Answer to Question #222806 in Mechanical Engineering for Subu

Question

locomotive semi-elliptical laminated spring has an overall length of 1m and
sustains a load of 70kN at its centre. The spring has 3 full length leaves and 15
graduated leaves with a central band of 100 mm width. All the leaves are to be
stressed to 400 MPa, when fully loaded. The ratio of the total spring depth to that
of width is 2. E=210 kN/mm2
. Determine
(i) The thickness and width of the leaves
(ii) The initial gap that should be provided between the full length and
graduated leaves before the band load is applied.
(iii)The load exerted on the band after the spring is assembled.

Answer 1

length = 1m

load = 70kN

Number of leaves = 3

Number of graduated leaves = 15

Central = 100mm width

Pressure = 400MPa = 400N/mm²

depth:width = 2

E = 210 kN/mm²

(i) t = thickness

b = width

from, $\dfrac{n× t}{b} = 2$

$b = \dfrac{15 ×t}{2} = 7.5t$

Effective length $= 2L = 2L_1 - l =$

$1000-100 = 900$

$L = 450$m

$\sigma= \dfrac{18.WL}{bt²(2n_G+ 3n_f)}$

$400= \dfrac{18 × 3500× 450}{7.5t(t²)(2(15) + 3(3))}$

$400 =\dfrac{ 96923.1}{t^3}$

$t³ = \dfrac{ 96923.1}{400} = 242.31$

$t= 6.2mm$

$b = 7.5t = 7.5 × 6.2 = 46.76mm$