For flight payloads or systems in free flight, Impedance Matched Multi-Axis Testing (IMMAT) can provide an accurate laboratory reproduction of the flight vibration environment at multiple response locations. IMMAT is performed by controlling multiple shakers attached to the system of interest, usually through slender rods so that the shakers impart negligible moments or shear forces at the attachment. The attachment usually requires that the shakers not physically support the system. Thus, IMMAT is different from other multi-degree of freedom testing where shakers for slip tables or with vertical bearings drastically change the impedance by their rigid attachment to the system or payload. Consequently, IMMAT shakers are generally smaller than used for traditional testing. In the laboratory IMMAT test, bungee cords can support the system to simulate free flight. For a system that is a flight payload, bungee cords can support a portion of the next level of assembly (such as a rack or rail) with the attached payload to greatly improve the laboratory reproduction of the payload environment with the approximate attachment impedance. Engineering judgment has historically been the basis for IMMAT test planning but provides no pre-test metrics to show whether the test setup can meet the desired requirements. For successful test planning, engineers need tools to optimize the number and location of shakers and predict the requirements for the shakers and amplifiers. Electrodynamic shakers and amplifiers have physical limitations such as maximum available amplifier current, voltage or power and shaker force or stroke. If shakers and amplifiers can barely meet required levels with a well-designed IMMAT test, improper shaker placement can cause exceedance of the limitations and failure of the test to meet required levels. We present a tool to optimize the number and locations of shakers with an objective function that performs a least square fit of the flight cross spectral density matrix while minimizing requirements on the amplifiers or shakers. In this work, an optimized IMMAT test with four shakers attached to a test article closely reproduces the vibration environment generated by a field acoustic test. The optimization is based on a model. The model consists of a modal model (derived from a finite element model) of the test article coupled to a simple calibrated electro-mechanical model of the shakers. The optimization selects shaker locations to minimize the required amplifier output voltage, but one can minimize shaker force, current, control error or some combination with appropriate physical limits.

中文翻译：

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多台振动台环境试验的振动台位置优化

对于自由飞行的飞行有效载荷或系统，阻抗匹配多轴测试 (IMMAT) 可以在多个响应位置提供飞行振动环境的准确实验室再现。IMMAT 是通过控制连接到感兴趣系统的多个振动器来执行的，通常是通过细长的杆，这样振动器在附件上传递的力矩或剪切力可以忽略不计。附件通常要求激振器不以物理方式支撑系统。因此，IMMAT 与其他多自由度测试不同，在其他多自由度测试中，用于滑动台或带有垂直轴承的振动器通过它们与系统或有效载荷的刚性连接而显着改变阻抗。因此，IMMAT 振动器通常比用于传统测试的小。在实验室IMMAT测试中，弹力绳可以支持系统模拟自由飞行。对于作为飞行有效载荷的系统，弹力绳可以通过连接的有效载荷支撑下一级组件（例如机架或导轨）的一部分，以极大地改善实验室再现具有近似连接阻抗的有效载荷环境。工程判断历来是 IMMAT 测试计划的基础，但没有提供预测试指标来显示测试设置是否能够满足所需的要求。为了成功进行测试规划，工程师需要工具来优化振动台的数量和位置，并预测对振动台和放大器的要求。电动振动台和放大器具有物理限制，例如最大可用放大器电流、电压或功率以及振动台力或冲程。如果通过精心设计的 IMMAT 测试，激振器和放大器几乎不能满足要求的水平，那么不正确的激振器放置可能会导致超出限制并导致测试无法满足要求的水平。我们提出了一种工具来优化振动器的数量和位置，其目标函数执行飞行交叉谱密度矩阵的最小二乘拟合，同时最小化对放大器或振动器的要求。在这项工作中，一个优化的 IMMAT 测试将四个振动器连接到测试物品上，紧密地再现了场声学测试产生的振动环境。优化基于模型。该模型由耦合到振动器的简单校准机电模型的测试物品的模态模型（源自有限元模型）组成。