Grinding noise can occur soon after starting to drve car, or almost anytime. Noise usually occurs between 20-40m/hr, although I have heard it at higher speeds. Sounds like it's coming from front of car, although last month it sounded like it was coming from back of car. 2 mechanics couldn't hear the sound--of course it didn't occur when they saw it!
Grinding noise accelerating at 20-40mph. I had brakes done Jan2010. on 2004 Honda Accord
Sounds like a possible wheel bearing issue? Definitely have to have a good technician check out the wheels for possible bearing noise. Wheel bearing noises are constant, and should not come and go. Not sure if your noise is intermittent or not.