Structural Dynamics of an Opposed-Piston Engine with Flexible Structure
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The following presentation will demonstrate the approach in structural dynamic durability analysis that we are taking at Achates Power. And we will also see some actual results that came from that work on structural sensitivity study and successful mitigation of a gear train resonance.
Here is the outline of the presentation. I will start with an introduction on the opposed-piston engine, in general. Then, I will give you an introduction into the model and boundary conditions as well as into a structural dynamics procedure that we are using here at Achates Power. We will have a results section that is divided into structural dynamics of the support structure and the gear resonance issue. Finally, I’ll show you a slide on model correlation and we’ll have a conclusion.
What is an opposed-piston engine? In an opposed-piston engine, two pistons come together at top dead center and move apart under combustion. Generally, two-stroke diesel opposed-piston engines have great cost and weight advantages due to their low complexity and, on top of that, great fuel efficiency.
At Achates Power, we chose to use ADAMS-based Virtual Engine. In general, at Achates Power, we have put a lot of emphasis on analysis both on the combustion but also on the durability and dynamics side. It is very important that we have an open architecture software with which we can model the unique mechanisms that we are looking at in all their complexity.
The Achates Power opposed-piston A40 mechanism is an innovative inside-out mechanism. Two crankshafts drive, we use six connecting rods, two pistons and one cylinder. The two crankshafts are connected by a gear train and when you look at the animation, you see that the connecting rods are permanently under tension. This leads to mirror compressive loads into the block structure rather than in conventional engines where combustion loads lead into high tensile loads into the caps. Additionally, the opposed motion of the pistons leads to partial cancellation of the gas loads at the location of the main bearings. These two effects allow for very light-weight support structure design. Even though the mechanism looks quite complicated and complex, it only has about half of the components of a conventional engine.
In this next slide, now, we see the model. As already mentioned, we’re using the engine and we usually start out with a kinematic model in constraint bearings and we evolve that into a fully flexible model in hydrodynamic bearings. The two crankshafts are connected through a gear train, which is shown in the lower picture. The output shaft is placed at the lower idler, which is depicted yellow, and a single flywheel is mounted to the output shaft. It is very important that we connect all the components of our cranktrain into one single model to get the full interaction of gear train dynamics and meshing arrows between the two crankshafts into the complete cranktrain dynamic analysis.
On this slide, we see the dynamic durability procedure as it is applied at Achates Power. We usually start out with a kinematic model in ADAMS VEngine. We apply boundary conditions as gas pressures, temperatures, oil viscosity and so forth. In the next step, we create finite element models of our major components like the crankshaft. We build an assembly of the components and run a modal analysis as a first indication of resonances to expect in the engine speed range. The next step is to perform, on a component level , a modal reduction—according to Craig Benton. What this does is it reduces the number of degrees of freedom by a huge amount. Typically, for example, for a crankshaft, of course depending on the size, we go from 1 million degrees of freedom to about 100 degrees of freedom, which has a huge impact on the later run time. We usually pick the degrees of freedom that we want to preserve and use as interface points later in the multi-body model, for example, for bearings and flywheels and so forth.
The modal reduction does not impact the information on mass and stiffness of the component, so we have full structural information of each of the components. At the same time, during the modal reduction, the stress modes can be calculated and used for later fatigue analysis—I’ll come back to that in a minute. We then take the modal components and put them into the multi-body model. Usually, we then run all of the results that we like to look at. For example, torsional and bending deflections of the crankshaft, loads like forces, moments and also bearing results including the minimum oil film thickness (MOFT).
Another result of the multi-body simulation is the participation factors. These can be combined with the modal stresses as mentioned before to a full-cycle stress evaluation of the component and we can also use that for further fatigue analysis. The limitation of this last step, however, is two linear components—meaning linear behavior, linear material, and so forth, because the method is modal based.
We’ll dive into the results section right now and I’ll start out with the structural sensitivity of our support structure, or engine block. What you see on the slide is the bending deformation of the crankshaft. We started out with a flexible crankshaft in a rigid block and you can clearly see in the upper picture that there is resonance in the fourth order at 3000 rpm. The lower picture then shows the result with a flexible support structure and you can clearly see that not only do we get responses in the crankshaft in orders 1-4, instead of just fourth order, but also the frequency content has shifted significantly. Even though those results fulfill the Achates Power requirements for crankshaft bending, we thought that some more stiffness would be beneficial for the overall solution so we added 20% as an overall blanket to the support structure and you see the result on the right bottom picture. The resonances are gone and the bending amplitudes have significantly diminished. So, in the next step, we used ADAMS Engine to provide local stiffness improvements and guide our design into the right direction by simultaneously keeping the weight low.
This next slide shows another effect of the support structure stiffness. We’re looking at pin bearing forces at this point. The upper left picture shows the purely kinematic result. When we move on to the right side, we see what the added inertia does to the bearing load characteristic and then, in the lower left picture, we see the influence of added crankshaft flexibility. You can clearly see that the load picks up on the dynamics of the crankshaft and, at the same time, the maximum load drops. The lower right picture, finally, shows a combination of all flexible components—crankshaft, connecting rod and block—and, again, we see an increase in dynamic and, interestingly, the maximum load goes up slightly, which is an indication that we cannot neglect support structure stiffness when we do bearing layout with particular focus on weight.
With this slide, we’ll move on to the gear resonance mitigation. During the A40 four-cylinder testing, we found a gear noise or resonance behavior. However, due to the limited instrumentation of the engine, we could not correlate the model. But, we could qualitatively describe with the analytical model what was going on on the test bench. It is described in the upper left picture. We’re looking at gear separation forces, which are an indication for the impulsiveness and the dynamics that are going on in the gear train. We see that over speed, the gear separation force rises up to about 1500 rpm and then immediately attenuates to very low levels. When we look into the time domain results of the gear separation force in the lower picture, one right in the resonance at 1500 rpm and the other in the attenuated zone at 1600 rpm, we can clearly see that the dynamics are quite different.
We used our VEngine model to do a sensitivity study on different kinds of influence factors to reduce the gear train noise resonance and the dynamics that were going on at that time. There were multiple solutions that came to mind and we had to categorize them into three different sections. Section 1 would be all solutions that had no, or very minor, impact on the design. Section 2 had medium impact on the design and Section 3, finally, were a major tear up of our current design.
Unfortunately, I cannot show all the results that we have been looking into so we’ll see some very representative results on this slide. On the upper picture, we see the results of the measures that had minor impact on the mechanism design, such as reducing the backlash and changing the inertia of the flywheel. You see that reducing the backlash had minor improvement whereas the flywheel had next to no impact on the gear resonance dynamics. The benefit of this, however, is that we were able to take out the flywheel of the mechanism, which saved us approximately 14 kilograms.
In the medium picture, you see the result of one of the medium impact design changes, which is moving the power take-off from the lower idler gear to the lower crankshaft. You can see that there’s significant improvement with this measure. In the lower picture, we see the influence of moving from one flywheel on the output shaft to two flywheels, one on each of the crankshafts. This has also a very beneficial influence on the dynamics. However, it’s a major impact in design. That said, we have seen that at least in the resonance speed, the moving of the power take-off to the lower crankshaft is beneficial. So we had to prove that this is a solution for the complete speed range. What you see in the left lower picture is the state where we started out as a waterfall blot over the complete speed and frequency range of the engine. On the right lower picture, you see the results after the tuning of the tortional vibration damper and the flywheel on top of moving the power take-off to the lower crankshaft and we can see that the resonance is gone, or basically, it has moved up above the upper speed range of the engine.
Finally, I’ll show you a slide on model correlation. Our results are only as good as the models that we produce them with. So we, at Achates Power, we put a lot of emphasis on model correlation. What you see here is crank nodes speed fluctuation signal. You see 1200 rpm on the left side and 2800 rpm on the right side of the picture. You see in the upper portion of the picture, the time domain data, which already looks like it’s correlating very well. However, we always have to look also at the frequency domain so we can make sure that we really also hit the right frequency content. When we look at the 1200 rpm, we see that there is a slight over-prediction in the fourth order. But, other than that, we have good correlation. At 2800, we can say nothing then that we have excellent correlation.
This brings us to the conclusion of this presentation. We can basically demonstrate four things. For one thing, with the ever-demanding requirements in fuel consumption and emissions, it’s not only important to focus on combustion development but also on the mechanical side of the engine development. We have demonstrated the use of the software to our benefit. We were able to do sensitivity studies on support structure and to mitigate a gear resonance. And, third, we could guide our design into the right direction with the means of the mechanical analysis. Last, but not least, we could demonstrate the integrity and sound design of the Achates Power A40 mechanism. We did show that it is a viable mechanism for power take-off in the opposed-piston engine.