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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 I covered the rear suspension of the
Human Powered Vehicle HPV). However, while there were some complexities involved
in its development, they pale into total insignificance when compared with the
front suspension... I absolutely take my hat off to anyone who has developed from
scratch the front suspension for any vehicle while getting good results in
camber change, castor change, anti-dive, roll centre height, end-view swing arm
length, rigidity and lightness.
It is an unbelievably difficult
exercise!
But first, there were some basic design decisions
to make. To achieve a decent outcome in terms of camber change, bump steer,
anti-dive and so on, double unequal length wishbones seemed to be by far the
best design choice. (See
Front Suspension Designs
for the
alternatives.) And of course there is plenty of design material around for
double wishbone suspension systems – in fact, more than for any other sort of
suspension.
However, I found it incredibly hard to gain any
useful information from these design resources.
Firstly, I figured I’d use one of the suspension
design software programs - Susprog 3D and Suspension Analyzer being the best
known. But at this beginning stage both were near useless. For starters, before
you can gain any useful design information at all, you need to know:
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Position of front upper wishbone mount
-
Position of rear upper wishbone mount
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Position of front lower wishbone mount
-
Position of rear lower wishbone mount
-
Position of upper ball-joint
-
Position of lower ball-joint
Considering that each mount is defined in its
position in three planes, that’s immediately 18 dimensions. The add to that
wheel offset and diameter, and inner and outer steering tie rod positions, and
you’re looking at 26 or more accurate dimensions needed before you can even
start. (Robert Small, the author of Susprog 3D, told me that in fact the
steering data didn’t need to be input for the program to work. But despite being
given a free copy of the program, spending hours on it and exchanging many
emails with Robert, I couldn’t make it work.)
These suspension design programs are nothing like
using (say) subwoofer enclosure design software or camshaft design software
where although a similar number of criteria may be needed, the specs are readily
available. In the case of a suspension design, all the specs need to be
measured. And what if you’re starting with literally a blank screen – you don’t
have any measurements because nothing has yet been decided? In that case you
just go round and round, punching in figures that become increasingly
meaningless. I’m very much a fan of computer aided design but in the case of the
suspension programs, I found the process extremely frustrating. (It would be far
better if a program allowed you to sketch the suspension on screen and then give
you an indication of how global changes affected things eg how changing the
inclination of the upper wishbone influences camber gained during bump.)
Having at least temporarily given up on the
software approach, I looked at lots of books. These were much better in giving
general guidelines but when it came to actually laying out the suspension, again
were not very helpful.
But What Was Wanted?
Of course, part of the problem in designing the
suspension was not knowing what was actually wanted! A car tyre works best if it
is kept as vertical as possible during cornering. (Negative camber – whether
static, dynamic through castor, or dynamic through bump – is used so that the
more heavily loaded outside wheel becomes vertical during cornering.) But a
bicycle tyre – effectively what an HPV tyre is – is designed to work well
through a range of cambers. That’s because in a bicycle application, during
cornering the tyre is always at an angle to the road.
I talked to Paul Sims – chief designer of the
Greenspeed trikes and a very helpful man to boot – and he suggested that a
static camber angle of about 5 degrees would give the best results. However, the
actual (ie dynamic) camber angle also depends on the castor, with more castor
giving more neg camber as lock is applied. Furthermore, in my application, I
could add even more negative camber during bump – easily achieved by making the
upper wishbone shorter. So the final suspension-induced camber achieved during
cornering depended on:
But each of these also has an associated minus –
too much static neg camber will cause uneven tyre wear and instability under
braking; too much castor will make the steering heavy; and too much dynamic neg
camber in bump will cause a jacking effect as the suspension starts acting like
a short lateral swing-arm. But the big potential benefit of lots of cornering
camber is heaps of camber thrust (a sideways force generated by the camber of
the wheels that helps resist cornering forces) and less tyre tuck-under.
And there’s another thing. Any body roll results
in a reduced actual camber angle between the tyre and the road. For example, a 5
degree body roll will result in 5 degrees less negative camber of the outside
(loaded) wheel – so you also need to know how much body roll there will be.
Which depends on the roll centre, the height of the centre of gravity, the
stiffness of the springs and swaybar.... Aaagh!
Chalk and Concrete
It was all rapidly growing too hard, so I went
back to chalk and a piece of bare concrete. Literally. As mentioned last week,
the dampers for all three wheels comprise ex-motorcycle steering dampers - the
stroke of these could be used as a starting point in determining some of the
suspension geometry. The other factor that could be used was the length of the
lower wishbone. To help minimise track change during suspension movement, the lower
wishbone should be as long as possible. In the case of the HPV, that meant
approaching half the track dimension, or about 400mm. So with the damper stroke
and lower wishbone length determined, some full-size chalk marks could be made
on the concrete.
The stroke of the dampers is about 70mm but I
wanted a front suspension travel of at least 100mm. To achieve this, the damper
needed to be installed at an angle from vertical, and/or the damper had to be
located with one pick-up point well in from the end of the wishbone. Obviously,
the damper body also needed to connect to the HPV frame. With these aspects
defined, the form of the suspension began to take shape.
The spacing between the wishbones was the next
decision. Wide-spaced wishbones are good for:
But unfortunately in my application, if the
spacing was too great, the suspension would intrude into the area of leg and
foot movement that occurs during pedalling. Too wide a vertical spacing between
the wishbones would also require odd, long mounts for the damper or
alternatively, would require that the damper be mounted more vertically,
reducing suspension travel. These points set the vertical distance between the
wishbone inner mounts at about 160mm centre-to-centre.
Next, where was the spring to go? As with the rear
suspension, it was intended that separately-mounted coil springs be used, rather
than having them wound concentrically with the damper. The advantages of
separate spring mounting were:
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No need to provide spring seats on the dampers
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The spring:damper stroke relationship could be
varied from1:1 – that is, it would be possible to use a different motion ratio
for the spring and damper
-
Tight clearances around the damper meant the
diameter and length of the spring would be less constrained
So instead of mounting the spring around the
damper shaft, it was mounted inboard of the upper wishbone mount. The base of
the spring acts against the lower wishbone while its top pushes against the
frame extension that is used to support the upper, inner wishbone mount.
(This spring location places a high bending load
on the lower wishbone – something I hadn’t thought through sufficiently at this
stage. Additionally, as the spring location is moved further inboard, the spring
rate goes up very fast to maintain a given wheel rate. If I was starting again
from scratch, I would place the spring as far outboard as possible, saving a lot
of weight in the spring as a much lighter spring could be then used. More on
this in the next part of this series.)
About this time, two further decisions were made.
The lower wishbone had always been intended to be an A-arm with a broad base.
The upper wishbone had also been intended to be an A-arm, shorter but otherwise
of much the same shape as the lower arm. However, when I started laying things
out accurately, I soon realised that if it remained the proposed shape, the
upper A-arm would foul the damper. Instead this arm became a pair of linkages
which were then integrated into one arm.
And the other decision? The frame extension
providing both the upper spring seat and the mount of the upper wishbone inner
pivot had been intended to be a simple cantilever side extension of the main
fore/aft frame tube. However, using the Greenspeed GTR as the guide, I realised
that this extension would foul the tension side of the chain. (The tension side
of the chain should be kept parallel to the long axis of the boom that supports
the front chain rings and pedals. This causes the boom to be subjected primarily
to compression rather than bending forces.) Instead, a more complex frame
arrangement was put into place that allowed the chain to pass without
hindrance.
Anti-Dive
It’s possible to build anti-dive into the front
suspension. If, when viewed from the side, the upper and lower wishbone frame
pivot axes are not parallel but instead converge towards the centre of the
vehicle wheelbase, under braking an element of anti-dive will be introduced.
Since dive uses up part of the suspension travel (leaving less to cope with
bumps experienced when braking), anti-dive sounds a good thing to have.
But how much should the axes be inclined? Again,
this can be calculated by suspension design programs but again, a helluva lot of
unknown information – including the centre of gravity height – needs to be
input. So why not simply configure the system to have a heap of anti-dive? The
problem is that too much anti-dive results in very harsh behaviour under bump.
This is because with anti-dive, the wheel moves forward as well as upwards when
the bump is met, so hitting the bump harder.
The upper inner wishbone pivots naturally have a 5
degree inclination towards the rear of the HPV - this is the case because the
main frame longitudinal slopes upwards by this angle. However, how much angle
should be provided in the bottom wishbone pivot axis? I didn’t know and so I
made this angle easily adjustable by providing multiple inner wishbone mounting
heights for both the front and rear bushes, with the default being the 5
degrees.
Ball-joints
As mentioned last week in
Building a
Human-Powered Vehicle, Part 2, the front and rear frame suspension pivots
comprised polyurethane bushes rotating on ex-shock absorber chrome-plated steel
shafts. These were chosen in preference to Heim (rose) joints primarily for
reasons of durability but also because they have some vibration and shock
absorption capability. For durability reasons I was also reluctant to use Heim
joints for the wheel upright’s steering pivots. This HPV will be used in wet and
dusty conditions and Heim joints normally have no protection from either
contaminant.
I looked at the smallest tie-rod ends I could find
for cars but they were too large and heavy. I also looked at the front
ball-joints from quad motorbikes and while they looked close to what was needed,
most were of the design where they are pressed into the suspension arm. That
requires accurate clearances and is best suited to steel arms rather than those
made from aluminium.
I finally settled on miniature female
aluminium-bodied ball-joints obtained from a bearing supplier. These come in a
variety of sizes and for the lower, more heavily loaded ball-joint I used the
pictured 12mm and for the upper ball-joint, 10mm. These ball-joints are able to
be greased and have a rubber protective cover. In the application I would expect
them to have a very long life but in any case, they are easy to replace and
available off the shelf as a standard part.
Castor
Vehicles run castor in order that the steering
self-centres. Castor (the angle the steering axis leans back from the vertical
when the vehicle is viewed from the side) causes the vehicle to be lifted as
lock is applied. This applies a self-straightening action – the wheel
automatically returns to a position where no body lift is occurring. In
addition, as mentioned above, the greater the amount of castor, the greater the
amount of neg camber that occurs during cornering. (On cars with lots of castor
this affect can be seen when the vehicle has been parked with the wheels on full
lock. The resulting camber can easily be seen by eye.)
HPVs use what in car design would be regarded as a
radical amount of castor. This is because the weight of an HPV is so much less
than a car that the self-correcting torque is also much lower. Paul Sims
suggested at least 16 degrees, while my Greenspeed GTR runs about 10 degrees.
But providing any castor at all caused me some
suspension design difficulties – and it’s all my fault. As mentioned, when I was
laying out the upper and lower wishbones, I used much the same A-arm shape, just
with the lower A-arm shorter. To clear the damper the upper arm had become a
pair of parallel links, but the centrelines of the upper and lower arms had
remained the same – that is, the upper pair of links were directly above the
centreline of the lower links. That put the two steering ball-joints one above
the other...which would naturally result in zero castor! Not what was wanted!
To gain anything like 16 degrees of castor, the
lower ball-joint would have to be 50mm further forward than the upper
ball-joint. If the lower ball-joint was to remain mounted at the apex of the
lower A-arm, and the upper ball-joint was to continue to be mounted mid-way
between the upper parallel arms, the apex of the lower A-arm would need to be
moved well forward. The whole lower arm couldn’t be moved forward because that
would have meant the spring rested asymmetrically on the lower arm and the
damper no longer fitting properly. Instead, just the lower ball-joint mount was
moved forward, courtesy of an angle bracket. This also allowed the bracket to be
drilled for multiple ball-joint positions, allowing castor to be adjustable.
(However, major changes subsequently needed to be made to this approach: see the
‘Failure!’ breakout box.)
Wheel Upright
The wheel upright supports the stub axle, disc
brake calliper, steering arm and upper and lower ball-joints. It needs to be
very stiff and, as its mass is entirely unsprung, light. It was made from 10mm
thick aluminium plate and incorporates the lower and upper ball-joint mounts and
the steering arms. Plenty of holes were drilled to lighten it and so despite
appearances, the assembly remains quite light at about 600g each. (This pic
shows an early version: some changes were later made as seen below.)
The 12mm steel stub axle (supplied by Greenspeed)
is supported by the upright by being placed through a drilled boss (machined on
the lathe) that in turn was placed through a hole drilled thought the plate,
being welded to the plate both sides. A shoulder machined on the tube determined
the wheel offset – this was set to precisely centre the disc within the
hydraulic caliper.
Scrub Radius
I’ve already described how the lower ball-joint
needed to be placed well forward of the upper ball-joint (or vice versa) to get
the desired castor. Well, to get the desired scrub radius, the upper ball joint
had to be positioned much further inboard than the lower ball-joint.
So what’s this about scrub radius? The term refers
to where an imaginary line drawn through the upper and lower ball-joint would
impinge on the road. When viewed from ahead, if this steering axis line touches
the road on the outside of the tyre’s centreline, the result is called negative
scrub radius. If the line touches the road on the inside of the tyre’s
centreline, it is called positive scrub radius. Both positive and negative scrub
radii will cause steering reactions when longitudinal loads are suddenly applied
to one tyre but not the other. In other words, braking say one wheel will cause
the vehicle to steer – if the scrub radius is positive, steer in the direction
of that slowed wheel. If the scrub radius is negative, steer in the direction of
the opposite wheel.
The Greenspeed trikes uses zero scrub radius
steering, sometimes called centre-point steering. However, some HPVs use
negative scrub radius steering, so that braking one wheel applies a
self-correcting torque to the vehicle. What happens is this: say, the right-hand
tyre is braked. This causes the steering to pull to the left, offsetting the
natural reaction for the vehicle to rotate clockwise as it attempts to pivot
around the slowing wheel. It sounds good in theory - and many cars use negative
scrub radius steering for similar reasons - but Greenspeed’s Paul Sims suggested
to me that the actual behaviour of an HPV with negative scrub radius steering
depends a lot on the frictional characteristics of the road surface – which also
seems to make sense.
As a result, I decided to set the scrub radius to
zero – centre-point steering.
Agggh, Steering Axis Inclination!
The decision might have been made to run zero
scrub radius – but what were the implications of that for the steering axis
inclination (sometimes still called kingpin inclination)? Making a simple
drawing and applying some trigonometry showed that to achieve zero scrub radius
steering, the line passing through both ball-joints needed to have an angle to
the vertical of 27 degrees. And that’s a bloody lot of steering axis
inclination!
A bloody lot!
So what does having a lot of steering axis
inclination matter?
The easiest way to see the affects of all these
angles is to make a simple model and twirl it in your fingers. I grabbed a
rubber door stopper and stuck a thin wire through the centre hole. I then bent
the wire up to 27 degrees from the vertical and held it so that it had zero
castor. (That is, when viewed as if from the end of the car, it had an angle of
27 degrees, but when viewed from side-on, the axis was vertical.) Held in this
way it can be clearly see that as the wheel is steered, it tends to move
downwards as lock is applied in either direction. Normally, the tyre would be in
contact with the road so the vehicle would be pushed upwards as lock is applied.
(This is why increasing steering axis inclination causes greater self-centring.)
At the same time as the wheel moved downwards, it could also be seen that its
camber went positive – not what you want when cornering!
But it gets worse. Throw in some castor (ie the
steering axis inclined backwards when the ‘car’ is viewed from the side) and the
wheel geometry looked pretty ugly. When the wheel was turned so that it was the
outside wheel in cornering, it gained neg camber (fine!), rose into the air
(steering lighter) before then starting to head back downwards (steering
heavier). When it was turned the other way it immediately assumed a lot of
positive camber and moved downwards rapidly (ie fast making the steering heavy).
No wonder the textbooks say that you shouldn’t go
overboard on steering axle inclination but plenty of castor is fine!
Ball-Joint Locations
But how could I achieve a steering axis
inclination of way less than 27 degrees? That angle had come about from using as
the wheel upright a flat, vertical aluminium plate positioned just inboard of
the disc, with the lower ball-joint as close to the upright as possible. Now it
looked like the lower ball joint had to be on the other side of the disc
– impossible. Of course the bicycle-style spoked wheels used on HPVs don’t have
a ‘dish’ like car wheels, so there’s no room for the ball-joint within the
wheel. Or is there? After pondering for a long time I figured the lower
ball-joint could go directly below the disc and on the same plane as the disc,
rather than about 45mm inside it where the original location placed it.
This meant redesigning (although thankfully not
remaking!) the wheel uprights and more seriously, a loss in ground clearance as
the ride height then also needed to decrease.
This pic shows how hard it was to achieve zero
scrub radius without making the steering axis inclination too great. Note the
position of the lower ball-joint further outboard than the disc brake!
Failure!
With
just the two lower wishbones and the wheel uprights complete, it was possible to
load them up – that is, to install these parts and the wheels and put some
weight on the front of the frame to see what happened. And the results were not
encouraging.
Firstly,
the extended angle bracket (the one that moved the bottom ball-joint forward to
obtain the correct castor) bent like a bloody banana! Yep, despite being made of
5mm aluminium plate, it was simply way too weak.
I
then moved the lower ball-joint locating bolt to the hole centred at the top of
the ‘A’, only to find that again that the camber of the wheel permanently
changed when load was applied! But what was happening this time? – there was no
apparent bending of the bracket.
This
failure was even more interesting. The 12mm bolt connecting the wishbone to the
ball-joint passed through the 5mm thick aluminium plate; the loads were high
enough that the plate was being crushed – ie the hole was elongated
vertically!
To
overcome these problems I decided that the lower ball-joint had to be mounted at
the top of the ‘A’. (The required castor could be gained by moving the top
ball-joint backwards, something that should have always been done.) The end of
the wishbone was then substantially modified in order that it better support the
ball-joint bolt. The very top of the ‘A’ was cut off and a cylinder of aluminium
turned-up. A hole was drilled through the cylinder. This hole size matched the
ball-joint bolt, while its outside diameter of the cylinder allowed it to be a
press-fit in the centre tube of the top of the wishbone. The aluminium cylinder
was welded into position and had a strengthening plate added at its outermost
end. An 80mm long Allen-key high tensile steel bolt was then inserted through
the aluminium cylinder - being supported along 50mm of its length – before
screwing into the ball-joint. (This photo shows the modified and original
wishbones, before the modified one was welded.)
This
achieved two things: (1) the ball-joint was mounted at the strongest part of the
wishbone; (2) the ball-joint mounting bolt was extremely well supported.
But
the ball-joint mounting wasn’t the only problem. Applying load to the front of
the frame showed that the lower wishbones themselves had quite a lot of
deflection. How much then? Well, the static load on the wishbones works out to
40kg per side, so with sudden vertical accelerations over bumps it seems
reasonable to at least double this to 80kg, or a total of 160kg on the front of
the frame. And with this mass (two people!) bearing down on the frame, the 300mm
long wishbones deflected by a total of 3mm! They didn’t take a permanent ‘set’
(ie stay bent) but this much deflection was too much for me to be comfortable
with.
(Why
so much bending? Two reasons: firstly, small diameter tubes are required to fit
everything into the tight available space, and secondly, the fact that the
spring location places the wishbone in bending rather than in compression. On
the other hand, the instantaneous damper loads – arguably much larger than the
spring loads but not able to be tested – place the wishbone in compression.)
To
reduce deflection, I added two tension braces to the underside of each wishbone.
Using 5 x 5mm solid aluminium bar, the weight gain was minimal and the ground
clearance change (5mm) also very small. However, the change in deflection was
massive – total deflection halved!
But
the whole episode had been rather sobering: despite just being a pedal-powered
machine, the expected loads require strength as well as lightness. In some
places, lots of strength! I went back to the design of the wheel upright
and added three small stiffening gussets...
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Roll Centres and Camber Gain
The roll centre is the virtual (ie invisible)
point about which the car rolls. It is determined by the geometry of the
suspension. If the roll centre is below the centre of gravity, the vehicle body
will roll conventionally ie lean away from the cornering line. The amount of
body roll that occurs with a given cornering force largely depends on the
relationship between the height of the centre of gravity and the roll centre.
Raising the suspension roll centre, or lowering the centre of gravity, will
decrease roll. However, while having a high roll centre therefore sounds
attractive, it has significant negatives associated with it. In fact, most well
set up cars run a roll centre at, slightly above, or slightly below ground
level. Most important is that the roll centre doesn’t move around much, either
laterally with body roll or vertically with poor suspension design.
All this stuff is far easier to understand when
the lines are drawn to show roll centres. In the case of a double wishbone
suspension, the lines of the two wishbones (ie through their pivots points) are
extended until they meet. This point is called the reaction point or instant
centre (‘A’). A line is then drawn from this point to the contact patch of the
tyres (‘C’). The roll centre (‘R’) is where this latter line crosses the
centreline of the car (ie the vertical line that passes through the centre of
gravity).
So let’s jump forward about 10 weeks in
construction and look at the roll centres of the front suspension on the near
complete HPV. (Click on the pics to enlarge them.)
This shows the wishbone angles with the HPV at its
normal ride height, ie loaded with my weight. The location of the roll centre
has been specified after Gillespie (Fundamentals of Vehicle Dynamics, page 265,
SAE – 1992). The roll centre height is approximately 75mm above ground. Note
that the red lines are drawn through the pivot points, which in the case of the
upper wishbone is not initially obvious.
As can be seen, the height of the roll centre
changes little (perhaps 10mm or so) when the suspension is at full bump. Note
that the piece of tube and plate the wheel is sitting on is 95mm high.
This diagram shows the roll centres at standard
ride height and at full bump. It doesn’t take into account lateral movement
caused by shifting of the centre of gravity due to body roll but as can be seen,
the vertical movement of the roll centre is very small.
At full droop the virtual swing arm becomes very
long and the roll centre rises just a little more.
This shows the camber increase gained in full
bump. Static is negative 5 degrees at normal ride height and dynamic adds about
another negative 7 degrees. The castor further adds camber when cornering.
However, body roll reduces the effective camber gain of the suspension.
You reckon it’s getting complicated?
Wait for next week when I design the springs and then have them made!
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