An engine, running at 150 r.p.m., drives a line shaft by means of a belt. The engine pulley is 750 mm diameter and the pulley on the line shaft being 450 mm. A 900 mm diameter pulley on the line shaft drives a 150 mm diameter pulley keyed to a dynamo shaft. Find the speed of the dynamo shaft, when 1. there is no slip, and 2. there is a slip of 2% at each drive.

 An engine, running at 150 r.p.m., drives a line shaft by means of a belt. The engine pulley is 750 mm diameter and the pulley on the line shaft being 450 mm. A 900 mm diameter pulley on the line shaft drives a 150 mm diameter pulley keyed to a dynamo shaft. Find the speed of the dynamo shaft, when 1. there is no slip, and 2. there is a slip of 2% at each drive.

Given :    $N_{1}=150 \text { r.p.m. } ; d_{1}=750 mm ; d_{2}=450 mm ; d_{3}=900 mm ; d_{4}=150 mm$

The arrangement of belt drive is shown in Fig. 11.10.

Let      $N_{4}$ = Speed of the dynamo shaft .

 

1. When there is no slip

We know that       $\frac{N_{4}}{N_{1}}=\frac{d_{1} \times d_{3}}{d_{2} \times d_{4}} \quad \text { or } \quad \frac{N_{4}}{150}=\frac{750 \times 900}{450 \times 150}=10$

$\therefore$      $N_{4}=150 \times 10=1500 \text { r.p.m. }$

2. When there is a slip of 2% at each drive

We know that        $\frac{N_{4}}{N_{1}}=\frac{d_{1} \times d_{3}}{d_{2} \times d_{4}}\left(1-\frac{s_{1}}{100}\right)\left(1-\frac{s_{2}}{100}\right)$

 

 

$\therefore$     $N_{4}=150 \times 9.6=1440 r.p.m$