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$N = ? , h = 20 mm$
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X = 120mm, Y = 100mm, r = 140mm

M = 4 kg , N mean = 300 rpm, c = 0.04

$h_1$ = 10 mm

1] N = ? , h = 20 mm

$\rightarrow$ $h = h_1 + h_2$

$20 = h_2 + 10$

$h_2 = 10\ mm$

2] s = ?

3] sensitiveness

4] s = ? for isochronous condition.

$\rightarrow$ increase in speed = $N_{mean} + 4$ % $N_{mean}$

$= 300 + \frac{4}{100} \times 300 = 312 \ rpm$

$\rightarrow$ $w_2 = \frac{2 \pi N_2}{60} = \frac{2 \pi \times 312}{60} = \ 32.67$

$\rightarrow$ $\frac{h_1}{y} = \frac{r – r_1}{X}$

$\frac{0.01}{0.1} = \frac{0.14 – r_1}{0.12}$

$r_1 = 0.128\ mm$

$\rightarrow$ $\frac{h_2}{y} = \frac{r_2 – r}{x}$

$\frac{0.01}{0.1} = \frac{r_2 – 0.14}{0.12}$

$r_2 = 0.152\ m$

$\rightarrow$ $F_c = mrw^2$

$= 4 \times 0.14 \times 31.41^2$

$F_c = 552.69\ N$

$\rightarrow$ $Fc_2 = mr_2 w_2^2$

$= 4 \times 0.152 \times 32.67^2$

$Fc_2 = 649.037N$

$\rightarrow$ $Fc = Fc_1 + (Fc_2 – Fc_1) [ \frac{r – r_1}{r_2 – r_1}]$

$552.69 = Fc_1 + (649.037 – Fc_1) [\frac{0.14 – 0.128}{0.152 – 0.128}]$

$Fc_1 = 456.343 \ N$

$\rightarrow$ $Fc_1 = mr_1 w_1^2$

$456.343 = 4 \times 0.128 \times w_1^2$

$w_1 = 29.85 \ rad/sec$

$N_1 = 285.09 \ rpm$