CN110765560A - Mechanical mechanism vibration prediction method based on time-varying damping - Google Patents
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Abstract
The invention relates to a time-varying damping-based mechanical mechanism vibration prediction method, and belongs to the field of mechanical vibration. According to the invention, a damping model with a damping coefficient as a variable is established through a wavelet transform theory, the change rule of the system model in the motion process can be accurately predicted through simulation analysis, and the damping model and the dynamic parameters at the corresponding moment can be obtained. The method solves the problem that the conventional method cannot accurately acquire the change rule of the damping parameters along with time, and provides a theoretical method for the analysis and prediction of the dynamic motion condition.
Description
Technical Field
The invention relates to a time-varying damping-based mechanical mechanism vibration prediction method, and belongs to the field of mechanical vibration.
Background
In the fields of mechanical engineering and aerospace, mechanical structure systems are developing in the direction of complexity and precision. When the engineering structure operates, factors such as clearance, temperature and load can generate influences of different degrees on the engineering mechanical structure, and the vibration characteristic of the structure changes along with the change of time, working conditions and the like. Under the operation state, the accurate prediction of the vibration characteristics of the mechanical system and the response estimation become technical difficulties which are needed to be solved at present. The method is used for accurately predicting the dynamic characteristics of the system changing along with time by constructing a time-varying system, and the dynamic response plays a crucial role in the development and development of mechanical structures.
The conventional method of predicting the vibration characteristics of the time-varying system mechanism by the time-invariant system is not suitable. Therefore, a great deal of research and analysis is carried out on a time-varying system by a plurality of scholars, the most common method is to independently separate input signals and output signals of the mechanical system into small sections, and the system in each section is assumed to be unchanged, so that the small sections are converted into the traditional time-invariant system to be analyzed, and further the problem of the time-varying system is solved.
Disclosure of Invention
The invention aims to solve the problem that vibration caused by nonlinear factors such as gaps cannot be accurately predicted in the fields of mechanical engineering and aerospace. In the field of aerospace, as the size of a spacecraft is larger and larger, the structure is more and more complex, and parts distributed on the spacecraft are more and more, such as a spacecraft space manipulator and a solar cell array (a cell panel).
The main mechanical part of the spacecraft space manipulator and the solar cell array (cell panel) is a multi-body system which consists of a joint, a manipulator rod and the like and operates in a space environment, the joint is the core part of the space manipulator and is used for completing tasks such as power transmission, position sensing, mechanical connection and the like, the multi-body system plays an important role in the mechanical arm dynamic characteristics, accurately and comprehensively understanding the dynamic characteristics of the joint, is the key for correctly analyzing and simulating the space motion characteristics of the manipulator system, and establishes an accurate mechanical arm dynamic model and predicts vibration, thereby being the basic application of the design, analysis and control of the mechanical arm system.
The invention provides a time-varying damping dynamic model building method based on wavelet transformation; the method establishes a damping model with a damping coefficient as a variable through a wavelet transform theory, can accurately predict the change rule of a system model in the motion process through simulation analysis, and can obtain the damping model and dynamic parameters at corresponding moments. The method solves the problem that the conventional method cannot accurately obtain the change rule of the damping parameters along with the time, and provides a theoretical method for the analysis and prediction of the dynamic motion condition. In the fields of mechanical engineering and aerospace, the method effectively solves the problem that the nonlinear vibration of a mechanical structure cannot be accurately predicted due to factors such as gaps, provides a theoretical basis for the design of the mechanical structure, and provides an accurate and reliable prediction method for the vibration prediction of the mechanical structure.
The purpose of the invention is realized by the following technical scheme.
The time-varying damping dynamics model building method based on wavelet transformation comprises the following steps:
step one, acquiring time-varying damping based on wavelet transformation and wavelet ridge
And determining a system mass matrix [ M ] and a rigidity matrix [ K ] of the mechanical structure according to the design parameters of the space manipulator. And selecting a measurement point to determine an output response. Performing wavelet transformation on the obtained output signals through MATLAB software, and solving the instantaneous amplitude A (t) of the output response of the mechanical system according to the wavelet transformation: the output signals comprise speed, acceleration and displacement signals;
establishing a relation between wavelet ridges and instantaneous amplitude of signal frequency, when the change rate of amplitude is far less than that of signal phase, signal xa(t) the expression form is written as follows:
xa(t)＝x(t)+jH[x(t)](1)
wherein:
x (t): the original signal.
j: plural form
H [ x (t) ]: hilbert transform of the original signal.
In order to determine the relation between wavelet coefficient and instantaneous frequency and amplitude, MATLAB is used to perform wavelet transform on the analytic signal to obtain wavelet coefficient W (a, t).
Because the shape of Morlet wavelet is close to the vibration response of dynamic system, it can better reflect the feature of vibration signal when selecting it as wavelet base function when identifying modal parameter.
When the central frequency ω of the wavelet is known0Wavelet transformation parameters
Obtaining a wavelet parameter a which meets the wavelet parameter a (t) corresponding to the time t:
the continuous wavelet transform amplitude values in response to x (t) are mainly concentrated on wavelet ridges, the amplitude values on the wavelet ridges are called skeletons, and instantaneous amplitude values A (t) can be obtained by using the skeletons and wavelet coefficients W (a (t),
instantaneous frequency of response ω0(t) can be obtained by the following formula:
wherein:
ω0- -center frequency of wavelet
ar(t) - - -wavelet ridge.
And step two, obtaining an instantaneous damping ratio ξ (t) according to the instantaneous amplitude and the instantaneous frequency.
Only the case of free vibration is considered here, so let f (t) be 0, the system mass matrix [ M ] and the stiffness matrix [ K ]. The damping matrix C is unknown, the response x can be expressed as,
x(t)＝A(t)cos(φ(t)) (6)
the amplitude A (t) and phase A (t) of the response are given by:
A(t)＝eξ(t)ω(t)t， (7)
in which ξ (t) -instantaneous damping ratio
From the above formula, one can obtain:
InA(t)＝-ξ(t)ω(t)t (9)
thus, the instantaneous damping ratio ξ (t) can be estimated by:
step three: establishing a time-varying damping model
The mass and stiffness of the mechanical structure are not time varying, whereby the time varying damping coefficients α, β of the system are expressed as:
α＝2(t)ξ(t) (11)
the damping ratio ξ (t) varies with time, and the time-varying damping coefficients α, β parametric functions are expressed as the instantaneous frequency ω (t), and the damping function c (t) is expressed as:
C(t)＝α[M]+β[K](13)
carrying out arrangement to obtain:
thereby obtaining a damping model which changes along with time, and the constructed time-varying damping model can be further expressed as:
according to the method, a time-varying damping model is obtained based on wavelet transformation, damping parameters at any moment are obtained according to actual output response of a mechanical structure with gaps in aerospace, a time-varying dynamic equation of the mechanical structure is constructed, the actual vibration condition of the mechanical structure is predicted, and the motion precision of the mechanical structure is improved. The method solves the problem that the conventional traditional method cannot accurately acquire the change rule of the damping parameters along with the time. A theoretical method is provided for analysis and prediction of dynamic motion conditions.
Advantageous effects
According to the invention, a time-varying damping model with a damping coefficient as a variable is established through a wavelet transformation theory, the damping model and the dynamic parameters corresponding to each moment can be accurately obtained through simulation analysis, the change rule of vibration in the motion process of a system model is predicted through a constructed dynamic equation, the motion precision of a mechanical mechanism is improved through the obtained change rule, and a theoretical basis is provided for the analysis and design of the mechanical motion condition.
Drawings
FIG. 1 is a diagram of signals output by a spacecraft space manipulator;
FIG. 2 is a graph comparing vibration response of spacecraft space manipulator test and vibration error of finite element simulation;
FIG. 3 is a graph comparing the vibration response of a solar array test and the vibration error of finite element simulation.
Detailed Description
The invention will be further illustrated with reference to the following examples and drawings:
example 1
In the field of aerospace, a mechanical part of a spacecraft space manipulator comprises a joint, a mechanical arm rod and other structural components to form a multi-body system which operates in a space environment, and a core component of the space manipulator is a joint component, so that the core component plays an important role in the operation of the whole space manipulator due to the functions of transmitting power, linking a mechanism, sensing the position and the like. The accurate damping model for predicting the link part has important significance for describing the motion characteristics of the mechanical arm and designing the structure. The invention takes a space manipulator as an example for theoretical verification. The correctness of the time-varying damping model is verified through comparison of simulation and test.
The time-varying damping system model establishing method based on wavelet transformation comprises the following specific steps:
the method comprises the following steps:
1. first, in the embodiment, the system mass matrix M and the degree matrix K of the machine are known. The output response is measured at the end of the structure, and other points may be selected. The output signal is selected to be a displacement signal as shown in fig. 1.
2. And carrying out noise reduction preprocessing on the output response signal in MATLAB.
3. Wavelet transformation is carried out on the obtained output response signal by utilizing a wavelet transformation tool box in MATLAB, and the instantaneous amplitude value is solved according to the wavelet transformation
The instantaneous frequency of the response ω (t) can be obtained by:
in the formula:
ω0- -center frequency of wavelet
ar(t) - - -wavelet ridge
Step two: solving for instantaneous damping ratio
Considering only the case of free vibration, the response x (t) of the system can be expressed as:
x(t)＝A(t)cos(Φ(t)) (19)
the amplitude a (t) and phase phi (t) of the response are represented by,
A(t)＝e-ξ(t)ω(t)t(20)
amplitude A (t) and instantaneous frequency ω (t), resulting in an instantaneous damping ratio,
step three:
1. establishing a time-varying damping model
Assuming that the mass and stiffness are invariant and known over time, the time-varying damping coefficient of the system can thus be expressed as:
C(t)＝α[M]+β[K](23)
carrying out arrangement to obtain:
2. comparison of test data with simulation data
| First order | Second stage | Third order | Fourth step | Fifth step | |
| Frequency of experiment | 32.9378 | 60.0767 | 198.9873 | 292.2487 | 308.0385 |
| Finite element frequency | 32.9424 | 60.0898 | 201.4652 | 294.0576 | 308.0710 |
| Error of the measurement | 0.0139％ | 0.0218％ | 1.2299％ | 0.6151％ | 0.0106％ |
By calculating the test frequency, the finite element frequency and the system error of the space manipulator and determining the damping parameter of the system according to the wavelet transform method, the frequency of each order of the system can be obtained, and meanwhile, the frequency of each order is compared with the finite element frequency. FIG. 2 is a comparison graph of the predicted simulated vibration displacement and the test vibration displacement obtained based on the theoretical method of the present invention, and the accuracy of the prediction of the time-varying damping model can be well matched with the actual vibration displacement of the test, so as to prove the correctness of the present invention. The method effectively solves the problem that the nonlinear vibration of the mechanical structure can not be accurately predicted due to factors such as gaps, provides a theoretical basis for the design of the mechanical structure, and provides an accurate and reliable prediction method for the vibration prediction of the mechanical structure.
3. Conclusion
The accuracy of the invention is proved by comparing the vibration test and the simulation data of the space manipulator. The time-varying damping parameter model of the space manipulator constructed by the wavelet transformation theory can accurately predict the vibration change rule of the manipulator in the motion process, solves the problem that the conventional method can not accurately obtain the change rule of the damping parameter of the manipulator along with time, provides a theoretical basis for the vibration analysis and design of mechanical motion, and provides a theoretical method for the analysis and prediction of the dynamic motion condition.
Example 2
In the field of aerospace, a spacecraft solar cell array is used as an energy storage device to provide an energy source for the whole spacecraft. The position and attitude of the battery array during the expansion process is critical to the overall device, and one of the main factors affecting the position and attitude is the gap between the links. The damping model of the accurate prediction link part has important significance for the motion characteristic description and the structure design of the battery panel. The invention takes a solar cell array as an example to carry out theoretical verification. The correctness of the time-varying damping model is verified through comparison of simulation and test.
The time-varying damping system model establishing method based on wavelet transformation comprises the following specific steps:
1. according to the mechanical structure parameters in the embodiment, a system quality matrix M and a degree matrix K of the battery array are determined. And measuring output responses on each of the panel models, the positions being selected to approximate the distal edge positions therebetween.
2. And carrying out noise reduction preprocessing on the output response signal in MATLAB.
3. Obtaining output response signals, carrying out wavelet transformation on the obtained signals based on a wavelet transformation theory, and obtaining instantaneous amplitude A (t) of output response and instantaneous frequency omega (t) of response through a wavelet tool box
In the formula:
ω0- -center frequency of wavelet
ar(t) - - -wavelet ridge
Step two: solving instantaneous damping ratio according to measured instantaneous amplitude and instantaneous frequency
4. Establishing a time-varying damping model according to an instantaneous damping ratio
Assuming that the mass and stiffness are invariant and known over time, the time-varying damping coefficient of the system can thus be expressed as:
C(t)＝α[M]+β[K](29)
carrying out arrangement to obtain:
the conclusion shown in fig. 3 was obtained by calculating the test frequency and finite element frequency and the system error for the solar cell array and based on the analysis method of the present invention. According to the method, the prediction accuracy of the time-varying damping model obtained through analysis in the graph can be well matched with the real vibration displacement of the test, the problem that the nonlinear vibration of the solar cell array structure caused by factors such as gaps cannot be accurately predicted can be effectively solved, an accurate and reliable prediction method is provided, and a theoretical basis is provided for the subsequent research of the gap damping model.
3. Conclusion
The correctness of the invention can be proved through errors of image contrast simulation and test data. Aiming at the problem that the vibration of the solar cell array caused by the gap in the stretching process cannot be predicted, a time-varying damping model is established based on the theory of wavelet transformation, the change rule of the vibration in the motion process of a system model can be accurately predicted, a theoretical basis is provided for the posture change problem in the subsequent stretching process, and a vibration prediction theoretical model is also provided.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (2)
1. The time-varying damping dynamics model building method based on wavelet transformation is characterized in that: the method comprises the following steps:
step one, acquiring time-varying damping based on wavelet transformation and wavelet ridge
And determining a system mass matrix [ M ] and a rigidity matrix [ K ] of the mechanical structure according to the design parameters of the space manipulator. And selecting a measurement point to determine an output response. Performing wavelet transformation on the obtained output signals through MATLAB software, and solving the instantaneous amplitude A (t) of the output response of the mechanical system according to the wavelet transformation: the output signals comprise speed, acceleration and displacement signals;
establishing a relation between wavelet ridges and instantaneous amplitude of signal frequency, when the change rate of amplitude is far less than that of signal phase, signal xa(t) the expression form is written as follows:
xa(t)＝x(t)+jH[x(t)](1)
wherein:
x (t): the original signal.
j: plural form
H [ x (t) ]: hilbert transform of the original signal.
In order to determine the relation between wavelet coefficient and instantaneous frequency and amplitude, MATLAB is used to perform wavelet transform on the analytic signal to obtain wavelet coefficient W (a, t).
Because the shape of Morlet wavelet is close to the vibration response of dynamic system, it can better reflect the feature of vibration signal when selecting it as wavelet base function when identifying modal parameter.
When the central frequency ω of the wavelet is known0Wavelet transformation parameters
Obtaining a wavelet parameter a which meets the wavelet parameter a (t) corresponding to the time t:
the continuous wavelet transform amplitude values in response to x (t) are mainly concentrated on wavelet ridges, the amplitude values on the wavelet ridges are called skeletons, and instantaneous amplitude values A (t) can be obtained by using the skeletons and wavelet coefficients W (a (t),
instantaneous frequency of response ω0(t) can be obtained by the following formula:
wherein:
ω0- -center frequency of wavelet
ar(t) - - -wavelet ridge.
And step two, obtaining an instantaneous damping ratio ξ (t) according to the instantaneous amplitude and the instantaneous frequency.
Only the case of free vibration is considered here, so let f (t) be 0, the system mass matrix [ M ] and the stiffness matrix [ K ]. The damping matrix C is unknown, the response x can be expressed as,
x(t)＝A(t)cos(φ(t)) (6)
the amplitude A (t) and phase A (t) of the response are given by:
A(t)＝eξ(t)ω(t)t， (7)
wherein ξ (t) is an instantaneous damping ratio
From the above formula, one can obtain:
InA(t)＝-ξ(t)ω(t)t (9)
thus, the instantaneous damping ratio ξ (t) can be estimated by:
step three: establishing a time-varying damping model
The mass and stiffness of the mechanical structure are not time varying, whereby the time varying damping coefficients α, β of the system are expressed as:
α＝2(t)ξ(t) (11)
the damping ratio ξ (t) varies with time, and the time-varying damping coefficients α, β parametric functions are expressed as the instantaneous frequency ω (t), and the damping function c (t) is expressed as:
C(t)＝α[M]+β[K](13)
carrying out arrangement to obtain:
thereby obtaining a damping model which changes along with time, and the constructed time-varying damping model can be further expressed as:
according to the time-varying damping model and the actual output response of the space manipulator in aerospace, the damping parameters at any moment are obtained, a time-varying kinetic equation of the space manipulator is constructed, the actual vibration condition of the space manipulator is predicted, and the motion precision of the manipulator is improved.
2. The wavelet transform-based time-varying damping dynamics model building method of claim 1, wherein: the wavelet transformation of the obtained output signal is realized by MATLAB software.
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| CN114117844A (en) * | 2021-11-08 | 2022-03-01 | 南京交通职业技术学院 | Active damper control method and system of nonlinear structure |
| US11996883B2 (en) | 2022-08-09 | 2024-05-28 | Ka Luen FUNG | Method and device for recovering sub-signals from composite signal of blind source |
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| US20100138107A1 (en) * | 2008-12-03 | 2010-06-03 | Gm Global Technology Operations, Inc. | Apparatus and method for regulating hybrid active damping state estimator |
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