SPRINGS

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Springs are resilient members and are extensively used to absorb shocks. The common application of springs.
1.To control vibration and force due to shock or impact loads.
Ex: springs of railway car and automobile.
2.To control the motion of links in mechanism.
Ex: springs to maintain contact between cam and its followers.
3.To apply the force to the members.
Ex: springs used in balances and dynamo meters.
4.To measure the force.
Ex: springs used in clock.
Spring materials:
Plain carbon steel of 0.9 – 1.0 % carbon is a common material for springs. Steel with 0.85 to 0.95% carbons and 0.3 to 0.4 % manganese is used for large size springs alloy steel such as chrome-vanadium and silicon-manganese steel are used for better grade springs. These alloy possess greater toughness and higher endurance limit and are better suited for springs subjected to fluctuating loads. Chromium steel phosphorous bronze andmonel metal can also be used in special cases to increase fatigue resistance corrosion resistance and heat resistance.
Definitions:
The definition of the terms used in helical springs are given below.
Springs index: It is the ratio of the mean coil diameter to the diameter of the spring wire.
Springs index C = D∕d
Where D = Mean diameter of the coil and
           d = diameter of the spring wire.
Stiffness: it is defined as the load per unit deflection.
Stiffness K = W/ δ;
Where W = load and
 d = deflection of the spring
Helix angle: It is the angle which the axis of the spring wire makes with horizontal line perpendicular to the axis of the spring.
Solid length: It is the length of spring measured along the axis when the spring is completely compressed i.e., the coils are touching each other.
Solid length = n.d
Where n = total number coils
 d = diameter of the spring wire
Free length: It is the length of spring measured along the axis when the spring is unloaded.
Free length = solid length + max. Compression + clearance
          = nd +δmax + 0.15δmax
Pitch: The axial distance between adjacent coil in uncompressed state is called pitch.
Pitch of coil p = free length/n-1

Types of springs:
Springs are used in a wide range of types and sizes. The following types are most commonly used in industrial applications.
  1. .                                  Helical springs
  2.                                      Leaf or laminated springs

The coil or helical spring consists of a wire or rod wound into a helix and is primarily intended for axial direct compression or tensile load helical springs may be further classified as
  1.        Close- coiled helical springs
  2.       Open- coiled helical springs

In close-coiled helical springs the angle the angle of helix is less than 10 the pitch (distance between the similar points on the adjacent coils of the springs) in close-coiled helical spring is very small as compared to open- coil helical spring.
The leaf or laminated spring is made by placing steel strips one over the other. All the strips of different lengths are bent to the same radius. The strips are clamped together tightly at one or more section. Leaf springs are common shock absorbing devices used in automobiles.  
Close-coiled helical springs:
Consider a close-coiled helical spring is made of round wire and stretched by axial load W. The pitch of the spring is very small and therefore the planes are perpendicular to the spring axis such springs are designed for torsion the effects of bending and direct shear are negligible.
Let     W =axial load
          R = radius of spring
          d = diameter of spring wire
          n = number of coils
          l = length of wire = 2π R.n
Torque        T = W.R
But    T =τ. Zp
          W.R = τ. πd³/16
Where τ = shear stress induced in the wire
          τ = 16 WR/ πd³
Consider the spring wire is fixed at one end and subjected to a torque (T= WR) at free end. Then the angle of twist is given by the relation.
                   Ѳ = Tl /Gj                       (T/l = GѲ/l)
                    = W.R.2Πr.N/Gπd⁴/32 = 64 WR².n/G.d⁴
Deflection of spring δ =R.Ѳ = 64WR³.n/G.d⁴
Stiffness (load required per unit deflection) of the spring,(spring constant) is given by
          s = W/δ = G.d⁴/64R³n
          The energy stored in the spring
          U = ½ W.δ = ½ W..R.Ѳ
          = T.Ѳ/2
BUT   T = τ.πd³/16 and Ѳ = 2τ.l/G.d                    (T/J =τ/R =G.Ѳ/l)
U =( τ.πd³/16 )( 2τ.l/G.d)
= τ²/4G X VOLUME OF THE WIRE     


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