Machine Elements Design

Homework 4:

1) A compression coil spring has square and ground ends, and the spring material G = 80 GPa, and has the following dimensions:
- Coil outer diameter is 85 mm, Coil inner diameter is 65 mm

- Total coils is 10
- Coil closed length is 140 mm, and the free length is 250 mm
When the spring is loaded the operating length found to be 170 mm, Find the maximum stress on the spring wire.

2) Spring “A” has a spring rate of 25 N/mm, spring “B” has a spring rate of 20 N/mm, and spring “C” has a spring rate of 30 N/mm. Find the spring rate of the following arrangements.
a- Springs “A”, “B” and “C” are connected in series.
b- Springs “A” and “B” are connected in parallel, then connected with “C” in series.
c- Springs “A”, “B” and “C” are connected in parallel.

Leaf spring:

Ex. 1) A car has a total weight of 12,000 N, and the weight distribution front/rear is 60/40. The car has a leaf spring dependent rear suspension. If the leaf spring length is 1100 mm, number of leaves (n) = 4, leaf width (b’) = 60 mm, leaf height (h) = 8 mm. Find the stress on the spring (σb)

Given:

          W_car = 12,000 N

          W_r = 40% W = 0.4 x 12000 = 4,800 N

          2F = 4800/2 = 2400 N,    F = 2400/2 = 1200 N

          2L = 1100 mm,    L =1100/2 = 550 mm

          n = 4

          b^’ = 60 mm

          h = 8 mm

Required:

          σ_b = ?

Solution:

          σ = (6 x 1200 x 550) / (4 x 60 x 8²) = 257.8 MPa

3- Find the number of leaves (n) for a leaf spring that has a total length 1.20 m, if the spring allowable stress not to exceed 300 MPa when loaded with a load of 4000 N. The spring leave dimensions are b^’ = 65 mm, and h = 6 mm.