Gerotor Pump Displacement Calculation

Gerotor Pump Displacement Formula:

\[ Disp = 2\pi (R_e^2 - R_i^2) W \]

Displacement (Disp):

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1. What is Gerotor Pump Displacement?

Gerotor pump displacement refers to the volume of fluid displaced per revolution of the pump. It is a critical parameter in hydraulic systems that determines the pump's flow rate capacity and is essential for proper system design and performance evaluation.

2. How Does the Calculator Work?

The calculator uses the gerotor pump displacement formula:

\[ Disp = 2\pi (R_e^2 - R_i^2) W \]

Where:

\( Disp \) — Displacement (in³/rev)
\( R_e \) — External radius (inches)
\( R_i \) — Internal radius (inches)
\( W \) — Width (inches)
\( \pi \) — Mathematical constant pi (approximately 3.1416)

Explanation: The formula calculates the annular area between the external and internal rotors multiplied by the width to determine the volumetric displacement per revolution.

3. Importance of Displacement Calculation

Details: Accurate displacement calculation is crucial for determining pump flow rates, sizing hydraulic systems, matching pumps to system requirements, and ensuring efficient operation of hydraulic equipment.

4. Using the Calculator

Tips: Enter external radius, internal radius, and width in inches. All values must be positive numbers, and the external radius must be greater than the internal radius for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a gerotor pump?
A: A gerotor pump is a positive displacement pump consisting of an inner and outer rotor with offset centers. The inner rotor has one less tooth than the outer rotor, creating chambers that expand and contract to move fluid.

Q2: How does displacement relate to flow rate?
A: Flow rate (in³/min) = Displacement (in³/rev) × Speed (RPM). Displacement determines how much fluid is moved per revolution, while speed determines how many revolutions occur per minute.

Q3: What are typical applications of gerotor pumps?
A: Gerotor pumps are commonly used in automotive applications (engine oil pumps, transmission pumps), hydraulic systems, lubrication systems, and various industrial fluid transfer applications.

Q4: What units should I use for the inputs?
A: This calculator uses inches for all linear dimensions. If you have measurements in other units, convert them to inches before entering the values.

Q5: Why must external radius be larger than internal radius?
A: The external rotor must be larger than the internal rotor to create the pumping chambers. If the internal radius equals or exceeds the external radius, no displacement occurs and the formula becomes invalid.