Method and device for simultaneously testing bending vibration and torsional vibration of rotating machine shaft
By simultaneous testing of the bending vibration and torsional vibration of the rotating mechanical shaft, the gear disc and eddy current sensors are used to detect the vibration signal of the shaft, which solves the problem that cannot be tested simultaneously in the prior art, and achieves low-cost, high-accuracy testing.
Patent Information
- Application Number
- CN202110269040.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-03-12
- Publication Date
- 2025-07-22
- Estimated Expiration
- 2041-03-12
AI Technical Summary
In the prior art, the detection instrument cannot achieve simultaneous testing of torsional and bending vibrations of rotating mechanical shafts, and requires the installation of their own dedicated analytical instruments, which is relatively expensive.
A rotating mechanical shaft bending vibration and torsional vibration simultaneous testing device is adopted, including a sensing part, a hardware part and a software part. The gear disc and eddy current sensor are used to detect the rotation shaft vibration signal, and the signal is processed through the signal preprocessor and the high-speed data acquisition card, and finally the signal is digitalized through data acquisition and signal analysis software.
Simultaneous testing of torsional vibration and bending vibration of rotating mechanical shaft is realized, reducing costs, and improving the accuracy of torsional vibration test through signal processing methods, alleviating the signal jitter caused by bending vibration.
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Figure CN113029322B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of rotating shaft vibration detection, and particularly to a method and device for simultaneously testing the bending vibration and torsional vibration of a rotating shaft of a rotating machine. Background Art
[0002] Torsional vibration and bending vibration have a great impact on the safe and stable operation of rotating machinery, and are the key points of unit condition monitoring. Since the rotating shaft is in a rotating state, non-contact measurement methods are mostly used for the vibration detection of the rotating shaft of rotating machinery. At present, the existing detection instruments cannot simultaneously test torsional vibration and bending vibration, and dedicated analysis instruments for each are required, resulting in a high cost. Summary of the Invention
[0003] The purpose of the present invention is to provide a method and device for simultaneously testing the bending vibration and torsional vibration of a rotating shaft of a rotating machine, aiming to solve the technical problem that the existing detection instruments cannot simultaneously test torsional vibration and bending vibration, and dedicated analysis instruments for each are required, resulting in a high cost.
[0004] To achieve the above purpose, the present invention provides a device for simultaneously testing the bending vibration and torsional vibration of a rotating shaft of a rotating machine, including a sensing part, a hardware part, and a software part. The sensing part includes a gear disk and an eddy current sensor. The gear disk is detachably connected to the rotating shaft to be measured and is located on the outer side wall of the rotating shaft to be measured. The hardware part includes a signal pre-processor and a high-speed data acquisition card. The eddy current sensor is electrically connected to the signal pre-processor and is located on the side of the gear disk. The high-speed acquisition card is electrically connected to the signal pre-processor and is used to collect the alternating voltage signal output by the eddy current sensor. The software part includes data acquisition software and signal analysis software. The data acquisition software is used to collect the alternating voltage signal, and the signal analysis software converts the alternating voltage signal input by the eddy current sensor into a digital signal.
[0005] Among them, the signal pre-processor includes a 24V DC power supply module and a signal conditioning module. The 24V DC power supply module provides the -24V DC power required for the eddy current sensor test, and the signal conditioning module adjusts the amplitude of the alternating voltage signal within ±10V to meet the requirements of the high-speed data acquisition card for the input signal amplitude.
[0006] The present invention also provides a test method using the above device for simultaneously testing the bending vibration and torsional vibration of a rotating shaft of a rotating machine, including the following steps:
[0007] Install the gear disk on the rotating shaft to be measured, install the eddy current sensor facing the gear disk along the bending vibration measurement direction, and connect the eddy current sensor to the hardware part;
[0008] Drive the gear disk to rotate by the rotating shaft to be measured, output an alternating voltage signal through the eddy current sensor, and convert it into a digital signal through the software part to obtain an original vibration signal;
[0009] Find the maximum value points from the original vibration signal to obtain the bending vibration signal, and subtract the bending vibration signal from the original vibration signal to obtain the sensor output signal without the influence of bending vibration;
[0010] Find the maximum value points from the sensor output signal again to obtain the torsional vibration angular velocity signal.
[0011] Among them, in the step of installing the gear disk on the rotating shaft to be measured, installing the eddy current sensor facing the gear disk along the bending vibration measurement direction, and connecting the eddy current sensor to the hardware part:
[0012] The sampling rate requirement of the data acquisition card is fs≥1MHz, where fs is the sampling frequency.
[0013] Among them, in the step of driving the gear disk to rotate by the rotating shaft to be measured, outputting an alternating voltage signal through the eddy current sensor, and converting it into a digital signal through the software part to obtain an original vibration signal:
[0014] When there is no bending vibration and torsional vibration of the rotating shaft, the output signal of the eddy current sensor is a set of sine signals with a constant frequency and stable signal, denoted as y(t), and can be written as:
[0015] y(t) = α·h·sin[2π·(nf)·t] (1)
[0016] In the formula, α is the sensor sensitivity, h is the tooth height of the gear disk, n is the number of teeth, f is the rotation frequency, and t is the sampling time;
[0017] When the rotating shaft has torsional vibration, the instantaneous angular velocity when the tooth top and tooth valley of the gear disk pass through the eddy current sensor is no longer a constant, and there will be fluctuations with the same frequency as the torsional vibration. Formula (1) becomes:
[0018] y(t) = α·h·sin[2π·(nf + f t )·t] (2)
[0019] In the formula, f t is the instantaneous frequency fluctuation caused by the torsional vibration of the rotating shaft;
[0020] When the rotating shaft has torsional vibration and also has bending vibration at the same time, formula (2) becomes:
[0021]
[0022] Wherein, A and f s , are respectively the amplitude, frequency and phase of the bending vibration of the rotating shaft. Since the number of teeth n of the gear disk 1 is relatively large, the bending vibration frequency f s is generally much lower than the instantaneous angular velocity frequency (nf + f t ).
[0023] Among them, in the steps of finding the maximum points from the original vibration signal to obtain the bending vibration signal, and subtracting the bending vibration signal from the original vibration signal to obtain the sensor output signal without the influence of bending vibration:
[0024] For the first time to find the maximum points, after detecting the output signal y(t) of the eddy current sensor, find the maximum points in the signal. Taking the i-th point as an example, use the 7 adjacent points before and after it for judgment. If:
[0025]
[0026] Then it is considered that the i-th point is the maximum point, and connect the maximum points to obtain the curve x(t);
[0027] The time period (t i , t i+1 ) corresponding to two maximum points is exactly the arc segment where the rotating shaft turns one tooth. Calculate the function value x(t) at time t between any two adjacent maximum points (t i , x i ) and (t i+1 , x i+1 ) by linear interpolation:
[0028]
[0029] Subtract the extracted bending vibration signal x(t) from the original signal of the eddy current sensor according to the time points to obtain the signal x1(t):
[0030] x1(t) = y(t) - x(t) (6)
[0031] Among them, in the steps of judging the maximum points by using 7 adjacent points in the original vibration signal and calculating the function value at any time between any two adjacent maximum points to form the bending vibration signal:
[0032] For the second time to find the maximum points, taking the i-th point as an example, use the 7 adjacent points before and after it for judgment. If:
[0033]
[0034] Calculate the instantaneous frequency of torsional vibration. Denote the maximum points in the signal x1(t) as z1, z2,..., zk , and the corresponding times are: t1, t2,..., t k , where k is the number of maximum points. During the time periods corresponding to adjacent points of the maximum values, the rotating shaft exactly rotates one tooth, and the rotated radian θ is the same:
[0035]
[0036] The time Δt taken to rotate through this radian is:
[0037] Δt = t i+1 - t i (9)
[0038] At different times t1, t2,..., t k-1 the instantaneous angular frequency of the rotating shaft is:
[0039]
[0040] By subtracting the rotational angular frequency from the instantaneous angular frequency of the rotating shaft , the instantaneous angular frequency of torsional vibration is obtained
[0041]
[0042] Connecting the angular frequencies of torsional vibration at different times, an instantaneous angular velocity signal of torsional vibration is obtained.
[0043] The beneficial effects of the present invention are as follows: By using this device, simultaneous testing of the torsional vibration and bending vibration of the rotating shaft can be achieved. The two types of vibration tests use the same set of sensors and instruments, resulting in lower costs; this method is also applicable to the case where the bending vibration or torsional vibration of the rotating shaft needs to be tested separately; by subtracting the influence of the bending vibration of the rotating shaft from the output signal of the eddy current sensor, the signal jitter phenomenon caused by the bending vibration of the rotating shaft to be measured can be effectively alleviated. Compared with the high-pass filtering method, the signal compensated by this method is relatively stable, and the accuracy of torsional vibration testing can be improved; the method of extracting the bending vibration and torsional vibration signals by finding the maximum points twice has a clear physical meaning and is simpler than the commonly used Hilbert transform method at present. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0045] Figure 1This is the schematic diagram of the device for simultaneously measuring the bending vibration and torsional vibration of the rotating shaft of a rotating machine in the present invention.
[0046] Figure 2 This is the structural schematic diagram of the sensing part of the device in the present invention.
[0047] Figure 3 This is the output schematic diagram of the eddy current sensor when there is no bending vibration and torsional vibration in the present invention.
[0048] Figure 4 This is the output schematic diagram of the eddy current sensor when there are bending vibration and torsional vibration in the present invention.
[0049] Figure 5 This is the output schematic diagram of the eddy current sensor when there are both torsional vibration and bending vibration in the present invention.
[0050] Figure 6 This is the schematic diagram of finding the maximum value point by using adjacent 7 points in the present invention.
[0051] Figure 7 This is the curve graph obtained by finding the maximum value point for the first time in the present invention.
[0052] Figure 8 This is the curve graph obtained by finding the maximum value point for the second time in the present invention.
[0053] Figure 9 This is the step flowchart of the test method for the device for simultaneously measuring the bending vibration and torsional vibration of the rotating shaft of a rotating machine in the present invention.
[0054] 1 - Gear disk, 2 - Eddy current sensor, 3 - Signal pre - processor, 4 - High - speed data acquisition card, 5 - Data acquisition software, 6 - Signal analysis software, 7 - 24V DC power supply module, 8 - Signal conditioning module. Detailed implementation mode
[0055] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described by referring to the drawings below are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.
[0056] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention. In addition, in the description of the present invention, the meaning of "a plurality" is two or more unless otherwise specifically defined.
[0057] Please refer to Figure 1 and Figure 2 , the present invention provides a technical solution: a device for simultaneously testing the bending vibration and torsional vibration of a rotating machine shaft, including a sensing part, a hardware part, and a software part. The sensing part includes a gear disk 1 and an eddy current sensor 2. The gear disk 1 is detachably connected to the shaft to be tested and is located on the outer side wall of the shaft to be tested. The hardware part includes a signal pre-processor 3 and a high-speed data acquisition card 4. The eddy current sensor 2 is electrically connected to the signal pre-processor 3 and is located on the side of the gear disk 1. The high-speed acquisition card is electrically connected to the signal pre-processor 3 and is used to collect the AC voltage signal output by the eddy current sensor 2. The software part includes data acquisition software 5 and signal analysis software 6. The data acquisition software 5 is used to collect the AC voltage signal, and the signal analysis software 6 converts the AC voltage signal input by the eddy current sensor 2 into a digital signal. The signal pre-processor 3 includes a 24V DC power supply module 7 and a signal conditioning module 8. The 24V DC power supply module 7 provides the -24V DC power required for the test of the eddy current sensor 2. The signal conditioning module 8 conditions the amplitude of the AC voltage signal within ±10V to meet the requirements of the high-speed data acquisition card 4 for the input signal amplitude.
[0058] In this embodiment, the gear disk 1 is driven to rotate by the shaft to be tested. The rotation characteristics of the gear disk 1 can replace the rotation characteristics of the shaft to be tested. The eddy current sensor 2 is used to detect the dynamic displacement change between the probe and the teeth on the gear disk 1 and input an AC voltage signal to the pre-processor. The 24V DC power supply module 7 provides power for the eddy current sensor 2. The signal conditioning module 8 conditions the amplitude of the AC voltage signal within ±10V and transmits it to the high-speed acquisition card. The data acquisition software 5 receives the conditioned AC voltage signal, and the signal analysis software 6 can convert the AC voltage signal input by the eddy current sensor 2 into a digital signal and display the original vibration signal as a function graph.
[0059] Please refer to Figures 3 to 9, the present invention also provides a test method using the above-mentioned test device for simultaneously measuring the bending vibration and torsional vibration of a rotating machine shaft, including the following steps:
[0060] S1: Install the gear disk 1 on the shaft to be tested, install the eddy current sensor 2 facing the gear disk 1 along the bending vibration measurement direction, and connect the eddy current sensor 2 to the hardware part;
[0061] S2: Drive the gear disk 1 to rotate by the shaft to be tested, output an AC voltage signal through the eddy current sensor 2, and convert it into a digital signal through the software part to obtain the original vibration signal;
[0062] S3: Find the maximum value point for the first time from the original vibration signal, and calculate the function value at any time between any two adjacent maximum value points through linear interpolation to form the bending vibration signal. Subtract the bending vibration signal from the original vibration signal to obtain the sensor output signal without the influence of bending vibration;
[0063] S4: Find the maximum value point for the second time from the sensor output signal, and calculate the instantaneous angular frequency between any two adjacent maximum value points to form the torsional vibration angle signal.
[0064] Among them, in step S1, on the selected test section of the shaft to be tested, install a gear disk 1 with uniform indexing, install the eddy current sensor 2 facing the gear disk 1, and the installation direction of the eddy current sensor 2 is the bending vibration direction to be tested.
[0065] In step S2, as Figure 3 shown, when the shaft has no bending vibration and torsional vibration, the output signal of the eddy current sensor 2 is a set of sine signals with a constant frequency and stable signal, denoted as y(t), and can be written as:
[0066] y(t) = α·h·sin[2π·(nf)·t] (1)
[0067] In the formula, α is the sensor sensitivity, h is the tooth height of the gear disk 1, n is the number of teeth, f is the rotation frequency, and t is the sampling time;
[0068] As Figure 4 shown, when the shaft undergoes torsional vibration, the instantaneous angular velocity when the tooth tip and tooth valley of the gear disk 1 pass through the eddy current sensor 2 is no longer a constant, and there will be fluctuations with the same frequency as the torsional vibration. Formula (1) becomes:
[0069] y(t) = α·h·sin[2π·(nf + f t )·t] (2)
[0070] In the formula, f tThe instantaneous frequency fluctuation caused by the torsional vibration of the rotating shaft;
[0071] As Figure 5 shown, when the rotating shaft undergoes torsional vibration and also undergoes bending vibration, Equation (2) becomes:
[0072]
[0073] In the formula, A, f s , are respectively the amplitude, frequency, and phase of the bending vibration of the rotating shaft. Because the number of teeth n of the gear disk 1 is relatively large, the bending vibration frequency f s is generally much lower than the instantaneous angular velocity frequency (nf + f t ).
[0074] In step S3, for the first time to find the maximum points, after detecting the output signal y(t) of the eddy current sensor 2, as Figure 6 shown, find the maximum points in the signal. Taking the i-th point as an example, use the 7 adjacent points before and after it to judge. If:
[0075]
[0076] Then it is considered that the i-th point is the maximum point. Connect the maximum points to obtain the curve x(t), as Figure 7 shown.
[0077] The time period (t i , t i+1 ) corresponding to two maximum points is exactly the arc segment where the rotating shaft turns one tooth. Calculate the function value x(t) at time t between any two adjacent maximum points (t i , x i ) and (t i+1 , x i+1 ) by the method of linear interpolation:
[0078]
[0079] It can be seen from Equation (3) that the curve x(t) reflects the bending vibration situation of the rotating shaft;
[0080] Deduct the extracted bending vibration signal x(t) from the original signal of the eddy current sensor 2 at each time point to obtain the signal x1(t):
[0081] x1(t) = y(t) - x(t) (6)
[0082] In step S4, for the second time to find the maximum points, use the same method as in step S3 to find the maximum points in the signal. Taking the i-th point as an example, use the 7 adjacent points before and after it to judge. If:
[0083]
[0084] The curve obtained by finding the maximum points for the second time is as Figure 8 shown. From Figure 8 it can be seen that the signal after deducting the influence of bending vibration by the above method is relatively stable;
[0085] Calculate the instantaneous frequency of torsional vibration. Denote the maximum points in the signal x1(t) as z1, z2,..., z k , and the corresponding time is: t1, t2,..., t k . k is the number of maximum points. During the time periods corresponding to adjacent maximum points, the rotating shaft just turns 1 tooth, and the rotated radian θ is the same:
[0086]
[0087] The time △t used to rotate this radian is:
[0088] △t = t i+1 -t i (9)
[0089] At different times t1, t2,..., t k-1 , the instantaneous angular frequency of the rotating shaft is:
[0090]
[0091] Deduct the rotational angular frequency from the instantaneous angular frequency of the rotating shaft to obtain the instantaneous angular frequency
[0092]
[0093] Connect the angular frequencies of torsional vibration at different times to obtain the instantaneous angular velocity signal of torsional vibration;
[0094] By the above calculation method, the method of deducting the influence of the bending vibration of the rotating shaft from the output signal of the eddy current sensor 2 above can effectively alleviate the signal jitter phenomenon caused by the bending vibration of the rotating shaft to be measured. Compared with the high-pass filtering method, the signal compensated by this method is relatively stable, and the accuracy of torsional vibration testing can be improved; the simultaneous testing of the torsional vibration and bending vibration of the rotating shaft is realized. The same set of sensors and instruments is used for the two types of vibration testing, and the cost is relatively low.
[0095] The above-disclosed is only a preferred embodiment of the present invention. Of course, it cannot be used to limit the scope of the rights of the present invention. Those of ordinary skill in the art can understand all or part of the processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.
Claims
1. A testing method for a testing device that simultaneously measures the bending vibration and torsional vibration of a rotating machinery shaft, characterized in that the testing device for simultaneously measuring the bending vibration and torsional vibration of the rotating machinery shaft includes a sensing part, a hardware part, and a software part. The sensing part includes a gear disk and an eddy current sensor. The gear disk is detachably connected to the shaft to be measured and is located on the outer sidewall of the shaft to be measured. The hardware part includes a signal pre-processor and a high-speed data acquisition card. The eddy current sensor is electrically connected to the signal pre-processor and is located on the side of the gear disk. The high-speed data acquisition card is electrically connected to the signal pre-processor and is used to collect the AC voltage signal output by the eddy current sensor. The software part includes data acquisition software and signal analysis software. The data acquisition software is used to collect the AC voltage signal, and the signal analysis software converts the AC voltage signal input by the eddy current sensor into a digital signal. The signal pre-processor includes a 24V DC power supply module and a signal conditioning module. The 24V DC power supply module provides the -24V DC power required for the eddy current sensor test. The signal conditioning module adjusts the amplitude of the AC voltage signal within ±10V to meet the requirements of the high-speed data acquisition card for the input signal amplitude. The testing method of the testing device for simultaneously measuring the bending vibration and torsional vibration of the rotating machinery shaft includes the following steps: Install the gear disk on the shaft to be measured, install the eddy current sensor facing the gear disk along the bending vibration measurement direction, and connect the eddy current sensor to the hardware part. Use the shaft to be measured to drive the gear disk to rotate, output an AC voltage signal through the eddy current sensor, and convert it into a digital signal through the software part to obtain the original vibration signal. Find the maximum value points from the original vibration signal to obtain the bending vibration signal, and subtract the bending vibration signal from the original vibration signal to obtain the sensor output signal without the influence of bending vibration. Find the maximum value points again from the sensor output signal to obtain the torsional vibration angular velocity signal. In the step of finding the maximum value points from the original vibration signal to obtain the bending vibration signal, and subtracting the bending vibration signal from the original vibration signal to obtain the sensor output signal without the influence of bending vibration: For the first time to find the maximum value points, after detecting the output signal y(t) of the eddy current sensor, find the maximum value points in the signal. Taking the i-th point as an example, use the 7 adjacent points before and after it for judgment. If: Then it is considered that the i-th point is the maximum value point, connect each maximum value point to obtain the curve x(t). The time periods (t i , t i+1 ) corresponding to the two maximum points are the arc segments where the inner shaft exactly rotates one tooth. By the method of linear interpolation, the function value x(t) at time t between any two adjacent maximum points (t i , x i ) and (t i+1 , x i+1 ) is calculated as follows: Subtract the extracted bending vibration signal x(t) from the original signal of the eddy current sensor according to the time point to obtain the signal x1(t): x1(t) = y(t) - x(t) (6).
2. The testing method of the testing device for simultaneously measuring the bending vibration and torsional vibration of the rotating shaft of a rotating machine according to claim 1, characterized in that In the step of installing the gear disk on the shaft to be measured, installing the eddy current sensor facing the gear disk along the bending vibration measurement direction, and connecting the eddy current sensor to the hardware part: The sampling rate requirement of the data acquisition card is fs≥1MHz, where fs is the sampling frequency.
3. The testing method of the testing device for simultaneously measuring the bending vibration and torsional vibration of the rotating shaft of a rotating machine according to claim 2, characterized in that In the step of driving the gear disk to rotate by the rotating shaft to be measured, outputting an alternating voltage signal through the eddy current sensor, and converting it into a digital signal through the software part to obtain the original vibration signal: When there is no bending vibration and torsional vibration of the rotating shaft, the output signal of the eddy current sensor is a set of sinusoidal signals with a constant frequency and stable signal, denoted as y(t), and can be written as: y(t) = α·h·sin[2π·(nf)·t] (1) In the formula, α is the sensor sensitivity, h is the tooth height of the gear disk, n is the number of teeth, f is the rotation frequency, and t is the sampling time; When torsional vibration occurs in the rotating shaft, the instantaneous angular velocity when the tooth tip and tooth valley of the gear disk pass through the eddy current sensor is no longer a constant, and fluctuations with the same frequency as the torsional vibration will appear. Formula (1) becomes: y(t) = α·h·sin[2π·(nf + f t )·t] (2) where f t is the instantaneous frequency fluctuation caused by the torsional vibration of the rotating shaft; When torsional vibration occurs in the rotating shaft and bending vibration also occurs at the same time, formula (2) becomes: In the formula, are respectively the amplitude, frequency and phase of the bending vibration of the rotating shaft. Since the number of teeth n of the gear disk 1 is relatively large, the bending vibration frequency f s is generally much lower than the instantaneous angular velocity frequency (nf + f t ).
4. The testing method of the testing device for simultaneously testing the bending vibration and torsional vibration of the rotating machine shaft according to claim 1, characterized in that, In the step of judging the maximum value points by using 7 adjacent points in the original vibration signal and calculating the function values at any time between any two adjacent maximum value points through linear interpolation to form the bending vibration signal: For the second time to find the maximum value point, taking the i-th point as an example, judge by using 7 adjacent points before and after it. If: Calculate the instantaneous frequency of torsional vibration. Denote the maximum points in the signal x1(t) as z1, z2,..., z k , and the corresponding time is: t1, t2,..., t k , where k is the number of maximum points. During the time periods corresponding to adjacent maximum points, the rotating shaft exactly rotates one tooth, and the rotated radian θ is the same: The time Δt used to turn through this radian is: Δt = t i+1 -t i (9) At different times t1, t2,..., t k-1 Instantaneous angular frequency of the lower rotating shaft is as follows: Subtract the rotational angular frequency from the instantaneous angular frequency of the rotating shaft to obtain the instantaneous angular frequency of torsional vibration Connect the torsional vibration angular frequencies at different times to obtain the torsional vibration instantaneous angular velocity signal.
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