At the risk of overextending an off topic discussion - more thoughts on home brew balancing.
The earlier orthogonal method is a conveniently simple method of single plane balancing but it falls short of true dynamic balancing because it ignores unbalance couples - forces generated by equal and opposite weight unbalance but located at different points along the length of the shaft. This is not too important in the twin wheel grinder case with individually balanced wheels, but is essential when balancing a turbine or the long armature of a high speed motor.
In this case, if freely suspended, the component axis movement can be considered as the combination of the static unbalance and the couple unbalance.
The static unbalance exerts a radial force that causes the component to move as a whole and describe a small cylinder parallel to the mechanical shaft axis and slightly displaced from it.
The couple unbalance exerts a twisting force trying to move the ends of the shaft in opposite directions so the movement describes something like a small diabolo - two cones apex to apex.
An accelerometer (or velocity sensor) mounted radially central between the the two bearings and near the C of G will reliably indicate the static unbalance component but ignore the couple component. With this, using the previous orthogonal balancing sequence, the static unbalance can be cancelled out either by weight adjustment at the centre of the armature or, if this is not convenient, by pairs of equal weights, at two chosen locations equidistant either side of centre.
With the component now static balanced the problem is to sense the couple unbalance while ignoring the static component. Commercial dynamic balancers do this by strategically using the outputs of more than one sensor combined in a way that cancels the static component but retains the couple element. This is a non-starter with our crude 2" speaker accelerometer because of uncontrolled phase errors.
Curiously enough, exactly the right direct measurement component is readily available . A properly balanced (balanced so that the needle position is unaffected by change of attitude) moving coil meter is ideal. The moving coil output voltage is a sensitive indication of the twisting movement generated by an unbalance couple.It is also almost totally insensitive to the lateral movement generated by static unbalance.
With one of these mounted above the component face down with the moving coil axis aimed to intersect the component shaft axis at right angles, the twisting couple component is directly indicated. It can be corrected by adding equal pairs of weights. one at 0 deg and one at 180deg at the chosen locations spaced along the armature.
This can be treated in exactly the same way as the orthogonal static balance with the pairs of weights trimmed independently at 0/180 and the quadrature pair at the 90/270 positions. PROVIDED that the weights are accurately equal and equally spaced about the C of G this has NO effect on the static balance.
In practise there are likely to be small errors in the equality in the weight and spacing of the added pairs and this will generate second order static unbalance errors. The joy of this system is the almost complete independence of the static and couple unbalance indication and adjustment. The error can be simply corrected by returning to the 2" speaker sensor, The new small static unbalance correction will have no significant effect on the correction for couple.
The scheme was tried using a 2" square 1mA 35 ohm taut band suspension meter. It behaved as expected but needs a bit more'scope gain than the speaker sensor.
However two new problems occur. Firstly the coil picks up the stray magnetic field from the motor and this swamps the wanted reading. Secondly it's not easy to add repeatably "identical" pairs of lumps of clay in pairs of locations. The random weight and position errors are large enough to compromise the independence of the static and couple correction indication.
The stray magnetic field problem can be solved by belt drive of the test piece or by taking the reading at the instant the motor power is removed.
The weight problem needs better precision. The weight adjustment needs to be capable of adding (or subtracting) closely matched adjustment pairs in well defined 90deg location pairs. A binary sequence of matched pairs of weight increments is convenient.
These are soluble problems for the serious user but it needs careful preparatory work. It's no longer a casual Sunday afternoon experiment
Jim