The purpose of mechanical environment testing is to prove that designs can withstand the loads imparted on them under operating conditions. This is dependent not only on the test article construction but also on the loads imparted through its boundary conditions. Current practices develop environment test specifications from field responses using a single degree of freedom input control with no consideration for the mild to severe deviations from the field motion caused by the laboratory boundary condition. Test specifications are considered conservative with the assumption that most of the steps taken to generate them (e.g., straight-line envelopes and adding 3 dB) result in appropriately conservative specifications. However, without an accurate quantifiable measure of conservatism, designs can be easily mis-tested yielding unnecessarily high costs. Previous work showed a modal model for components excited through base-mounted fixtures to generate specifications with much lower uncertainty and with guaranteed quantifiable conservatism. The method focused on reproducing in-service modal energy in the test configuration by controlling the 6 degree-of-freedom input motion. That work generated test specifications with enough conservatism to account for unit-to-unit variability in the damping of the test article. This paper focuses on generating conservative specifications while considering resonant frequency shifts as a parameter for unit-to-unit variability.
The outline for this presentation includes: Motivation, Test hardware and loads, Modal test of RC on 6 DOF test fixture, and Analysis--develop one specification accounting for unit-to-unit variability and develop independently tailored test specifications for unit-to-unit variability.
The main point of mechanical environment testing is to prove that designs can withstand the loads imparted on them while being exposed to in-service conditions. This is dependent not only on the test article construction, but also the loads imparted through its boundary conditions. Current practices for developing environment test specification are typically based on inadequate information reduced to single input point control with large uncertainty as compared to the field environment. Yet the test specifications are considered conservative, with the assumption that most of the adjustment for uncertainty is conservatism. For base mounted components, a modal model is presented that can be used to generate specifications with much lower uncertainty and with guaranteed quantifiable conservatism. In this method, the modal energies in the fixed base modes of the article due to the in-service loads are determined. Using the fixed base modes of the test article as a basis, the test specification is derived by determining what fixture motion is required to emulate the in-service environment. The specification method accounts for frequency shifts between the in-service and test configurations. Variability in nominal test articles can be included in the derivation of the test specifications. Real hardware under in-service environment loads and in a ground test fixture and loading configuration are considered.
Flight testing provides an opportunity to characterize a system under realistic, combined environments. Unfortunately, the prospect of characterizing flight environments is often accompanied by restrictive instrumentation budgets, thereby limiting the information collected during flight testing. Instrumentation selection is often a result of bargaining to characterize environments at key locations/sub-systems, but may be inadequate to characterize the overall environments or performance of a system. This work seeks to provide an improved method for flight environment characterization through a hybrid experimental-analytical method, modal response extraction, and model expansion. Topics of discussion will include hardware design, assessment of hardware under flight environments, instrumentation planning, and data acquisition challenges. Ground testing and model updating to provide accurate models for expansion will also be presented.
One can estimate unmeasured acceleration spectral density responses of a structure utilizing measured responses from a relatively small number of accelerometers and the active mode shapes provided from a finite element model. The objective in this paper is to demonstrate a similar concept, but purely based on information from a laboratory pre-test. Response predictions can only be calculated at degrees of freedom that have been instrumented in the experimental pre-test, but greater accuracy may be possible than with a finite element-based expansion. A multi-reference set of frequency response functions is gathered in the laboratory pre-test of the field hardware. Two response instrumentation sets are included in the pre-test. One set corresponds to the measurements that will be taken in the field environment. The second set is the field responses that are of great interest but will not be measured in the field environment due to logistical constraints. For example, the second set would provide definition of the component field environment. A set of basis vectors is extracted from the pre-test experimental data in each of multiple frequency bands. Then the field environment is applied to the hardware and the data gathered from the field accelerometers. The basis vectors are then used to expand the response from the field accelerations to the other locations of interest. The proof of concept is provided with an acoustic test environment on the Modal Analysis Test Vehicle. Predicted acceleration spectral density simulations at 14 degrees of freedom (known as “truth responses”) are compared against truth acceleration measurements collected for this work from the acoustic environment. Due to the segregated bandwidth analysis, the required number of field accelerometers to provide the simulation is much smaller than the number of modes in the entire frequency bandwidth.
Many test articles exhibit slight nonlinearities which result in natural frequencies shifting between data from different references. This shifting can confound mode fitting algorithms because a single mode can appear as multiple modes when the data from multiple references are combined in a single data set. For this reason, modal test engineers at Sandia National Laboratories often fit data from each reference separately. However, this creates complexity when selecting a final set of modes, because a given mode may be fit from a number of reference data sets. The color-coded complex mode indicator function was developed as a tool that could be used to reduce a complex data set into a manageable figure that displays the number of modes in a given frequency range and also the reference that best excites the mode. The tool is wrapped in a graphical user interface that allows the test engineer to easily iterate on the selected set of modes, visualize the MAC matrix, quickly resynthesize data to check fits, and export the modes to a report-ready table. This tool has proven valuable, and has been used on very complex modal tests with hundreds of response channels and a handful of reference locations.
Several recent studies (Mayes, R.L., Pacini, B.R., Roettgen, D.R.: A modal model to simulate typical structural dynamics nonlinearity. In: Proceedings of the 34th International Modal Analysis Conference. Orlando, FL, (2016); Pacini, B.R., Mayes, R.L., Owens, B.C., Schultz, R.: Nonlinear finite element model updating, part I: experimental techniques and nonlinear modal model parameter extraction. In: Proceedings of the 35th international modal analysis conference, Garden Grove, CA, (2017)) have investigated predicting nonlinear structural vibration responses using modified modal models. In such models, a nonlinear element is added in parallel to the traditional linear spring and damping elements. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. Previous studies have predominantly applied this method to idealistic structures. In this work, the nonlinear modal modeling technique is applied to a more realistic industrial aerospace structure which exhibits complex bilinear behavior. Linear natural frequencies, damping values, and mode shapes are first extracted from low level shaker testing. Subsequently, the structure is excited using high level tailored shaker inputs. The resulting response data are modally filtered and used to empirically derive the nonlinear elements which, together with their linear counterparts, comprise the nonlinear modal model. This model is then used in both modal and physical domain simulations. Comparisons to measured data are made and the performance of the nonlinear modal model to predict this complex bilinear behavior is discussed.