Belleville Spring. The relation between the load F and the axial deflection y of each disc. Maximum stress induced at the inner edge

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Lynn Morgan
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1 Belleville Spring Disc spring, also called Belleville spring are used where high capacity compression springs must fit into small spaces. Each spring consists of several annular discs that are dished to a conical shape as shown in figure. They are stacked up one on top of another as shown in above figure. When the load is applied, the discs tend to flatten out, and this elastic deformation constitutes the spring action. In safety valve the disc springs are used. The relation between the load F and the axial deflection y of each disc Maximum stress induced at the inner edge Maximum stress at the outer edge

Where C 1 and C 2 are constraints t = thickness h = height of spring M = constant F = axial force d o = outer diameter d i = inner diameter = Poisson s ratio E = Modulus of elasticity

2 Where C 1 and C 2 are constraints t = thickness h = height of spring M = constant F = axial force d o = outer diameter d i = inner diameter = Poisson s ratio E = Modulus of elasticity y = axial deflection The ratio should be lie between 1.5 and 3 Torsion springs They are used in any application where torque is required, such as door hinges, automobile starters, etc

Types of ends used on extension springs An extension spring is an open-coil helical spring that is designed to offer resistance to a tensile force applied axially.

3 Types of ends used on extension springs An extension spring is an open-coil helical spring that is designed to offer resistance to a tensile force applied axially. Unlike compression springs, they have specially designed hooks at both ends. They provide wide range of load-deflection curves. Standard springs have constant diameter and pitch, thus providing a constant spring rate. Ends for extension springs (1) Usual design; stress at A is due to combined axial force and bending moment. (2) Side view of part a; stress is mostly torsion at B. (3) Improved design; stress at A is due to combined axial force and bending moment. (4) Side view of part c; stress at B is mostly torsion

4 RUBBER SPRINGS Rubber springs have good damping properties and hence it is used in vibration loading. Rubber is usually bonded to metal plates and can be in tension, compression and shear. In Shear rubber displays maximum elastic properties and in compression it displays maximum stiffness. At high temperature and in oil rubber cannot be used. Problem 24 A Helical torsional spring of mean diameter 50mm is made of a round wire of 5mm diameter. If a torque of 5Nm is applied on this spring, find the bending stress, maximum stress and deflection of the spring in degrees. Modulus of elasticity =200GPa and number of effective turns 10. Data D = 50mm, d = 5mm, M t = 5Nm = 5000N-mm, E = 200GPa = 200Χ10 3 N/mm 2, i=10 Solution Spring Index c = = = 10 When c=10, Stress factor = 1.08 Bending Stress induced = = = N/mm 2 Maximum Stress σ= + = = N/mm 2 Axial deflection y = = = 32 mm Also y= Ѳ i.e. 32 = Ѳ Ѳ = 1.28 radians = 1.28 =

5 Problem 24 A Belleville spring is made of 3 mm sheet steel with an outside diameter of 125mm and an inside diameter of 50mm. The spring is dished 5mm. The maximum stress is to be 500MPa. Determine (i) (ii) (iii) (iv) Safe load carried by the spring Deflection at this load Stress produced at the outer edge Load for flattening the spring Assume poison s ratio, ѵ = 0.3 and E= 200 GPa Data: t=3mm, =125 mm, =50mm, h=5 mm, =500MPa, =0.3, E=200GPa=200 3 N/mm 2 Solution: For = = 2.5 M= 0.75, C 1 =1.325, C 2 =1.54 (i) Deflection Stress at the inner edge = [ (h- ) + t] i.e. 500 = [1.325 (5- ) + ] = y ( y +4.62) = y y 2 i.e y y = 0 y =

6 y= 16.36mm or 0.615m Deflection y = mm ( y < h) (ii) Safe Load F = [(h-y) (h- )t + ] F = [( ) (5- ) 3 + ] F = N (iii) Stress at the outer edge = [ (h- ) - t ] = [1.325 (5 ) ] = N/mm 2 (iv) Load for flattering the spring When y= h, the spring will become flat F = = F= N

7 Problem 25 A multi leaf spring with camber is fitted to the chassis of an automobile over a span of 1.2m to absorb shocks due to a maximum load of 20kN. The spring material can sustain a maximum stress of 0.4GPa. All the leaves of the spring were to receive the same stress. The spring is required at least 2 full length leaves out of 8 leaves. The leaves are assembled with bolts over a span of 159mm width at the middle. Design the spring for a maximum deflection of 50mm. Given data: L = 1.2m = 1200mm; 2F = 20kN = 20000N F = 10000N; σ = 0.4Gpa = 400N/mm 2 ( equally stressed); i f = i =2; i g = 6; i=8; l b = 150mm; y = 50mm. Solution: Effective length Assume E = GPa = x10 3 N/mm 2 α =6; β = 2, Width and thickness of spring leaves Maximum equalized stress b h 2 = (1) Deflection

8 b h 3 = (2) Equation (2) Divided by (1) gives Take thickness of spring h= 9.5mm Substituting in equation (1) b = 109mm Substitution in equation (2) b = mm Select bigger value as the permissible value Width of spring leaves b = 109mm. (ii) Initial space between full length and graduated leaves Camber Load on the central band Load on the band

Question Paper Code : 11410

Reg. No. : Question Paper Code : 11410 B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2011 Fourth Semester Mechanical Engineering ME 2254 STRENGTH OF MATERIALS (Common to Automobile Engineering and Production