Abstract
Regenerative machine tool chatter is investigated for milling operations with helical tools. The stability of a two-degrees-of-freedom milling model is analyzed, where the cutting-force is modeled as a force system distributed along the rake face of the tool. Introducing a distributed force system instead of a concentrated cutting-force results in an additional short, periodically varying distributed delay in the governing equations of the system. It is shown that the additional delay significantly affects the stability of the machining operation, especially at low spindle speeds. This phenomenon is referred to as the short regenerative effect, and is studied by computing the stability lobe diagrams of milling operations via the semi-discretization technique. The sensitivity of the stability charts to the shape of the force distribution and the contact length between the chip and tool is investigated.
Highlights
The occurrence of harmful vibrations during metal cutting processes is an important problem in manufacturing technology
Regenerative machine tool chatter is investigated for milling operations with helical tools
The stability of a two-degreesof-freedom milling model is analyzed, where the cutting-force is modeled as a force system distributed along the rake face of the tool
Summary
The occurrence of harmful vibrations (chatter) during metal cutting processes is an important problem in manufacturing technology. 1 (t, z) eσ θ +1 , j (t,z) const : Using these functions we assume that the shape of the force distribution is essentially the same for the different cutting teeth and axial immersions. It is important to clarify that during semi-discretization we fix the period resolution p and not the time step h This way it is possible to calculate several approximate quantities independently of the delay τ and of the spindle speed Ω. Note that the dependency on the axial depth of cut ap cannot be transformed out in a similar manner Another important issue in the time-efficient computation of the stability charts is the construction of the monodromy matrix. The agreement between the stability boundaries in the presented parameter range is good
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