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Research Papers

Dynamics Behavior of a Guided Spline Spinning Disk, Subjected to Conservative In-Plane Edge Loads, Analytical and Experimental Investigation

[+] Author and Article Information
Ahmad Mohammadpanah

Department of Mechanical Engineering,
The University of British Columbia,
FPInnovations,
Vancouver, BC V6T 1Z4, Canada
e-mail: ahmadpa20@gmail.com

Stanley G. Hutton

Professor Emeritus
Department of Mechanical Engineering,
The University of British Columbia,
FPInnovations,
Vancouver, BC V6T 1Z4, Canada

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 9, 2014; final manuscript received April 7, 2016; published online May 19, 2016. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 138(4), 041005 (May 19, 2016) (11 pages) Paper No: VIB-14-1340; doi: 10.1115/1.4033456 History: Received September 09, 2014; Revised April 07, 2016

The governing linear equations of transverse motion of a spinning disk with a splined inner radius and constrained from lateral motion by guide pads are derived. The disk is driven by a matching spline arbor that offers no restraint to the disk in the lateral direction. Rigid body translational and tilting degrees-of-freedom are included in the analysis of total motion of the spinning disk. The disk is subjected to lateral constraints and loads. Also considered are applied conservative in-plane edge loads at the outer and inner boundaries. The numerical solution of these equations is used to investigate the effect of the loads and constraints on the natural frequencies, critical speeds, and stability of a spinning disk. The sensitivity of eigenvalues of spline spinning disk to the in-plane edge loads is analyzed by taking the derivative of the spinning disk's eigenvalues with respect to the loads. An expression for the energy induced in the spinning disk by the in-plane loads, and their interaction at the inner radius, is derived by computation of the rate of work done by the lateral component of the edge loads. Experimental idling and cutting tests for a guided spline saw are conducted at the critical speed, super critical speeds, and at the flutter instability speed. The cutting results at different speeds are compared to show that the idling results of a guided spline disk can be used to predict stable operation speeds of the system during cutting.

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References

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Figures

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Fig. 1

(a) Schematic of guided spline saw and (b) idealizing the blade as a spinning disk

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Fig. 2

Schematic of disk subjected to in-plane edge loads, and their inner interaction loads

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Fig. 3

Variation of eigenvalues as a function of rotation speed, (– – straight lines) free spinning spline rigid disk (the 2Ω line is a free spinning disk, and the horizontal line is the disk, constrained by a lateral spring kz=104N/m), (– solid line) the rigid body motions are coupled by a lateral spring, (– –) free spinning spline rigid disk, subjected to a radial load, (– solid line) spinning spline rigid disk, constrained by a lateral spring, subjected to a radial load

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Fig. 4

Variation of imaginary part of eigenvalues as a function of rotation speed, (– –) free spinning guided spline disk, (–solid lines)free spinning guided spline disk, subjected to edge loads

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Fig. 5

Variation of real part of eigenvalues as a function of rotation speed, (– –) free spinning guided spline disk, (–solid lines) free spinning guided spline disk, subjected to edge loads

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Fig. 6

Transverse vibration of the disk computed for outer radius at α=45 deg, Subjected to (a) a concentrated radial in-plane edge load, (b) a concentrated tangential in-plane edge load, (c) concentrated radial and tangential in-plane edge load, (insignificant amplitude) Ω=42 Hz, (insignificant amplitude) Ω=50 Hz, (large amplitude) Ω=53 Hz

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Fig. 7

Rate of work done by the edge loads, at rotating speed (a) 42 Hz, (b) 50 Hz, and (c) 53 Hz

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Fig. 8

Rate of work done by the tangential and radial edge loads, disk running at a flutter instability speed (Ω=53 Hz)

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Fig. 9

Schematic of the experimental setup

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Fig. 10

Variations of excited frequencies as a function of rotation speed, guided spline saw

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Fig. 11

Schematic of cutting test setup

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Fig. 12

Cut profile for test 1, cutting at 3200 rpm (critical speed)

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Fig. 13

Cut profile for test 2, cutting at 3600 rpm (a super critical speed)

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Fig. 14

Cut profile for test 3, cutting at 4000 rpm (a flutter speed)

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