Optimization of Spring

Optimization of Steel Helical Spring by Composite Spring

Journal: International Journal of Multidisciplinary Sciences and Engineering, Vol. 3, No. 6, June 2012

Author: Mehdi Bakhshesh and Majid Bakhshesh

Summary by:

Abhinav Jaiswal, 2

PGDIE 42 

Abstract:

Springs that can reserve high level of potential energy, have undeniable role in industries. Helical spring is the most common element that has been used in car suspension system. In this   research,   steel   helical   spring   related   to   light   vehicle suspension system under the effect of a uniform loading has been studied and finite element analysis has been compared with analytical solution. Afterwards, steel spring has been replaced by three different composite helical springs including E-glass/Epoxy, Carbon/Epoxy and Kevlar/Epoxy.   Spring   weight, maximum stress and deflection have been compared with steel helical spring and factors of safety under the effect of applied loads have been calculated.  It   has been shown that spring optimization by material spring changing causes reduction of spring weight and maximum stress considerably. In any case, with changing fiber angle relative to spring axial, composite spring properties have been investigated.

Introduction

Helical springs are simple forms of springs, commonly used for the suspension system in wheeled vehicles. Vehicle suspension system is made out of springs that have basic role in power transfer, vehicle motion and driving. Therefore, springs performance optimization plays important role in improvement of car dynamic. The automobile industry tends to improve the comfort of user and reach appropriate balance of comfort riding qualities and economy. There is increased interest in the replacement of steel helical spring with composite helical spring due to high strength to weight ratio. On the other hand, there is a limitation at the amount of applied loads in springs. The increase in applied load makes problem at geometrical alignment of car height and erodes other parts of car. So, springs design in point of strength and durability is very important. Reduction of spring weight is also principal parameter in improvement of car dynamic. By replacement of steel helical spring with composite helical spring will reduce spring weight in addition to resistance raise under the effect of applied loads.  In this research, a static analysis is employed to investigate behaviour of steel and composite helical spring related to light vehicle suspension system. Steel spring has been replaced by three different composite helical in ANSYS software and results have been compared with analytical solution. The objective is to compare the load carrying  capacity, stiffness and  weight savings  of composite  helical  spring  with  that  of  steel  helical  spring.

Advanced composite fibers such as glass, carbon and Kevlar- reinforced suitable resins, are expected to be widely used in vehicle  suspension  system  application  so  that  spring  of different  shapes  can  be  obtained.  This refers to the high specific strength (strength-to-density ratio) and high specific modules (modules-to-density ratio) of this advanced composite materials. The method used for the production of the springs is a variation of the RTM (Resin Transfer Molding) process. Through this method, the dry braids are positioned in the mold before being impregnated with the resin, making production very clean. In this case, an open mold consisting of a helically grooved mandrel is used, and the braids are impregnated by plunging in a bowl filled with resin.

Many studies are carried out to investigate the behaviour of composite springs. Senthil Kumart and Vijayarangan investigated behaviour of composite leaf spring for light passenger vehicles. Compared to steel spring, the composite leaf spring was found to have lesser stress, higher stiffness and higher natural frequency than that of existing steel leaf spring and weight of spring was reduced by using optimized composite leaf spring. They also concluded that fatigue life of composite leaf spring was more than that of conventional steel leaf spring.

Solid Modeling of Metal Helical Spring

Helical springs have the characteristic parameters that affect their behaviours. In addition to the physical properties of its material, the wire diameter (d), loop diameter (D), number of loops (Na) and the distance between two consecutive loops (P) are the parameters that affect the behaviour of spring. These parameters have been illustrated in Fig. below:

                           

Before analysis of helical spring, the rate of spring, shear modulus and poison coefficient are needed to be calculated.

Simulation of Steel Helical Spring

Spring  Geometry is  modeled  in  SOLIDWORKS  software and  then  is  analyzed  under  uniform  loading  condition  in ANSYS Software. Axial displacement and shear stress have been compared with analytical results. Load is in direction of spring axis and is exerted on the one end of spring and other end is fixed in X, Y and Z directions. Meshes with different resolutions are generated to insure grid independence. Element selected for this analysis is SOLID45. SHELL element does not show stress variation in the course of diameter. BEAM element represented stress along the length only and doesn't show other information about stress. SOLID92 is a pyramid element that increases time of calculations and it has error in nonlinear complex models.  Therefore, a cubic SOLID45 element has been used in the stress analysis. This element is defined  by eight nodes  having three degrees of freedom  at  each  node:   translations  in  nodal  x,  y  and  z directions.

Replacement Steel Spring with Composite Spring

Steel helical spring has been replaced by three different composite helical springs including E-glass/Epoxy, Carbon/Epoxy and Kevlar/Epoxy. The loading conditions are assumed to be static. Spring Shear stress has been obtained using FEM and has been compared with steel helical spring. Composite spring properties have been studied with changing fiber angle relative to spring axial. The element is SOLID 46, which is a layered version of the 8-nodes structural solid element to model layered thick shell or solids. The element has three degree of freedom at each node and allows up to 250 different material layers.

A. Composite helical spring weight

Before modeling of composite helical spring, its weight has been calculated and compared with steel helical spring. Helical spring weight can be written as:

where, Na is no. of active loops, d is wire diameter 

and p is weight per unit volume that can be calculated by

where; V_f , p_m is fiber volume and its density, V_m , p_f  is resin volume and its density.

Results for different percentage of fiber have been shown in Table below: 

Compared to steel helical spring, Composite helical spring has been found to have lesser weight. Also it is concluded that changing percentage of fiber, especially at Carbon/Epoxy composite, does not affect spring weight.

B. Direction of Fiber in Composite Helical Spring

Spring strength must be calculated at fiber along and fiber vertical direction and can be written as:

where, E_a is strength of composite helical spring at along of fiber and E_m is its strength in vertical direction of fiber.

Angle fiber has been changed so that fiber position has been considered in direction of loading, perpendicular to loading and at angles of 30 and 45 degree relative to applied loads. In every case, three different composite helical springs including E-glass/Epoxy, Carbon/Epoxy and Kevlar/Epoxy have been considered and longitudinal displacement and shear stress have been calculated to analyze the effect of spring material upon spring behaviour. Longitudinal displacement under the effect of fiber angle has been shown in Fig. below :

Spring has the least longitudinal displacement when fiber position has been considered to be in direction of loading. With changing fiber angle, spring longitudinal displacement increases so that it reaches the greatest value when fiber position has been considered to be perpendicular to loading. Also, it shows that E-glass/epoxy composite helical spring has the most flexibility and Carbon/Epoxy composite helical spring has the least displacement.

Shear stress under effect of fiber angle has been shown in Fig. below:

Spring has the most Shear stress when fiber position has been considered to be in direction of loading. With changing fiber angle, Shear stress reduces so that it reaches the least value when fiber position has been considered to be perpendicular to loading.

Factors of safety under the effect of applied loads have been calculated with changing fiber angles. Results have been presented graphically in Figure below:

Fig. shows that for a composite helical spring, the most safety factor under the effect of applied loads is related to case that fiber position has been considered to be perpendicular to loading. Also, Carbon/Epoxy composite helical spring has more safety factor at any fiber angle in comparison with other composite helical springs. Therefore, that composite helical spring is more suitable at this aspect.

Conclusion

In this paper, a helical steel spring has been replaced by three different composite helical springs.  Numerical results have been compared with theoretical results and found to be in good agreement. Compared to steel spring, the composite helical spring has been found to have lesser stress and has the most value when fiber position has been considered to be in direction of loading. Weight of spring has been reduced and has been shown that changing percentage of fiber, especially at Carbon/Epoxy composite, does not affect spring weight. Longitudinal displacement in composite helical spring is more than that of steel helical spring and has the least value when fiber position has been considered to be in direction of loading. The most safety factor is related to case that fiber position has been considered to be perpendicular to loading and it is for Carbon/Epoxy composite helical spring.

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