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

It is known that chatter in machining can be avoidedby machining at stable process parameters obtained from the stability lobediagram. The accuracy of the stability lobe diagram depends on the accuratedetermination of micro-end mill dynamics.

It is not trivial to experimentallydetermine 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. Hencevarious approaches have been developed to estimate the micro-end mill dynamicssuch as, experimental technique using reciprocity theory and receptancecoupling substructure analysis (RCSA). RCSA combines the frequency responsefunctions (FRFs) for the two substructures (machine tool-spindle-tool holder witha portion of shank and the micro-end mill) to determine the tool-tip dynamics. Theaccuracy of the receptance coupling method may be compromised due to variousissues, most notably, because of the matrix inversion step involved in thismethod.

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RCSA requires a very fine resolution in frequency content of the FRFfor coupling of substructures dynamics which makes it computationally expensive.Moreover, it uses only two locations for determining the FRF one at thecoupling and other at tip which can affect the accuracy. Consequently, thispaper is focused on developing an alternative approach for determining thetool-tip dynamics via component mode synthesis (CMS) which allows use of modeshapes at multiple points in the substructures.

The CMS approach adopted in thepresent work contains the position dependent modes along the length ofsubstructures. 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 isaffected by the machine tool compliance which needs to be accounted for.

Hence,a component mode synthesis of the two substructures, machine tool-spindle-toolholder-tool shank and the micro-end mill is carried out. The mode shapes of machine-tool-spindle-shanksubstructure are determined experimentally whereas the micro-end mill modeshapes are determined via finite element method (FEM). The predicted micro-end milldynamics with machine tool compliance has been experimentally validated and havealso been compared with receptance coupling method (RCM). Finally, the stabilitylobe diagrams for high speed micromilling of Ti6Al4V has been made using thetool-tip dynamics from CMS, RCSA and experimental technique using reciprocitytheory and validated against experimental measurements for onset ofinstability.