Design and Analysis of High-Frequency Periodically Layered Isolators for Helicopter Gearbox Isolation

Vibration generation by meshing gear pairs is a significant source of vibration and cabin noise in rotorcraft transmissions. This tonal, high-frequency gearbox noise (500 Hz – 2000 Hz) is primarily transmitted to the fuselage through rigid connections, which do not appreciably attenuate vibratory energy. Because periodically-layered elastomer and metal isolators exhibit transmissibility “stop bands”, or frequency ranges in which there is very low transmissibility, they may provide an elegant passive vibration control solution. Realistic design constraints associated with helicopter gearbox isolator mass, axial stiffness, and elastomeric fatigue are estimated. An optimization routine is then used in concert with design constraints and an axisymmetric isolator model to determine layered isolator passive performance limits. The optimization results suggest that layered isolators cannot always be designed to meet target frequencies given a certain set of constraints. Therefore, passive performance enhancements to layered isolators are considered. The use of embedded fluid elements in the metal layers results in a combination of advantageous performance benefits, including motion amplification and vibration absorber effects. The enhanced layered isolators are capable of passively providing broadband noise attenuation, as well as dramatic attenuation at discrete problematic tones. INTRODUCTION Dynamically-tuned flexible mounts are frequently used for passive isolation of mechanical components subject to vibration. Elastomeric materials are incorporated into many mounts to provide a combination of low stiffness and moderate damping. Typical isolation mounts are designed to attenuate motion or force at low frequencies, usually below 100 Hz. The principles of vibration isolation in this frequency range are well understood. Elastomeric mounts employed for low frequency isolation may be simultaneously subjected to higher-frequency, machine-generated vibro-acoustic energy. Standard isolation techniques, however, may not be appropriate for forcing frequencies much higher than the fundamental system frequency, due to the presence of wave effects. Wave effects occur at high frequencies when the elasticity and the distributed mass of the mount interact to create sharp transmissibility peaks (Ref. 1). Refs. 2 and 3 report that periodically-layered metallic and elastomeric mounts are potential attenuators of dynamic stresses at high frequencies. The impedance difference between layers is the attenuation mechanism, in which an incident wave is scattered and essentially split into a reflected and refracted wave (Ref. 4). The device becomes increasingly effective with a larger impedance mismatch between the isolator materials. A one-dimensional analysis of periodicallylayered isolators in compression is presented in reference (Ref. 4). Motivation for the research effort was isolation of reactor components and structures from seismic, impact, or other accident-induced loads. A time-domain solution was obtained for plane stress 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Confere 7-10 April 2003, Norfolk, Virginia AIAA 2003-1784 Copyright © 2003 by Joseph Szefi. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. 2 American Institute of Aeronautics and Astronautics wave excitation through layered composites. The analysis makes use of continuity of stress and displacement at the layer interfaces. Plane longitudinal stress waves with particular wavelengths are attenuated in periodically-layered elastic mounts, whereas no attenuation is exhibited by an undamped homogeneous elastic medium. A one-dimensional analysis of layered isolators, based on the theory of shear waves in infinite, periodically layered media is presented in Refs. 2 and 3. Floquet theory is used to solve the equations for the propagation of plane waves through a laminated system of parallel plates. The plates consist of two alternating materials, and the direction of propagation is normal to the plates. The theory predicts high frequency “stop bands” within which vibratory energy is attenuated. The analysis includes a method for predicting the beginning and end frequencies of stop bands. Thus, the layered isolator behaves as a mechanical notch filter. The existence of the predicted stop bands was corroborated by testing of layered specimens in shear. The test specimens were of finite length, and therefore edge effects and reflections from the top and bottom layers were observed in the experiment. These effects, however, did not obscure the basic physical phenomenon of stop bands. The effects of three-dimensional elasticity on periodically layered isolators in compression were examined in Ref. 5. A detailed finite element analysis of periodically layered isolators was conducted to gain an improved understanding of three-dimensional effects on isolator performance. The isolator models consisted of alternating, cylindrical layers of elastomer and metal. Axisymmetric solid elements were used to model each layer of cylindrical isolators. Each element had eight nodes and forty-eight degrees of freedom. The first four mode shapes of a typical three-celled isolator are shown in Figure 1, where a cell is a single elastomer and metal layer combination. The mode shapes of the isolator were then examined (Refs. 5, 6). For an isolator with n cells, there are (n-1) isolator modes below the beginning of the stop band. The stop band frequency range begins at the n isolator mode and continues until the (n+1) isolator mode. In the first n modes, each elastomer layer associated with these frequencies undergoes approximately uniform axial strain. In fact, the metal layers behave essentially like n discrete masses supported by n axial springs in series. Invariably, in the first mode, every elastomer layer exhibits either uniform tension or compression. In the next (n-1) modes, the mode shapes of the individual layers are observed to contain different combinations of layerwise compression and tension. The (n+1) mode (e.g., mode 4 in Figure 1) is the first mode in which an elastomer layer exhibits a ‘thickness’ mode. Physically, this mode involves both tension and compression within the elastomer layer and minimal net axial motion of the constraining metal layers. This mode is associated with the end of the stop band frequency range. The first three modes in Figure 1 also exhibit significant lateral motion of the middle of each elastomer layer. This is due to fact that the upper and lower surfaces of each layer are constrained and that elastomeric materials are nearly incompressible. Consequently, the effective three-dimensional stiffness of each layer differs from that predicted by onedimensional theory, which only addresses axial motion. Figure 1. First four axisymmetric mode shapes of a cylindrical three-celled isolator in compression. Stop Band Mode 1 Mode 2 Mode 3 Mode 4