A pivoted double-block brake, similar to that in Fig. 12.12, has two shoes, which subtend an angle (2θ ) of 100°. The diameter of the brake drum is 500 mm and the width of the friction lining is 100 mm. The coefficient of friction is 0.2 and the maximum intensity of pressure between the lining

Question

A pivoted double-block brake, similar to that in Fig. 12.12, has two shoes, which subtend an angle (2θ ) of 100°. The diameter of the brake drum is 500 mm and the width of the friction lining is 100 mm. The coefficient of friction is 0.2 and the maximum intensity of pressure between the lining and the brake drum is 0.5 N/mm². The pivot of each shoe is located in such a manner that the moment of the frictional force on the shoe is zero.
Calculate:
(i) the distance of the pivot from the axis of the brake drum;
(ii) the torque capacity of each shoe; and
(iii) the reactions at the pivot.

Accepted Answer

[latex] ext { Given } \quad D=500 mm \quad w=100 mm \quad \mu=0.2 [/latex].

[latex] p_{\max .}=0.5 N / mm ^{2} \quad 2 heta=100^{\circ} [/latex].

Step I Distance of pivot from axis of drum
From Eq. (12.12),

[latex] h=\frac{4 R \sin heta}{2 heta+\sin 2 heta} [/latex] (12.12).

[latex] h=\frac{4 R \sin heta}{2 heta+\sin 2 heta}=\frac{4(250) \sin \left(50^{\circ} ight)}{\left(\frac{100 \pi}{180} ight)+\sin \left(100^{\circ} ight)} [/latex].

= 280.59 mm (i)
Step II Torque capacity of each shoe
From Eq. (12.13),

[latex] M_{t}=2 \mu R^{2} w p_{\max } \sin heta [/latex] (12.13).

[latex] M_{t}=2 \mu R^{2} w p_{\max .} \sin heta [/latex].

[latex] =2(0.2)(250)^{2}(100)(0.5) \sin \left(50^{\circ} ight) [/latex].

= 957 555 N-mm (ii)
Step III Reactions at pivot
From Eqs (12.14) and (12.15),

[latex] R_{X}=\frac{1}{2} R w p_{\max }(2 heta+\sin 2 heta) [/latex] (12.14).

[latex] R_{Y}=\frac{1}{2} \mu R w p_{\max }(2 heta+\sin 2 heta) [/latex] (12.15).

[latex] R_{X}=\frac{1}{2} R w p_{\max }(2 heta+\sin 2 heta) [/latex].

[latex] =\frac{1}{2}(250)(100)(0.5)\left[\left(\frac{100 \pi}{180} ight)+\sin \left(100^{\circ} ight) ight] [/latex].

= 17063 N.

[latex] R_{Y}=\frac{1}{2} \mu R w p_{\max }(2 heta+\sin 2 heta) [/latex].

[latex] =\mu R_{x}=0.2(17063)=3412.6 N [/latex] (iii).

Question 12.7: A pivoted double-block brake, similar to that in Fig. 12.12,...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions