A semi-elliptic multi-leaf spring is used for the suspension of the rear axle of a truck. It consists of two extra full-length leaves and ten graduated-length leaves including the master leaf. The centre-to-centre distance between the spring eyes is 1.2 m. The leaves are made of steel 55Si2Mo90

Question

A semi-elliptic multi-leaf spring is used for the suspension of the rear axle of a truck. It consists of two extra full-length leaves and ten graduated-length leaves including the master leaf. The centre-to-centre distance between the spring eyes is 1.2 m. The leaves are made of steel [latex] 55 \operatorname{Si2Mo90}\left(S_{v t}=1500 N / mm ^{2} ext { and } E=207000 ight. \left.N / mm ^{2} ight) [/latex] and the factor of safety is 2.5. The spring is to be designed for a maximum force of 30 kN. The leaves are pre-stressed so as to equalize stresses in all leaves. Determine
(i) the cross-section of leaves; and
(ii) the deflection at the end of the spring.

Accepted Answer

[latex] ext { Given } 2 P=30 kN \quad 2 L=1.2 m \quad n_{f}=2 \quad n_{g}=10 [/latex].

[latex] E =207000 N / mm ^{2} \quad S_{y t}=1500 N / mm ^{2} \quad(f s)=2.5 [/latex].

Step I Cross-section of the leaves
2 P = 30 kN or P = 15 000 N
2 L = 1.2 m or L = 600 mm.

[latex] \sigma_{b}=\frac{S_{y t}}{(f s)}=\frac{1500}{2.5}=600 N / mm ^{2} [/latex].

From Eq. (10.41),

[latex] \sigma_{b}=\frac{6 P L}{n b t^{2}} [/latex] (10.41).

[latex] \sigma_{b}=\frac{6 P L}{n b t^{2}} \quad ext { or } \quad(600)=\frac{6(15000)(600)}{(2+10) b t^{2}} [/latex].

[latex] b t^{2}=7500 mm ^{3} [/latex].

Assuming a standard width of 60 mm,

[latex] t^{2}=\frac{7500}{60} ext { or } t=11.18 ext { or } 12 mm [/latex].

Cross-section of the leaves = 60 × 12 mm (i)
Step II Deflection at the end of the spring

From Eq. (10.38),
[latex] \delta=\frac{12 P L^{3}}{E b t^{3}\left(3 n_{f}+2 n_{g} ight)} [/latex] (10.38).

[latex] \delta=\frac{12 P L^{3}}{E b t^{3}\left(3 n_{f}+2 n_{g} ight)} [/latex].

[latex] =\frac{12(15000)(600)^{3}}{(207000)(60)(12)^{3}(3 imes 2+2 imes 10)} [/latex].

= 69.68 mm (ii).

Question 10.25: A semi-elliptic multi-leaf spring is used for the suspension...

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