Dynamic Environments Testing, Volume 7

The use of vibration testing to complete qualification of critical components is important for a wide variety of industries to understand the life cycles of their products in operational environments. A common problem with testing components to failure is the time and cost associated with mimicking the full life of a part, creating a need for shorter-duration testing that provides comparable life cycle information. The most common methods that accelerate damage tests use Miner’s Rule, an equation that sums damage percentages caused by varying stress amplitudes. The aim of using Miner’s Rule in damage analysis is to find a shorter-duration test cycle that will provide equivalent damage to the part’s real-world environment. This method has demonstrated accuracy under constant amplitude loading but loses reliability under variable amplitude loadings due to its lack of regard toward the loading sequence. Furthermore, translating from a stress-cycle (SN) curve to design amplitudes for testing requires system knowledge. Finally, the entire process of damage equivalence for additively manufactured (AM) parts is minimally explored in current research. This study seeks to improve the quality of test acceleration by utilizing models of the system under test to not only provide a method for faster, more accurate equivalent damage analysis but also to fill a void of a lack of information regarding test compression of AM parts. To do this, AM specimens designed with a failure point under a complex stress history are evaluated. First, parts are vibration tested on a shaker to achieve experimental failure time. Next, the base inputs used for experimentation are modeled in simulation to evaluate theoretical failure time. Finally, test results of the experimental setup and simulated environment were compared to evaluate the accuracy of Miner’s rule in equivalent damage analysis, as well as test accuracy of SN curves for designing tests of AM parts.

The shock response spectrum (SRS) is commonly used to characterize pyroshock environments created by mechanical impacts and explosives. One limitation is that a single SRS may be computed from different acceleration time histories (time domain signals). As a result, variables from acceleration time histories such as peak amplitude, duration have been introduced as an alternative method to better characterize pyroshock environments. This chapter investigates the producibility of resonant plate test when time domain variables are used as specifications parameters. Time domain variable will be evaluated for various test setup parameters such as plate, projectile weight, and projectile velocity.

Expansion methods are commonly used to compute the response at locations not measured during physical testing. The System Equivalent Reduction Expansion Process (SEREP) produces responses at finite-element degrees of freedom through the mode shapes of that model. Measurements used for expansion are often acceleration, strain, and displacement and operate only on like sets of data. For example, expanding acceleration data produces only additional acceleration data and does not provide insight into the test article’s stress or strain state. Stress and strain are often desired to evaluate yield limits and create fatigue models. The engineer may have acceleration measurements available but desire a component’s stress and strain state. This chapter evaluates a physical experiment from which acceleration is measured and a full set of strain, stress, and displacement data is obtained through SEREP and integration. Honeywell Federal Manufacturing & Technologies, LLC, operates the Kansas City National Security Campus for the United States Department of Energy/National Nuclear Security Administration under Contract Number DE-NA0002839.

Engineers are interested in the ability to compare dynamic environments for many reasons. Current methods of comparing environments compare the measured acceleration at the same physical point via a direct measurement during the two environments. Comparing the acceleration at a defined point only provides a comparison of response at that location. However, the stress and strain of the structure are defined by the global response of all the points in a structure. This chapter uses modal filtering to transform a set of measurements at physical degrees of freedom into modal degrees of freedom that quantify the global response of the structure. Once the global response of the structure is quantified, two environments can be more reliably and accurately compared. This chapter compares the response of an aerospace component in a service environment to the response of the same component in a laboratory test environment. The comparison first compares the mode shapes between the two environments. Once it is determined that the same mode shapes are present in both configurations, the modal accelerations are compared in order to determine the similarity of the global response of the component.

Comparison of pure sinusoidal vibration to random vibration or combinations of the two is an important and useful subject for dynamic testing. The objective of this chapter is to succinctly document the technical background for converting a sine-sweep test specification into an equivalent random vibration test specification. The information can also be used in reverse, i.e., to compare a random vibe spec with a sine-sweep, although that is less common in practice. Because of inherent assumptions involved in such conversions, it is always preferable to test to original specifications and conduct this conversion when other options are impractical.

This chapter outlines the theoretical premise and relevant equations. An example of implementation with hypothetical but realistic data is provided that captures the conversion of a sinusoid to an equivalent ASD. The example also demonstrates how to account for the rate of sine-sweep to the duration of the random vibration.

A significant content of this chapter is the discussion on the statistical distribution of peaks in a narrow-band random signal and the consequences of that on the damage imparted to a structure. Numerical simulations were carried out to capture the effect of various combinations of narrow-band random and pure sinusoid superimposed on each other. The consequences of this are captured to provide guidance on accuracy and conservatism.

Mechanical shock testing utilizing different types of resonating fixtures is an aerospace environmental testing practice useful in simulating mid-field pyroshock. Qualification tests using these methods may be specified in single or multiple test axes, with each axis performed individually or sometimes all at once. Simple structures such as bars, beams, and plates have been used to repeatably perform single-axis resonant shock tests, while plates of varying sizes along with a 90 degree bracket have been used to perform tests that meet all axes requirements in a single shock test event.

This work will evaluate a different fixture concept, used in conjunction with a resonant plate. The fixture is designed to create a controlled resonant response in two axes, which when combined with the plate motion in the third axis can achieve a repeatable resonant shock response in all axes at once, with minimal setup time or operator trial and error. Modal properties of a combined fixture and plate assembly are used as performance objectives for the fixture design. Finite element modeling is used to evaluate and modify the fixture design. A fixture is then fabricated and tested in several configurations to evaluate modal response characteristics, shock response performance, and the performance of the model when predicting those quantities of interest.

Modal characterization of a structure is necessary to inform predictive simulation models. Unfortunately, cost and schedule limitations tend to prioritize other dynamic tests, which can lead to inadequate or nonexistent modal testing. To utilize the dynamic test data that is acquired, analysts can extract operational deflection shapes (ODS) which can then be used as a substitute for modal data in model updating and structure characterization. However, extremely high levels of excitation during vibration testing may introduce nonlinear behavior that distorts the ODS prediction. This chapter investigates the reliability of using ODS as a replacement for traditional modal testing on an academic structure designed to respond with intermittent impact. This chapter calculates ODS from responses at several input excitation levels, and the influence of nonlinear impact on the resulting operating modes is discussed.

The Environmental Test group at KCNSC performs various mechanical tests to evaluate the production lifetime of components. The majority of these tests are performed on an electromagnetic (EM) shaker. An EM shaker is a device that converts electrical energy to mechanical vibrations using the principles of electromagnetism. This vibration testing is highly useful for field testing components that are routinely subjected to repetitive vibrations and shocks.

In order to facilitate a reduction in unnecessary testing time, simulation of the shaker using finite element modeling (FEM) is an invaluable tool to predict real-world outcomes. Full dynamic characterization of the shaker as well as its interaction with adapters and test fixtures is difficult to capture but is nonetheless fundamental to understanding the response of a unit undergoing test. Inputs to achieve reliable predictive simulation results require accurate design, a proper understanding of coupling behavior, and precise test article definition.

At KCNSC, we are performing modal and dynamic analyses using our FEM model of an electromagnetic shaker. This abstract intends to examine some of the design challenges our team has faced such as model creation, boundary condition definition, and response matching to test specifications. We will also examine future challenges we are working to overcome which could allow for better prediction of input parameters prior to simulation.

Sequential single-axis vibration testing strategies often produce over-testing when qualifying system hardware. Rarely does the test article experience equivalent cumulative vibration response between laboratory and service environments when using traditional single-axis testing methodologies. Multi-axis excitation techniques can simulate realistic service environments, but the hardware and testing-strategies needed to do so tend to be costly and complex. Test engineers instead must execute sequential tests on single-axis shaker tables to excite each degree of freedom, which the previous two decades of vibration testing literature have shown to cause extensive over-testing when considering cross-axis responses in assessing the severity of the applied test environments. Traditional assessments assume that the test article responds only in the axis of excitation, but often significant response occurs in the off-axes as well. This chapter proposes a method to address the over-testing problem by approximating a simultaneous multi-axis test using readily available, single-axis shaker tables. By optimizing the angle of excitation and the boundary condition through dynamic test fixture design, the test article can be rapidly and inexpensively tested using a single-input, multiple-output (SIMO) test in a way that approximates a multiple-input, multiple-output (MIMO) test. This chapter shows the proposed method in simulation with a 2D finite-element box assembly with removable component (BARC) model attached to springs with variable stiffness. The results include quantified test quality assessment metrics with comparison to standard sequential testing. The proposed method enables wide access to rapid, approximate multi-axis testing using existing hardware, thereby reducing the over-conservatism of sequential single-axis tests and requisite over-design of systems.

The main goal of a successful environmental vibration control test is ultimately to replicate in the laboratory the same load path and stress responses that a test article experiences when subjected to operational vibrations. Poor replications can lead to an unacceptable time to failure estimation for the unit under test and different failure modes. When performing a vibration control test, it is however necessary to deal with the differences between real-life and testing boundary conditions and excitation mechanisms. In case of in-flight random vibration environments, these differences become particularly critical due to the distributed nature of the aerodynamic loads. Multi-input multi-output (MIMO) random vibration control is a technology that allows to explore new possibilities for the replication of these environments. With MIMO random control, it is possible to increase the number of inputs and the number of acceleration control channels on the structure; when combined with the operational impedance matching, the approach can lead to an optimal replication of the in-service acceleration responses. The main goal of this work is to show a new possibility in the MIMO random control testing practice: simultaneous control of multiple strain responses. The underlying idea is to directly target the replication of stress propagation mechanisms while making use of the well-known advantages of MIMO random control.

Nearly everyone carries a cell phone in their pocket, including field technicians, engineers, and plant managers. Extracting vibration signals from a cell phone or tablet video offers a low-cost alternative to traditional methods for monitoring the health of plant operating equipment.

In this chapter, two case studies are presented where vibration signals are extracted from cell phone videos and used to diagnose machinery faults. It is shown how time-based or frequency-based operating deflection shapes (ODSs) of a machine or structure can be used to visualize and analyze machine faults.

In each case study, diagnosis of a real-world machine fault is presented. In the second case study, the video results are compared with accelerometer results to confirm the validity of this new non-contacting measurement method.

Several factors can prevent MIMO environment reconstruction tests from being successful, including the locations of the shakers and their directions, the set of accelerometers that are controlled to, and the upper and lower bounds of a shaker’s dynamic range. This work explores these issues for a simple component that flew on a sounding rocket in 2019, and which was instrumented with accelerometers to capture the operational environment in detail. Electrical models were estimated for three modal shakers to predict whether a certain configuration of shakers can recreate the environment without exceeding their input voltage capabilities. Tests are performed controlling to various sets of accelerometers. Finally, the condition number threshold and stinger length are investigated as potential solutions to insufficient shaker dynamic range. These factors are all studied by simulating a MIMO test using transfer functions measured in impact hammer testing, and physical MIMO testing is performed on the most promising test configurations using six modal shakers.

The importance of user-accessible multiple-input/multiple-output (MIMO) control methods has been highlighted in recent years. Several user-created control laws have been integrated into Rattlesnake, an open-source MIMO vibration controller developed at Sandia National Laboratories. Much of the effort to date has focused on stationary random vibration control. However, there are many field environments which are not well captured by stationary random vibration testing, for example shock, sine, or arbitrary waveform environments. This work details a time waveform replication technique that uses frequency domain deconvolution, including a theoretical overview and implementation details. Example usage is demonstrated using a simple structural dynamics system and complicated control waveforms at multiple degrees of freedom.

Multiple-input/multiple-output (MIMO) vibration control often relies on a least-squares solution utilizing a matrix pseudo-inverse. While this is simple and effective for many cases, it lacks flexibility in assigning preference to specific control channels or degrees of freedom (DOFs). For example, the user may have some DOFs where accuracy is very important and other DOFs where accuracy is less important. This chapter shows a method for assigning weighting to control channels in the MIMO vibration control process. These weights can be constant or frequency-dependent functions depending on the application. An algorithm is presented for automatically selecting DOF weights based on a frequency-dependent data quality metric to ensure the control solution is only using the best, linear data. An example problem is presented to demonstrate the effectiveness of the weighted solution.

Electrodynamic shaker systems are a staple in shock and vibration environments testing, yet the specific performance limits of these systems are not well characterized. Manufacturer ratings give a general idea of a system’s capability, but the details of their performance remain uncharacterized, often leaving test engineers using their best judgment to determine if a test is feasible. This work applies dynamic substructuring to better predict shaker capability throughout the system’s full range. By modeling a shaker system, insight is gained into the potential performance, but the difficulty remains that the dynamics of the system will change depending on how the test configuration is defined. If no analytical model of the article exists, it is challenging to make evaluations of the new coupled system’s behavior. An experimental model of the test article is developed through modal impact testing, without the need of a shaker. This experimental model is then coupled to a 4-DOF lumped-parameter electromechanical shaker model through dynamic substructuring. The coupled system can then be used for shaker capability estimation for a specific test configuration. By utilizing a modal test and substructuring to estimate performance, no time is lost with the article on the shaker determining if a test specification is achievable. Beyond time savings, the modal model could be coupled to multiple shaker models to determine the best machine for a given test.