Design optimization and experimental validation of the additively manufactured passive vibration isolator of an inertial measurement unit in aerospace applications

Abstract

Vibration is an environmental factor that can affect structures for various reasons and create unwanted consequences on engineering systems. Designers should consider the effects of vibration phenomena and take necessary precautions within the design processes. Especially in aerospace systems, pressure fluctuations, and irregular flow can cause vibrations on structures. Although structural strength is achieved against these vibrations, there may be situations where sensitive avionics systems within aerospace systems cannot operate as desired in this vibration environment affecting them. Inertial measurement units, which are commonly used in aerospace engineering systems such as guided missiles, measure linear acceleration and angular velocity in six degrees of freedom. These measurements are fed to the missile's controller, which controls the missile's control surfaces. Random vibrations that affect the missile over a wide frequency band due to pressure fluctuations and irregular flow can disrupt the measurements made by the inertial measurement unit. While the low-frequency measurements made by the inertial measurement unit are used by the controller, high-frequency measurements need to be eliminated. This way, only low-frequency movements that truly represent the missile's motion are measured and used by the controller. High-frequency filtering can be done digitally or mechanically using passive vibration isolators. Passive vibration isolation is achieved by placing materials such as elastomers with much lower stiffness compared to the structures to be isolated between the isolated structure and the structure that causes excitation. In this way, the elastomer exhibits dynamic behavior under incoming vibrations by resonating, showing the damping of high-frequency excitations to transmit to the structure to be isolated. In this study, a similar approach was taken to isolate an inertial measurement unit (IMU) within a guided missile from vibrations that occur within a broad frequency band induced by fluid flow. Because the IMU measures motion with six degrees of freedom, the mechanical design of the IMU isolation system differs from other passive vibration isolation applications. The decoupled mode shapes of the isolation system enable the IMU to respond minimally to vibrations in other axes when an excitation acts on a particular axis. In other words, since the isolation system does not respond to vibrations in the other axes due to the axis where the excitation originates, the IMU does not make a faulty measurement due to the dynamics of the isolation system in axes where the excitation is absent. The decoupling of the system's mode shapes occurs when the mass center and elastic center of the isolation system coincide. When the mass and elastic centers cannot coincide and the modes are coupled, the system may make a combined movement in various axes at the resonance frequency. For example, if an excitation acts on the IMU as linear acceleration when the mode shapes of the system are not decoupled, it may cause the IMU to make an angular velocity measurement as if it were making an angular movement that the system is not actually making. In this case, the controller will try to control the system as if it were making a movement that it is not happening. Avoiding this situation is critical in systems such as guided missiles. Since the primary goal in aviation systems is generally low mass and surface area, small-volume subsystems are used. In systems where the available space is limited, it may not be easy to coincide the mass and elastic centers. The design of the ring-shaped passive vibration isolator provides an advantage in terms of adding a small volume elastomer layer and coinciding with the mass/elastic centers. Viscoelastic materials used in passive vibration isolation exhibit nonlinear mechanical behavior under factors such as temperature, frequency, and excitation amplitude. When these materials are used in systems that work in extreme environments, such as aerospace, these nonlinear effects must be strictly taken into account. Therefore, a silicone material that can maintain its viscoelastic properties over a wide temperature range is used as a passive vibration isolation element in aerospace applications. However, producing silicone-like materials in complex shapes can create disadvantages in terms of cost and practicality. On the other hand, with the developing additive manufacturing method and innovative materials, complex shapes can be produced in a practical way. For optimum passive vibration isolation, a passive vibration isolator with a complex shape can be produced using viscoelastic material and additive manufacturing methods. In this study, a design of a passive vibration isolator made from an elastomer-like material using the additive manufacturing method, which cannot be produced by conventional methods, was created, and its usability was investigated through simulations and tests.Additionally, a passive vibration isolator design methodology has been proposed for an inertial measurement unit to be used within a specified missile geometry throughout this study. Firstly, the limited dimensions of a ring-shaped vibration isolator were obtained by adhering to the usable area limits where the elastomer material design could be integrated, which were dictated by the unmodifiable missile and inertial measurement unit geometries. In passive vibration isolation, the natural frequency of the system determines the frequency band of the isolation. The ring-shaped passive vibration isolator was parameterized, and the natural frequency of the system was made changeable through systematic extrusion from the isolator geometry. The systematic extrusion were made in such a way that the coincidence of mass and elastic center was continuously ensured. In order to model with the finite element method, the mechanical properties of the thermoplastic polyurethane material used in the additive manufacturing process were obtained through dynamic mechanical analysis (DMA). The temperature and frequency-dependent non-linear mechanical properties of the material was obtained such as the storage and loss modulus. Hence, the temperature and frequency-dependent viscosity change of the thermoplastic polyurethane material were modeled using the Williams-Landel-Ferry (WLF) function by using time-temperature superposition. The parametrized geometry of the passive vibration isolator was optimized through a simplified finite element model to ensure that the natural frequencies determining the vibration isolation were within a certain frequency range. During optimization, the modal shapes of different geometries were controlled by including the modal assurance criterion (MAC) parameter in the optimization. As a result, the optimum geometry of the passive vibration isolator was obtained and analyzed in depth with a detailed nonlinear finite element model to investigate the isolation performance of the system. The isolation performance of the system, and the effect of excitation frequency and temperature on the natural frequency, were obtained with this detailed model. Nonlinearly simulated optimum vibration isolator geometry was produced using the additive manufacturing method. The produced passive vibration isolator was tested and vibration transmissibility measured experimentally to investigate its vibration isolation performance. In the experimental studies, sine sweep and random vibration tests were performed on the system in two different translational axes. By changing the amplitudes and frequency sweep rates used in sine sweep tests, the vibration isolation performance and behavior of the thermoplastic polyurethane (TPU85A) were investigated. In addition, the random vibration that the missile was exposed to under operational conditions in a wide frequency range was experimentally examined by applying random vibration tests to the test setup. Finally, the test results were compared with the simulation. In conclusion, this study presents a methodology for designing passive vibration isolation for an inertial measurement unit. The issues to be considered in the design of an inertia measurement unit passive vibration isolator, which requires special attention in terms of vibration isolation, are discussed in detail. The vibration isolation performance of the optimized geometry from a non-linear material was obtained in the simulation environment by using the finite element method. Afterward, the passive vibration isolator was manufactured and tested by additive manufacturing. Finally, the simulation and test results, in a good agreement with each other, showed that the desired vibration isolation performance was achieved in the temperature regime where TPU85A showed rubber properties, which were determined by the results of dynamic mechanical analysis.