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As
the name suggests, this series is about the design and building of a
human-powered vehicle (HPV). In fact, one that’s powered by pedals.
Now
you might ask what such a series is doing in a high performance on-line magazine
devoted to cars. It’s in here because with the exception of the motive power,
much of the decisions were the same as taken when building a one-off car -
perhaps a kit car or one designed for the track.
For
example, the design of the suspension; the decision to use either a monocoque or
stressed tubular space-frame; the weight distribution; brakes; stiffness (in
bending, torsion and roll); measuring and eliminating bump-steer; spring and
damper rates; and so on. I’ve drawn primarily on automotive technology in design
of the machine – in fact it’s been much more about ‘cars’ than ‘bicycles’.
So
if you want stuff on the fundamentals of vehicle design and construction, read
on. Yep, even if this machine is powered by pedals...
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Last week in
Building a Human-Powered
Vehicle, Part 1
we covered the basics of the proposed design:
-
Square tube frame made from aluminium with lots of
holes cut in it
-
Rear swing-arm and front double wishbone
suspension, each with lots of travel
-
20 inch wheels in a ‘tadpole’ configuration (two
front steering, one rear driven)
-
Recumbent hammock seat
-
Hydraulic front disc brakes
-
63+ gears comprising front and rear derailleurs
and a 3-speed internal rear hub
-
A steering mechanism yet to be decided
upon
...and with the basic layout of the wheelbase,
track, seat shape and so on based around the pictured Greenspeed GTR.
But now it’s time to forget the theory and start
the practice, beginning with the rear suspension.
The Design
As mentioned last week, the rear suspension design is a
longitudinal swing-arm. Two interconnected parallel arms support the rear axle,
being pivoted near their opposite ends. As the wheel moves upward, the part of
the arm forward of the pivot moves downwards, in this case compressing a coil
spring and at the same time, extending the damper.
Oddly enough, the first important decision that
had to be taken about the rear suspension was the nature of the pivot.
Pivots
In automotive applications, suspension pivots
almost always comprise rubber bushes. An inner crush tube is bonded to a rubber
cylinder that in turn is bonded within another metal tube. The rubber twists
torsionally when the inner and outers move relative to one another. In racing
machines, pictured Heim (or rose) joints are often used, taking out the flex
associated with rubber. Car manufacturers use rubber bushes for these reasons:
they’re cheap, absorb vibration, and allow suspension rotations that are not
perfectly axial. (A Holden engineer once told me their
trailing-arm-with-an-extra-link rear suspension would bind solid if rubber
bushes weren’t used.)
On the other hand, most makers of HPVs use Heim
joints, while high performance mountain bikes use ball bearings or small
diameter graphite tubes.
My preference was for conventional car-type
bushes, but using polyurethane instead of rubber. (The use of the plastic
necessitates that the bush rotates on the crush tube.) The benefits are
extremely good durability (the loads are far less than on a car but the bushes
are similarly sized), some vibration absorption, and custom sizing easily
catered for.
I wanted to use as the outer bush housing
aluminium tube with an ID of 25.4mm (ie 1 inch), an outer diameter of 32.4mm,
and a through-bolt diameter of 8mm. Polyurethane bush manufacturer Super Pro
were able to offer off the shelf bushes to suit this – the SPF0107K which are
normally used as replacements in the front spring shackles of a ‘85 Jeep (or the
rear shackles in a ‘57-‘65 Gordon Keeble or Tempest!).
These bushes are 25.4mm outside diameter and have
a total length - including a single end flange - of 30mm. The end flange is
chamfered and including the chamfer, is 7.7mm thick. The diameter of the flange
is 34mm. The bushes are designed to be inserted from each end of the tube that
holds them. The flange gives lateral location and the chamfer reduces the amount
of polyurethane which is in contact with the bracket, reducing stiction and
potential squeaks.
In the rear suspension application the bushes in
use have a small (~7mm) gap between them within the sleeve. But this is of no
consequence as there’s still plenty of polyurethane to take the forces.
The crush tube used through the middle of the bush
(on which the bush rotates) was made from 12.5mm (just under 1/2 inch) shock
absorber shafting. Using a lathe, the shaft was shortened and then drilled and
tapped to take an 8mm bolt at each end. The huge advantage of using this
material for the crush tube is that the shock absorber shaft is hard chrome
plated (for wear resistance) and is strong with a very smooth surface finish.
The downside of the whole assembly is weight – but IMHO it is a weight penalty
well spent.
Pivot Location
If you think of a swing-arm as being like a
see-saw, the wheel is at one end, the pivot somewhere along the length, and the
spring at the opposite end to the wheel. The closer to the far end that the
pivot is placed,
-
the greater the leverage on the spring – and so
the stiffer the spring has to be for a given wheel rate
-
the smaller the compression of the spring for a
given wheel movement
-
the less the ends of the spring will become angled
during compression and extension
-
the less the spring intrudes on the space
available within the wheelbase
That’s quite a list to consider and in the end I
made the decision to place the pivot point about one-third way along the
swing-arm. (The detailed geometry of the front and ear suspension is covered
later in this series.) However, unlike every other HPV with a rear swing arm
that I’ve seen, I decided to use two pivot points widely spaced but located
along the same axis. Widely spaced? How?
Looking straight down on the rear wheel, the
swing-arm comprises two parallel arms, one that goes to each end of the wheel’s
axle. In the case of a recumbent trike, the rear axle is quite long as it needs
to accommodate the wide hub and gear cluster. Widely-spaced arms give greater
strength and if the forward pivot points are equally widely-spaced, the rear
wheel will be well supported in side-load, such as generated when cornering.
(Contrast this with if the widely-spaced arms join at one forward point, with a
single bush used to pivot it.) It’s an interesting fact that when people make
HPVs using the suspension rear forks from a mountain bike, the lateral loadings
of the trike usually end up breaking the rear suspension arms...
And there’s another reason for widely-spaced
pivots. As mentioned last week, if the tension side of the chain pulls along a
line which is greatly above or below the pivot axis, with each pedal stroke the
swing-arm will be either extended (if chain pulls below the axis) or compressed (if chain pulls above the pivot axis). Either effect will cause suspension
‘pogo-ing’.
Most mountain bikes and suspended recumbents place
the chain axis a little above or below the suspension pivot, because the
physical presence of the pivot prevents the designers doing anything else.
However, if two in-line widely-spaced pivots are used, the chain can pass
through this axis, running between the two pivots. (Or, as was later actually
done, an adjustable height guide pulley can be used in development, with the
chain location able to be moved over a wide range without it fouling
anything.)
Spring Location
Looking at the shape of the Greenspeed GTR (on
which the basic dimensions of the new machine were being based), it could be
seen that there’s plenty of room under the inclined hammock-like seat for the
spring and damper. This allowed the spring to mounted vertically, bearing at its
lower end on the main frame longitudinal (or in fact on the adjustable lower
spring platform, but we’ll get to that later), and the upper end bearing against
an extension of the swing-arm.
But to achieve this, the swing-arm had to be an
unusual shape – so maybe I’d better cover the swing-arm design now!
Oops – the First Swing-Arm
The first swing-arm looked like this. In
operation, the arm was going to be subjected primarily to the upwards push of
the wheel (red arrow), the downwards pull of the suspension bush (blue arrow),
and the upwards push of the spring (green arrow). I was pretty happy with this
design, which during bump placed all but the gusset (tension) and the spring-arm
(bending) in compression.
However, at 4am I suddenly awoke with a start. The
design was wrong! If roughly one-third of the total weight of HPV and rider is
borne by the back wheel, the vertical load would be only about 30kg – say 60 or
even 90kg, the latter if the vertical acceleration over a bump reached 2G. But
the pull by the chain could be substantially more than that.
A recumbent allows the rider to push against the
seat, not against just their weight. As a result, the pull on the chain could be
expected to be way more than the upwards force of a bump. And my grand design
failed miserably when the forward pull of the chain was considered. In fact, in
that case, the gusset would be subjected to compression – exactly what it was
never meant to do...
I started the rear suspension again...
Better – the Second Swing-Arm
Starting on the basis that the greatest force on
the rear swing-arm would be the pull of the chain required that a member be
positioned to take this in compression. This was made from 40 x 40mm x 3mm
square aluminium tube, located largely horizontally. This tube connected at an
acute angle to a larger 50 x 50 x 3mm tube positioned at its forward end.
Next, the upwards forces of bumps had to be taken.
A 3mm sheet gusset was positioned beneath the horizontal member to take this
bending force and turn it into a tension – ie the upwards force was trying to
stretch the gusset. That was fine in bump, but in rebound (where the damper
resists the downwards movement of the wheel) there was little strength in the
assembly. To absorb this force, a second gusset was positioned above the
horizontal. This gave a rigid assembly with the tube extremely strong in
compression (caused by chain tension), and very strong in upwards bending
(caused by bumps) and downwards bending (caused by the damper extension in
rebound).
To operate the spring, an extra piece of
rectangular tube was placed parallel to the horizontal part of the arm,
extending forwards from the top of the larger upright-angled tube. (This small
extension piece was the only bit I could re-use from the first design!)
The round aluminium tube to take the polyurethane
bushes was positioned in a hole drilled right through the 50 x 50mm tube. But
this wasn’t the only hole drilled – numerous holes were strategically made to
lighten the whole assembly. (Incidentally, when the first arm proved a flop, I
decided to test part of it to destruction. As can be seen at
Making Things, Part 2
, bending it proved very
difficult – even when supporting the back-end weight of a car!)
So far I’ve only described one half of the
swing-arm. But of course there are two mirror-image halves – and they needed to
be joined together. Two tubes are used to make this connection. The first is in
40 x 40mm tube and joins the two ‘spring operating’ extensions. In fact, it is
this tube that bears down on the spring. The second connector piece is in larger
50 x 50mm tube and is positioned as close as possible to the wheel axle. This
piece also carries one of the rear wheel mudguard mounts.
Welding
The rear swing-arm was the first part of the HPV
that I built. As a result, it was also the first part that I needed to have
welded.
Welding of aluminium can be by MIG or TIG, with
MIG the most commonly used welding technique. However, while it is faster, it is
also less suited to small components and gives a less pleasing visual result
that is potentially weaker. TIG needs a very steady hand, a good welding machine
and takes much longer. Good TIG tradespeople are also much harder to find than
good MIG welders.
However, after chasing around on the phone (in
this sort of search, being passed by word of mouth from one welder to the next
is best) I managed to locate a brilliant TIG welder who was close, cheap and
flexible in working hours.
Welding the rear swing-arm took about four hours
of careful work but the results were stunning – superb welding and a very rigid,
relatively light weight (2.2kg) assembly.
Damper and Spring
The details of the springs and dampers will be
covered later in this series but – in brief – what do they consist of?
In fact, the very first components bought in the
build of the HPV were the dampers. After looking at mountain bike spring/damper
combinations, I decided to steer well clear of any of them. Why? Because of
their ridiculous cost. Many are just air springs (which should cost next to
nothing) while others are oil/gas with external concentric coil springs and
adjustable damping.
But as far as I could see, all the rear bike
dampers were way overpriced - AUD$500 seemed common. Also, there didn’t seem to
be the professionalism of support that I thought I’d need – at minimum, I
expected to have to rebuild the damper to achieve the front and rear damping
behaviour I desired. And when I mentioned damper rebuilding, bicycle shop staff
backed away in terror... Perhaps I just went to the wrong shops, but these dampers
do seem incredibly overpriced for what they are.
Instead I bought three second-hand motorcycle
steering dampers. This design uses a large diameter steel shaft which passes
right through the body of the damper (so reducing their required size by avoiding the need for a twin tube design),
aluminium bodies, and are rebuildable and so can have their damping behaviour
altered. They’re also cheap – I paid AUD$75 each for them second-hand. The
downside is that their overall mass is high (500g each) and the damping
behaviour is symmetrical (ie when used unmodified in a suspension application,
bump and rebound damping will be the same).
Spring Seat
As already mentioned, the spring is a conventional
coil spring mounted vertically. It needs to be adjustable for preload, primarily
so that the same ride height can be achieved with different weights on the rear
carrier. I used my lathe to turn-up a cup that formed the lower spring seat.
This sits on the shoulder of a long externally threaded upright that rotates
within an internally threaded tube welded vertically within the main
longitudinal frame tube. A large knurled aluminium knob allows easy adjustment.
While I am happy with the end result, a quick check with the scales showed the
assembly adds about 200g over the weight of the bare lower spring cup. I was
starting to find that every feature added mass...
Pivot Adjustment
So that the rear wheel could be aligned,
adjustment was built into the rear pivot points. This took the form of castor
adjusters used in karts which incorporate an eccentric able to be adjusted by
rotating the collar.
Next week: the nightmare of designing and
building the front suspension
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