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# How do I Calculate Displacement of Gerotor?

A portmanteau of the words "generated rotor," a gerotor is a positive-displacement pump that uses an inner and outer gear to move fluid. The inner gear has one fewer teeth than the ring-shaped outer gear; the volume of the inner rotor's "missing tooth" multiplied by the number of actual teeth on the centre gear determines the pump's theoretical displacement per revolution. However, you'll still need to account for efficiency losses with rpm to determine the pump's actual output.

Remove the gerotor's centre gear from the shaft; it should just pull off of the shaft. Measure the centre gear's base circle with a set of dial calipers. The base circle is the shortest distance between the closest points on the centre gear, which will typically be at the bottom of the depressions between the teeth. Measure the diameter of the centre shaft hole, and measure the thickness of the gear. Example: our gerotor gear has a base circle of 100-mm, a centre shaft hole of 10-mm and is 20-mm thick.

Calculate the volume of the centre gear's base circle by multiplying the diameter by pi (3.14) and then by the gear's thickness. In our example, this works out to 6,280 cubic-mm (100 x 3.14 x 20 = 6,280). Determine the centre shaft hole volume using the same method: diameter x pi x thickness. This comes out to 628 cubic-mm. Subtract the shaft hole volume from the base circle volume, and divide by 1000 to convert it to cubic centimetres. In our example, this comes out to 5,652 cubic-mm (6,280 - 626 = 5,652), which equals 5.652-cc for the base circle minus the shaft hole.

Drop a few drops of dish detergent into your water container. The dish detergent will break the water's surface tension, allowing it to settle in the beaker and give a more accurate measurement. You don't need much; three or four drops of detergent per litre of water will suffice. Stir the mixture.

Pour some of the soapy water mixture into the beaker to about double your base circle measurement; the exact amount isn't important, as long as it's enough to completely submerge the gear. Record the measurement. In our example, we'll fill the beaker to exactly 14-cc.

Carefully lower the gear into the beaker. Allow the gear and bubbles time to settle and record the new water level measurement. Subtract the new water level from the old water level to determine the absolute volume of the gear, then subtract the base-circle-minus-shaft-hole measurement from that to determine the volume of the teeth. In our example, the water level rose by 13.5-cc; that 13.5 minus the base-circle-minus-shaft-hole volume of 5.652 gives us a tooth volume of 7.848-cc. This is the amount of fluid your gerotor pump will theoretically displace per revolution.

#### Tip

No gerotor will actually pump its exact displacement per revolution, since internal leakage reduces efficiency. The gerotor will operate most efficiently at low output-pressure levels and will lose efficiency and flow as the pressure goes up. You'll need to consult your pump manufacturer's data to determine exact loss rates, but most pumps will lose efficiency linearly from zero rpm (where it's effectively 100 per cent) to about 80 per cent at the maximum rated rpm.

#### Things You'll Need

• Graduated beaker with cc markings
• Dial calipers
• Basic hand tools