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Special Section: Micromanufacturing

Microendmill Dynamics Including the Actual Fluted Geometry and Setup Errors—Part I: Model Development and Numerical Solution

[+] Author and Article Information
Sinan Filiz

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

O. Burak Ozdoganlar1

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213ozdoganlar@cmu.edu

1

Corresponding author.

J. Manuf. Sci. Eng 130(3), 031119 (Jun 13, 2008) (10 pages) doi:10.1115/1.2917321 History: Received July 24, 2007; Revised February 25, 2008; Published June 13, 2008

This paper presents an analytical model for the microendmill dynamics, including the setup errors, the axial force, the sectioned tool geometry, and the actual crosssection of the twisted fluted section. Different tool geometries and tool-grinding errors can also be incorporated in the presented model. To include the shear deformations and rotary inertia effects arising from the stubby nature of the microendmill, the Timoshenko beam equations are used in the derivation. The boundary-value problem is derived for each of the shank, taper, and fluted sections of the microendmill, and a component mode synthesis technique is used to combine the individual sections. A new spectral-Tchebychev technique is utilized to obtain the numerical solution of the boundary-value problem without resorting to the finite-elements technique. As a result, a simple yet accurate description of the microendmill dynamics is obtained. The solution is experimentally validated in Part II of the paper.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

A microendmill and its geometric parameters

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Figure 2

The setup errors and deflected tool position

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Figure 3

An infinitesimal tool portion distorted under combined bending and shear

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Figure 4

The moving frame and reference frame related through bending angles

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Figure 5

The SEM images of ((a) and (b)) a two-fluted microendmill and ((d) and (e)) a four-fluted microendmill. The cross sections extracted from the SEM images for (c) the two-fluted microendmill and (f) the four-fluted microendmill.

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Figure 6

Variation of the moments of inertia for a two-fluted microendmill with 250μm diameter

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Figure 7

The boundaries and sections of the microendmill geometry

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Figure 8

Convergence behavior for (a) the first, (b) the second, and (c) the third rotating frame natural frequencies of a four-fluted microendmill with dt=250μm, ds=3mm, Lt∕dt=5, L=20mm, γ=15deg and η=15deg while rotating at 2kHz with fixed-free boundary conditions

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