A humming furnace may sound troubling, but most solutions are easier than they may at first appear. Start by pinpointing where the hum originates. Once you do, you may find the repairs are something you feel ready to handle. If you do run into a problem, a service professional can lend a hand.
The volume of air that pushes through the furnace and the motion of the motors that are part of the system cause vibrations during normal operations. Over time, these vibrations can cause screws to back out a turn or two, and they may loosen bolts. The inside of the furnace has a collection of small components that help run the unit. Check that each of these is tightened securely, and correct those that are loose. A small piece of plastic or cardboard slipped under a component that is not likely to get hot can soften humming noises.
Ductwork and Plenum
The metal used to create the plenum and ducting is relatively thin and soft. Long duct runs and large plenums may hum as air passes through them. Stiffen joints between ducts with sheet metal screws. Tape the seams for added noise reduction. You can add tie straps to better secure ductwork to the joists. Eliminating some of the flex in ducts and the plenum reduces vibration which, in turn, suppresses some of the humming.
The transformer takes normal household current and steps it down to a level used by the furnace. It is located in different places in different furnaces, but is typically near the rest of the electrical components. As current passes through some transformers, a humming noise results. While it does not mean the transformer is about to fail, the hum can be irritating. Sometimes, the transformer will stop making noise as it wears in. You can also tighten its hold-down bolts as a means of preventing the hum.
A blower motor or inducer motor on its way toward failing may also make a loud humming noise. Once the motor fails, it leaves you with a furnace that will not function -- not something you want to happen in the middle of the heating season. Failing motors are best serviced and replaced by trained furnace pros, who will match the motor and wiring harness correctly.