Question

An Aluminium Alloy roller with diameter 25mm and length 50mm rolls on the inside of a cast iron ring

having an inside radius of 100mm, which is 50mm thick. Find the maximum force ‘F’ that can be used if

the maximum pressure is not exceeding 100 Mpa.

Answer 1

$b=\sqrt{\frac{2F}{\pi L}\frac{(\frac{1-v_1^2}{E_1}+\frac{1-v_2^2}{E_2})}{(\frac{1}{d_1}+\frac{1}{d_2})}}$

$b=\sqrt{\frac{2F}{\pi 50}\frac{(\frac{1-0.333^2}{10.9}+\frac{1-0.211^2}{14.5})}{(\frac{1}{25}+\frac{1}{200})}}$

b=0.204F^0.5

$\tau_{max}=0.3P_{max}=0.3*100=30$

$P_{max}=\frac{2F}{\pi bL}$

$30=\frac{2*F}{\pi *0.204F^{0.5}850}$

F=4085.64N