Analysis and Control of Vibrations of a Cartesian Cutting Machine Using an Equivalent Robotic Model

The vibrations of a Cartesian cutting machine caused by the pneumatic tool are studied with a sub-system approach. The cutting head is modeled as an equivalent robot arm which is able to mimic the measured resonances, The Cartesian structure is modeled according to the mode superposition approach. The full model is able to predict the variations in the response of the machine to tool excitation that are caused by the motion of the head along the rails of the Cartesian structure. Comparisons with experimental results are made. Finally, the mathematical model is used for assessing the effectiveness of a vibration absorber tuned to main resonance frequency of the cutting head.