External Gear Pump

Why an external gear pump?

After much consideration of many different pumps and ways that our wind turbine could attain a completely mechanical system, one of our main functional requirements, we decided to use an external gear pump to power our water function for several reasons.

Relatively low start-up torque is required and the torque over RPM increases (almost) linearly at low RPMs
Small footprint and straightforward driveshaft connections
Can be fabricated in-house (pumps online were $300 +, needed 3000 > rpm and had in-built motors)

We considered an Archimedes screw pump, centrifugal pump, water wheel, and lobe pump, but for the reasons above narrowed down on an external gear pump.

Fig 1: Exploded View of Final Gear Pump

V2 Drawing and Component Package

Gear Pump Assem Drawing.pdf

Final (V2) Gear Pump Design

Our final gear pump assembly consists of several stacked plastic gears, Delrin shim plates, stacked-wave disc springs, an o-ring, and rotary seal. Our design decisions for the final pump came from results from our analysis and testing V1 pump.

Design Decisions for V2 gear pump:

No water leakage
- Due to the o-ring, rotary seal, and (3/4) enclosed bearings
Gears rotate consistently with around 1Nm of torque
- Plastic gears did not rust, which caused friction in V1
Minimal friction between the gears and housing
- Delrin shim and disc spring compression allow for a tight seal (increase efficiency) while having low-friction properties
- Smaller diameter and taller gears require less torque to spin and less face friction friction
- Taller gears allowed for more volume displacement per revolution
- The gear diameter was reduced to lower the required torque

Final Pump Results (Testing)

Unfortunately, when testing our final pump, we found that more torque was needed to rotate the shaft than expected and there was internal leakage. Although our pump still effectively pumps water, it did not match our expectations.

From inspecting the pump and further testing, we've determined that the problems stem from the plastic gears we had bought from McMaster being larger than specified. The gears rub slightly on the housing walls as it was designed for minimal clearance to improve efficiency.

We expect the leakage to be unavoidable from using water (low viscosity) over oil (high viscosity) since this pump is often for hydraulic applications. However, our shim plates are also undersized and may be allowing more leakage than expected.

CFD Analysis and Testing

While most gear pumps run at around 700-3000 rpm, according to Fundamentals of External Gear Pump Design (Logan T. Williams), but there was little information about torque needed work the pump, which was necessary for our pulley and gear system.

Torque needed to drive pump can be found through the equation below from the research paper mentioned, but it required us knowing our pressure difference across our system.

To find the torque needed for our pump, we performed Ansys CFD and built a pump to test and show proof of concept, especially since external gear pumps are made for oil instead of water. For the CFD, we modelled our pump's static pressure across pump as laminar flow and did a rotational fluent study by applying equations for gears to spin at 800 rpm in opposing directions. The working fluid was set to water, the inlet set to velocity inlet and the outlet set to pressure outlet. Running the studies, we got detailed plots for pressure and velocity across the pump allowing us to visualise the fluid dynamics for our pump. Once the pressure difference was plugged into our torque equation, we got a torque of 0.15 Nm.

For further validation, we built our V1 gear pump, since we did not have a torque sensor or have a motor with a known torque and only needed a sense of the order of magnitude for torque, we approximated it as the torque our fingers can exert to rotate the shaft, found to be approximately between 0.1 and 0.5 Nm torque.

Fig 2: Ansys Fluent contour plot for pressure across pump at 800 rpm

Fig 3. Ansys Fluent contour plot for pump water velocity at 800 rpm

Fig 4: Pump Torque Equation

Torque equation to drive gear pump

ΔP = Pressure difference across pump

V = Volume displacement per revolution (m3/s)

ηm = Mechanical efficiency

Fig 5: Flow rate vs RPM for Gear Pump

Fig 6: Torque required vs RPM for Gear Pump (0.15Nm)

Fig 7: Average water exit velocity across pump

For modelling the average water velocity and the flow rate for our gear pump, we input our pressure difference from the CFD, which gave us our values for torque across rpm. We modelled our RPM up to 2,000 since that was the RPM limit the hand drill that we used to test V1 and V2 of our pumps.

Our torque was found to be 0.15Nm (also can be done through equation), which was close to our approximated finger-torque range from 0.1-0.5Nm torque. However, due to friction and our gears being larger than the part specified to be online, in real life more torque than this was required to move the gears.

The exit velocity of the water contour plot from the CFD and the exit velocity line plot seem to roughly match. At 800 rpm the line plot says that average velocity should be 1.55 m/s and the velocity change at exit discharge in CFD is about 1.52 m/s, which is very close.

The flow rate also matched what we were seeing and we tested to see how quickly a tub with known volume could fill up and results closely matched.

Unfortunately, neither the CFD nor the line plots can predict the losses due to friction in ours system, which proved to be a problem.

Gear Pump Fabrication

The housing and lid were made completely with aluminum and all components have anti-corrosive properties

The housing was made on the 2.5-axis Bridgeport using sketch and hole pattern features for the round/repetitive operations. We chose to use the Bridgeport for two main reasons: ablitity to use a boring bar (more accurate bore for the gear housing than CNC) and to fit the large .499" reamer (used for bearing housings)
The lid was machined using the Tormach Mill, followed by reaming on the Bridgeport
Delrin shim plates were laser-cut (material selection for water compatibility and low-friction properties)
Spacers were made out of brass on the lathe (water-compatible and lower friction around spinning shafts)
1/4 NPT holes drilled and tapped for the 1/4 NPT to 1/4 barb fittings (tight seal, cheap, easy-to-attach tubing)
Shafts were keyed and gears were broached
Reamed dowel pin holes to ensure alignment of the lid and housing

Fig 8: Exploded view for the V1 Gear Pump

V1 Gear Pump

Our version 1 for this pump served as a proof of concept and to approximate torque needed to drive our pump. We had waterjet the gears from steel despite being warned not to: kerf. Despite being only 1/8" thick, the kerf, or chamfer as some may call it, caused the gears to mesh poorly and have inconsistent spacing within the housing walls. The gears also rusted rapidly and water leaked through the unsealed lid and bearings. Finally, the lid could not be fully tightened without seizing the pump due to misalignment of the lid and housing and poorly fabricated gears.

PUMP.MOV

V1 Pump Video

VIDEOS FROM OUR PUMP WORKING!! :)

PUMP2.MOV

V2 Pump Video

Future Work and Possible Improvements

Using a gear cutter to make custom gears
- Limited and expensive options for gears with a large height and small diameter
- Mcmaster plastic gears were not to the claimed specification
Minimise leakage with better-fitting Delrin plates

Conclusion

Designing, analyzing, fabricating, testing, and iterating on these pumps was a fantastic experience. All aspects had their own challenges: rotating CFD studies, complex design, and tight-tolerance fabrication developed many skills throughout the process.

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