Experimental Statistical Energy Analysis Applied To A Rolling Piston-Type Rotary Compressor

Hermetic rotary compressors are one of the most important components in air-conditioners and refrigerators since they control both the performance and noise level of these products. Noise and vibration control of hermetic compressors should start with the identification of their sources of noise and vibration since the noise sources within a compressor play a determining role in the noise radiation from the compressor shell. Many approaches have been used to identify compressor noise sources in the past. However, compressor noise source identification has proven difficult since the characteristics of compressor noise are complicated due to the interaction of the numerous components within the compressor. In particular, a compressor possesses a number of partially coherent excitation mechanisms within its small inner space. The fact that several mechanisms operate simultaneously makes the identification of the source of compressor noise more difficult since noise is generated both by pressure pulsations within the refrigerant gas and by the compressor body vibration due to unbalanced internal dynamic forces. Therefore experimental Statistical Energy Analysis has been investigated as a noise control tool for the development of low noisy hermetic-type compressors since that procedure can be used to trace energy flow through the system and identify transmission paths from the noise source to the exterior sound field. INTRODUCTION For noise source identification and sound level evaluation, Statistical Energy Analysis (SEA) has been applied recently to design problems in the HVAC industry since it can quantify the flow of energy through compressor components and trace their noise transmission paths. In particular, SEA can be a modeling procedure for the theoretical estimation of the dynamic characteristics of the vibrational response and the noise radiation from complex structures using energy flow relationships. Therefore SEA can be used to predict the interactions between resonant structures and reverberant sound fields in acoustic volumes. Theoretical SEA, however, has a limitation when it is applied to small, hermetic-type compressors since the individual compressor components may have insufficient modes in the frequency bands of interest. For this reason, it is necessary to use Experimental Statistical Energy Analysis (ESEA) to circumvent some of the limitations of theoretical SEA. In the work described in this paper, the main parameters of ESEA models, such as modal density, damping loss factor, and coupling loss factor between the individual components of the rotary compressor, were obtained experimentally. The modal densities were measured by the mobility method and the damping loss factors by the half-bandwidth method. For the evaluation of the sound radiation from the compressor body, the radiation ratio was estimated from vibration measurements on the compressor surface and sound intensity measurements in an anechoic room. MODAL DENSITY The vibrational and acoustical response of structural elements, and the acoustical response of volume elements, to random excitations are often determined by the resonant response of contiguous structural and acoustic modes. For example, when a structure is excited by some form of broadband structural excitation, the dominant structural response is resonant. When a structure is also acoustically excited, the dominant response is generally resonant [Norton]. Therefore the energy flow between groups of resonant modes can be a primary concern in the SEA method. The modal density is therefore a very important parameter for establishing the resonant response of a system to a given forcing function. The modal density indicates the number of modes per unit frequency and is analogous to the thermal capacity of a thermal system. Asymptotic modal density formulae are available in the literature for a range of idealized subsystems such as bars, beams, flat plates, thin-walled cylinders, acoustical volumes, etc. However, theoretical estimates are not readily available for non-ideal subsystems such as compressor components. For this reason, in practical engineering problems an experimental technique is more suitable for obtaining modal densities. To establish an appropriate modal density estimation procedure, comparisons between analytic solutions and experimental measurements for ideal models such as beams and plates were performed. After these verification tests, experimental measurements for various compressor components were performed. Experimental Method In SEA, the spatial and time averages of a variety of different signals, rather than their instantaneous values, are considered. Therefore it is necessary to measure the vibration at numerous locations and over some specific time interval to obtain an averaged vibration level. In this experiment, this spatial average was obtained by an arithmetic average of the responses at several measurement points. Point mobility measurement Mobility is a complex frequency response function that is commonly referred to as a transfer function between an output velocity and an input force. The real part of the mobility is a function of the modal density of the structure, and the real part is of primary concern since it represents the mean energy flow that can be dissipated. The imaginary part of the point mobility represents the reactive energy exchange in the region of the coupling point. Therefore the imaginary part is not considered when the modal density is considered. The modal density can be defined as, )] ( Re[ 4 ) ( ω ρ ω Y S n s = (1) where: S is the surface area of the test structure, s ρ is the surface mass (mass per unit area), and )] ( Re[ ω Y is the space-average of the real part of the mobility. Test results of modal density Plate and beam A flat plate and beam were chosen to verify the experimental procedure since the analytical solutions of these components are presented in many references: e.g., [Lyon]. The modal density of a flat plate and beam are shown in Figures 1 and 2, respectively. There is good agreement between experimental and analytical results. The analytical solution for the plate was obtained based on flexural vibration modes and it has a constant value. The modal density of the beam, however, is inversely proportional to the frequency. Compressor shell Among the compressor components, the modal density of the shell is presented here since its shape is similar to a theoretical thin-walled shell. Figure 3 shows the experimental, analytical, and ANSYS (i.e., finite element) results for this case. The difference between the experimental and analytical solution shows that the analytical solution below the ring frequency (the frequency at which the cylinder vibrates uniformly in the breathing mode) is not suitable for describing the compressor shell. The compressor shell ring frequency was 14 kHz. To verify this difference, the numerical modal density was calculated using ANSYS at the locations of the experimental measurements. The ANSYS result agrees well with the experimental data between 2 kHz and 10 kHz. Thus an ANSYS analysis based on thin shell theory agrees well with the measured modal density of a compressor shell below the ring frequency. DAMPING LOSS FACTOR In general, damping exists in all real systems and there are many different types of damping in practice. The most commonly encountered damping types are structural (hysteretic) damping, coulomb (dry-friction) damping, and velocity-squared (aerodynamic drag) damping. Among them, the form of damping that is most relevant to engineering noise and vibration control is structural damping and structural damping is of two types: viscous and hysteretic. Viscous damping is usually chosen for mathematical convenience, since it yields simple solution for transient response. Hysteretic damping, based on the concept of a complex modulus, can often be utilized in the calculation of steady state response. The principal difference between a viscous-damped system and a hysteretic-damped system is that for the viscous system the energy dissipated per cycle depends linearly on the frequency of oscillation, whereas for the hysteretic case it is independent of the frequency. Energy is thus conserved only for the particular case of free undamped vibrations since there are no excitation or damping forces present. However, when considering practical engineering components such as compressor components, there should be an energy dissipation due to the damping inherent to their material properties. Therefore viscous damping is assumed in order to estimate the damping loss factor of compressor components.The two most common techniques for obtaining damping loss factors are the half-power bandwidth technique and the envelope decay technique. The halfpower bandwidth technique utilizes the standard half-power bandwidth relationship which is associated with a 3 dB drop in response from the associated steady-state frequency response function peak. The other, envelope decay (reverberation), technique is based on the logarithmic decrement of the transient structural response subsequent to gating of the excitation source. For the measurement of damping loss factors in compressor components, the halfpower bandwidth technique is used: i.e.,