Carbon Brushes do not make any noise - a faint clicking at most.
The noise from rotating electrical machinery will be caused by some mechanical movement - rotating bearings etc - but most of the noise (90%) will be from the movement of air - an electric drill motor has an impeller to develop a cooling air flow - any reduced size motor will create excessive heat and will need forced air cooling - your vacuum cleaner for instance.
I do not believe that dishwashers have carbon brush motors - clothes washing machines do have brushes - they have more work to do.
You should also consider the wattage of the motor - more Watts will require more cooling and will make more air-noise.
This is a how to mend it site - it's not basic physics - electrical engineering for dummies or We Settle Your Bets.
You're fortunate that I feel sorry for you.
Personal research can be fun - try it.
May 2015