Essentially you measure the amplitude of the accelerometer after filtering at the fundamental frequency and compare the phase to a trigger signal. You then add a known trial mass and repeat. Using vector analysis you can determine the balancing mass and position relative to the trial mass.
"Rick" wrote in message news:nli0l.10324$ firstname.lastname@example.org...
Most of the balancers that I'm familiar with, and I've owned two, use a velocimeter and a strobe unit. The velocimeter out put is an integration of the accelerometer and is used because less knowledge of the system is required to produce a balanced system. I have been using these balancers on helicopter main and tail rotors as well as the helicopter engine itself. There are conditions that can cause the phase measurments performed by the combination of the velocimeter and the strobe that can cause you to pull your hair out. To go into detail here would get rather lengthy. There is also a technique whereby all you need is the velocimeter out put filtered to the fundamental frequency. e.g. at 3600 the single plane 1/rev out-of-balance frequency would be 60hz. In fact, I wrote an article for the Experimental Helo Magazine about balancing helicopter rotors without the phase information and a reader successfully balanced his tail rotor using only a dial indicator. It seems that for an out-of-balance rotating shaft operating at an rpm below the critical one will cause a deflection of the dial indicator that is brought up to contact the rotating shaft. Further the response of the dial indicator is such that for a set of higher rpms it is a peak detector. The peak reading recorded and used with a series of placement of known weights at known locations can provide data for a graphical solution that tells you where and how much weight to add to correct the out-of-balance condition. The Russians have long used this graphical technique that avoids some of the problems caused by attempting to derive the phase information where the operating frequency is close to a "critical" frequency where the phase angle is very sensitive to rpm. My balancing experience to-date is limited to the single plane. I have not investigated the issues involved with two plane balancing.
The better you understand the fundimentals of dynamic balancing, the less equipment you will need to do the job. I use an old IRD box model
310 or 320 I cant remember the madel off hand but it has a tunable freqency filter which can double as a calibrated oscillator to drive a strobe to measure rpm of a shaft. There are two sensor inputs and you can measure either displacement or acceleration of the item you are measuring. With a little instruction you can interpet the noises that the sensor picks up by knowing the noise frequency and looking at the gear reduction and each shaft rpm. One way is to use the strobe that is trigered to the freq and look fot the strobe stopped item.
As the others have intimated it's not that complicated, although it can be a compromise on complicated rotors.
A once per rev mark on the shaft is used as a datum from which all angular measurements are taken and all weights are placed.
One transducer per balancing plane. Often two transducers per plane because on a horizontal shaft with bearing pedestals (or any shaft where the bearing mounts aren't symmetrical) the response will be different horizontally and vertically. In that case, balancing can be a compromise. The quickest results are obtained when all balancing planes are measured at once, since on a multi plane/multi bearing/super-critical rotor, a weight at one plane will affect the vibration at several planes.
A datum run is made to measure the vibration of the shaft as is. Vibration can be measured as acceleration, velocity or displacement. It makes no difference to the calculation, only makes a difference if you measure one way and want to compare to a limit another way.
(acceleration is 2*PI*Velocity*revs-per-second, similarly for displacement and velocity)
The datum run will give the vibration phasors at each transducer location as amplitude and phase angle.
Now a trial weight is added to one of the balancing planes. Usually experience will be used for size and placement, but any location will give a result. Another run is made and the vibrations are re-measured.
Now the datum readings are subtracted from the trial readings. This is either done with polar graph paper, ruler and protractor. or by converting the amplitude/phase to complex (x +jy) numbers and arithmetic. Note that the complex numbers are just a way of going from length/angle. polar notation to north/east, map type notation. the first can be worked on graphically, the second can be done with an adding stick.
Sticking with the graphical method, cause it's easier to visualize...
You now have a change in vibration for each balancing plane. This can be presented as vibration per ounce/gram/weight at whatever phase angle away from the weight's position. This is the sensitivity of that vibration plane to weights at that balance plane. For a multi plane rotor, a similar trial run will be done for each balance plane.
Now you need to work out the weight ant position needed to get the vibration back to zero amplitude. For a single plane, the amount of weight and its angle can be worked out by seeing the amplitude and angle needed to move the vibration back to the origin of the graph. dividing the amplitude change needed by the sensitivity and subtracting the angle of the sensitivity from angle of the change needed.
Where there are more than two balance planes, it is much easier to convert the readings to complex numbers (coordinates), then solve the problem as a set of simultaneous equations, since you need the combination of weights on each plane that will give the best overall result. where there are exactly two balance planes, then you can treat the balancing job as a combination of an average out of balance and a couple and still do the job without arithmetic. In that method, you to trial runs with weights in the same position at each plane and with weights at 180deg to each other on the two planes. Then using the first set of figures, minimize the average vibration, which effectively leaves the rotor wobbling around with each end going in the opposite direction. Then the second set of figures is used to minimize the remaining vibration be applying weights as a couple.
If you've got to the end of that, it might seem complicated, but it's actually fairly simple. Where it gets to be a black art is things like power generation rotor lines that might have fifteen balance planes and eight bearings, very different responses in vertical and horizontal vibration, three major critical speeds and rotors that have bent due to a gland rubbing and bend more or less with heat. In cases like those experience of what bits aren't important makes a big difference and perfect results don't happen.
Might be simpler to read it in a book written by someone that's literate!
Mark: I like your explanation. It comes from a different angle than I've seen presented before. I've done the single plane balancing with and without the phase information, but I've never seen anyone use the breakdown to complex numbers. My technique on the helicopter is to get the magnitude and phase information, position the rotor to that angle described by the phase, sight over the velocimeter, and "Add Opposite" or add a weight on the opposite side of the shaft from the velocimeter. Due to possible places to add weight being restrictive on the rotor blade this usually involves a breakdown into spanwise balancing and chordwise balancing. As long as I'm below the "critical" speed this works to the limits of my balancers noise level where the phase data just gets noisy. Of course if I'm above the critical speed "Add Opposite" is replaced with "Add Same". Again I liked your explanation. It appears that you work in this field and have some extensive experience?
Did a few years in the Rotor Dynamics Department in my career's horrible downward progression from Steam turbine performance test engineer to the current Senior computer wrangler. Did both on site work on steam turbine balancing and wrote software to try to get better answers from rotors that were too complicated for manual calculations. The complex number approach is the logical one to take when one throws a computer at the problem, more so when one is using least--square fits to try to get the best result from conflicting measurements. I'd do it by hand (and have) for a two plane balance, but it gets to be hard work with a complicated rotor.
Do you also end up adjusting the attack angles of the individual rotor blades?
Mark Rand (who burned out three 2500hp cooling tower fan motors in trying to get the tower to meet specifications by winding the blades up "just a little more") RTFM
Yes actually the first thing that is done prior to balancing is the tracking. This is checked first at a low rpm to insure that the blades are tracked close enough to allow balancing. There are currently several ways of doing that. I have two small different color led lights that I can attach to the end of my blades looking back at me. Out of track gives me two different light streaks. The light colors obviously give me the high and low tracking blades. At full rpm,1/8 turn of a turnbuckle gives me 1/8" travel on the tip. These lights let you check track at forward flight to check and see if you might have a climbing blade due to airfoil differences. Of course, forward flight is deferred until the balance runs are complete. I understand the conflicting measurements. I have to do the balance runs on my tail rotor with the ship setting on grass and not concrete or blacktop where the vibrations from the engine turning at the same speed gets vibrations to the concrete and reflections back into the frame and down the tail boom an on to my velocimeter. Bad design to run tail rotor at same speed as engine. Are you then a M.E? Stu Fields retired E.E now having to learn a bunch of M.E. stuff. Maybe I chose the wrong career field.
John: I've tried the "Chalk on a stick" and an "F" shaped banner on a stick and now for the stick process I use a center from a paper towel holder taped on some foam attached to the end of a piced of PVC piping and two different colored greas pencils to put a different colored streak on each of the blade tips. This creates two different color streaks on the paper towel center. Adjusment is done until there is only one streak of merged colors.
I thoroughly understand. I now have a 16X40 Victor lathe with DRO, a Bridgeport with DRO a Miller Tig welder that I love, and a Plasma cutter; not to mention box brake, roller, throatless shear and a bunch of sheet metal tools. My education as a EE did not prepare me for this. My basement electronics lab is closer to it but not used as much as the other tools. At least I did know how to do VSWR measurements on my antenna installations. I also designed and built a rotor speed alarm using SMT devices. That didn't take much college education though. The rotor balancing really occupied a bunch of my time to the extent that I built up some bench testing capability for looking at the performance of the electronic balancers and the phase angle changes due to critical speeds. Got a big fat A in dynamics in school and that is a help at least.
I'm an M.E. with a strong statics or slooow turning leaning... probably comes from my early training as tool & die maker, where movement and vibration (the unwanted type) were the bane of our existence.
Among (many) other things I build 1/16" scale sized steam turbo- generators for model steam locomotives. These will easily light up 3 or 4 2.5 volt flashlight bulbs.
The problem is dynamic balancing of the rotor assembly, which turn at about 60,000 rpm. The turbine rotor is 5/8" dia. x 3/16" long, and overhung. The alternator rotor is 3/8" dia. x 3/8" long. Assembly is on two ball bearings.
I've fooled around with an induction type sensor using an oscilloscope for display (that's how I know the rpm). My son built a trigger circuit that will fire a timing light (LED) at peak voltage from the sensor, to illuminate a timing mark on the turbine rotor. The T/G is on a compliant base restricting motion in the vertical plane for the sensor, an old magnetic earphone with the diaphragm stuck to the T/G base.
The problem is that the timing mark moves with the changing speed of the rotor, and while I understand the logic of why this happens, I know too little about the mathematics to deal with it. As a matter of fact that timing mark will move in a complete circle with increasing speed from 5,000 rpm to 60,000 rpm.
If any of you knowledgeable people could point me in the direction for a solution it would be greatly appreciated. I'd be prepared to build a small desk top balancing machine, but need help with appropriate sensors, computer interface, and software or calculation algorithms.