Vibration and Shock Handbook 15

Vibration and Shock Handbook 15 Every so often, a reference book appears that stands apart from all others, destined to become the definitive work in its field. The Vibration and Shock Handbook is just such a reference. From its ambitious scope to its impressive list of contributors, this handbook delivers all of the techniques, tools, instrumentation, and data needed to model, analyze, monitor, modify, and control vibration, shock, noise, and acoustics. Providing convenient, thorough, up-to-date, and authoritative coverage, the editor summarizes important and complex concepts and results into “snapshot” windows to make quick access to this critical information even easier. The Handbook’s nine sections encompass: fundamentals and analytical techniques; computer techniques, tools, and signal analysis; shock and vibration methodologies; instrumentation and testing; vibration suppression, damping, and control; monitoring and diagnosis; seismic vibration and related regulatory issues; system design, application, and control implementation; and acoustics and noise suppression. The book also features an extensive glossary and convenient cross-referencing, plus references at the end of each chapter. Brimming with illustrations, equations, examples, and case studies, the Vibration and Shock Handbook is the most extensive, practical, and comprehensive reference in the field. It is a must-have for anyone, beginner or expert, who is serious about investigating and controlling vibration and acoustics.

Instrumentation and Testing IV IV-1 © 2005 by Taylor & Francis Group, LLC 15 Vibration Instrumentation 15.1 Introduction 15-1 15.2 Vibration Exciters 15-3 Shaker Selection † Dynamics of Electromagnetic Shakers 15.3 Control System 15-15 Components of a Shaker Controller Equipment † Signal-Generating 15.4 Performance Specification 15-21 Parameters for Performance Specification † Linearity Instrument Ratings † Accuracy and Precision † 15.5 Motion Sensors and Transducers 15-27 Potentiometer † Variable-Inductance Transducers † Mutual-Induction Proximity Sensor † Selfinduction Transducers † Permanent-Magnet Transducers † Alternating Current Permanent-Magnet Tachometer † Alternating Current Induction Tachometer † Eddy Current Transducers † Variable-Capacitance Transducers † Piezoelectric Transducers 15.6 Torque, Force, and Other Sensors 15-50 Strain Gage Sensors Clarence W de Silva The University of British Columbia † Miscellaneous Sensors Appendix 15A Virtual Instrumentation for Data Acquisition, Analysis, and Presentation 15-73 Summary Devices useful in instrumenting a mechanical vibrating system are presented in this chapter Shakers, which generate vibration excitations, are discussed and compared A variety of sensors, including motion sensors, proximity sensors, force/torque sensors, and other miscellaneous sensors, are considered Performance specification in the time domain and the frequency domain is addressed Rating parameters of instruments are given 15.1 Introduction Measurement and associated experimental techniques play a significant role in the practice of vibration Academic exposure to vibration instrumentation usually arises in laboratories, in the context of learning, training, and research In vibration practice, perhaps the most important task of instrumentation is the measurement or sensing of vibration Vibration sensing is useful in the following applications: Design and development of a product Testing (screening) of a finished product for quality assurance Qualification of a good-quality product to determine its suitability for a specific application 15-1 © 2005 by Taylor & Francis Group, LLC 15-2 Vibration and Shock Handbook Mechanical aging of a product prior to carrying out a test program Exploratory testing of a product to determine its dynamic characteristics such as resonances, mode shapes, and even a complete dynamic model Vibration monitoring for performance evaluation Control and suppression of vibration Figure 15.1 indicates a procedure typical of experimental vibration, highlighting the essential instrumentation Vibrations are generated in a device, the test object, in response to some excitation In some experimental procedures, primarily in vibration testing (see Figure 15.1), the excitation signal has to be generated in a signal generator in accordance with some requirement (specification), and applied to the object through an exciter after amplification and conditioning In some other situations, primarily in performance monitoring and vibration control, the excitations are generated as an integral part of the operating environment of the vibrating object and may originate either within the object (e.g., engine excitations in an automobile) or in the environment with which the object interacts during operation (e.g., road disturbances on an automobile) Sensors are needed to measure vibrations in the test object In particular, a control sensor is used to check whether the specified excitation is applied to the object, and one or more response sensors may be used to measure the resulting vibrations at key locations of the object The sensor signals have to be properly conditioned, for example by filtering and amplification, and modified, for example through modulation, demodulation, and analog-to-digital conversion, prior to recording, analyzing, and display The purpose of the controller is to guarantee that the excitation is correctly applied to the test object If the signal from the control sensor deviates from the required excitation, the controller modifies the signal to the exciter so as to reduce this deviation Furthermore, the controller will stabilize or limit (compress) the vibrations in the object It follows that instruments in experimental vibration may be generally classified into the following categories: Signal-generating devices Vibration exciters Sensors and transducers Signal conditioning/modifying devices Signal analysis devices Control devices Vibration recording and display devices Response Sensor Mounting Fixtures Power Amplifier Filter/ Amplifier Test Object Exciter Control Sensor Filter/ Amplifier Digital Analog/ Signal Digital Recorder, Interface Analyzer, Display Swivel Base Signal Generator and Exciter Controller Reference (Required) Signal (Specification) FIGURE 15.1 © 2005 by Taylor & Francis Group, LLC Typical instrumentation in experimental vibration Vibration Instrumentation 15-3 Note that one instrument may perform the tasks of more than one category listed here Also, more than one instrument may be needed to carry out tasks in a single category In the following sections we will provide some examples of the types of vibration instrumentation, giving characteristics, operating principles, and important practical considerations Also, we will describe several experiments which can be found in a typical vibration laboratory An experimental vibration system generally consists of four main subsystems: Test object Excitation system Control system Signal acquisition and modification system Signal Modification System Test Object Control System Vibration Exciter (Shaker) System FIGURE 15.2 Interactions between major subsystems of an experimental vibration system These are schematically shown in Figure 15.2 Note that various components shown in Figure 15.1 may be incorporated into one of these subsystems In particular, component matching hardware and object mounting fixtures may be considered interfacing devices that are introduced through the interaction between the main subsystems, as shown in Figure 15.2 Some important issues of vibration testing and instrumentation are summarized in Box 15.1 15.2 Vibration Exciters Vibration experimentation may require an external exciter to generate the necessary vibration This is the case in controlled experiments such as product testing where a specified level of vibration is applied to the test object and the resulting response is monitored A variety of vibration exciters are available, with different capabilities and principles of operation Three basic types of vibration exciters (shakers) are widely used: hydraulic shakers, inertial shakers, and electromagnetic shakers The operation-capability ranges of typical exciters in these three categories are summarized in Table 15.1 Stroke, or maximum displacement, is the largest displacement the exciter is capable of imparting onto a test object whose weight is assumed to be within its design load limit Maximum velocity and acceleration are similarly defined Maximum force is the largest force that could be applied by the shaker to a test object of acceptable weight (one within the design load) The values given in Table 15.1 should be interpreted with caution Maximum displacement is achieved only at very low frequencies The achievement of maximum velocity corresponds to intermediate frequencies in the operating frequency range of the shaker Maximum acceleration and force ratings are usually achieved at high frequencies It is not feasible, for example, to operate a vibration exciter at its maximum displacement and its maximum acceleration simultaneously Consider a loaded exciter that is executing harmonic motion Its displacement is given by x ẳ s sin vt 15:1ị in which s is the displacement amplitude (or stroke) Corresponding velocity and acceleration are © 2005 by Taylor & Francis Group, LLC x_ ẳ sv cos vt 15:2ị x ẳ 2sv2 sin vt ð15:3Þ 15-4 Vibration and Shock Handbook Box 15.1 VIBRATION INSTRUMENTATION Vibration Testing Applications for Products: * * * Design and Development Production Screening and Quality Assessment Utilization and Qualification for Special Applications Testing Instrumentation: * * * * * Exciter (excites the test object) Controller (controls the exciter for accurate excitation) Sensors and Transducers (measure excitations and responses and provide excitation error signals to controller) Signal Conditioning (converts signals to appropriate form) Recording and Display (perform processing, storage, and documentation) Exciters: * * Shakers Electrodynamic (high bandwidth, moderate power, complex and multifrequency excitations) Hydraulic (moderate to high bandwidth, high power, complex and multifrequency excitations) Inertial (low bandwidth, low power, single-frequency harmonic excitations) Transient/Initial Condition Hammers (impulsive, bump tests) Cable Release (step excitations) Drop (impulsive) Signal Conditioning: * * * * Filters Amplifiers Amplifiers Modulators/Demodulators ADC/DAC Sensors: * * Motion (displacement, velocity, acceleration) Force (strain, torque) If the velocity amplitude is denoted by v and the acceleration amplitude by a, it follows from Equation 15.2 and Equation 15.3 that 15:4ị v ẳ vs and a ẳ vv â 2005 by Taylor & Francis Group, LLC ð15:5Þ Vibration Instrumentation TABLE 15.1 Typical Operation-Capability Ranges for Various Shaker Types Typical Operational Capabilities Shaker Type Frequency Maximum Displacement (Stroke) Maximum Velocity Maximum Acceleration Intermediate (50 in/sec; 125 cm/sec) Intermediate (50 in/sec; 125 cm/sec) Intermediate (50 in/sec; 125 cm/sec) Intermediate (20 g) High (100,000 lbf; 450,000 N) Average flexibility (simple to complex and random) Intermediate (20 g) Intermediate (1,000 lbf; 4,500 N) Sinusoidal only High (100 g) Low to intermediate (450 lbf; 2,000 N) High flexibility and accuracy (simple to complex and random) Hydraulic (electrohydraulic) Low (0.1 –500 Hz) High (20 in; 50 cm) Inertial (counter-rotating mass) Intermediate (2– 50 Hz) Low (1 in; 2.5 cm) Electromagnetic (electrodynamic) High (2– 10,000 Hz) Low (1 in; 2.5 cm) Excitation Waveform 15-5 © 2005 by Taylor & Francis Group, LLC Maximum Force 15-6 Vibration and Shock Handbook Peak Velocity (cm/s) Peak Velocity (cm/s) An idealized performance curve of a shaker Max has a constant displacement–amplitude region, a Velocity Ac M constant velocity –amplitude region, and a conit ce ax im 100 ler stant acceleration – amplitude region for low, L e ati k on intermediate, and high frequencies, respectively, rt o S in the operating frequency range Such an ideal Full No 10 performance curve is shown in Figure 15.3(a) on a Load Load frequency –velocity plane Logarithmic axes are used In practice, typical shaker performance curves would be fairly smooth yet nonlinear, 0.1 10 100 curves, similar to those shown in Figure 15.3(b) (a) Frequency (Hz) As the mass increases, the performance curve compresses Note that the acceleration limit of a shaker depends on the mass of the test object (load) Full load corresponds to the heaviest object that could be tested The “no load” condition 100 corresponds to a shaker without a test object To standardize the performance curves, they are usually defined at the rated load of the shaker A No 10 Full Load performance curve in the frequency – velocity Load plane may be converted to a curve in the frequency –acceleration plane simply by increasing 0.1 10 100 the slope of the curve by a unit magnitude (i.e., (b) Frequency (Hz) 20 db/decade) Several general observations can be made from Equation 15.4 and Equation 15.5 In the constant- FIGURE 15.3 Performance curve of a vibration exciter peak displacement region of the performance in the frequency– velocity plane (log): (a) ideal; (b) curve, the peak velocity increases proportionally typical with the excitation frequency, and the peak acceleration increases with the square of the excitation frequency In the constant-peak velocity region, the peak displacement varies inversely with the excitation frequency, and the peak acceleration increases proportionately In the constant-peak acceleration region, the peak displacement varies inversely with the square of the excitation frequency, and the peak velocity varies inversely with the excitation frequency This further explains why rated stroke, maximum velocity, and maximum acceleration values are not simultaneously realized 15.2.1 Shaker Selection Vibration testing is accomplished by applying a specified excitation to the test package, using a shaker apparatus, and monitoring the response of the test object Test excitation may be represented by its response spectrum The test requires that the response spectrum of the actual excitation, known as the test response spectrum (TRS), envelops the response spectrum specified for the particular test, known as the required response spectrum (RRS) A major step in the planning of any vibration testing program is the selection of a proper shaker (exciter) system for a given test package The three specifications that are of primary importance in selecting a shaker are the force rating, the power rating, and the stroke (maximum displacement) rating Force and power ratings are particularly useful in moderate to high frequency excitations and the stroke rating is the determining factor for low frequency excitations In this section, a procedure is given to determine conservative estimates for these parameters in a specified test for a given test package Frequency domain considerations are used here © 2005 by Taylor & Francis Group, LLC Vibration Instrumentation 15.2.1.1 15-7 Force Rating In the frequency domain, the (complex) force at the exciter (shaker) head is given by F ẳ mHvịas vị 15:6ị in which v is the excitation frequency variable, m is the total mass of the test package including mounting fixture and attachments, as ðvÞ is the Fourier spectrum of the support-location (exciter head) acceleration, and H(v) is frequency response function that takes into account the flexibility and damping effects (dynamics) of the test package apart from its inertia In the simplified case where the test package can be represented by a simple oscillator of natural frequency and damping ratio by zt ; this function becomes Hvị ẳ {1 ỵ 2jzt v=vn }={1 v=vn ị2 ỵ 2jzt v=vn } 15:7ị p in which j ¼ 21: This approximation is adequate for most practical purposes The static weight of the test object is not included in Equation 15.6 Most heavy-duty shakers, which are typically hydraulic, have static load support systems such as pneumatic cushion arrangements that can exactly balance the dead load The exciter provides only the dynamic force In cases where shaker directly supports the gravity load, in the vertical test configuration Equation 15.6 should be modified by adding a term to represent this weight A common practice in vibration test applications is to specify the excitation signal by its response spectrum This is simply the peak response of a simple oscillator expressed as a function of its natural frequency when its support location is excited by the specified signal Clearly, the damping of the simple oscillator is an added parameter in a response spectrum specification Typical damping ratios ðzr Þ used in response spectra specifications are less than 0.1 (or 10%) It follows that an approximate relationship between the Fourier spectrum of the support acceleration and its response spectrum is as ẳ 2jzr ar vị 15:8ị The magnitude lar vịl is the response spectrum Equation 15.8 substituted into Equation 15.6 gives F ẳ mHvị2jzr ar vị 15:9ị In view of Equation 15.7, for test packages having low damping the peak value of H(v) is approximately 1=ð2jzt Þ; this should be used in computing the force rating if the test package has a resonance within the frequency range of testing On the other hand, if the test package is assumed to be rigid, then HðvÞ ø 1: A conservative estimate for the force rating is Fmax ẳ mzr =zt ịlar vịlmax ð15:10Þ It should be noted that lar ðvÞlmax is the peak value of the specified (required) response spectrum (RRS) for acceleration 15.2.1.2 Power Rating The exciter head does not develop its maximum force when driven at maximum velocity Output power is determined by using p ẳ ReẵFvs vị 15:11ị in which vs ðvÞ is the Fourier spectrum of the exciter velocity, and Re [ ] denotes the real part of a complex function Note that as ¼ jvvs : Substituting Equation 15.6 and Equation 15.8 into Equation 15.11 gives p ẳ 4mz2r =vịReẵjHvịa2r vị 15:12ị It follows that a conservative estimate for the power rating is pmax ¼ 2mðz2r =zt ịẵlar vịl2 =v â 2005 by Taylor & Francis Group, LLC max ð15:13Þ 15-8 Vibration and Shock Handbook Representative segments of typical acceleration RRS curves have slope n, as given by a ¼ k1 It should be clear from Equation 15.13 that the maximum output power is given by pmax ẳ k2 v2n21 15:14ị 15:15ị This is an increasing function for n 1=2 and a decreasing function for n , 1=2: It follows that the power rating corresponds to the highest point of contact between the acceleration RRS curve and a line of slope equal to 1/2 A similar relationship may be derived if velocity RRS curves (having slopes n 1) are used 15.2.1.3 Stroke Rating From Equation 15.8, it should be clear that the Fourier spectrum, xs, of the exciter displacement time history can be expressed as xs ẳ 2zr ar vị=jv2 15:16ị An estimate for stroke rating is xmax ẳ 2zr ẵlar vịl=v2 15:17ị max This is of the form xmax ẳ kvn22 15:18ị It follows that the stroke rating corresponds to the highest point of contact between the acceleration RRS curve and a line of slope equal to two me ace nt sta n Co F,P nst ant Di spl 10 y cit lo Ve Co Acceleration (g) A test package of overall mass 100 kg is to be subjected to dynamic excitation represented by the acceleration RRS (at 5% damping) as shown in Figure 15.4 The estimated damping of the test package is 7% The test package is known to have a resonance within the frequency range of the specified test Determine the exciter specifications for the test nt Example 15.1 1.0 S 0.1 Solution 0.1 1.0 10 100 Frequency (Hz) From the development presented in the previous section, it is clear that the point F (or P) in Figure 15.4 corresponds to the force and output FIGURE 15.4 Test excitation specified by an accelerapower ratings, and the point S corresponds to tion RRS (5% damping) the stroke rating The co-ordinates of these critical points are F; P ẳ 4:2 Hz; 4:0 gị; and S ẳ 0:8 Hz; 0:75 gị: Equation 15.10 gives the force rating as Fmax ẳ 100 Ê 0:05=0:07ị Ê 4:0 £ 9:81 N ¼ 2803 N Equation 15.13 gives the power rating as pmax ¼ £ 100 £ 0:052 =0:07ị Ê ẵ4:0 Ê 9:81ị2 =4:2 Ê 2p watts ¼ 417 W Equation 15.17 gives the stroke rating as xmax ẳ Ê 0:05 Ê ẵ0:75 Ê 9:8ị=0:8 Ê 2pị2 m ẳ cm â 2005 by Taylor & Francis Group, LLC Vibration Instrumentation 15.2.1.4 15-9 Hydraulic Shakers A typical hydraulic shaker consists of a piston-cylinder arrangement (also called a ram), a servo-valve, a fluid pump, and a driving electric motor Hydraulic fluid (oil) is pressurized (typical operating pressure: 4000 psi) and pumped into the cylinder through a servo-valve by means of a pump that is driven by an electric motor (typical power, 150 hp) The flow (typical rate: 100 gal/min) that enters the cylinder is controlled (modulated) by the servo-valve, which, in effect, controls the resulting piston (ram) motion A typical servo-valve consists of a two-stage spool valve, which provides a pressure difference and a controlled (modulated) flow to the piston, which sets it in motion The servo-valve itself is moved by means of a linear torque motor, which is driven by the excitationinput signal (electrical) A primary function of the servo-valve is to provide a stabilizing feedback to the ram In this respect, the servo-valve complements the main control system of the test setup The ram is coupled to the shaker table by means of a link with some flexibility The cylinder frame is mounted on the support foundation with swivel joints This allows for some angular and lateral misalignment, which might be caused primarily by test-object dynamics as the table moves Two-degree-of-freedom (Two-DoF) testing requires two independent sets of actuators, and three-DoF testing requires three independent actuator sets Each independent actuator set can consist of several actuators operated in parallel, using the same pump and the same excitation-input signal to the torque motors If the test table is directly supported on the vertical actuators, they must withstand the total dead weight (i.e., the weight of the test table, the test object, the mounting fixtures, and the instrumentation) This is requirement is usually prevented by providing a pressurized air cushion in the gap between the test table and the foundation walls Air should be pressurized so as to balance the total dead weight exactly (typical required gage pressure: psi) Figure 15.5(a) shows the basic components of a typical hydraulic shaker The corresponding operational block diagram is shown in Figure 15.5(b) It is desirable to locate the actuators in a pit in the test laboratory so that the test tabletop is flushed with the test laboratory floor under no-load conditions This minimizes the effort required to place the test object on the test table Otherwise, the test object has to be lifted onto the test table with a forklift Also, installation of an aircushion to support the system dead weight is difficult under these circumstances of elevated mounting Hydraulic actuators are most suitable for heavy load testing and are widely used in industrial and civil engineering applications They can be operated at very low frequencies (almost direct current [DC]), as well as at intermediate frequencies (see Table 15.1) Large displacements (stroke) are possible at low frequencies Hydraulic shakers have the advantage of providing high flexibility of operation during the test; their capabilities include variable-force and constant-force testing and wide-band random-input testing The velocity and acceleration capabilities of hydraulic shakers are moderate Although any general excitationinput motion (for example, sine wave, sine beat, wide-band random) can be used in hydraulic shakers, faithful reproduction of these signals is virtually impossible at high frequencies because of distortion and higher-order harmonics introduced by the high noise levels that are common in hydraulic systems This is only a minor drawback in heavy-duty, intermediate-frequency applications Dynamic interactions are reduced through feedback control 15.2.1.5 Inertial Shakers In inertial shakers, or “mechanical exciters,” the force that causes the shaker-table motion is generated by inertia forces (accelerating masses) Counter-rotating-mass inertial shakers are typical in this category To understand their principle of operation, consider two equal masses rotating in opposite directions at the same angular speed v and in the same circle of radius r (see Figure 15.6) This produces a resultant force equal to 2mv2 r cos vt in a fixed direction (the direction of symmetry of the two rotating arms) Consequently, a sinusoidal force with a frequency of v and an amplitude proportional to v2 is generated This reaction force is applied to the shaker table Figure 15.7 shows a sketch of a typical counter-rotating-mass inertial shaker It consists of two identical rods rotating at the same speed in opposite directions Each rod has a series of slots in which to © 2005 by Taylor & Francis Group, LLC 15-104 Vibration and Shock Handbook Complete the following basic steps to display results on a waterfall graph: Initialize the display Send data to the display Close the waterfall display Figure 15A.52 shows the Waterfall window 15A.9.1.1 Initializing the Display Use the SVL Initialize Waterfall Display VI to create a reference to a waterfall display If you are displaying octave spectra, use the SVT Initialize Waterfall Display for Octave VI Both of the initializing VIs also enable one to define graph properties, including the window title, the bounds of the external window, and the colors used in the waterfall display 15A.9.1.2 Sending Data to the Display FIGURE 15A.51 Acquired SRS (Maximax) The Waterfall window does not open until it receives data sent to it Use the SVL Send Data to Waterfall VI to send data to a waterfall display Use the SVT Send Data to Waterfall for Octave VI to send octave data to a waterfall display The SVL Send Data to Waterfall VI is polymorphic and accepts an array of spectra, such as that returned by a power spectrum, a twodimensional (2D) array, or a STFT 15A.9.1.3 Analysis Waterfall Display for Frequency The following example shows how to accumulate FIGURE 15A.52 Waterfall display for frequency 20 spectra and display them in a waterfall graph analysis Figure 15A.53 shows the block diagram for the VI Twenty data blocks of 1024 samples are acquired The power spectrum is computed on each block The autoindexing capability of the For Loop is used to build an array of 20 spectra The array or spectra is sent to the waterfall display Refer to the LabVIEW Help for information about autoindexing 15A.9.1.4 Waterfall Display for Transient Analysis This example illustrates how to use the waterfall display in conjunction with the Transient Analysis VIs Figure 15A.54 shows the block diagram for the example VI FIGURE 15A.53 © 2005 by Taylor & Francis Group, LLC Waterfall display for frequency analysis VI block diagram Virtual Instrumentation for Data Acquisition, Analysis, and Presentation FIGURE 15A.54 STFT VI block diagram The data are scaled and sent to the SVT STFT vs Time VI The SVT STFT vs Time VI returns a 2D array You can use the results in the 2D array in an intensity graph or connect the 2D array directly to the SVL Send Data to Waterfall VI Figure 15A.54 shows the 2D array connected directly to the Waterfall VI The while loop keeps the waterfall display open until the Stop control is set to TRUE Note: Connect f and delta f and y and delta y on the SVL Send Data to Waterfall VI to ensure the graph shows the proper scales Figure 15A.55 shows the result obtained with the STFT VI illustrated in Figure 15A.54 15A.9.1.5 15-105 FIGURE 15A.55 STFT waterfall display Waterfall Display for Octave Spectra To display octave spectra in a waterfall display, use the SVT Initialize Waterfall Display for Octave and SVT Send Data to Waterfall for Octave VIs Figure 15A.56 shows the block diagram for a VI displaying octave spectra in a waterfall display Figure 15A.57 shows the waterfall display created by the VI in Figure 15A.56 15A.10 Swept-Sine Measurements This Appendix discusses using the swept-sine VIs located on the Swept Sine palette (see Chapter 17) The swept-sine measurements include dynamic measurements for stimulus level, response level, frequency response (gain and phase), THD, and individual harmonic distortion 15A.10.1 Swept-Sine Overview Swept sine is a technique for characterizing the frequency response of the DUT Two techniques are commonly used in swept-sine measurements The first technique slowly sweeps through a range of FIGURE 15A.56 © 2005 by Taylor & Francis Group, LLC Block diagram for VI displaying octave spectra 15-106 Vibration and Shock Handbook frequencies in a manner similar to a chirp Figure 15A.58 shows an example of the excitation signal for this form of swept-sine measurement The second technique steps through a range of frequencies Figure 15A.59 shows an example of the excitation signal for this form of swept-sine measurement The swept sine implemented in the Sound and Vibration Toolkit generates an excitation signal that steps through a range of test frequencies, similar to the signal in Figure 15A.59 Both techniques can yield similar results However, they require very different measurement analysis FIGURE 15A.57 Waterfall display for octave spectra processes analysis Swept-sine frequency-response measurements compare a response signal to the stimulus tone in order to compute the FRF of the DUT The magnitude of the FRF is equivalent to gain and represents the ratio of the output level to the input level for each test frequency The phase of the FRF is equivalent to the phase lag introduced by the DUT for each test frequency Swept-sine measurements require a signal source The stimulus signal is always a single tone that excites the DUT at the test frequency Since the stimulus is a single tone, swept-sine analysis can measure the harmonic distortion while simultaneously measuring the linear response 15A.10.2 Choosing Swept-Sine vs FFT Measurements The frequency response of the DUT is a useful tool The Sound and Vibration Toolkit provides two distinct techniques to measure the frequency response The swept-sine technique performs single –tone FIGURE 15A.58 Sweeping swept sine example FIGURE 15A.59 Stepping swept sine example © 2005 by Taylor & Francis Group, LLC Virtual Instrumentation for Data Acquisition, Analysis, and Presentation TABLE 15A.8 15-107 Swept Sine and FFT Differences Swept-Sine Frequency Response FFT-Based Frequency Response Single-tone excitation Can measure harmonics Arbitrary test frequencies Longer test time for many test frequencies Better dynamic range possibility Broadband excitation Cannot measure harmonics Linearly spaced frequency resolution measurements at each test frequency The FFTbased technique measures the response over the entire acquisition bandwidth Table 15A.8 lists the basic differences between swept-sine and FFTbased techniques for measuring frequency response Swept-sine measurements offer superior dynamic range over FFT-based measurements because you can optimize the signal level and input ranges at each test frequency FFT-based FIGURE 15A.60 Swept-sine and FFT measurements techniques must specify a signal level and input ranges appropriate for the maximum broadband response Figure 15A.60 shows the simulated frequency response function for a four-DoF system The peak at 17.6 Hz has a magnitude roughly 1000 times larger than the peak at 5.8 Hz To use an FFT-based technique, use broadband excitation to excite the entire frequency range of interest, to measure the frequency response This situation forces one to set the input range so that the overall response does not overload the DUT or the acquisition device Therefore, when you measure the response at 5.8 Hz, you lose 60 dB of measurement dynamic range The swept-sine technique allows you to tailor the excitation amplitude to the specific test frequency, preserving the full measurement dynamic range FFT-based measurements are limited to a linearly spaced frequency resolution determined by the sample rate and the block size Refer to Appendix 15A.7 for more information on FFT-based measurements When the response changes rapidly, this frequency resolution may not yield enough information about the dynamic response Also, a linear resolution may yield an excessive amount of information in frequency regions where the dynamic response is relatively constant Swept-sine analysis has the ability to test arbitrary frequency resolutions that are linear, logarithmic, or adapted to the dynamic response of the DUT When the frequency resolution is adapted to the DUT dynamic response, you can test more frequencies in regions where the dynamic response is of interest to your application and fewer where it is not The main benefit of swept-sine analysis is the ability to measure harmonic distortion simultaneously with linear response FFT-based analysis offers a speed advantage for broadband measurements with many test frequencies 15A.10.3 Taking a Swept-Sine Measurement Use the SVT Initialize Swept Sine VI to create a new swept-sine task for the designated device, source channel settings, and acquisition channel settings Swept sine in the Sound and Vibration Toolkit only supports measurements on a single device with output and input capabilities Use configure swept sine VIs in the configure swept sine palette to configure the scaling, test frequencies, averaging, delays, and other measurement settings These configuration VIs allow control over basic and advanced measurement parameters The order in which you place the configuration VIs is important, as it allows you to customize a swept-sine measurement For example, you can easily generate © 2005 by Taylor & Francis Group, LLC 15-108 Vibration and Shock Handbook FIGURE 15A.61 Customizing a swept-sine measurement 100 logarithmically spaced test frequencies in the audio range, then apply inverse A-weighted scaling to the excitation level by adding code similar to that in Figure 15A.61 into your swept-sine application You can use the swept-sine configuration VIs to customize your swept-sine application For example, to speed up a swept-sine measurement, reduce the settling or integration time specified by the SVT Set Swept Sine Averaging VI You also can configure the device IEPE with the SVT Set Swept Sine Coupling and IEPE Excitation (DAQmx) VI You also can reduce the block duration input to SVT Set Swept Sine Block Duration VI Note: The minimum block duration is limited by the capabilities of the computer processing the measurement A very small block duration can result in a loss of continuous processing, causing the swept-sine measurement to stop and return an error Use the SVT Start Swept Sine VI to begin the generation and acquisition The VI fills the device output buffer with zeros before writing the first test frequency excitation The SVT Swept Sine Engine VI continually acquires data and processes it to remove samples acquired during delays, transitions, and settling periods The SVT Swept Sine Engine VI performs measurement analysis on samples acquired during integration periods The SVT Swept Sine Engine VI updates the excitation to excite the DUT at the next test frequency after it integrates sufficient data at the current test frequency Note: The transition to the next excitation tone, both frequency and amplitude, always occurs at a zero crossing to minimize transients introduced to the DUT Use the Read Swept Sine Measurements VIs in the Read Swept Sine Measurements palette to read the raw measurements, scale the measurements, and perform additional conversions to display and report the data in the desired format Use the SVT Close Swept Sine VI to stop the generation and acquisition, and clear the sweptsine task 15A.10.4 Swept-Sine Measurement Example This example of a swept-sine application measures the frequency response and harmonic distortion of a notch filter In this example, a NI PXI-4461 generates the excitation signal and acquires the stimulus and response signals Figure 15A.62 illustrates the connection scheme used in this example to measure the dynamic response of the DUT using a swept-sine measurement The acquired stimulus signal on the analog input channel 0, the AI0, is the generated excitation signal from the analog output channel 0, AO0 The NI PXI-4461 converts the desired stimulus signal from digital data to an analog signal and outputs that signal on AO0 The excitation signal is © 2005 by Taylor & Francis Group, LLC FIGURE 15A.62 diagram Swept-sine measurement connection Virtual Instrumentation for Data Acquisition, Analysis, and Presentation FIGURE 15A.63 TABLE 15A.9 10 11 12 Block diagram of SVXMPL_swept sine FRF DAQmx VI Swept Sine Measurement Steps Step Number 15-109 Description Initialize a swept-sine measurement by specifying the hardware device and channel settings Specify the scaling that will be applied to the acquired stimulus and response data Configure the source by specifying the test frequencies, amplitude, and whether or not the sweep automatically restarts after completion Set the settling and integration parameters to allow sufficient time for the DUT to settle before the measurement is performed at the new test frequency and that there is sufficient integration time to achieve the desired level of accuracy Set the block duration input terminal for the measurement to be small enough to give a reasonable test time and large enough so that it does not put the test computer at risk of being unable to continuously generate and read the signals The smaller the block size, the faster the swept sine can transition from one test frequency to the next Explicitly set the sample rate for the measurement The rate is automatically selected if this VI is not used The same rate is used for input and output channels Specify the propagation time terminal input specific to the DAQ device being used for the measurement You can measure the device propagation time using the SVL Measure Propagation Delay VI Refer to Appendix 3, Scaling and Calibration, for more information Configure the harmonic distortion measurement by specifying the maximum harmonic to use in the computation of the THD Only those harmonics specified in the harmonics to visualize array return individual harmonic components Start the swept sine to perform the hardware configuration and start the output and input tasks Channel synchronization is performed internally in this VI Generate the excitation and acquire the stimulus and response data at each test frequency Convert the raw data to the specified format in order to display and report measurement results Stop the swept-sine measurement and clear the output and input tasks to release the device Optional or Required Required Optional Required Required Optional Optional Optional Required if performing distortion measurements Required Required Required Required connected to both the stimulus input channel AI0 and the input terminal of the DUT The response signal is connected from the output terminal of the DUT to the response input channel AI1 The DUT for this example is a notch filter centered at kHz Figure 15A.63 shows the block diagram of the example SVXMPL_swept sine FRF DAQmx VI, which ships with the Sound and Vibration Toolkit © 2005 by Taylor & Francis Group, LLC 15-110 Vibration and Shock Handbook FIGURE 15A.64 FIGURE 15A.65 Magnitude and phase response of a kHz notch filter FIGURE 15A.66 © 2005 by Taylor & Francis Group, LLC Time-domain results THD vs frequency Virtual Instrumentation for Data Acquisition, Analysis, and Presentation FIGURE 15A.67 15-111 THD vs frequency results Table 15A.9 documents the actions performed by the VIs in Figure 15A.63 Some steps are required and must be done for the VI to function correctly The optional steps allow you to customize your measurement The while loop in Figure 15A.63 controls the synchronized generation and acquisition Display controls and measurement indicators are updated inside the while loop This loop allows for the monitoring of intermediate results Many of the steps in Table 15A.9 are configuration steps Through the Sound and Vibration Toolkit swept-sine configuration VIs, you can specify numerous configuration parameters to achieve fine control of the swept-sine measurement parameters For many applications two or three configuration VIs are sufficient It is important to allow for the propagation delay of the DAQ or DSA device This delay is specific to the device used to perform the measurement To determine the device propagation delay, refer to the device documentation or measure the delay with the SVL Measure Propagation Delay VI Figures 15A.64 to 15A.67 display measurement results obtained with the SVXMPL_swept sine FRF DAQmx VI example program Figure 15A.64 shows the time-domain stimulus and response signals for the 138.49 Hz test frequency From the time-domain data, you can see that the notch filter has attenuated the signal and introduced a phase shift Figure 15A.65 shows the magnitude and phase responses of the notch filter at all the test frequencies in the magnitude and phase spectra in the Bode plot In addition to measuring the frequency response, this example simultaneously measures the harmonic distortion at each test frequency Figure 15A.66 shows the graph of THD vs frequency You expect to see a peak in the THD at the notch frequency The peak occurs because the fundamental frequency is attenuated at the notch frequency However, the graph indicates that this measurement has failed to accurately identify the power in the harmonic distortion components For the example in Figure 15A.66, the number of integration cycles is two More integration cycles must be specified to perform accurate harmonic distortion measurements If you change the number of integration cycles to ten and rerun the example, you obtain the THD vs frequency results displayed in Figure 15A.67 Now, with a sufficient number of integration cycles specified, you can see the characteristic peak in the THD at the center frequency of the notch filter © 2005 by Taylor & Francis Group, LLC 15-112 Vibration and Shock Handbook Bibliography Crocker and Malcolm, J 1998 Handbook of Acoustics, Wiley, New York Design Response of Weighting Networks for Acoustical Measurements, ANSI S1.42-2001, American National Standards Institute, Washington, 1986 Electroacoustics — Sound Level Meters, International Standard IEC 61672, 1st ed., 2002–2005, International Electrotechnical Commission, Geneva, Switzerland, 2002 Hassall, J.R and Zaveri, K 1988 Acoustic Noise Measurements, Bruel & Kjær, Nærum, Denmark Measurement of Audio-Frequency Noise Voltage Level in Sound Broadcasting, ITU-R Recommendation 468-4, 1986 Octave-Band and Fractional Octave-Band Filters, International Standard IEC 1260, 1st ed., 1995-07 International Electrotechnical Commission, Geneva, Switzerland, 1995 Preferred Frequencies for Measurements, International Standard IEC 266, 1st ed., 1975-07-15, International Electrotechnical Commission, Geneva, Switzerland, 1975 Psophometer for Use on Telephone-Type Circuits, ITU-T Recommendation O.41, Revised, 1993–1996 Telecommunication Standardization Sector of the International Telecommunication Union, 1995 Randall, R.B 1987 Frequency Analysis, BrYăel & Kjổr, Nổrum, Denmark Smallwood, D., An improved recursive formula for calculating shock response spectra, Shock Vib Bull., 51, Pt 2, 211 –217, 1981, May 1981 Specification for Octave-Band and Fractional Octave-Band Analog and Digital Filters, ANSI S1.11-1986, Acoustical Society of America, New York, 1986b Specification for Sound Level Meters, ANSI S1.4-1983, American National Standards Institute, Washington, 1983 © 2005 by Taylor & Francis Group, LLC ... generator Random Signal 15- 20 Vibration and Shock Handbook specified standard (e.g., the Communication and Telemetry Standard of the Intermediate Range Instrumentation Group (IRIG Standard 106-66)... Vibration and Shock Handbook Box 15. 1 VIBRATION INSTRUMENTATION Vibration Testing Applications for Products: * * * Design and Development Production Screening and Quality Assessment Utilization and. . .15 Vibration Instrumentation 15. 1 Introduction 15- 1 15. 2 Vibration Exciters 15- 3 Shaker Selection † Dynamics of Electromagnetic Shakers 15. 3 Control System 15- 15