Parametric beam modeling to predict the first natural bending frequency of thin wall box-shaped structures verified using experimental modal analysis

Structural stiffness loaded with bending force is influenced by its dimension, especially by height and cross section. As the natural frequency of the structure depends on the structural stiffness, therefore the changes in the structure dimension will also change its natural frequency. In machining process of thin wall box-shaped workpiece using vertical milling machine the workpiece can be treated as a structure subject to bending force due to the cutting force. Therefore the structural stiffness of the workpiece is a crucial aspect to be considered. The natural frequency of the workpiece, especially its first natural frequency serves as a preliminary information of the workpiece modal parameter to avoid the self excited vibration called chatter. A new model based on parametric beam modeling was developed and implemented on computer programming to predict the first natural frequency of thin wall box-shaped workpieces. The first natural frequency of thin wall box-shaped workpiece can be calculated using this model for varying wall thickness, height, and length to width ratio of the workpiece cross section. The result of the parametric beam modeling is verified though an experimental modal analysis and also compared to a finite element numerical analysis.