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Research Papers

Directional Order Tracking in Rotating Machines

[+] Author and Article Information
Izhak Bucher

Dynamics Laboratory,
Mechanical Engineering,
Technion—Israel Institute of Technology,
Haifa 32000, Israel
e-mail: bucher@technion.ac.il

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received September 3, 2012; final manuscript received March 11, 2013; published online June 19, 2013. Assoc. Editor: Philippe Velex.

J. Vib. Acoust 135(6), 061004 (Jun 19, 2013) (10 pages) Paper No: VIB-12-1249; doi: 10.1115/1.4024052 History: Received September 03, 2012; Revised March 11, 2013

This paper describes a computationally simple method to isolate transient vibration from rotating components whose frequency is tightly linked to rotation and to modes of vibration. The results can be viewed as an enhancement of computed order tracking or amplitude demodulation of multiple crossing frequency terms. By measuring the response with an array of sensors, one can compute the relative, instantaneous phase between different sensors and thus obtain information about the spatial behavior of different components with different wavelengths, frequencies, and traveling directions. An array of sensors would thus exploit spatial information to separate different vibration modes and thus gain deeper insight into the dynamical behavior. The proposed method is suitable for whirling shafts and rotating disk-like structures. It is computationally simple and fast while providing better separation of components than single sensor based approaches, in particular when ordinary methods fail to separate close frequencies. It is demonstrated that through the exploitation of cyclic symmetry of rotating structures and the angular periodicity of the vibration modes, the spectral contents of different modes can be separated. Simulated and measured data demonstrate the merits of the proposed algorithm.

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Figures

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Fig. 1

Rotating disk with a circular array of sensors, engine fan model with illustrated array of sensors, and a bladed disk with continuous (circle) and discrete sensors (arrows)

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Fig. 2

Time response of s1(t) containing several components according to Eq. (20)

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Fig. 3

A rotating disk with a stationary array of eight sensors

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Fig. 4

A spectrogram computed with a single sensor during acceleration

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Fig. 5

Basic quadrature demodulation or order tracking of the mth engine order from the nth sensor—graphical representation

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Fig. 6

Graphical representation of the multidimensional, directional order-tracking procedure

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Fig. 7

Waterfall (spectrogram) representation of the signal in Fig. 2 and Eq. (20)

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Fig. 8

Extracted spatial vibration components along φ2(t) from a simulated rotating disk using seven sensors. Also shown is the attempt to track this order with a single sensor, s1(t) (shifted for clarity—continuous line) and the spatially decomposed components with nodal diameters in the range (–3 · · · +3).

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Fig. 9

Laboratory system showing rotating disk, two shaft sensors

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Fig. 10

Forward and backward components of order 1, ϕ·(t) = Ω(t) for the vibrating shaft during speed change. Measured on the system in Fig. 9.

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Fig. 11

Complex amplitudes (see Fig. 10) of the forward and backward whirl along the first engine-order (EO-1, ϕ·(t) = Ω(t)) measured with two sensors on the system in Fig. 9 during rotation speed change

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Fig. 12

Engine orders of a rotating disk for EO-1 in inertial coordinates using eight equally-spaced sensors as in Fig. 2 but measured on the system in Fig. 9

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Fig. 13

Decomposed spatial components of EO-1 vibrations measured on a rotating disk transformed to body-fixed coordinates

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Fig. 14

Subtracting engine orders: original Fig. 4, bottom: subtracted orders (combined), top: resulting spectrogram after subtracting EO-1…4, inertial coordinates

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Fig. 15

A Finite element model of a mistuned structure with cyclic-symmetry. Showing one mode under different levels of mistuning (from left to right): (i) near perfect, no mistuning, (ii) 3% blade thickness variations, and (iii) 9% blade thickness variations.

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Fig. 16

Time-frequency map measured on a single blade in a direction normal to the blade while the force in Eq. (24) was acting on the system from Fig. 15. Note the abrupt increase in amplitude (indicated by local color changes) upon excitation of modes by the engine-orders.

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Fig. 17

A single engine order at 2 × Ω (2EO) decomposed into contribution of several nodal diameters in the range ND = −3…3. The plots correspond to the systems depicted in Fig. 15 where (i) left: near perfect, no mistuning, (ii) middle: 3% mistuning of random blade thickness variations, and (iii) right: 9% blade or random thickness variations.

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