Diagnosis
No, it's not. The DIR-X1560 has a small internal cooling fan that should be mostly inaudible. A loud grinding or buzzing noise means the fan bearing is failing or dust/debris is hitting the blades.
How to Fix It
Power off and unplug the router. Look at the ventilation slots, usually on the sides and bottom. Use a can of compressed air to blow short bursts into the vents to dislodge any dust bunnies. Don't tilt the can or shake it. This might clear an obstruction.
If That Didn't Work
The fan itself is likely failing. This model isn't really designed for user service. If it's under warranty, contact D-Link support. If not, the only fix is living with the noise, trying to position it for better passive cooling, or replacing the unit, as opening the case will void any warranty and is tricky.
Heads Up
Don't block the vents or lay the router on a soft surface like a carpet. Overheating from poor airflow can cause other problems like random reboots, making the fan work even harder.