Some Notes on Springs

Some Notes On Springs

by Mr. H.J. Coventry

The Modelmaker, Volume 7, Number 4, April 1930

How many times has the question been asked by the amateur model maker "what size material shall I use" or how man springs have been made of different sizes of material, different number of coil springs, or different thickness, width and number of leaves in leaf springs in an endeavor to obtain one that will suit a given set of conditions?

If we analyze the factors that make up spring design, we will find the following interrelated main groups. Those factors that may be classed as "physical" and a second group that may be classed as "dynamic." Under the former heading we would have the dimensions of the spring as a whole as well as its parts, while the latter would embrace the loads and the deflections or movement under any particular load.

We will now have to consider particular types of springs, and while there are quite a variety made to meet particular conditions the amateur model maker will probably only need "leaf springs" of the type known as "semi" or "full elliptic" and "spiral springs" of round wire.

Taking a leaf spring (Fig. 1) we will note that it consists of a number of leaves of certain thickness and width also that the longest leaf is a definite distance from eye to eye or span and the others are evenly reduced or graduated in length. If we support the spring by its eyes and place a "load" on its center it will be seen to deflect and in doing so will "stress" the material of which the spring is made. "Stress" is a definite load per unit of area, usually one square inch, and this term must not be used when "load" is meant.

Now we have seven factors to deal with and perhaps it may be seen why a mere hit and miss method of spring making is likely to benefit no one but the metal merchant. All seven factors must harmonize to produce any desired spring and this harmony can be expressed as an equation. Before doing this however, let us consider a single plate or leaf cut diamond shape, Fig. 2, supported at ends and loaded at center with load (W). The equation that harmonizes the load factors above mentioned is given by

where

W = Maximum safe load in pounds

S = Safe stress in pounds per square inch

t = Thickness of plate in inches

L = Span in inches

Now the stress in such a plate will be uniform throughout its length and if we clip off a narrow strip each side and keep on till the middle strip is reached and then pile all the pairs of strips on one another, we will obtain a theoretical ideal spring. In other words instead of having a wide one leaf spring, we will have a multiple narrow leaf spring of exactly the same characteristics as far as load capacity and deflection is concerned. It will now be apparent why springs of this type have leaves of evenly decreasing length and also why the ends should be either pointed or tapered. It will also be seen that an ideal spring would have a very short bottom leaf. Practical considerations will, of course, modify, for we must have a buckle and also the ends of top leaf must be square to take hangers or eyes, but the nearer to the ideal form the spring is made the better.

We can now write our equation:

W = 2 S n b t^2 / 3 L

because instead of using one leaf of width B we will use a number of leaves (n) each of width (b). Expressed in terms this merely means that: the load W is numerically equal to twice the stress multiplied by the number of leaves, the width of leaves and the thickness squared (i.e. the thickness multiplied by itself) and divided by three times the span.

For spring steel the stress is usually taken by 80,000 lbs. per sq. in. and by placing this in our equation and eliminating the numerals we obtain

W = 53,333 n b t^2 / L

This is the usual form and may be taken for any size semi-elliptic spring whether model or full size. If definite values are placed in and the equation worked out the amateur will very readily discovered why an actual spring, say a locomotive spring when exactly reduced to scale would be far too stiff for the model.

Now a clear idea of relative proportioning can be obtained by merely examining this formula. Thus we can say that the Capacity or Maximum safe load is:

• (a) Directly proportional to the number of leaves
• (b) Directly proportional to the width of leaves
• (c) Directly proportional to the square thickness of leaf
• (d) Indirectly proportional to span

Thus we may increase the capacity of any given spring by increasing the number of leaves, their width or both, or by decreasing the span, the capacity increasing in exact proportion with the changes, but if we increase the thickness of leaves the capacity will be much more rapidly augmented, doubling the thickness would raise the capacity four times.

Before we are in a position to design any particular spring we have to consider the relation between the load and the deflection; as in the above equation we have only considered the capacity or maximum safe load in relation to the resistance or strength of the material.

The deflection for the load W is given by

d = L^2 / 1270 t

where (d) equals the deflection in inches and (L) and (t) as before.

Now note that the deflection is directly proportional to the square of the span and indirectly proportional to the thickness of leaf, also note that the width and number of leaves do not influence the deflection, (L) and (t), being constant. that is to say the addition of leaves to a spring will increase the carrying capacity but the deflection under this increased load will be precisely the same as that under the capacity load before the alteration.

To illustrate use of above considerations, suppose we need a leaf spring of 2 inch span, to carry 10 pounds maximum load and constructional requirements limit the width of leaves to 1/4 inch, and the deflection under this is to be 3/8 inch.