CN113704955A - Global analysis method for rolling bearing complex bounce behavior trigger mechanism - Google Patents

Global analysis method for rolling bearing complex bounce behavior trigger mechanism Download PDF

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CN113704955A
CN113704955A CN202110566415.5A CN202110566415A CN113704955A CN 113704955 A CN113704955 A CN 113704955A CN 202110566415 A CN202110566415 A CN 202110566415A CN 113704955 A CN113704955 A CN 113704955A
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rolling bearing
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张智勇
李轩
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Nanjing University of Science and Technology
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Abstract

The invention discloses a global analysis method of a rolling bearing complex bounce behavior trigger mechanism, which comprises the steps of collecting basic parameters of a rolling bearing, and establishing a rolling bearing system compliance parameter resonance kinetic model; solving a variable-flexibility parameter resonance dynamic model of the rolling bearing system to obtain an amplitude-frequency response curve of variable-flexibility vibration of the system; estimating the natural frequency of the system, and accordingly obtaining the main resonance position and the possible combined resonance position of the rolling bearing system; determining a complex response interval of the combined resonance, analyzing the main frequency component, and determining the type of the combined resonance; and (5) reversely calculating the resonance position, comparing the resonance position with the estimated main resonance position, determining a combined resonance interval, and completing the overall analysis of the complex beating behavior trigger mechanism of the rolling bearing. The method greatly expands the analysis range of the complex bouncing behavior of the rolling bearing, improves the efficiency of the trigger mechanism analysis of the complex bouncing behavior of the rolling bearing, and provides a theoretical basis for inhibiting the system combination resonance and the complex response.

Description

Global analysis method for rolling bearing complex bounce behavior trigger mechanism
Technical Field
The invention relates to the field of dynamic response analysis and response type classification of rolling bearings, in particular to a global analysis method for a complex bouncing behavior trigger mechanism of a rolling bearing.
Background
The rolling bearing belongs to an intrinsic nonlinear mechanical part (Ongben pure three, 2003) and is influenced by various nonlinear factors including Hertzian contact between a rolling body and a raceway, bearing play, VC excitation and the like. At present, the researchers have conducted some independent studies on the main resonance characteristic and the sub-resonance characteristic of the rolling bearing.
Fukata et al analyzed a classical two-degree-of-freedom bearing model considering Hertzian contact and bearing radial play nonlinearity, and found that the system has various complex motion behaviors such as sub-harmonic, quasi-periodic and chaos-like (chaos-like) motion in a first-order VC resonance frequency range (Fukata S et al 1985). Further, theoretical and experimental researches show that the model has a multiple-cycle bifurcation instability phenomenon in a first-order critical rotating speed interval and causes a system to generate chaotic motion (Mevel B, Guyader J L.1993). Sankaravelu et al, by combining the shooting method with the homotopy continuation method, found that the VC vibration amplitude-frequency response curve of the rolling bearing has a hysteresis jump behavior (Sankaravelu A et al 1994). Yamamoto. In 1954, the inventor of Japan discovered that the rolling bearing vibration has a combined resonance characteristic, and through experiments, the bearing vibration has a sub-harmonic resonance component, but no in-depth analysis was conducted (Yamamoto et al 1954). The above researches are independent researches on the main resonance and the sub-harmonic resonance of the rolling bearing VC, and global analysis is not carried out. Zhang Chiagong et al have conducted the dynamics mechanism research of the complex sub-harmonic resonance behavior of the rolling bearing. On the basis, the patent provides a method for globally analyzing a rolling bearing complex bouncing behavior trigger mechanism by adopting a global analysis theory, and the rolling bearing complex bouncing behavior trigger mechanism can be efficiently analyzed.
Disclosure of Invention
The invention aims to provide a method for globally analyzing a rolling bearing complex bounce behavior trigger mechanism.
The technical solution for realizing the purpose of the invention is as follows: a global analysis method for a rolling bearing complex run-out behavior trigger mechanism comprises the following steps:
step 1, collecting basic parameters of a rolling bearing, including the geometric size of the rolling bearing, the number of balls, contact rigidity and equivalent damping;
step 2, substituting the basic parameters of the rolling bearing in the step 1 into a rolling bearing flexibility-variable vibration equation based on a two-degree-of-freedom rolling bearing system, and establishing a flexibility-variable parameter resonance dynamic model of the rolling bearing system;
step 3, solving the rolling bearing system variable flexibility parameter resonance dynamic model in the step 2 by adopting a numerical analysis method to obtain an amplitude-frequency response curve of system variable flexibility vibration;
step 4, estimating the dynamic stiffness of the system through a two-freedom-degree direction dynamic stiffness estimation formula according to the amplitude-frequency response obtained in the step 3, estimating the natural frequency of the system through a two-freedom-degree direction dynamic natural frequency estimation formula, and obtaining the main resonance position and the possible combined resonance position of the rolling bearing system according to the estimation result;
step 5, determining a complex response interval of the combined resonance according to the amplitude-frequency response obtained in the step 3 and the possible existing combined resonance position obtained in the step 4, analyzing the main frequency component, and determining the type of the combined resonance;
and 6, calculating the resonance position of the complex response according to the main frequency component of the complex response obtained in the step 5, comparing the resonance position with the estimated main resonance position, determining a combined resonance interval causing the complex response, and completing the overall analysis of the complex bouncing behavior trigger mechanism of the rolling bearing.
In step 2, inputting the basic parameters of the rolling bearing in the step 1 into a variable-flexibility vibration equation of the rolling bearing with two degrees of freedom, and establishing a radial variable-flexibility vibration dynamics model of the rolling bearing system:
Figure BDA0003080877050000021
and is
Figure BDA0003080877050000022
δi＝xcosθi+ysinθi-δ0 (3)
θi＝2π(i-1)/Nb+Ωt (4)
Ω＝ωs(1-Db/Dh)/2 (5)
ΩVC＝Nb·Ω (6)
In the formulas (1) to (6), x and y are systemsRadial displacement in two freedom directions; fx、FyBearing counter forces in the x and y directions of the system are set; t is a time independent variable; m is the equivalent mass of the bearing system; c is equivalent damping; w is the steady load borne by the system; cbThe contact stiffness coefficient is Hertzian, and alpha is 3/2 and 10/9 which respectively correspond to a rolling bearing and a rolling bearing system; h [. C]Is the Heaviside function representing the contact condition, describes the contact condition of the rolling body and the rolling path, and generates the contact H [ ·]A value of 1, loss of contact a value of 0; n is a radical ofbIs the number of rolling elements, and δiAnd thetaiRadial deformation and instantaneous angular position of the ith rolling element respectively; 2 delta0The radial working clearance of the bearing is adopted; omega is the cage velocity and omegas、DbAnd DhRespectively the speed of a system rotating shaft, the diameter of a bearing rolling body and the diameter of a pitch circle; omegaVCAngular velocity is excited for a variable compliance parameter.
In step 4, according to the amplitude-frequency response obtained in step 3, estimating the dynamic stiffness of the system by a two-degree-of-freedom direction dynamic stiffness estimation formula, estimating the natural frequency of the system by using a two-degree-of-freedom direction dynamic natural frequency estimation formula, and accordingly obtaining the main resonance position and the possible combined resonance position of the rolling bearing system, the specific method is as follows:
two-degree-of-freedom direction dynamic stiffness k provided by measurexx(t)、kyy(t) estimation formula:
Figure BDA0003080877050000031
two-degree-of-freedom direction dynamic natural frequency omega proposed by Mevelxx(t)、ωxx(t) estimation formula:
Figure BDA0003080877050000032
calculating to obtain the main resonance positions of the system in two freedom directions at the moment, namely the x direction omegax0And y direction omegay0The calculation formula is as follows:
Figure BDA0003080877050000033
wherein, KintCalculating step number for numerical integration;
four possible combined resonance positions omega are obtained by the main resonance position frequencyVCRespectively: omegax0+ωy0， 1/2·(ωx0+ωy0)，1/2·(1/2·ωx0+ωy0) And 1/2 (ω)x0+1/2·ωy0)。
In step 5, determining a complex response interval of the combined resonance according to the amplitude-frequency response obtained in step 3 and the possible existing combined resonance position obtained in step 4, analyzing the main frequency component, and determining the type of the combined resonance, wherein the specific method comprises the following steps:
if the main frequency components p and q of the complex response in the x and y two-degree-of-freedom directions are obtained through the analysis of the main frequency components, and when p + q is equal to 1, the type of the combined resonance causing the complex response is judged to be omegax0+ωy0＝ΩVCWhen 1/2 · (p + q) ═ 1, it is determined that the type of combined resonance that causes a complex response is 1/2 · (ω) of the combined resonance typex0+ωy0)＝ΩVCCombined resonance, when 1/2 · (1/2p + q) ═ 1, then a combined resonance type 1/2 · (1/2 ω) that causes a complex response is judgedx0+ωy0)＝ΩVCWhen 1/2 · (p +1/2q) ═ 1, then a combined resonance type 1/2 · (ω) that causes a complex response is determinedx0+1/2ωy0)＝ΩVC。
In step 6, according to the main frequency component of the complex response obtained in step 5, calculating the resonance position of the complex response, comparing the resonance position with the estimated main resonance position, determining the combined resonance interval causing the complex response, and completing the global analysis of the rolling bearing complex bounce behavior trigger mechanism, wherein the specific method comprises the following steps:
comparing the resonance position obtained by the inverse calculation of the main frequency component with the estimated main resonance position:
Figure BDA0003080877050000034
a global analysis method for a rolling bearing complex run-out behavior trigger mechanism is based on the global analysis method for the rolling bearing complex run-out behavior trigger mechanism, and global analysis of the rolling bearing complex run-out behavior trigger mechanism is achieved.
When the processor executes the computer program, the global analysis of the rolling bearing complex run-out behavior trigger mechanism is realized based on the global analysis method of the rolling bearing complex run-out behavior trigger mechanism.
A computer readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a global analysis of a rolling bearing complex bouncing behavior triggering mechanism based on the global analysis method of the rolling bearing complex bouncing behavior triggering mechanism.
Compared with the prior art, the invention has the following remarkable advantages: 1) based on a common differential equation numerical integration method, through calculation and analysis of a two-degree-of-freedom rolling bearing model, a variable flexibility vibration main resonance amplitude-frequency response curve of a rolling bearing system can be quickly analyzed, and further the dynamic natural frequency, the main resonance position and the combined resonance position of the system are obtained; 2) the method obtains the system main frequency through frequency spectrum characteristic analysis, classifies the complex response main frequency possibly excited by the combined resonance according to the frequency superposition property of the combined resonance, and quickly determines the type of the combined resonance exciting the complex response; 3) The invention can verify that the complex response is caused by the combined resonance of the corresponding type by comparing the resonance position of the complex response which is inversely calculated by the main frequency component with the calculated resonance position. 4) According to the method, the combined resonance type causing the complex response is identified through the main resonance and main frequency analysis of the complex response, the trigger mechanism of the complex response can be obtained quickly, and the harmful complex response of the system can be inhibited more efficiently.
Drawings
FIG. 1 is a diagram of a two-DOF rolling bearing compliance-variable vibration dynamics model according to an embodiment of the present invention, wherein (a) is a rolling bearing system and (b) is a two-DOF spring model of the system.
FIG. 2 is a graph illustrating the response characteristic of the present invention in analyzing a complex response region, bearing play δ0VC periodic frequency-response curves for x (black line), y (red line) direction stable (solid line) and unstable (dashed line) 4.0 μm.
FIG. 3 is a graph illustrating the response characteristic bearing play δ of the present invention in analyzing a complex response interval0VC quasi-periodic motion response characteristics (a) are trajectory (black line) and poincare map (gray line) and (b) are spectrogram when 4.0 μm and Ω 363 rad/s.
FIG. 4 is a graph illustrating the response characteristic bearing play δ of the present invention in analyzing a complex response interval0When the amplitude is 4.0 μm and Ω is 353rad/s, the VC chaotic motion response characteristic is represented by (a) a trajectory (black line) and a poincare map (gray line) and (b) a spectrogram.
FIG. 5 is a graph illustrating the response characteristic bearing play δ of the present invention in analyzing a complex response interval0VC cycle 35 motion response characteristics (a) are trajectory (black line) and poincare map (gray line) and (b) are spectrogram when 4.0 μm, Ω 357 rad/s.
FIG. 6 is a graph showing the response characteristic bearing play δ of the present invention in analyzing a complex response interval0VC cycle 8 motion response characteristics at 4.0 μm, and 355rad/s, (a) trajectory (black line) and poincare map (gray line), and (b) spectrogram.
FIG. 7 is a graph showing the response characteristic bearing play δ of the present invention in analyzing a complex response interval0VC quasi-periodic motion response characteristics at 4.0 μm and Ω 181.2rad/s, (a) trajectory (black line) and poincare map (gray line), and (b) spectrogram.
FIG. 8 is a graph showing the response characteristic bearing play δ of the present invention in analyzing a complex response interval0VC cycle 4 motion response characteristics (a) are trajectory (black line) and poincare map (gray line) and (b) are spectrogram at 4.0 μm and Ω 180 rad/s.
FIG. 9 is a graph showing the response characteristic bearing play δ of the present invention in analyzing a complex response interval0VC chaotic motion response characteristic when being equal to 4.0 mu m and being equal to 154.5rad/s, and (a) is a trajectory (black line) andpoincare map (gray line), (b) is a time chart and a spectrogram.
FIG. 10 is a flowchart of a method for globally analyzing a rolling bearing complex run-out behavior triggering mechanism according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The invention provides a bearing clearance selection method for adjusting radial bearing rigidity of a rolling bearing, which comprises the following steps:
step 1, acquiring basic parameters of the geometric size, the number of balls, the contact rigidity and the equivalent damping of a rolling bearing;
step 2, inputting the basic parameters of the rolling bearing in the step 1 into a variable-compliance vibration equation of the rolling bearing with two degrees of freedom, and establishing a radial variable-compliance vibration dynamics model of the rolling bearing system as follows:
Figure BDA0003080877050000051
eyes of a user
Figure BDA0003080877050000052
δi＝xcosθi+ysinθi-δ0 (3)
θi＝2π(i-1)/Nb+Ωt (4)
Ω＝ωs(1-Db/Dh)/2 (5)
ΩVC＝Nb·Ω (6)
In the formulas (1) to (6), x and y are radial displacement of the system in two freedom directions; fx、FyBearing counter forces in the x and y directions of the system are set; t is a time independent variable; m is the equivalent mass of the bearing system; c is equivalent damping; w is the steady state of the systemLoading; cbThe contact stiffness coefficient is Hertzian, and alpha is 3/2 and 10/9 which respectively correspond to a rolling bearing and a rolling bearing system; h [. C]Is the Heaviside function representing the contact condition and describes the contact condition of the rolling body and the raceway (the contact H [. The]A value of 1, loss of contact a value of 0); n is a radical ofbIs the number of rolling elements, and δiAnd thetaiRadial deformation and instantaneous angular position of the ith rolling element respectively; 2 delta0The radial working clearance of the bearing is adopted; omega is the cage velocity and omegas、DbAnd DhRespectively the speed of a system rotating shaft, the diameter of a bearing rolling body and the diameter of a pitch circle; omegaVCAngular velocity is excited for a variable compliance parameter.
And 3, solving a Variable Compliance (VC) parameter resonance dynamic model of the rolling bearing system in the step 2 by adopting a numerical analysis method to obtain an amplitude-frequency response curve of system variable compliance vibration.
And (4) estimating the dynamic stiffness of the system through a two-degree-of-freedom direction dynamic stiffness estimation formula according to the system response obtained in the step (3). And estimating the natural frequency of the system by using a two-freedom-degree direction dynamic natural frequency estimation formula, and obtaining the main resonance position and the possible combined resonance position according to the estimated natural frequency.
The two-freedom-degree direction dynamic stiffness estimation formula provided by Mevel is as follows:
Figure BDA0003080877050000061
and a two-degree-of-freedom direction dynamic natural frequency estimation formula provided by Mevel:
Figure BDA0003080877050000062
further calculation can obtain the main resonance positions of the system in two freedom directions at the moment, namely the x direction omegax0And y direction omegay0The calculation formula is as follows:
Figure BDA0003080877050000063
wherein KintCalculating step number for numerical integration;
the calculation is made by the primary resonance location frequency: omegax0+ωy0＝ΩVC，1/2·(ωx0+ωy0)＝ΩVC，1/2·(1/2·ωx0+ ωy0)＝ΩVCAnd 1/2 (ω)x0+1/2·ωy0)＝ΩVCThe location of the possible combined resonance is obtained.
Step 5, acquiring a complex response interval of the combined resonance, analyzing the main frequency component, and determining the type of the combined resonance;
if the main frequency components p and q of the complex response in the x and y two-degree-of-freedom directions are obtained through the analysis of the main frequency components, and when p + q is equal to 1, the type of the combined resonance causing the complex response is judged to be omegax0+ωy0＝ΩVCWhen 1/2 · (p + q) ═ 1, it is determined that the type of combined resonance that causes a complex response is 1/2 · (ω) of the combined resonance typex0+ωy0)＝ΩVCCombined resonance, when 1/2 · (1/2p + q) ═ 1, then a combined resonance type 1/2 · (1/2 ω) that causes a complex response is judgedx0+ωy0)＝ΩVCWhen 1/2 · (p +1/2q) ═ 1, then a combined resonance type 1/2 · (ω) that causes a complex response is determinedx0+1/2ωy0)＝ΩVC。
Step 6, calculating the resonance position of the complex response according to the main frequency component of the complex response, comparing the resonance position with the estimated main resonance position, judging whether the resonance position is consistent with the estimated main resonance position, and determining a combined resonance interval;
and comparing with the resonance position obtained by inverse calculation of the main frequency component:
Figure BDA0003080877050000071
and if the comparison results are consistent, determining the resonance interval as a corresponding combined resonance interval.
The invention further provides a global analysis method of the rolling bearing complex bouncing behavior trigger mechanism, and the global analysis of the rolling bearing complex bouncing behavior trigger mechanism is realized based on the global analysis method of the rolling bearing complex bouncing behavior trigger mechanism.
When the processor executes the computer program, the global analysis of the rolling bearing complex run-out behavior trigger mechanism is realized based on the global analysis method of the rolling bearing complex run-out behavior trigger mechanism.
A computer readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a global analysis of a rolling bearing complex bouncing behavior triggering mechanism based on the global analysis method of the rolling bearing complex bouncing behavior triggering mechanism.
According to the calculated main frequency component and response characteristic, the invention can perform inductive analysis on the complex response and the main frequency component thereof to obtain the trigger mechanism of the overall complex jitter behavior of the system.
Examples
To verify the effectiveness of the method of the present invention, the following simulation was performed. Specific parameters of a rolling bearing of a certain type JIS6306 are given as shown in table 1.
TABLE 1 JIS6306 Rolling bearing System parameters
Figure BDA0003080877050000072
For the two-degree-of-freedom rolling bearing variable-compliance vibration dynamics model shown in fig. 1, a classical numerical integration method is adopted to quickly obtain an amplitude-frequency response curve of system variable-compliance vibration response, which is shown in fig. 2. And then, estimating the dynamic stiffness of the system by a two-degree-of-freedom direction dynamic stiffness estimation formula provided by Mevel. Then, the dynamic natural frequency estimation formula in the two-degree-of-freedom direction proposed by the measure is brought into, and the dynamic natural frequency of the system is calculated.
Then, further calculation is carried out to obtain the two-degree-of-freedom direction of the system at the momentEffective resonance position, respectively x-direction: omegax01881.47rad/s and y direction: omegay01047.21 rad/s. From the peak-to-peak system amplitude-frequency curve, as shown in FIG. 2, one can find the R of the corresponding frequency in the graph1The x-direction main resonance position in the section, and R2The y-direction primary resonance position in the section has a large peak. Calculation of omega by the primary resonance position frequencyx0+ωy0＝ΩVC，1/2·(ωx0+ωy0)＝ΩVC， 1/2·(1/2·ωx0+ωy0)＝ΩVCAnd 1/2 (ω)x0+1/2·ωy0)＝ΩVCThe location of possible combined resonances is estimated.
Then, taking the intervals with complex response such as 180rad/s, 154.5rad/s, 181.2rad/s, 363rad/s, 357rad/s, 355rad/s and 353rad/s for omega as examples, the frequency components and traces are obtained by performing spectrum feature analysis, as shown in FIG. 3 to FIG. 9. The main frequency components p and q are verified, and the following results are found:
1. a periodic 35 motion occurs at 357rad/s as shown in figure 5. The main components of the system at this time are respectively: main frequency component p in x direction4The maximum position of the peak value of the amplitude excited by the frequency component in the x direction; rate component q in the y direction4And is also the maximum position of the amplitude peak excited by the frequency component in the y-direction. p is a radical of4+q4The combined resonance exciting the complex response of the interval system is omega 1x0+ωy0＝ΩVCThe resonances are combined.
2. And when the omega is 353rad/s, triggering chaotic motion, as shown in figure 4. Taking the frequency principal component in the x-direction p separately3And the y direction q3. Calculation of discovery p3+q3The combined resonance exciting the complex response of the interval system is omega 1x0+ωy0＝ΩVCThe resonances are combined.
3. The cycle 8 motion occurs at 355rad/s, as shown in fig. 6. The main components of the system at this time are respectively: main frequency component p in x direction5The maximum position of the peak value of the amplitude excited by the frequency component in the x direction; rate component q in the y direction5Also excited by the frequency component in the y directionThe maximum position of the amplitude peak. p is a radical of5+q5The combined resonance exciting the complex response of the interval system is omega 1x0+ωy0＝ΩVCThe resonances are combined.
4. VC quasi-periodic motion occurs at 363rad/s, as shown in fig. 3. The main components of the system at this time are respectively: main frequency component p in x direction2The maximum position of the peak value of the amplitude excited by the frequency component in the x direction; rate component q in the y direction2And is also the maximum position of the amplitude peak excited by the frequency component in the y-direction. p is a radical of2+q2The combined resonance exciting the complex response of the interval system is omega 1x0+ωy0＝ΩVCThe resonances are combined.
5. VC quasi-periodic motion occurs at 181.2rad/s, as shown in FIG. 7. The main components of the system at this time are respectively: the main frequency component p in the x direction is the maximum position of the amplitude peak value excited by the frequency component in the x direction; the y-direction rate component q is also the maximum position of the peak of the amplitude excited by the y-direction frequency component. 1/2 (p + q) · 1, the combined resonance that excites the complex response of the interval system is 1/2 (ω)x0+ωy0)＝ΩVCThe resonances are combined.
6. VC cycle 4 motion occurs at 180rad/s as shown in fig. 8. The main components of the system at this time are respectively: the main frequency component p in the x direction is the maximum position of the amplitude peak value excited by the frequency component in the x direction; the y-direction rate component q is also the maximum position of the peak of the amplitude excited by the y-direction frequency component. 1/2 (p + q) · 1, the combined resonance that excites the complex response of the interval system is 1/2 (ω)x0+ωy0)＝ΩVCThe resonances are combined.
7. VC chaotic motion occurs at 154.5rad/s, as shown in fig. 9. The main components of the system at this time are respectively: the main frequency component p in the x direction is the maximum position of the amplitude peak value excited by the frequency component in the x direction; the y-direction rate component q is a dimensionless VC excitation frequency 1. 1/2 (p +1/2q) ═ 1, and the combined resonance exciting the complex response of the interval system is 1/2 (ω)x0+1/2·ωy0)＝ΩVCThe resonances are combined.
Further, according to the main frequency component of the complex response interval, the resonance position is calculated reversely, compared with the estimated resonance position, whether the two are consistent or not is judged, and whether the resonance interval is a combined resonance interval or not is determined. In the following, the resonance positions are verified by inverse calculation, taking examples of Ω as 357rad/s, Ω as 353rad/s, and Ω as 181.2rad/s respectively:
1. and the system resonance position obtained by a two-degree-of-freedom direction dynamic natural frequency estimation formula is as follows:
Figure BDA0003080877050000091
comparing the resonance position obtained by inverse calculation according to the main frequency with the system resonance position obtained by a dynamic natural frequency estimation formula in the two-degree-of-freedom direction:
Figure BDA0003080877050000092
the results are substantially consistent, and the combined resonance exciting the complex response of the system is determined to be omegax0+ωy0＝ΩVCThe resonances are combined.
2. And (3) when the omega is 353rad/s, the system resonance position obtained by the two-degree-of-freedom direction dynamic natural frequency estimation formula is still:
Figure BDA0003080877050000093
comparing the resonance position obtained by inverse calculation according to the main frequency with the system resonance position obtained by a dynamic natural frequency estimation formula in the two-degree-of-freedom direction:
Figure BDA0003080877050000094
the results are substantially consistent, and the combined resonance exciting the complex response of the system is determined to be omegax0+ωy0＝ΩVCThe resonances are combined.
3. And omega is 181.2rad/s, and the system resonance position obtained by the two-degree-of-freedom direction dynamic natural frequency estimation formula is still:
Figure BDA0003080877050000095
comparing the resonance position obtained by inverse calculation according to the main frequency with the system resonance position obtained by a dynamic natural frequency estimation formula in the two-degree-of-freedom direction:
Figure BDA0003080877050000101
the results are substantially consistent, and the combined resonance exciting the complex response of the system is determined to be omegax0+ωy0＝ΩVCThe resonances are combined.
The other inverse calculation verification processes of the complex response interval are consistent with the above process, and the reason causing the complex response interval can be judged to be the corresponding combination resonance found in the foregoing.
In conclusion, the method and the device can efficiently analyze and obtain the trigger mechanism of the complex response of the variable-compliance vibration of the rolling bearing system, quickly find the combined resonance type causing the complex response of the variable-compliance vibration of the rolling bearing system, and are beneficial to more efficiently identifying and analyzing the trigger mechanism of the harmful complex response of the system, so that the method and the measure for inhibiting the trigger mechanism of the harmful complex response of the system are more quickly provided, and the method and the measure have important values on the complex response analysis and the vibration noise control of the actual bearing supporting system.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (8)

1. A global analysis method for a rolling bearing complex run-out behavior trigger mechanism is characterized by comprising the following steps:
step 1, collecting basic parameters of a rolling bearing, including the geometric size of the rolling bearing, the number of balls, contact rigidity and equivalent damping;
step 2, substituting the basic parameters of the rolling bearing in the step 1 into a rolling bearing flexibility-variable vibration equation based on a two-degree-of-freedom rolling bearing system, and establishing a flexibility-variable parameter resonance dynamic model of the rolling bearing system;
step 3, solving the rolling bearing system variable flexibility parameter resonance dynamic model in the step 2 by adopting a numerical analysis method to obtain an amplitude-frequency response curve of system variable flexibility vibration;
step 4, estimating the dynamic stiffness of the system through a two-freedom-degree direction dynamic stiffness estimation formula according to the amplitude-frequency response obtained in the step 3, estimating the natural frequency of the system through a two-freedom-degree direction dynamic natural frequency estimation formula, and obtaining the main resonance position and the possible combined resonance position of the rolling bearing system according to the estimation result;
step 5, determining a complex response interval of the combined resonance according to the amplitude-frequency response obtained in the step 3 and the possible existing combined resonance position obtained in the step 4, analyzing the main frequency component, and determining the type of the combined resonance;
and 6, calculating the resonance position of the complex response according to the main frequency component of the complex response obtained in the step 5, comparing the resonance position with the estimated main resonance position, determining a combined resonance interval causing the complex response, and completing the overall analysis of the complex bouncing behavior trigger mechanism of the rolling bearing.
2. The global analysis method for the rolling bearing complex run-out behavior trigger mechanism according to claim 1, wherein in step 2, the basic parameters of the rolling bearing in step 1 are input into a variable-compliance vibration equation of the rolling bearing with two degrees of freedom, and a radial variable-compliance vibration dynamics model of the rolling bearing system is established:
Figure FDA0003080877040000011
and is
Figure FDA0003080877040000012
δi＝xcosθi+ysinθi-δ0 (3)
θi＝2π(i-1)/Nb+Ωt (4)
Ω＝ωs(1-Db/Dh)/2 (5)
ΩVC＝Nb·Ω (6)
In the formulas (1) to (6), x and y are radial displacement of the system in two freedom directions; fx、FyBearing counter forces in the x and y directions of the system are set; t is a time independent variable; m is the equivalent mass of the bearing system; c is equivalent damping; w is the steady load borne by the system; cbThe contact stiffness coefficient is Hertzian, and alpha is 3/2 and 10/9 which respectively correspond to a rolling bearing and a rolling bearing system; h [. C]Is the Heaviside function representing the contact condition, describes the contact condition of the rolling body and the rolling path, and generates the contact H [ ·]A value of 1, loss of contact a value of 0; n is a radical ofbIs the number of rolling elements, and δiAnd thetaiRadial deformation and instantaneous angular position of the ith rolling element respectively; 2 delta0The radial working clearance of the bearing is adopted; omega is the cage velocity and omegas、DbAnd DhRespectively the speed of a system rotating shaft, the diameter of a bearing rolling body and the diameter of a pitch circle; omegaVCAngular velocity is excited for a variable compliance parameter.
3. The global analysis method for the rolling bearing complex bounce behavior trigger mechanism according to claim 1, characterized in that in step 4, according to the amplitude-frequency response obtained in step 3, the dynamic stiffness of the system is estimated by a two-degree-of-freedom directional dynamic stiffness estimation formula, the natural frequency of the system is estimated by using a two-degree-of-freedom directional dynamic natural frequency estimation formula, and the main resonance position and the possible combined resonance position of the rolling bearing system are obtained according to the estimation formula, and the specific method is as follows:
two-degree-of-freedom direction dynamic stiffness k provided by measurexx(t)、kyy(t) estimation formula:
Figure FDA0003080877040000021
two-degree-of-freedom direction dynamic natural frequency omega proposed by Mevelxx(t)、ωxx(t) estimation formula:
Figure FDA0003080877040000022
calculating to obtain the main resonance positions of the system in two freedom directions at the moment, namely the x direction omegax0And y direction omegay0The calculation formula is as follows:
Figure FDA0003080877040000023
wherein, KintCalculating step number for numerical integration;
four possible combined resonance positions omega are obtained by the main resonance position frequencyVCRespectively: omegax0+ωy0，1/2·(ωx0+ωy0),1/2·(1/2·ωx0+ωy0) And 1/2 (ω)x0+1/2·ωy0)。
4. The global analysis method for the rolling bearing complex bounce behavior trigger mechanism according to claim 1, characterized in that in step 5, the complex response interval of the combined resonance is determined according to the amplitude-frequency response obtained in step 3 and the possible existing combined resonance position obtained in step 4, the analysis of the main frequency component is performed, and the type of the combined resonance is determined, and the specific method is as follows:
if the main frequency components p and q of the complex response in the x and y two-degree-of-freedom directions are obtained through the analysis of the main frequency components, and when p + q is equal to 1, the type of the combined resonance causing the complex response is judged to be omegax0+ωy0＝ΩVCWhen 1/2 · (p + q) ═ 1, it is determined that the type of combined resonance that causes a complex response is 1/2 · (ω) of the combined resonance typex0+ωy0)＝ΩVCCombined resonance, when 1/2 · (1/2p + q) ═ 1, then a combined resonance type 1/2 · (1/2 ω) that causes a complex response is judgedx0+ωy0)＝ΩVCWhen 1/2 · (p +1/2q) ═ 1, then a combined resonance type 1/2 · (ω) that causes a complex response is determinedx0+1/2ωy0)＝ΩVC，ωx0、ωy0The main resonance position in the two-degree-of-freedom direction.
5. The global analysis method for the rolling bearing complex run-out behavior trigger mechanism according to claim 1, wherein in step 6, the resonance position is inversely calculated according to the main frequency component of the complex response obtained in step 5, and compared with the estimated main resonance position, the combined resonance interval causing the complex response is determined, and the global analysis of the rolling bearing complex run-out behavior trigger mechanism is completed, and the specific method is as follows:
comparing the resonance position obtained by the inverse calculation of the main frequency component with the estimated main resonance position:
Figure FDA0003080877040000031
in the formula, NbIs the number of rolling elements, omega is the speed of the retainer, p and q are the main frequency components in the two freedom directions, omegax0、ωy0Is the estimated main resonance position in the two-degree-of-freedom direction.
6. A global analysis method for a rolling bearing complex run-out behavior trigger mechanism is characterized in that the global analysis of the rolling bearing complex run-out behavior trigger mechanism is realized based on the global analysis method for the rolling bearing complex run-out behavior trigger mechanism of any one of claims 1 to 5.
7. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor, when executing the computer program, implements a global analysis of a rolling bearing complex run-out behavior trigger mechanism based on the global analysis method of a rolling bearing complex run-out behavior trigger mechanism as claimed in any one of claims 1 to 5.
8. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements a global analysis of a rolling bearing complex run-out behavior trigger mechanism based on the global analysis method of a rolling bearing complex run-out behavior trigger mechanism of any of claims 1 to 5.
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