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Research Papers

Analytical Modeling of Process Damping in Machining

[+] Author and Article Information
Oguzhan Tuysuz

Department of Mechanical Engineering,
Manufacturing Automation Laboratory (MAL),
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC, Canada V6T 1Z4
e-mail: oguzhan.tuysuz@alumni.ubc.ca

Yusuf Altintas

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

1Corresponding author.

Manuscript received October 7, 2018; final manuscript received March 20, 2019; published online April 12, 2019. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 141(6), 061006 (Apr 12, 2019) (16 pages) Paper No: MANU-18-1709; doi: 10.1115/1.4043310 History: Received October 07, 2018; Accepted March 20, 2019

The machining process induced damping caused by the indentation of the cutting edge into the wavy cut surface greatly affects the process stability in low-speed machining of thermally resistant alloys and hardened steel, which have high-frequency vibration marks packed with short wavelengths. This paper presents an analytical model to predict the process damping forces and chatter stability in low-speed machining operations. The indentation boundaries are evaluated using the cutting edge geometry and the undulated surface waveform. Contact pressure due to the interference of the rounded and straight sections of the rigid cutting edge with the elastic-plastic work material is analytically estimated at discrete positions along the wavy surface. The overall contact pressure is obtained as a function of the cutting edge geometry, vibration frequency and amplitude, and the material properties of the workpiece. The resulting specific indentation force is evaluated by integrating the overall pressure along the contact length. Then, the process damping force is linearized by an equivalent specific viscous damping, which is used in the frequency domain chatter stability analysis. The newly proposed analytical process damping model is experimentally validated by predicting the chatter stability in orthogonal turning, end milling, and five-axis milling of flexible blades. It is shown that the proposed model can replace currently used empirical models, which require extensive experimental calibration approach or computationally prohibitive finite elements based numerical simulation methods.

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Figures

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Fig. 1

(a) Two-dimensional cutting edge geometry, static chip generation and material SP and (b) machining process damping due to the cutting edge indentation and the associated forces

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Fig. 2

(a) Indentation geometry, surface waveform, and discrete process damping calculation points and (b) general contact pressure distribution at the interface between the cutting edge element and the workpiece surface

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Fig. 3

Flow chart for the analytical estimation of process damping

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Fig. 4

Schematic illustration of an axially discretized milling tool and TWE

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Fig. 5

Comparison of the experimentally identified equivalent process damping against the prediction of the proposed analytical model for AISI 1045 in the radial direction

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Fig. 6

(a) Comparison of the stability lobes predicted using equivalent specific process damping (ceq) and the experimentally identified process damping force coefficient (Ci) for the parameters in Table 1. Work material: AISI 1045; structural parameters: natural frequency (ɷn) = 450.7 Hz, modal mass (mr) = 0.8081 kg, modal stiffness (kr) = 6.48 × 106 N/m, modal damping (cr) = 145 Ns/m; cutting force coefficient: Kr = 1384 MPa and (b) frequency spectra of the measured cutting forces.

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Fig. 7

Comparison of the numerically (FE) identified equivalent process damping against the prediction of the proposed analytical model for AISI 1045 in the radial direction

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Fig. 8

Comparison of the experimentally identified equivalent process damping against the prediction of the proposed analytical model for (a) AISI 1018 and (b) Ti6Al4V work materials

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Fig. 9

(a) Comparison of the stability lobes predicted using equivalent specific process damping (ceq) and the experimentally identified process damping coefficient (cp,r) for the parameters in Table 3. Work material: AISI 1018; structural parameters: natural frequency (ɷn) = 1403 Hz, modal stiffness (kr) = 21 × 106 N/m, modal damping ratio (ξr) = 2.2%; cutting force coefficient: Kr = 1375 MPa and (b) frequency spectra of the measured tool accelerations.

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Fig. 10

(a) Comparison of the stability lobes predicted using the equivalent specific process damping (ceq) and the experimentally identified process damping coefficient (cp,r) for the parameters in Table 4. Work material: AISI 1018; cutter: three fluted flat-end tool with 19 mm diameter, 30° helix angle; immersion: 100% radial; cutting force coefficients: Ktrc = {1550 480}MPa; structural parameters: given in Table 5 and (b) frequency spectra of the recorded cutting sound.

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Fig. 11

(a and b) Effect of the parameter uncertainty on low speed region of the predicted stability lobes (A0, vibration amplitude; χ, material separation angle; p, mean plastic contact pressure)

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Fig. 12

(a) Experimental setup and (b) dimensions of a single blade

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Fig. 13

(a) Predicted chatter regions and (b) chatter frequencies in five-axis machining with a two-fluted ball-end mill having 16 mm shank diameter. Predicted variation of the first blade mode: ωn={49645166533553845461} Hz, modal damping ratio ξr = 0.12%; (c) experimentally identified chatter frequencies and cutting sound of a sample toolpath segment, and (d) Fourier spectrum analysis (FFT) of the sample sound data.

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