How do you make a Woodie into a Werebeaver?

In Don’t Starve, Woodie will become the Werebeaver when he hits a Tree with an Axe too much in a short space of time or during a Full Moon. It does not matter which Axe is used in the process. It takes approximately 38 swings with Lucy to transform. All of the HUD will disappear and be replaced by the Beaverness Meter.