Question

A differential band brake has brake drum of diameter 500 mm and the maximum torque on the drum is 1000 N-m. The brake embraces 2/3 ${}^{rd}$ of the circumference. The band brake is lined with asbestos fabric having a coefficient of friction 0.3. The permissible stress is 70 MPa in tension. The bearing pressure for the brake lining should not exceed 0.2 MPa. For this band brake, the thickness (mm) of the band is ________

Answer 1

$\frac{2}{3}\text{of circumference =}\frac{2}{3}\times 360={240}^{\circ }=\frac{4\pi }{3}$

$\frac{T_1}{T_2}=e^{\mu \theta }$

$\frac{T_1}{T_2}=e^{(0.3\times 4\pi /3)}$

$\frac{T_1}{T_2}=3.25----\left(1\right)$

$(T_1-T_2)\times 0.25=1000$

$T_1-T_2=4000----\left(2\right)$

$\text{From (1) and (2)}$

$T_1=5587.3N$

$T_2=1587.3N$

$\text{Bearing pressure =}P=\frac{2T}{D\times W}$

$P_{max}=\frac{2T_{max}}{500\times W}=\frac{2T_1}{500\times W}$

$=\frac{2\times 5587.3}{500\times W}=0.2$

$W=111.75mm$

$T_1=\text{permissible stress}\times W\times t$

$5587.3=70\times 111.75\times t$

$\Rightarrow t=0.71mm$