Finite element analysis of the structural dynamics of a vertical milling machine

The structural stiffness of a machine tool is one of the main criteria that establishes its ability to produce accurate precision components. High stiffness is required both statically and dynamically each affecting different aspects of the machining process. The need for high static stiffness arises from the requirement to produce parts to a desired size and shape [1] and although finish machining often takes place with small depths of cut and correspondingly light cutting forces, the resulting deflections can still be excessively large if the machine has inadequate static stiffness. The resulting deflection can thus produce out of tolerance work-pieces. The need for high dynamic stiffness results from two separate aspects of the machining process. In the first case inadequate dynamic stiffness will result in poor quality surface finish of the machined parts due to relatively low levels of vibration occurring during finish machining operations. In the second case low dynamic stiffness can have more serious consequences when under heavy machining conditions the resulting vibration might be sufficiently high to cause the process to be terminated in-order prevent possible damage to the machine. Traditionally machine tool structures were designed from experience with limited aid from manually carried out calculations using classical theory for such as beam bending, twist and shear. With the advent of powerful desktop computers and the associated Finite Element Software, at costs that are within the grasp of the typical machine tool manufacturer, it is now possible to determine the structural stiffness values for machine tools to a high order of accuracy and in a relatively short time scale. This paper outlines the static and dynamic structural analyses of a vertical milling machine that were to be subsequently validated against measured results [2, 3].