1] Belt material selection

(Leather, $\mathrm{E}=80 \mathrm{MPa},\quad [\sigma]=5 M P a, \quad \sigma^{-1}=6 M P a$ and $\rho=\frac{1400 \mathrm{kg}}{\mathrm{m}^{3}}$ and $\mu= 0.3)$

2] Belt and pulley geometry

$i=\frac{d_{2}}{d_{1}}=\frac{n_{1}}{n_{2}} \quad $ ------ without slip

$d_1$ - Diameter of larger pulley (mm)

$n_1$ - Speed of the larger pulley (rpm)

$d_2$ - Diameter of small pulley (mm)

$n_2$ - Speed of the small pulley (rpm)

i- velocity ratio

Using empirical relation find $d_{1}=1000 \times \sqrt[3]{k W / n_{1}}$

Select the standard pulley diameter $d_1$
and tolerances $\quad$ PSG 7.54

Considering slip (s) $\frac{d_{2}}{d_{1}\left(1-{s} / 100\right)}=\frac{n_{1}}{n_{2}}$

Find actual $n_2$ and actual velocity ratio $i = n_1 / n_2$

Find $d_2$ and Select the standard pulley diameter $d_2$
and tolerances $\quad$ PSG 7.54

Assume center distance as $C = 2 \times d_2$

Arc of Contact = $180^{\circ}-\frac{d_{2}-d_{1}}{c} \times 60^{\circ}$ $\quad$ PSG 7.54

Length of belt

• a) Open Drive $\quad L=2 C+\frac{\pi}{2}(D+d)+\frac{(D-d)^{2}}{4 C}$ $\quad$ PSG 7.53
• b) Crossed Drive $\quad L=2 C+\frac{\pi}{2}(D+d)+\frac{(D+d)^{2}}{4 C}$ PSG 7.53

3] Belt Cross section

Belt Tensions $\frac{T_{1}}{T_{2}}=e^{\mu \theta}$

Belt Velocity $v=\frac{\pi d_{1} n_{1}}{60} m/sec$

Using power $P=\left(T_{1}-T_{2}\right) \times v$ determine belt tensions.

Maximum stress induced in the belt is given by,

$\sigma_{\max }=\sigma_{t}+\sigma_{c}+\sigma_{b}$

Where, $\sigma_{t}(\text { Tensile stress })= {T_{1}} / b \times t$

$\sigma_{c}(\text {Stress due to centrifugal tension})=\rho v^{2}$

$\sigma_{b}(\text {Bending stress)}=E t / d_{1}$

Assume ${d_{1}} / t$ = 25 to 30 and find thickness of belt 't'

Using $\sigma_{max}$ = [$\sigma$] Determine the value of the width of belt 'b'

Select standard width 'b' PSG 7.55

Determine maximum stress induced in the belt $\sigma_{max}$

4] Life of Belt

Find the life of belt (H) in hours using the following equation

$\sigma_{\max }^{m} \times \frac{v}{L} \times n_{p} \times H \times 3600=\left(\sigma^{-1}\right)^{m} \times 10^{7}$

Where $n_p$ = number of pulleys 2 and $\mathrm{m}$ constant = 5 to 6

5] Design Pulley Proportion & Construction $\quad$ PSG 7.56 and 7.57

• a) Select type of Pulley.
• b) Drawing and Details of Pulley Construction