeeds.
But it was riding one of the Greenspeeds that
really made me realise how heavy my machine is. The Greenspeed was the pictured
X5 and at well under half the mass of my trike, it didn’t just feel lighter, it
felt that I had about 50 per cent more power in my legs! But of course, none of
the Greenspeeds (yet!) run any suspension...
So, is it possible to have niceties like dynamic
camber increase on bump, Ackermann steering correction, zero scrub radius, 15
degrees of castor, 100mm of suspension travel, a sub-2Hz suspension natural
frequency, good damping, fluid steering feel – and still have a total vehicle
mass of (say) 23kg or under?
I don’t know – but we’ll all find out!
(Incidentally, one of the reasons I am prepared to
cover in AutoSpeed another oddity like the new machine is because it gets back
to vehicle fundamentals in a way that is usually not possible in cars. Before I
built my first Human Powered Vehicle, I’d have been hard-pushed to define
suspension natural frequency, let alone understand its implications for ride
comfort. Ditto for dynamic camber gain on bump and even scrub radius. I might
have vaguely known the definitions but not the significance of what the terms
describe.)
But enough of the preamble, let’s get straight
into one of the most challenging areas of all – springs.
Springing Media
In the first HPV I used steel coil springs. I
don’t think that in itself was a mistake, but the motion ratio I used
(especially for the front suspension) definitely was.
The motion ratio is the leverage relationship
between the wheel movement and the spring movement. In most suspension systems,
the wheel moves further up and down than the spring, but because the
relationship between the spring and wheel rates is the motion ratio
squared, shifting the spring even a little further inboard dramatically
increases the required spring stiffness. And, if keeping the internal stress
levels the same, a stiffer spring is a heavier spring.
In short, to reduce the loads being fed into the
frame and to reduce the required stiffness (and so weight) of the spring,
springs should be mounted as far outboard as possible.
But what of torsion bar suspension designs? These
mount the springs as far inboard as possible – in fact, usually at the
pivot points of the suspension! Would it be possible to use something much
lighter than steel, so allowing the inboard mounting of the springs (benefits in
reducing unsprung mass and allowing more clearance for suspension arms to move a
long way up and down) but without the spring weighing too much? In fact, what
about using plastic rod as torsion bars?
My rough design load for each wheel of the new
machine is 30kg. That is, each wheel will need to support a static sprung mass
of 30kg, obviously with the rider on board. If each suspension arm is 30cm long,
at rest a torque of 90Nm will be applied to the torsion bar. That will double to
180Nm in a 1g vertical acceleration bump. But how much twist of the torsion bar
should occur at 180Nm torque? Some trigonometry with the suspension arm length
and the required wheel travel shows the answer is about 20 degrees.
So the number-crunching yields a quite specific
target behaviour – a springy bar that will twist by about 20 degrees when about
180Nm is applied. Not stated in that description but equally important is that
when the load is removed, the bar needs to spring all the way back (ie not take
a ‘set’) and that it must have a long life (ie be fatigue resistant).
So I started experimenting. I bench tested plastic
bars of polycarbonate (Lexan) which worked great until a little
overloaded, whereupon the bar shattered like glass. Very exciting to watch; not
so good on the road. (however, it should be said that if designed very carefully
with progressive external bump stops, I think such an approach could be
successful. But there’s not much margin for error.)
I scoured engineering resources for plastics
suitable for use as springs. This led me to the acetal range of plastics. I then
tried bars of acetal – not as stiff as polycarbonate but the same end
behaviour.
I tried good old steel – but if the steel
wasn’t to take a permanent set, a long bar was needed. (In fact – and think
about this – a bar about as long as a steel compression spring unwound....) I even
thought of using the front torsion bars from an old Volkswagen Beetle, as these cars use use torsion bars formed from long, different width leaves of steel – and
it would be easy enough to use just a few of the narrow leaves. But that took me
straight back to high weight.
So I gave up on torsion bars – those that were
light enough failed catastrophically when overloaded. Those that had the energy
absorption capacity were too heavy.
Then I thought of using rubber. Best results are
obtained if the rubber is in both compression and shear, an approach used (with
very high motion ratios – 5:1!) on the famous Mini suspension shown here.
I bench tested a number of different rubber
springs. All were being assessed for use with 100mm of suspension travel with a
wheel rate of about 0.6kg/mm (ie a mass of 30kg causes about 50mm deflection).
Bench testing was done with various length levers and weights, where it was very
quickly obvious whether the spring would be suitable or not.
First up was a rubber engine mount from an
older small car, a mount that uses three bonded plates. (I was unable to
ascertain the exact origin of the mount.) It deflected appropriately with high
motion ratio loads. However, the motion ratio had to be exactly right if the
wheel travel versus spring movement was to remain in an even roughly linear part
of the spring’s travel.
An engine mount (left-hand front, Daewoo
Matiz) looked great on paper, with the rubber arranged to act both in shear and
compression, and top and bottom bump stops built in (all exaggerated here in
green). However, with a motion ratio that translated its small movement to
decent suspension travel, the rubber was far too soft.
Another engine mount, this time a
hydraulically damped design (left-hand front Daewoo Nubria). With a motion ratio
that translated its small movement to decent suspension travel, the mount was
again far too soft. Despite using a cone-shaped rubber (rather like some rubber
suspended cars), it had even less travel than the above mount.
A steel-sleeved bonded rubber bush from a
suspension system (rear lateral locating arm, Mitsubishi Galant). Far less
torsional stiffness than required.
A car suspension bump rubber (Daewoo Matiz rear)
was a superb, progressive design but it didn’t have the required stiffness.
Rubber in Tension
So if rubber in compression and shear generally
had too much deflection at high motion ratios, what about rubber in tension –
like rubber bands? One benefit of this approach is that it’s easy to add or
subtract rubber, so changing the spring rate.
I tested rubber loops (automotive exhaust
hangers) in tension. They initially worked fine but literally tore apart when
subjected to high and sustained loads (and interestingly, broke without warning
in the middle of the night!). I also tried synthetic rubber hangers but they had
much less stiffness than conventional rubber ones.
I also tested elastic seat webbing usually
used in upholstered chairs. But a very great length was needed to provide
appropriate spring rates when even a moderate motion ratio was used – in other
words, it wasn’t stiff enough.
Exotics
But what about the exotic materials – elastomers,
carbon fibre; stuff like that? My budget doesn’t extend to getting exotic
springs made to suit, so that meant that something off the shelf would be
needed.
I bought a pair of flexible carbon fibre
snow skis. Cutting one in half showed that in fact it used an interesting
mixture of timber, plastic and carbon fibre. The skis worked very well as
cantilever springs, however, unless the full length of the ski was to be used,
it was too stiff. (I had thought of using a ski transversely across the front as
the combined spring and lower control arm of the suspension. But unless the HPV
was going to be 1.8 metres wide, the ski didn’t deflect enough ....)
I then sourced a golf club with a carbon
fibre shaft. The tapered shaft had an interesting mix of stiffness and
flexibility. But applying either bending or torsion loads caused it to quickly
break.
Elastomers like polyurethane I found to
have constant creep under load (they just kept on flowing, day after day!) and
to be largely inferior to rubber.
Other spring materials I considered included
fibreglass leaf springs (they’ve been used in the Corvette for decades) but
nothing was available off the shelf and I couldn’t find any design literature
that showed what would be needed.
Where to From Here?
The time I spent testing all the different
materials highlighted certain requirements.
Not only do high motion ratios require a much
stiffer spring, they’re also hard to work with. Why? Well, tiny differences in
the spring material or linkages cause major changes in wheel rate (and so ride
height). Also, any deficiencies in the spring (for example, a rate that rises
too quickly or a travel that is too short) are much amplified by the motion
ratio. So for these reasons (as well as reducing frame input loads), I think
suspension designs with high motion ratios should be avoided.
But if the motion ratio needs to be low, spring
deflection will be high – say three-quarters of the wheel travel. So with 100mm
of suspension travel, the springs require at least 75mm deflection. If the
spring is to be kept a manageable length, it therefore has to be made of
material that will compress a long way. (Imagine how long a rubber block would
have to be that could compress 75mm!)
So what springs have a long-travel but are still
compact? When you start to think about it, very few. Steel coil springs,
especially those wound in the pictured bee-hive shape (that compress further
before coil-bind) are long travel and compact. But bee-hive shape coils need to
be wound on a specially made mandrel – expensive. And designing with such a
variable rate spring is very difficult indeed. Plus we’re back to (heavy) steel.
What’s needed is a spring that compresses a long
way and is light. Hmmm, what about airbag springs?
Next: bench testing airbags
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