GB/T 11349.2-1989 Test determination of mechanical sodium conduction - Single-point excitation measurement using an exciter
Some standard content:
National Standard of the People's Republic of China
Experimental determination of mechanical mobility-Mesurments uslng single-point translation excitatlon with an attached vibration exciter1 Subject content and scope of application
GB 11349.289
This standard specifies the method for measuring the mechanical mobility or other frequency response functions of structures (such as buildings, machines and vehicles) by excitation with a single contact vibration exciter.
This standard applies to single-point or multi-point measurement disk admittance, acceleration admittance or displacement admittance under single-point excitation, which can be the measurement disk of the driving point admittance at the excitation point (driving point measurement) or the measurement of the transfer admittance between the driving point and other points (transfer measurement). It is also applicable to the determination of the inverse of these frequency response functions, such as the measurement of free acceleration impedance (free effective mass). 2 Reference standards
GB 2298 Mechanical vibration, shock terminology GB10084 Vibration, shock data analysis and expression methods GB7670 Description of characteristics of electric vibration table
GB11349.1 Overview of machine admittance - Experimental determination - Basic definitions and sensors 3 Overall structure of the measurement system
According to this standard, the admittance measurement is carried out. The measurement system should include the basic parts shown in Figure 1. Amplitude control
Signal generator
Recording position
Signal analysis
Grapher
Other output equipment
Monitor oscilloscope
National Technical Supervision Bureau 1989-05-08 Approved Signal slope amplification
Admittance measurement system diagram
Exciter
Electrical device
Test face structure
Motion response sensor
Basic
Optional
1990-01- 01 Implementation
is to carry out the admittance test according to the test requirements,
【Measurement under support conditions
. Unless otherwise stated, the support of the test structure should represent the support conditions of the structure in actual application. The test report should state the measurement under the free suspension condition of the support
GB 113,2-8
Time-synchronous averaging of response waveforms. It is recommended to repeat these waveforms. 5.1.4.1 Pseudo-random excitation
According to the required excitation spectrum, the excitation signal is digitally synthesized in the frequency domain. Perform an inverse Fourier transform to obtain a periodic digital signal, which is used to drive the exciter after digital-to-analog conversion: 5.1.4.2 Periodic sine fast sweep excitation
Periodic sine fast sweep is a repeated fast sine scanning signal whose frequency scans up and down in the selected frequency band. The signal can be digitally synthesized or generated by a scanning oscillator and synchronized with the signal processor being averaged to improve the signal-to-noise ratio. 5.1.4.3 Periodic pulse excitation
Periodic pulses are usually obtained by repeating a digitally synthesized pulse function of appropriate shape. The signal processor should be synchronized with the signal generator. In order to meet the requirements of the excitation frequency, the shape of the pulse function should be selected ( Such as half-sine function, etc.). 5.1.4.4 Periodic random excitation
Periodic random excitation combines the advantages of pure random and pseudo-random excitation. It not only meets the periodic conditions, but also changes with time, and excites the structure in a truly random manner. In one cycle, it first outputs a pseudo-random signal, and when the structure reaches a steady-state vibration, it performs a measurement, and then outputs another unrelated pseudo-random signal. When the structure reaches a new steady-state vibration, it is measured again. Periodic random excitation measurement can be achieved by averaging the results of multiple measurements. 3.2 Vibrator
The vibrator is a device usually attached to the test structure to provide the required input power. There are electric, electro-hydraulic and piezoelectric exciters (see GB7670-87). Figure 2 shows the frequency range that each type of vibrator is generally applicable to. GB11849.2-88
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GB 11$48.2—88
The basic requirement for the shaker is that it provide sufficient force and displacement so that admittance measurements can be made with an appropriate signal-to-noise ratio over the entire frequency range of interest. In order to provide sufficiently broadband random excitation of the structure, a shaker with a larger excitation force than is required for sinusoidal excitation is required. If bandwidth is limited or time-domain averaging of the excitation and response waveforms is used, a shaker with a smaller excitation force can be used (see 5.1.4). The excitation force input into the structure will cause a reaction force on the shaker due to the inertia of the shaker support or the shaker itself. These situations are illustrated in Figures 3(a) and 3(b). If necessary, an additional mass should be added to the shaker to increase the shaker's own inertia. Figure 3(c) is an incorrect solution, as it causes the reaction force of the shaker to be transmitted to the structure through the common base supporting the shaker and the structure rather than entirely through the force sensor. Structural suspension
Exciter performance
Data source
777777777
Reaction of external supports
An example of incorrect installation
Figure 3 Reaction of exciter
5.3 Avoiding additional forces and additional moments
Reaction of exciter inertia
The basic requirement for admittance measurement is that the excitation force should be applied at a certain point on the structure in a certain direction. Any additional force and additional moment (not the predetermined excitation force and moment at the excitation point in the predetermined direction) will cause errors in the admittance data. Except for the support points, other measuring points on the structure should be able to respond freely. Dynamic interactions between the structure and the sensor and between the structure and the exciter should also be avoided. In order to avoid additional forces and additional moments, the relevant factors of 5.3.1 to 5.3.31 should be considered. 5.3.1 Sensor mass load
At each sensor connection point, additional inertial forces are generated by the movement of the sensor. The measurement error caused by mass load can be minimized by selecting the smallest mass sensor that meets the sensitivity requirements. When measuring the drive point admittance, the force sensor load can be compensated to a certain extent by electrical methods (see 6.2). 5.8.2 Sensor rotational inertia load
At each sensor connection point, the sensor generates additional inertial moments due to angular acceleration (especially impedance heads with large rotational inertia). Sensors with small moments of inertia about their mounting points should be selected to minimize these additional moments of inertia. 5.3.3 Shaker connection constraints
At the shaker connection points, additional moments and lateral forces are generated due to the rotational and lateral response of the test structure's drive point being constrained. For example, the constraints caused by the shaker-impedance head combination can adversely affect the measurement of low-order modes of the test structure. At the connection point between the test structure and the shaker, a cone or spherical head with a smaller area can be used to make it closer to the point drive. Note: If not considered carefully, a cone or spherical head may generate additional torque. When the shaker is fixedly connected to a light structure for admittance measurement, the shaker connection constraints often occur. In order to avoid measurement errors caused by severe connection constraints, the following points should be considered: b. Use a non-contact shaker.
b. Design a support system for the inertial control shaker so that the reaction of the force acting on the test structure will not cause any rotation of the shaker or any lateral movement of the force sensor axis. c. Install the drive rod connecting the shaker and the force sensor. The drive rod should be designed to have high axial stiffness and sufficient flexibility in other directions. Therefore, a slender rod is often used. The effect may be better if a rod with thinner ends is used. Care should be taken to make the shaker and the drive rod collinear with the force sensor axis. If a flexible drive rod is used; the accelerometer should not be connected to the structure through any intermediate device (such as the drive rod, whose axial flexibility may invalidate the motion response measurement) (see Figure 4 (a)), but should be connected directly to the structure. The force sensor should measure the force transmitted to the structure by the drive rod (see Figure 4 (b)). If the force sensor has to be placed at the shaker end of the rod (see Figures 4 (c) and 4 (d)), the effect of the flexibility of the drive rod should be checked as described in GB11349.1, and the mass of the drive rod should be compensated using the method specified in 6.2. Note: Bending modes of the drive rod with natural frequencies in the frequency range of interest may affect the admittance test. In addition, the bending motion of the exciter motion system can also produce moments on the structure that affect the response measurement. Test structure
Test structure
GB 11349.2-—89
Impedance head
Drive rod
Connection of drive rod
Exciter
Drive rod
Force sensor
Acceleration sensor
Due to the axial flexibility of the drive rod. The acceleration measurement of the impedance head is invalid. A large mass correction is required to determine the actual excitation force. Incorrect method
Force and acceleration measurement
Improper method
Impedance head
Drive rod
Connection of drive rod
Exciter
Optimal method
Figure 4 Connection of drive rod of exciter. A small mass correction is required to determine the actual excitation force.
Test structure
GB11349.2—89
Exciter
Force sensor
Driving rod
Acceleration sensor
Determine the actual exciting force
Need to make a large mass correction
(c] Connection of the exciter driving rod - Folding table method A Explosion quantity
Driving rod
Impedance head
Test structure
Impedance head plus The filterability measurement is not affected by the flexibility of the actuator rod. A small mass correction is required to determine the actual excitation force, but when the flexibility of the structure is quite large, it should be noted that the moment of inertia of the impedance head cannot be ignored and will significantly affect the data. Connection of the actuator rod - method B continued Figure 4 6 Measurement of excitation force and motion response GB 11349.2--- 88
GB11349.1-89 has stipulated the basic criteria and requirements for selecting motion sensors, force sensors and impedance heads, as well as the methods for determining the characteristics of these sensors.
The sensors commonly used to measure the frequency response of structures are piezoelectric accelerometers, piezoelectric force sensors and impedance heads. Displacement sensors or velocity sensors can also be used instead of accelerometers. Some displacement sensors also have the advantage of non-contact measurement. When pulse excitation is used, piezoresistive accelerometers have certain advantages. The frequency response and linear range of the sensor used should be wide enough. For each frequency, the relationship between the displacement x, velocity and acceleration measured by the motion sensor is: a=(32) =(2) 1 x
武中=-,
f related frequency, Hz.
6.1 Sensor connection
Force sensors and motion sensors should be mounted on the structure with bolts or adhesive. The excitation force should be transmitted to the structure directly through the force sensor or impedance head with as few intermediate parts as possible. If the surface of the sensor mounting point on the structure is uneven, a fixing pad of some appropriate shape can be used. A thin film of viscous liquid (such as heavy oil or lubricating sleeve) between the sensor and the mounting surface can improve the coupling of the sensor at high frequencies. The influence of connection flexibility should be checked as described in GB11349.1-89. The force sensor should be tightened according to the tightening torque recommended by the sensor manufacturer. The sensor is tightened. .2 Mass Plate Loading and Mass Plate Compensation
As mentioned in 5.3.1, the mass added to the structure for the test should be as small as possible. When testing light structures, circuits can be used to compensate for the total effective mass m· of the sensor and the attachment at the structure's drive point. Mass compensation should be considered when the drive point admittance of the test structure is less than 0.01/m· at all frequencies (in Hz) within the frequency range of interest. The mass m· is the sum of the mass of the attachment and the effective end mass of the force sensor or impedance head. The method of mass compensation is: in the analog circuit or digital circuit, the acceleration signal obtained at the excitation point is multiplied by the total effective mass to be compensated. This product is the part of the exciter output force that is required to produce an acceleration of the effective mass attached to the structure. In order to obtain the net excitation force acting on the test structure, this force signal should be subtracted from the force sensor signal in the analog circuit or digital circuit.
Note: ① If an acceleration sensor is installed under the force sensor, the mass disk of this acceleration sensor should also be included in the total effective mass disk mt. ② When measuring the admittance at the sudden movement point, the acceleration sensor used for the structural response of the measuring disk can also provide the signal of the force required to make the effective mass disk produce acceleration, but when the measuring disk transmits admittance, a separate acceleration sensor is required at the main movement point of the structure to obtain the acceleration signal required for mass compensation.
③ The circuit compensation of the mass cannot compensate for the rotational inertia load. It can only compensate for the inertial load at the main movement point and in the direction of the excitation. All other additional forces can only be minimized by selecting a sensor with small inertia. The inertial load of the structure that is not compensated will cause measurement errors. These measurement errors include the deviation of the response rate.
@Before adopting the mass disk compensation method, the selection of sensors and the redesign of connectors should be given priority. In addition, in order to avoid large measurement errors, mass compensation is only performed when the ratio of the effective mass of the connection and sensor to the free effective mass of the test structure at the driving point is greater than 0.1H and less than 0.5.
6.8 Signal amplifier
Piezoelectric force sensors and motion sensors need to be used in conjunction with charge amplifiers or high input impedance voltage amplifiers. Note: ① Some piezoelectric sensors are equipped with internal electronic circuits, which require amplifiers that match this circuit. ② The sensitivity of the voltage amplifier is affected by the impedance of the sensor cable. The low-frequency response of the voltage amplifier is more stringent than that of the charge amplifier. 6.4 Calibration
GB11349.1-89 specifies the requirements for basic calibration and supplementary calibration of sensors. It can determine the suitability of piezoelectric sensors for admittance measurement.
GB 11349.2-80
System calibration is completed by measuring the admittance or acceleration admittance of a freely suspended and known mass block (calibration block). The measurement system should be the same as that used in the test. The error between the measured frequency response of the calibration block and the theoretical value should be within ±5%; the theoretical amplitude of the acceleration admittance of the calibration block is 1/m, and the admittance is 1/(2 yuan fm), where m is the mass of the calibration block. The connections used in the system calibration should be the same as those used in the measurement, so that the error caused by the connection flexibility can be detected (see GB1.1349.1-89). The mass of the calibration block is selected so that its admittance is representative within the measured admittance range. If necessary, in order to cover the maximum admittance range measured, several calibration blocks should be used for several system calibrations.
7 Processing of sensor signals
7.1. Determination of frequency response function
Both the motion signal and the force signal should be processed by a signal analyzer capable of filtering (and, if required, compensation), and the amplitude ratio and phase difference between the two should be determined. The amplitude and phase difference are functions of the frequency. The analyzer shall also perform the mathematical operations required to convert the measured frequency response function to some other form (e.g., acceleration admittance to admittance) (see Clause 6). 7.1.1 and 7.1.2 specify the processing requirements for the various excitation forms discussed in 5.1. 7.1.1 Sinusoidal Excitation
The amplitude of the frequency response function is the ratio of the phasor (complex loss) amplitudes of two sinusoidal signals and may be determined by analog or digital methods. The phase of the frequency response function is determined by measuring the phase difference between the two signals. NOTE If stepped sine excitation is used, several frequency response functions may be obtained by switching a single response channel from one responding sensor to the next responding sensor at each excitation frequency during the measurement. If slow-sweep sine excitation is used, each response channel may measure the frequency response function at only one point in a sweep.
7.1.2 Random Excitation
Sensor signals generated by random, periodic random, pseudo-random, periodic sine fast sweep, or pulsed excitation shall be processed by a digital Fourier transform analyzer. As described in GB11349.1-89, the frequency response function can be obtained by dividing the cross-spectral density of the motion response and the excitation force by the auto-spectral density of the excitation force. By weighting the excitation and response signals in the time domain (see 7.4.2) Perform a discrete Fourier transform to calculate the above spectra. At each resonant frequency, in order to make the confidence level greater than 90%, that is, the random error of the driving point admittance calculated at each common grip frequency is less than 5%, a sufficient number of spectra should be averaged (see Appendix A). At least the same number of spectra should be averaged when calculating the corresponding transfer admittance.
Juice: ① When measuring the transfer admittance, it is impossible to achieve the above disk-level confidence level, especially when the transfer admittance value is very small. In this case, it is not very useful to increase the number of average spectra beyond the number of average spectra required for the corresponding driving point admittance test. ② Dual-channel Fourier analysis can only obtain a single frequency response function in one measurement. If you want to measure multiple frequency response functions simultaneously, you can use multi-channel signal analysis.
7.2 Filtering
7.2.1 Sine Excitation
The frequency response function can be calculated using the response and excitation signal components corresponding to the excitation frequency. The use of tracking filters or synchronous digital sampling can minimize the noise and harmonic components without changing the phase difference between the excitation signal and the response signal. 7.2.2 Random Excitation
When random excitation is used, it is impossible to filter out noise and harmonic components from the excitation signal and the response signal. The use of band-limited (thinning) technology can improve the signal-to-noise ratio, but the appropriate filter should be selected to limit the excitation bandwidth as described in. 4.2. When using digital resolution 7.4 Frequency resolution
GB 11848.2 89
In the frequency range of interest, the resolution should be high enough to distinguish all the eigenfrequencies of the test structure and estimate the modal damping. 7.4.1 Sine Excitation
For slow-sweep sine excitation and discrete-step sine excitation, the excitation frequency must change slowly enough to obtain effective resonant frequency resolution (see 8.1).
7.4.2 Random Excitation
For the excitation waveforms described in 5.1, 3 and 5.1.4, a small frequency increment is required in the discrete Fourier transform to obtain adequate frequency resolution. The frequency increment (spectral line spacing) should be determined by the modal density and modal damping of the test structure. The selection of a Henning window or other appropriate window function to weight the signal in the time domain should improve the frequency resolution. Note: ① For structures with low damping, the number of data samples required to calculate the excitation and response signals over the entire frequency range of interest is very large. Alternatively, Fourier analysis (refinement) limited to a selected frequency band can be used; or these two methods can be combined. ② Random excitation can be combined with the method. In either case, the total time required (record length) is the inverse of the required frequency increment (resolution). ② Random excitation can be expressed as a time sequence of pulse functions (Duhamel method). The response at the beginning of a data block is mainly the result of the previous excitation. Such a response does not correspond to the excitation (coherent). There is still excitation near the end of the data block, but the response has been truncated. The effect of truncation is related to the ratio of the sampling time to the total sampling time of the data block and the position of the excitation pulse in the data block, which will cause coherence. The part of the excitation and response data that is well correlated can be found in the data block. Sometimes it is recommended to use Heining density to improve the coherence of the admittance data. 7.4.3 Periodic excitation
Periodic random, periodic sine fast sweep and pulse excitation are different from the situation described in 7.4.2. Because periodic excitation produces a sequence of data blocks connected end to end, the transient value at the beginning is transferred to the next data block. After a certain time, each data block contains all the response data. In principle, averaging is not required. In some cases, the coherence function can be used to estimate the effect of external noise and guide the selection of the number of signal averages (see Appendix A).
8 Control of excitation
To obtain adequate frequency resolution, the excitation time needs to be controlled, and to obtain adequate dynamic range, the excitation amplitude usually needs to be controlled.
8.1 Time Required for Sine Excitation
Whether sweeping or stepped sine excitation is used, the rate of change of the excitation frequency (or step size and rate) should be controlled to obtain the required frequency resolution. In order to accurately determine the amplitude and phase and obtain correct information for calculating the natural frequencies and structural damping, a high resolution is required in the resonant and anti-resonant regions of the structure. Table 1.1 Discrete Stepped Sine Excitation
When stepped sine excitation is applied, the excitation frequency closest to each resonant frequency of the structure will not differ from that resonant frequency by more than half the frequency step increment. Thus, the maximum error in determining the resonant frequency is 1/2 of the frequency increment. In addition, the amplitude of the measured structural peak response is likely to be smaller than the true common-mode peak. The upper bound of the error is given in the table. Errors in measuring the peak response of the structure will lead to an overestimation of the modal damping of the structure.
Within the frequency range of ±10% of the common frequency, the frequency increment should be selected so that the difference between the amplitude of the measured peak response and the modal damping ratio and its true value is less than 5%.
The maximum error of the amplitude of the motion response when measuring the resonance of the structure using discrete step sine excitation is shown in the following table. Ratio of the step frequency increment to the true half-power bandwidth of the structural mode
GB 11349.2—89
Maximum error in the measurement of the peak response
Appendix B gives the formula for determining the maximum frequency increment that meets this requirement. The duration of the excitation at each frequency is also given. For frequencies other than ±10% of the resonant frequency or anti-resonant frequency, a larger frequency increment and a shorter duration can be used. 8.1.2 Slow sweep sine excitation
When slow sweep sine excitation is used, the frequency changes as a linear function of time or as a logarithmic function of time. The scanning rate should be selected so that the amplitude of the measured structural motion response within ±10% of the non-vibration frequency deviates from the true value by less than 5%. For linear scanning excitation, the maximum scanning rate Sm: (Hz/min) should be: Sm* <54(Fn) 2/02.**
For logarithmic scanning excitation, the maximum scanning rate sm% (oct/min) should be Smx <77.6fa/Q2
In the above two equations, f,
estimated resonant frequency, Hz!
-estimated quality factor of the structural mode at the resonant frequency. If the above two equations are satisfied, the measurement is essentially a steady-state measurement. 8.2 Time required for random excitation
The duration of applying the excitation and measuring the response should be long enough to average the number of spectra specified in 7.1, 2. (2)
The number of spectra to be averaged is a function of the signal-to-noise ratio of the measurement system. The coherence function between the excitation force signal and the motion response signal should be used to determine the minimum number of spectra that must be averaged to keep the random error less than 5% within a 90% confidence level (see A2). The required de-excitation time for each harmonic should be the inverse of the frequency increment of the discrete Fourier transform (see Note to 7.4.2). 8.3 Dynamic Range
The admittance amplitude range of a lightly damped structure may be greater than 105:1 (10 dB). Each data channel has a minimum voltage in addition to a maximum operating voltage. Above the maximum voltage, saturation occurs, and below the minimum voltage, circuit noise and noise associated with digitization processing in digital systems become significant compared to the signal. For accurate measurements, the excitation should be controlled so that the voltages in both channels are within specified limits. In order to obtain the appropriate dynamic range, guidance on excitation amplitude control when using different types of excitation waveforms is given in 8.3.1 and 18.3.2. 8.3.1 Sinusoidal Excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by the admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.4 Frequency resolution
GB 11848 .2 89
In the frequency range of interest; the resolution should be high enough to distinguish all the characteristic frequencies of the test structure and estimate the modal damping. 7.4.1 Sine excitation
For slow-sweep sine excitation and discrete-step sine excitation, in order to obtain effective resonant frequency resolution, the change of the excitation frequency is required to be slow enough (see 8.1).
7.4.2 Random excitation
For the excitation waveforms described in 5.1, 3 and 5.1.4, a small frequency increment is required in the discrete Fourier transform to obtain appropriate frequency resolution. The frequency increment (spectral line spacing) should be determined by the modal density and modal damping of the test structure. The selection of a Heining window or other appropriate window function to weight the signal in the time domain should improve the frequency resolution. Note: ① For structures with low damping, the number of data samples required to calculate the excitation and response signals over the entire frequency range of interest is very large. Alternatively, Fourier analysis limited to a selected frequency band can be used (refinement); or a combination of the two methods can be used. In either case, the total time required (record length) is the inverse of the required frequency increment (resolution). ② Random excitation can be expressed as a time sequence of pulse functions (Duhamel method). The response at the beginning of a data block is mainly the result of the previous excitation, so the response does not correspond to the excitation (coherent). There is still excitation near the end of the data block, but the response has been truncated. The effect of truncation is related to the ratio of the sampling time to the total sampling time of the data block and the position of the excitation pulse in the data block, which will cause coherence. The best part of the coherence between the excitation and response data can be found in the data block. It is sometimes recommended to use Heining density to improve the coherence of the admittance data. 7.4.3 Periodic excitation
Periodic random, periodic sine fast sweep, and pulse excitation are different from the cases described in 7.4.2. Because periodic excitation produces a sequence of data blocks connected end to end, the transient value at the beginning is transferred to the next data block, and after a certain period of time, each data block contains the complete response data. In principle, averaging is not required. In some cases, the coherence function can be used to estimate the influence of external noise and guide the selection of the number of signal averages (see Appendix A).
8 Control of excitation
To obtain appropriate frequency resolution, it is necessary to control the excitation time, and to obtain appropriate dynamic range, it is usually necessary to control the excitation amplitude.
8.1 Time required for sinusoidal excitation
Whether sweeping or stepped sine excitation is used, the rate of change of the excitation frequency (or step size and rate) should be controlled to obtain the required frequency resolution. In order to accurately determine the amplitude and phase and obtain correct information for calculating the natural frequency and structural damping, a high resolution is required in the resonant and antiresonant regions of the structure. Table 1.1 Discrete Stepped Sine Excitation
When step-sine excitation is applied, the excitation frequency closest to each resonant frequency of the structure will not differ from the resonant frequency of that order by more than half the frequency step increment. Thus, the maximum error in determining the resonant frequency is 1/2 of the frequency increment. In addition, the amplitude of the measured structural peak response is likely to be smaller than the true peak of the common frequency. The upper bound of the error is given in the table. Errors in measuring the peak of the structural response can lead to an overestimation of the modal damping of the structure.
In the frequency range of ± 10% of the common frequency, the frequency increment should be chosen so that the amplitude of the measured peak response and the modal damping ratio differ from their true values by less than 5%.
The maximum errors in the amplitude of the motion response when measuring structural resonances using discrete step-sine excitation are shown in the table below. Ratio of step frequency increment to true half-power bandwidth of structural mode
GB 11349.2—89
Maximum error of response peak measurement
Appendix B gives the formula for determining the maximum frequency increment that meets this requirement. The duration of excitation at each frequency is also given. For frequencies other than ±10% of the resonant frequency or anti-resonant frequency, a larger frequency increment and a shorter duration can be used. 8.1.2 Slow scan sinusoidal excitation
When slow scan sinusoidal excitation is used, the frequency changes as a linear function of time or as a logarithmic function of time. The scanning rate should be selected so that the deviation between the amplitude of the structural motion response measured within ±10% of the non-vibration frequency and the true value is less than 5%. For linear scan excitation, the maximum scan rate Sm: (Hz/min) shall be: S m* < 54( Fn) 2/02 .**
For logarithmic scan excitation, the maximum scan rate sm% (oct/min) shall be S mx < 77.6fa/Q2
In the above two equations, f,
estimated resonant frequency, Hz!
-estimated quality factor of the structural mode at this resonant frequency. If the above two equations are satisfied, the measurement is essentially a steady-state measurement. 8.2 Time required for random excitation
The duration of applying the excitation and measuring the response shall be long enough to average the number of spectra specified in 7.1, 2. (2)
The number of spectra to be averaged is a function of the signal-to-noise ratio of the measurement system. The coherence function between the excitation force signal and the motion response signal should be used to determine the minimum number of spectra that must be averaged to keep the random error less than 5% within a 90% confidence level (see A2). The required de-excitation time for each harmonic should be the inverse of the frequency increment of the discrete Fourier transform (see Note to 7.4.2). 8.3 Dynamic Range
The admittance amplitude range of a lightly damped structure may be greater than 105:1 (10 dB). Each data channel has a minimum voltage in addition to a maximum operating voltage. Above the maximum voltage, saturation occurs, and below the minimum voltage, circuit noise and noise associated with digitization processing in digital systems become significant compared to the signal. For accurate measurements, the excitation should be controlled so that the voltages in both channels are within specified limits. In order to obtain the appropriate dynamic range, guidance on excitation amplitude control when using different types of excitation waveforms is given in 8.3.1 and 18.3.2. 8.3.1 Sinusoidal Excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by the admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.4 Frequency resolution
GB 11848 .2 89
In the frequency range of interest; the resolution should be high enough to distinguish all the characteristic frequencies of the test structure and estimate the modal damping. 7.4.1 Sine excitation
For slow-sweep sine excitation and discrete-step sine excitation, in order to obtain effective resonant frequency resolution, the change of the excitation frequency is required to be slow enough (see 8.1).
7.4.2 Random excitation
For the excitation waveforms described in 5.1, 3 and 5.1.4, a small frequency increment is required in the discrete Fourier transform to obtain appropriate frequency resolution. The frequency increment (spectral line spacing) should be determined by the modal density and modal damping of the test structure. The selection of a Heining window or other appropriate window function to weight the signal in the time domain should improve the frequency resolution. Note: ① For structures with low damping, the number of data samples required to calculate the excitation and response signals over the entire frequency range of interest is very large. Alternatively, Fourier analysis limited to a selected frequency band can be used (refinement); or a combination of the two methods can be used. In either case, the total time required (record length) is the inverse of the required frequency increment (resolution). ② Random excitation can be expressed as a time sequence of pulse functions (Duhamel method). The response at the beginning of a data block is mainly the result of the previous excitation, so the response does not correspond to the excitation (coherent). There is still excitation near the end of the data block, but the response has been truncated. The effect of truncation is related to the ratio of the sampling time to the total sampling time of the data block and the position of the excitation pulse in the data block, which will cause coherence. The best part of the coherence between the excitation and response data can be found in the data block. It is sometimes recommended to use Heining density to improve the coherence of the admittance data. 7.4.3 Periodic excitation
Periodic random, periodic sine fast sweep, and pulse excitation are different from the cases described in 7.4.2. Because periodic excitation produces a sequence of data blocks connected end to end, the transient value at the beginning is transferred to the next data block, and after a certain period of time, each data block contains the complete response data. In principle, averaging is not required. In some cases, the coherence function can be used to estimate the influence of external noise and guide the selection of the number of signal averages (see Appendix A). bzxz.net
8 Control of excitation
To obtain appropriate frequency resolution, it is necessary to control the excitation time, and to obtain appropriate dynamic range, it is usually necessary to control the excitation amplitude.
8.1 Time required for sinusoidal excitation
Whether sweeping or stepped sine excitation is used, the rate of change of the excitation frequency (or step size and rate) should be controlled to obtain the required frequency resolution. In order to accurately determine the amplitude and phase and obtain correct information for calculating the natural frequency and structural damping, a high resolution is required in the resonant and antiresonant regions of the structure. Table 1.1 Discrete Stepped Sine Excitation
When step-sine excitation is applied, the excitation frequency closest to each resonant frequency of the structure will not differ from the resonant frequency of that order by more than half the frequency step increment. Thus, the maximum error in determining the resonant frequency is 1/2 of the frequency increment. In addition, the amplitude of the measured structural peak response is likely to be smaller than the true peak of the common frequency. The upper bound of the error is given in the table. Errors in measuring the peak of the structural response can lead to an overestimation of the modal damping of the structure.
In the frequency range of ± 10% of the common frequency, the frequency increment should be chosen so that the amplitude of the measured peak response and the modal damping ratio differ from their true values by less than 5%.
The maximum errors in the amplitude of the motion response when measuring structural resonances using discrete step-sine excitation are shown in the table below. Ratio of step frequency increment to true half-power bandwidth of structural mode
GB 11349.2—89
Maximum error of response peak measurement
Appendix B gives the formula for determining the maximum frequency increment that meets this requirement. The duration of excitation at each frequency is also given. For frequencies other than ±10% of the resonant frequency or anti-resonant frequency, a larger frequency increment and a shorter duration can be used. 8.1.2 Slow scan sinusoidal excitation
When slow scan sinusoidal excitation is used, the frequency changes as a linear function of time or as a logarithmic function of time. The scanning rate should be selected so that the deviation between the amplitude of the structural motion response measured within ±10% of the non-vibration frequency and the true value is less than 5%. For linear scan excitation, the maximum scan rate Sm: (Hz/min) shall be: S m* < 54( Fn) 2/02 .**
For logarithmic scan excitation, the maximum scan rate sm% (oct/min) shall be S mx < 77.6fa/Q2
In the above two equations, f,
estimated resonant frequency, Hz!
-estimated quality factor of the structural mode at this resonant frequency. If the above two equations are satisfied, the measurement is essentially a steady-state measurement. 8.2 Time required for random excitation
The duration of applying the excitation and measuring the response shall be long enough to average the number of spectra specified in 7.1, 2. (2)
The number of spectra to be averaged is a function of the signal-to-noise ratio of the measurement system. The coherence function between the excitation force signal and the motion response signal should be used to determine the minimum number of spectra that must be averaged to keep the random error less than 5% within a 90% confidence level (see A2). The required de-excitation time for each harmonic should be the inverse of the frequency increment of the discrete Fourier transform (see Note to 7.4.2). 8.3 Dynamic Range
The admittance amplitude range of a lightly damped structure may be greater than 105:1 (10 dB). Each data channel has a minimum voltage in addition to a maximum operating voltage. Above the maximum voltage, saturation occurs, and below the minimum voltage, circuit noise and noise associated with digitization processing in digital systems become significant compared to the signal. For accurate measurements, the excitation should be controlled so that the voltages in both channels are within specified limits. In order to obtain the appropriate dynamic range, guidance on excitation amplitude control when using different types of excitation waveforms is given in 8.3.1 and 18.3.2. 8.3.1 Sinusoidal Excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by the admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.2. Because periodic excitation produces a sequence of data blocks that are connected end to end, the transient values at the beginning are transferred to the next data block, and after a certain period of time, each data block contains the complete response data. In principle, averaging is not required. In some cases, the coherence function can be used to estimate the influence of external noise and guide the selection of the number of signal averages (see Appendix A).
8 Control of excitation
To obtain appropriate frequency resolution, it is necessary to control the excitation time, and to obtain appropriate dynamic range, it is usually necessary to control the amplitude of the excitation.
8.1 Time required for sinusoidal excitation
Whether swept or stepped sine excitation is used, the rate of change of the excitation frequency (or step size and rate) should be controlled to obtain the required frequency resolution. In order to accurately determine the amplitude and phase and obtain correct information for calculating the natural frequency and structural damping, a high resolution is required in the resonant and anti-resonant regions of the structure. Table 1.1 Discrete Stepped Sine Excitation
When step-sine excitation is applied, the excitation frequency closest to each resonant frequency of the structure will not differ from the resonant frequency of that order by more than half the frequency step increment. Thus, the maximum error in determining the resonant frequency is 1/2 of the frequency increment. In addition, the amplitude of the measured structural peak response is likely to be smaller than the true peak of the common frequency. The upper bound of the error is given in the table. Errors in measuring the peak of the structural response can lead to an overestimation of the modal damping of the structure.
In the frequency range of ± 10% of the common frequency, the frequency increment should be chosen so that the amplitude of the measured peak response and the modal damping ratio differ from their true values by less than 5%.
The maximum errors in the amplitude of the motion response when measuring structural resonances using discrete step-sine excitation are shown in the table below. Ratio of step frequency increment to true half-power bandwidth of structural mode
GB 11349.2—89
Maximum error of response peak measurement
Appendix B gives the formula for determining the maximum frequency increment that meets this requirement. The duration of excitation at each frequency is also given. For frequencies other than ±10% of the resonant frequency or anti-resonant frequency, a larger frequency increment and a shorter duration can be used. 8.1.2 Slow scan sinusoidal excitation
When slow scan sinusoidal excitation is used, the frequency changes as a linear function of time or as a logarithmic function of time. The scanning rate should be selected so that the deviation between the amplitude of the structural motion response measured within ±10% of the non-vibration frequency and the true value is less than 5%. For linear scan excitation, the maximum scan rate Sm: (Hz/min) shall be: S m* < 54( Fn) 2/02 .**
For logarithmic scan excitation, the maximum scan rate sm% (oct/min) shall be S mx < 77.6fa/Q2
In the above two equations, f,
estimated resonant frequency, Hz!
-estimated quality factor of the structural mode at this resonant frequency. If the above two equations are satisfied, the measurement is essentially a steady-state measurement. 8.2 Time required for random excitation
The duration of applying the excitation and measuring the response shall be long enough to average the number of spectra specified in 7.1, 2. (2)
The number of spectra to be averaged is a function of the signal-to-noise ratio of the measurement system. The coherence function between the excitation force signal and the motion response signal should be used to determine the minimum number of spectra that must be averaged to keep the random error less than 5% within a 90% confidence level (see A2). The required de-excitation time for each harmonic should be the inverse of the frequency increment of the discrete Fourier transform (see Note to 7.4.2). 8.3 Dynamic Range
The admittance amplitude range of a lightly damped structure may be greater than 105:1 (10 dB). Each data channel has a minimum voltage in addition to a maximum operating voltage. Above the maximum voltage, saturation occurs, and below the minimum voltage, circuit noise and noise associated with digitization processing in digital systems become significant compared to the signal. For accurate measurements, the excitation should be controlled so that the voltages in both channels are within specified limits. In order to obtain the appropriate dynamic range, guidance on excitation amplitude control when using different types of excitation waveforms is given in 8.3.1 and 18.3.2. 8.3.1 Sinusoidal Excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by the admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.2. Because periodic excitation produces a sequence of data blocks that are connected end to end, the transient values at the beginning are transferred to the next data block, and after a certain period of time, each data block contains the complete response data. In principle, averaging is not required. In some cases, the coherence function can be used to estimate the influence of external noise and guide the selection of the number of signal averages (see Appendix A).
8 Control of excitation
To obtain appropriate frequency resolution, it is necessary to control the excitation time, and to obtain appropriate dynamic range, it is usually necessary to control the amplitude of the excitation.
8.1 Time required for sinusoidal excitation
Whether swept or stepped sine excitation is used, the rate of change of the excitation frequency (or step size and rate) should be controlled to obtain the required frequency resolution. In order to accurately determine the amplitude and phase and obtain correct information for calculating the natural frequency and structural damping, a high resolution is required in the resonant and anti-resonant regions of the structure. Table 1.1 Discrete Stepped Sine Excitation
When step-sine excitation is applied, the excitation frequency closest to each resonant frequency of the structure will not differ from the resonant frequency of that order by more than half the frequency step increment. Thus, the maximum error in determining the resonant frequency is 1/2 of the frequency increment. In addition, the amplitude of the measured structural peak response is likely to be smaller than the true peak of the common frequency. The upper bound of the error is given in the table. Errors in measuring the peak of the structural response can lead to an overestimation of the modal damping of the structure.
In the frequency range of ± 10% of the common frequency, the frequency increment should be chosen so that the amplitude of the measured peak response and the modal damping ratio differ from their true values by less than 5%.
The maximum errors in the amplitude of the motion response when measuring structural resonances using discrete step-sine excitation are shown in the table below. Ratio of step frequency increment to true half-power bandwidth of structural mode
GB 11349.2—89
Maximum error of response peak measurement
Appendix B gives the formula for determining the maximum frequency increment that meets this requirement. The duration of excitation at each frequency is also given. For frequencies other than ±10% of the resonant frequency or anti-resonant frequency, a larger frequency increment and a shorter duration can be used. 8.1.2 Slow scan sinusoidal excitation
When slow scan sinusoidal excitation is used, the frequency changes as a linear function of time or as a logarithmic function of time. The scanning rate should be selected so that the deviation between the amplitude of the structural motion response measured within ±10% of the non-vibration frequency and the true value is less than 5%. For linear scan excitation, the maximum scan rate Sm: (Hz/min) shall be: S m* < 54( Fn) 2/02 .**
For logarithmic scan excitation, the maximum scan rate sm% (oct/min) shall be S mx < 77.6fa/Q2
In the above two equations, f,
estimated resonant frequency, Hz!
-estimated quality factor of the structural mode at this resonant frequency. If the above two equations are satisfied, the measurement is essentially a steady-state measurement. 8.2 Time required for random excitation
The duration of applying the excitation and measuring the response shall be long enough to average the number of spectra specified in 7.1, 2. (2)
The number of spectra to be averaged is a function of the signal-to-noise ratio of the measurement system. The coherence function between the excitation force signal and the motion response signal should be used to determine the minimum number of spectra that must be averaged to keep the random error less than 5% within a 90% confidence level (see A2). The required de-excitation time for each harmonic should be the inverse of the frequency increment of the discrete Fourier transform (see Note to 7.4.2). 8.3 Dynamic Range
The admittance amplitude range of a lightly damped structure may be greater than 105:1 (10 dB). Each data channel has a minimum voltage in addition to a maximum operating voltage. Above the maximum voltage, saturation occurs, and below the minimum voltage, circuit noise and noise associated with digitization processing in digital systems become significant compared to the signal. For accurate measurements, the excitation should be controlled so that the voltages in both channels are within specified limits. In order to obtain the appropriate dynamic range, guidance on excitation amplitude control when using different types of excitation waveforms is given in 8.3.1 and 18.3.2. 8.3.1 Sinusoidal Excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by the admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.1 Sine excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.1 Sine excitation
When constant amplitude excitation is used, the maximum dynamic range that can be obtained by admittance measurement is the dynamic range of the measurement system response signal channel (generally 300:1 or 50dB). In order to increase the achievable range, the excitation amplitude should be reduced near each resonant frequency, and the excitation amplitude should be increased near each anti-resonant frequency. Figure 5 (a) illustrates the limitations of the dynamic range that can be achieved using constant amplitude excitation. When using constant amplitude excitation, the maximum motion response value measured is less than the actual maximum motion response due to amplifier saturation when measuring the maximum motion response. Circuit noise also limits the measurement of the actual motion response of the structural anti-resonance. Figure 5 (b) illustrates that the dynamic range that can be achieved can be improved by properly controlling the excitation force amplitude.
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