The efficiency of the milling process is limited due to excessive vibrations that negatively impact the tool and work-piece quality. This becomes even more of a concern in micro-milling where sudden tool breakage occurs before the operator can adjust cutting parameters. Due to different chip formation mechanisms in micro-milling, an increased tool-radius to feed-rate ratio, and higher spindle speeds, micro-milling is a highly non-linear process which can produce multiple and broadband frequencies which increase the probability of tool failure. This paper investigates micro-milling through the development and analysis of a 3-D nonlinear micro-milling dynamic model. A lumped mass, spring, damper system is assumed for modeling the dynamic properties of the tool. The force mechanism utilized is a slip-line field model that provides the advantages of being highly dynamic by accounting for the constantly changing effective rake angle and slip-line variables. Accurate prediction of the chip thickness is important in correctly predicting the dynamics of the system since the force mechanism and its variables are a function of the chip thickness. A novel approach for calculating the instantaneous chip thickness which accounts for the tool jumping out of the cut and elastic recovery of the work-piece is presented. The derivation for the effective rake angle is given and the helical angle is accounted for resulting in a 3-D micro-milling model. The results of simulating the model demonstrate its capability of producing the high frequency force components that are seen in experimental data available in literature. The advantages of using this approach over the constant empirical force coefficient approach when studying micro-milling dynamics is discussed and the instability of the system is investigated utilizing instantaneous frequency.

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