The cups are just press fit on a steel shaft and will pry off. When you pull off the cups pry between the anemometer housing and the cup hub a little at a time while rotating the cups to apply this pressure evenly all around the hub. This helps to keep it straight and not distort the plastic hub shaft. There are 2 small roller bearings on a steel shaft that supports the cups. When you remove the cups two things can happen. 1. the cup assembly slides off and leaves the steel shaft in place, or, 2. the cup assembly is firmly attached to the steel shaft so it pulls the shaft out of the bearings. One bearing you will see and the other is inside and you need to disassemble the housing to get to.
Attachment shows the screws to remove. There is a thin rubber seal that runs around the housing halves joint. When reassembling the housing be sure this seal is in place and doesn't get pinched.
Good luck.
