Principles of Dairy Machine Design

Module 7. Springs

Lesson 31
DESIGN AND SELECTION OF SPRINGS

31.1 Introduction

Two types of springs which are mainly used are, helical springs and leaf springs. We shall consider in this course the design aspects of two types of springs.

• Helical Spring
• Leaf Spring

31.2 Helical Spring

The figures below show the schematic representation of a helical spring acted upon by a tensile load F and compressive load F. 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.

Fig. 31.1 Helical spring

31.2.1 Stresses in the helical spring wire

From the free body diagram, we have to find 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.no31.2. 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 crack, is always initiated from the inner radius of the spring.

Fig. 31.2 Stresses in the helical spring wire

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

T=F*(D/2)

If d is the diameter of the coil wire and polar moment of inertia, I_P= (πd⁴ / 32) the shear stress in the spring wire due to torsion is

The above equation gives maximum shear stress occurring in a spring. Ks & KW the shear stress correction factor when the spring is in static loading and is in fatigue loading.

31.2.2 Deflection of helical spring

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 some material contact with the spring. Normally the same spring wire 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.

31.3 Leaf Spring

A Leaf spring is a simple form of spring commonly used in the suspension of vehicles.

Fig. 31.3 Leaf spring

Characteristics

Leaf spring, is also called as a semi-elliptical spring; as it takes the form of a slender arc shaped length of spring steel of rectangular cross section.

• The center of the arc provides the location for the axle, while the tie holes are provided at either end for attaching to the vehicle body.
• Leaves are stacked one upon the other to ensure rigidity and strength.
• It provides dampness and springing function.
• It can be attached directly to the frame at the both ends or attached directly to one end, usually at the front, with the other end attached through a shackle, a short swinging arm.
• The shackle takes up the tendency of the leaf spring to elongate when it gets compressed and by which the spring becomes softer.

• Thus depending upon the load bearing capacity of the vehicle the leaf spring is designed with graduated and un-graduated leaves.

31.3.2 Leaf springs-fabrication stages

Because of the difference in the leaf length, different stress will be there at each leaf. To compensate the stress level, prestressing is to be done.Prestressing is achieved by bending the leaves to different radius of curvature before they are assembled with the center clip. The radius of curvature decreases with shorter leaves.

The extra initial gap found between the extra full length leaf and graduated length leaf is called as nip. Such prestressing achieved by a difference in the radius of curvature is known as nipping.

31.3.3 Nipping in leaf springs

31.3.3.1 Applications

Mainly in automobiles suspension systems.

31.3.3.2 Advantages

It can carry lateral loads.

It provides braking torque.

It takes driving torque and withstands the shocks provided by the vehicles.

Fig. 31.4 Nipping in leaf spring

31.3.4 Design of leaf spring

Consider a single plate fixed at one end and loaded at the other end as shown in Fig.31.5. This plate may be used as a flat spring.

Let t = Thickness of plate,

b = Width of plate, and

L = Length of plate or distance of the load W from the cantilever end. We know that the maximum bending moment at the cantilever end A,

Flat Spring (Cantilever Type)

M = W.L

Fig. 31.5 Design of leaf spring

If the spring is not of cantilever type but it is like simply supported beam, and load 2W act at the centre, as shown then

Fig. 31.6 Flat spring

31.3.4.1 Length of leaf spring leaves

The length of the leaf spring leaves may be obtained as discussed below:

Let 2L1 = Length of span or overall length of the spring,

l = Width of band or distance between centres of U-bolts. It is the ineffective length of the spring,

nF = Number of full length leaves,

nG = Number of graduated leaves, and

n = Total number of leaves = nF + nG.

We have already discussed that the effective length of the spring,

2L = 2L1 – l ...(When band is used) =2L1-(2\3)L ... (When U-bolts are used)

It may be noted that when there is only one full length leaf (i.e. master leaf only), then the number of leaves to cut will be n and when there are two full length leaves (including one masters leaf)then the number of leaves to be cut will be (n-1). If a leaf spring has two full length leaves, then the length of leaves is obtained as follows: