A method of machining ceramic matrix composite components includes providing an ultrasonic vibration tool having a tool tip, and exciting the tool by providing a control current, such that the tool tip is repeatedly vibrated towards and away from a ceramic matrix composite workpiece. A slurry feed is supplied including abrasive particles to a surface to be machined by the tool tip. A vibration amplitude of the tool tip is controlled by sensing load on the tool and communicating with a computing device. The computing device controls the vibration amplitude of the tool tip. The computing device is provided with at least one memory programmed with historic data, and is operable to modify the vibration amplitude signal being sent to the tool, and comparing resulting load levels due to the change in vibration amplitude signals, and storing the change in vibration amplitude signals at the memory.