The fast constant engagement offsetting method for generating milling tool paths

Abstract

It is a well-established fact that when equidistant tool paths are used for 2.5D milling operations tool load varies based on the functions of path curvature. This phenomenon makes the optimal selection of cutting parameters more difficult, and the local load peaks are also detrimental to machining stability and tool life. Numerous publications address possible solutions to eliminate the problems caused by varied cutting parameters. The best solution for this is to keep the cutter engagement at a constant value. Nowadays, several methods are available to generate tool paths which are able to maintain constant cutter engagement, but the widespread use of such solutions is significantly hindered, because in this scenario complex calculations are required. This article offers a solution to this problem by presenting a new non-equidistant offsetting method for ensuring a constant cutter engagement angle. The algorithm developed for this purpose is based on simple geometrical equations and allows for its widespread use just like pixel-based methods. Concerning this new solution, computation needs and uniform tool load are verified by simulation and through experiments. The experiments have shown favourable results. Keywords Tool path generation. Cutter engagement. High-speed milling. Cutting force. Non-equidistant offsetting Nomenclature a e Effective radial immersion [mm] a p Axial depth of cut [mm] c(t) Parametric representation of workpiece contour [{mm, mm}] f z Feed per tooth [mm] h ex Maximum chip thickness [mm] i, j Step index [−] n Spindle speed [1/min] p(t) Parametric representation of tool path [{mm, mm}] r tool Tool radius [mm] s Stepover [mm] t Free parameter of curve equations [−] v Feed vector [{mm, mm}] v c Cutting speed [m/min] v f Feed rate [mm/min] w Trochoidal step [mm] z Number of teeth [−] C Entry point of the cutting edge [{mm, mm}] D tool Tool diameter [mm] MRR Material removal rate [mm 3 /min] P Tool path point [{mm, mm}] Q Exit point of cutting edge [{mm, mm}] V(x, y) Vector field [{mm, mm}, {mm, mm}] a, β Angle parameters [ ∘ ] Δs Stepsize[−] θ Cutter engagement angle [ ∘ ]

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