I just want the knowledge of how to test armatures and windings on electric motors,for hand tools, pumps, saws, etc.

Considering the average domestic quality power drill has a design life of about 10 hours your saw probably isn't doing too badly.

I don't have a wiring diagram but the series-wound brush type motor hardly varies regardless of it's application. These motors are electrically very noisy and a high powered version is perpetually almost at the point of self destruction and so to prevent radio frequency interference they have to be heavily suppressed and suppression also helps protect the motor from itself.
Some manufacturers use discrete components for this purpose but some use a single component that is a network of capacitors and inductors, that necessarily is compact and therefore highly stressed and these do fail sometimes.

As a saw doesn't usually have a speed control, all the components can be checked for continuity with a multimeter unless it is fitted with a soft start, the testing of which is beyond the scope of home testing. If everything else is found to be ok the problem is likely with the soft start (if fitted).
The current usually flows through a series wound motor from the switch to a field coil, through the field coil to an armature brush, through the armature to the other brush and then through the other field coil to the neutral. There can be slight variations to this but basically the armature is in series with the field coils.

If you have power to everywhere except the brushes it would suggest a break in a field coil which is very unusual...
No power to the brushes would mean no power to one of the field coils which would mean you don't have power everywhere.

I suggest you begin dismantling and testing again...

The is no oil insite to change only grease a special bosch lubrication or and the ballbearings insite have grease but you can also lubricate the transmission with Paragon Renolith from Dewalt easier to find in you country , simple ball bearing grease can also, but when its getting hot look at your electric field and also the armature if that color is correct nice brass colored thread windings instead of brown black colored and the commutator (collectors) on the armature is nice the place where the carbon brushes are on the armature are nice colored .because the tool can be on its end .if its noisy and if its worth to repair be aware before repair. how old is the tool or have it second hand bought its maybe a problem.

I believe the motor is a brush style unit (only an educated guess) I would revers the wire going to the armature. Most small brush style motors are polarity sensitive.

If you have verified that the cord and switch have continuity through them, I would check the brushes on the motor and make sure that they are making contact with the communtator bars, and that they of acceptable length, and move freely within the brush holders. If this is so, you may have an open in the windings of the armature or field, or a dead bar on the armature itself. While you are in there, I would also check the condition of all wires, and test accordingly.

not if you are mechanically inclined and have a bearing puller. first unplug the tool and lay it on its backside to expose the motor, remove the brushes and the 4 screws that hold the motor housing to the diaphragm, remove the armature and then remove the bearings, press the new ones on, and reassemble, I would also replace the brushes unless they look really good.

There are no rebuilding kits per say. Rebuilding a motor entails stripping it down and replacing what's bad. whole inside should be cleaned of debris, dust, rust etc. Almost always bearing are replaced. Armature, rotor and stator are cleaned, motor windings tested, start/run caps tested and replaced as necessary. Thermal overload, contactor, relay, centrifugal switch, etc, tested and replaced if needed. You can order bearings and capacitors from several places online, other parts can be harder to find. I local pump repair shop may sell you parts as well.

Hello, the brushes are two gray sprung loaded electrical conductors. They are located on the inner main spindel of the motor (armature), when they start to wear out you will find that most electrical motors will slow down in revolutions. Experience has taught me that when an electrical motor emits smoke it has normally burnded out the armature. This in all honesty is not worth fixing as it is an expensive job, it is cheaper to buy a new saw. Sorry to convey bad news but I hope this clarifies thing for you.

turn the motor housing slightly until you can put a screwdriver between the housing and diaphragm, pull on the one side and push with the driver and it will come apart, I just did one yesterday. To get the armature out of the fan bearing you will need a dead blow hammer to tap on the diaphragm while pulling on the armature. The bearing is held in place with 2 screws, hope this helps.

Either the brushes are bad, OR worse iis that one of the armature windings has shorted or is open. Brishes are easy fix, shorted armature is more expensive.

I had a customer bring me a saw with this same problem. All components tested OK on my growler. I went on a limb since the speed control and the armature tested OK. I replaced the feild since to me it seemed to be the only component that could cause the motor to run in reverse. Tool now works properly and have had no more problems with the tool.