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This article was first published in AutoSpeed.
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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?
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
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).
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.
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.
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.
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
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’
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?
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.
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.
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.
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.
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.
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.
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More on X-Frames
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.
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Building the Suspension
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.)
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.
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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