1、 Institute of Environmental Sciences and Technology IEST-RP-DTE022.1 Design, Test, and Evaluation Division Recommended Practice 022.1 Multi-shaker Test and Control Arlington Place One 2340 S. Arlington Heights Road, Suite 620 Arlington Heights, IL 60005-4510 Phone: (847) 981-0100 Fax: (847) 981-4130
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13、7) 981-4130 E-mail copyrightiest.org Web www.iest.org2 IEST 2014 All rights reserved Institute of Environmental Sciences and Technology IEST-RP-DTE022.1 This Recommended Practice was prepared by and is under the jurisdiction of Working Group 22 of the IEST Design, Test, and Evaluation Division (WG-D
14、TE022). The following WG voting members contributed to the development of this edition of this Recommended Practice. Tony Keller, WG-DTE022 Chair, Spectral Dynamics Brad Allen, Moog CSA Robert L. (Andy) Anderson, National Technical Systems Russ Ayres, Spectral Dynamics David Banaszak, US Air Force R
15、esearch Laboratory Richard Cellary, NSWC IHEODTD Naval PHST Center William H. Connon III, US Army Aberdeen Test Center Michael T. Hale, Redstone Test Center Joel Hoksbergen, Team Corporation Samuel Kouretas, NSWC IHEODTD DET PICATINNY Randy Patrick, Army Yuma Test Center Stanley Poynor, Lockheed Mar
16、tin Missiles on measured field vibration data; or on a combination of those two specifications? The answer to this question will determine the complexity of the test, what kind of data will be required, and how much, if any, off-line processing of field data will be necessary. IEST-RP-DTE022.1 Insti
17、tute of Environmental Sciences and Technology IEST 2014 All rights reserved 9 As described in section 5.3, a multiple-shaker test setup may involve a complex UUT, some fixturing, bearings to permit the desired motion and protect the shakers, the exciters, power amplifiers, transducers, and cables. T
18、his combination is best defined in a matrix formulation, relating inputs and outputs as an SDM. If measured field vibration data will be used, it is critical to have good phase and coherence measurements in addition to measured PSD values (see Appendix B: Underwood, Ayres, and Keller, 2009). Conside
19、r, for example, a test of an aircraft missile that is secured under a wing by two attachment points. Field measurements may include magnitude, phase, and coherence values between two points measured near the missile attachment points. If the exciters are to be attached directly to the missile attach
20、ment points, most of the required information may be available. However, if the laboratory simulation is to take place with shakers attached to the aircraft fuselage or wheel carriages, information about the frequency response functions between fuselage excitation points and missile control points w
21、ill also be necessary. The available data must be sufficient to fill in the entire system matrix to achieve successful simulation using field data. 5.3 Theory Many multi-shaker vibration tests are performed on the basis of having one control accelerometer per shaker. This setup is termed “square con
22、trol” and assumes N control points for N shakers. Additional channels may also be available for response measurements and limit control of amplitudes without affecting phase parameters. Controlling multiple shakers simultaneously requires an understanding that the drive signal to any one shaker will
23、 have an effect on all control points, not just the point nearest the shaker being driven. Thus, the solution of a multi-shaker control problem is best defined in matrix terms, involving all drive and control signals simultaneously. Figure 1 shows a block concept of a typical four-shaker excitation
24、and control system. In a controlled test environment, the drive signals will come from the multi-shaker digital vibration control system (MSDVCS) and the control signals (shown in Figure 1 as response vectors) will be fed back to the MSDVCS. The relationship between these signals, described as a com
25、plete system matrix, is shown in Figure 2. Figure 1Block concept of four-actuator (shaker) test system. nullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnu
26、ll nullnullnullnullnullnullnullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnullnullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnullnullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnull
27、nullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullnullFigure 2Matrix formulation of system inputs and outputs. In Figure 2, the control signals, ci(f), and the drive signals, di(f), are related by the set of co
28、mplex frequency response functions, hij(f). Equation 1 puts this into a more compact notation. C(f) = H(f)D(f) (1) This says that the frequency response function multiplied by the drive gives the control value. However, at the start of a test, having measured the systems frequency response function
29、matrix, the control system must calculate the set of “first drive” signals. This requires the calculation of the inverse of the H(f) matrix as seen in equation 2. Z(f) = H(f)-1 (2) 10 IEST 2014 All rights reserved Institute of Environmental Sciences and Technology IEST-RP-DTE022.1 If some of the ant
30、i-resonances measured in the H(f) matrix have very low values, the inversion of this matrix may produce uncontrollable singularities while using the impedance (or system sensitivity) matrix, Z(f), to calculate the system drives. D0( f ) = Z( f )R( f ) (3) where R( f ) is the reference vector. (Note
31、that a different formulation is required for MIMO random.) In such cases, special care should be taken when inverting the frequency response function matrix and calculating system drive signals as shown in equations 2 and 3. One characteristic of a MIMO control system must be that it is stable under
32、 all test conditions. For the case of MIMO random, equations 1 and 3 take the form shown in equations 1a and 3a. nullGccf HfGddfHf*(1a) where Gcc(f) and Gdd(f) are, respectively, the control-response and drive SDM, H(f) is the frequency response matrix (FRM) of the system under test, and H(f)* is it
33、s conjugate-transpose. Gddf Zf Grrf Zf *(3a) where Gdd(f) and Grr(f) are, respectively, the initial drive and reference SDM, Z(f) is the inverse FRM of the system under test, and Z(f)* is its conjugate-transpose. 5.4 Testing in multiple axes Six unique displacement vectors define the location and or
34、ientation in space of an object. “Unique” means there are no redundant displacement vectors. Each displacement vector can be viewed kinematically as a link arm with a swivel joint on each end, a single degree of constraint. An example of a redundant load path would be the placement of more than two
35、parallel links on the same line. All rigid-body motions are defined by 6 DOF. Cartesian coordinates are expressed in terms of three translations and three rotations about the X,Y, and Z axes. In fact the body motions need not be orthogonally oriented and may be described by a unique set of six vecto
36、r coordinates, Si (Figure 3). Figure 3Unique set of six vectors describing rigid-body motion. Consider the replacement of a rigid link with a hydraulic actuator, a “hydrashaker.” The actuator can replace one or all of the links. For each actuator installed, the degrees of motion are increased from 0
37、 to 6 or some number in between. Replacing just one link with a hydrashaker enables motion in 1 DOF. The motion, a combination of translations and rotations, is determined by the geometry of the five fixed links and the motion link. IEST-RP-DTE022.1 Institute of Environmental Sciences and Technology
38、 IEST 2014 All rights reserved 11 Typical hydraulic shakers function as position devices at low frequency, transitioning to velocity functions at higher frequencies. These hydrashakers are driven with flow control valves; i.e., voltage input translates to velocity (or position). One style of system
39、providing full control over all 6 DOF uses an arrangement of six actuators in a “3-2-1” geome-try. The 3-2-1 nomenclature refers to the arrangement of actuators. Figure 4 illustrates this geometry: 3 vertical or Z, 2 in X, and 1 in Y. The three actuators in the vertical orientation produce and contr
40、ol vertical translation, pitch, and roll. The two actuators in the X axis produce one horizontal translation and yaw. The actuator in the Y axis produces and controls the second horizontal translation. This arrangement eliminates “over constraint” (see section 5.5). Figure 4A 6-DOF system with 3-2-1
41、 geometry. Figure 5 shows a cutaway view of a 6-DOF vibration table with 2-2-2 orthogonal geometry, or two actuators each in X, Y, and Z orientations. Each pair of actuators produces and controls one translation and one rotation by operating either in or out of phase. This is another example of a sy
42、stem that eliminates the possibility of over constraint. Note that for this configuration, the natural center of rotation is about the center of the applied forces by the respective actuator pairs. Figure 5Cutaway view of a 6-DOF system. Hydraulic shakers operating as “forcing functions” By using pr
43、essure control valves rather than flow control valves, a hydraulic shaker is converted from a positioning function to a forcing function. This modification effectively changes a hydraulic shaker from a stiff spring to a much softer spring. Changing the stiffness, or “spring rate,” of a hydraulic sha
44、ker allows multiple forcing functions to be applied to a rigid body in a single DOF with a reduced chance of producing undesired loading in the rigid body. For example, if the dynamic response of the test object produces local opposing forces higher than those being applied by the shaker, a hydrauli
45、c actuator fitted with pressure control valves will deflect. In the same situation, if the hydraulic actuator is fitted with flow control valves, the extremely stiff spring of the oil column within the shaker will not deflect, imposing potentially high momentary loads and lock-in static loads into t
46、he test object. Dynamic response of the test object is 12 IEST 2014 All rights reserved Institute of Environmental Sciences and Technology IEST-RP-DTE022.1 not the only possible means of producing localized, momentary loading. This may also occur with unintended out-of-phase actuator commands. Good
47、engineering practices should take this potentiality into account in system design. For multiple forcing functions on a rigid body in space, the kinematic rules no longer apply. Any number of forces can be applied to a rigid body. The only requirement is the body must be tethered off to keep it in so
48、me rough position and orientation. 5.5 Controlling rotations and bending In a single DOF system, a single line of motion is active with the remaining 5 DOF constrained by some type of bearing, typically linear mechanical or hydrostatic bearings in the case of a slip table. Adding DOF requires replac
49、ement of some or all of the linear bearings with active actuators. To produce a single, pure line of motion, actuator(s) are used to actively control off axis, rotational response, or both. The effectiveness of this control is dependent on the quality of the actuator-to-table connection and the test controller-to-actuator dynamic response. “Over-actuated” (also “over-constrained” or “over-excited”) is a t
