Some of my most popular posts world-wide are the torsional discussions. So, I thought for my 100th blog post I'd spend a little time writing about the nature of these twisty harmonics, where they come from and what they look like in rotating machinery...
- The four stroke and how torque looks to the transmission of a vehicle.
When ignition takes place there is a sudden rise in pressure inside the combustion chamber. This pressure is essentially what gets turned into motive force as the crank shaft inertia carries it over top dead center and the gasses are allowed to expand as they burn the fuel at some f/a mixture. Most engines these days are 4-stroke thermodynamic cycles... Atkinson, Miller, Otto, Diesel, lots of thermodynamic nuances are associated with the various cycles but they have one thing in common so they all look similar (not exactly the same) but very similar to the torque that ends up at the flywheel.
So 4 strokes... just to catch up some of my non-technical readers, is the description given to the number of times the piston either rises or falls during a complete combustion cycle. For example, in a common diesel engine and starting from an arbitrary top dead center position let us define these "strokes."
1st stroke if you will, the starter motor turns the flywheel which is attached to the crankshaft. The inlet valve opens and in comes a fresh charge of air in our Diesel Cycle, gasoline and air in our Otto Cycle. As the piston arrives at the bottom of it's first stroke, the inlet valve closes. This turns the combustion chamber into a closed pressure vessel for the moment. This is called the Intake Stroke.
2nd stroke is the crankshafts turning now advancing the piston up from bottom dead center, with inlet and exhaust valves closed. As the piston compresses the air in the diesel cycle, temperature rises. Pv=nRT remember. So as pressure climbs, so does temperature. The same thing is happening in the Otto Cycle or gasoline (benzene engine) only the pressure rise is much lower. Why? that's a discussion for another day. Lets just acknowledge that the two different fuels ignite at different temperatures with different burn rates and energy release. These different chemistries require the different pressures to yield useful power to the crankshaft. Somewhere near top dead center of the second stroke, an injector atomizes diesel fuel into the combustion chamber - the temperature rise created by compression then ignites the fuel/air in the Diesel Cycle, or the spark plug ignites the gasoline engine's charge of fuel and air in the Otto Cycle. So a few crankshaft degrees away from TDC the charge ignites. The pressure increase in great and fast, and the flywheel inertia beats the burn rate induced pressure to get us back to TDC with rotational momentum. This is called the Compression Stroke.
The 3rd strike then, is the piston traveling back down the cylinder bore. The valves are closed and the pressure rises as the fuel is burned and the various chemical reactions take place. As the piston nears Bottom Dead Center (BDC) the exhaust valve pops open... This is called the Power Stroke.
The final stroke is the piston travel up from BDC with exhaust valve open. The piston pushes out the burned gases and as it nears TDC the exhaust valve closes, and the inlet valve starts to open... In actuality the valves open and close with durations that overlap. This is useful for a lot of reasons, but again, fodder for another discussion on emissions and volumetric efficiency.
Now we return to the 1st stoke all over again... suck, squeeze, boom, blow... that's how a 4 stroke cycle engine works.
Now think for a moment on what that sudden pressure rise looks like to the flywheel. The entire process takes 4 strokes, which require two crankshaft revolutions to complete. DING. Imagine two complete revolutions with one large asymmetric torque rise in the repeating cycle. That describes in words why we have harmonics. Now lets see a visual on that...
What does this look like then?
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The top line is combustion pressures effect on the slider-crank mechanism - torque, the lines below show the descretized sine waves that summate to the original wave form. So note, phase, frequency, and amplitude are a function of the conrod length, piston mass, crank length, boost, valve overlap and fuel charge rate and consequent fuel burn rate... The lines below the "torque curve" are referred to as "orders" - basically multiples of crankshaft speed for ease of use in building the resonant speed diagram for a system and later in understanding what order may be exciting a system mode dynamically.
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Another post on what to do with this information and how it gets used in a forced response model is coming! I'll eventually write up the numerical solution to the set of ODE's that drive the forced response simulation. For me, this has always been one of the most enjoyable areas of engineering. There's crankshaft angles, coupling heat load capacity, and a lot of other details to ponder. The intersection of the engineer's application of math to the solution of torsional vibration problems is one of those existential pleasures of engineering!
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| The development and solution of the equations are pretty straight forward, however there is a lot of detail in how you treat damping, various crank throw stiffness, inertia torque (which is opposed to gas torque) and other interesting phenomena. Electric drives and gearboxes all have their own effects... as well as drive shafts, chains, tires, axles, propellers, impellers, ... they all make up the system and they all provide vibratory energy storage which means they all to a greater or lesser extent shape the modal response curve. The pic is from a book I wrote a Torsional Vibration chapter in many years ago. Identifying resonances and synthesizing drivetrains is a very interesting engineering activity. |
Summer is flying by, so that's all for now,
Lee
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