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. A global analytical model is obtained coupling the aforementioned models, and is solved in MATLAB. 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.