A semielliptic leaf spring shown below consists of three ful

A semi-elliptic leaf spring shown below consists of three full-length leaves and 15 graduated length leaves. The total length of the spring is 1 m (2 times L = 1 m). The maximum force act on the spring is 75 kN (2 times F = 75 kN). For each leaf, the ratio of the width to thickness is 9:1. The Young\'s modulus of the leaf material is 207000 N/mm^2. After applying the pre=load, the stresses of all leaves are equal to 450 N/mm^2. Determine (a) the width and the thickness of the leaves, (b) the initial gap/nip, and (c) the initial preload to close the initial gap.

Solution

Design stress not given, for E= 200000 N/mm2 is about 350 MPa

b/h = 9

For uniform leaf, stress= 3FL/(bh² ), defln = 2FL³ /(Ebh³ )

for non unform leaf, same stress, defln 3FL³/( )

Need tro know maxm allowable defln

From the above eqns can get b = 3FL/(stress* h² )

b/h = 9

h^{3 =} FL/3stress)

h, b known for each leaf

For lminated, b =b/N

For the nip: work backwards from the defln eqns and the initial prestress.