WO2023115510A1 - 一种系统阻尼比的相位斜率确定方法 - Google Patents

一种系统阻尼比的相位斜率确定方法 Download PDF

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Publication number
WO2023115510A1
WO2023115510A1 PCT/CN2021/141079 CN2021141079W WO2023115510A1 WO 2023115510 A1 WO2023115510 A1 WO 2023115510A1 CN 2021141079 W CN2021141079 W CN 2021141079W WO 2023115510 A1 WO2023115510 A1 WO 2023115510A1
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particle
phase angle
ratio
domain interval
angle function
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PCT/CN2021/141079
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English (en)
French (fr)
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方兴
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方兴
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Priority to PCT/CN2021/141079 priority Critical patent/WO2023115510A1/zh
Publication of WO2023115510A1 publication Critical patent/WO2023115510A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table

Definitions

  • the present application relates to the technical field of dynamics, in particular to a method for determining the phase slope of a system damping ratio.
  • Q max is the dimensionless amplification ratio at the resonance point
  • Half power bandwidth method (wherein, f is the resonance frequency, and f 1 and f 2 are the frequency values corresponding to 0.707 times the resonance peak in the spectrogram and the two intersection points on the resonance curve).
  • the simpler methods are 4 and 7, which identify the damping ratio of the structure and system at resonance.
  • the damping C in the expressions of methods 1 and 2 is an item to be sought, which is almost impossible to apply in engineering.
  • the obtained damping ratio is the damping characteristic of the whole structure or system, which does not completely correspond to each dynamic characteristic parameter.
  • the purpose of the present application is to provide a method for determining the phase slope of the system damping ratio, and the present application provides a method for obtaining the damping ratio with simple calculation and higher accuracy.
  • the first aspect of the present application provides a method for determining the phase slope of the system damping ratio, including: obtaining the characteristic parameters of the vibration mechanics of the particle system; based on the characteristic parameters of the vibration mechanics of the particle system, calculating The equation of motion determines the frequency ratio of the particle system; when the frequency ratio is greater than or equal to zero and the frequency ratio is less than 1, the first definition domain interval phase angle function is determined according to the frequency ratio; when the frequency ratio is equal to 1 , determine that the phase angle function of the second domain interval is ⁇ /2; when the frequency ratio is greater than 1, determine the phase angle function of the third domain interval according to the frequency ratio; obtain the phase angle of the first domain interval function, the phase angle function of the second domain interval, and the derivative of the phase angle function of the third domain interval with respect to the frequency ratio, so as to obtain the system damping ratio through the phase slope.
  • said obtaining the vibration characteristic parameters of the particle system includes: obtaining external excitation parameters of the particle system; obtaining multi-degree-of-freedom mode shapes of the particle system.
  • said obtaining the characteristic parameters of vibration mechanics of the mass point system further includes: determining the static deflection of the mass point system and determining the initial damping ratio of the mass point system according to the external excitation parameters of the mass point system.
  • the motion equation of the mass point system after calculating the motion equation of the mass point system based on the detection data, it further includes: determining the natural frequency of the mass point system according to the vibration characteristic parameters of the mass point system.
  • the calculation of the motion equation of the particle system based on the detection data also includes: calculating the motion equation of the particle system based on the vibration characteristic parameters of the particle system; determining the excitation phase angle of the particle system according to the motion equation of the particle system and the response phase angle of the particle system to obtain the target phase angle of the particle system.
  • the derivation of the phase angle function of the first domain interval, the phase angle function of the second domain interval and the phase angle function of the third domain interval to the frequency ratio includes:
  • the target phase angle of the particle system is expressed as The frequency ratio of the particle system is expressed as ⁇
  • the initial damping ratio of the particle system is expressed as ⁇
  • the phase angle function of the first domain interval is The second domain interval phase angle function
  • the third domain interval phase angle function is The derivatives of the first domain interval phase angle function, the second domain interval phase angle function and the third domain interval phase angle function to the frequency ratio are
  • the calculation of the motion equation of the mass point system based on the characteristic parameters of the vibration mechanics of the mass point system includes: when the number of the mass point degrees of freedom is greater than 1 and the number of the mass point degrees of freedom is a certain value, obtaining the mass point Resonance or the motion data of each mass point when resonance occurs; according to the detection data and the motion data of each mass point, determine the frequency ratio of each mass point in the multi-degree-of-freedom system at different resonance frequencies.
  • the calculation of the motion equation of the particle system based on the characteristic parameters of vibration mechanics of the particle system also includes: when the number of degrees of freedom of the particle system approaches infinity, the particle system is a continuous particle system; Discretize the continuous mass point system with finite element; obtain the motion data of each mass point when the continuous mass point system resonates or resonates; determine the phase angle function of each mass point according to the detection data and the motion data of each mass point, so as to obtain System dynamics characteristics of continuous particle system;
  • the frequency ratio of the particle in the multi-degree-of-freedom system is obtained.
  • a device for determining the phase slope of the system damping ratio including:
  • the obtaining module is used to obtain the characteristic parameters of vibration mechanics of the particle system;
  • the phase angle determination module is based on the characteristic parameters of vibration mechanics of the particle system, calculates the equation of motion of the particle system, and determines the frequency ratio of the particle system; when the frequency ratio is greater than When it is equal to zero and the frequency ratio is less than 1, determine the phase angle function of the first domain interval according to the frequency ratio; when the frequency ratio is equal to 1, determine that the phase angle function of the second domain interval is ⁇ /2; when the When the frequency ratio is greater than 1, determine the third domain interval phase angle function according to the frequency ratio; the damping ratio determination module obtains the first domain interval phase angle function and the second domain interval phase angle function and the derivative of the phase angle function of the third domain interval to the frequency ratio, so as to obtain the system damping ratio through the phase slope.
  • an electronic device including: a processor, a memory, and a program or instruction stored on the memory and operable on the processor, and the program or instruction is processed by the The steps of the method for determining the phase slope of the above-mentioned system damping ratio are realized when the controller is executed.
  • a readable storage medium on which a program or instruction is stored, and when the program or instruction is executed by a processor, the method for determining the phase slope of the above-mentioned system damping ratio is realized. step.
  • the phase slope method used in this application is used to solve the resonance damping ratio, and the high-order resonance damping ratio of the structural system can be obtained.
  • the numerical consistency of the multi-measurement points is good, and the obtained results are in line with the general cognition in engineering.
  • the resonance damping ratio of the mechanism can be obtained more accurately than the existing methods, and the data values obtained from different measuring points are basically the same.
  • 1A is a schematic diagram of a structural system test of a method for determining the phase slope of a system damping ratio according to an embodiment of the present application
  • FIG. 1B is a schematic diagram of a mechanism system test 1 of a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • Fig. 1C is a schematic diagram of another test of the mechanism system according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • Fig. 2A is a schematic diagram of the transfer curve of each measuring point of the X-direction structural system test according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 2B is a schematic diagram of the phase-frequency ratio curve of the X-direction structural system test measuring point according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 3A is a schematic diagram of the transfer curve of each measuring point in the Z-direction structural system test according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 3B is a schematic diagram of the phase-frequency curve of the Z-direction structural system test measuring point according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 4A is a schematic diagram of the transfer ratio curve of the Y-direction mechanism system test point according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 4B is a schematic diagram of the transmission ratio curve of the measurement point of the Y-direction mechanism system test servo machine in the first state (servo mechanism locked) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 4C is a schematic diagram of the transmission ratio curve of the measurement point of the Y-direction mechanism system test servo machine in the second state (servo mechanism free) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • Fig. 4D is a schematic diagram of the phase frequency ratio curve of the Y-direction mechanism system test servo machine first state (servo mechanism locked) measuring point according to the phase slope determination method of a system damping ratio according to the embodiment of the present application;
  • 4E is a schematic diagram of the phase-frequency ratio curve of the measurement point of the Y-direction mechanism system test servo machine in the second state (servo mechanism free) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • Fig. 5A is a schematic diagram of the transmission ratio curve of the Z-direction mechanism system test point according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 5B is a schematic diagram of the transmission ratio curve of the measurement point of the Z-direction mechanism system test servo machine in the first state (servo mechanism locked) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • Fig. 5C is a schematic diagram of the transmission ratio curve of the measuring point of the Z-direction mechanism system test servo machine in the second state (servo mechanism free) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 5D is a schematic diagram of the phase-frequency ratio curve of the measurement point of the Z-direction mechanism system test servo machine in the first state (servo mechanism locked) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • 5E is a schematic diagram of the phase-frequency ratio curve of the measuring point of the Z-direction mechanism system test servo machine in the second state (servo mechanism free) according to a method for determining the phase slope of the system damping ratio according to an embodiment of the present application;
  • FIG. 6 is a schematic flowchart of a method for determining the phase slope of a system damping ratio according to an embodiment of the present application
  • FIG. 7 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
  • Fig. 8 is a schematic diagram of a hardware structure of an electronic device according to an embodiment of the present application.
  • FIG. 1 A schematic diagram of a layer structure according to an embodiment of the present application is shown in the accompanying drawings.
  • the figures are not drawn to scale, with certain details exaggerated and possibly omitted for clarity.
  • the shapes of the various regions and layers shown in the figure, as well as their relative sizes and positional relationships are only exemplary, and may deviate due to manufacturing tolerances or technical limitations in practice, and those skilled in the art will Regions/layers with different shapes, sizes, and relative positions can be additionally designed as needed.
  • Embodiment 1 Method for determining phase slope of system damping ratio
  • the embodiment of the present application provides a method for determining the phase slope of the system damping ratio, including: obtaining the characteristic parameters of the vibration mechanics of the particle system; calculating the equation of motion of the particle system based on the characteristic parameters of the vibration mechanics of the particle system, Determine the frequency ratio of the particle system; when the frequency ratio is greater than or equal to zero and the frequency ratio is less than 1, determine the phase angle function of the first domain interval according to the frequency ratio; when the frequency ratio is equal to 1, determine the phase angle function of the second domain interval as ⁇ /2; when the frequency ratio is greater than 1, determine the phase angle function of the third domain interval according to the frequency ratio; calculate the phase angle function of the first domain interval, the phase angle function of the second domain interval and the phase angle of the third domain interval The derivative of the function with respect to the frequency ratio to find the damping ratio of the system (at or at resonance) via the phase slope.
  • the phase slope method used in the embodiment of this application is used to solve the resonance damping ratio, and the high-order resonance damping ratio of the structural system can be obtained.
  • the numerical consistency of the multi-measurement points is good, and the obtained results are in line with the general cognition in engineering.
  • the resonance damping ratio of the mechanism can be obtained more accurately, and the data values obtained from different measuring points are basically the same.
  • the damping ratio of large structures and mechanisms at resonance is obtained by using the phase-frequency ratio curve in the frequency domain (hereinafter referred to as "phase curve").
  • phase curve a test device that obtains the damping ratio of a system or structure from phase information.
  • the test piece of the test device includes a model part and a model part support, a model cabin, a load support, a load support and The shaker excites the connection.
  • the model piece, model support, model cabin and load support have the same centerline, which is the centerline of the test piece, and a plurality of test points are distributed along the centerline on the outer surface of the test piece 6 to detect Vibration parameters.
  • the vibration test device can carry out X-direction vertical vibration test and Y-direction horizontal vibration test.
  • the model has test points 1#-7# from top to bottom. There are test point 8# and test point 9# on the model support, and test point 8# and test point 9# are respectively arranged on the upper part and the lower part of the model support.
  • the simulation chamber has test points 10# and 11#, which are respectively set at the upper and lower parts of the simulation chamber.
  • the upper end of the load support has a test point 12#. All test points are distributed along the center line, and adjacent test points correspond to the upper and lower positions of the component joints.
  • the engine nozzle is connected to the engine frame through a gimbal, which is a movable part that can rotate around two orthogonal axes. After the nozzle is connected with this, it can form a rotation around a point in space.
  • the direction of the nozzle of the nozzle is changed through the actuation of the servo mechanism.
  • the spray pipe cannot rotate freely, and at this moment the whole is in a structural form.
  • the locking state of the servo mechanism is released, the nozzle can produce a rigid body rotation around a certain point, and at this time the whole becomes a mechanism.
  • measuring point 20# is the measuring point on the engine frame (gimbal seat installation foundation), measuring point 16# ⁇ 19# is the measuring point on the nozzle (the position relationship is shown in the figure).
  • measuring point 16# ⁇ 19# is the measuring point on the nozzle (the position relationship is shown in the figure).
  • the servo is not locked and "the vibrating table is still"
  • the measuring point 20# has no displacement or acceleration response, but 16# ⁇ 19# may have displacement or acceleration.
  • This mechanism system is used for illustration. In the mechanism system, the solution method of this application is more accurate and applicable than the existing amplification factor method and half power bandwidth method.
  • the servo mechanism is unlocked, (in the Y-direction test) in the phase curve, the phase change is clearer and the different measuring points on the same nozzle are more consistent.
  • the more complex numerical fitting method in the embodiment of the present application is simplified. At the same time, it avoids the problem of wide distribution range of Q max value when using Q max solution in large structural parts; and Q max and half power bandwidth in mechanism system resonance Get the problem of low precision. This method can solve the problem of solving resonance and resonance damping ratio in most engineering practices when the amount of data in the frequency domain is sufficient.
  • the free vibration equation representing attenuation in the particle system is
  • the general solution of the motion equation representing the forced vibration under the action of sinusoidal force in the particle system is
  • static deflection Frequency ratio ⁇ ⁇ /p
  • natural frequency Damping ratio ⁇ c/c c
  • critical damping coefficient c c 2mp.
  • the particle mass is expressed as m
  • the initial damping of the particle is expressed as c
  • the stiffness of the particle is expressed as k
  • the external excitation is expressed as F 0
  • the circular frequency of the known external excitation is expressed as ⁇
  • the time of the known external excitation is expressed as t
  • the time-domain signal is Fourier-processed into a frequency-domain signal, which includes three pieces of information: amplitude, phase, and frequency.
  • the prior art utilizes the amplitude + frequency information in the frequency domain to obtain the resonance and the resonance damping ratio (that is, compare the two amplitudes to obtain the transfer ratio, and use the transfer ratio to obtain the damping ratio).
  • the damping ratio is obtained by using the phase + frequency information, and the phase ⁇ is written as a continuous explicit function of the frequency ratio ⁇ , and its derivative is obtained. The relationship with the damping ratio ⁇ .
  • obtaining the characteristic parameters of vibration mechanics of the particle system includes: obtaining external excitation parameters of the particle system; obtaining multi-degree-of-freedom mode shapes of the particle system.
  • the damping ratio can be obtained only from the response.
  • obtaining the characteristic parameters of the vibration dynamics of the mass point system further includes: determining the static deflection of the mass point system and determining the initial damping ratio of the mass point system according to the external excitation parameters of the mass point system.
  • the motion equation of the mass point system after calculating the motion equation of the mass point system based on the detection data, it further includes: determining the natural frequency of the mass point system according to the characteristic parameters of the vibration mechanics of the mass point system.
  • calculating the motion equation of the particle system based on the detection data further includes: calculating the motion equation of the particle system based on the vibration characteristic parameters of the particle system; The response phase angle of the system to obtain the target phase angle of the particle system.
  • obtaining the derivatives of the first domain interval phase angle function, the second domain interval phase angle function, and the third domain interval phase angle function with respect to the frequency ratio comprises:
  • the target phase angle of the particle system is expressed as
  • the frequency ratio of the particle system is expressed as ⁇
  • the initial damping ratio of the particle system is expressed as ⁇ .
  • y arctan(x)
  • its domain is x ⁇ R
  • the phase angle is obtained as the above formula
  • the function ⁇ ( ⁇ ) is a continuous function in its domain of definition.
  • the interval phase angle function of the first definition domain is
  • the second definition domain interval phase angle function is
  • the third domain interval phase angle function is The derivatives of the phase angle function of the first domain interval, the phase angle function of the second domain interval and the phase angle function of the third domain interval with respect to the frequency ratio are expressed as
  • calculating the equation of motion of the particle system based on the characteristic parameters of the particle system's vibration dynamics includes: when the number of degrees of freedom of the particle is greater than 1 and the number of degrees of freedom of the particle is a certain value, obtaining resonance or resonance of the particle The motion data of each mass point; according to the detection data and the motion data of each mass point, determine the frequency ratio of each mass point in the multi-degree-of-freedom system at different resonance frequencies.
  • calculating the motion equation of the particle system based on the characteristic parameters of the particle system's vibration dynamics also includes: when the number of degrees of freedom of the particle system approaches infinity, the particle system is a continuous particle system; Element discretization processing; obtain the motion data of each particle when the continuous particle system resonates or resonates; determine the phase angle function of each particle according to the detection data and the motion data of each particle, so as to obtain the system dynamics characteristics of the continuous particle system; The equation of motion of the particle in the continuous system, the frequency ratio of the particle in the multi-degree-of-freedom system is obtained.
  • Another embodiment of the present application also provides an electronic device, including: a processor, a memory, and a program or instruction stored in the memory and operable on the processor.
  • a processor a memory
  • a program or instruction stored in the memory and operable on the processor.
  • Embodiment 3 readable storage medium
  • Another embodiment of the present application also provides a readable storage medium, on which a program or instruction is stored, and when the program or instruction is executed by a processor, the steps of the above-mentioned method for determining the phase slope of the system damping ratio are implemented.
  • Equation (8-3) is the motion equation of n single degrees of freedom:
  • the first term of the above formula represents the free vibration attenuation
  • the second term is the forced vibration of the system under the action of the sinusoidal force. It can be seen from formula (10) that in the forced vibration, the amplitude of each degree of freedom of the system is different, but the phase lag angle relative to the orbiting force is consistent and the same.
  • the damping ratio of the i-th order system can be obtained from the i-th order resonance phase of any degree of freedom.
  • the damping ratio ⁇ is not greater than 0.2, and the natural frequencies of each order are not very close, there is At this time there is Then the phase of each degree of freedom can be used to obtain the damping ratio corresponding to each degree of freedom.
  • the system damping ratio is analyzed from the forced motion term, and the process does not impose requirements on the damping ratio, natural frequency and mode shape, so the relational expressions (5) and (5') are generally applicable to any damping ratio.
  • the system resonance damping ratio can be obtained through any degree of freedom (or measurement point).
  • a laboratory vibrating table is used for vibrating sinusoidal scanning environment excitation, and the excitation is carried out by the vibration environment excitation of the test piece at the "vibration table excitation" in the figure.
  • the test starts from a low frequency of 3Hz to 5Hz (the initial frequency is determined by the resonant frequency of the test piece), and the logarithmic sweep is performed at a rate of 4oct/min to 100Hz, and the vibration magnitude is about 1g.
  • the formula derivation of the above-mentioned embodiment of the present application is carried out under the sinusoidal winding force, and the benchmark of its displacement description is the displacement described by the winding force parameter, so the phase in the formula is the phase difference of two motion quantities (displacement).
  • the acceleration control is used in the test, that is, the amount of movement is controlled; the test data uses the phase difference as the acceleration phase difference:
  • Example 4 Structural system test of a method for determining the phase slope of the system damping ratio
  • phase curves As shown in Figure 1A, except for the measuring point 3#, they are arranged above and below the joint surface of each section of the test piece.
  • the frequency domain transfer curves and relative phase (rad)-frequency ratio curves (hereinafter referred to as "phase curves") of each measuring point in the test to the control point (the lower end surface of the load support) are given in the accompanying drawings, from which the transfer ratio curve can be obtained get the resonant frequency of the structural system.
  • Table 1 and Table 2 respectively list the calculation of the damping ratio of the X-direction test and the Y-direction test.
  • () in the table indicates that the data is non-resonant data, and only the data are listed); "/" indicates that there is no obvious resonance, and it is difficult to obtain the data.
  • Table 1 Calculated damping ratio of each measuring point at the test resonance frequency of the X-direction test structure system
  • the average damping value calculated from the slope of the phase curve in the X-direction test is close to and smaller than the calculation result of the transfer ratio; the calculation results of the two methods are about half of the calculation results of the half-power method.
  • the phase calculation method is smaller than the two existing calculation methods: it is about 1/4 of the transfer ratio method and 1/10 of the half power bandwidth.
  • the damping ratio calculated from the X-direction test shows that the resonance damping ratio of the whole system should be about 0.08, and the damping ratio obtained by the phase slope calculation method is less than about 10% less than the transfer ratio method; the damping ratio calculated by the half-power bandwidth point method is 0.16.
  • the overall damping ratio of the structure obtained from the phase slope is between 0.067 and 0.03, and the damping ratio calculated by the half power bandwidth is about 0.06; the result of the transfer ratio method is 0.3 to 0.15.
  • the method of the present application obtains relatively consistent values from the phase slope method of measuring points at different positions, and is roughly the same as the value obtained by an existing method; in the Y direction At the high-order resonance, the values obtained by the phase slope method are consistent with the general cognition in practice ( ⁇ 0.2).
  • the application scenario is a rocket engine test.
  • the engine is connected to the rocket through the frame, and the reaction force generated by the jet of combustion hot air through the nozzle pushes the entire rocket to fly.
  • the action of the servo mechanism acts on the nozzle to cause it to deflect, thereby changing the rocket's flight trajectory.
  • the servo mechanism can make the nozzle produce rigid body displacement and rotation, the whole engine system is a mechanism system.
  • nozzle A, nozzle B and their corresponding engines have the same structural design, and they are all connected to the frame through a servo A, a servo B and the same gimbal (which can rotate around the Y and Z axes).
  • the test was carried out under the locked state of the servo mechanism (install the fixture of the servo mechanism to prevent its servo actuating rod from moving in the direction of the rod) and the free state of the servo mechanism (remove the fixture of the servo mechanism).
  • the first-order resonance damping ratio of the nozzle of acquisition was carried out under the locked state of the servo mechanism (install the fixture of the servo mechanism to prevent its servo actuating rod from moving in the direction of the rod) and the free state of the servo mechanism (remove the fixture of the servo mechanism).
  • the test was carried out in two directions of Y and Z.
  • the attached figure shows the frequency domain transfer curve and phase curve of the measuring point (1# ⁇ 4#) on the nozzle and the measuring point (5#) on the installation foundation (frame) in the test, and the spraying ratio curve can be obtained from the transfer ratio curve.
  • the resonant frequency at the pipe (the locked state is approximately a structural system, and the free state is a mechanism system).
  • Table 3 and Table 4 show the calculation results of the damping ratio in the test.
  • the result difference ratio in the table (maximum damping ratio-minimum damping ratio)/maximum damping ratio, wherein the maximum and minimum damping ratios are the calculation results of different points on the same nozzle.
  • the transfer curve of nozzle B in the free state of the servo mechanism has an interference peak at 12.78 Hz after 12.59 Hz.
  • the half-power bandwidth method is calculated by the linear extension of the transfer ratio curve after resonance; the phase slope method is affected by the difference between the two measuring points large value phenomenon.
  • the difference in damping ratio at different positions of the same nozzle obtained by the phase slope method is less than 5%; the results obtained by the other two methods have a difference of 14% to 85%.
  • Table 4 except for the damping ratio of nozzle B in the free state of the servo mechanism, the difference in the damping ratio of different positions of the same nozzle obtained by the phase slope method in other data is less than 7%; the results obtained by the other two methods are 15% to 28%. difference.
  • both the transfer ratio and the half-power bandwidth method show that the resonance damping ratio in the free state of the servo mechanism is an order of magnitude greater than the damping ratio in the locked state of the servo mechanism.
  • the resonance damping ratios obtained by the three methods are in the same theoretical order (namely: 1 ⁇ 10 -3 order of magnitude).
  • Figure 5A according to the transmission ratio curve, it can be seen that the transmission ratio curves after resonance at different frequencies (18.54Hz, 14.94Hz) are approximately "step" type decline, so the resonance damping ratio of the different servo states should be approximately same. Comparing the data in Table 4, it can be seen that the damping ratio calculated by the phase slope corresponds well to the transmission ratio curve. It can be seen that, in a special system, the resonance damping ratio obtained by the phase slope method is more accurate.
  • Embodiment 5 A device implementing a method for determining the phase slope of the system damping ratio
  • the executing subject may be a device for determining the phase slope of the system damping ratio, or one of the devices for determining the phase slope of the system damping ratio
  • a control module for implementing a phase slope determination method for a system damping ratio is taken as an example to illustrate a device for determining the phase slope of the system damping ratio provided by the embodiment of the present application.
  • the device for determining the phase slope of the system damping ratio in the embodiment of the present application may be a device, or a component in a terminal, an integrated circuit, or a chip.
  • the device may be a mobile electronic device or a non-mobile electronic device.
  • the mobile electronic device may be a mobile phone, a tablet computer, a notebook computer, a handheld computer, a vehicle electronic device, a wearable device, an ultra-mobile personal computer (ultra-mobile personal computer, UMPC), a netbook or a personal digital assistant (personal digital assistant).
  • non-mobile electronic devices can be servers, network attached storage (Network Attached Storage, NAS), personal computer (personal computer, PC), television (television, TV), teller machine or self-service machine, etc., this application Examples are not specifically limited.
  • Network Attached Storage NAS
  • personal computer personal computer, PC
  • television television
  • teller machine or self-service machine etc.
  • a device for determining the phase slope of the system damping ratio in the embodiment of the present application may be a device with an operating system.
  • the operating system may be an Android (Android) operating system, an ios operating system, or other possible operating systems, which are not specifically limited in this embodiment of the present application.
  • the device for determining the phase slope of the damping ratio of the system provided by the embodiment of the present application can realize various processes realized by the method embodiments in FIG. 1 to FIG. 6 , and details are not repeated here to avoid repetition.
  • the embodiment of the present application further provides an electronic device 1700, including a processor 1701, a memory 1702, and programs or instructions stored in the memory 1702 and operable on the processor 1701,
  • an electronic device 1700 including a processor 1701, a memory 1702, and programs or instructions stored in the memory 1702 and operable on the processor 1701,
  • the program or instruction is executed by the processor 1701, each process in the above-mentioned embodiment of the method for determining the phase slope of the system damping ratio can be realized, and the same technical effect can be achieved. To avoid repetition, details are not repeated here.
  • the electronic equipment in this embodiment includes the above-mentioned mobile electronic equipment and non-mobile electronic equipment.
  • FIG. 8 is a schematic diagram of a hardware structure of an electronic device implementing an embodiment of the present application.
  • the electronic device 1800 includes but not limited to: an acquisition module 1801 , a phase angle determination module 1802 , a damping ratio determination module 1803 and other components.
  • the electronic device 1800 can also include a power supply (such as a battery) for supplying power to various components, and the power supply can be logically connected to the processor 1810 through the power management system, so that the management of charging, discharging, and function can be realized through the power management system. Consumption management and other functions.
  • a power supply such as a battery
  • the structure of the electronic device shown in FIG. 18 does not constitute a limitation to the electronic device.
  • the electronic device may include more or fewer components than shown in the figure, or combine certain components, or arrange different components, and details will not be repeated here. .
  • the obtaining module 1801 is used to obtain the characteristic parameters of vibration mechanics of the particle system
  • the phase angle determination module 1802 calculates the motion equation of the particle system based on the vibration characteristic parameters of the particle system, and determines the frequency ratio of the particle system; when the frequency ratio is greater than or equal to zero and the frequency ratio is less than 1, according to the The frequency ratio determines the phase angle function of the first domain interval; when the frequency ratio is equal to 1, it is determined that the phase angle function of the second domain interval is ⁇ /2; when the frequency ratio is greater than 1, it is determined according to the frequency ratio The third domain interval phase angle function;
  • the damping ratio determination module 1803 is to calculate the derivatives of the phase angle function of the first domain interval, the phase angle function of the second domain interval, and the phase angle function of the third domain interval with respect to the frequency ratio, so as to pass The phase slope is used to obtain the system damping ratio.
  • This embodiment also provides a readable storage medium, on which a program or instruction is stored.
  • a program or instruction is stored.
  • each of the above embodiments of the method for determining the phase slope of the system damping ratio can be realized. process, and can achieve the same technical effect, in order to avoid repetition, it will not be repeated here.
  • the processor is the processor in the electronic device described in the above embodiments.
  • the readable storage medium includes computer readable storage medium, such as computer read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disk, etc.
  • This embodiment further provides a chip, the chip includes a processor and a communication interface, the communication interface is coupled to the processor, and the processor is used to run programs or instructions to realize the phase of the above-mentioned system damping ratio
  • the various processes in the embodiments of the slope determination method can achieve the same technical effect, and are not repeated here to avoid repetition.
  • the chip mentioned in this embodiment may also be called a system-on-chip, a system-on-chip, a system-on-a-chip, or a system-on-a-chip, or the like.
  • the term “comprising”, “comprising” or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article or apparatus comprising a set of elements includes not only those elements, It also includes other elements not expressly listed, or elements inherent in the process, method, article, or device. Without further limitations, an element defined by the phrase “comprising a " does not preclude the presence of additional identical elements in the process, method, article, or apparatus comprising that element.
  • the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved. Functions are performed, for example, the described methods may be performed in an order different from that described, and various steps may also be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.
  • the phase slope method adopted in the present application is used to solve the resonance damping ratio, and the high-order resonance damping ratio of the structural system can be obtained, and the numerical consistency of the multi-measuring points is good, and the calculation The composite results are in line with the general cognition in engineering.
  • the resonance damping ratio of the mechanism can be obtained more accurately, and the data values obtained by measuring points at different positions are basically the same.

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Abstract

本申请提供一种系统阻尼比的相位斜率确定方法,包括：获取质点系统的振动力学特征参数；基于质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；当频率比大于等于零且频率比小于1时，根据频率比确定第一定义域区间相位角函数；当频率比等于1时，确定第二定义域区间相位角函数为π/2；当频率比大于1时，根据频率比确定第三定义域区间相位角函数；求取第一定义域区间相位角函数、第二定义域区间相位角函数和第三定义域区间相位角函数对频率比的导数，以通过相位斜率求取系统阻尼比。本申请通过相位斜率方法求解阻尼比，可以求得系统高阶谐振阻尼比，其多测点获取数值一致性较好，且求得结果符合工程中的一般认知。

Description

一种系统阻尼比的相位斜率确定方法 技术领域
本申请涉及动力学技术领域，尤其涉及一种系统阻尼比的相位斜率确定方法。
背景技术
在工程实践中，许多结构、系统都是处于振动环境，或在振动环境下工作；其损坏或失效都与其动力学特性相关。结构、系统动力学特性参数有三个量，分别为模态频率、模态振型和模态阻尼比。三个参数中，阻尼比的获取准确度最低。
对小阻尼情况有如下7中求解方法：
1)用定义计算ξ＝C/C 0(其中，ξ表示阻尼比，C代表阻尼，C_0代表)；
2)
Figure PCTCN2021141079-appb-000001
(其中，m表示质量，其中ω为结构圆频率)；
3)ξ＝η/2(其中，η为材料损耗系数)；
4)
Figure PCTCN2021141079-appb-000002
(其中，Q max为共振点处无量纲放大比)；
5)
Figure PCTCN2021141079-appb-000003
(其中，δ为无量纲的对数衰减率)；
6)
Figure PCTCN2021141079-appb-000004
(其中，E d为损耗能，W为机械能)；
7)半功率带宽法
Figure PCTCN2021141079-appb-000005
(其中，f为共振频率，f 1、f 2为频谱图中共振峰值0.707倍与共振曲线上两个交点对应的频率值)。
其中较为简单的方法是4、7，在共振时进行结构、系统的阻尼比识别。方法1、2表达式中阻尼C为待求项，工程中几乎无法应用。其他方法中，所得到的阻尼比为整个结构或系统的阻尼特性，不完全与其每个动力学特征参数对应。
在工程中，从结构振动响应的时域信号中识别阻尼方法也有很多，如：自相关衰减、ITD随机减量、谱曲线拟合、小波变换、最大熵估计、HHT、AR和ARMA方法等。目前实践应用中较多的是谱分析方法、基于随机减量技术的一类识别方法以及HHT方法等。(段志平,张亚.结构阻尼识别 的方法及比较[J].福州大学学报(自然科学版),2005,33(10):208-212.)上述三种方法中，对于阻尼或阻尼比的获取，均要基于频域中的响应幅值进行，只有HHT方法中引入了相位随时间变化的信息；但其首先要对数据分解为若干固有模式函数的和。由此可以看到，相位信息在结构阻尼(阻尼比)识别中没有得到广泛关注。
发明内容
(一)发明目的
本申请的目的是提供一种系统阻尼比的相位斜率确定方法，本申请提供一种计算简单且精度更高的获取阻尼比的方式。
(二)技术方案
为解决上述问题，本申请的第一方面，提供了一种系统阻尼比的相位斜率确定方法,包括：获取质点系统的振动力学特征参数；基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；当所述频率比大于等于零且所述频率比小于1时，根据所述频率比确定第一定义域区间相位角函数；当所述频率比等于1时，确定第二定义域区间相位角函数为π/2；当所述频率比大于1时，根据所述频率比确定第三定义域区间相位角函数；求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数，以通过相位斜率求取系统阻尼比。
其中，所述获取质点系统的振动力学特征参数包括：获取质点系统的外激励参数；获取质点系统的多自由度振型。
其中，所述获取质点系统的振动力学特征参数还包括：根据所述质点系统的外激励参数，确定质点系统的静挠度和确定质点系统的初始阻尼比。
其中，在基于所述检测数据计算质点系统的运动方程之后，还包括：根据所述质点系统的振动力学特征参数，确定所述质点的固有频率。
其中，所述基于所述检测数据计算质点系统的运动方程还包括：基于所述质点系统的振动力学特征参数，计算质点系统的运动方程；根据质点系统的运动方程，确定质点系统的激励相位角和质点系统的响应相位角，以得到质点系统的目标相位角。
其中，所述求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数，包括：
Figure PCTCN2021141079-appb-000006
Figure PCTCN2021141079-appb-000007
其中，质点系统的目标相位角表示为
Figure PCTCN2021141079-appb-000008
质点系统的频率比表示为γ，质点系统的初始阻尼比表示为ξ，所述第一定义域区间相位角函数为
Figure PCTCN2021141079-appb-000009
所述第二定义域区间相位角函数为
Figure PCTCN2021141079-appb-000010
所述第三定义域区间相位角函数为
Figure PCTCN2021141079-appb-000011
所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数为
Figure PCTCN2021141079-appb-000012
其中，所述基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，包括：当所述质点自由度的数量大于1且所述质点自由度的数量为确定一数值时，获取质点发生谐振或共振时各质点的运动数据；根据所述检测数据和所述各质点的运动数据，确定多自由度系统中各质点在不同谐振频率下的频率比。
其中，所述基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，还包括：当所述质点自由度的数量趋近于无穷时，所述质点系统为连续质点系统；对所述连续质点系统进行有限元离散化处理；获取连续质点系统发生谐振或共振时各质点的运动数据；根据所述检测数据和所述各质点的运动数据，确定各质点的相位角函数，以获取连续质点系统的系统动力学特性；
根据所述连续系统中质点的运动方程，得到多自由度系统中质点的频率比。
根据申请的第二方面，提供一种系统阻尼比的相位斜率确定装置,包括：
获取模块，用于获取质点系统的振动力学特征参数；相位角确定模块，基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；当所述频率比大于等于零且所述频率比小于1时，根据所述频率比确定第一定义域区间相位角函数；当所述频率比等于1时，确定第二定义域区间相位角函数为π/2；当所述频率比大于1时，根据所述频率比确定第三定义域区间相位角函数；阻尼比确定模块，求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数，以通过相位斜率求取系统阻尼比。
根据本申请的第三方面，提供一种电子设备，包括：处理器，存储器及存储在所述存储器上并可在所述处理器上运行的程序或指令，所述程序或指令被所述处理器执行时实现上述的系统阻尼比的相位斜率确定方法的步骤。
根据本申请的第四方面，提供一种可读存储介质，所述可读存储介质上存储程序或指令，所述程序或指令被处理器执行时实现上述的系统阻尼比的相位斜率确定方法的步骤。
(三)有益效果
本申请中采用的相位斜率方法求解谐振阻尼比，可以求得结构系统高阶谐振阻尼比，其多测点获取数值一致性较好，且求得结果符合工程中的一般认知。在机构系统中，可以比现有方法更为准确地求得机构谐振阻尼比，并且不同位置测点获取数据值基本相同。
附图说明
图1A是根据本申请实施例一种系统阻尼比的相位斜率确定方法的结构系统试验示意图；
图1B是根据本申请实施例一种系统阻尼比的相位斜率确定方法的机构系统试验一的示意图；
图1C是根据本申请实施例一种系统阻尼比的相位斜率确定方法的机构系统另一试验的示意图；
图2A是根据本申请实施例一种系统阻尼比的相位斜率确定方法的X向结构系统试验各测点传递曲线的示意图；
图2B是根据本申请实施例一种系统阻尼比的相位斜率确定方法的X向结构系统试验测点相位频率比曲线的示意图；
图3A是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向结构系统试验各测点传递曲线的示意图；
图3B是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向结构系统试验测点相位频率曲线的示意图；
图4A是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Y向机构系统试验测点传递比曲线的示意图；
图4B是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Y向机构系统试验伺服机第一状态(伺服机构锁止)测点传递比曲线的示意图；
图4C是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Y向机构系统试验伺服机第二状态(伺服机构自由)测点传递比曲线的示意图；
图4D是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Y向机构系统试验伺服机第 一状态(伺服机构锁止)测点相位频率比曲线的示意图；
图4E是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Y向机构系统试验伺服机第二状态(伺服机构自由)测点相位频率比曲线的示意图；
图5A是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向机构系统试验测点传递比曲线的示意图；
图5B是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向机构系统试验伺服机第一状态(伺服机构锁止)测点传递比曲线的示意图；
图5C是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向机构系统试验伺服机第二状态(伺服机构自由)测点传递比曲线的示意图；
图5D是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向机构系统试验伺服机第一状态(伺服机构锁止)测点相位频率比曲线的示意图；
图5E是根据本申请实施例一种系统阻尼比的相位斜率确定方法的Z向机构系统试验伺服机第二状态(伺服机构自由)测点相位频率比曲线的示意图；
图6是根据本申请实施例一种系统阻尼比的相位斜率确定方法的流程示意图；
图7是根据本申请实施例一种电子设备的结构示意图；
图8是根据本申请实施例一种电子设备的硬件结构示意图。
具体实施方式
为使本申请的目的、技术方案和优点更加清楚明了，下面结合具体实施方式并参照附图，对本申请进一步详细说明。应该理解，这些描述只是示例性的，而并非要限制本申请的范围。此外，在以下说明中，省略了对公知结构和技术的描述，以避免不必要地混淆本申请的概念。
在附图中示出了根据本申请实施例的层结构示意图。这些图并非是按比例绘制的，其中为了清楚的目的，放大了某些细节，并且可能省略了某些细节。图中所示出的各种区域、层的形状以及它们之间的相对大小、位置关系仅是示例性的，实际中可能由于制造公差或技术限制而有所偏差，并且本领域技术人员根据实际所需可以另外设计具有不同形状、大小、相对位置的区域/层。
显然，所描述的实施例是本申请一部分实施例，而不是全部的实施例。基于本申请中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本申请保护的范围。
此外，下面所描述的本申请不同实施方式中所涉及的技术特征只要彼此之间未构成冲突就可以相互结合。
以下将参照附图更详细地描述本申请。在各个附图中，相同的元件采用类似的附图标记来表示。为了清楚起见，附图中的各个部分没有按比例绘制。
实施例1：系统阻尼比的相位斜率确定方法
如图6所示，本申请实施例提供了一种系统阻尼比的相位斜率确定方法,包括：获取质点系统的振动力学特征参数；基于质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；当频率比大于等于零且频率比小于1时，根据频率比确定第一定义域区间相位角函数；当频率比等于1时，确定第二定义域区间相位角函数为π/2；当频率比大于1时，根据频率比确定第三定义域区间相位角函数；求取第一定义域区间相位角函数、第二定义域区间相位角函数和第三定义域区间相位角函数对频率比的导数，以通过相位斜率求取系统(谐振或共振时)阻尼比。本申请实施例中采用的相位斜率方法求解谐振阻尼比，可以求得结构系统高阶谐振阻尼比，其多测点获取数值一致性较好，且求得结果符合工程中的一般认知。在机构系统中，可以较为准确地求得机构谐振阻尼比，并且不同位置测点获取数据值基本相同。
在一相关实施例中，对于工程中常用的阻尼识别方法
Figure PCTCN2021141079-appb-000013
来说，在结构系统高阶共振或谐振频率下，结构响应放大比Q max值分布的范围较广，进而从多个测点求出的阻尼比ξ差异较大。因此在动力学参数识别中，大型结构的高阶模态阻尼比求解准确性大幅降低。在机构系统谐振时，曲线形态与教科书中的标准共振曲线存在很大差异，导致Q max值以及半功率带宽
Figure PCTCN2021141079-appb-000014
很难准确获得。
如图1A、1B和1C所示，在本申请一实施例中，通过利用频域中的相位频率比曲线(以下简称“相位曲线”)求取大型结构、机构谐振时阻尼比。如图1A所示，一种从相位信息中获取系统或结构阻尼比的试验装置,试验装置的试验件包括模型件以及模型件下方依次设置的模型件支架、模型舱、载荷支架,载荷支架和振动台激励连接。模型件、模型支架、模型舱和载荷支架具有相同的中心线,该中心线即为所述试验件的中心线,且在试验件6外表面上沿所述中心线分布多个测试点以检测振动参数。振动试验装置能够进行X向竖直振动试验,也能够进行Y向水平振动试验。模型件自上向下具有测试点1#-7#。模型支架上具有测试点8#和测试点9#，测试点8#和测试点9#分别设置于模型支架的上部和下部。模拟仓具有测试点10#和11#，测试点10#和11#分别设置于模拟仓的上部和下部。载荷支架上端具有测试点12#。所有测试点均沿所述中心线分布，相邻测点对应为部件对接面上、下位置。
如图1B和1C所示，发动机喷管通过常平座与发动机机架连接，常平座为可绕两个正交轴的活动部件。喷管与此连接后，可形成绕空间一点的转动。实际飞行中，通过伺服机构的作动，改 变喷管喷口的方向。当伺服机构被锁止后，喷管无法自由转动，此时整体为一结构形式。当解除伺服机构的锁止状态，喷管可产生绕某一点的刚体转动，此时整体变为一机构。各测点关系可由图示得知：测点20#为发动机机架上测点(常平座安装基础)，测点16#～19#为喷管上测点(位置关系如图示)。当伺服非锁止状态且“振动台静止不动”时，测点20#无位移或加速度响应，而16#～19#可存在位移或加速度。本机构系统用于说明，在机构系统中，本申请的求解方法比现有的放大系数法、半功率带宽法更为准确且适用。当伺服机构解除锁止时，(Y向试验中)在相位曲线中，相位变化更为清晰且同一喷管上不同测点较为一致。现有方法需应用传递比曲线，传递曲线在谐振处无特征明显的响应峰。(Z向试验中)由传递比、半功率带宽法求得不同状态阻尼比存在明显差异；而相位曲线在谐振处的变化，却很好的重合，由此判断对于机构系统，采用传递函数曲线求取阻尼比存在一定的不适用。
本申请实施例较复杂的数值拟合方法简单化。同时避免了，大型结构件中采用Q max求解时Q max值分布范围较宽的困扰；以及在机构系统谐振中Q max、半功率带宽
Figure PCTCN2021141079-appb-000015
获取精度不高的问题。该方法在频域数据量足够的情况下，可解决多数工程实践中对谐振、共振阻尼比的求解问题。
在一实施例中，在有阻尼单自由度系统在正弦扰动力下的强迫振动中，质点系统中代表衰减的自由振动运动方程为
Figure PCTCN2021141079-appb-000016
质点系统中代表正弦绕力作用下的强迫振动的运动方程通解为
Figure PCTCN2021141079-appb-000017
对于强迫振动，进行参数化后有公式(1)，其中：静挠度
Figure PCTCN2021141079-appb-000018
频率比γ＝ω/p，固有频率
Figure PCTCN2021141079-appb-000019
阻尼比ξ＝c/c c，临界阻尼系数c c＝2mp。(其中，质点质量表示为m，质点的初始阻尼表示为c，质点的刚度表示为k，外激励表示为F 0，已知外激励的圆频率表示为ω，已知外激励的时间表示为t)
Figure PCTCN2021141079-appb-000020
相对于落后绕动力的相位角为
Figure PCTCN2021141079-appb-000021
其中，
φ＝φ 激励力-φ 响应     (3)
在一些实施例中，时域信号进行傅里叶处理为频域信号后，包含幅值、相位、频率三个信息。现有技术利用频域中的幅值+频率信息求取谐振、共振阻尼比(即对两个幅值求比得到传递比，利用传递比求阻尼比)。本申请实施例通过利用相位+频率的信息求得阻尼比，将相位φ写成频率比γ 的连续显函数，并对其进行求导，得到了
Figure PCTCN2021141079-appb-000022
与阻尼比ξ的关系。
在一些实施例中，获取质点系统的振动力学特征参数包括：获取质点系统的外激励参数；获取质点系统的多自由度振型。当能够证明外激励F 0与频率比
Figure PCTCN2021141079-appb-000023
无关时，那么可仅由响应求取阻尼比。
在一些实施例中，获取质点系统的振动力学特征参数还包括：根据质点系统的外激励参数，确定质点系统的静挠度和确定质点系统的初始阻尼比。
在一些实施例中，在基于检测数据计算质点系统的运动方程之后，还包括：根据质点系统的振动力学特征参数，确定质点的固有频率。
在一些实施例中，基于检测数据计算质点系统的运动方程还包括：基于质点系统的振动力学特征参数，计算质点系统的运动方程；根据质点系统的运动方程，确定质点系统的激励相位角和质点系统的响应相位角，以得到质点系统的目标相位角。
在一些实施例中，求取第一定义域区间相位角函数、第二定义域区间相位角函数和第三定义域区间相位角函数对频率比的导数，包括：
Figure PCTCN2021141079-appb-000024
Figure PCTCN2021141079-appb-000025
其中，质点系统的目标相位角表示为
Figure PCTCN2021141079-appb-000026
质点系统的频率比表示为γ，质点系统的初始阻尼比表示为ξ。对于反三角函数y＝arctan(x)，其定义域为x∈R，
Figure PCTCN2021141079-appb-000027
而
Figure PCTCN2021141079-appb-000028
因此求得相位角如上式，函数φ(γ)在其定义域内为连续函数。第一定义域区间相位角函数为
Figure PCTCN2021141079-appb-000029
第二定义域区间相位角函数为
Figure PCTCN2021141079-appb-000030
第三定义域区间相位角函数为
Figure PCTCN2021141079-appb-000031
第一定义域区间相位角函数、第二定义域区间相位角函数和第三定义域区间相位角函数对频率比的导数表示为
Figure PCTCN2021141079-appb-000032
在一些实施例中，基于质点系统的振动力学特征参数，计算质点系统的运动方程，包括：当 质点自由度的数量大于1且质点自由度的数量为确定一数值时，获取质点发生谐振或共振时各质点的运动数据；根据检测数据和各质点的运动数据，确定多自由度系统中各质点在不同谐振频率下的频率比。
在一些实施例中，基于质点系统的振动力学特征参数，计算质点系统的运动方程，还包括：当质点自由度的数量趋近于无穷时，质点系统为连续质点系统；对连续质点系统进行有限元离散化处理；获取连续质点系统发生谐振或共振时各质点的运动数据；根据检测数据和各质点的运动数据，确定各质点的相位角函数，以获取连续质点系统的系统动力学特性；根据连续系统中质点的运动方程，得到多自由度系统中质点的频率比。
实施例2：电子设备
本申请另一实施例还提供一种电子设备，包括：处理器，存储器及存储在存储器上并可在处理器上运行的程序或指令，程序或指令被处理器执行时实现上述的系统阻尼比的相位斜率确定方法的步骤。
实施例3：可读存储介质
本申请的又一实施例还提供一种可读存储介质，可读存储介质上存储程序或指令，程序或指令被处理器执行时实现上述的系统阻尼比的相位斜率确定方法的步骤。
对于多自由度系统在正弦扰动力下的强迫振动中有运动方程(粗体大写代表矩阵，粗体小写代表向量)：
Figure PCTCN2021141079-appb-000033
对应无阻尼系统运动方程
Figure PCTCN2021141079-appb-000034
对于方程(7)存在n个主振型(自由度)，对第i阶主振型φ i，令
Figure PCTCN2021141079-appb-000035
将式(6)左乘
Figure PCTCN2021141079-appb-000036
并将式(8)带入有：
Figure PCTCN2021141079-appb-000037
以及
Figure PCTCN2021141079-appb-000038
再将式(8)带入有：
Figure PCTCN2021141079-appb-000039
其中
Figure PCTCN2021141079-appb-000040
分别为第i阶系统质量、系统阻尼和系统刚度。方程(8-3)为n个单自由度运动方程：
Figure PCTCN2021141079-appb-000041
其中s为第s个自由度。令
Figure PCTCN2021141079-appb-000042
则有：
Figure PCTCN2021141079-appb-000043
对于第i阶系统参数有
Figure PCTCN2021141079-appb-000044
那么对于x s有表达式：
Figure PCTCN2021141079-appb-000045
类似于单自由度正弦扰动力下的受迫振动：上式第一项为代表衰减的自由振动，第二项为系统在正弦绕力作用下的强迫振动。从式(10)中可看到，在强迫振动中，系统各自由度振幅大小不同，但相对绕动力的相位落后角一致相同。
在本实施例的多自由度系统中，各阶主振型之间不发生能量交换，因此在研究第i阶强迫振动时可只研究式(10)右端的第二项。在第i阶谐振处(或在极小的ε范围内，ε＞0，且ε→0)，类似单自由度系统，对每个自由度s有同一关系式：
Figure PCTCN2021141079-appb-000046
和
Figure PCTCN2021141079-appb-000047
从而第i阶系统阻尼比可由任一自由度的第i阶谐振相位求得。
当阻尼为比例阻尼(即C＝aM+bK)，阻尼比ξ不大于0.2，并且各阶固有频率不非常接近时，对于第s个自由度有
Figure PCTCN2021141079-appb-000048
此时有
Figure PCTCN2021141079-appb-000049
那么可利用各自由度的相位求得各自由度对应的阻尼比。
在本实施例的连续系统中，在对连续体进行有限元离散化时，s个节点即为多自由度中的s个自由度。当s→∞时，有限元离散点即成为连续体，此时式(2’)、(5’)对应为结构件第i阶共振时的运动相位关系。
在本实施例中，从强迫运动项分析出系统阻尼比，其过程未对阻尼比、固有频率及其振型做要求，因此关系式(5)、(5’)对任意阻尼比普遍适用。在多自由度系统(或连续系统)中，可通过任一自由度(或测量点)求得系统谐振阻尼比。当能够证明外激励φ 激励力不是频率比γ的函数时，可由响应相位φ 响应求取系统谐振阻尼比，即：
Figure PCTCN2021141079-appb-000050
需要注意的是，当工程实践中谐振频率非常接近时，可能会因数据分辨率较差而产生较大偏 差。
在一些实施例中，采用试验室振动台进行振动正弦扫描环境激励，激励由图示中“振动台激励”处进行试验件的振动环境激励。试验由低频3Hz～5Hz起始(起始频率由试验件谐振频率决定)，按速率4oct/min对数扫描至100Hz，振动量级约1g。求取试验件系统谐振频率处的阻尼比，分别采用加速度传递比曲线，应用传递比(公式
Figure PCTCN2021141079-appb-000051
)和半功率带宽(公式
Figure PCTCN2021141079-appb-000052
)，以及相位斜率方法(取频率比γ＝1左右各两个数据点，求取两点间的斜率)，得到谐振阻尼比。
本申请上述实施例的公式推导是在正弦绕力下进行，其位移描述的基准为用绕动力参数描述的位移量，因此公式中的相位为两个运动量(位移)的相位差。试验中采用的为加速度控制，即控制运动量；试验数据采用相位差为加速度相位差为：
φ＝φ 激励-φ 响应(3’)
加速度相位与位移相位存在π的差异，在做减法时已消除，因此式(3’)即为理论依据中2的相位角φ。
实施例4：一种系统阻尼比的相位斜率确定方法的结构系统试验
如图1A所示，除测点3#外均布置在试验件各部段对接面上下。附图中给出试验中各测点对控制点(载荷支架下端面)的频域传递曲线和相对相位(rad)——频率比曲线(以下简称“相位曲线”)，由传递比曲线可求得结构系统的谐振频率。
如图2A-图3B所示，表1、表2分别列出X向试验、Y向试验阻尼比的计算情况。(表中“()”，表示数据为非谐振数据，仅列出数据)；“/”表示无明显谐振，难以获得数据。)
表1：X向试验结构系统试验谐振频率处各测点计算阻尼比情况
测点号 传递比方法 半功率带宽方法 相位斜率方法
1# 0.0893 0.1992 0.0712
2# 0.0877 0.2182 0.0734
3# 0.0638 0.06820 0.0719
4# 0.0708 0.1468 0.0742
5# 0.0714 0.1513 0.0793
6# 0.0721 0.1513 0.0780
7# 0.0745 0.1529 0.0780
8# 0.0826 0.1599 0.0793
9# 0.0857 0.1655 0.0807
10# 0.1038 0.1727 0.0836
11# 0.1607 0.2111 0.0885
12# (0.3785) / (0.2486)
平均 0.0875 0.1634 0.0780
标准偏差 0.0268 0.0405 0.00521
表2：Y向试验结构系统试验谐振频率处各测点计算阻尼比情况
Figure PCTCN2021141079-appb-000053
表1中，X向试验中由相位曲线斜率计算得到的阻尼平均值接近且小于传递比计算结果；两种方法计算结果均约为半功率法计算结果的一半。统计标准偏差方面，相位计算方法小于现有两种计算方法：约为传递比方法的1/4，半功率带宽的1/10。
表2中，不同谐振频率处，由相位曲线斜率和半功率法计算得到的阻尼平均数值相近，且均小于传递比方法结果一个数量级。在统计标准偏差方面，传递比方法均大于另外两种方法。
从X向试验计算得到阻尼比可知，整个系统谐振阻尼比应在0.08左右，相位斜率计算方法得出阻尼比结果小于传递比方法约10％以内；半功率带宽点方法计算阻尼比在0.16。Y向试验中，由相位斜率求得结构整体阻尼比在0.067～0.03之间，半功率带宽计算阻尼比在0.06左右；传递比方法结果则在0.3～0.15。从多测点获取的结构系统谐振阻尼比数据结果上可知，本申请的方法从不同位置测点相位斜率方法求出的数值较为一致，并与现有一种方法获取的数值大体相同；在Y向高阶谐振处，相位斜率方法求得数值上均符合实践中的一般认知(ξ＜0.2)。
在本申请一些实施例中应用场景为某火箭发动机试验。发动机通过机架连接于火箭上，通过喷管喷射出燃烧热气流产生的反作用力推动整个火箭飞行。飞行过程中，伺服机构的动作作用于喷管使其产生偏移，进而改变火箭的飞行轨迹。由于伺服机构可以使喷管产生刚体位移转动，因此整个发动机系统为一机构系统。试验中，喷管A、喷管B及其对应发动机结构设计相同，均通过一个伺服A、一个伺服B和相同的常平座(可绕Y、Z轴转动)与机架链接。试验在相同的激励环境下，进行伺服机构锁止状态(安装伺服机构夹具，阻止其伺服作动杆产生杆向运动)和伺服机构自由状态(拆除伺服机构夹具)下喷管一阶谐振阻尼比的获取。
如图4A-5E所示，试验进行Y、Z两方向试验。附图中给出试验中喷管上测点(1#～4#)对其安装基础(机架)测点(5#)的频域传递曲线和相位曲线，由传递比曲线可求得喷管处(锁止状态为近似为结构系统，自由状态为机构系统)的谐振频率。表3、表4给出试验中阻尼比计算结果。表中结果差比＝(最大阻尼比-最小阻尼比)/最大阻尼比，其中最大、最小阻尼比为同一喷管上不同点计算结果。
表3：Y向试验喷管谐振频率处各测点计算阻尼比情况
Figure PCTCN2021141079-appb-000054
Figure PCTCN2021141079-appb-000055
表4：Z向试验喷管谐振频率处各测点计算阻尼比情况
Figure PCTCN2021141079-appb-000056
注：伺服机构自由状态喷管B传递曲线在12.59Hz后的12.78Hz处有干扰峰值出现，半功率带宽法采用谐振后传递比曲线线性外延的方法计算；相位斜率法受影响出现两测点差值较大现象。
表3中，相位斜率法得到的同一喷管不同位置阻尼比差异在5％以下；另外两种方法得到的结果有14％～85％的差异。表4中，除伺服机构自由状态喷管B阻尼比外，其他数据中相位斜率法得到的同一喷管不同位置阻尼比差异在7％以下；另外两种方法得到的结果有15％～28％的差异。
对质点系统中频率为8Hz处曲线局部的放大显示：在伺服机构自由状态下，传递比曲线较难或无法找到明显谐振峰值(求取阻尼比参数时，采用局部最大值进行相应计算)；而此时相位曲线在频率比＝1附近存在一致性较好、且清晰的增大变化。此时，采用相位斜率计算阻尼比的方法明显由于其他两种方法。
表4中，传递比、半功率带宽法均显示：伺服机构自由状态谐振阻尼比要大于伺服机构锁止状态阻尼比1个数量级。在伺服锁止状态，三种方法得到的谐振阻尼比处于同一理数量级(即：1×10 -3量级)。再如图5A所示，根据传递比曲线上可知，在不同频率(18.54Hz、14.94Hz)谐振后传递比曲线均近似为“阶跃”式下降，因此其不同伺服状态的谐振阻尼比应大致相同。对比表4中数据可知，相位斜率计算出的阻尼比结果与传递比曲线情况能够较好地对应。由此看出，在特殊系统中，相位斜率方法得到的谐振阻尼比更为准确。
目前相关技术得到的阻尼比结果，差异较大，无法对相位曲线基本重合进行解释。本申请实施例中在结构系统中精度与准确性比现有方法更优，且本申请实施例能求得高阶谐振阻尼比。在机构系统中的特定环境下原有方法基本失效，而本申请实施例仍可适用。从相位曲线在频率比“1”附近变化可看到，伺服自由、锁止状态两状态相位变化曲线基本重合，与得到阻尼比相近的结果相符合。
实施例5：执行一种系统阻尼比的相位斜率确定方法的装置
需要说明的是，本申请实施例提供的一种系统阻尼比的相位斜率确定方法，执行主体可以为一种系统阻尼比的相位斜率确定装置，或者该一种系统阻尼比的相位斜率确定装置中的用于执行系统阻尼比的相位斜率确定方法的控制模块。本实施例中以一种系统阻尼比的相位斜率确定装置执行一种系统阻尼比的相位斜率确定方法为例，说明本申请实施例提供的一种系统阻尼比的相位斜率确定装置。
本申请实施例中的一种系统阻尼比的相位斜率确定装置可以是装置，也可以是终端中的部件、集成电路、或芯片。该装置可以是移动电子设备，也可以为非移动电子设备。示例性的，移动电子设备可以为手机、平板电脑、笔记本电脑、掌上电脑、车载电子设备、可穿戴设备、超级移动个人计算机(ultra-mobile personal computer，UMPC)、上网本或者个人数字助理(personal digital assistant，PDA)等，非移动电子设备可以为服务器、网络附属存储器(Network Attached Storage，NAS)、个人计算机(personal computer，PC)、电视机(television，TV)、柜员机或 者自助机等，本申请实施例不作具体限定。
本申请实施例中的一种系统阻尼比的相位斜率确定装置可以为具有操作系统的装置。该操作系统可以为安卓(Android)操作系统，可以为ios操作系统，还可以为其他可能的操作系统，本申请实施例不作具体限定。
本申请实施例提供的种系统阻尼比的相位斜率确定装置能够实现图1至图6的方法实施例实现的各个过程，为避免重复，这里不再赘述。
可选地，如图7所示，本申请实施例还提供一种电子设备1700，包括处理器1701，存储器1702，存储在存储器1702上并可在所述处理器1701上运行的程序或指令，该程序或指令被处理器1701执行时实现上述一种系统阻尼比的相位斜率确定方法实施例中的各个过程，且能达到相同的技术效果，为避免重复，这里不再赘述。
需要说明的是，本实施例中的电子设备包括上述所述的移动电子设备和非移动电子设备。
图8为实现本申请实施例的一种电子设备的硬件结构示意图。
该电子设备1800包括但不限于：获取模块1801、相位角确定模块1802和阻尼比确定模块1803等部件。
本领域技术人员可以理解，电子设备1800还可以包括给各个部件供电的电源(比如电池)，电源可以通过电源管理系统与处理器1810逻辑相连，从而通过电源管理系统实现管理充电、放电、以及功耗管理等功能。图18中示出的电子设备结构并不构成对电子设备的限定，电子设备可以包括比图示更多或更少的部件，或者组合某些部件，或者不同的部件布置，在此不再赘述。
其中，获取模块1801，用于获取质点系统的振动力学特征参数；
相位角确定模块1802，基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；当所述频率比大于等于零且所述频率比小于1时，根据所述频率比确定第一定义域区间相位角函数；当所述频率比等于1时，确定第二定义域区间相位角函数为π/2；当所述频率比大于1时，根据所述频率比确定第三定义域区间相位角函数；
阻尼比确定模块1803，求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数，以通过相位斜率求取系统阻尼比。
本实施例还提供一种可读存储介质，所述可读存储介质上存储有程序或指令，该程序或指令被处理器执行时实现上述一种系统阻尼比的相位斜率确定方法实施例的各个过程，且能达到相同的技术效果，为避免重复，这里不再赘述。
其中，所述处理器为上述实施例中所述的电子设备中的处理器。所述可读存储介质，包括计算机可读存储介质，如计算机只读存储器(Read-Only Memory，ROM)、随机存取存储器(Random  Access Memory，RAM)、磁碟或者光盘等。
本实施例另提供了一种芯片，所述芯片包括处理器和通信接口，所述通信接口和所述处理器耦合，所述处理器用于运行程序或指令，实现上述一种系统阻尼比的相位斜率确定方法实施例的各个过程，且能达到相同的技术效果，为避免重复，这里不再赘述。
应理解，本实施例提到的芯片还可以称为系统级芯片、系统芯片、芯片系统或片上系统芯片等。
需要说明的是，在本文中，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、物品或者装置不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、物品或者装置所固有的要素。在没有更多限制的情况下，由语句“包括一个……”限定的要素，并不排除在包括该要素的过程、方法、物品或者装置中还存在另外的相同要素。此外，需要指出的是，本申请实施方式中的方法和装置的范围不限按示出或讨论的顺序来执行功能，还可包括根据所涉及的功能按基本同时的方式或按相反的顺序来执行功能，例如，可以按不同于所描述的次序来执行所描述的方法，并且还可以添加、省去、或组合各种步骤。另外，参照某些示例所描述的特征可在其他示例中被组合。
通过以上的实施方式的描述，本领域的技术人员可以清楚地了解到上述实施例方法可借助软件加必需的通用硬件平台的方式来实现，当然也可以通过硬件，但很多情况下前者是更佳的实施方式。基于这样的理解，本申请的技术方案本质上或者说对现有技术做出贡献的部分可以以计算机软件产品的形式体现出来，该计算机软件产品存储在一个存储介质(如ROM/RAM、磁碟、光盘)中，包括若干指令用以使得一台终端(可以是手机，计算机，服务器，或者网络设备等)执行本申请各个实施例所述的方法。
本申请的上述技术方案具有如下有益的技术效果：本申请中采用的相位斜率方法求解谐振阻尼比，可以求得结构系统高阶谐振阻尼比，其多测点获取数值一致性较好，且求得结果复合符合工程中的一般认知。在机构中，可以较为准确地求得机构谐振阻尼比，并且不同位置测点获取数据值基本相同。
应当理解的是，本申请的上述具体实施方式仅仅用于示例性说明或解释本申请的原理，而不构成对本申请的限制。因此，在不偏离本申请的精神和范围的情况下所做的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。此外，本申请所附权利要求旨在涵盖落入所附权利要求范围和边界、或者这种范围和边界的等同形式内的全部变化和修改例。

Claims (11)

  1. 一种系统阻尼比的相位斜率确定方法,包括：
    获取质点系统的振动力学特征参数；
    基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；
    当所述频率比大于等于零且所述频率比小于1时，根据所述频率比确定第一定义域区间相位角函数；
    当所述频率比等于1时，确定第二定义域区间相位角函数为π/2；
    当所述频率比大于1时，根据所述频率比确定第三定义域区间相位角函数；
    求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数，以通过相位斜率求取系统阻尼比。
  2. 根据权利要求1所述的方法，其中，所述获取质点系统的振动力学特征参数包括：
    获取质点系统的外激励参数；
    获取质点系统的多自由度振型。
  3. 根据权利要求2所述的方法，其中，所述获取质点系统的振动力学特征参数还包括：
    根据所述质点系统的外激励参数，确定质点系统的静挠度和确定质点系统的初始阻尼比。
  4. 根据权利要求1所述的方法，其中，在基于所述检测数据计算质点系统的运动方程之后，还包括：根据所述质点系统的振动力学特征参数，确定所述质点的固有频率。
  5. 根据权利要求4所述的方法，其中，所述基于所述检测数据计算质点系统的运动方程还包括：
    基于所述质点系统的振动力学特征参数，计算质点系统的运动方程；
    根据质点系统的运动方程，确定质点系统的激励相位角和质点系统的响应相位角，以得到质点系统的目标相位角。
  6. 根据权利要求1所述的方法，其中，所述求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数，包括：
    Figure PCTCN2021141079-appb-100001
    Figure PCTCN2021141079-appb-100002
    其中，质点系统的目标相位角表示为
    Figure PCTCN2021141079-appb-100003
    质点系统的频率比表示为γ，质点系统的阻尼比表示为ξ，所述第一定义域区间相位角函数为
    Figure PCTCN2021141079-appb-100004
    所述第二定义域区间相位角函数为
    Figure PCTCN2021141079-appb-100005
    所述第三定义域区间相位角函数为
    Figure PCTCN2021141079-appb-100006
    所述第一定义域区间相位角函数、所述第二定义域区间相位角函数和所述第三定义域区间相位角函数对所述频率比的导数为
    Figure PCTCN2021141079-appb-100007
  7. 根据权利要求1所述的方法，其中，所述基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，包括：
    当所述质点自由度的数量大于1且所述质点自由度的数量为确定一数值时，获取质点发生谐振或共振时各质点的运动数据；根据所述检测数据和所述各质点的运动数据，确定多自由度系统中各质点在不同谐振频率下的频率比。
  8. 根据权利要求1所述的方法，其中，所述基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，还包括：
    当所述质点自由度的数量趋近于无穷时，所述质点系统为连续质点系统；
    对所述连续质点系统进行有限元离散化处理；
    获取连续质点系统发生谐振或共振时各质点的运动数据；
    根据所述检测数据和所述各质点的运动数据，确定各质点的相位角函数，以获取连续质点系统的系统动力学特性；
    根据所述连续系统中质点的运动方程，得到多自由度系统中质点的频率比。
  9. 一种系统阻尼比的相位斜率确定装置,包括：
    获取模块，用于获取质点系统的振动力学特征参数；
    相位角确定模块，基于所述质点系统的振动力学特征参数，计算质点系统的运动方程，确定质点系统的频率比；当所述频率比大于等于零且所述频率比小于1时，根据所述频率比确定第一定义域区间相位角函数；当所述频率比等于1时，确定第二定义域区间相位角函数为π/2；当所述频率比大于1时，根据所述频率比确定第三定义域区间相位角函数；
    阻尼比确定模块，求取所述第一定义域区间相位角函数、所述第二定义域区间相位角函数 和所述第三定义域区间相位角函数对所述频率比的导数，以通过相位斜率求取系统阻尼比。
  10. 一种电子设备，其特征在于，包括：处理器，存储器及存储在所述存储器上并可在所述处理器上运行的程序或指令，所述程序或指令被所述处理器执行时实现如权利要求1-8任一项所述的系统阻尼比的相位斜率确定方法的步骤。
  11. 一种可读存储介质，所述可读存储介质上存储程序或指令，所述程序或指令被处理器执行时实现如权利要求1-8任一项所述的系统阻尼比的相位斜率确定方法的步骤。
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