How to Solve Compressor and Motor Pulley Diameter and RPM Numericals: Formulas and Examples

Understanding the Relationship between Pulley Diameters and RPMs

In the field of mechanical engineering, it is often necessary to solve problems involving the relationship between the pulley diameters and rotational speeds (RPMs). Whether you are dealing with a compressor or a motor, understanding this relationship is crucial for the proper operation of your machinery. Here, we will discuss the key concepts and formulas used to solve such problems.

Key Concepts and Formulas

Pulley Diameter Relationship:

The diameters of the pulleys and their respective RPMs are inversely proportional. This means that if one pulley has a larger diameter, it will rotate slower than a smaller pulley, assuming they are connected. This relationship can be expressed as:

Speed Ratio N1/N2 D2/D1

Where:

N1 RPM of the first pulley (motor) N2 RPM of the second pulley (compressor) D1 Diameter of the first pulley (motor) D2 Diameter of the second pulley (compressor)

Formulas for Calculations

With the speed ratio formula, you can easily find the RPM of the second pulley, or vice versa, depending on what information is available. Here are the key formulas:

1. Finding RPM of the Second Pulley:

Reorganize the speed ratio formula to find N2:

N2 N1 × (D1/D2)

2. Finding Diameter of the Second Pulley:

If you know the RPMs and one diameter, you can find the other diameter:

D2 D1 × (N1/N2)

Example Problem

Suppose you are given the following parameters:

Pulley diameter of the motor, D1 4 inches RPM of the motor, N1 1800 RPM Diameter of the compressor pulley, D2 to be found RPM of the compressor, N2 600 RPM

Steps to Solve:

Use the formula to find D2: D2 D1 × (N1/N2) D2 4 inches × (1800 RPM / 600 RPM) D2 4 inches × 3 12 inches

So, the diameter of the compressor pulley is 12 inches.

Shaft Speed Calculation for Belt-Driven Machines

Knowing the correct shaft speed of both shafts on a belt-driven machine is crucial for performing machinery diagnostics. Typically, you would identify the input and output speeds using a strobe light photo tach or laser tach. However, if you can't access the fan shaft but still have the pulley diameter data, you can calculate the output speed and the multiplication factor using the following formula:

RPM Input/RPM Output Diameter Out/Diameter In

Summary

To solve problems involving the pulley diameters and RPMs of compressors and motors, use the speed ratio formula. Rearrange it as needed based on the given information and what you need to find. For specific problems or numerical examples, feel free to share them and I can assist you in working through them!

Understanding these principles can help you optimize your machinery and ensure efficient operation. If you have any questions or need further assistance, don't hesitate to reach out.