Spring Design a Designer s Guide

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Springs & Pressings


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Nobody ever thinks about springs at

all, until theyre broken! Its true. And,

I get many visitors to my home in Bolton,

wanting to see my steam workshops. As

well as my steam engines, theres also a

good b i t o f indust r ia l s tu f f and

engineering tackle that Ive saved from

the scrap man and put to good use. You

see, engines have always fascinated me

right from being a kid.

When I was approached to write the

foreword for this book, I started to

consider all the machines that Ive come

anyway, how do you choose which spring

is right for your application when they

vary so much in type and design? Theres

wire or flat strip, the tolerance to specify,

and will the heat treatment lead to

dimensional variation? What about

surface finish: do you need to paint,

electroplate, shot-peen or what? Its all

rather interesting once you get into it,but you do need advice you can trust.

Now take this grand little book here. It

provides guidance on all these points and


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Spring 1. a spring is a device for storing mechanical energy when displaced.2. a good spring is one which under load can take considerable deflection, and

return to its equilibrium without undergoing any lasting dimensional change.

Springs are everywhere!Almost every machi ne t hat i s

developed incorporates some form of

spring, from telephones, and domesticappliances through to engines and

medical devices and unless the spring

is working correctly, the application

will fail. Spring reliability is crucial,

and statistics show that correct springdesign is the most important factor in

ensuring long life.

and redesign costs and ensures that

the spring design is the most reliable,

cost-efficient and long-lasting it

can be.

The spring designer is a valuable

partner to engineering designers in

both streamlining new product and

machine design as well as reducingrisk, and this book will take an

engineering designers perspective.

Springs and pressings manufactured


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Spring Materials - The right material for the jobSpring materials are chosen for their strength and are amongst the strongest materials

used in industry. Springs are designed to work to far greater working stresses than virtually

any another component. For instance, helically wound compression springs are able to bestressed to 70% or greater, than the ultimate tensile strength of the material. Also spring

materials have to be able to work in extreme environments such as elevated or low

temperatures and corrosive solutions and be able to undergo extreme dynamic loading,

and shock loading. Spring materials are also utilised for their electrical and magnetic

capabilities.

There are many different types of materials available to the spring designer. In this section

we will deal with the more commonly used spring wire materials. Strip materials will be

discussed later.

For general engineering purposes spring steels are the best choice for the designer, due to

their relative low cost and their wide availability. They also are the strongest materials that

the designer can choose.


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The grades also refer to the material surface finish and therefore dynamic qualities

as follows:

Due to the fact that the mechanical strength is obtained through the drawing process, asthe size of wire increases, so the ultimate tensile strength of the material decreases.

Some of the above grades are available pre-drawn with a zinc or aluminium/zinc coating

that will give sufficient corrosion protection for non-arduous applications. Otherwise

the above materials, like all carbon or low alloy steels will require some form ofcorrosive protection.

Other types of spring material are low alloy or carbon pre-hardened and tempered steels.

These materials are drawn annealed and are then hardened by the wire manufacturer to

produce a high strength material. These are stronger than cold drawn materials above the

size of 2.00mm. The mechanical strength for these materials is obtained through thehardening process, so the ultimate tensile strength does not depend on the wire size. In


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mechanical properties and corrosion protection. Generally stainless steels are about 20%

weaker than spring steels of the same size, but there are precipitation hardening grades

that are nearly of equivalent strength.

Stainless steel grades are covered by BS2056 1991, and the grades generally used are301526, 302526 both similar having 17%/18% chromium and 7%/8% nickel respectively.

These grades are used widely, but for greater corrosion resistance especially salt water,

grades 316533 and 316542 are used, having molybdenum added for improved resistance

to chlorides.

The stainless grades detailed above all get their strength from the cold drawing process.

This process makes the materials slightly magnetic. If very low magnetic permeability is

required there are two stainless grades that can be used. These are 305511 and 904514,

which are virtually free from residual magnetism.

If greater strength is required, precipitation-hardening stainless steels can be used. After

the springs are manufactured they are heat treated at 480C. This causes small

precipitates to grow through the material, increasing the ultimate tensile strength. For

example, in the as drawn condition, l.OOmm wire has a minimum ultimate tensile strengthof 1710 N/mm2, while after heat treatment this is increased to 2030N/mm*. This increaseis at the cost of a slightly inferior corrosion performance than 302526 and 301526.


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It is generally recommended that all spring materials are subjected to a stress-relieving

operation after forming. In the case of cold drawn spring steel this would be at a

temperature between 220C and 375C for 10 minutes to 1 hour depending on the type ofspring and its application. The object of this is to reduce the stresses introduced during

coiling, especially in the case of compression and extension springs, as these stresses are

not beneficial. Stress relieving also slightly increases the elastic limit of the material

and stabilises the springs dimensions. The problem with stress relieving is that as

the coiled in stresses are removed, the spring will move and this leads to dimensionalchange. This dimensional change has to be taken into account by the spring maker

before coiling.

Stress relieving is often not carried out on extension springs as the heat treatment reduces

the amount of initial tension.

Compression springs are widely used throughout industry as they are relatively simple to

produce and have excellent static and dynamic properties.

Given that compression springs are the most widely used helically wound springs,

more detail will be given here than in the next chapter on extension or torsion springs.

However, many of the design details listed below are equally relevant to extension and


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Nomenclature and Units


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The spring rate is the increase in load for a given deflection. If the loads and deflection of

a spring are known, spring rate can be easily calculated using the following equation:

For a compression spring of known dimensions the following formula can be used:

It should be noted that in the above formula the wire size is to the fourth power and the

mean diameter is cubed, therefore small changes in wire diameter and mean diameter can

lead to large changes in spring rate. This is an important consideration in calculating

spring tolerances.

Therefore the load at any deflection can be calculated from:

The theoretical solid load can be calculated from:


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The factor K is the curvature correction factor, used to correct for the uneven stress

distribution across the section stemming from the curvature of the wire. The formula

below is the Sopwith curvature correction factor.

It should be noted that the greatest stress is at the inside face of the spring. This is

why when the spring is operating over a shaft, great care must be taken to give the

correct clearances.

The MATERIAL REFERENCE TABLE on page 6 gives the maximum allowable static stresses

as a percentage of the ultimate tensile strength of different materials. Values of ultimate

tensile strength can be found in the relevant British Standards.

If the spring is operating dynamically, more care needs to be taken with the design(see section on Factors affecting the Fatigue Performance of Helically Wound Springs, page 21).

Conical Springs are used when the application requires a non-linear spring rate and/or

where space is limited.

The non-linear spring rate is created when the spring is coiled so that when the spring is

deflected, coils begin to contact. The larger coils move farther as they have the lowest

Conical springs can also be coiled so that when the spring is compressed the coils lie inside


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Conical springs can also be coiled so that when the spring is compressed the coils lie inside

each other. The spring will then have a solid length of one wire diameter. This is very useful

when the space is restricted (see diagram 3).

The design of conical compression springs is much more complex than that of parallel-sided springs. The calculations can only give an approximation of the springs behaviour

as small changes in the pitch of the spring can produce large changes in the load/

deflection characteristics.

Nesting springs means to have one or more springs sitting inside a larger spring. Nested

springs enable the spring designer to get more loadbearing material into a fixed space. By

so doing, the springs are able to support a greater load than one spring alone could


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The difference between helical compression and helical extension springs is in the

direction of load application and the method by which it is applied. In order to apply the

force, special end forms generally have to be used, either utilising the formed end coils,or special screwed-in inserts. Examples of end form inserts are shown below.

The more complex the end formation, the greater the manufacturing tolerances and the

greater the likely manufacturing cost.

The formulae used to calculate extension springs are very similar to those of compression

springs except for an extra property called initial tension.


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Initial tension can be calculated by taking measured loads at lengths and using the

formula below:

The spring rate of an extension springs is calculated using the same formula as forcalculating compression springs:

It should be noted that in the above formula the wire size is to the fourth power and themean diameter is cubed, therefore small changes in wire diameter and mean diameter can

lead to large changes in spring rate, an important factor in calculating spring tolerances.

Therefore the load at any deflection can be calculated from:

If th i i ti d i ll d t b t k ith th i d i


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If the spring is operating dynamically, more care needs to be taken with the springs design

(see section on Factors affecting the Fatigue Performance of Helically Wound Springs).

The mode of operation of torsion springs is different from compression springs and

extension springs. Compression and extension springs are stressed in torsion,

whereas torsion springs are stressed in bending. A torsion spring is, in effect, a wound-up cantilever.

Torsion springs supply or withstand torque, tosupply this torque torsion springs require

some form of spring leg. The type of spring leg is dictated by the application and can be

as simple as a tangential straight leg or much more complex. It should be noted that it is

best to keep the legs as simple as possible to reduce manufacturing tolerances and

manufacturing difficulties.

A number of leg forms can be seen below.


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It should be remembered that when torque is applied to a torsion spring, thefollowing happens:

l The number of coils increases hence the body length increases. The body length

increases by one wire size for every 360 of deflection. This can mean that, if not

enough space has been allowed within the application, the spring will bind, and this

will probably lead to spring failure.

l The mean diameter of the spring decreases. This is important to remember as most

torsion springs work over a shaft. If not enough clearance is allowed between the shaft

and the spring the spring will bind onto the shaft The legs will then take all of the

If the springs dimensions are known, the following formula can be used:


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If the springs dimensions are known, the following formula can be used:

The above formula takes into account the deflection due to the applied torque.

The torque/deflection curve for a torsion spring is generally not a straight line. It is more

like the diagram shown below.

The torque when unloading is less than the torque when winding up for the same position.

This is due to friction within the spring and the mechanism. One way to reduce this is to

In the springs working position the body length is:


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The bending stress for torsion springs can be calculated using the following:

Where K, the stress correction factor, = Cc - 0.75

With torsion springs, the applied stress is in bending. Because of this torsion springs

can be operated to higher stress levels than compression and extension springs.

Unprestressed torsion springs can be stressed up to 70% of the ultimate tensile strength

of the material, and prestressed torsion springs can be stressed up to 100% of the ultimate

tensile strength.

The spring designer should reduce these figures by 15% to ensure that the spring is never

overstressed either in operation or during installation.

If the spring is operating dynamically, more care needs to be taken with its design (see

The factors that affect the fatigue performance of springs in the main are:


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g p p g

l Working Stress

l Material Surface Quality

l Wear

In operation springs generally work between two fixed positions. The working stress at

these positions can simply be calculated, the results can then be used to predict the

working life of the spring. To do this, Goodman diagrams need to be used, these are based

on data that has been obtained through many years of experimentation at centres such as

The Institute of Spring Technology. Goodman diagrams are available for the many different

grades and types of material used.

An example of a Goodman diagram is shown below. To calculate the expected life of -the

spring the working stresses are plotted against the relevant axis. If the intersection of the

plotted stresses falls within the shaded area, the spring can be expected to work for the

number of cycles the graph represents. Generally the graphs represent 95% surety, i.e. 95%

of the springs can be expected to achieve the number of cycles.

The majority of Goodman diagrams only apply to compression springs.

Extension springs suffer a number of problems when operating in a dynamic environment,


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they are:

l Breakage near the loop

The most common cause of failure in extension springs is when the loop of the spring

breaks off in the area where the hook meets the body of the spring. This point of

transition between the spring body and the loop is generally the point of highest

stress. The loops are subjected to a bending stress and torsion stress and the majority

of Goodman diagrams for spring materials are for materials stressed in torsion.

l Tooling marks creating stressWhen loops are formed in extension springs small tooling marks are unavoidably

created. Such marks are stress raisers which increase the likelihood of a failure at

this point.

l Loop bends too small

Another reason is that sometimes loops are formed using bends that are too small.

A small radius is a stress raiser.

Different types of end loop will lead to different fatigue performances.

There are two available solutions:

l Use a loop with a transition radius between the spring body and the end loop of

approximately the body radius.

If an extension spring is required to work dynamically, it must be remembered that


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extension springs have approximately 20% lower performance with regard to fatigue than

compression springs.

4 The lower the working stresses the greater the expected life of the spring.

Material surface quality is important when seeking to avoid risk of spring failure. Fatigue

cracks generally propagate from the surface of the material, therefore the greater the

surface quality, the better the fatigue performance. It is possible to improve the surfacequality by a number of methods. Most popular is Shot-peening.

Shot-peening involves firing small rounded beads of material at the surface of the spring.

This will lead to a small residual compressive stress on the material surface which lowers

the chance of a fatigue crack propagating and increases the working stresses possible.Shot-peening is generally carried out only on compression springs and large leaf springs

as the shot would get trapped in the coils of close wound torsion and extension springs.

Also, the inside face of the coils would not be peened and this would eliminate the benefitsof the process.

* The betterthe surface quality ofthe material, the betterthefatigue performance.

This is mainly due to the friction and wear between the spring and the shaft that it is


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working over and the leg fixings. This can be reduced by good design, but is unlikely to be

eliminated.

Other factors that affect the fatigue performance include corrosion, material cleanlinessand speed of operation. Any questions regarding these or any of the above should be

directed to the author.

* Removing the possibility of wear in a spring application will improve the springs

fatigue performance.

When a spring is prestressed there are dimensional changes. This means that the

springmaker must allow for this during manufacture.

The prestressing operation for compression springs is relatively simple. Once the spring has

been coiled, stress relieved and ground, the spring is placed on a press or similar and


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As with wire, there is a wide range of strip materials available to the spring manufacturer.

As many parts produced in strip are not primarily used as a spring, many low strength

alloys are used, generally for their formability and electrical conductivity.

Strip materials can be obtained in different grades of hardness, and some spring materials

are able to be heat treated to increase their strength and hardness.

Due to the vast range of materials available this section will deal with carbon steels,stainless steels and copper alloys only. If you require more information on materials such

as nickel alloys, please contact the author.

There are a number of grades of carbon steel strip. These grades are classified according

to the carbon content, the method of manufacture and whether a heat treatment is used.

Annealed carbon steel strip is used where formability is required, a heat treatment after

forming will increase the materials strength and hardness. Where formability is not an

issue there are heat treated grades of spring steel and texture rolled materials. These

materials are obtained in the hard condition and are used in applications such as clock

springs and seat belt retaining springs.

British Standards for annealed spring steels include BS5770 Pt 2 and CS95


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These materials are widely used for their corrosion resistance, their ability to withstand

elevated temperatures and their resistance to relaxation.

Stainless steels are generally obtained in the hard rolled condition, strip components

designed to be manufactured from stainless steels should take the effect of spring

hardness into account.

Stainless steels are about 20% weaker than heat treated springs steels of the same size.As the hardness of stainless steel is generated during the cold rolling process, the work

hardening will cause the stainless steel to be slightly magnetic.

British Standards covering stainless steel strip materials include BS5770 Pt 4 302525,

301521, 316516. All these grades can be obtained in varying levels of spring hardness,depending on the thickness of the material.

Copper-based alloys are used where high electrical and thermal conductivity and or where

being non-magnetic is a priority. Copper-alloys also exhibit good atmospheric corrosion

resistance, but as the majority of copper-alloy strip components are used as electrical

contacts many copper parts are electro-plated.


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The fatigue performance of strip materials is greatly affected by the edge and surface

condition. It is possible to purchase some strip materials with a dressed or rounded edge

which greatly improves the fatigue performance, but if the components are punched outof the material, the edge finish will depend of the performance of the tooling.

Flat strip parts can be very complicated in their form. Inside many products such as mobile

phones, computers and medical equipment there are a wide variety of shapes all formed

from a simple coil or sheet of flat material. Many flat strip parts are designed to perform

more than one mechanical function thereby reducing the number of components.

The number of different variations of strip parts is virtually infinite. The only obstacle to

strip design is the imagination of the designer, and the practical limitations of

manufacture.

The simplest strip spring is probably a leaf spring operating as a cantilever, with simple-to-calculate loads and deflections. Many strip parts are, in effect, made up of a number of

sections operating as cantilevers.

Strip springs are not limited to just simple cantilevers. There are spring washers such as

disc springs which are able to provide a high spring rates over a small movement, and


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t = thickness

The direction of rolling is along the strip.

The bend radius refers to the inside bend radius.

Going below the above figures would prove to be difficult, and may lead to cracking of thematerial on the outside bend radius of the material.

As can be seen, the orientation of the bend on the strip affects the minimum bend radius.

If a component requires bends perpendicular to each other with radii close the minimum

bend radius, it is good design practice to orientate the component by 45 relative to the

rolling direction.

Avoid punched holes or slots too close to the edge of the component or another hole.

This can cause the hole to deform the edge or the other hole.


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Due to the complexity of strip parts, the calculations of force and stress are much more

complex than those for helical compression, extension and torsion springs.

Depending on the shape and loading of the component a number of standard equations

exists (see diagram 71).

If the part does not correspond to any of these parts, more complex solutions must

be sought.

A more accurate calculation tool is Custiglianos 2nd theorem. The component is brokendown into a number of sections comprising of beams and curved sections. The sections can


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There are a number of ways flat strip components can be produced, generally depending

on the volume required. When a small number of components are required e.g. prototype

samples, it is possible to produce most parts without tooling. Wire-eroding or chemical

milling can produce development blanks where required, and standard tools can be used

to form the parts to the required dimensions. This process is time consuming but allows

the customers to have parts without investing in production tooling.

If the volume is larger, components can be blanked out on tooling, and formed in

subsequent operations on separate equipment. The tooling cost is relatively small and

increases the production speed considerably over the previous process. For medium to high

volume production, the flat strip component is manufactured complete on one piece of

equipment. The two main ways on achieving this is by using progression tooling or multi-slide form tools.

When producing parts on progression and multi-slide tooling, the developed components

are not completely blanked out. A small section of material is left to carry the part

forwards to the subsequent forming stages.

In progression tools the material is indexed forward to each forming stage. As the part

progresses through the tool the component undergoes a sequence of forming operations,

until the part is fully formed. The last stage cuts out the section of material that has

In multi-slide tools there is an initial blanking stage, but then the material is indexed

forward to where a number of forming slides operate These slides are able to move


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forward to where a number of forming slides operate. These slides are able to move

forward and backwards along their axis, controlled by either cams or servomotors. On the

ends of the slides there are forming tools designed specifically for the component. During

the forming operation the slides move inwards in a predetermined pattern, bending thematerial as desired, and parting the component from the strip. The number of slides

employed in this procedure is determined by the complexity of the finished component

(see diagram 13).

These tools are complex to design but are ableto produce finished parts at very high speed

allowing very low unit prices.

Using new CAD technology it is possible to

design tooling for strip components preciselyand very quickly, allowing us to design the

tooling as efficiently as possible.

The simplest method is to simply oil or grease the springs. This should give sufficient

corrosion protection for springs in transit or in storage pro iding the conditions are not


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corrosion protection for springs in transit, or in storage providing the conditions are not

too testing.

Another method of protecting the springs from corrosion is by either plastic coating orpainting. The problem with this method is that the protection is only effective until it is

damaged. The spring material will then be liable to corrosion underneath the finish.

A metallic finish is more generally used. The easiest method is as stated earlier, to

manufacture the spring from carbon steel, wire drawn with a galvanised coating. This may

be sufficient in some circumstances, if not, a better protection is required.

A popular method of obtaining a metallic finish is to electroplate the springs. It is

important to use the correct electroplated metal as this is the key to good corrosionresistance. Zinc plate and cadmium (rarely used due to its toxicity) corrode in preference

to steel and so will protect even when the surface coating is damaged. Nickel, copper and

chromium plate, when damaged, will lead to the steel corroding in preference to. the

surface coating and so is not recommended. Nickel plate is only generally used when the

component will undergo soldering, and so is used widely in the electronics industry.

It is important to note that with electroplating there is a risk of hydrogen embrittlement.

This ill lead to component fail re hen it is loaded To minimise the risk a


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Documents

Spring Design a Designer s Guide