- Oct 18, 2003
- Saline Michigan
The whole topic of PSRU's and drive shafts and torsional vibration has been talked around and I keep seeing the same difficulty in the thinking of the involved folks. Since we on HBA tend to be an intelligent bunch, I got to thinking about how much I had to work to get my arms around the whole issue. So, this little lecture was put up on a thread, and now we are trying to make it a sticky to help everyone who is interested get a grip on the basics.
Let's start off by saying that the science of vibration control and management has lots of smart people working at achieving the goal of the dead smooth system, and at minimum weight. And there are still new things happening out there, but mostly, it is exploration of existing knowledge.
Every field has its nomenclature. Let's define a few words so that we all know what we are talking about.
Components - Masses are things that resist changes in speed and require forces to accomplish those changes in speed. Springs are things that store energy and have a force associated with them when deflected. For our purposes, let's assume that our deflections are all elastic, meaning that load and deflection are related by a fixed spring rate, and that when the load is removed, the spring goes back to its original length. Spring rate is k, mass is m.
Frequency - this is the rate at which a component or system is vibrating, usually in whole cycles per second.
Orders - this is the number of times per rotation of a device that something occurs. A single cylinder four stroke engine has firing at one-half order (a firing pulse every other rotation), and a V8 has firing at fourth order. In addition to the firing order, we also have other vibrations at twice the firing order (from the pistons going up and down in the cylinders), three times and four times the firing order from other imbalanced movements, and fractions of the firing order because the various cylinders do not have exactly the same firing pulses.
Systems - This is everything in a chain of structure that is connected together. Usually, these structures have a purpose, like transmitting power, and the power does not come through dead smooth. If you have a system with masses (not springy) connected by springs (no mass), you have the easiest schemes to conceive of and model. Think two masses with a spring between them. They also pretty neatly describe a lot of what is out there as many parts are relatively light and springy or relatively massive and stiff. The other end of the scale is systems made up entirely of components that have significant mass and are springy. They are a little more difficult to manage mathematically. Think of a conventional radio antenna on a car, vibrating in the wind or a strings on a musical instrument. Understand that generally, most systems have six degrees of freedom - three linear and three rotational. Yes, motion in some degrees of freedom is more limited than in others, but it still exists. For simplicity, we will work in rotation along the intended rotation axis. If it helps you to think in terms of linear motion, go ahead, the theory works the same.
Mode - This is the shape of each of the vibrations that a system can do. In the case of a string of masses and springs, there is one mode (in each degree of freedom) for each pair of masses in the system. Two masses on a spring has one mode, where the two masses vibrate towards each other and then away from each other, and the frequency is set by the ratio of mass to spring rate. Three masses and two springs have three primary modes - M1 vs M2, M1 vs M3, M2 vs M3, and the frequency that each runs at is dependant upon the ratio of the mass to spring rates of each set. That same set of three masses will also have a modes where two masses will move together vs the other mass. More masses means more modes to manage and the number of modes go up faster than the number of masses.
Resonance - If you have a forcing function (firing pulses from the engine, imbalance, universal joints running at even small angles, gear teeth engaging/disengaging, turbine blade passing frequency, bearing defects, propeller blade/wake interference, and more) that occurs at the same frequency as one of the modes, you will amplify the mode, and there is no theoretical upper bound on how much. This is how a swing can go so high - we pump its oscillation with inputs timed to the oscillation. It does not have to be every stroke, and it does not have to be strong, just repeated.
Amplification - When the mass vibrates more than the forcing function does, the vibration is being amplified. The system will amplify when the forcing frequency is "near" a resonant mode.
Damping - Let's stick with the engineering version. Damping is energy removed from the motion of the system and is generally converted to heat. Elastic structures have very little damping. In metal structures, it is generally below 1%. Strike and hold a key on a piano, and it takes a while for the note to die out. Composites are also very low on damping. Wood is a little better. Rubber does even better. If you want to take out energy faster than you can dissipate energy to the environment, your damper will increase in temperature. And air, well, it will only develop much energy loss if the speed of the motion is high. Yes, the prop is moving fast, but even destructive vibration is at tiny distances and equally small speeds. Usually, we can ignore damping of a device vibrating at small displacements in air without significant errors.
Absorbers - Three types, those that are tuned to a frequency, those that are tuned to an order, and those that are actually dampers.
Frequency tuned absorbers are a free mass on a spring attached to a vibrating part of a system. To be effective they have to be as close as possible to the vibrating mass that we are attempting to tame, and they have to be tuned to vibrate at the frequency that the mass is vibrating at. When sized and tuned and located correctly, they will prevent the resonance, but at frequencies near the resonance, they will cause modest increases in response of the system. Neat if they work.
Order tuned absorber are devices that will respond to a particular order regardless of speed. Torsional pendulums have been in aircraft engines since the 1930's. The device is a short pendulum that is mounted on a rotating machine, and its natural frequency is dependant upon the speed it is spinning, so you can tune them to any order of rotation you want. Neat. And they are noted for being able to pick off as much as 95% of vibration in a particular order... There are others.
Dampers, well, you make an energy sink and hope that you do not need the energy thrown away. Rubber elements can convert quite a bit of energy, but are difficult to cool. Hydrodynamic devices do similar things and exist for many engines. You can put in a clutch or use belts to drive something, and then let them slip enough to take off the peaks of the forcing function, but you will be able to measure this loss in airplane performance, and you will have significant cooling needs here too.
So, if you have a resonant mode in the range of the forcing functions, you will amplify. If you match a resonant mode with a forcing function, it will amplify hugely. If you apply much damping to the motion, you will have to cool the damping device. If you can pick off the resonance with a tuned absorber, you will still have amplification at frequencies near the resonance that you have to be able to handle. Best solution is to adjust your resonance modes to be out of the range of your forcing functions. Next best is to at least drive the resonance modes to an area where you have little exposure AND little energy to drive the resonance.
We change the resonant frequency of a mode by changing mass or changing spring rates. Each mode's resonant frequency varies directly with the square root of k/m. If you want to double the resonant frequency, well, you have to quadruple the ratio of spring rate to mass. While it is easy to increase mass of something, it is undesirable in airplanes so you have to consider the big picture while you do it. Spring rates, well, if you were weight conscious in the first place, you started near minimum spring rate too. Increasing spring rate requires adding diameter or thickness or both.
If you really need to drop spring rate somewhere and can not do it with a component that already exists, you can put in a spring deliberately. This is called a spring isolator and they are widely used. Get this, they are called dampers - misnomers exist. While they do have some damping, springs rubbing on their housings and the like, they are primarily soft springs in the system. Ground vehicles and stationary engines use them between the engine and the shaft going to powered device. We use them in manual transmissions, automatic transmissions, and even hybrid powertrains. The biggest single reason for using them behind engines is to avoid exposing the downstream components to the full fury of the firing pulses. The gadget sucks up the energy of the pulse and distributes it later as the pulse eases. You still get the firing pulse at the firing order, but the peak is greatly reduced, and the valley is not as low... Putting a really big flywheel on the engine would do the same thing, but a spring isolator is so much more compact and lighter. And you had better believe that their rates and travels matter. I have made a big portion of my living since 1996 working with these guys to make our ground vehicles smoother and more fuel efficient.
So, on to common discussion topics:
If you change one spring rate or inertia in your system, you will change not only the resonance frequency of the pair of inertias attached to the spring, but you also influence all of the modes that those two inertias participate in. You fundamentally can not isolate one vibrating element and let the others do their thing. Changing one shifts many of the others;
You can put in more flywheel effect to reduce the amplitude of a forcing function and to move the resonance downscale, but the forcing function is still there and still at its original frequency. Just understand that while you drive down one mode's frequency, you drove down some others too. Common to get one mode out of the way and drag in another mode (or two). Also remember that your biggest rotating inertia (by far) is your propeller in most airplanes. In boats, the propeller may also have significant inertia, but it will usually be much smaller.
You can change the spring rate or put in spring devices to shift things, but just remember that shifting one mode out of the way does drag other modes too.
Airplanes have very little damping in their systems unless you put it in there, so much of base resonance theory holds in airplanes. The things we get away with in cars looks like murder by comparison. We have so much compliance (low spring rate elements), and so much energy absorption (rubber and hydraulic mounts, isolator hysteresis, torque converter losses, tuned absorbers with rubber in them, tires, suspension components with rubber and hydraulic mounts). If you put in damping, remember to find a way to cool it adequately.
Motorcycle systems - wow, completely different from cars and planes. Generally they can have very low order forcing functions (H-D racing v-twins run 45-645 degree firing spacing, so they behave like a really big single, the production ones use 315-405 spacing), and so would require a positively huge isolator. Instead they go for hanging a rubber isolator at the back wheel. And they recognize that the back tire is slipping at high torques, and the high perf end is in active engine management due to tractive limits until way up in the speed range. Yeah, they cut back on power to keep the back tire from running away.