CN110702313B - Method for high-precision identification of unbalanced excitation force of flexible rotor based on variable-speed starting - Google Patents
Method for high-precision identification of unbalanced excitation force of flexible rotor based on variable-speed starting Download PDFInfo
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Abstract
The invention provides a method for identifying unbalanced excitation force of a flexible rotor based on variable-speed starting high precision. Firstly, establishing a transient motion equation of a rotor system by adopting a transfer matrix method, and calculating by a Newmark integration method to obtain transient motion response data; then, calculating to obtain a frequency domain load spectral vector of the unbalanced excitation force of the rotor system by utilizing a method combining load identification and modal coordinate conversion; and finally, carrying out inverse Fourier transform on the spectrum vector and filtering the spectrum vector by using a specific filter to obtain the transient unbalance excitation force of the rotor. The method only utilizes the motion response data of the rotor in the process of one-time acceleration starting, has high solving efficiency, has high balancing precision of the rotor by solving the unbalanced excitation force, and can be used for transient balancing of the rotor.
Description
Technical Field
The invention belongs to the technical field of mechanical vibration, and particularly relates to a method for identifying unbalanced excitation force of a flexible rotor based on variable-speed starting high-precision.
Background
The vibration problem is a difficult problem which must be faced in the development process of the aeroengine. Excessive vibration can cause the rotor to generate larger deformation and stress, so that connection looseness, excessive bearing load, poor work and damage are caused, and a flight accident is caused in serious cases. Engine vibration is caused by a variety of causes, and research and engineering practice has shown that rotor imbalance is a major cause. These faults will also disappear once the rotor equilibrium conditions are improved by various means. Therefore, a balancing method is required to regulate the unbalance of the rotor.
Because the unbalance amount of the rotor system exists in the unbalanced excitation force, the unbalance excitation force of the rotor only needs to be calculated, and then the rotor can be balanced according to the calculated unbalance excitation force, which is a step that needs to be carried out before the rotor is put into use. The unbalance excitation force of the rotor is difficult to directly measure due to the limitation of technical and economic conditions, and no research report of actually measuring the unbalance excitation force of the rotor is found at present. Therefore, the method is an important technical problem in the field of rotor transient balance by calculating the instantaneous unbalance excitation force of the rotor by using the actually measured rotor transient motion response data and further solving the unbalance of the rotor.
Meanwhile, the existing load identification methods are all load identification processes with system input as steady-state response data, and the identification effect is good. However, for the research of multi-frequency load identification of the system input of actually measured transient response data, the problems that too many doped frequency components exist in signals, and non-dominant frequency and high-frequency signals are easy to mix, so that the identification precision of the system output response is low are caused. Therefore, how to improve the accuracy of load identification of transient response data input by a system is an important technical problem facing the field of load identification.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for identifying the unbalanced excitation force of a flexible rotor based on variable-speed starting high precision. Firstly, establishing a transient motion equation of a rotor system by adopting a transfer matrix method, and calculating by a Newmark integration method to obtain transient motion response data; then, calculating to obtain a frequency domain load spectral vector of the unbalanced excitation force of the rotor system by utilizing a method combining load identification and modal coordinate conversion; and finally, carrying out inverse Fourier transform on the spectrum vector and filtering the spectrum vector by using a specific filter to obtain the transient unbalance excitation force of the rotor.
A method for identifying unbalanced excitation force of a flexible rotor based on variable-speed starting high precision is characterized by comprising the following steps:
step 1: establishing a transient motion equation of the N-disk rotor system with normalized mass by adopting a transfer matrix method, and calculating transient motion information of the rotor system under constant angular acceleration by using a Newmark integration method, wherein the transient motion information comprises rotor transient response, a rotor Bode diagram and a modal shape; intercepting transient response data U (t) in any time period before the rotor reaches the critical rotating speed as load identification input data;
step 2: by utilizing a method combining load identification and modal coordinate conversion, calculating to obtain a frequency domain load spectral vector F (omega) of the unbalanced excitation force of the rotor system, namely:
F(ω)＝U(ω)/Φhq(ω)ΦT (1)
wherein U (ω) is the fourier transform of U (t), ω represents the frequency domain frequency; Φ is the rotor mode shape matrix, expressed as:
wherein the content of the first and second substances,
the rotor system is the r-th order modal shape, and N is the number of the rotor characteristic disks;
hq(ω) is the modal admittance matrix of the rotor system, expressed as:
hq(ω)＝diag[h1(ω),h2(ω),···,hr(ω),···,h4N(ω)] (3)
hr(ω)＝1/(ωr 2-ω2+2jωξrωr)，(r＝1,2,···,4N) (4)
wherein, ω isrAnd xirThe order r of the system is natural frequency and modal damping ratio respectively;
and step 3: performing inverse Fourier transform on the F (omega) to obtain the rotor system unbalanced excitation force F (t) with normalized mass, wherein the rotor system unbalanced excitation force F (t) is as follows:
F(t)＝M·f(t) (5)
wherein M is a mass matrix of the rotor;
then, using a cut-off frequency fmaxThe FIR filter filters the F (t) to obtain the final rotor unbalance exciting force; wherein the content of the first and second substances,
the maximum angular velocity value of the rotor for the intercepted transient response time period.
The invention has the beneficial effects that: the whole solving process only takes the transient motion response of the rotor as input, so that the solving efficiency is high; because the unbalanced excitation force of the rotor contains the unbalanced information thereof, the rotor balancing precision is high by solving the unbalanced excitation force, and the guidance can be provided for the transient balance of the rotor; the transient motion response of the rotor corresponds to a plurality of frequencies, so that the practical application of engineering can be expanded, and the unbalanced excitation force of the rotor can be monitored in real time; the FIR filter is suitable for the transient motion process of multiple frequencies, and has stable data, good digital property and high operation speed, so that the solving precision and the solving efficiency of the transient unbalanced excitation force can be greatly improved.
Drawings
FIG. 1 is a flow chart of a method for identifying the unbalanced excitation force of a flexible rotor based on variable-speed starting high precision in the invention
FIG. 2 is a diagram of a single disk cantilever rotor model according to an embodiment of the present invention
In the figure, 1-rotor feature disk; 2-rotor left end bearing; 3-rotor right end support; 4-rotor end.
FIG. 3 is a graph of rotor system x-direction transient response
FIG. 4 is a y-direction transient response diagram of a rotor system
FIG. 5 is a Bode diagram of a rotor system
FIG. 6 is a modal shape diagram of a rotor system
FIG. 7 is a graph of the x-direction transient response of a rotor system before the selection of the critical speed
FIG. 8 is a y-direction transient response diagram of a rotor system before selecting a critical speed
FIG. 9 is a Fourier transformed rotor x-direction transient response plot
FIG. 10 is a Fourier transformed rotor y-direction transient response plot
FIG. 11 is a comparison graph of the x-direction unbalanced excitation force results obtained by the method of the present invention and the real results
FIG. 12 is a comparison graph of the y-direction unbalanced excitation force results obtained by the method of the present invention and the real results
FIG. 13 is a comparison graph of the local amplification of the x-direction unbalanced excitation force result and the real result obtained by the method of the present invention
FIG. 14 is a partial enlarged comparison graph of the Y-direction unbalanced excitation force result and the real result obtained by the method of the present invention
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
As shown in fig. 1, the present invention provides a method for identifying unbalanced excitation force of a flexible rotor based on variable speed starting with high accuracy. In this embodiment, an isotropic single-disk cantilever rotor model shown in fig. 2 is used as a processing object, and the structural parameters of the rotor are shown in table 1.
TABLE 1
Step 1: the transient motion equation of the rotor system with the mass normalization is established by adopting a transfer matrix method, and the constant angular acceleration of the rotor system is calculated by a Newmark integration method to obtain 20rad/s2The transient motion information comprises the transient response of the rotor, a Bode diagram of the rotor and a mode shape, as shown in figures 3, 4, 5 and 6. Wherein the axis of abscissa of fig. 3 and 4 represents time and the axis of ordinate represents the rotor system transient response; the axis of abscissa in fig. 5 represents the rotational speed, and the axis of ordinate represents the rotor system amplitude. The critical speed of the rotor was 2960rpm and the natural frequency was 50.17 Hz.
In engineering practice, the rotor hardly reaches the critical speed due to the influence of unbalance, and the system has a stabilizing process in the initial starting process, so the transient response data in a certain time period before the rotor reaches the critical speed is intercepted as load identification input data, and for the embodiment, the transient response data U (t) before the rotor is critical (3s-10s) is intercepted, as shown in fig. 7 and 8. The angular speed of the rotor system during this period is 60rad/s to 200 rad/s.
Step 2: by utilizing a method combining load identification and modal coordinate conversion, calculating to obtain a rotor system frequency domain load spectral vector F (omega), namely:
F(ω)＝U(ω)/Φhq(ω)ΦT (6)
wherein U (ω) is the fourier transform of U (t), ω represents the frequency domain frequency; Φ is the rotor mode shape matrix, expressed as:
wherein the content of the first and second substances,
the mode shape of the r-th order of the rotor system is, N is the number of characteristic disks of the rotor, and the embodiment is an isotropic single-disk cantilever rotor system, so that N is 1, and the main mode shapes of all orders in phi are the same;
hq(ω) is the modal admittance matrix of the rotor system, expressed as:
hq(ω)＝diag[h1(ω),h2(ω),···,hr(ω),···,h4N(ω)] (8)
hr(ω)＝1/(ωr 2-ω2+2jωξrωr)，(r＝1,2,···,4N) (9)
wherein, ω isrAnd xirThe system's r order natural frequency and modal damping ratio, h1(ω)＝h2(ω)＝h3(ω)＝h4(ω)，ω1＝50.17Hz。
And step 3: performing inverse Fourier transform on the F (omega) to obtain the rotor system unbalanced excitation force F (t) with normalized mass, wherein the rotor system unbalanced excitation force F (t) is as follows:
F(t)＝M·f(t) (10)
where M is the rotor mass matrix.
Then, using a cut-off frequency fmaxThe FIR filter (F), (t) filters the frequency (F), (t) to obtain the final rotor unbalance excitation force. Wherein the content of the first and second substances,
for the maximum angular velocity value, f, of the rotor in the time interval 3s-10s before the rotor reaches the critical speedmaxI.e. the highest frequency of the truncated transient response U (omega) in the frequency domainThe ratio, U (ω), is as shown in FIGS. 9 and 10 (the axis of abscissa indicates frequency and the axis of ordinate indicates response amplitude after Fourier transform), and f in this embodimentmax＝31.83Hz。
The comparison between the rotor imbalance excitation force calculated by the method of the present invention and the actual rotor imbalance excitation force is shown in fig. 11 and 12 (the abscissa axis represents time, and the ordinate axis represents the imbalance excitation force), and the local amplification result is shown in fig. 13 and 14. As can be seen from fig. 11, 12, 13, and 14, the fitting situation of the solution result and the actual rotor imbalance excitation force is good, the accuracy is high, and the effectiveness of the method of the present invention is illustrated.
Claims (1)
1. A method for identifying unbalanced excitation force of a flexible rotor based on variable-speed starting high precision is characterized by comprising the following steps:
step 1: establishing a transient motion equation of the N-disk rotor system with normalized mass by adopting a transfer matrix method, and calculating transient motion information of the rotor system under constant angular acceleration by using a Newmark integration method, wherein the transient motion information comprises rotor transient response, a rotor Bode diagram and a modal shape; intercepting transient response data U (t) in any time period before the rotor reaches the critical rotating speed as load identification input data;
step 2: by utilizing a method combining load identification and modal coordinate conversion, calculating to obtain a frequency domain load spectral vector F (omega) of the unbalanced excitation force of the rotor system, namely:
F(ω)＝U(ω)/Φhq(ω)ΦT (1)
wherein U (ω) is the fourier transform of U (t), ω represents the frequency domain frequency; Φ is the rotor mode shape matrix, expressed as:
wherein the content of the first and second substances,
is the r-th order mode vibration mode of the rotor system, and N is the number of characteristic disks of the rotor；
hq(ω) is the modal admittance matrix of the rotor system, expressed as:
hq(ω)＝diag[h1(ω),h2(ω),···,hr(ω),···,h4N(ω)] (3)
hr(ω)＝1/(ωr 2-ω2+2jωξrωr)，r＝1,2,···,4N (4)
wherein, ω isrAnd xirThe order r of the system is natural frequency and modal damping ratio respectively;
and step 3: performing inverse Fourier transform on the F (omega) to obtain the rotor system unbalanced excitation force F (t) with normalized mass, wherein the rotor system unbalanced excitation force F (t) is as follows:
F(t)＝M·f(t) (5)
wherein M is a mass matrix of the rotor;
then, using a cut-off frequency fmaxThe FIR filter filters the F (t) to obtain the final rotor unbalance exciting force; wherein the content of the first and second substances,
the maximum angular velocity value of the rotor for the intercepted transient response time period.
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