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Research Papers

Nonlinear Interactions in Systems of Multiple Order Centrifugal Pendulum Vibration Absorbers

[+] Author and Article Information
Brendan J. Vidmar

e-mail: vidmarbr@msu.edu

Brian F. Feeny

Dynamics and Vibrations Laboratory,
Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824

Bruce K. Geist

Chrysler Group LLC, Auburn Hills,
MI 48326
e-mail: bruce.geist@chrysler.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 12, 2012; final manuscript received June 18, 2013; published online August 6, 2013. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 135(6), 061012 (Aug 06, 2013) (9 pages) Paper No: VIB-12-1286; doi: 10.1115/1.4024969 History: Received October 12, 2012; Revised June 18, 2013

We consider nonlinear interactions in systems of order-tuned torsional vibration absorbers with sets of absorbers tuned to different orders. In all current applications, absorber systems are designed to reduce torsional vibrations at a single order. However, when two or more excitation orders are present and absorbers are introduced to address different orders, nonlinear interactions become possible under certain resonance conditions. Under these conditions, a common example of which occurs for orders n and 2n, crosstalk between the absorbers, acting through the rotor inertia, can result in instabilities that are detrimental to system response. In order to design absorber systems that avoid these interactions, and to explore possible improved performance with sets of absorbers tuned to different orders, we develop predictive models that allow one to examine the effects of absorber mass distribution and tuning. These models are based on perturbation methods applied to the system equations of motion, and they yield system response features, including absorber and rotor response amplitudes and stability, as a function of parameters of interest. The model-based analytical results are compared against numerical simulations of the complete nonlinear equations of motion, and are shown to be in good agreement. These results are useful for the selection of absorber parameters to achieve desired performance. For example, they allow for approximate closed form expressions for the ratio of absorber masses at the two orders that yield optimal performance. It is also found that utilizing multiple order absorber systems can be beneficial for system stability, even when only a single excitation order is present.

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References

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Figures

Grahic Jump Location
Fig. 1

Schematic of a rigid rotor fitted with absorbers tuned to n˜ and 2n˜

Grahic Jump Location
Fig. 2

Simulated responses of a system composed of four tautochronic absorbers, two each at orders 1.5 (sn) and order 3(s2n), subjected to a torque composed of a linear combination of orders 1.5 and 3. Note the different scales used for depicting the responses. (a) Torque harmonic amplitude space Γ3 versus Γ1.5, with boundaries of the desired synchronous response indicated schematically; solid line depicts a subharmonic instability boundary and dotted (dashed) line depicts a symmetry-breaking instability boundary to nonsynchronous responses of the order 1.5 (3) absorbers. (b) Mutually synchronous response at point W. (c) Response at point X; the order 1.5 absorbers have become nonsynchronous and are in a transition towards their amplitude limits. (d) Response at point Y; similar to W, only with reversed relative amplitudes. (e) Response at point Z; the order 1.5 absorbers have become subharmonic and are in transition toward their amplitude limits, as shown in (f). (f) Response at point Z, depicted over a long time interval; the order n absorber instability eventually results in large amplitude motion; the cusp amplitudes are the maximum possible amplitudes for these absorbers.

Grahic Jump Location
Fig. 3

Predicted and simulated steady-state absorber amplitudes as a function of the order n torque amplitude; the order 2n torque amplitude is zero. The cusp values are amplitude limits set by hardware constraints. System parameters: m3/m1.5 = 0.1, ε = 0.05.

Grahic Jump Location
Fig. 4

Order n and 2n harmonic components of the rotor angular acceleration as a function of the order n applied fluctuating torque amplitude, for the same conditions as Fig. 3. The solid line is the reference response for the absorbers locked.

Grahic Jump Location
Fig. 5

Absorber amplitudes as a function of order n fluctuating torque amplitude; the order 2n torque amplitude is zero. System parameters: m3/m1.5 = 0.62, ε = 0.05. The absorbers reach their respective cusps at approximately the same level of excitation.

Grahic Jump Location
Fig. 6

Order n = 1.5 absorber synchronous response stability boundary as a function of the driving torques, for ϕ = 0. Torques outside the range of this curve result in nonsynchronous responses of the order n absorbers.

Grahic Jump Location
Fig. 7

Order n applied torque versus the mass ratio of the different order absorbers, when assuming a synchronous response

Grahic Jump Location
Fig. 8

Order n applied torque versus the mass ratio of the different order absorbers. As evident, using a small amount of order 2n absorbers can stabilize the order n absorbers.

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