Understanding Compound Belt Drives and Pulley Speed

A compound belt drive involves multiple pulleys mounted on shafts, where intermediate shafts carry two pulleys each. In such a system, the speed ratio between the first driver and the final driven pulley is the product of the speed ratios of each pair of pulleys in the train.

The fundamental principle governing the relationship between the speed and diameter of pulleys connected by a belt is that the linear belt speed is constant (assuming no slip). This leads to the relationship:

$\qquad N_1 D_1 = N_2 D_2$

Where:

• $N_1$ is the speed of the driving pulley
• $D_1$ is the diameter of the driving pulley
• $N_2$ is the speed of the driven pulley
• $D_2$ is the diameter of the driven pulley

Step-by-Step Calculation of Dynamo Pulley Speed

Let's apply this principle to the given compound belt drive system.

We have:

• Engine Pulley A (Driver): $D_A = 750$ mm, $N_A = 150$ RPM
• Pulley B (Driven by A): $D_B = 450$ mm
• Pulley C (on same shaft as B, Driver for Dynamo): $D_C = 900$ mm
• Dynamo Pulley D (Driven by C): $D_D = 150$ mm

Step 1: Calculate the speed of Pulley B

Pulley A drives Pulley B. Using the speed-diameter relationship:

$\qquad N_A D_A = N_B D_B$

Substituting the given values:

$\qquad 150 \text{ RPM} \times 750 \text{ mm} = N_B \times 450 \text{ mm}$

Solving for $N_B$:

$\qquad N_B = \frac{150 \times 750}{450}$

$\qquad N_B = \frac{150 \times (3 \times 250)}{150 \times 3}$

$\qquad N_B = 250$ RPM

So, the speed of Pulley B is 250 RPM.

Step 2: Determine the speed of Pulley C

Pulley C is keyed to the same shaft as Pulley B. This means they rotate at the same speed.

$\qquad N_C = N_B$

$\qquad N_C = 250$ RPM

The speed of Pulley C is 250 RPM.

Step 3: Calculate the speed of the Dynamo Pulley (D)

Pulley C drives the Dynamo Pulley (D). Using the speed-diameter relationship again:

$\qquad N_C D_C = N_D D_D$

Substituting the known values:

$\qquad 250 \text{ RPM} \times 900 \text{ mm} = N_D \times 150 \text{ mm}$

Solving for $N_D$:

$\qquad N_D = \frac{250 \times 900}{150}$

$\qquad N_D = \frac{250 \times (6 \times 150)}{150}$

$\qquad N_D = 250 \times 6$

$\qquad N_D = 1500$ RPM

The speed of the dynamo pulley is 1500 RPM.

Summary of Pulleys and Speeds

The final calculated speed for the dynamo pulley is 1500 RPM.