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RESEARCH PAPERS

Tautochronic Vibration Absorbers for Rotating Systems

[+] Author and Article Information
Steven W. Shaw1

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226shawsw@msu.edu

Peter M. Schmitz

Integrated Defense Systems, The Boeing Company, Philadelphia, PA 19142Peter.m.schmitz@boeing.com

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226haddow@msu.edu

In the case of a constant field, such as local gravitation, the cycloid is both the brachristichrone and the tautochrone.

Inertia $J$ includes all components that rotate at the same rate as the rotor. Thus it includes the moments of inertia of the absorber masses about their respective centers of mass, since these rotate with the rotor due to the bifilar suspension employed.

Note that multiple absorbers are typically used in practice due to balancing and space-limitation issues.

It is worth noting that it was not feasible to run the experiment at orders near 1 or 2, because the servo motor experienced small inherent speed fluctuations at these orders, which interfered with measuring the magnitude of angular acceleration at those orders. Hence the absorbers were designed to be tuned to an order close to $ñ=1.50$, thus avoiding these problematic orders.

As will be seen in Sec. 42, when two absorbers are active the resonance $n2$ is further removed from the perfect tuning point, see Fig. 6.

1

Corresponding author.

J. Comput. Nonlinear Dynam 1(4), 283-293 (Apr 15, 2006) (11 pages) doi:10.1115/1.2338652 History: Received November 21, 2005; Revised April 15, 2006

Abstract

This paper describes an analytical and experimental investigation of the dynamic response and performance of a special type of centrifugal pendulum vibration absorber used for reducing torsional vibrations in rotating systems. This absorber has the property that it behaves linearly out to large amplitudes, and thus experiences no frequency detuning. Previous analytical work on such tautochronic absorbers has considered the response, dynamic stability, and performance of single- and multi-absorber systems. In particular, it is known that these absorbers, when perfectly tuned to the order of the applied torque, do not exhibit hysteretic jumps in the response, but multi-absorber systems can experience instabilities that destroy the symmetry of their synchronous response. In this work we extend the theory to include linear de-tuning of the absorbers, which can be used as a design parameter to influence absorber performance, both in terms of rotor vibration reduction and operating range. This paper reviews the basic analysis, which employs scaling and averaging, and extends it to include the detuning. In addition, systematic experiments of systems with one and two absorbers are carried out. The experimental results are unique in that the test facility is capable of varying the excitation order, thereby allowing one to obtain order-response curves that are useful for design purposes. The experimental results are found to be in excellent agreement with the analytical predictions, and these clearly demonstrate the tradeoffs faced when selecting absorber tuning.

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Figures

Figure 1

General CPVA model, shown for N=3 absorbers

Figure 2

Block diagram of experimental setup showing basic components and signal paths

Figure 3

Physical experimental setup

Figure 4

Close-up of one absorber and its associated mounting hardware. Its motion is constrained to move along a tautochronic path as the thin steel bands wrap around the specially shaped cheeks. The encoder has a light arm attached to it that follows the motion of the absorber. The complete assembly is attached to the rotor on the test-rig (see Fig. 3).

Figure 5

Order sweep at T̂θ=0.198Nm and ϵ=0.07531 for one absorber. (a) rotor angular acceleration ∣θ̈∣, (b) absorber amplitude ∣S∕L∣.

Figure 6

Order sweep at T̂θ=0.205Nm and ϵ=0.16290 for two absorbers. (a) rotor angular acceleration ∣θ̈∣, (b) absorber amplitude ∣S∕L∣.

Figure 7

∣θ̈∣ versus T̂θ for one absorber at various levels of mistuning

Figure 8

Absorber amplitude ∣S∕L∣ versus T̂θ for one absorber at various levels of mistuning

Figure 9

∣θ̈∣ versus T̂θ for two absorbers at various levels of mistuning

Figure 10

Absorber amplitudes, ∣S1,2∕L∣, versus T̂θ for various levels of mistuning, for two absorbers

Figure 11

Absorber response time traces S1,2∕L for two different T̂θ values from Fig. 1 (0% mistuning) (a)T̂θ=1.03Nm(b)T̂θ=1.92Nm

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