Design and Manufacturing of Springs

NATIONAL INSTITUTE OF INDUSTRIAL ENGINEERING

Component: Spring

 

By

Abhinav Jaiswal, 2

Ashish Tomar, 20

Design of Springs

Introduction

Spring is defined as an elastic body, whose function is to distort when loaded and to recover to its original shape when the load is removed.

Objectives of Spring

Following are the objectives of a spring when used as a machine member:

1. Cushioning, absorbing, or controlling of energy due to shock and vibration.

Car springs or railway buffers

To control energy, springs-supports and vibration dampers.

2. Control of motion

Maintaining contact between two elements (cam and its follower)

In a cam and a follower arrangement, widely used in numerous applications, a spring maintains contact between the two elements. It primarily controls the motion.

Creation of the necessary pressure in a friction device (a brake or a clutch)

A person driving a car uses a brake or a clutch for controlling the car motion. A spring system keep the brake in disengaged position until applied to stop the car. The clutch has also got a spring system (single springs or multiple springs) which engages and disengages the engine with the transmission system.

Restoration of a machine part to its normal position when the applied force is withdrawn (a governor or valve)

A typical example is a governor for turbine speed control. A governor system uses a spring controlled valve to regulate flow of fluid through the turbine, thereby controlling the turbine speed.

3. Measuring forces

Spring balances, gages

4. Storing of energy

In clocks or starters

The clock has spiral type of spring which is wound to coil and then the stored energy helps gradual recoil of the spring when in operation. Nowadays we do not find much use of the winding clocks.

Before considering the design aspects of springs we will have a quick look at the spring materials and manufacturing methods.

Commonly used spring materials

One of the important considerations in spring design is the choice of the spring material. Some of the common spring materials are given below.

·         Hard-drawn wire:

This is cold drawn, cheapest spring steel. Normally used for low stress and static load. The material is not suitable at subzero temperatures or at temperatures above 1200C.

·         Oil-tempered wire:

It is a cold drawn, quenched, tempered, and general purpose spring steel. However, it is not suitable for fatigue or sudden loads, at subzero temperatures and at temperatures above 1800C.

When we go for highly stressed conditions then alloy steels are useful.

·         Chrome Vanadium:

This alloy spring steel is used for high stress conditions and at high temperature up to 2200C. It is good for fatigue resistance and long endurance for shock and impact loads.

·         Chrome Silicon:

This material can be used for highly stressed springs. It offers excellent service for long life, shock loading and for temperature up to 2500C.

·         Music wire:

This spring material is most widely used for small springs. It is the toughest and has highest tensile strength and can withstand repeated loading at high stresses. However, it cannot be used at subzero temperatures or at temperatures above 1200C.

Normally when we talk about springs we will find that the music wire is a common choice for springs.

·         Stainless steel:

Widely used alloy spring materials.

·         Phosphor Bronze / Spring Brass:

It has good corrosion resistance and electrical conductivity. That’s the reason it is commonly used for contacts in electrical switches. Spring brass can be used at subzero temperatures.

Spring manufacturing processes

If springs are of very small diameter and the wire diameter is also small then the springs are normally manufactured by a cold drawn process through a mangle. However, for very large springs having also large coil diameter and wire diameter one has to go for manufacture by hot processes. First one has to heat the wire and then use a proper mangle to wind the coils.

Helical spring

The figures below show the schematic representation of a helical spring acted upon by a tensile load F (Fig.7.1.1) and compressive load F (Fig.7.1.2). The circles denote the cross section of the spring wire. The cut section, i.e. from the entire coil somewhere we make a cut, is indicated as a circle with shade.

 If we look at the free body diagram of the shaded region only (the cut section) then we shall see that at the cut section, vertical equilibrium of forces will give us force, F as indicated in the figure. This F is the shear force. The torque T, at the cut section and it’s direction is also marked in the figure. There is no horizontal force coming into the picture because externally there is no horizontal force present. So from the fundamental understanding of the free body diagram one can see that any section of the spring is experiencing a torque and a force. Shear force will always be associated with a bending moment.

However, in an ideal situation, when force is acting at the centre of the circular spring and the coils of spring are almost parallel to each other, no bending moment would result at any section of the spring (no moment arm), except torsion and shear force. The Fig.7.1.3 will explain the fact stated above.

Stresses in the helical spring wire:

From the free body diagram, we have found out the direction of the internal torsion T and internal shear force F at the section due to the external load F acting at the centre of the coil.

The cut sections of the spring, subjected to tensile and compressive loads respectively, are shown separately in the Fig.7.1.4 and 7.1.5. The broken arrows show the shear stresses ( τ_T ) arising due to the torsion T and solid arrows show the shear stresses ( τ_F ) due to the force F. It is observed that for both tensile load as well as compressive load on the spring, maximum shear stress (τ_T + τ_F) always occurs at the inner side of the spring. Hence, failure of the spring, in the form of crake, is always initiated from the inner radius of the spring.

The radius of the spring is given by D/2. Note that D is the mean diameter of the spring.

The torque T acting on the spring is

                                                                                                               (7.1.1)

If d is the diameter of the coil wire, then polar moment of inertia, 

 

The shear stress in the spring wire due to torsion is

                                                                                                                 (7.1.3)

Average shear stress in the spring wire due to force F is

                                                                                                                 (7.1.3)

Therefore, maximum shear stress the spring wire is

                                                                                                                                             (7.1.4)

The above equation gives maximum shear stress occurring in a spring. K_s is the shear stress correction factor.

Stresses in helical spring with curvature effect:

What is curvature effect? Let us look at a small section of a circular spring, as shown in the Fig.7.1.6. Suppose we hold the section b-c fixed and give a rotation to the section a-d in the anti clockwise direction as indicated in the figure, then it is observed that line a-d rotates and it takes up another position, say a'-d'. The inner length a-b being smaller compared to the outer length c-d, the shear strain γ_i at the inside of the spring will be more than the shear strain γ_o at the outside of the spring. Hence, for a given wire diameter, a spring with smaller diameter will experience more difference of shear strain between outside surface and inside surface compared to its larger counterpart. The above phenomenon is termed as curvature effect. So more is the spring index (C=D/d) the lesser will be the curvature effect. For example, the suspensions in the railway carriages use helical springs. These springs have large wire diameter compared to the diameter of the spring itself. In this case curvature effect will be predominantly high.

To take care of the curvature effect, the earlier equation for maximum shear stress in the spring wire is modified as,

Where, K_W is Wahl correction factor, which takes care of both curvature effect and shear stress correction factor and is expressed as,

Deflection of helical spring:

                            

Consider a small segment of spring of length ds, subtending an angle of dβ at the center of the spring coil as shown in Fig.7.1.7(b). Let this small spring segment be considered to be an active portion and remaining portion is rigid. Hence, we consider only the deflection of spring arising due to application of force F. The rotation, dφ, of the section a-d with respect to b-c is given as,

 The rotation, dφ will cause the end of the spring O to rotate to O', shown in Fig. 7.1.7(a). From geometry, O-O' is given as,

However, the vertical component of O-O' only will contributes towards spring deflection. Due to symmetric condition, there is no lateral deflection of spring, ie, the horizontal component of O-O' gets cancelled.

The vertical component of O-O', dδ, is given as, 

Total deflection of spring, δ, can be obtained by integrating the above expression for entire length of the spring wire.

Simplifying the above expression we get,

Where, N is the number of active turns and G is the shear modulus of elasticity. Now what is an active coil? The force F cannot just hang in space, it has to have some material contact with the spring. Normally the same spring wire e will be given a shape of a hook to support the force F. The hook etc., although is a part of the spring, they do not contribute to the deflection of the spring. Apart from these coils, other coils which take part in imparting deflection to the spring are known as active coils.

The above equation is used to compute the deflection of a helical spring. Another important design parameter often used is the spring rate. It is defined as,

Here we conclude on the discussion for important design features, namely, stress, deflection and spring rate of a helical spring.

Design of helical spring for variable load

In the case of a spring, whether it is a compression spring or an extension spring, reverse loading is not possible. For example, let us consider a compression spring placed between two plates. The spring under varying load can be compressed to some maximum value and at the most can return to zero compression state (in practice, some amount of initial compression is always present), otherwise, spring will loose contact with the plates and will get displace from its seat. Similar reason holds good for an extension spring, it will experience certain amount of extension and again return to at the most to zero extension state, but it will never go to compression zone. Due to varying load, the stress pattern which occurs in a spring with respect to time is shown in Fig.7.2.1. The load which causes such stress pattern is called repeated load. The spring materials, instead of testing under reversed bending, are tested under repeated torsion.

From Fig.7.2.1 we see that,

                                                                                                                          (7.2.1)

Where, τ_a is known as the stress amplitude and τ_m is known as the mean stress or the average stress. We know that for varying stress, the material can withstand stress not exceeding endurance limit value. Hence, for repeated torsion experiment, the mean stress and the stress amplitude become,

                                                                                                                           (7.2.2)

Soderberg failure criterion:

The modified Soderberg diagram for repeated stress is shown in the Fig 7.2.2.

The stress being repeated in nature, the co-ordinate of the point a is ( τ_e/2, τ_e/2). For safe design, the design data for the mean and average stresses, τ_a and τ_m respectively_, should be below the line a-b. If we choose a value of factor of safety (FS), the line a-b shifts to a newer position as shown in the figure. This line e-f in the figure is called a safe stress line and the point A (τ_m, τ_a) is a typical safe design point.

Considering two similar triangles, abc and Aed respectively, a relationship between the stresses may be developed and is given as,

                                                                                                                              (7.2.3)

where τ_Y is the shear yield point of the spring material.

In simplified form, the equation for Soderberg failure criterion for springs is

                                                                                                                               (7.2.4)

The above equation is further modified by considering the shear correction factor, K_s and Wahl correction factor, K_w. It is a normal practice to multiply τ_m by K_s and to multiply τ_a by K_w.

                                                                                                                               (7.2.5)

The above equation for Soderberg failure criterion for will be utilized for the designing of springs subjected to variable load.

Estimation of material strength

It is a very important aspect in any design to obtain correct material property. The best way is to perform an experiment with the specimen of desired material. Tensile test experiments as we know is relatively simple and less time consuming. This experiment is used to obtain yield strength and ultimate strength of any given material. However, tests to determine endurance limit is extremely time consuming. Hence, the ways to obtain material properties is to consult design data book or to use available relationships, developed through experiments, between various material properties. For the design of springs, we will discuss briefly, the steps normally used to obtain the material properties.

One of the relationships to find out ultimate strength of a spring wire of diameter d is,

                                                                                                               (7.2.6)

For some selected materials, which are commonly used in spring design, the values of A_s and m_s are given in the table below.

The above formula gives the value of ultimate stress in MPa for wire diameter in mm. Once the value of ultimate strength is estimated, the shear yield strength and shear endurance limit can be obtained from the following table developed through experiments for repeated load.

Hence, as a rough guideline and on a conservative side, values for shear yield point and shear endurance limit for major types of spring wires can be obtained from ultimate strength as,

                                                                                                                                 (7.2.7)

With the knowledge of material properties and load requirements, one can easily utilize Soderberg equation to obtain spring design parameters.

Types of springs

There are mainly two types of helical springs, compression springs and extension springs. Here we will have a brief look at the types of springs and their nomenclature.

1.     Compression springs

Following are the types of compression springs used in the design.

In the above nomenclature for the spring, N is the number of active coils, i.e., only these coils take part in the spring action. However, few other coils may be present due to manufacturing consideration, thus total number of coils, N_T may vary from total number of active coils.

Solid length, L_S is that length of the spring, when pressed, all the spring coils will clash with each other and will appear as a solid cylindrical body.

The spring length under no load condition is the free length of a spring. Naturally, the length that we visualise in the above diagram is the free length.

Maximum amount of compression the spring can have is denoted as δ_max , which is calculated from the design requirement. The addition of solid length and the δ_max  should be sufficient to get the free length of a spring. However, designers consider an additional length given as δ_allowance. This allowance is provided to avoid clash between to consecutive spring coils. As a guideline, the value of δ_allowance is generally 15% of δ_max.

The concept of pitch in a spring is the same as that in a screw.

The top and bottom of the spring is grounded as seen in the figure. Here, due to grounding, one total coil is inactive.

In the Fig 7.2.5 it is observed that both the top as well as the bottom spring is being pressed to make it parallel to the ground instead of having a helix angle. Here, it is seen that two full coils are inactive.

It is observed that both the top as well as the bottom spring, as earlier one, is being pressed to make it parallel to the ground, further the faces are grounded to allow for proper seat. Here also two full coils are inactive.

2.     Extension springs

Part of an extension spring with a hook is shown in Fig.7.2.7. The nomenclature for the extension spring is given below.

Body length, L_B: d (N + 1)

Free length, L : L_B + 2 hook diameter.

here, N stands for the number of active coils. By putting the hook certain amount of stress concentration comes in the bent zone of the hook and these are substantially weaker zones than the other part of the spring. One should take up steps so that stress concentration in this region is reduced. For the reduction of stress concentration at the hook some of the modifications of spring are shown in Fig 7.2.8.

Buckling of compression spring

Buckling is an instability that is normally shown up when a long bar or a column is applied with compressive type of load. Similar situation arise if a spring is too slender and long then it sways sideways and the failure is known as buckling failure. Buckling takes place for a compressive type of springs. Hence, the steps to be followed in design to avoid buckling are given below.

Free length (L) should be less than 4 times the coil diameter (D) to avoid buckling for most situations. For slender springs central guide rod is necessary.

A guideline for free length (L) of a spring to avoid buckling is as follows,

 For steel,

Where, C_e is the end condition and its values are given below

Ce                 End condition

2.0         fixed and free end

1.0         hinged at both ends

0.707   hinged and fixed end

0.5         fixed at both ends

If the spring is placed between two rigid plates, then end condition may be taken as 0.5. If after calculation it is found that the spring is likely to buckle then one has to use a guide rod passing through the center of the spring axis along which the compression action of the spring takes place.

Spring surge (critical frequency)

If a load F act on a spring there is a downward movement of the spring and due to this movement a wave travels along the spring in downward direction and a to and fro motion continues. This phenomenon can also be observed in closed water body where a disturbance moves toward the wall and then again returns back to the starting of the disturbance. This particular situation is called surge of spring. If the frequency of surging becomes equal to the natural frequency of the spring the resonant frequency will occur which may cause failure of the spring. Hence, one has to calculate natural frequency, known as the fundamental frequency of the spring and use a judgment to specify the operational frequency of the spring.

The fundamental frequency can be obtained from the relationship given below.

Fundamental frequency :

                                                                                                                                                                                                  Both ends within flat plates           (7.2.9)

                                                                                                                                                                    One end free and other end on flat plate.   (7.2.10)

Where,

K: Spring rate

W_S : Spring weight = 2.47γd²DN

            and d is the wire diameter, D is the coil diameter, N is the number of active coils and γ is the specific weight of spring material.

The operational frequency of the spring should be at least 15-20 times less than its fundamental frequency. This will ensure that the spring surge will not occur and even other higher modes of frequency can also be taken care of.

Spring Manufacturing Process