Research Papers

Identification of Machining Process Damping Using Output-Only Modal Analysis

[+] Author and Article Information
K. Ahmadi

Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: kahmadi@mail.ubc.ca

Y. Altintas

Fellow ASME
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: altintas@mech.ubc.ca

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received February 12, 2014; final manuscript received May 6, 2014; published online August 12, 2014. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 136(5), 051017 (Aug 12, 2014) (13 pages) Paper No: MANU-14-1061; doi: 10.1115/1.4027676 History: Received February 12, 2014; Revised May 06, 2014

The existing chatter stability prediction algorithms fail in low-speed machining of difficult to cut alloys, unless process damping contributed by the tool flank face–finish surface contact is considered. This paper presents a new method in predicting the material dependent process damping coefficient from chatter free orthogonal cutting tests. An equivalent process damping coefficient of the dynamic system is estimated from the frequency domain decomposition (FDD) of the vibration signals measured during stable cutting tests. Subsequently, the specific indentation force of the workpiece material is identified from the process damping coefficients obtained over a range of cutting speeds. The specific indentation force coefficient is used in an explicit formula of process damping which considers the radius and clearance angle of the cutting edge. It is experimentally shown that when the proposed process damping model is included, the accuracy of chatter stability predictions in turning and milling improves significantly at low cutting speeds.

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Fig. 1

(a) Schematic of chip generation mechanism around the separation point on the honed edge of cutting tools; (b) area of the indented volume; and (c) triangular indented area with flank wear and without hone radius

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Fig. 2

(a) Milling geometry and (b) computing the indented area in milling

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Fig. 4

Frequency response function (FRF) of the turning tool measured at its tip; solid line: measured FRF and dashed line: fitted single degree of freedom system; modal stiffness 56 N/μm, modal damping ratio 3%, and natural frequency 1500 Hz; structural damping coefficient csr = 2ξsrωn1mr = 356.5 Ns/m

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Fig. 3

Orthogonal cutting test setup for process damping identification

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Fig. 5

(a) |H11|2 in the vicinity of the dominant mode at 1500 Hz with 3% structural damping ratio and (b) inverse Fourier transformation of |H11|2

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Fig. 12

(a) Milling stability lobes with process damping (Ksp = 14,130 N/mm3); three fluted endmill, 15 μm hone radius, and 8 deg clearance angle; Kt = 1550 MPa and Kr = 480 MPa; dynamic parameters are given in Table 2; measured cutting forces in normal direction (b1 and b2); computed tool tip vibration (c1 and c2); recorded cutting sound (d1 and d2) and FFT of the recorded cutting sounds (e1 and f2) at 3.5 mm depth of cut and 650 rev/min stable point and at 1000 rev/min unstable point; workpiece: AISI1018

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Fig. 6

Extraction of damping coefficient from the spectral analysis of measured acceleration signals during stable orthogonal tube turning tests; cutting conditions: workpiece material AISI 1018 with 133 HB hardness, cutting speed 90 m/min, feed rate = 0.08 mm/rev, width of cut b = 2.1 mm, edge radius rε = 60 μm, clearance angle γ = 7 deg, rake angle = 0 deg; overall damping is identified as ξr = 7.3%

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Fig. 10

(a) Critical stability limit computed using the identified process damping (Ksp = 14,130 N/mm3) with tool having rε = 60 μm, γ = 7 deg, kr = 21 N/μm, ωn1 = 8810 rad/s (i.e., 1403 Hz), ξrs = 2.2%, Kr = 1375 MPa; b1 and b2: measured accelerations at the tool tip; c1 and c2: frequency spectra of the accelerations; d1 and d2: measured cutting sounds (e1 and e2) frequency spectra of the cutting sounds; workpiece material: AISI 1018

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Fig. 11

Critical stability limit computed using the identified process damping (Ksp = 14,130 N/mm3) and rε = 16 μm, γ = 3 deg, rake angle = 11 deg, kr = 14 N/μm, ωn1 = 7065 rad/s (i.e., 1125 Hz), ξrs = 2%, Kr = 725 MPa; workpiece material: AISI1018

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Fig. 7

Extraction of damping coefficient from the spectral analysis of measured acceleration signals during stable orthogonal tube turning tests; the cutting conditions are as the same as in Fig. 6, except that the cutting speed is 268 m/min; overall damping is identified as ξr = 3.8%

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Fig. 8

Identified overall damping ratios at different cutting speeds; the specific indentation force is identified as Ksp = 14,130 N/mm3; hone radius 60 μm, and clearance angle 7 deg; workpiece material: AISI1018 steel

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Fig. 9

Identified process damping ratios at different cutting speeds (circles and triangles) and Eq. (5) fitted on the identified points to extract the specific indentation force (Ksp); material: Ti6Al4V with 344 HB hardness and width of cut b = 1.8 mm; the inserts have both zero rake angle but with different edge radii and clearance angles

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Fig. 13

Variation of estimated process damping coefficient in feed direction at different vibration amplitudes; in this figure, vibration amplitude in Y-direction is assumed constant Y0 = 10 μm



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