Old Library

Andy Nguyen wrote:

>>>   If one consider each coil as a separate straight leaf spring,
>>>   then a smaller-diameter coil has higher rate than a larger-diameter
>>>   one, being a shorter leaf spring.

>> Yup, so far, so good.

>>> So, the purpose of decreasing
>>> the coil diameter is to make the spring a progressive spring.

>> Now we part company.
>> This, in and of itself does not make a spring progresive.

>   So are you saying that making the spring progressive is not
>   the purpose, or that decreasing coil diameter does not
>   necessarily make a spring progressive?  I would be most interested
>   in hearing your answer.

The latter.  I've been stewing on how to explain this without resorting
to equations.  Here goes:

Take a "simple" 100 lb/in straight-rate spring, composed of 4 identical
evenly spaced coils.   Apply 100# of force.  The spring compresses 1".
Each coils compresses 1/4".  Add another 100# and the spring compresses
and additional 1" (2" total) and each coil is now compressed an
additional 1/4" (1/2"total).  This continues linearly until the coils
begin to bind (at which point you no longer have a spring).   From
observing this spring, we can deduce that each coil has a rate of 400
lb/inch.

Now lets reduce the diameter of two of those coils.  In fact let's
reduce them to 70.7% of their original diameter.  This reduces the
length of the wire in each coil by 50% and doubles their rate.   So what
happens when we put 100# on the spring?   Each of the original size
coils still compress 1/4", but the two smaller coils only compress 1/8"
each, for a total of compression of 3/4".  The entire spring has a rate
of 133 lb/in.  Add another 100# of force and you get another 3/4"
(total) compression, but you still have a straight-rate spring.

So a spring that has different rates in different coils is not
intrinsically progressive.

What makes a spring progressive is a geometry where some of the coils
bind up partway through the anticipated travel.  For instance let's take
our original spring and play with the coil spacing.  Let's wind it so
that the first two coils only have 1/4" of air between them while the
other two coils have substantially more.   Put 100# on the spring, it
compresses 1".  But at that point, two of the coils can't compress any
more.  Add another 100# and it only compresses 1/2"; i.e. the rate of
the spring has doubled to 200 lb/in!

Although a change in coil (or wire) diameter does not make a progressive
spring, it can be used to make a spring more progressive.  If we take
our second spring and make the two smaller diameter coils widely spaced
while the bigger coils are only 1/4" apart... Put 100# of force on this
spring.  It compresses 3/4", rate is 133 lb/in.  Add another 100 lb. The
big coils are already bound up, so only the small coils can compress;
they each compress only 1/8" for a total of 1/4" or a 400 lb/in rate.
So instead of a 2:1 change in rate, we've now got a 3:1 change...

Any questions?

-Uwe-