This spreadsheet is based on a Nicolet application note (#11, October 1977) for balancing with a Real Time Analyzer (RTA), which is a type of spectrum analyzer. An RTA is not strictly necessary if the speed of rotation, and thus the signal frequency, remains constant. Any type of filter, like a GR 1564-A Sound and Vibration Analyzer, an HP 3581-A Selective Voltmeter or simple DIY op-amp bandpass filter, tuned to the frequency of interest, will suffice to eliminate extraneous signals that complicate the measurement.
Typically you will measure the RPM of the device-under-test (DUT), say 1740 RPM for a motor, divide by 60 to get RPS, and set your bandpass filter to that number, 29 Hz. You can dispense with the filter if the signal of interest is pure, but most machines and mechanisms have additional rotating parts that will contribute their own out-of-balance signal and contaminate the measurement. Note that low speed devices of a few hundred RPM have very low rotational frequencies, and will require correspondingly low filter frequencies.
Four vibration amplitude measurements must be made using an accelerometer or displacement gage. The first is made with the DUT in its unbalanced state, this is R0. The DUT is then stopped and a zero degree reference mark is made. A trial weight is attached at the mark and a second vibration amplitude measurement made, this is R1. The DUT is stopped, and the weight is shifted to a new angle, "a". A third measurement is made, this is R2. The DUT is stopped and the weight is shifted to "-a". The fourth measurement is made, this is R3. The resulting numbers are entered into the balance equations, resulting in the location and mass for material addition or removal to achieve balance.
Note that the angle around the device is measured from the zero reference mark, ideally 120 degrees in one direction, -120 degrees in the other. It doesn't matter which way is chosen for + and -, as long as it's consistent. The first direction chosen on the following page will be defined as positive. It is assumed that all test and correction masses are placed on the same radius!
Two plane balancing can also be done by alternately restraining the device at each of two planes, typically near the ends, such that it can only pivot. Balance the plane away from the pivot as described above. Switch the pivot to the balanced plane and balance the other plane. This will result in fully dynamic balance. A test stand with support bearings and pivots that can be engaged and disengaged is typically constructed for this type of work.
More information can be found in textbooks on Mechanical Vibration, but modern works tend to be mathematically dense and rather useless in terms of practical application. Texts from the 1950s are far more useful, say Mechanical Vibrations by Den Hartog (McGraw-Hill, 1956), or better yet Theory of Vibrations for Engineers by E.B. Cole (Crosby Lockwood & Son Ltd., 1950). There are also some newer books available on Amazon by Victor Wowk, though I don't have copies yet
What if I don't have an accelerometer and a filter?
See note below about using a smart phone!
These items can be expensive unless you can locate them surplus. If you have more time than money, and a bit of creativity, it's possible to make suitable tools and do just as good a job as with commercial tools.
For an accelerometer, you can use a small loudspeaker. Find something in the 1"-4" diameter range from an old radio or such. Glue a mass to the cone near the center, around the dust cap. This can be a ring made of a few turns of plumbing solder, a machined brass ring or some other non-ferrous thing lying about the shop. The magnet on the back will be handy to hold the speaker on the device to be measured. Or, dispense with the extra weight and couple directly to the cone. This may only be practical when using a balance stand to support the DUT.
There are also inexpensive chip-based accelerometers available now. See the Analog Devices website for part numbers like the ADXL320 and also various hobbiest websites like Spark Fun Electronics that sell the sensors on small circuit boards. These chips will give you the maximum sensitivity and best results.
Next, you'll need some way to measure the signal. If you're handy with electronics, it's easy enough to build an amplifier and filter. Use an opamp and maybe a digital filter chip. If you're not handy with electronics, no problem. Just download one of the free spectrum analyzer programs available and use your PC. Connect the modified loudspeaker or other accelerometer to the microphone input of the PC and you'll have a very sophisticated measurement system for almost no investment.
Note that when using a spectrum analyzer, you'll only be concerned with the amplitude at the rotational frequency of what you're trying to balance. The frequencies will be low, so optimize the settings for less than 1kHz and average to get a clean trace.
There may be other ways to sense the vibration. A laser pointer can be attached to the device and the beam deflection measured on the wall across the room, or a mirror can be mounted on the device and the laser reflected off it. The traditional method was to use a dial indicator and a test stand that allowed for significant deflection. Though the rapid pointer motion probably isn't good for it, the dial indicator will act as a low pass filter and should give a quite useable TIR. Anything that will let you assign a number to the vibration level is fair game, though acceleration measurements usually give better results than displacement.
Most smart phones now have built in accelerometers. You can use these to take the required measurements. On the iPhone the Vibration app by Diffraction Limited Design is a good app, because it allows you to plot the data in the frequency domain with RPM as x-Axis. However this is a paid app. If that is a concern just look for an app that at least gives you peak and RMS acceleration values.
Many thanks to Nick Ivanov from http://www.aerialphotoimage.com for helping to sort this out- have a look at their very nice aerial photography!
Original Excel calculator by Conrad Hoffman, Deep Run Design, Send Mail
Conversion from Excel to HTML5/Javascript by Greg Carter, Send Mail
Have questions? Post them in the Practical Machinist forum thread about this calculator.