Yes this can happen if you dont have the work piece secure but hole saws of this size tend to let the magic smoke out of cordless drills. DAMHIKT.:gar-Bi
For what it is worth I generally agree with the suggestion to use a corded drill with one caveat. You can use a cordless drill if it has a sufficiently low gear that you can run the drill wide open and not ride the speed controller constantly, but even then there is some risk of burning up the motor if you do not allow it to cool down periodically (most cordless drill motors are not intended to be run for extended periods under heavy load without regular breaks -- they are ordinarily an intermittent tool). Take care never to cover the ventilation openings when running any drill hard (some drill designs tend to encourage the user to inadvertently cover ventilation openings during certain operations). If you constantly ride the speed control in an effort to go even slower then you tend to risk burning out the speed controller as they have very limited heatsinking and they are often trapped within the handle where there is little airflow. Corded drills usually hold up better to such loads, though you should still allow the speed controller to cool off periodically, though either can be used if you allow for regular cooldown periods of a couple minutes for each minute or so of drilling time. Drills geared towards metal work are a much better choice than drills geared towards woodwork as the metal drilling drills have much lower gearing with more torque -- which means less strain on the motor and more cooling air over the motor for a given RPM at the bit.
But if you can drill holes on a drill press instead, such as with an unfinished project, then that is the easiest as you can select the optimal bit speed, clamp the work, and go to town drilling holes all day long in a drill press with no worries. As also suggested, plunge routers with plunge style bits (upcut spiral preferred) and a trammel (circle cutting jig) attachment also work well if you have adequate work space to manueuver the router and trammel assembly (such is generally not an option if trying to drill such holes in finished cabinets, for example, due to space constraints).
In addition to lower RPM metal work oriented drills, 1/2" drills with a T-handle can be very handy for maintaining control and resisting the torque created with larger hole saws. It is also nice if the drill includes either a mechanical or electronic clutch that automatically releases excessive torque should the bit/hole saw bind or catch and try to wrench itself from your hands (electronic clutches just shut down the motor until you restart it while mechanical clutches simply disengage the motor from the bit momentarily until the overload event subsides but otherwise continue to drive the motor unless you release the trigger -- both help the user maintain full control and add to user safety).
As suggested already, it can be very helpful to drill a 3/8", or so, relief hole (one or two) on the waste side of the hole (usually the interior) such that the outer edge of the relief hole just penetrates the groove cut by the hole saw (it helps to first use the hole saw to score the perimeter of the hole do you know exactly where it's cut line is. As mentioned, the relief hole provides a path for the sawdust to escape as many hole saw designs tend to trap the waste within the kerf creating a lot of unnecessary heat and making for very slow cutting. There are, however, some hole saws available these days that incorporate slits in the side of the saw that themselves provide an escape path without the need for relief holes, but if the hole saw has a continuous perimeter then relief holes can help a great deal in thicker and harder or more resinous woods (and especially with hard abrasive wood products like MDF and HDF).
Like Fred, I have sacrificed a number of corded and cordless drills to the Gods of Woodworking/Masonry/Metal over the years, so give them regular breaks to cool down if they are working hard so as to help extend their lives -- I hate losing what was a very good tool just because I got in a hurry and did not allow it a chance to cool off!
The above all said, in most materials 3" holes are not too bad to drill, in my experience at least, (but 4"+ is starting to get up there for some materials and drills), if the material is 3/4", or less, in thickness, but beyond that you start placing a much greater load on both the operator and the drill and the more it helps to have a low speed (metal work) drill with a T-handle and release clutch (mechanical or electronic) to assist you in maintaining control, particularly if you are working in tight quarters where you may not have optimal hold or footing. Just take things slow initially and let the hole saw do most of the work rather than putting a lot of pressure on the bit (which increases the risk of binding or catching and adds to heat buildup) until you get a feel for how your combination of hole saw, drill, and wood behave for you and you should do just fine. Start with the smaller holes first until you get a feel for things and build your confidence, then go for the larger holes.
Best wishes on your project!
