527.2-22 tailoring guidance

527.2-2 SIGNAL TRANSFORMATION

For a situation in which the reference signals for a 6-DOF test are provided in the traditional translational (X, Y, and Z) and rotational (Pitch (rotation about Y), Roll (rotation about X), and Yaw (rotation about Z)) engineering units (EU), one may wish to transform between appropriately placed linear transducers and traditional 6-DOF EUs. Since there are many combinations of exciters that may be employed for a given MDOF test, the transformation matrix between linear accelerometers and traditional 6-DOF EUs, the transformation matrix will be test specific. In addition, one may wish to apply non-uniform weighting across the exciters for a given DOF, or even include non-rotational or non-translational degrees-of-freedom such as tensional response into consideration in developing the control law for a given test. Kinematics based output-signal transformations are also very useful in addressing over-actuated systems to ensure properly compensated signals are sent to exciters with common mechanical degrees-of-freedom. A detailed discussion of signal transformation is given in paragraph 6.1, references g and n.

527.2-2 ANALYSIS CONSIDERATIONS FOR A PROCEDURE I MET

527.2-2 ANALYSIS CONSIDERATIONS FOR A PROCEDURE II MET

527.2-2 FACILITIES AND INSTRUMENTATION

527.2-2.1 Reference Data Considerations

The first step in performing a MET in the laboratory begins with acquiring sufficient reference data. In addition to the standard concerns related to the dynamic range and frequency response characteristics of the transducers and recording equipment used in the field data acquisition phase, the quantity and spatial locations of the transducers become critical test parameters. Understanding the underlying dynamics of MDOF systems, and the physical constraints such systems place on the spatial locations of reference transducers in order to perform true MDOF laboratory motion replication, is not trivial. Similarly, it is essential that the test operators are able to understand the dynamics of an arbitrary data set that may be provided by an outside source for use as reference data in a laboratory test.

527.2-2.1 Addressing Translational Motion

Since linear transducers are generally the measurement transducers of choice, translational measurements will be readily available. One needs only to have a well-defined coordinate system established.

527.2-2.1 MESA and MEMA Specification Parameters

The classical metrics addressed in Method 514.8 for control of SESA vibration tests are insufficient for the analysis of a MET. In the conduct of either a MESA or MEMA Procedure II vibration test, both auto-spectral density (ASD) and cross-spectral density (CSD) terms are required test parameters. As one would expect, the configuration of a MET will influence the reference spectral requirements. For example, consider defining a random test for the two MET systems illustrated in Figures 527.2-2 and 527.2-3. Table 527.2D-I illustrates a spectral density matrix (SDM) construct, the 2-DOF MET shown in Figure 527.2-2 and similarly, Table 527.2D-II illustrates the format of spectral information required in specifying the 3-DOF MET of the system shown in Figure 527.2-3. Observe that the format of a Spectral Density Matrix (SDM) consists of auto-spectral density (power spectral density) terms on the diagonal and cross-spectral density terms on the off-diagonal. Also, note the Hermitian structure for the case in which the SDM is square.

Ideally, field measurements will be available to define both auto and cross spectral densities. One note regarding the development of vibration criteria for a Procedure II MET is that, unlike the SESA case, it is difficult to develop a

MIL-STD-810H

METHOD

527.2-2.1 Facilities

The development of a LVTS will require access to the test item of interest (or a dynamically equivalent surrogate), access to the carrier vehicle, appropriately placed transducers, signal conditioning and data acquisition hardware, and a controlled environment for collecting input data (e.g., a road course for wheeled and/or tracked vehicles, waterway for watercraft, airspace for aircraft, rotorcraft, and/or spacecraft).

2.1.1 Effects of the MET Environment

In general, all in-service measured environments require multiple axis response measurements for complete description. Generally, a MET will distribute excitation energy to the test item and minimize the effects of in-service boundary conditions. The following is a partial list of effects to materiel that may be better replicated in the laboratory under a MET than a SET.

• a. Fatigue, cracking, and rupture sensitive to multi-axis excitation.
• b. Deformation of materiel structure, e.g., protruding parts.
• c. Loosening of seals and connections.
• d. Displacement of components.
• e. Chafing of surfaces with single-axis design.
• f. Contact, short-circuiting, or degradation of electrical components.
• g. Misalignment of materiel components (e.g., optical).

527.2-2.1.1 Cross Spectral Density Structure

Most of the commercially available MET control systems provide a method of entering the CSD terms in the form of relative phase and coherence. For example, if one wished to conduct a vertical only test using the two-exciter configuration illustrated in Figure 527.2-2, the ideal reference would be a phase setting of 0 degrees with a coherence of 1.0. Similarly, if the motion desired was pure pitch, the ideal reference would be a phase setting of 180 degrees with a coherence of 1.0. Unfortunately, selecting a coherence setting of 1.0 results in a singular SDM. Furthermore, it is very rare to find perfectly coherent measurements in practice due to noise and system non-linearities. Experience has shown that when specifying highly coherent measurements in a MET, a coherence selection that is slightly less than 1.0, ( γ ij = .95 to .98), greatly reduces the numerical concerns associated with a singular SDM, and the desired frequency and temporal characteristics are still achieved to a high degree.

Direct knowledge of the CSD characteristics of the field environment is desired as the phasing characteristics between mechanical DOF’s may have a significant effect on the response of the UUT. Modal characteristics of the UUT may highly influence response dynamics as a function of the relative phasing of the reference (drive) signals.

2.1.2 Sequence Among Other Methods

• a. General. See Part One of this Standard, paragraph 5.5.
• b. Unique to this Method. Generally, a MET-specified environment may occur at any time during the life cycle of the materiel, and may be interspersed among specially designed multiple axis SET environments, e.g., shock. Perform tests representing critical end-of-mission environments last. For most tests, this can be varied if necessary to accommodate test facility schedules, or for other practical reasons.

527.2-2.2 Reference Point Kinematics

A unified discussion on the use of linear accelerometers for motion reconstruction is addressed in paragraph 6.1, reference f. Specifically, paragraph 6.1, reference f, investigated the number of uni-axial transducers required, and the placement of these transducers in the field data acquisition phase for 6-DOF motion reconstruction. The principal analysis is performed in the time domain using kinematical relationships from classical mechanics.

MIL-STD-810H METHOD

527.2-2.2 Addressing Angular Motion

Auto-Spectral Density (ASD) analysis provides a general spectral view of the reference data; however, it contains no phase information. It is the differences in phase and amplitude between collinear accelerometers that indicate the presence of angular motion. One method of investigating the presence of angular acceleration (either pure or combined with translational acceleration) from a suite of linear accelerometers is to perform complex transfer functions between collinear pairs of linear accelerometers. Subsequently, performing the same transfer function analysis between the same locations in the laboratory provides another metric for measuring the fidelity of the laboratory test. Analyzing the transfer functions corresponding to the field and laboratory measurements often indicates where the mechanical impedance between field and laboratory begin to diverge. Referring back to the ASD measurements, one is able to gain some perspective as to the amount of energy present as a function of frequency, providing perspective into the deviations expected as a result of divergence in mechanical impedance. Similarities between the reference and laboratory transfer functions indicate field and laboratory rotations are also similar.

In an effort to address the actual level and fidelity associated with rotational degrees-of-freedom from a test controlled entirely by feedback obtained from linear accelerometers, computations of angular motion can be developed. Perform computations from both the reference data and corresponding laboratory control accelerometer pairs, and compare results. The computation takes the form of a small angle approximation; however, since the reference plane on which the accelerometer is mounted is actually rotating, there is no computation error as a function of angle as in the case of a fixed plane small angle approximation. To illustrate, consider two linear accelerometers positioned to measure z- axis motion mounted a distance / inches from their relative centerline along the y-axis. An estimate of Roll (Rx) axis rad (a1-a2)*386 angular motion in units of at the centerline between the two transducers can be computed as ܐܨ 21

Ideally this technique will provide a good metric for analyzing the angular motion for the “rigid body” case. The frequency, at which the field data and laboratory data begin to diverge is an indication of where the mechanical impedance between tactical field mechanical interface and laboratory fixturing begins to differ. The magnitude of the divergence provides some idea of the quality of the impedance match, and provides a key data point in understanding if the test fidelity is sufficient in addressing a test-specific criteria. In general, the instantaneous center of rotation (ICR) may not coincide exactly with the ICR of the test platform, and that the angular motion estimates may, in fact, be vectors that are not perfectly orthogonal with respect to the true axis of rotation. However, as long as the laboratory reference linear accelerometers used to make the angular acceleration estimates correlate to the exact location and phase of the reference measurements, a localized angular motion comparison is still of interest in addressing replication fidelity.

MIL-STD-810H

METHOD

527.2-2.2 Control Hierarchy

In earlier MET control algorithms as discussed in paragraph 6.1, reference h, in the hierarchy of control for a MET, correction of the ASD terms were generally given priority. CSD terms were then corrected to the degree possible without corrupting the ASD terms. In modern MET algorithms, the drive signals are updated such that the SDM matrix has minimal mean-squared error. The degree of accuracy in replicating the CSD terms in a MEMA test are often test-specific, and associated tolerances should be tailored as appropriate. For example, consider a 6-DOF MET designed to address functional performance of a component such as a gimble-based stabilization platform for which one may have interest in the rotational degrees of freedom to a frequency that is much less than the full test bandwidth. For such cases, maintaining accurate CSD characteristics between control points will be predefined by the test performance objectives and the CSD characteristics at frequencies higher than the bandwidth of the required functional test are not considered critical.

527.2-2.2 Instrumentation

• a. LVTSs are generally defined in terms of acceleration units. The transducer of choice for making acceleration measurements is an accelerometer. This Annex will address LVTS development in terms of acceleration.
• b. It is strongly recommended that the same model of accelerometer and signal conditioning is employed at all instrumented locations to preserve phase characteristics during both the field acquisition and laboratory test phase of any MDOF test. Refer to the guidelines in Military Standard (MIL-STD)-810H1* and Institute of Environmental Sciences and Technology (IEST) Recommended Practice IEST-RP-DTE012.22 for recommended accuracy of the transducers and associated signal conditioning.

2.2.1 Procedure Selection Considerations

Based on the test data requirements, determine if this Method is applicable. In particular, determine if there is carefully measured and properly processed materiel field measurement configuration information available in the form of band- limited time histories or auto- and cross-spectral density estimates as appropriate to be consistent with the laboratory MET configuration and vibration control system vendor software specification requirements. Basic consideration is given to an environment in a single-axis requiring multiple exciters, or an environment in multiple axes requiring multiple exciters. Generally, the MEMA procedure exceeds the complexity of the MESA procedure, so attempts should be made to minimize the test procedure complexity to the degree possible.

Materiel in-service use, along with significant environment energy distribution effects, should assist in procedure selection. One major consideration, in selection of Procedure I, is the ability to address scenarios in which the reference signal statistics are not stationary and Gaussian. Procedure II should be considered in the event that the reference data are stationary, and the ensemble of signals representing the service life may be reasonably represented by a Gaussian probability density function, and/or when time compression techniques are to be employed. Refer to the guidance provided in paragraph 4.2.2.1 of Method 514.8 regarding manipulation of kurtosis to address non-Gaussian behavior.

527.2-2.2.1 Measured Data Available

When in-service measurement data have been obtained, it is assumed that the data are processed in accordance with good data analysis procedures (see paragraph 6.1, references d and e). In particular, an adequate number of statistical degrees-of-freedom has been obtained to provide information with acceptable statistical error. Generally, careful attention must be given to the field measurement configuration. In particular, the location of the measurement points and qualification of the points as to whether they are structural points on the materiel capable of describing overall vibration characteristics of the materiel, or are response points on the materiel local to specific component response definition of the materiel. Consideration must be given to not only statistical error in auto-spectral density estimates, but also in cross-spectral density estimates (including transfer, coherence function estimates). For cross-spectral density transfer function estimates, it is important to correctly diagnose the coherence or lack of coherence among measurements. Ideally, the field and laboratory phase and coherence would match, implying an accurate match of boundary conditions. However, in practice this is rarely the case. Inspection of the field measured CSD terms is recommended to select key frequency bands in which one desires optimal coherence and phase matching as discussed in reference 19 of Annex E.

Low coherence implies that the vibration energy between measurements is uncorrelated, so that multiple exciters may be employed without cross-spectral information. Low coherence may also be viewed as a relaxation of strict cross- spectral information and perhaps use of the cross-spectral information that occurs naturally in the laboratory test configuration.

2.2.2 Measured Data Not Available

When measurement data are not available and only specification level auto-spectral density information is available, it almost always needs to be assumed that excitation environments are independent of one another (coherence values are near zero). In addition, the effects of in-service and laboratory boundary condition impedance cannot be assessed. Normal mode information from the materiel is important in allowing the general decoupling of vibration modes of response. Careful attention must be given to the specification of the “control” and “monitoring” measurement points.

MIL-STD-810H

METHOD

2.2.3 Use of 1-DOF References

Employing highly conservative vibration specifications originally designed for a 1-DOF laboratory test as uncorrelated reference ASD’s for a MDOF test should be addressed with caution. Vibration specifications developed for 1-DOF scenarios are often purposely conservative, in part to account for the fact that no significant coupling between mechanical DOF’s is expected in the laboratory. However, such coupling between mechanical DOF’s is certainly possible in the field or in a MDOF laboratory setting. Therefore, employing highly conservative spectra as references in a MDOF test could yield uncharacteristically high response in the event the unit under test has closely coupled structural modes between mechanical DOF’s. If the conservatism characteristics of the 1-DOF references are clearly defined, it may be possible to develop an alternative set of uncorrelated references with reduced conservatism to address MDOF scenarios.

2.3.1 Laboratory Test Data Input

Acceptable engineering practice as described in paragraph 6.1, reference e, should be used to provide in-service materiel response measurement data that may be used directly in specifying one of the procedures for a MET, or may be inferred as representative of an environment that may be indirectly specified for one of the procedures for a MET. In either direct or indirect use of measurements, particular measurements are made relatively independent of materiel structure or in “zones” of the materiel that are insensitive to local conditions. It is also assumed that in-service, materiel response measurements correspond with materiel response measurements to be made in the laboratory under a MET. It is essential that the mass properties of the materiel be determined, including center-of-gravity and the mass and product moments of inertia. Whenever practical, obtain a modal survey of both the in-service and the laboratory materiel configurations. This will allow assessment of the overall dynamic characteristics of the two configurations, in addition to identifying any non-linearities as a result of materiel joints, etc. Proper interpretation of the normal mode analysis will assist in determining an optimum laboratory test configuration based on in-service measurements. Even a simple mass/stiffness analytical model will greatly assist in establishing an optimum laboratory test

MIL-STD-810H

METHOD 527.2

configuration. Give careful attention to the form and nature of the input information into the MET vendor supplied software.

2.3.1.1 Cross-Spectral Density Considerations

In the conduct of a MET, the definition of the cross-spectral density (CSD) terms play a major role in the degree to which the characteristics of the laboratory motion correlates to the field measurements in terms of both joint spectral and temporal characteristics. In the case of Procedure I (time domain reference) the CSD information is preserved within the individual time histories to be used as reference criteria. In the case of Procedure II (frequency domain reference) the CSD terms need to be specified based on CSD estimates computed from field data. Annex D addresses the control of CSD terms in more detail.

2.3.1.2 General

Identify the test conditions, particularly with respect to temperature conditions. Exercise extreme care in consideration of the details in the tailoring process. Base these selections on the requirements documents, the Life Cycle Environmental Profile, and information provided with this procedure.

2.3.2 Laboratory Test Output

In addition to the considerations in paragraph 2.3.1, the test item may be instrumented at locations other than the points of MET “control,” and these points are generally termed per discussion in paragraph 2.3.1 “monitoring” points. Such measurement points may be useful for other purposes such as analytical modeling of materiel and materiel components. Such measurement information and its use will not be discussed further here.