Acoustic Radiation Efficiency Models of a Simple Gearbox

Acoustic intensity measurements were conducted on a simple spur gear transmission in a welded steel housing. The radiation efficiency of the housing was computed from the intensity data for the first three harmonics of mesh frequency. Finite element and boundary element methods (FEM/BEM) were used jointly to model acoustics and dynamics of the top plate of the housing. For a simply supported elastic plate, reasonable agreement was achieved between experimental radiation efficiencies and those predicted with FEM/BEM. However, predictions of the housing characteristics were only partially successful. Four simple analytical models were examined to judge their ability to predict the radiation efficiency. These models do not simulate the modal characteristics of a gearbox; therefore their predictions yield only general trends. Discrepancies are believed to be related to inaccurate modeling of the excitation of the structure as well as to interactions between modes of vibration. INTRODUCTION Much effort has been expended during the design process in recent years to predict the noise of machinery in order to reduce it. The mesh excitation of gear transmissions has been analyzed, and a method has been developed to model the transmission of vibration through bearings into the housing (Lim, 1989). The remaining step is to predict the characteristics of noise radiation from a vibrating structure. Seybert discusses a method for predicting radiation by a boundary element analysis of a vibrating surface (Seybert et al., 1994). Several studies have examined the sound radiation characteristics of single flat plates (panels) under various boundary conditions. A general review is given in Lim and Singh (1989). Other work includes Wallace (1972), Beranek (l971), Fahy (1985), Guyader (l994), and Cremer et al. (1973). Others have tried to correlate gearbox-radiated noise with structural excitation (Oswald et al., 1992; Seybert et al., 1991; Kato et al., 1994; Sabot and Perret-Liaudet, 1994; VanRoosmalen, 1994; Lim, 1989; and Heath and Bossler, l993). Many other studies are summarized in Lim and Singh (1989). Since acoustic radiation efficiency is the link between structural vibrations and the radiated sound power, it should be studied when attempts are being made to predict noise. This paper looks at several acoustic radiation efficiency models and compares them to experimental results. Identifying the usefulness of these models in housing design is the main focus of this paper. APPARATUS The gear noise test rig at NASA Lewis Research Center is equipped to accommodate spur and helical gears. Several types of measurements, including sound pressure, acoustic intensity, and housing acceleration, can be made on this rig (Oswald et al., 1992). The test rig consists of a single-mesh gear pair powered by a 150-kW (200 hp) variable-speed electric motor. An eddy-current dynamometer loads the output shaft. The gearbox can operate at speeds up to 6000 rpm. For this study, the gears were identical 28-tooth spur gears with a 6.35-mm face width; they were manufactured to AGMA class-15 accuracy. The gears have a linear profile modification (tip relief) of 11 mm (0.00045 in.) that extends 90 percent of the distance from the tip to the high point of single tooth contact. For these gears, the transmission error is minimized at a load of 45 N·m (400 in·lbf). The housing is made of 6.35-mm-thick steel plates. The four corners of the base plate are bolted to a foundation that is assumed to be rigid. The sides of the box are welded to each other and to the base plate; the top plate is bolted down, but can be removed to change test gears. The whole rig is within a room whose floors, walls, and ceiling are covered with acoustic absorbing 1Currently at Ford Motor Company, Dearborn, Michigan.