NOT a 4wheel drive...same sound and hubs/rotors are newish

Rubbing sound when turning rightonly while moving (not while stopped) when I turn the wheel even slightly to the right the sounds happens...it does not make any sound turning left at any speed..the sound gets louder at higher speeds...also I do know that my ABS unit is not operating properly even though the light does not come on. Moreonly while moving (not while stopped) when I turn the wheel even slightly to the right the sounds happens...it does not make any sound turning left at any speed..the sound gets louder at higher speeds...also I do know that my ABS unit is not operating properly even though the light does not come on. Okay...well I cleaned both sides front...removed all rust (wasn't much because rotors are about 1 and half years old)...and cleaned brake parts (also gave me a chance to clean the wheels really good)...the humming souncd persists...and I should say it is more of a humming than a rubbing...and it happens after 15-20 miles per hour and only while turning right...sounds like the sound large deep tread tires makes on off road tires (which I do not have and in fact the tires are new) Also checked the joints for looseness and everything seems tight