A method for resonant frequency modification of a flexible rotor system for bearing slip suppression

Abstract

The present invention discloses a method for resonant frequency modification of a flexible rotor system for bearing slip suppression; first, a modal test is conducted on a flexible rotor system test bench, a power spectrum curve is obtained based on an autoregressive model, and each order of modal frequency is identified using an automatic peak picking algorithm, while each order of damping ratio is identified based on a VMD‑SSI algorithm; secondly, a finite element simulation model of the flexible rotor system is constructed and the simulation mode is calculated, and the simulation model is modified to obtain a twin simulation model; then, the frequency range of resonant slip caused by the flexible rotor system is determined based on the cage slip rate curve of the bearing running in the full speed range and the half-power bandwidth theory; finally, a method for resonant frequency modification of a flexible rotor system for bearing slip suppression is proposed from three aspects: support stiffness, bearing position, and rotor structure. The present invention combines the resonance characteristics of the flexible rotor system to perform bearing slip analysis, and the flexible rotor system modification method of the proposed system has certain theoretical and practical value.

Description

Technical Field

[0001] The invention relates to the field of bearing retainer slippage, and in particular to a method for resonant frequency transformation of a flexible rotor system for bearing slippage suppression. Background Art

[0002] Bearing slippage is a typical fault that causes bearing failure, and its failure frequency accounts for about 37% of the total number of failures. At present, domestic and foreign scholars have conducted certain research on bearing slippage failure, and studied the influence of operating parameters (speed, load and lubrication conditions) and structural parameters (clearance, friction coefficient, cage guide method, number of rollers) on bearing cage slippage and proposed corresponding measures to suppress bearing slippage. However, related studies are basically based on the analysis of bearing slippage mechanism for a single bearing. In fact, in addition to operating parameters and structural parameters, the characteristics of the rotor system are the most critical and even decisive factors affecting the slip rate of the bearing cage. Especially for flexible rotor systems, due to the significant "flexibility" of flexible rotor systems, flexible rotor systems generally operate across one or even multiple critical speeds. Studies have shown that the resonance of the flexible rotor system when it runs across the critical speed will have a serious impact on the slippage of the bearing cage, and these impacts are far greater than the influence of operating parameters and structural parameters on bearing slippage. Therefore, it is very necessary to study the bearing slippage suppression measures in combination with the resonant frequency of the flexible rotor system.

[0003] In the study of the resonant frequency of the flexible rotor system, the research on the three parameters of support stiffness, bearing position and rotor structure is the most common. The present invention modifies the three parameters of support stiffness, bearing position and rotor structure and combines the resonant characteristics of the flexible rotor system to perform slip analysis, and proposes a systematic method for adaptively modifying the resonant frequency of the flexible rotor system to suppress bearing slip. The relevant method can effectively suppress bearing slip and has high practicality and creativity. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide a method for modifying the resonant frequency of a flexible rotor system for suppressing bearing slippage, which can achieve adaptive modification of the resonant frequency of the flexible rotor system by adjusting the support stiffness, bearing position and rotor structure, thereby reducing the slip rate of the bearing retainer and improving the operating state of the rotor system.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for resonant frequency transformation of a flexible rotor system for bearing slip suppression comprises the following steps:

[0007] Step S1, performing a modal test on a flexible rotor system test bench, obtaining a power spectrum curve based on an autoregressive model, and identifying each modal frequency using an automatic peak picking algorithm, while identifying the damping ratio using a VMD variational modal decomposition algorithm and an SSI random subspace algorithm;

[0008] Step S2, constructing a finite element simulation model of the flexible rotor system and calculating the simulation mode using Patran software, and modifying the finite element simulation model of the flexible rotor system according to the parameters obtained in step S1 to obtain a twin simulation model of the flexible rotor system;

[0009] Step S3, measuring the bearing cage slip rate at different speeds of the bearing inner ring based on the flexible rotor system test bench and drawing the bearing cage slip rate curve at different speeds of the bearing inner ring, and determining the ideal resonance frequency of the flexible rotor system test bench and the bearing inner ring rotation frequency interval threshold when the flexible rotor system test bench is running smoothly according to the half-power bandwidth theory;

[0010] Step S4, according to the stable operating speed range threshold obtained in step S3, combined with the flexible rotor system twin simulation model obtained in step S2, the support stiffness, bearing position and rotor structure of the flexible rotor system test bench are improved, so that the flexible rotor system test bench avoids the resonance zone within the actual working speed range and reduces the slip rate of the bearing cage.

[0011] Preferably, the implementation process of step S1 is:

[0012] Step S101: performing a modal test on a flexible rotor system test bench:

[0013] The flexible rotor system test bench is struck with a hammer, and sensors are attached to the points where the deformation is greater than 0.1% to measure the vibration acceleration signal; when performing the modal test, each point where the deformation is greater than 0.1% is struck m times, and the input signals δ1, δ2, ..., δ m And the vibration acceleration output signal a c1 ,a c2 ,...,a cm , the average value of the input signal of m taps is taken as the final input signal at each point Take the average value of the vibration acceleration output signal of m knocks as the final vibration acceleration output signal

[0014] Step S102: based on the input signal obtained by the modal test in step S101 And vibration acceleration output signal Use the autoregressive model to obtain the power spectrum P of the output signal AR (e jω ), as shown in formula (1):

[0015]

[0016] Where: For input signal The variance of r (l r ) is the autocorrelation function; d r is the order of the autoregressive model; l r is the parameter; is the coefficient of the autoregressive model;

[0017] Step S103: Obtain the modal test frequency curve P based on step S102 AR (e jω ), and use the automatic peak picking algorithm to identify the modal frequencies of each order as ω1, ω2, ..., ω n , where n is the order of the mode;

[0018] Step S104: Based on the vibration acceleration output signal obtained from the modal test in step S101, the damping ratio is identified using the VMD variational modal decomposition algorithm and the SSI random subspace algorithm:

[0019] The order n of the mode obtained in step S103 is used as the specified decomposition layer number of the VMD variational modal decomposition algorithm, and the vibration acceleration output signal obtained in step S101 is decomposed using the VMD variational modal decomposition algorithm, and the calculation is shown in formula (2):

[0020]

[0021] Where: is the vibration acceleration output signal at time t; parameter k r =1,2,...,n;u r (t) is the single component signal obtained by VMD variational mode decomposition algorithm; for u r (t) the instantaneous amplitude; for u r The instantaneous phase of (t); is the instantaneous frequency;

[0022] The single component signal u obtained by VMD variational mode decomposition algorithm is decomposed using SSI random subspace algorithm. r Damping ratio (t) for identification.

[0023] Preferably, the implementation process of step S2 is:

[0024] Step S201: construct a finite element simulation model of the flexible rotor system and use Patran software to calculate the simulation mode:

[0025] Based on the structure of the flexible rotor system test bench, a finite element simulation model of the flexible rotor system is built based on the Solidworks modeling software and the Hypermesh meshing software. At the same time, initial parameters of each component of the finite element simulation model of the flexible rotor system are given, including initial elastic modulus, Poisson's ratio and density. The simulation modes of each order of the finite element simulation model of the flexible rotor system are calculated using Patran software.

[0026] Step S202: modifying the finite element simulation model of the flexible rotor system established in step S201 to obtain a twin simulation model of the flexible rotor system:

[0027] The damping ratio obtained in step S104 is Assign the finite element simulation model of the flexible rotor system; at the same time, according to the modal frequency ω obtained in step S103 n The finite element simulation model of the flexible rotor system established in step S201 is modified to obtain a twin simulation model of the flexible rotor system.

[0028] Preferably, the implementation process of step S3 is:

[0029] Step S301, based on the flexible rotor system test bench, the bearing cage slip rate at different speeds of the bearing inner ring is measured and the bearing cage slip rate curve of the flexible rotor system test bench at different speeds of the bearing inner ring is drawn:

[0030] Adjust the inner ring speed of the flexible rotor system test bench from 0 to the rated value and measure the bearing cage bearing slip rate S a , bearing cage slip rate S a Calculate as formula (3):

[0031]

[0032] Where: c is the actual speed of the bearing cage; ω cm is the theoretical speed of the bearing cage, calculated as formula (4):

[0033]

[0034] Where: R w is the bearing roller radius; R m is the bearing pitch radius; ω i is the bearing inner ring speed;

[0035] Plotting the bearing cage slip rate S a The curve of the bearing inner ring rotation frequency f and the bearing cage slip rate S a Maximum S max The corresponding frequency is the resonant frequency f of the flexible rotor system test benchcri ;

[0036] Step S302: Determine the ideal resonance frequency of the flexible rotor system test bench and the threshold value of the bearing inner ring rotation frequency range when the flexible rotor system test bench is running smoothly according to the half-power bandwidth theory:

[0037] According to the half-power bandwidth theory, the bearing cage slip rate is determined as The corresponding bearing inner ring speed f po ; Then the threshold value of the bearing inner ring speed frequency interval χ when the flexible rotor system test bench is running smoothly is as follows:

[0038]

[0039] When the bearing inner ring rotation frequency f satisfies (f cri -f po )f cri When ×100%<χ, the flexible rotor system test bench will run unsteadily; when the rotation frequency f of the inner ring of the bearing meets (f cri -f po )f cri When ×100%>χ, the flexible rotor system test bench operates smoothly;

[0040] According to the actual operating conditions of the flexible rotor system test bench, the ideal resonance frequency f of the flexible rotor system test bench is determined by combining the threshold value of the inner ring speed frequency range of the unstable operation bearing of the flexible rotor system test bench. ideal for:

[0041]

[0042] Where: f α It is the upper limit of the speed frequency range of the inner ring of the bearing under the actual operating conditions of the flexible rotor system test bench;

[0043] Preferably, the implementation process of step S4 is:

[0044] Step S401: According to the bearing inner ring speed frequency interval threshold value χ obtained in step S302 when the flexible rotor system test bench is running smoothly, the support stiffness of the flexible rotor system test bench is improved in combination with the flexible rotor system twin simulation model obtained in step S202, and the modal of the flexible rotor system test bench after the support stiffness is modified is calculated using Patran software, so that the resonant frequency of the flexible rotor system test bench is equal to the ideal resonant frequency f obtained in step S302 ideal ;

[0045] Step S402: According to the threshold value of the frequency range of the inner ring of the bearing of the flexible rotor system test bench for stable operation obtained in step S302, the bearing position of the flexible rotor system test bench is improved in combination with the twin simulation model of the flexible rotor system obtained in step S202, and the modal state of the flexible rotor system test bench after the bearing position is modified is calculated by using Patran software, so that the resonant frequency of the flexible rotor system test bench is equal to the ideal resonant frequency f in step S302. ideal ;

[0046] Step S403: According to the threshold value of the frequency range of the inner ring of the bearing of the flexible rotor system test bench for stable operation obtained in step S302, the rotor structure of the flexible rotor system test bench is improved in combination with the twin simulation model of the flexible rotor system obtained in step S202, and the modal state of the flexible rotor system test bench after the rotor structure is modified is calculated by using Patran software, so that the resonant frequency of the flexible rotor system test bench is equal to the ideal resonant frequency f in step S302. ideal .

[0047] The beneficial effects of the present invention are:

[0048] 1. The present invention combines modal testing and model correction technology to build a twin simulation model of a flexible rotor system, which can realize real-time and accurate measurement of the rotation speed and modal frequency of the bearing cage, and then obtain the bearing cage slip rate and the resonant frequency of the flexible rotor system test bench, which provides a model basis for studying the influence of the characteristics of the flexible rotor system test bench on the bearing cage slip rate;

[0049] 2. The present invention improves the characteristics of the flexible rotor system test bench by combining the support stiffness, bearing position and rotor structure, and realizes the adjustment of the modal frequency of the flexible rotor system test bench;

[0050] 3. The present invention uses the half-power bandwidth theory to determine the threshold value of the frequency range of the inner ring of the bearing of the flexible rotor system test bench for stable operation, and suppresses the bearing slippage by improving the rotor structure and motion characteristics, which can effectively extend the service life of the flexible rotor system test bench and improve the performance of the flexible rotor system test bench. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A schematic flow chart of a method for resonant frequency modification of a flexible rotor system for bearing slip suppression provided in Example 1;

[0052] Figure 2 The modal test input and output signals provided in Example 1, wherein a is the impact force input signal and b is the vibration acceleration output signal;

[0053] Figure 3is the modal test vibration shape of the transmission shaft of the flexible rotor system test bench provided in Example 1, wherein a is the first-order modal test vibration shape, b is the second-order modal test vibration shape, and c is the third-order modal test vibration shape;

[0054] Figure 4 The power spectrum of the flexible rotor system test bench provided in Example 1;

[0055] Figure 5 The damping ratio identification based on VMD-SSI provided in Example 1;

[0056] Figure 6 The damping ratio identification results of each order mode under different noise proportions provided in Example 1, wherein a is the damping ratio identification result of the first order mode, b is the damping ratio identification result of the second order mode, and c is the damping ratio identification result of the third order mode;

[0057] Figure 7 is the modal calculation result of the finite element simulation model of the flexible rotor system provided in Example 1, wherein a is the modal calculation result of the finite element simulation model of the flexible rotor system of the first order modal, b is the modal calculation result of the finite element simulation model of the flexible rotor system of the second order modal, and c is the modal calculation result of the finite element simulation model of the flexible rotor system of the third order modal;

[0058] Figure 8 is the model correction result provided in Example 1, wherein a is the elastic modulus and Poisson's ratio optimization curve, and b is the frequency modal error optimization curve;

[0059] Fig. 9 is a bearing cage slip curve of the flexible rotor system test bench provided in Example 1;

[0060] Fig.10 The finite element calculation results of the variable support stiffness provided in Example 1, wherein a is the stiffness calculation result of the variable stiffness support with a thickness of 15 mm, b is the stiffness calculation result of the variable stiffness support with a thickness of 30 mm, and c is the stiffness calculation result of the variable stiffness support with a thickness of 40 mm;

[0061] Fig.11 It is the twin simulation model mode of the flexible rotor system with a variable stiffness support thickness of 15 mm provided in Example 1, wherein a is the first-order twin simulation model mode of the flexible rotor system, b is the second-order twin simulation model mode of the flexible rotor system, and c is the third-order twin simulation model mode of the flexible rotor system;

[0062] Fig.12It is the twin simulation model mode of the flexible rotor system with a variable stiffness support thickness of 30 mm provided in Example 1, wherein a is the first-order twin simulation model mode of the flexible rotor system, b is the second-order twin simulation model mode of the flexible rotor system, and c is the third-order twin simulation model mode of the flexible rotor system;

[0063] Fig.13 It is the twin simulation model mode of the flexible rotor system with a bearing position distance of 40 mm provided in Example 1, wherein a is the first-order twin simulation model mode of the flexible rotor system, b is the second-order twin simulation model mode of the flexible rotor system, and c is the third-order twin simulation model mode of the flexible rotor system;

[0064] Fig.14 It is the twin simulation model mode of the flexible rotor system with a bearing position distance of 100 mm provided in Example 1, wherein a is the first-order twin simulation model mode of the flexible rotor system, b is the second-order twin simulation model mode of the flexible rotor system, and c is the third-order twin simulation model mode of the flexible rotor system;

[0065] Fig.15 The twin simulation model mode of the flexible rotor system with a hollow rotor provided in Example 1, wherein a is the first-order twin simulation model mode of the flexible rotor system, b is the second-order twin simulation model mode of the flexible rotor system, and c is the third-order twin simulation model mode of the flexible rotor system. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] Example 1

[0068] See also Figure 1-Figure 15 This embodiment provides a method for resonant frequency modification of a flexible rotor system for bearing slip suppression. The process of the method is as follows: Figure 1 As shown, this embodiment uses a flexible rotor system test bench as an example to verify the algorithm performance. The strategy specifically includes the following steps:

[0069] Step S1, performing a modal test on a flexible rotor system test bench, obtaining a power spectrum curve based on an autoregressive model, and identifying each modal frequency using an automatic peak picking algorithm, while identifying the damping ratio using a VMD variational modal decomposition algorithm and an SSI random subspace algorithm;

[0070] Specifically, in this embodiment, step S1 includes:

[0071] Step S101: performing a modal test on a flexible rotor system test bench:

[0072] Use a hammer to hit the points with significant modal characteristics of the flexible rotor test bench. Paste sensors at points where the deformation is greater than 0.1% in the modal test to measure the vibration acceleration signal. During the modal test, hit each point m times in turn to obtain m knocking force input signals δ1, δ2, ..., δ m And the corresponding vibration acceleration output signal a c1 ,a c2 ,...,a cm , take the average value of m modal tests at each point as the final impact force input signal And vibration acceleration output signal The impact force input signal used in modal testing is as follows: Figure 2 As shown in a, the vibration acceleration output signal is as follows Figure 2 b. The first three modal formations of the transmission shaft of the flexible rotor system test bench are shown in Figure 3 As shown, the modal frequencies of the transmission shaft of the flexible rotor test bench are shown in Table 1:

[0073] Table 1 Modal frequency of transmission shaft of flexible rotor system test bench

[0074] First order modal frequency / Hz Second order modal frequency / Hz The third modal frequency / Hz 178.04 206.51 657.92

[0075] Step S102: Based on the striking force input signal obtained from the modal test in step S101 And vibration acceleration output signal Using the autoregressive model to obtain the power spectrum P AR (e jω )as follows:

[0076]

[0077] Where: For signal The variance of r (l r ) is the autocorrelation function; d r is the order of the autoregressive model; l r is the parameter; is the coefficient of the autoregressive model; the power spectrum of the flexible rotor test bench is as follows Figure 4 shown.

[0078] Step S103: Obtain the modal test frequency curve P based on step S102 AR (e jω), using the automatic peak picking algorithm to identify the modal frequencies of each order as ω1, ω2, ..., ω n , where n is the modal order of the structure;

[0079] Step S104: Based on the vibration acceleration output signal obtained from the modal test in step S101, the damping ratio is identified using the VMD-SSI algorithm:

[0080] The structural modal order n obtained in step S103 is used as the specified decomposition level of VMD decomposition, and the vibration acceleration output signal obtained in step S101 is decomposed by VMD. Decompose it and the calculation formula is as follows:

[0081]

[0082] Where: k r =1,2,...,n;u r (t) is the single component signal obtained by VMD decomposition (variational mode decomposition); for u r (t) the instantaneous amplitude; for u r The instantaneous phase of (t); is the instantaneous frequency; the damping ratio is calculated by VMD-SSI To identify;

[0083] The damping ratio identification results based on VMD-SSI are as follows: Figure 5 As shown in the figure, the identification results of damping ratio of each order mode under different noise proportions are as follows Figure 6 As shown, the identification results of the first-order modal damping ratio are shown in Table 2:

[0084] Table 2 Identification results of the first-order modal damping ratio under different noise proportions

[0085]

[0086]

[0087] The identification results of the second-order modal damping ratio are shown in Table 3:

[0088] Table 3 Identification results of the second-order modal damping ratio under different noise proportions

[0089] Serial number Noise ratio / % SSI Damping Ratio Identification VMD-SSI Damping Ratio Identification 1 2 0.016249 0.012996 2 7 0.021560 0.016249 3 11 0.0204665 0.014125 4 16 0.026905 0.017311 5 20 0.026871 0.018342

[0090] The identification results of the third-order modal damping ratio are shown in Table 4:

[0091] Table 4 Identification results of the third-order modal damping ratio under different noise proportions

[0092] Serial number Noise ratio / % SSI Damping Ratio Identification VMD-SSI Damping Ratio Identification 1 2 0.025340 0.022544 2 7 0.033203 0.026422 3 11 0.035435 0.022242 4 16 0.043434 0.028342 5 20 0.043212 0.031454

[0093] Step S2, building a finite element simulation model of the flexible rotor system and calculating the simulation mode using Patran software, and modifying the simulation model according to the parameters obtained in step S1 to obtain a twin simulation model;

[0094] Specifically, in this embodiment, step S2 includes:

[0095] Step S201, construct a finite element simulation model of the flexible rotor system and use Patran software to calculate the simulation mode, and modify the finite element simulation model of the flexible rotor system according to the parameters obtained in step S1 to obtain a twin simulation model of the flexible rotor system:

[0096] Based on the Solidworks modeling software and Hypermesh meshing software, a finite element simulation model of the flexible rotor system was built according to the structure of the flexible rotor system test bench. At the same time, the initial elastic modulus of different components of the finite element simulation model of the flexible rotor system was given as 210Gpa, Poisson's ratio as 0.25 and density as 7890kg / m 3 The various modes of the finite element simulation model of the flexible rotor system are calculated using Patran software. Figure 7 The modal frequencies of each order are shown in Table 5:

[0097] Table 5 Modal frequencies of the finite element simulation model of the flexible rotor system

[0098] First order modal frequency / Hz Second order modal frequency / Hz The third modal frequency / Hz 237.58 259.88 286.43

[0099] Step S202: Correct the simulation model according to the flexible rotor test bench parameters obtained in step S103 and step S104 to obtain a twin simulation model:

[0100] The damping ratio of the flexible rotor test bench obtained in step S104 is assigned to the finite element simulation model of the flexible rotor system; at the same time, the model is corrected for the finite element simulation model of the flexible rotor system according to the modal frequency of the flexible rotor test bench obtained in step S103, and an accurate elastic modulus of 170 GPa, a Poisson's ratio of 0.29 and a density of 7890 kg / m 3 The accurate values ​​of parameters such as , and then the twin simulation model of the flexible rotor system is obtained; the model correction optimization curve is as follows Figure 8 The optimization results are shown in Table 6:

[0101] Table 6 Finite element model modification results of flexible rotor system

[0102] Modal Order Test modal frequency Modal frequency before correction Corrected modal frequency Modal frequency error 1 240.32 252.32 237.58 1.14％ 2 258.23 247.48 259.88 0.64％ 3 285.92 280.92 286.43 0.18％

[0103] Step S3, measuring the bearing cage slip rate at different speeds of the bearing inner ring based on the flexible rotor system test bench and drawing the bearing cage slip rate curve at different speeds of the bearing inner ring, and determining the ideal resonance frequency of the flexible rotor system test bench and the bearing inner ring rotation frequency interval threshold when the flexible rotor system test bench is running smoothly according to the half-power bandwidth theory;

[0104] Specifically, in this embodiment, step S3 includes:

[0105] Step S301: measuring the bearing cage slip rate in the full speed range based on the flexible rotor system test bench and drawing a bearing cage slip rate curve:

[0106] Adjust the speed of the flexible rotor system test bench from 0 to the rated value, conduct a slip test on the flexible rotor system test bench in the full speed range, and measure the bearing cage slip rate at different bearing inner ring speeds. a The calculation formula is as follows:

[0107]

[0108] Where: c is the actual speed of the bearing cage; ω cm is the theoretical speed of the bearing cage, which satisfies:

[0109]

[0110] Where: R w is the bearing roller radius; R m is the bearing pitch radius; ω i is the bearing inner ring speed;

[0111] Based on the measured bearing cage slip rate in the full speed range, the bearing cage slip rate versus inner ring rotation frequency curve is plotted. It can be found that the bearing cage slip curve of the flexible rotor system test bench is a parabola, and the frequency corresponding to the maximum slip rate is the resonant frequency of the flexible rotor system test bench. The bearing cage slip curve of the flexible rotor system test bench is as follows: Fig. 9 shown.

[0112] Step S302: Determine the ideal resonance frequency of the flexible rotor system test bench and the threshold value of the bearing inner ring rotation frequency range when the flexible rotor system test bench is running smoothly according to the half-power bandwidth theory:

[0113] The half-power bandwidth theory is based on the peak Determine the damping ratio based on the peak The corresponding frequency determines the power bandwidth range; based on the bearing cage slip curve of the flexible rotor system test bench obtained in step S301, assuming that the maximum bearing slip rate is S maxAnd the corresponding resonant frequency of the flexible rotor system test bench is f cri =197Hz, then according to the half-power bandwidth theory, the slip rate is determined as The corresponding bearing inner ring speed f po =175Hz; further determine the threshold value of the frequency range of the inner ring of the bearing of the flexible rotor system test bench for stable operation as:

[0114]

[0115] When the bearing inner ring rotation frequency f satisfies (f cri -f po )f cri When ×100%<χ, the flexible rotor system test bench will run unsteadily; when the rotation frequency f of the inner ring of the bearing meets (f cri -f po )f cri When ×100%>χ, the flexible rotor system test bench operates smoothly. According to the actual operating conditions of the flexible rotor system test bench, the operating speed frequency range of the inner ring of the flexible rotor system test bench bearing is [0Hz, 220Hz]. Combined with the unstable operation of the flexible rotor system test bench bearing inner ring speed frequency interval threshold χ, the ideal resonance frequency f of the flexible rotor system test bench is determined. ideal for:

[0116]

[0117] Where: f α The upper limit of the operating speed frequency range of the inner ring of the flexible rotor system test bench bearing;

[0118] Step S4, according to the stable operation speed interval threshold obtained in step S3, combined with the flexible rotor system twin simulation model obtained in step S2, the support stiffness, bearing position and rotor structure of the rotor system are improved, so that the rotor system avoids the resonance area within the actual working speed range and reduces the slip rate of the bearing cage;

[0119] Specifically, in this embodiment, step S4 includes:

[0120] Step S401: According to the frequency range threshold of the inner ring of the stable running bearing obtained in step S302, the support stiffness of the rotor system is improved in combination with the twin simulation model of the flexible rotor system obtained in step S2, and the rotor system mode after the support stiffness is modified is calculated using Patran software to make the resonance frequency equal to the ideal resonance frequency in step S302; the finite element calculation results of the variable support stiffness are as follows: Fig.10 The specific values ​​are shown in Table 7:

[0121] Table 7 Finite element calculation results of variable support stiffness

[0122]

[0123]

[0124] The modal finite element calculation results of the twin simulation model of the flexible rotor system when the variable stiffness support thickness is 15 mm are as follows: Fig.11 The specific values ​​are shown in Table 8:

[0125] Table 8 Modal frequencies of the simulation model of the flexible rotor system when the thickness of the variable stiffness support is 15 mm

[0126] First order modal frequency / Hz Second order modal frequency / Hz The third modal frequency / Hz 231.44 263.26 294.56

[0127] The modal finite element calculation results of the twin simulation model of the flexible rotor system when the variable stiffness support thickness is 30 mm are as follows: Fig.12 The specific values ​​are shown in Table 9:

[0128] Table 9 Modal frequencies of the simulation model of the flexible rotor system when the variable stiffness support thickness is 30 mm

[0129] First order modal frequency / Hz Second order modal frequency / Hz The third modal frequency / Hz 236.05 266.44 301.96

[0130] Step S402: According to the stable operation bearing inner ring speed frequency interval threshold obtained in step S302, the bearing position of the rotor system is improved in combination with the flexible rotor system twin simulation model obtained in step S2, and the rotor system mode after the bearing position is modified is calculated using Patran software to make the resonance frequency equal to the ideal resonance frequency in step S302; the modal finite element calculation results of the flexible rotor system twin simulation model with a bearing position distance of 40 mm are as follows: Fig.13 The specific values ​​are shown in Table 10:

[0131] Table 10 Modal frequencies of the simulation model of the flexible rotor system when the bearing position distance is 40 mm

[0132] First order modal frequency / Hz Second order modal frequency / Hz The third modal frequency / Hz 241.60 290.66 317.55

[0133] The modal finite element calculation results of the twin simulation model of the flexible rotor system with a bearing position distance of 100 mm are as follows: Fig.14 The specific values ​​are shown in Table 11:

[0134] Table 11 Modal frequencies of the simulation model of the flexible rotor system when the bearing position distance is 100 mm

[0135] First order modal frequency / Hz Second order modal frequency / Hz The third modal frequency / Hz 246.93 327.21 346.90

[0136] Step S403: Improve the rotor structure of the rotor system according to the stable operation bearing inner ring speed range threshold obtained in step S302 and the flexible rotor system twin simulation model obtained in step S2, and use Patran software to calculate the rotor system mode after the rotor structure is modified, so that the resonance frequency is equal to the ideal resonance frequency in step S302. The modal finite element calculation results of the flexible rotor system twin simulation model when the rotor is hollow are as follows: Fig.15 The specific values ​​are shown in Table 12:

[0137] Table 12 Modal frequencies of simulation model of flexible rotor system when the rotor is hollow

[0138]

[0139]

[0140] The above results show that the purpose of changing the modal frequency of the rotor system can be achieved by modifying the support stiffness, bearing position and rotor structure, thereby obtaining a flexible rotor system transformation method that meets the requirements.

[0141] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0142] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for resonant frequency modification of a flexible rotor system for bearing slip suppression, characterized in that: The following steps are involved: Step S1, performing a modal test on a flexible rotor system test bench, obtaining a power spectrum curve based on an autoregressive model, and identifying each modal frequency using an automatic peak picking algorithm, while identifying the damping ratio using a VMD variational modal decomposition algorithm and an SSI random subspace algorithm; Step S2, constructing a finite element simulation model of the flexible rotor system and calculating the simulation mode using Patran software, and modifying the finite element simulation model of the flexible rotor system according to the parameters obtained in step S1 to obtain a twin simulation model of the flexible rotor system; Step S3, measuring the bearing cage slip rate at different speeds of the bearing inner ring based on the flexible rotor system test bench and drawing the bearing cage slip rate curve at different speeds of the bearing inner ring, and determining the ideal resonance frequency of the flexible rotor system test bench and the bearing inner ring rotation frequency interval threshold when the flexible rotor system test bench is running smoothly according to the half-power bandwidth theory; Step S4, according to the stable operation speed range threshold obtained in step S3, combined with the flexible rotor system twin simulation model obtained in step S2, the support stiffness, bearing position and rotor structure of the flexible rotor system test bench are improved, so that the flexible rotor system test bench avoids the resonance zone within the actual working speed range and reduces the slip rate of the bearing cage; The implementation process of step S1 is: Step S101: performing a modal test on a flexible rotor system test bench: The flexible rotor system test bench is struck with a hammer, and sensors are attached to the points where the deformation is greater than 0.1% to measure the vibration acceleration signal; when performing the modal test, each point where the deformation is greater than 0.1% is struck m times, and the input signals δ1, δ2, ..., δ m And the vibration acceleration output signal a c1 ,a c2 ,...,a cm , the average value of the input signal of m taps is taken as the final input signal at each point Take the average value of the vibration acceleration output signal of m knocks as the final vibration acceleration output signal Step S102: based on the input signal obtained by the modal test in step S101 And vibration acceleration output signal Use the autoregressive model to obtain the power spectrum P of the output signal AR (e jω ), as shown in formula (1): Where: For input signal The variance of r (l r ) is the autocorrelation function; d r is the order of the autoregressive model; l r is a parameter; lr is the coefficient of the autoregressive model; Step S103: Obtain the modal test frequency curve P based on step S102 AR (e jω ), and use the automatic peak picking algorithm to identify the modal frequencies of each order as ω1, ω2, …, ω n , where n is the order of the mode; Step S104: Based on the vibration acceleration output signal obtained from the modal test in step S101, the damping ratio is identified using the VMD variational modal decomposition algorithm and the SSI random subspace algorithm: The order n of the mode obtained in step S103 is used as the specified decomposition layer number of the VMD variational modal decomposition algorithm, and the vibration acceleration output signal obtained in step S101 is decomposed using the VMD variational modal decomposition algorithm, and the calculation is shown in formula (2): Where: is the vibration acceleration output signal at time t; parameter k r =1,2,…,n;u r (t) is the single component signal obtained by VMD variational mode decomposition algorithm; for u r (t) the instantaneous amplitude; for u r The instantaneous phase of (t); is the instantaneous frequency; The single component signal u obtained by VMD variational mode decomposition algorithm is decomposed using SSI random subspace algorithm. r The damping ratio ξ of (t) kr To identify; The implementation process of step S2 is: Step S201: construct a finite element simulation model of the flexible rotor system and use Patran software to calculate the simulation mode: Based on the structure of the flexible rotor system test bench, a finite element simulation model of the flexible rotor system is built based on the Solidworks modeling software and the Hypermesh meshing software. At the same time, initial parameters of each component of the finite element simulation model of the flexible rotor system are given, including initial elastic modulus, Poisson's ratio and density. The simulation modes of each order of the finite element simulation model of the flexible rotor system are calculated using Patran software. Step S202: modifying the finite element simulation model of the flexible rotor system established in step S201 to obtain a twin simulation model of the flexible rotor system: The damping ratio ξ obtained in step S104 is kr Assign the finite element simulation model of the flexible rotor system; at the same time, according to the modal frequency ω obtained in step S103 n The finite element simulation model of the flexible rotor system established in step S201 is modified to obtain a twin simulation model of the flexible rotor system; The implementation process of step S3 is: Step S301, based on the flexible rotor system test bench, the bearing cage slip rate at different speeds of the bearing inner ring is measured and the bearing cage slip rate curve of the flexible rotor system test bench at different speeds of the bearing inner ring is drawn: Adjust the inner ring speed of the flexible rotor system test bench from 0 to the rated value and measure the bearing cage bearing slip rate S a , bearing cage slip rate S a Calculate as formula (3): Where: c is the actual speed of the bearing cage; ω cm is the theoretical speed of the bearing cage, calculated as formula (4): Where: R w is the bearing roller radius; R m is the bearing pitch radius; ω i is the bearing inner ring speed; Plotting the bearing cage slip rate S a The curve of the bearing inner ring rotation frequency f shows the bearing cage slip rate S a Maximum S max The corresponding frequency is the resonant frequency f of the flexible rotor system test bench cri ; Step S302: Determine the ideal resonant frequency of the flexible rotor system test bench and the threshold value of the bearing inner ring rotation frequency range when the flexible rotor system test bench is running smoothly according to the half-power bandwidth theory: According to the half-power bandwidth theory, the bearing cage slip rate is determined as The corresponding bearing inner ring speed f po ; Then the threshold value of the bearing inner ring speed frequency interval χ when the flexible rotor system test bench is running smoothly is as follows: When the bearing inner ring rotation frequency f satisfies (f cri -f po ) / f cri When ×100%<χ, the flexible rotor system test bench will run unsteadily; when the rotation frequency f of the inner ring of the bearing meets (f cri -f po ) / f cri When ×100%>χ, the flexible rotor system test bench operates smoothly; According to the actual operating conditions of the flexible rotor system test bench, the ideal resonance frequency f of the flexible rotor system test bench is determined by combining the threshold value of the inner ring speed frequency range of the unstable operation bearing of the flexible rotor system test bench. ideal for: Where: f α It is the upper limit of the speed frequency range of the inner ring of the bearing under the actual operating conditions of the flexible rotor system test bench; The implementation process of step S4 is: Step S401: According to the bearing inner ring speed frequency interval threshold value χ obtained in step S302 when the flexible rotor system test bench is running smoothly, the support stiffness of the flexible rotor system test bench is improved in combination with the flexible rotor system twin simulation model obtained in step S202, and the modal of the flexible rotor system test bench after the support stiffness is modified is calculated using Patran software, so that the resonant frequency of the flexible rotor system test bench is equal to the ideal resonant frequency f obtained in step S302 ideal ; Step S402: According to the threshold value of the frequency range of the inner ring of the bearing of the flexible rotor system test bench for stable operation obtained in step S302, the bearing position of the flexible rotor system test bench is improved in combination with the twin simulation model of the flexible rotor system obtained in step S202, and the modal state of the flexible rotor system test bench after the bearing position is modified is calculated by using Patran software, so that the resonant frequency of the flexible rotor system test bench is equal to the ideal resonant frequency f in step S302. ideal ; Step S403: According to the threshold value of the frequency range of the inner ring of the bearing of the flexible rotor system test bench for stable operation obtained in step S302, the rotor structure of the flexible rotor system test bench is improved in combination with the twin simulation model of the flexible rotor system obtained in step S202, and the modal state of the flexible rotor system test bench after the rotor structure is modified is calculated by using Patran software, so that the resonant frequency of the flexible rotor system test bench is equal to the ideal resonant frequency f in step S302. ideal .

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