A source-path-receiver approach is presented for the design of an isolator for a reaction wheel assembly (RWA) that will reduce angular vibrations of a device on a flexible satellite body. One objective of this study is to determine, with minimum trial and error, the stiffness of a passive isolator for the RWA that will satisfy strict quantitative requirements of receiver vibration. First, based on measurements of blocked forces during operations, the RWA was characterized as a vibration source with lumped parameters. Second, a finite element model of a truss structure with a thick plate on it, chosen as a substitute for a satellite and an imaging device, respectively, was prepared using a commercial finite element tool (ABAQUS), and the model was tuned for accuracy. Then, a way to select the stiffness of the isolators to be installed between the RWA and the truss structure was proposed with minimum trial and error in the total range of frequency and rotation speed to meet the requirements of angular vibration of the receiver part. For the purpose of a comparison, the conventional approach, based simply on vibration transmissibility across a vibration isolator, which cannot take the flexibility of the path structure into account, was used to determine the isolator stiffness. Vibration isolators with stiffnesses determined by both approaches were manufactured and applied to the RWA truss structure, and it was evaluated as to whether or not the quantitative requirement was satisfied.

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Hydraulic mounts used in vehicles for better isolation of vibrations were often approximated by lumped or mechanical mass-damper-spring (m-c-k) models, although deficiency in such modeling was pointed out and “hydraulic” modeling was proposed as an alternative. In this paper, a brief review on the mechanical m-c-k modeling and “hydraulic” modeling of the hydraulic mounts is presented. A simplest system consisting of a single mass and a hydraulic mount is used to illustrate both equivalence and difference in a closed form between the two modeling approaches. Then, modal analyses are done on an apparently three degrees-of-freedom (DOF) quarter car with a hydraulic mount, where the key idea is to use an internal variable for the movement of fluid mass which is responsible for a “latent” vibration mode. Equations of motion for the apparently 3DOF system, 4DOF system in fact, by the two modeling are formulated. Modal parameters by the proposed “hydraulic” modeling of the hydraulic mount are compared with those by the m-c-k modeling. Forced responses to transient base excitations are also compared between the two modeling approaches to illustrate how much errors can arise in the frequency and time domain analysis. To be more realistic, the modal and forced response analysis on a full car of an apparently 10DOF (3DOF for powertrain, 3DOF for car body, and 4DOF for knuckles and tires) with two more DOF internally for two hydraulic mounts between the powertrain and car body is presented.

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