Time machine failures on new MBA with 3 year old WD 500GB Drive

I purchased a new MacBook Air and hooked it up to my existing 3 year old WD 500gb my book studio edition.   It mounts fine, time machine sees it and trys to back up, but after only a short time, the back up fails.  I have run disk utility in mac and cannot find any problems there.  I did trash all previous backups on the WD before moving it to this new macbook air. Any suggestions?

Fixed!  Did a disk erase in disk utility an it’s running smooth now. 

Stand corrected, back up got about 15 % done and failed again.  I did a disk Erase and still won’t work right.