A shaft runs at 80 rpm and drives another shaft at 150 rpm through belt drive. The diameter of the driving pulley is 600 mm.¹ What will be the diameter of the driven pulley assuming belt thickness as 5 mm?

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SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

Step 1: Account for belt thickness in effective diameters

The effective diameter increases by the belt thickness:

\( D_{\text{eff1}} = D_1 + t = 600 + 5 = 605 \, \text{mm} \)

Let the effective diameter of the driven pulley be \( D_{\text{eff2}} = D_2 + t \).

Step 2: Apply the speed ratio formula for belt drives

The speed ratio is inversely proportional to the effective diameters:

\( \frac{N_2}{N_1} = \frac{D_{\text{eff 1}}}{D_{\text{eff 2}}} \)

\( \frac{150}{80} = \frac{605}{D_2 + 5} \)

\( D_2 + 5 = \frac{605 \times 80}{150} \)

\( D_2 + 5 = 322.67 \, \text{mm} \)

\( D_2 = 322.67 - 5 = 317.67 \, \text{mm} \)