Hybrid coupling method to nonlinear acoustic source and linear duct system using parameter identification of the input impedance in fluid machinery
Nederland | Journal of Sound and Vibration
2014-10-14 | 바로가기
Cited by 2
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Journal of Sound and Vibration
Received 14 October 2014, Revised 24 November 2015, Accepted 26 November 2015, Available online 18 December 2015.
Seungjae Oha, Semyung Wanga, Sungman Chob
a School of Mechatronics, Gwangju Institute of Science and Technology (GIST)
b Home Appliance Laboratory, LG Electronics Inc.
The acoustic source in fluid machinery is described as nonlinear. However, acoustic wave propagation in the muffler is represented by a linear system. Therefore, the acoustic source is modeled in the time domain, and the acoustic propagation is expressed in the frequency domain. The method of analyzing the acoustic in different domains is known as hybrid coupling. In this paper, a developed non-iterative hybrid coupling method was suggested, where the parameter identification using the rational fractional polynomial method is performed with the measured input impedance of the muffler described in the frequency domain. In this case, the relationship of the polynomial order of the denominator and numerator was determined from the analogy of a mechanical system. The approximated input impedance model is transformed to the state space model, which is described in the time domain. Finally, this model is coupled to a nonlinear acoustic source to analyze in the time domain. The proposed method can be used in more diverse condition than the other method. Simultaneously, a transient response can be obtained. The proposed method was experimentally verified using the suction part of a linear compressor, which is representative of fluid machinery.
In terms of energy efficiency and noise of fluid machinery, acoustic analysis has become an important issue. As previously mentioned, the acoustic wave propagation in the suction muffler is represented by a linear system. However, the acoustic source in the suction part of the fluid machinery is known to have a nonlinear characteristic. Therefore, a hybrid coupling method is necessary.
The Coupling by Mechanical Analogy is the most recently released hybrid coupling method . The input impedance was derived using an analogy between vibration and an acoustic system. In the Coupling by Mechanical Analogy, the acoustical modal mass, modal damping and modal stiffness were obtained using the Peak Picking Method with a measured input impedance. The hybrid coupling analysis was performed in the time domain by constructing N uncoupled Ordinary Differential Equations.
However, when the input impedance in the suction muffler of the compressor, which is a representative fluid machinery, was measured, it is often found with notably closely coupled mode and heavily damped mode. Thus, a more advanced hybrid coupling method than the Coupling by Mechanical Analogy is required.
This study proposed a method where an approximated model is constructed regardless of the mode characteristics using the rational fractional polynomial method, which is an Multi-DOF modal parameter identification method. It is notably important to determine the polynomial order of the denominator and numerator when parameter identification is performed using the rational fractional polynomial method. The denominator and numerator should have equal polynomial orders to make a stable and accurate approximate model. This model can be physically inferred from the analogy between a mechanical vibration system and an acoustic system. This result was confirmed using the stabilization charts in the modal analysis. The stable and accurate approximate input impedance model is transformed into a discrete state space model. The discrete state space model is coupled with a nonlinear acoustic source in the time domain. The proposed hybrid coupling method was experimentally verified using the suction part of a linear compressor.
This study developed an existing non-iterative hybrid coupling method by applying Multi-DOF modal parameter identification method in the vibration problem. In addition, a physically reasonable relationship polynomial order of the denominator and numerator in the rational fractional polynomial method was identified.
The proposed hybrid coupling method in this paper will be efficiently used to couple acoustic sources and propagation systems in fluid machinery and can be applied to reduce the noise and increase the energy efficiency.
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