The Lotus Grand Tourers

Pete Boole wrote:It's hard to tell from the photos but the rears are also conically wound giving a progressive rate.

Pete

This looks like a very competent, professional restoration Pete - you just take everything in your stride!

One rather pedantic point about the springs - the fact that they are conical doesn't mean they are progressive. Only a varying wire thickness would achieve that. The conical shape of the spring will give it greater compression however.

ATB Richard

richardw wrote:

Pete Boole wrote:It's hard to tell from the photos but the rears are also conically wound giving a progressive rate.

Pete

This looks like a very competent, professional restoration Pete - you just take everything in your stride!

One rather pedantic point about the springs - the fact that they are conical doesn't mean they are progressive. Only a varying wire thickness would achieve that. The conical shape of the spring will give it greater compression however.

ATB Richard

I don't quite understand the logic.

If the wire thickness is constant and the number of turns are uniformly spaced then - IF the outside diameter of the coil progressively increases - the spring rate along the (conical) progression will vary.

ie a conical spring will show 'progression'. the small diameter end of the cone will absorb high frequency harshness and the larger diameter portion will resist the big corner loads.

Spring rate factors are:

• wire thickness
  number of coils
  diameter of the coil

Change any one of the above along the free length of the spring and the spring rate will vary along the free length of the spring ie it will be 'progressive'.

That's the way I understand it anyway. Or have I missed something obvious?

From what I can see on the springs, the progression would come from the change in diameter as the spring is depressed.
The next coil would be a different diameter to the one above it which has already been compressed.

My understanding (and I'm open to being corrected) is that a coil spring is in effect a coiled torsion bar. The degree to which the bar twists (distortion) under a given force per unit of length is proportional to the diameter of the bar (or spring wire). The overall diameter of a coil spring together with with the number of coils determines the length of the 'bar' but variations in the coil spring diameter do not lead to progressive spring effects, as the distortion per unit of length remains constant for any given force.

ATB Richard

OK I got it the wrong way around...

The larger diameter of the cone is more likely to absorb the harshness-type loads because the rate is lower, the smaller diameter of the cone will have a higher rate ( resist the cornering weight transfer loads) according to the spring calculator below.

I've varied ONLY the outside diameter of the spring.

By adjusting the outside diameter of the spring, you are adjusting the length of the coiled wire, which will alter the spring rate. In a conical spring of constant wire thickness, the length of the wire is constant, therefore the spring rate is constant.

richardw wrote:By adjusting the outside diameter of the spring, you are adjusting the length of the coiled wire, which will alter the spring rate. In a conical spring of constant wire thickness, the length of the wire is constant, therefore the spring rate is constant.

Still can't agree. Nothing to do with spring length as far as I can see.

When I alter the spring length ONLY within the calculator the rate stays the same!

I think you are looking at it one dimensionally....some sort of linear extrapolation. The behaviour changes as soon as you wrap a 3D helical spring. I.e. the coils of a helix have a specific behaviour you haven't accounted for.

The compression force on the top of the spring wants to uncoil the spring. The coils try to expand outwards a tad. The tighter the coil diameter the more difficult is is to uncoil the spring - hence the small diameter has a higher rate.

Richard's anti-roll bar analogy is a good one (but he's still wrong!! ): the resistance to bending is affected by the thickness, or the leverage on it. A conically wound spring effectively has varying leverage from one coil to the next, giving it a non-linear rate. In fact if you want to make a conical spring with a constant rate you have to make it with tapered wire.

Pete

Pete Boole wrote:Richard's anti-roll bar analogy is a good one (but he's still wrong!! ): the resistance to bending is affected by the thickness, or the leverage on it. A conically wound spring effectively has varying leverage from one coil to the next, giving it a non-linear rate. In fact if you want to make a conical spring with a constant rate you have to make it with tapered wire.

Pete

That makes a lot more sense than my explanation ... at least I was on the right track.

I imagined a spring coil made out of floppy plastic - like a coiled water hose ...when you compress it - the coils expand / tries to unwind -the tighter winds need more energy applied for them to unwind - a bit of a left-field approach maybe - but fairly close to reality

I was trying to find an equation for a progressive spring to explain it but can't find one.

Sooo here goes.... a standard spring "linear" has the same spacing of coils, wire diameter and coil diameter throughout.

"K" stiffness is the result of deflection of coil v weight added. I.e if you add a 300kg weight to the coil it lengthen 1 inch and if you add a further 300kg it lengthens another inch to a total of 2 inches.
In effect the "K" number is the same for the whole spring.

For a progressive spring rate, in this case the progressive spring has different diameter coils. You would have to break the spring down into 2 different "K" numbers.
For example - One part of the spring 50mm diameter, 10mm wire thick x number of would be K1 and the next part of the spring where the diameter changes to say 65mm diameter coil would be a separate equation.
As the spring is depressed the load across each part (K1 and K2) is proportional but the deflection is not, as each part of the spring has a different response because of the stiffness.

If you cut the spring in two where the diameter changes and enter the details of both parts seperately into the above table you would see that each section has a different K number or lb/in spring rate.
Ergo stick the two parts back together again and the entire spring is not linear in rate, it is progressive.

Sorry I've caused this major hijack of your restoration thread Pete!

However I have some empirical results that show that the rear springs do not have a progressive rate. I ran some tests with Mike Taylor at Lotusbits back in 2014, putting a rear spring in a press, and we measured the following figures:

1" compression: 49.5Kg
2" compression: 98.5Kg
3" compression: 149.0Kg
4" compression: 198.0Kg
5" compression: 249.5Kg
6" compression: 301.0Kg

The purpose of this test was to see if the old spring which we tested matched the Lotus figure of 115lb/in. It was very close at 110.4lb/in.

ATB Richard

richardw wrote:Sorry I've caused this major hijack of your restoration thread Pete!

However I have some empirical results that show that the rear springs do not have a progressive rate. I ran some tests with Mike Taylor at Lotusbits back in 2014, putting a rear spring in a press, and we measured the following figures:

1" compression: 49.5Kg
2" compression: 98.5Kg
3" compression: 149.0Kg
4" compression: 198.0Kg
5" compression: 249.5Kg
6" compression: 301.0Kg


The purpose of this test was to see if the old spring which we tested matched the Lotus figure of 115lb/in. It was very close at 110.4lb/in.


ATB Richard

There is more than one way to think about progression.

Those data are just forces at compressed lengths. i.e the compound length progresses in equal steps as you have observed... and can clearly see in your force data table.

It's not accounting for rate progression within the coil length.

But if you were to observe the way in which the cone compresses at each stage, the larger diameter coils will have moved closer together than the smaller diameter coils - the spring compression is progressive due to the changes in rate throughout the length.

That should translate on the car. The large coils respond to the small inputs more rapidly and it feels less harsh /softer on rebound as the smaller coils resonate less. The resonance is progressive along the length.

richardw wrote:By adjusting the outside diameter of the spring, you are adjusting the length of the coiled wire, which will alter the spring rate. In a conical spring of constant wire thickness, the length of the wire is constant, therefore the spring rate is constant.

There is one exception to the statement above - if a spring is designed with variable pitch (i.e spacing between coils)
but constant wire diameter, then this will exhibit progressive rate characteristics as, at some point of compression, the more closely spaced coils will start to rest against each other, removing themselves from further distortion as compression increases. This has the effect of progressively shortening the spring wire, thus increasing spring rate with load.

ATB Richard

richardw wrote:

richardw wrote:By adjusting the outside diameter of the spring, you are adjusting the length of the coiled wire, which will alter the spring rate. In a conical spring of constant wire thickness, the length of the wire is constant, therefore the spring rate is constant.

There is one exception to the statement above - if a spring is designed with variable pitch (i.e spacing between coils)
but constant wire diameter, then this will exhibit progressive rate characteristics as, at some point of compression, the more closely spaced coils will start to rest against each other, removing themselves from further distortion as compression increases. This has the effect of progressively shortening the spring wire, thus increasing spring rate with load.

ATB Richard

True but you need to give credit for the change in coil diameter throughout the length too.

Spring rate factors:

• Wire diameter - vary along length and the rate varies along length ( as Pete B said.)
  Number of coils - vary along length and the rate varies along length (as you have just said )
  Coil diameter - vary along length and the rate varies along length (as we have said - but you seem to overlook )

All of the above modifications give progressive rates along the length.

All of above will have ONE COMPOUND RATE along its length - which you demonstrated in your data table of forces at compressed lengths.

That's what I understand by the term 'progressive springs' anyhow.

What's your definition of 'progressive'?

Lotus-e-Clan wrote: What's your definition of 'progressive'?

Linear rate springs require equal amounts of additional force to be applied for any given deflection at any point in their compression (until they become coil bound anyway.) This is demonstrated in the table of spring deflections shown in my earlier post.

Progressive rate springs require increasing amounts of additional force to be applied for any given deflection as compression increases. If the spring in my table were progressive, then the additional force required to deflect the spring by a further 1" would progressively increase as the spring is compressed.

ATB Richard