I've recently had to fit a new wheel and rebalance my 8" twin wheel grinder. The method I use is pretty straightforward but may be of interest because it doesn't seem to be well known
A good start is to dress both wheels and then remove and individually statically balance each wheel. This only a partial cure because even a small amount of eccentricity in remounting the wheels can result in significant vibration.
Balancing the wheels when mounted on the grinder is much more difficult because it's not easy to find out how much weight is needed, where, and on which wheel.
This normally needs a proper dynamic balancer but, with a bit of patience, the job can be done with an oscilloscope and an old 2" computer loudspeaker.
The speaker is converted into an accelerometer by epoxying a
5/8" dia x 5/8" brass slug to the front of the voice coil. This drops the bass resonant frequency to about 75Hz. A small 50 to 100uf electrolytic is shunted across the voice coil to get rid of most of the high frequency bearing noise.The rear of the speaker magnet is anchored to the pick off location on the grinder. One wheel is removed and the scope is then used to measure the vibration level generated by the remaining wheel.
The grinder is located on a piece of thick carpet or bungy rubber feet.
The balance weight holder that I use a is cup shaped similar to tin lid. This is bolted facing outwards on the side of the wheel and the balance weights are lumps of modelling clay pressed to the inside of the cup rim. It's convenient to roll the modelling clay into a long cylinder which can then be cut into appropriate lump sizes.
The balancing method is based on orthoganol balance weight placement.
Mark positions 1,2,3,4 each 90deg apart on the cup. Put a sufficiently large lump of clay on position 1 to roughly double the vibration amplitude. Then by successively halving the lump size and alternating as necessary between positions 1 and 3 reduce the vibration amplitude as much as possible. Unless you are lucky with your first choice of position this first reduction may be fairly small.
Now repeat the exercise but using positions 2 and 4. This will allow further reduction. Because these weights are positioned at 90 deg to the 1-3 axis (orthoganol), this weight change on the 2 - 4 axis does NOT affect the correctness of the weight added on the 1 - 3 axis.
However with the reduced vibration amplitude you can now increase the 'scope sensitivity and rebalance 1 - 3 more accurately. The balance can be improved with smaller weights and higher sensitivity settings until the display becomes too noisy to detect the basic sinusoidal unbalance signal or shows a consistent slow beat.
This beat results from the beat frequency between the 2F torque vibration produced by a single phase motor and the slightly below 1F frequency of the unbalance signal (F=supply frequency). It's easily distinguished by observing the unbalance signal change as the motor is switched off. Once you're down to this level further balance adjustment is pointless.
It's vital to be methodical in steadily reducing the size of the correcting weights that you add as you approach correct balance. This is because the 'scope only tells you the amount of the unbalance signal - not heavy or light. An improved reading can result from either not quite enough added weight or a bit too much - the result is the same. This ambiguity is first resolved by trying the same added weight at both the 1 & 3 (or 2 & 4) position - the result tells you which way to go.
Once you're getting near balance the 1 & 3 readings may be similar because the added weight is just enough to almost symmetrically bracket too heavy and too light. This is resolved by trying 1 & 3 again with the next smaller weight.
Once balanced, dress the wheel and check that the balance hasn't changed
With the first wheel safely balanced, add the second wheel and repeat the process.
P.S Pressed down and properly located on the inside rim of the cup modelling clay is OK as a permanent solution. However in the enthusiasm of making useful progress it is easy to carelessly dab a piece on and to find it later flying across the workshop. Be warned - a small piece of clay may not be life threatening but it's better not to stand in the line of fire!
Jim