Anal retentive springs: long..

["Mark Battley" <m.battley@domain.elided>]

Since we have bounced back to springs again...

Hit the page down key (a few times!) if you are bored already, read if you
are anal retentive enough to be interested in how reality fits with theory
:-))

Eric kindly listed the appropriate formula for coil spring rate:

   c = G*d^4/(8*n*D^3)
   where
   c = spring rate
   G = shear modulus of elasticity
   d = diameter of wire
   n = number of coils
   D = diameter of spring.

Which is based on small deflections, linear behaviour of materials etc. You
can of course get more sophisticated if you can be bothered.

Note that n is the number of ACTIVE coils, not the total number: there is a
region of coil at each end that does not directly contribute to the spring
rate. You need to assume/guess/calculate what the actual number of active
coils is.

As an example, I started with (as far as I know) standard front springs
(6.75 coils, 16.7mm wire diameter, 60.5mm coil radius) from a 1973 105
series 2000 GT Veloce. I measured the load deflection curve (typically at 6
or more points) in a standard electro/mechanical testing machine (between
flat platens). The standard rubber pads were used at each end, mainly to
make sure that the spring didn't slide anywhere (yes I did have other
security measures in place to keep things safe). I don't believe that the
rubbers will significantly affect the rate, and they are part of the system
in the car anyhow.

Both springs were within 1% of each other (deflection for given load),
standard and modified (actually quite impressive for anybody who's ever
tried testing anything!).

Summary of results: 

 Lengths (mm):
                                Standard    - 0.5 coil     - 1 coil
Static (change)            320          313  (-7)    290  (-30)
Loaded (change)          182          174   (-8)    162  (-20)
(at 2250lb/1023kg)

Probably a fluke, but prior to the test I predicted a 20mm reduction in
loaded
length for one coil. Factory specs for 115 series USA 2000 GTV are static
length of 320, loaded 200 (I measured 195): does anyone have the
corresponding figures for the 105 series 2000 GTV?

   Measured rates:
                                Standard    - 0.5 coil     - 1 coil
(N/mm)                        74               78               85
(lb/in)                          419             446             487
Increase                                           6%             16%

The rate is not completely linear: these are from a least squares fit to the
overall curve. The initial rate for the original springs was 61 N/mm, rising
to 81 at full load: the effective length of the coil reduces as the ends
compress against the seats.

Removing only half a coil makes only a relatively small difference to the
length and rate. This first half is at a very shallow helix angle and is not
very "active". Once you get beyond this things change more quickly.

Using the standard formula can give good predictions: if you assume the
appropriate number of active coils. If you don't reshape the ends (I
didn't), the number of inactive coils reduces. Of course without testing you
have to make some sort of estimate. Here's what matched the experimental
data:
                                 Standard    - 0.5 coil     - 1 coil
Actual coils                   6.75           6.25           5.75
Assumed inactive coils    0.9              0.7             0.7
Active coils                   5.85            5.55          5.05
Predicted rate (N/mm)    74               78             86                 
                 
Measured rates               74               78             85

And on the car?

I haven't ever loaded and measured the car exactly as specified in the
factory specifications so I don't know for sure how its ride height compares
to standard. However Dana Loomis collected some data from about 10 cars,
some supposedly standard, some modified, and based on these mine seemed to
be about 20-25mm lower than "standard USA" when I got it (it had 25mm of
spacers between the spring pans and wishbones). After removing these washers
(which would raise the car) and fitting 1 coil shorter springs it is now
about 55mm lower than what we believe are stock cars and about 35mm down on
where it was. I still not clear on what the difference in factory ride
height was between 115 and 105 cars. Note that because of the geometry of
the wishbones and spring position there there is an approximately 3:1 ration
between wheel height and spring deflection. I did find that a 10mm spring
spacer resulted in a change of ride height of approximately 30mm (It has the
spacers in place).

However this doesn't explain why the 25mm of washers only lowered it an
apparent 20mm. Unless a PO fitted Berlina springs (which for the 1750 are
longer, anybody got the 2000 data?) and lowered the spring pans to bring the
car back to a more "normal" height. But then the unloaded length of the
springs matched the USA GTV specs ... And it'd be a bit of a fluke (although
not impossible) for both springs to "sag" exactly the same amount. This bit
annoys me, because everything else has behaved as expected and predicted.

A WELL designed and manufactured set of aftermarket springs matched to an
appropriate set of dampers is probably be the best solution to modifying a
car's behaviour to your requirements. However cutting springs is easy,
cheap, and not seriously detrimental to you or your car (just be careful
removing and replacing them!). Probably the main downside to cutting springs
is that it only makes a relatively small difference to the rate since the
rate is (more-or-less) linearly proportional to the spring length. To
significantly increase the rate (if that is what you think you want..)
requires an increase in diameter of the wire (d^4).

In summary:

*The basic formula can be used to predict the rate of standard and modified
springs. The accuracy of the results depend on the assumed number of active
coils

*Reducing the length of a spring has a relatively small effect on its rate

*Cutting one coil off a 105 2000 GTV (?) front spring reduced its compressed
length by 20mm, increased the rate by 16%, and appears to have reduced the
ride height by about 55mm

Now did anybody make it to the end of that???

Mark Battley,    Anal retentive engineer: when in doubt, measure something!
Auckland, New Zealand.

1973 Alfa Romeo 2000 GT Veloce
Happy again with new clutch, gearbox mount, rear crank seal, driveshaft
giubo.

Alfa Romeo 105 series Bertone Coupe home page and register at:
      http://www.geocities.com/MotorCity/1806/105GTV.HTML

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End of alfa-digest V7 #754
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