From digest.v6.n277 Fri Mar 7 11:56:47 1997
From: Pete Read <read_at_arl.bna.boeing.com>
Date: Tue, 25 Feb 1997 11:54:49 -0800
Subject: Re: <All> Progressive Spring Mechanics
Thomas Murphy and Jennifer Stork weren't convinced by my earlier
description of how progressive springs work. Of course, my first
reaction was that they are crazy <grin> -- actually more like
panic because I hate to put out misleading information. Fortunately
they both were gracious enough to give their reasoning rather than
just calling _me_ crazy.
After a moment of self-doubt, I quickly removed the spring from a
ball-point pen in my desk to double-check myself (more below). I'm
still quite sure my statements are accurate. Let me draw a better
picture and give more details. Maybe after this you'll either agree
or be too worn down to care any more.
Thomas Murphy writes:
>In Pete Reads last post on this subject he postulated that progressive
>springs compress in steps. My mind would like to disagree. As the
>coils compress, I think they make contact with each other in the same
>way that your foot hits the ground: ie, the heel first, rolling towards
>the toe. If this is true, then the change in spring frequency would
>be more or less continuously variable, not variable in "steps".
Jennifer Stork writes:
>While a spring does look like a series of active coils when it's
>viewed from the side, it actually is all a single, continuous coil,
>and any "bottoming" that takes place (compaction of the spring) is
>going to proceed millimeter by millimeter up through the spring--much
>more gradual than the sort of coil-by-coil progression you describe.
>While there would be some sort of "step" effect if the progressive
>rate springs were made of wire that increased in thickness in big
>jumps, I believe that the tapers (or thickening) of the wire in a
>spring is much more gradual than this.
Both aren't convinced that spring coils compress in a parallel
fashion. Thomas talks about the coils hitting "heel first" and
rolling forward. Jennifer says any bottoming proceeds millimeter
by millimeter up through the spring....tapers (or thicking) of
the wire in a spring is much more gradual.
Well first of all, my point was in regard to progressive springs
using constant diameter spring wire. I briefly mentioned tapered
wire as another method for creating progressive springs, but it's
much more expensive to manufacture. Most suspension coil springs
are made from fixed diameter wire with constant pitch or distance
between coils (there is usually a slight change in pitch at the
ends so they can be more square with the spring seats). The
normal aftermarket progressive springs are usually constant diameter
wire with varying pitch to dynamically change the number of active
coils (one or more coils touch).
Suspensions don't bottom on the coil springs. That would damage
both the springs and the suspension mounts. Instead some type of
rubber bump stop is always used to limit travel. Normal constant
pitch springs don't touch coils at all (except a little at the ends
because of the slight change in pitch as mentioned above).
Progressive springs do intentionally touch one or more coils to
reduce the number of active coils and increase the rate.
As Jennifer says, springs are all one continuous coil or wire. The
BMW springs I've seen have all been right-hand wound, meaning that
the spring coils move farther away as you travel clockwise along
the wire (right hand rule). If the pitch is constant, you can place
a vernier caliper anywhere between the coils and the distance will
be the same.
Think about unwinding the spring so that it's just a straight
metal bar. Twist in opposite directions from both sides. The bar
(spring wire) will be put in torsion. Because the wire is constant
diameter, the deflection (twist) will be even all along the bar.
Now wind the bar back into a spring coil. When the spring is
compressed, the spring wire twists the same way -- evenly along its
length. The coils start out equidistant (parallel) and remain that
way because the deflection is even all along the wire as the spring
is compressed. If coils bottom on each other, the parallel motion
of the coils ensures that the whole coil touches virtually at the
same time -- not step-by-step or millimeter-by-millimeter.
Progressive versus Straight Rate Spring
Here's an example. I'm looking at a catalog picture of some Eibach
Pro-Kit springs. The front springs are constant rate while the
rears are progressive. The rear springs have 10 total coils, with
the top and bottom coils wound much closer together (less pitch).
I'm going to assume the end coils are inactive because they rest on
the spring seats. This leaves eight active coils.
Below, I've tried to draw cross-sections of progressive and straight
rate springs, both at normal ride height and compressed. This still
doesn't look quite right because the coils are actually at an angle
because of the winding. To use some numbers, let's say that the
starting rate is 175 lb/in for both.
Spring rate is inversely related to the number of active coils (see
Calculating Spring Rate below). The straight rate spring remains
at 175 lb/in because no coils touch as the spring is compressed.
On the progressive rate spring, notice that coils 1&2 and 7&8 are
wound more closely together (less pitch than the other coils). As
the spring compresses, those coils bottom on each other, reducing
the number of active coils and increasing the spring rate.
Progressive Rate Spring Straight Rate Spring
Normal Compressed Normal Compressed
- ---------- -------------- ---------- ----------
O (1) O
O (1) O 1&2 7&8
\ smaller O (2) O all
O (2) O / pitch \ same
O (3) O
O (3) O O (1) O
O (1) O \ 1&2 O (4) O O (2) O
O (4) O O (2) O / touch
O (3) O
O (3) O O (5) O
O (5) O O (4) O
O (4) O
O (6) O O (5) O
O (6) O O (5) O
O (6) O
O (6) O O (7) O
O (7) O O (7) O
O (7) O \ 7&8
O (8) O O (8) O / touch O (8) O O (8) O
- ------------- ---------------------- ------------ -------------
Eight Active Six Active Coils Eight Active Coils
Coils (two less 1&2, 7&8 touch) (coils do not touch)
175 lb/in, 8 active coils
Rate when coils 1&2 touch
200 lb/in 7 active coils (175 x 8/7)
Rate when coils 1&2 and 7&8 touch
233 lb/in 6 active coils (175 x 8/6)
In this example, the progressive spring rate changes in 25-33 lb/in
steps (1&2 and 7&8 don't initially touch at the same time).
Calculating Spring Rate
W^4 x G
Spring Rate K (lbs/in) = -------------
8 x N x D^3
W - Wire diameter of spring
G - 12,000,000 for steel springs
D - Spring coil center diameter (inches). Measure to middle of
spring coil, not outer diameter.
N - Number of active coils, free to move, not touching other
This is the general equation for calculating spring rate. It
shows that spring rate is directly related to the number of
active coils, N (e.g. reduce the number of coils by half and
double the rate).
It also illustrates the importance of wire diameter, W (increases
to the forth power). Many times, wire diameter is the only change
between different springs for a series of cars.
For example, the E28 528e and 535i have similar front springs with
the same seven coils, but slightly different diameter spring wire
(535i = 0.527 inch, 528e = 0.514 inch). Because the springs are the
same except for wire diameter, the percent difference in spring rate
is easily found.
- = 1.105 = 10.5 percent higher rate for 535i
Ball-Point Pen Test
And finally, a real world look at springs. Disassemble a click-type
ball-point pen. Notice that the spring wire is constant diameter and
the pitch (except for the very ends) is also constant -- a straight
Compress the spring completely and see that the coils all touch at
the same time. Now grab the coils at the center point (halving the
number of active coils) and notice that the spring rate doubles.
Is everyone convinced yet or just worn down?
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