Don't tell me you got your Lotus!! Jealous man, I'm jealous. Which one - the Elise or Exige? Anyway, congrats and enjoy that 2ZZ-GE "lift" - with that platform, should be a rocket.
As for your grinding, is it still present when the engine is started from a dead cold or after it has fully warmed up? The way it is acting, rhythmic pulsing that starts out slow, peaks at a certain frequency/engine speed and then disappears at high engine speeds makes it sound like a resonance issue with something inside the engine or attached to the engine. My guess would be the serpentine belt tensioner has gone bad, or one of the pulleys is starting to go. You can quickly test that by revving the engine (cold start only, don't do this when warm) to those RPM ranges and see if the noise is still there. As long as you don't drive around like that, won't hurt the engine to run this short test for diagnostic purposes.
If the noise is still there, then you are looking at something internal or not related to the pulleys. Could be as simple as a heatshield that is touching the engine or loose exhaust component, loose wiring harness that is touching the engine. But that particular RPM range has me a little concerned as that is right around when the VVT-i has max overlap. Could be anything from a sludged up VVTi actuator to an excessively worn timing chain/sprocket/chain guide. Double check that the oil levels are spot on, even down a 1/2 quart can cause/mask certain issues with the engine. Same with the oil filter, if you haven't changed out the oil, I'd go ahead and change out oil and oil filter. I had an oil filter collapse internally (FRAM filter), made the car rattle like it was on its last legs. Swapped the filter with a different make - car was automagically better.
I did! An '06 Elise. It's incredible! There is absolutely nothing like it!
I made a video of my issue. Sounds are within my vehicle and you might have to increase the volume to hear the engine. The video doesn't do it justice in terms of how loud that grinding screech is.
Unfortunately, the screeching grind still occurs despite a cold engine. I changed my oil a couple weekends ago. I didn't change my oil filter since I only had 3200 miles on the oil filter. I checked the oil level today, its full and barely over full (as usual when I do an oil change = I put in 4 quarts).
Ha! I think I found it! While I had somebody push down on the accelerator, I noticed the sound was very close to the firewall. Then I heard that it was deep and I saw that the shield for either the steering rack or the axle (can't tell which). Either way, that shield/cover gets fastened to the transmission mount (closest to the firewall, towards the center of the car just to the left (driver's side) of the exhaust manifold/downpipe. The bolt is gone, that flange is rubbing against the mount and I'm curious what kind of bolt that is.
Any ideas?
Thanks.