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Gear Type Pump Mathematical Model

Project Brief

A mathematical model for fixed displacement internal-external and external-external gear pumps used in automatic transmissions was created at Southwest Research Institute (SwRI). Applications for this model include predicting the performance for the following pumps:

• Involute with crescent

• Hypocycloid with crescent

• Duocentric pumps

• Gear-on-gear pumps

Differences in the dimensions and clearances of the gears, modifications to the crescent and housing, as well as changes in the material and fluid properties can be distinguished with the model.
 

The gear type pump mathematical model provides the following information:

Pump Power

• Ideal pump input power

• Viscous torque losses

• Frictional losses

Flow or Delivery

• Ideal flow output

• Flow leakage

Efficiencies

• Volumetric

• Mechanical

• Overall

All theoretical data are verified with actual test data. The versatility in the model is demonstrated by the overall efficiency of the five pumps as shown below.

The model is capable of correlating the following input conditions for crescent and noncrescent pumps:

• Operating temperatures and associated fluid viscosity (lb*sec/in.²)

• Displacement (in.³/rev)—Displacement can be determined by knowing the tooth cavity volume bounded by the internal gear and crescent and the external gear and crescent. Displacement may also be determined from experimental data.

• Axial clearance (inches)—Gross distance from the gear faces to the pump housing

• Outer clearance (inches)—Gross distance from the outer diameter of the internal gear to the housing inner diameter

• Tooth clearance (inches)—Gross distance radially from the external gear tooth to the crescent divider, or between radially in-line tangent teeth

• Internal gear to crescent clearance (inches)—Gross distance radially from the internal gear tooth to the crescent divider.

External Gear

• Inner diameter (inches)

• Dedendum circle radius (inches)

• Gear teeth face area (inches²)—Face area of the gear teeth

• Addendum circle radius (inches)

• Crescent contact area (inches²)—Contact area of the gear teeth with the crescent divider

Internal Gear

• Outer diameter (inches)

• Addendum circle radius (inches)

• Dedendum circle radius (inches)

• Gear width (inches)

• Gear teeth face area (inches²)—Face area of the gear teeth

• Crescent contact are (inches²)—Contact area of the gear teeth with the crescent divider

For more information about drivetrain engineering capabilities and past project briefs at SwRI or how you can contract with SwRI, please contact Douglas Fussner at dfussner@swri.org or (210) 522-3972. 

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Southwest Research Institute® (SwRI®), headquartered in San Antonio, Texas, is a multidisciplinary, independent, nonprofit, applied engineering and physical sciences research and development organization with 11 technical divisions.

September 30, 2008