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Question:

Why do AC supplied electric tools commonly have a brushed motor instead of an induction motor?

Why do AC supplied electric tools commonly have a brushed motor instead of an induction motor?

Answer:

Cheaper? don't know about that one.. More compact, able to tolerate overload more easily, can be more easily/ cheaply speed- controlled.
They are cheaper
DC brush motors are typically more efficient for the package they are in. An even more efficient motor would be brushless...but that makes the cost prohibitive. Induction motors will have to be a lot bigger to in order to provide the same power as a DC motor. Plus you have the added benefit of the motor being reversible, and being variable speed. When my company bought these motors in large quantities, they only cost like 2-4 dollars from China or Taiwan, depending on the model. You will also see a lot of other products supplied with AC power and using a Brush motor. Look at hair dryers, electric shavers, mixers, printers and all sorts of other things. Believe it or not...they can be made very cheap, if you buy enough of the like a large company would normally buy. And if material costs on copper are kept low, it's the perfect solution for a product that is fed AC, especially if it's only designe for a few years of life.
The brushed motor is called series motor. All winding are connected in series. This connection has a great advantage: When the load, or the resistance on, say the drill bit, becomes larger when it hits something hard. The drill slows down because of the greater resistance. But this makes the current larger and so do the torque of the drill. This larger torque overcomes the resistance and it keeps drilling. Therefore it is very commonly used on drills and other power tools. It has other advantage is light-weight. Also note that this kind of motor works well on DC. The direction of rotation can be reversed by reversing the current to the armature (The rotor), ie at the brushes. I added a switch on my drill so that it can spin in reverse direction by a flick on the switch. The I used it as a electric screwdriver after I added a dimmer on the power cord. For induction motors, they are heavier and do not have the good torque characteristic.

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