If you put a wrench on the nut on the other end of the shaft, you have a 50/50 chance that the nut you want loose will come loose. If the wrong one comes loose, you can remove that nut completely (and the wheel) then take the nut with you to the store to buy another one. Then put two nuts back on and tighten them together as a jamb nut. Then try again. If the wrong nut still turns, you have to tighten the pair of nuts together tighter.
Clamp the shaft behind one wheel with 'Channelock' or 'Visegrip' pliers, then tighten both nuts. Check the new wheels for 'off-center' running by spinning them with your hand. They may fit the shaft tight enough that there is no centering adjustment--use a 'wheel dresser' (either a stone type or a multi-wheel type) to true up the wheel so that there is no radial wobble. Hope this helps!
I know this is an old post, but maybe it will help others looking for information.
I have the Craftsman 1/3-HP grinder models: 397.19580 & 397.19581.
They are Split-Phase single voltage (115 V), and use a Klixon start-up current style relay - 2CR14-224.
The relay is normally open. When the large starting current in the main/run winding circuit is sensed by the the relay coil (term 3 & 4) which is in series with the main winding, the relay contacts close (term 2 & 4).
The one end of the start-up winding is connected to the main coil's BLK wire in the coil pack.
When the relay contacts close the start-up winding is energized. The start-up coil is used to provide a boost to over-come the resting inertia of the rotor.
Once the rotor reaches between 65% - 75% of operating speed, the current through the main winding circuit is reduced to the point that the relay coil cannot over come the return-springs force, acting on the relay contact arm. With the contacts open, the start-up winding is no longer energized.
This should take about 2-3 seconds, if the relay malfunctions, the high current through the start-up windings (thin wires) may be damaged.
First of all I must warn you of the dangers bench grinders can represent. Here in Britain no one connected with a business is allowed to carry out any maintenance on any none-portable grinding machine unless they have attended and passed a course on the subject and every employer must keep a register recording what maintenance has been carried out and by whom. Grinding machines have been responsible for many industrial "accidents".
Householders and private individuals are exempt from the Law but cannot afford to be less well informed even though the five and six inch bench grinders sold to the domestic user represent a somewhat reduced risk, great care and precautions are still required, not the least of which is the use of good eye protection even if the grinder is fitted with shields.
The first problem about dressing the grinding wheel of a grinder intended for the domestic market is the tool rests are usually too small and insubstantial for the vibrating star-wheel type wheel dressing tool to be used correctly.
A demonstration would be the best way to learn how to dress a grinding wheel and there are many available on Youtube and here is a link to a particularly good video.
Finally, it is best to be aware of one little thought about problem. There is an optimum speed range when a grinding wheel works efficiently and small domestic grinders barely turn fast enough for them to be properly efficient, probably because it is reckoned price and user safety takes priority over efficiency.
The speed that is of concern is the surface or peripheral speed of the grinding surface rather than the rpm of the spindle and should that speed fall too low the wheel will not be able to operate efficiently, will become dull more quickly with a greater tendency to clog and the wheel will become hot in use and hot grinding wheels soon become dangerous.
I hope you will be able to see that by reducing the diameter of a grinding wheel by dressing it also reduces the surface speed of the grinding surface even though the spindle speed remains the same. The relationship between surface speed and spindle speed is why small grinding points need to spin at 20,000 rpm and an eight foot wheel at just a few hundred rpm - in both cases the surface speed is similar.
A domestic grinder should not be used for heavy work but as the size of the wheel is reduced it should be used only for increasingly light work and if it is desired to carry out "normal" grinding operations it would be better to replace the wheel sooner rather than later.
Sears Craftsman is usually easy as Sears Parts Direct has diagrams and part numbers.
However your switch number 31919063033 is no longer available. I would suggest checking out online places like Digikey or Newark for a switch that will work for you. As long as the Voltage, amperage and number of poles and will fit in the space provided you should be OK.
Link to Sears Parts Direct. Searching Model For Search Your Way 31919063 2
Link to Newark Switches Relays 60 674 Products Found
Link to Digikey Electronic Components