Piano Forum

one or two bpm variation is a something that science can detect, but is not IMHO important to art.
Everybody has a steady rhythm circuit in their brain.  That is how we walk on two feet without falling down.  We learn to do that age two, so it is not inherently difficult to walk in steady rhythm.  Connecting that rhythm circuit to the hands is the trick.  So much blather in books about the heartbeat.  My heartbeat varies all over with emotion and stess, but  the rhythm of my feet when I am on a  walk does not.   Learn to hook up the rhythm circuits in  your brain to your hands.  
I have a metronome, but the wind up Seth Thomas decoration stops after two or three minutes.  That is fine, I never had a teacher that complained about my sense of rhythm.  I found the connection in the brain early.  I just use the metronome to find out that Beethoven and later composers thought their pieces should sound like.  
Just be aware that the student temptation to slow down on the hard parts, and speed up on the easy parts, is laughable and inartistic.  The trick is to find out what the speed of the hard part is today, then play everything else about that speed.  Slowing down and speeding up for emotional reasons are still allowed, if you keep the speed below this "I can go this fast" limit on the piece.