Fan starts making noise and air flow is reduced considerably

Possibly it stalls, an aviation term. It means the angle of attack of the fan blades is too much and they creates turbulence as opposed to blowing the air.

You can try to gently reduce the blades' pitch by bending the attack edge of the blades slightly flatter.

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Edit

A prominent symptom of stall is delayed vibration. All the signs points to the fan stalling and because of worn bushing going into a wild vibration. If you can open the safety cage, try to reduce the angle of attack of the blades as in my answer.

When a fan with a small AC motor in it like this one develops a "squeal" and slows down after running for a short time, it indicates that the motor bearings (usually porous bronze bushings saturated with oil) are worn out or that they need to be cleaned out and relubricated with oil.

You will find a piece of felt surrounding each motor bearing which is soaked with light machine oil (SAE 10 typically) at the factory. The felt feeds oil into the porous structure of the bronze bushing to maintain the space between the motor shaft and the bushing wet with oil. When the oil is all used up, the bearing goes dry and begins to squeal or "chatter". If you stop the fan, it gives the remaining oil a chance to seep into the bearing which lubricates it for a short time; the fan then runs normally for a short time and then starts squealing again, etc.

Using a small oil can full of SAE 10 motor oil, carefully drip some oil onto the exposed portion of the felt block or (if you are lucky) into the oil fill pipe sticking out of the bushing (on more expensive types of motor). Continue adding oil until the felt wick no longer soaks it up, and test the fan.

If the squeal stops, you are good. If it does not, the bushings are worn out and the motor must be replaced.