A Comprehensive Dynamic End Milling Simulation Model

[+] Author and Article Information
Hongqi Li, Yung C. Shin

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Manuf. Sci. Eng 128(1), 86-95 (Jan 31, 2005) (10 pages) doi:10.1115/1.2035694 History: Received June 01, 2004; Revised January 31, 2005

This paper presents a comprehensive time domain model that simulates end milling processes under general cutting conditions. Over an extensive range of axial depths of cut, the model can accurately predict regenerative forces and dynamic responses by considering varying dynamics along the cutting depth, three-dimensional forces, and cutting tool geometries. The prediction of stability limit is validated under cutting conditions of both large depths and very small radial immersions. In addition, three-dimensional surface profiles under both stable and chatter conditions are predicted and compared with measured ones. A new method to extract cutting pressure coefficients is also introduced and applied to the experimental validations.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

End mill geometry and force model

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Figure 2

Expanded engagement sections with discretized disks

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Figure 3

Expanded engagement sections and corresponding force signature in x direction

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Figure 4

(a) Extracted pressure coefficients, (b) extracted chip flow angles, (c) comparison of cutting forces used for extraction (thick lines, obtained from (35)) and simulated ones using the extracted coefficients. Gray cast iron, uncoated carbide tool, 30 helix angle, depth of cut 0.75 in., down milling, half immersion.

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Figure 5

Time domain simulation for end milling process

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Figure 6

Experiment setup for milling thin webs

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Figure 7

Cross sectional dimensions of the thin webs of the workpiece (unit: mm)

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Figure 8

Cutting pressure coefficients (Kf and Kn) and chip flow angle (CFA)

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Figure 9

Cutting force comparison for axial depth of cut of 0.05 in.

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Figure 10

Simulated peak-to-peak force value in feed direction. Axial depths of cut 0.05–0.09 in. with 0.01 in. interval and 0.1–0.8 in. with 0.05 in. interval

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Figure 11

Chatter stability lobes from time domain model vs experimental results

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Figure 12

FFT plots of vibrations

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Figure 13

Predicted stability lobes using different methods

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Figure 14

Predicted and measured surface topographies for stable test case 5

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Figure 15

Surface topography of chatter test case 6 (a) Predicted surface topography. (b) Topography of the machined surface.

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Figure 16

Predicted stability lobes (solid line) and experimental results (× unstable; ● stable) in Refs. 22-23

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Figure 17

Predicted continuous time histories of vibration (X), 1∕rev sampled vibrations (Xn), and Poincaré sections for point A, B, C, and D in Fig. 1 (unit, mm)

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Figure 18

FFT plots of predicted vibrations for point A, B, C, and D in Fig. 1. (A) and (C) are stable points, where the dominant frequencies correspond to the multiplicities of the spindle speed. (B) is a chatter point, where the dominant frequency, 147.5 Hz, is the chatter frequency. (D) is an unstable point due to interruption, where the dominant frequency, 149.6 Hz, is as 2.5 times as the spindle speed.

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Figure 19

Predicted cutting forces in steady states for point A, B, C, and D in Fig. 1. (A) and (C) are stable points, where the forces appear in every revolution. (B) is a chatter point, where the force shows chatter related frequencies. (D) is an unstable point due to interruption, where the force appears in every other revolution



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