It micro-end mill due to relatively small diameters (10

It is known that chatter in machining can be avoided
by machining at stable process parameters obtained from the stability lobe
diagram. The accuracy of the stability lobe diagram depends on the accurate
determination of micro-end mill dynamics. It is not trivial to experimentally
determine the dynamics of a micro-end mill due to relatively small diameters
(10 µm to 500 µm) as impacting the tool-tip will invariably damage the tool. Hence
various approaches have been developed to estimate the micro-end mill dynamics
such as, experimental technique using reciprocity theory and receptance
coupling substructure analysis (RCSA). RCSA combines the frequency response
functions (FRFs) for the two substructures (machine tool-spindle-tool holder with
a portion of shank and the micro-end mill) to determine the tool-tip dynamics. The
accuracy of the receptance coupling method may be compromised due to various
issues, most notably, because of the matrix inversion step involved in this
method. RCSA requires a very fine resolution in frequency content of the FRF
for coupling of substructures dynamics which makes it computationally expensive.
Moreover, it uses only two locations for determining the FRF one at the
coupling and other at tip which can affect the accuracy. Consequently, this
paper is focused on developing an alternative approach for determining the
tool-tip dynamics via component mode synthesis (CMS) which allows use of mode
shapes at multiple points in the substructures. The CMS approach adopted in the
present work contains the position dependent modes along the length of
substructures. In order to benchmark CMS results, a test case of a cantilever micro-
end mill has been analyzed. Note that the actual micro-end mill dynamics is
affected by the machine tool compliance which needs to be accounted for. Hence,
a component mode synthesis of the two substructures, machine tool-spindle-tool
holder-tool shank and the micro-end mill is carried out. The mode shapes of machine-tool-spindle-shank
substructure are determined experimentally whereas the micro-end mill mode
shapes are determined via finite element method (FEM). The predicted micro-end mill
dynamics with machine tool compliance has been experimentally validated and have
also been compared with receptance coupling method (RCM). Finally, the stability
lobe diagrams for high speed micromilling of Ti6Al4V has been made using the
tool-tip dynamics from CMS, RCSA and experimental technique using reciprocity
theory and validated against experimental measurements for onset of