GB/T 11349.3-1992 Test determination of mechanical admittance - Impact excitation method
Some standard content:
National Standard of the People's Republic of China
Experimental determination of mechanical mobilityMeasurements using impact excltationThis standard is the third of a series of national standards on the experimental determination of mechanical mobility. 1 Subject content and scope of application
GB/T 11349.3-92
This standard recommends methods for measuring mechanical admittance and other frequency response functions using pulse excitation generated by an exciter not connected to the structure, and provides basic criteria for the selection and use of measuring and analyzing instruments. This standard is applicable to the precise measurement of admittance, acceleration admittance and displacement admittance under impact excitation, and can be used for both driving point admittance measurement and transfer admittance measurement. The impact excitation method can also be used for the rough measurement of frequency response functions. The signal analysis methods involved in this standard are all based on the Fourier transform. Its scope of application is limited only by the capabilities of the instruments that implement these methods and the experience of use, and does not exclude the use of other methods currently under development. 2 Reference standards
GB2298 Mechanical vibration and shock terminology
GB10084 Grip, shock data analysis and representation methods GB113419.1 Experimental determination of mechanical admittance Basic definitions and sensors G1311349.2 Experimental determination of mechanical admittance Use an exciter to make single-point excitation measurements 3 Terminology
3.1 Driving point admittance (rj) driving point mobility Except for the support point, the other measuring points of the structure have no constraints. At this time, the frequency response function composed of the ratio of the velocity response of the point to the excitation force applied at the same point (unit m/s·N) is called the sudden motion point admittance. Note: "point" refers to "a position and a direction": "coordinate" has the same meaning as "point". 3.2 Transfer admittance (Fr) Except for the support points, there are no other constraints on the measurement points of the structure. The frequency response function composed of the ratio of the velocity response of the point to the excitation force applied (unit: m/s·N) is called transfer admittance: 3.3 Energy spectrum density Energy spectrum density The power spectrum density multiplied by the mathematical record length (unit: s) used for FFT calculation in transient signal analysis is called energy spectrum density. Note: This technical spectrum assumes that the entire transient signal is contained in the record. In order to obtain a spectrum that is related to the record length used in the finite element Rieger transform, this is necessary:
4 Characteristics of the impulse excitation method
4.1 Overview
Due to the advantages of fast speed and low cost, impulse excitation has become a common method for measuring the frequency response of structures; its measurement accuracy depends to a large extent on the characteristics of the structure under test and the test technology. In some cases, it is difficult or even impossible to obtain the same accuracy as continuous excitation with a connected shaker using impulse excitation, and this method may also increase the total measurement error. However, as long as it is used properly, it is still a very useful micro-technique. State Administration of Technical Supervision 1992 1 2 -07 approved 1993-1001 implementation
GB/T 11349.3-92
For the admittance measurement of structures with obvious nonlinearity, it is very important to keep the amplitude and direction of the excitation force unchanged. In this regard, the stopped string excitation technique is easier to control. If a hand hammer is used for impact excitation, the amplitude of each impact may vary greatly, and the direction of the excitation force is difficult to maintain, so this method has poor repeatability. In this case, it is best to use a connected shaker for stopped string or random excitation.
4.2.2 Signal-to-noise ratio problem
When measuring impulses, since the average level of the signal is lower than the peak level, the test environment noise is required to be low and the dynamic range of the measurement system is large, so it is generally not suitable to use an analog tape recorder. Since the duration of the force signal is shorter than the record length, the mean square value of the instrument electrical noise and the background noise induced by mechanical reasons is not negligible compared to the mean square value of the input force signal. This noise can be reduced by the windowing method described in Section 7.5. 4.2.3 Frequency resolution limit
The rate increment (in units of HIz) of the discrete Fourier transform (including finite bandwidth or "refined" analysis) is equal to the reciprocal of the record length (in units of 5!). Since each record represents a single impact event, the length of the record can be taken as the time required for the impulse response of the structure to decay to a level equivalent to the background noise. Therefore, the frequency resolution obtained depends not only on the response of the structure, but also on the size of the background noise. In some cases, it may be unrealistic (and unnecessary) to directly obtain the frequency resolution specified in GB11349.2 using impact excitation. If the modal density of the test structure is quite high, that is, there are multiple resonance peaks in a narrow frequency band, it may be difficult to obtain fine resolution. . In this case, it is best to use a steady-state excitation method with a sufficiently small frequency variation. However, for most applications, accurate admittance values with sufficient resolution can still be obtained at discrete frequency points. According to the inherent characteristics of the impact, its spectrum ranges from zero frequency to a certain upper frequency limit (see Chapter 5). The inability to control the excitation frequency band limits the effect of improving the frequency resolution of impact measurements by "refined" analysis. This further increases the requirements on the dynamic range of the measurement system.
4.2.4 Damping limitation
Impact excitation has limitations for testing highly damped structures. This is because the time history of the stress signal is short, which requires people to make a compromise between frequency resolution and background noise level (as described in Section 4.2.3). This limitation can also be explained by the fact that in Under an impact of a given amplitude, the average energy of the response of a heavily damped structure is lower. A heavily damped structure may require higher energy continuous excitation to balance its higher internal energy dissipation and provide sufficient response data for accurate measurement. For structures with extremely low damping, the frequency response function exhibits very sharp resonance peaks. As discussed in Section 4.2.3, this requires high-resolution refinement analysis methods to accurately determine the resonance peaks. Using an exponential window to add a known attenuation to the data can help solve this problem. If an exponential window is used, the final admittance test results must be corrected (see Section 7.5 and Appendix A (Supplement)). 4.2.5 Dependence on Operator Skill
The accuracy of admittance measurements made with a hand-held impact hammer depends on the operator maintaining correct control. The ability to accurately determine the impact location and direction. If the impact is applied carefully, these effects can usually be controlled within acceptable limits, but if the structure is small and very precise spatial positioning is required, these effects cannot be ignored.
Avoiding hammer rebound also requires the operator to have a high level of skill: see 5.4, 5 Impact Excitation
5.1 Impact Hammer
As shown in Figure 2, a typical impact hammer consists of a rigid mass block (including a replaceable mass block), a force sensor fastened to the end of the mass block, and a hammer head fastened to the other end of the force sensor. The rigidity of the head and the mass of the hammer can be selected according to 5.3 to control the width of the force pulse and avoid rebound.
For media
Replaceable hammer
GB/T 11349.3- 92
Figure 2 Typical Hand-held Impact Hammer
Replaceable Mass
Small-mass impact hammers are usually made in the form of hand hammers with replaceable hammer heads and masses. For small test structures, a suitable mechanical device may be required to keep the impact hammer excited at a specific position and direction of the structure. For large structure tests requiring higher energy, the large-mass hammer can be suspended by a cable and subjected to impact microexcitation by free fall or swing of the mass, or the smaller mass can be accelerated to a higher impact velocity by using a spring, electromagnetic magnet, air cannon or other method. The impact surface area of the hammer head should be sufficient to withstand the maximum impact force applied without causing permanent deformation of the hammer head and the test structure. On the other hand, if the impact position needs to be precisely located, the head area should be small. The velocity vector of the impact hammer at the moment of impact should be along the vertical axis of the force sensor, and its deviation should be less than 10. A slender impact hammer is easy to maintain the appropriate impact direction. 5.2 Characteristics of force pulses
An ideal pulse contains the same energy at all frequencies. However, the bandwidth of actual force pulses is limited and inversely proportional to the pulse width. This provides a method to concentrate the excitation energy below the highest frequency of interest: In fact, a typical single force pulse spectrum usually has high side lobes following the main frequency, and their amplitude decreases rapidly with increasing frequency. Figure 3 shows a force pulse and its energy spectral density. The usable frequency range of this pulse is up to 1007. In discrete Fourier transform, the time domain resolution and the time domain resolution are contradictory and need to be weighed. In order to obtain the maximum frequency resolution, the analysis frequency range is slightly higher than the maximum value of the frequency of interest. Due to the sampling relationship of discrete Fourier transform (see 7.3), the waveform is represented by only a few discrete samples in the digital record, and the waveform is deformed by the anti-aliasing filter. If the resolution is not close to the usable frequency of the pulse, the digital record is not suitable for monitoring the force waveform. Figure 4 shows a force pulse that is similar to Figure 3. However, a low-pass filter with a cutoff frequency of 1000 is performed. It can be seen that the shape and peak value of the digital force waveform shown in Figure 3 are obviously different from those in Figure 3, but their energy spectrum density is very similar,
GB/T11349.3-92
Time, 5
Unfiltered impact energy spectrum density
Figure 3 Typical force pulse and spectrum
3000,+
GB/T11349.3--92
Time, s
GB/ T11349.3—92
Energy should be checked. If necessary, the characteristic trace of the impact hammer should be adjusted to obtain the required frequency range: 5.4 Avoid impact rebound
If there are two impacts with a frequency of 1 in a data record, the Fourier transform of the pulse will cancel its frequency components at certain frequencies, resulting in some sharp calls in the force spectrum (as shown in Figure 5). Since the signal-to-noise ratio of the force spectrum is low at these frequency points, the admittance measurement results at these frequency points [:] will have large errors, which is very sensitive to the structure. Point, if a heavier hammer is used for excitation. Even if the impact is applied very carefully, rebound is sometimes inevitable. The solution to this problem is to reduce the mass of the hammer and then adjust the stiffness of the hammer head to achieve the required excitation frequency range. If the first impact is smaller than the initial impact, the force spectrum may show slight fluctuations instead of sharp depressions. Such fluctuations are usually allowed. The second impact can be easily found by checking the force spectrum of each impact position in the field or observing the unfiltered force signal with a storage oscilloscope.
It should be noted that , never use a "force window" (see 7. Lv Qin) before Fourier transformation to eliminate the second impact in the force record. When using a force window to reduce noise in the force signal, be careful not to mask the actual multiple impacts, otherwise the response will still include the impact of multiple impacts, which will lead to errors in the frequency response function estimation. 1
Time,
aDouble impact force time history
Figure 5 The impact of two impacts on the force spectrum in the force record,
6Sensor systembzxZ.net
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Dry sheep.Bz
hAssume that the impact force energy spectrum density
Continued Figure 5
6.1 Overview
The sensor system consisting of the sensor and the signal conditioner should be selected according to the criteria given in the admittance measurement standards CR11349.1 and GB11.3-19.2. For impact measurement, it is particularly important that the system has low noise and a large linear dynamic range. 6.2 Impact hammer calibration
Although the effective mass between the force sensor and the test structure has little effect on the motion response signal, it has an effect on the impact hammer force. The following system calibration should be performed at the beginning and end of each set of measurements. System calibration is basically the same as the steps described in clause i.5 of the admittance measurement standard GLt11349.2. Measure the admittance or acceleration admittance of a freely suspended, de-masted, linear calibration block. The difference between the frequency response of the calibration block measured over the frequency range of interest and the known value (e.g. the amplitude of the acceleration admittance is 1/m: where m is the total mass of the calibration block, including the mass of the sensor attached to it) should be small. When calibrating, a sensor with a known response should be used, and the calibration constant of the force signal should be adjusted to obtain the correct sequence admittance or amplitude of the acceleration admittance: other sensors to be used in the test (e.g. multi-axial sensors) should also be systematically calibrated. The configuration of the entire system and the impact key should be alternated during calibration and during use, and the mass of the calibration block should be selected so that its admittance value can adapt to the admittance range to be measured.
T Sensor Signal Processing
7.1 Filtering
Before sampling and digitizing the data with a single-leaf analyzer, the sensor system signal must be low-pass filtered in reverse order to prevent aliasing caused by erroneous mixing of out-of-band signals into the analysis frequency. Most analyzers have built-in filters whose cutoff frequencies are adapted to the frequency used before the analyzer: the effect of anti-aliasing can be checked with a high-quality signal generator. During the check, the analyzer is fed with full-scale pulses at several frequencies outside the analysis band, and then the output spectrum is checked for spurious frequency components within the analysis frequency band: the frequency used for the check should preferably be greater than or equal to the difference between the sampling frequency and the analysis frequency. GB/T 11349.3 92
Another important characteristic of the filter is the matching of the gain and phase of each channel within the passband. The matching performance of the filters and the channels of the analyzer can be checked by inputting the same broadband (random or impulse) signal into all filter channels and then measuring the "frequency response function" between each pair of channels. Its amplitude should be equal to 1 within a tolerance of ±5% and its phase difference should be equal within a tolerance of ±5% over the frequency range of interest.
In order to make full use of the dynamic range of the analyzer, a high-pass filter can be used to attenuate the signal components below the lower limit of the frequency range of interest, but care should be taken to ensure that it does not produce gain or position errors within the frequency range of interest. When using windowing (see 7.5), the "AC coupled" input mode of the analyzer can be used to eliminate the DC component of the sensor system signal. 7.2 Transient capture
The digital record of each impulse should be obtained using the transient capture mode of the analyzer so that the starting point of the data is placed near the beginning of the digital record. The digital record should include a small amount of pre-trigger data to ensure that the leading edge of the impulse is not lost, see Figure 6. If the analyzer does not have a pre-trigger function, it is best to use an external trigger for the untransmitted force signal: .3 Sampling
Each digital record used for Fourier transform processing consists of a fixed number of N points, which are equally spaced samples of the filtered analog waveform. Due to the needs of the discrete Fourier transform (DFT) algorithm, the block size N of the DFT is usually an integer power of 2. A commonly used block size is 1024. The record length is = N × 1, which is the sampling interval in seconds. The sampling frequency is 1/A, and the DFT of the record produces (N/2) + 1 complex Fourier coefficients, which represent the half-frequency from zero frequency to the sampling frequency. The frequency range (called Vyguist frequency or folding frequency) is the spectrum value at a discrete frequency point between A/-1/T (Hz). Because the filter is not ideal, in order to prevent aliasing, the filter cutoff frequency must be lower than the Nyquist frequency. The typical practice is to take the sampling frequency as 2.56 to 4.00 times the filter cutoff frequency, and the specific multiple depends on the cutoff characteristics of the filter. For a block size of 1024, DFT will produce 400 to 256 valid frequency domain "spectral lines\. 300
Pre-triggering micro data
Electromagnetic point
Time·8
Figure 6 Time history of transient auxiliary with pre-triggering When all transient data are also included in the digital record, LFT is consistent with the actual Fourier transform over the measured frequency range, that is, the discrete spectrum values of IHT are samples of the ideal continuous spectrum. When a linear structure is subjected to impulse excitation, the response signal is a sum of exponentially decaying stop signals plus background noise. In order to truncate the response signal only after it reaches the background noise level, a longer record is required. Although this improves the frequency resolution, it reduces the signal-to-noise ratio of the measurement. Using shorter records can lead to excessive truncation of the response signal and increase the oil leakage error. Therefore, it is usually best if the response signal reaches the initial amplitude at the end of the record.8 92
The record length is equal to the product of the block size and the sampling interval. The block size of a Fourier analyzer is fixed, and the sampling rate is determined by the required frequency range, so the record length cannot be controlled by changing the block size and the sampling interval. For structures with very little damping, the following two methods can be used. Before Fourier processing, a known artificial attenuation can be added to the data by using exponential density (Clause 7.5); b, the effective record length can be increased by using thinning processing without actually increasing the block size. Thinning processing can improve the frequency resolution within a reduced analysis band.
7.4 Avoiding Saturation (Clipping)
The probability of saturating the measurement system due to impulse excitation is particularly high because of the large amount of out-of-band energy that may be present in the signal. It is often necessary to use the maximum dynamic range in the test, which will make the peak of the signal very close to the saturation limit of the measurement system. As mentioned in the note to Section 5.2, the digital record used in the test may introduce waveform distortion and cannot be relied upon to check for saturation. The best way to avoid saturation is to monitor the unfiltered signal using a storage oscilloscope with a bandwidth far exceeding the signal bandwidth. If this is not possible, a Fourier analyzer can be used to sample the conductance at a rate far above the highest frequency in the data. This should be checked at each point before the admittance measurement, using a force as close to the maximum value that will be used in the test. Saturation problems do not always manifest themselves in the form of waveform clipping, and attention should be paid to the manufacturer's specifications for maximum voltage for linear operation. Saturation can be eliminated by reducing the force appropriately, reducing the gain of the signal amplifier or Fourier analyzer, or choosing a less sensitive sensor.
7.5 Windowing Techniques
7.5.1 Force Signal Windowing
Since the force signal is only a small part (generally less than 1) of the digital record used for analysis, even small noise levels can produce large errors in the force autospectrum. This is especially true when using thin or large data blocks, because noise is mixed in the force autospectrum and cannot be reduced by averaging. Before Fourier processing, random noise can be greatly reduced by multiplying the force signal record by a "force window". The force window gives a gain of 1 to the force signal portion of the record (including the filter response) and zeros the rest (see Figure 8c): this does not cause distortion as long as the force signal data is not reduced and the background noise is broadband. Figure 7 compares the energy density spectrum before and after a typical pulse windowing. It should be noted that if there are large periodic noise or DC components in the force record, the use of a force window can reduce their amplitude in the spectrum. However, the leakage caused by the truncation of the continuous noise signal during Fourier processing will cause the noise spectrum to spread over a relatively wide frequency range. Therefore, noise generated at discrete frequencies of no interest (such as zero frequency or power supply frequency) will contaminate a considerable part of the frequency range of interest after windowing. Although the use of a force window that smooths the transitions between 1 and 0 can limit the leakage to a relatively narrow frequency band, it is best to eliminate all periodic and DC noise components from the data before using the force window. This also applies to the exponential window described below. Figure 8 shows the effect of applying a rectangular force window to a force signal with a lot of noise at 6 Hz. 7.5.2 Response Signal Windowing
As mentioned in 7.3, the response signal should be attenuated to about 1 of its initial value at the end of the digital record to prevent truncation errors. A convenient way to check this is to verify that the peak response signal at the midpoint of the record is 105 of the maximum peak response. For small damping structures, this requirement is impractical because it requires the analyzer to have a large data block or a very narrow refinement bandwidth: if very fine frequency resolution is not required, a better method is to apply an exponential window to the response data before Fourier processing. The exponential window has an initial value of 1 and then decays exponentially to a final value at the end of the time record. Figure 9 shows a small damping response record and the corresponding frequency response function estimate. Figure 10 shows the same data as Figure + after using an exponential window decaying to the initial value of 5. The frequency response in Figure 9 shows the characteristics of a "leakage" error, a large phase domain change and some noise amplitude. Furthermore, the unwindowed frequency response function will underestimate the magnitude of each megasurge by an unpredictable amount that depends on the fraction of the total response that is truncated in the time domain record. It can be seen that the distortion in Figure 10 is significantly reduced, although all of the response peaks are reduced. These amplitudes can be corrected by following the procedure given in Appendix A (Supplementary). The apparent damping of each vibration mode in the windowed data is determined, and then the known damping due to the exponential density is removed. As a general rule, the response signal is digitally The record should decay naturally to 25% or less of the initial value. Otherwise, the amplitude correction will be very sensitive to any errors in the damping estimate. GB/T11349.392
Even if the time record is long enough to capture essentially all the response data, an exponential window can be used to improve the signal-to-noise ratio of the measurement. This is because it increases the weight of the high-amplitude part of the response. 7.6 Averaging Techniques
In order to improve the frequency response function estimate, the frequency domain average of several impact data at the same point can be performed. The frequency response function is obtained by dividing the average cross-spectrum of the response and force by the average auto-spectrum of the force. Spectral averaging is also required for the calculation of the coherence function (see Section 8.1): In a low-noise environment, 3 to 1 averages are usually sufficient to ensure data quality. Multiple averages can reduce the influence of uncorrelated noise in the response signal. However, if the number of averages is too large, the hammer method loses its advantage of speed. When the background noise cannot be reduced, other methods should be considered.
Note: Before each next impact, it should be confirmed that the response of the structure has decayed to the background noise level. Otherwise, any residual damping will affect the response signal immediately afterwards. For small structures or structures with small damping, the damping structure can be used to damp the response. 2
In the energy density adjustment section without using the force window
Energy density using force density
Figure 7 Effect of force separation
GB/T11349.3-92
a Force time history with long-term sound
h Energy spectrum density of the wave with the force window
Figure 8 Drain error caused by the force window1 Force Signal Windowing
Since the force signal is a small fraction of the digital record used for analysis (typically less than 1), even small noise levels can produce significant errors in the force autospectra. This is especially true when using thin or very large data blocks, since the noise is mixed in the force autoresonances and cannot be reduced by averaging. Before Fourier processing, random noise can be greatly reduced by multiplying the force signal record by a "force window". The force window gives a gain of 1 to the force signal (including the filter response) portion of the record and zeros the rest (see Figure 8c): this does not cause distortion as long as the force signal data is not reduced and the background noise is broadband. Figure 7 compares the energy spectral density before and after a typical pulse windowing. It should be noted that if there are large periodic noise or DC components in the force record, the use of a force window can reduce their amplitude in the spectrum. However, the leakage caused by the truncation of the continuous noise signal when performing F1 will cause the noise spectrum to spread over a fairly wide frequency range. Therefore, noise generated at discrete frequencies of no interest (such as zero frequency or power frequency) will contaminate a significant portion of the frequency range of interest after windowing. Although the use of a force window that smoothes the transitions between 1 and 0 can limit leakage to a relatively narrow frequency band, it is best to remove all periodic and DC noise components from the data before applying the force window. This also applies to the exponential window described below. Figure 8 shows the effect of a rectangular force window on a force signal with a lot of noise at 6 Hz. 7.5.2 Response Signal Windowing
As described in Section 7.3, the response signal should be reduced to about 1 of its initial value at the end of the digital record to prevent truncation errors. A convenient check is to verify that the peak response signal at the midpoint of the record is 105 of the maximum peak response. For lightly damped structures, this requirement is impractical because it requires the analyzer to have a large data block or a very narrow refinement bandwidth: if very fine frequency resolution is not required, a better approach is to exponentially window the response data before Fourier processing. The exponential window is initialized to 1 and then decays exponentially to a final value at the end of the time record. Figure 9 shows a small vibration response record and the corresponding frequency response function estimate. Figure 10 shows the same data as Figure + after using an exponential window that decays to an initial value of 5. The frequency response in Figure 9 exhibits the characteristics of a "leakage" error, a large phase domain change, and a certain noise amplitude. Moreover, the unwindowed frequency response function will underestimate the mode of each megasurge. The amount of underestimation is unpredictable and depends on the proportion of the total response to the particular vibration mode that is truncated in the time domain record. It can be seen that the distortion in Figure 10 is significantly reduced. Although all the response peaks are reduced, these amplitudes can be corrected according to the steps given in Appendix A (Supplement). First determine the apparent damping of each vibration mode in the windowed data, and then remove the known damping added by the exponential density. As a general rule, the vibration signal is digitally The record should decay naturally to 25% or less of the initial value. Otherwise, the amplitude correction will be very sensitive to any errors in the damping estimate. GB/T11349.392
Even if the time record is long enough to capture essentially all the response data, an exponential window can be used to improve the signal-to-noise ratio of the measurement. This is because it increases the weight of the high-amplitude part of the response. 7.6 Averaging Techniques
In order to improve the frequency response function estimate, the frequency domain average of several impact data at the same point can be performed. The frequency response function is obtained by dividing the average cross-spectrum of the response and force by the average auto-spectrum of the force. Spectral averaging is also required for the calculation of the coherence function (see Section 8.1): In a low-noise environment, 3 to 1 averages are usually sufficient to ensure data quality. Multiple averages can reduce the influence of uncorrelated noise in the response signal. However, if the number of averages is too large, the hammer method loses its advantage of speed. When the background noise cannot be reduced, other methods should be considered.
Note: Before each next impact, it should be confirmed that the response of the structure has decayed to the background noise level. Otherwise, any residual damping will affect the response signal immediately afterwards. For small structures or structures with small damping, the damping structure can be used to damp the response. 2
In the energy density adjustment section without using the force window
Energy density using force density
Figure 7 Effect of force separation
GB/T11349.3-92
a Force time history with long-term sound
h Energy spectrum density of the wave with the force window
Figure 8 Drain error caused by the force window1 Force Signal Windowing
Since the force signal is a small fraction of the digital record used for analysis (typically less than 1), even small noise levels can produce significant errors in the force autospectra. This is especially true when using thin or very large data blocks, since the noise is mixed in the force autoresonances and cannot be reduced by averaging. Before Fourier processing, random noise can be greatly reduced by multiplying the force signal record by a "force window". The force window gives a gain of 1 to the force signal (including the filter response) portion of the record and zeros the rest (see Figure 8c): this does not cause distortion as long as the force signal data is not reduced and the background noise is broadband. Figure 7 compares the energy spectral density before and after a typical pulse windowing. It should be noted that if there are large periodic noise or DC components in the force record, the use of a force window can reduce their amplitude in the spectrum. However, the leakage caused by the truncation of the continuous noise signal when performing F1 will cause the noise spectrum to spread over a fairly wide frequency range. Therefore, noise generated at discrete frequencies of no interest (such as zero frequency or power frequency) will contaminate a significant portion of the frequency range of interest after windowing. Although the use of a force window that smoothes the transitions between 1 and 0 can limit leakage to a relatively narrow frequency band, it is best to remove all periodic and DC noise components from the data before applying the force window. This also applies to the exponential window described below. Figure 8 shows the effect of a rectangular force window on a force signal with a lot of noise at 6 Hz. 7.5.2 Response Signal Windowing
As described in Section 7.3, the response signal should be reduced to about 1 of its initial value at the end of the digital record to prevent truncation errors. A convenient check is to verify that the peak response signal at the midpoint of the record is 105 of the maximum peak response. For lightly damped structures, this requirement is impractical because it requires the analyzer to have a large data block or a very narrow refinement bandwidth: if very fine frequency resolution is not required, a better approach is to exponentially window the response data before Fourier processing. The exponential window is initialized to 1 and then decays exponentially to a final value at the end of the time record. Figure 9 shows a small vibration response record and the corresponding frequency response function estimate. Figure 10 shows the same data as Figure + after using an exponential window that decays to an initial value of 5. The frequency response in Figure 9 exhibits the characteristics of a "leakage" error, a large phase domain change, and a certain noise amplitude. Moreover, the unwindowed frequency response function will underestimate the mode of each megasurge. The amount of underestimation is unpredictable and depends on the proportion of the total response to the particular vibration mode that is truncated in the time domain record. It can be seen that the distortion in Figure 10 is significantly reduced. Although all the response peaks are reduced, these amplitudes can be corrected according to the steps given in Appendix A (Supplement). First determine the apparent damping of each vibration mode in the windowed data, and then remove the known damping added by the exponential density. As a general rule, the vibration signal is digitally The record should decay naturally to 25% or less of the initial value. Otherwise, the amplitude correction will be very sensitive to any errors in the damping estimate. GB/T11349.392
Even if the time record is long enough to capture essentially all the response data, an exponential window can be used to improve the signal-to-noise ratio of the measurement. This is because it increases the weight of the high-amplitude part of the response. 7.6 Averaging Techniques
In order to improve the frequency response function estimate, the frequency domain average of several impact data at the same point can be performed. The frequency response function is obtained by dividing the average cross-spectrum of the response and force by the average auto-spectrum of the force. Spectral averaging is also required for the calculation of the coherence function (see Section 8.1): In a low-noise environment, 3 to 1 averages are usually sufficient to ensure data quality. Multiple averages can reduce the influence of uncorrelated noise in the response signal. However, if the number of averages is too large, the hammer method loses its advantage of speed. When the background noise cannot be reduced, other methods should be considered.
Note: Before each next impact, it should be confirmed that the response of the structure has decayed to the background noise level. Otherwise, any residual damping will affect the response signal immediately afterwards. For small structures or structures with small damping, the damping structure can be used to damp the response. 2
In the energy density adjustment section without using the force window
Energy density using force density
Figure 7 Effect of force separation
GB/T11349.3-92
a Force time history with long-term sound
h Energy spectrum density of the wave with the force window
Figure 8 Drain error caused by the force window
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