Evaluation of the stiffness chain on the deflection of end-mills under cutting forces

This study presents the investigation of the stiffness of the system formed by the machine-tool, shank and toolholder, collet and tool. Cutting forces induce the deflection of the system, and consequently an error appears on the machined surface. Comparing values obtained from cantilever beam models applied to the cutting tool, analytical or FEM, with those experimentally obtained, large differences have been observed, which in some cases are more than 50%. For this reason, we have proceeded to evaluate the stiffness of each of the existing elements between the machine bed and the tool tip. Thus, deflections of the machine-tool, toolholder and toolholder clamping in the spindle, tool clamping in the toolholder, and tool itself, were measured experimentally under the effects of known forces. The final application is the ball-end milling of complex surfaces, an operation commonly performed in the finishing of moulds or forging dies, where errors of more than 70 μm are not unusual. A great part of this error comes from the deflection of the machine-tool assembly, spindle, shank and tool, due to the high cutting forces of the high speed machining of tempered steels. Cutting forces can be estimated using a semi-empirical approach, and from here some values of probable errors may be taken into account to check if the CNC programs are sufficiently adapted. However, a previous study of the deflection chain in the cutting process is needed, as is presented in this work. Results show that stiffness of the slender and flexible tools is 15 times lower than that of the machine and toolholder system. But this correlation is only 5–7 times lower for shorter and thicker tools.