Research Papers

Finite Strip Modeling of the Varying Dynamics of Shell-Like Structures During Machining Processes

[+] Author and Article Information
J. Stefani

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8P 5C2, Canada
e-mail: josiahstefani@gmail.com

K. Ahmadi

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8P 5C2, Canada
e-mail: kvahmadi@uvic.ca

O. Tuysuz

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

Manuscript received June 20, 2017; final manuscript received January 12, 2018; published online February 14, 2018. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 140(4), 041015 (Feb 14, 2018) (10 pages) Paper No: MANU-17-1381; doi: 10.1115/1.4039107 History: Received June 20, 2017; Revised January 12, 2018

The efficiency of the finite strip method (FSM) in modeling the varying dynamics of shell-like structures during machining operations is investigated. The workpiece is modeled as a shallow, helicoidal, cantilevered shell, and the natural modes are computed using FSM. In the FSM solution, the workpiece is discretized only in the chordwise direction, and the membrane and bending displacement fields of the shell in the spanwise direction are approximated by a set of basis functions that satisfy clamped-free boundary conditions. The displacement fields in the chordwise direction are approximated using polynomial functions. The efficiency of the presented FSM is investigated by comparing the computed natural vibration modes against the ones obtained using the finite element method (FEM). The FSM model was found to yield results of greater or comparable accuracy, even with up to 40% fewer degrees-of-freedom (DOFs). Also, the accuracy of the presented model is verified by comparing the predicted frequency response functions (FRFs) against the FRFs that were measured by conducting impulse hammer tests in various stages of machining a generic curved blade.

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Fig. 2

B3 spline synthesis

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Fig. 1

(a) Shell discretization using helicoidal strips and (b) strip dimensions

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Fig. 3

Mode shapes of the uniform cylindrical blade

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Fig. 4

(a) Dimensions of the step blade and (b) variation of its natural frequencies during material removal

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Fig. 5

Variation of the mode shapes of the cylindrical shell as its thickness reduces (initial mode shape is shown in light gray and darker lines are used as more material is removed)

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Fig. 6

(a) The geometry of the blade studied in the experiments, (b) impulse hammer test setup, and (c) coordinates of the measurement points in global coordinate system

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Fig. 7

Direct FRFs of the twisted blade with uniform 10 mm thickness. The locations of the measurement points 1–9 are shown in Fig. 6.

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Fig. 8

Shapes of the first four modes of the twisted blade obtained using FSM with two strips and four trigonometric terms

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Fig. 9

Direct FRFs of the twisted blade at various stages of machining. The locations of the measurement points 1, 5, and 9 are shown in Fig. 6.



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