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Research Papers

A Model for Bending, Torsional, and Axial Vibrations of Micro- and Macro-Drills Including Actual Drill Geometry—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

Admissible functions are those that satisfy the essential (displacement) boundary conditions (28).

1

Corresponding author.

J. Manuf. Sci. Eng 132(4), 041017 (Aug 06, 2010) (8 pages) doi:10.1115/1.4001720 History: Received June 22, 2009; Revised April 28, 2010; Published August 06, 2010; Online August 06, 2010

Part I of this work presents a combined one-dimensional/three-dimensional approach for obtaining a unified model for the dynamics of micro- and macro-drills. To increase the numerical efficiency of the model, portions of the drill with circular cross-section (shank, extension, and tapered sections) are modeled using one-dimensional beam models without compromising model accuracy. A three-dimensional model is used for an accurate representation of the fluted section, considering the actual geometry with the pretwisted shape and axially varying (nonaxisymmetric) cross-section. The actual cross-section of the drills is incorporated to the model through a polynomial mapping while the pretwist effect is captured by defining a rotating reference frame. The boundary-value problem for both one- and three-dimensional models are derived using a variational approach, based on the extended Hamilton’s principle, and are subsequently solved by applying the spectral-Tchebychev technique. A component-mode synthesis is used for connecting the individual sections to obtain the dynamic model for the entire drill. Convergence of the model is studied by varying the number of polynomials for each section. The experimental validation of the model is included in Part II for both macro- and micro-drills. Also included in Part II is an analysis of drill dynamics for varying drill-geometry parameters and axial (thrust) force.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 5

The convergence of the fluted section (3D) solution: percent convergence ratios for (a) the first bending-mode pair (B11) and (b) the first torsion-axial mode (TA1)

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Figure 1

Geometry of (a) a macro-drill and (b) a micro-drill

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Figure 3

A fourth-order polynomial mapping of the actual cross-section to a rectangular domain. (a) the cross-section in the physical coordinate frame and (b) the domain in the mapping coordinate frame

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Figure 4

The convergence of the shank section (1D) solution: (a) the first bending-mode pair along the first principal direction (B11) and (b) the first torsion-axial mode (T1)

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Figure 2

Geometric mapping: (a) the geometry in the physical coordinates, (b) after the twist is removed using a local reference frame, and (c) after cross-sectional mapping

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