Abstract
Chatter is an old enemy to machinists but, even today, is far from being defeated. Current requirements around aerospace components call for stronger and thinner workpieces which are more prone to vibrations. This study presents the stability analysis for a single degree of freedom down-milling operation in a thin-walled workpiece. The stability charts were computed by means of the enhanced multistage homotopy perturbation (EMHP) method, which includes the helix angle but also, most importantly, the runout and cutting speed effects. Our experimental validation shows the importance of this kind of analysis through a comparison with a common analysis without them, especially when machining aluminum alloys. The proposed analysis demands more computation time, since it includes the calculation of cutting forces for each combination of axial depth of cut and spindle speed. This EMHP algorithm is compared with the semi-discretization, Chebyshev collocation, and full-discretization methods in terms of convergence and computation efficiency, and ultimately proves to be the most efficient method among the ones studied.
Highlights
Chatter is a dynamic instability phenomenon that diminishes the quality of parts and tool performance
To obtain the stability lobes of Equation (1), we proposed a solution procedure based on the enhanced multistage homotopy perturbation (EMHP) algorithm [18], which relies on a sequence of subintervals that provide approximate solutions requiring less CPU time in comparison with other methods found in the literature
A monolithic artifact of Al7075T6 was designed to reproduce the dynamic response of a single degree of freedom system in the y-axis, which is orthogonal to the feedrate direction
Summary
Chatter is a dynamic instability phenomenon that diminishes the quality of parts and tool performance. It is an old adversary for machinists, and one of the most common issues in manufacturing. Nowadays, due to the rapid growth of global competition to reduce cost and the increased dimensional accuracy in monolithic and thin geometries demanded by aeronautical industries, research has been focused on more accurate predictive models and methods for optimizing metal removal rates without chatter. Those models are delay-differential equations (DDE) with infinite dimensional state space. According to the Floquet theory, the stability properties are determined by the system’s monodromic operator
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