Flywheels are used to store kinetic energy. Once a flywheel is accelerated to some rotational speed, it will only slow down because it is transferring energy to a load. By accurately measuring the flywheel’s rate of rotation versus time, we can determine the rate at which the flywheel’s energy is being transferred to the the friction sources of an un-powered engine.
This article will cover some of my results in testing the 3D printed Stirling engine. Although this engine is very small, the same technique can be used on any engine or rotating machine of any size. The next article will describe how to make the measurements and reduce the data. It only requires a single Hall-effect sensor to detect each passage of a magnet attached to the flywheel. A simple microcontroller (an Arduino in my case) records the exact time and sends it to my computer. The motor-generator shown in the photo above is not used for these tests.
Figure 1 Complete engine
The upper plot in figure 1 shows the friction power in mW versus the rotation speed in Hz for the complete, ready to run Stirling engine with no heating. In this configuration the engine is actually acting as a heat pump when the flywheel is turned. You can see from the graph that at 5 Hz (300 rpm) the engine requires about 38 mW of power from the flywheel. The blue and red data points are from two separate data sets. The lines in this figure correspond to the approximate curve-fitting equations shown adjacent to them.
The lower plot in figure 1 is for the same engine configuration except that it is not sealed (NS notation). The engine was unsealed by separating the hot plate from the body by approximately 1mm. This change eliminates compression by the power piston and removes at least some of the internal air resistance as the displacer cycles up and down, forcing air through the regenerator. For this case the graph shows about 21 mW for the total frictional power loss at 5 Hz.
When this engine is running unloaded at 5 Hz it must be producing more that 21 mW to overcome all frictional sources, but probably something less than the 38 mW to run the engine as a heat pump. We can also look at the friction sources divided into various engine components.
Figure 2 Frictional power loss of the flywheel and power piston
For the middle plot in figure 2, the yellow and green data points, show the friction for the engine disassembled so that only the flywheel is attached to the crankshaft and spinning in the ball bearings. For this case the graph shows approximately 4.7 mW at 5 Hz. The data appears a little noisy for this case because low friction of the bearings makes the rate at which the flywheel’s speed drops very slow.
The upper plot in figure 2 shows the results of testing the engine with just the flywheel (FW) and the power piston (PP) connected. The power piston is cycling up and down in the power cylinder, but the engine is not sealed so there is no compression work.
By subtracting the flywheel alone case (using the approximate curve equation) from the curve equation for the flywheel with power piston, I created the lower plot in figure 2 which should correspond to the friction of just the power piston reciprocating in the power cylinder including associated friction such and the crank pin rotating in the connecting rod. It appears to be about 1.2 mW according to the graph. This is quite low friction, but as we will see in a moment, the power piston is not so perfect with compression.
Figure 3 Frictional losses for power piston compression.
The lower plot in figure 3 is the same flywheel plus power piston configuration without compression shown in upper plot of figure 2. The upper plot in figure 3 shows the results for the same configuration except the engine is sealed in this case so it adds the power associated with the power piston going through compression and expansion cycles. The difference between the upper and lower plots in figure 3 (the middle plot) show net power consumed by operating power piston with compression. At 5 Hz the additional power required for the compression and expansion cycle is 10 mW.
The compression and expansion friction loss in this engine should have two primary causes.
First, air leaks out of (or into) the engine when the internal pressure is higher (or lower) than the external pressure. As the flywheel turns around the power piston alternately compresses and then expands the air inside the engine. If the engine friction is low and it does not leak, the piston behaves almost as though it is compressing a spring and then getting most of the more back. The leak means that it is not getting as much of the work back.
The second source of frictional loss is due to the increased pressure on the crank pins, connecting rod, and off-axis force on the power piston in the cylinder. The increased forces causes more friction than when the power piston is cycling unloaded.
My measurements and computations for the increased friction due to the air leaking corresponds to only about 2 mW. I measured the engine leak rate at 1.8 cm3/sec-kPa (or 9.5 cm3/sec-psi). When I simulated the engine with this leak rate, I was surprised to find that the additional work from this source doesn’t vary much over the tested speed range. At high speed not much air leaks out during the each cycle, but there are more cycles. A low speed more air leaks out during each cycle, but there are fewer cycles.
I have not measured the increased frictional work from the second source so I haven’t made any firm conclusions about this frictional contribution. Perhaps I’ll visit that topic in a future article.
Figure 4 frictional loss due to the displacer
The lower plot in figure 4 is just the power loss due to the flywheel and crankshaft rotating. The upper plot shows the total power loss due to the flywheel plus the displacer cycling, but unsealed. The difference between the two is the middle plot that indicates the displacer adds about 14 mW at 5 Hz.
(revised 02/12/2013. Figure 5 added plus some text)
Figure 5 shows the frictional power loss contribution of each part of this particular Stirling engine according to my measurements. The complete engine friction is for the engine operating as a heat pump. There is no temperature differential between the hot and cold plates. As a heat pump the power piston compression friction will be greater than would be the case for the engine running as an engine. The displacer gas friction should not change whether the engine is running as a heat pump or an engine.
I am reluctant to subtract the entire contribution of the power piston compression-related friction. My computations show that about 2 mW at 5 Hz will be lost due to gas leakage from the engine. (It leaks gas at 1.8 cm3/sec-kPa.) I have decided it was best to leave chart representing the data as measured for the engine as a heat pump.
The data shows 7 mW of power lost to displacer gas friction at 5 Hz. This 7mW is the work done by the displacer to force the gas back and forth through the regenerator.
Now I have a good idea of the main sources of frictional power loss in the engine. I could run more detailed tests for additional information. For example, I could remove the regenerator and see what difference it makes to the displacer frictional load.
My interest in making these measurements is both to understand the sources of power loss in the engine, but also to determine how much power the engine must produce just to overcome the unloaded engine friction. This information lets me compute how much power the engine is producing thermodynamically when it is running unloaded.
How to make your own engine friction tests
My next article will cover in detail how to perform the engine friction testing using flywheel deceleration for this engine or any engine.
As you may have noticed in the photo at the top of the page, the engine setup now has a motor/generator that can be connected to the engine for testing with the Stirling engine loaded. That should show up in a future article too.