CN114486261B - Bearing outer ring fault positioning method based on synchronous root-mean-square ratio - Google Patents

Bearing outer ring fault positioning method based on synchronous root-mean-square ratio Download PDF

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CN114486261B
CN114486261B CN202210071039.7A CN202210071039A CN114486261B CN 114486261 B CN114486261 B CN 114486261B CN 202210071039 A CN202210071039 A CN 202210071039A CN 114486261 B CN114486261 B CN 114486261B
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outer ring
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CN114486261A (en
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李献文
石怀涛
李思慧
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Shenyang Kewangtong Information Technology Co ltd
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Abstract

The invention belongs to the technical field of bearing fault positioning, and particularly relates to a bearing outer ring fault positioning method based on a synchronous root-mean-square ratio, which comprises the steps of establishing a bearing nonlinear contact dynamic model, inputting bearing system parameters and bearing simulation fault parameters into the bearing nonlinear contact dynamic model, and outputting a simulation vibration signal of a fault point position; taking three measuring points, obtaining vibration signals of the three measuring points according to the simulated vibration signals of the fault point positions and the attenuation parameters of the bearing system, carrying out synchronous root mean square processing on the vibration signals of the three measuring points, providing a bearing fault positioning index curve based on the synchronous root mean square processing, and fitting a relational expression between the bearing fault positioning index curve and the fault angle position, namely a bearing outer ring fault position identification model; collecting actual signals of three measuring points on a bearing with faults; and inputting the acquired actual signal into a bearing outer ring fault position identification model to obtain a specific fault angle position. The invention realizes the positioning of the bearing fault.

Description

Bearing outer ring fault positioning method based on synchronous root-mean-square ratio
Technical Field
The invention belongs to the technical field of bearing fault positioning, and particularly relates to a bearing outer ring fault positioning method based on a synchronous root-mean-square ratio.
Background
The rolling bearing is one of the most common and most vulnerable key components in mechanical equipment, and the operation precision of the rolling bearing directly influences the operation precision of the equipment. Aiming at non-high-precision rotating equipment, when a rolling bearing breaks down, the running precision of the equipment is slightly influenced due to the fact that the fault degree is relatively low, the normal operation of the equipment is hardly influenced, and the production can be normally carried out. However, as the degree of failure increases, failure of the rolling bearing can result in excessive vibration of the rotor system, rotor rub, and even machine failure, resulting in production and economic losses. In order to reduce the influence of the rolling bearing fault on the whole production plan, the residual service life of the rolling bearing can be predicted in advance according to the bearing fault, the production plan is reasonably arranged according to the residual service life of the bearing, and the fault equipment is maintained. The positioning of the bearing outer ring defect plays an important role in fault elimination, fault reason analysis and residual life analysis of the rolling bearing, for example, when other factors are the same, the closer the fault position of the bearing outer ring is to the load center, the faster the defect expansion is, and the less the residual life of the bearing is; the faults at different positions correspond to different fault reasons.
At present, vibration bearing faults are analyzed, most of the vibration bearing faults are judged and qualitatively analyzed, namely whether faults exist or not is judged, or parts with faults of the bearing are distinguished, the bearing faults are analyzed and researched less, and especially, the fault positions are analyzed and qualitatively. At present, the research on the fault position of the bearing outer ring is mostly concentrated near a load center, the research range is small, and the actual requirement cannot be met.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a bearing outer ring fault positioning method based on the synchronous root-mean-square ratio, so that the bearing fault can be accurately positioned.
The invention is realized in this way, and provides a bearing outer ring fault positioning method based on the synchronous root-mean-square ratio, which comprises the following steps:
1) establishing a bearing nonlinear contact dynamic model, inputting bearing system parameters and bearing simulation fault parameters into the bearing nonlinear contact dynamic model, and outputting a simulation vibration signal of a fault point position;
2) taking three measuring points, obtaining vibration signals of the three measuring points according to the simulated vibration signals of the fault point positions in the step 1) and the attenuation parameters of the bearing system, carrying out synchronous root mean square processing on the vibration signals of the three measuring points, providing a bearing fault positioning index curve based on the synchronous root mean square processing, and fitting a relational expression between the bearing fault positioning index curve and the fault point position;
3) collecting actual signals of three measuring points on a bearing with faults;
4) inputting the actual signals acquired in the step 3) into the bearing outer ring fault position identification model established in the step 2) to obtain a specific fault angle position.
Preferably, in the step 1), the bearing local fault is described based on a geometric boundary fault model theory pair, and the bearing nonlinear contact dynamic model expression is as follows:
Figure BDA0003482085460000021
wherein m is the bearing mass, c and k are the damping and rigidity of the bearing system, Z is the number of balls in the bearing, and x and y are the vibration signal vectors in the horizontal and vertical directions,
Figure BDA0003482085460000022
The included angle between the connecting line between the observation ball and the circle center and the horizontal direction is observed;
for the outer ring fault passing fault depth H, the included angle of the defect width relative to the circle center of the bearing
Figure BDA0003482085460000023
And defect position angle
Figure BDA0003482085460000024
Three parameters are used for describing the fault depth of the jth ball passing through the outer ring defect
Figure BDA0003482085460000025
Comprises the following steps:
Figure BDA0003482085460000026
Figure BDA0003482085460000031
wherein r is 1 Is the radius r of the raceway of the outer ring b Is the ball radius; from the geometrical relationship of the bearing system, the elastic deformation of the jth ball
Figure BDA0003482085460000032
Expressed as:
Figure BDA0003482085460000033
wherein, c r Radial play of bearing, the contact load according to Hertz contact theory
Figure BDA0003482085460000034
Expressed as:
Figure BDA0003482085460000035
wherein K represents the hertzian contact stiffness.
Further preferably, considering that a certain distance exists between a bearing fault position and a measuring point, a certain attenuation inevitably exists in the vibration signal in the transmission process, the attenuation process is similar to exponential attenuation, so that a vibration attenuation factor is introduced into a bearing dynamic system, and the attenuated vibration signal is expressed as:
Figure BDA0003482085460000036
in the formula, s l For the damped vibration signal, s is the vibration signal generated at the fault position, i.e. s is the sum of the x vibration signal vector and the y vibration signal vector, l is the distance between the bearing fault point and the measuring point, r 0 Is the radius of the vibration source, f 0 Is the system vibration source frequency xi 0 Is a geometric attenuation coefficient, α 0 Is the energy attenuation coefficient;
due to the existence of attenuation, when the outer ring of the bearing has a fault, the vibration signals obtained at different measuring points are different, and the different measuring points are analyzedIdentifying the fault position by mapping relation between the point vibration signal and the bearing fault position, and taking three measuring points x on the outer ring of the bearing 1 、x 2 、y 1 ，s x1 、s x2 、s y1 Respectively representing the vibration signals of the three measuring points, and firstly, carrying out synchronous root mean square processing on the vibration signals of the three measuring points to obtain an SRMS y1 、SRMS x1 、SRMS x2 And a bearing fault location index HHVSRMS is provided on the basis that:
Figure BDA0003482085460000041
DSRMS＝ΔSRMS 1 /ΔSRMS 2 (8)
Figure BDA0003482085460000042
the HHVSRMS curves are obtained according to the equations (7), (8) and (9), and it is known that HHVSRMS is monotonously symmetrical in two intervals of about 270 DEG, and only one of them is considered
Figure BDA0003482085460000043
And then judging whether the fault is on the left side or the right side of 270 degrees according to the value of the intermediate parameter DSRPS to obtain the final fault position, wherein the relational expression of the HHVSRMS and the fault angle position is as follows:
Figure BDA0003482085460000044
Figure BDA0003482085460000045
formula (10) is a fault angle
Figure BDA0003482085460000046
Time HHVSRMS value and fault angle location
Figure BDA0003482085460000047
Corresponding relation of (1), wherein p 1 、p 2 、p 3 、p 4 Is a trimming coefficient, and f represents an intermediate quantity angle calculated by equation (10).
Preferably, in step 3), a bearing fault signal acquisition mechanism is used to acquire actual signals of three measurement points on a bearing with a fault, the bearing fault signal acquisition mechanism includes a doorframe-type machine body, two side frames and an upper frame of the machine body are respectively provided with a strip hole, a slide block is movably connected to the frame outside each strip hole, three surfaces of the three slide blocks close to each other are respectively and fixedly connected with a non-contact vibration sensor, when the actual signals are acquired, the bearing is placed in the middle diameter of the machine body, and the three non-contact vibration sensors acquire fault vibration signals of the three measurement points of the fault bearing.
Compared with the prior art, the invention has the advantages that:
analyzing bearing faults based on a bearing fault dynamics mechanism, and according to the provided new bearing outer ring fault position identification method: horizontal-vertical synchronous rms method. The diagnosis method is used for local bearing vibration signal attenuation law in the transmission process, and the signal acquisition mechanism provided by the patent is applied to signal acquisition. The method solves the problem of small outer ring fault identification range, expands the outer ring fault identification range to 230-310 degrees, and simultaneously solves the problem of difficult sensor installation.
Drawings
FIG. 1 is a schematic diagram of a defect;
FIG. 2 is a graph showing a contact force applied to a ball;
FIG. 3 is a graph showing the contact force of the balls in the horizontal direction;
FIG. 4 is a graph of contact force in the vertical direction of the ball bearing;
FIG. 5 shows the variation of the horizontal contact force of the balls in the event of a failure of the outer ring
Figure BDA0003482085460000051
FIG. 6 shows the variation of the contact force of the balls in the vertical direction when the outer ring fails
Figure BDA0003482085460000052
FIG. 7 is a schematic view of outer ring measuring points;
FIG. 8 is a correspondence of HHVSRMS to outer ring fault location;
FIG. 9 is a schematic view of a signal acquisition mechanism;
FIG. 10 is a flow chart of a method for identifying the location of a bearing outer ring fault.
Detailed Description
The invention is further explained below with reference to the figures and the specific examples:
the method is based on the attenuation rule of the bearing vibration signal in the transmission process and the vibration signal acquisition at different measuring points of the bearing outer ring, provides a method for positioning the fault of the bearing outer ring based on a horizontal-vertical synchronous root mean square method, and develops a signal acquisition mechanism for matching the acquisition of multi-point signals. The method analyzes the internal relation between signals and enlarges the fault identification position of the outer ring of the bearing. The method provides a new method for quantitative analysis of the fault position of the bearing outer ring, and the feasibility of the method is verified in simulation and practice.
1) Bearing nonlinear dynamic model
Establishing a bearing nonlinear dynamical model, bringing relevant parameters of a bearing to be tested into the bearing nonlinear dynamical model, and describing a local fault of the bearing based on a geometric boundary fault model theory pair, as shown in fig. 1. The bearing nonlinear dynamics model expression is as follows
Figure BDA0003482085460000061
Wherein m is the bearing mass, c and k are the damping and rigidity of the bearing system respectively, Z is the number of the bearing rolling elements, x and y are vibration signal vectors in two directions,
Figure BDA0003482085460000062
the included angle between the connecting line between the ball and the circle center and the horizontal direction is observed.
For the outer ring fault passing fault depth H, the included angle of the defect width relative to the center of a circle of the bearing
Figure BDA0003482085460000063
And defect position angle
Figure BDA0003482085460000064
Three parameters are described, and the geometrical relationship is shown in figure 1. The depth of failure of the jth ball passing through the outer ring defect
Figure BDA0003482085460000065
Figure BDA0003482085460000066
Figure BDA0003482085460000067
From the geometrical relationship of the bearing system, the elastic deformation of the jth ball
Figure BDA0003482085460000068
Expressed as:
Figure BDA0003482085460000069
in the formula c r Radial play of bearing, the contact load according to Hertz contact theory
Figure BDA00034820854600000610
Expressed as:
Figure BDA00034820854600000611
when the bearing is defect-free, the conditions of the contact force applied to the first ball in the bearing can be obtained through simulation as shown in fig. 2, fig. 3 and fig. 4. Contact force F applied to the ball qj Left-right symmetry about 270 degrees as a boundary when the ball is positioned
Figure BDA00034820854600000612
At 270 deg. its contact force is greatest, when the ball is in position
Figure BDA0003482085460000071
Away from 270 deg. its contact force decreases as shown in figure 2. Horizontal contact force F of ball qjx Is approximately at
Figure BDA0003482085460000072
A varying sine function curve centered at 270 deg., as shown in fig. 3. Ball vertical direction contact force F qjx Is approximately at
Figure BDA0003482085460000073
A modified cosine function curve centered at 270 deg., as shown in fig. 4.
When the outer ring of the bearing has defects, the defects are positioned
Figure BDA0003482085460000074
In the internal variation, the contact force distribution of the ball in the horizontal direction and the vertical direction in one period is shown in fig. 5 and 6. The sudden change of the ball contact load is caused by the fact that the ball passes through the defect, and it can be seen that the sudden change of the ball contact load can follow the position of the defect in the bearing loading interval
Figure BDA0003482085460000075
May vary.
2) HHVSRMS vs. fault angle location relationship
When the rolling elements pass through a fault, the contact generates a sudden change, which not only generates an excitation effect on the system, but also is a main source for generating fault characteristic signals. And assuming that a fault vibration signal generated at the fault position of the outer ring is transmitted to a measuring point along the outer ring, and the transmission medium is only the outer ring of the bearing. Considering that a certain distance exists between a fault position and a measuring point, certain attenuation inevitably exists in the signal transmission process, the attenuation process is similar to exponential attenuation, and therefore vibration attenuation factors are introduced into a bearing dynamic system
Figure BDA0003482085460000076
Where l is the distance between the fault and the measurement point, s is the vibration signal generated at the fault location, s l For the damped vibration signal, r 0 Is the radius of the vibration source, f 0 System source frequency xi 0 Is a geometric attenuation coefficient, α 0 Is the energy attenuation coefficient.
Due to attenuation in the signal transmission process, when the bearing has an outer ring fault, vibration signals obtained at different measuring points are different, and the fault position can be identified by analyzing the mapping relation between the vibration signals at the different measuring points and the fault position of the bearing. As shown in FIG. 7, three measuring points x are taken on the outer ring of the bearing 1 、x 2 、y 1 Then s x1 、s x2 、s y1 Representing the vibration signal at the three measurement points, respectively. Firstly, synchronous root mean square processing is carried out on the three-measuring-point signals to obtain SRMS y1 、SRMS x1 、SRMS x2 And a bearing fault location index HHVSRMS is provided on the basis that:
Figure BDA0003482085460000081
DSRMS＝ΔSRMS 1 /ΔSRMS 2 (8)
Figure BDA0003482085460000082
the results of the HHVSRMS curves are shown in fig. 8, where HHVSRMS is monotonically symmetric in two intervals around 270 °.
Then only consideration may be given toOne is as follows
Figure BDA0003482085460000083
And (3) according to the corresponding relation between the HHVSRMS and the fault angle position, fitting a relational expression between the HHVSRMS and the fault angle position according to the corresponding relation, identifying a fault angle, and then judging whether the fault is positioned on the left side or the right side of 270 degrees according to the value of the intermediate parameter DSRPS to obtain a final fault position.
3) Acquisition of the actual signal
The signal acquisition mechanism is shown in fig. 9. The mechanism is matched with a signal acquisition system for use, and the problems that an equipment sensor is not easy to place and multi-point signals are acquired simultaneously can be solved.
Each sliding block is driven by a servo motor and moves in a corresponding sliding groove according to a designated route, and a non-contact vibration sensor is arranged on each sliding block. The sensor reaches the designated position under the drive of the sliding block, is locked with the locking knob, and then carries out signal acquisition.
The left sliding block of the mechanism is matched with the left sliding groove, and the left sliding block can move up and down in the left sliding groove under the driving of the motor by moving the adjusting knob. Meanwhile, the left non-contact vibration sensor is fixed on the left sliding block, so that the position of the left non-contact vibration sensor can move up and down to collect data at a point to be measured.
The right mechanism principle is similar to the left.
The upper sliding block of the mechanism is matched with the upper chute, and the upper sliding block can move left and right in the upper chute under the driving of the motor by moving the adjusting knob. Meanwhile, the upper non-contact vibration sensor is fixed on the upper sliding block, so that the position of the upper non-contact vibration sensor can move left and right, and data at a point to be measured is collected.
And adjusting the position of each non-contact vibration sensor before signal acquisition, and connecting a signal acquisition system after the position adjustment is finished to acquire signals.
4) Identification of bearing outer ring fault location
And processing the acquired data according to the formulas (7), (8) and (9) to obtain a bearing fault positioning index HHVSRMS. Then the fault position of the bearing outer ring is brought into an identification formula:
Figure BDA0003482085460000091
Figure BDA0003482085460000092
formula (10) is a fault angle
Figure BDA0003482085460000093
Time HHVSRMS value and fault angle location
Figure BDA0003482085460000094
Corresponding relation of (1), in which p 1 、p 2 、p 3 、p 4 Is the trim factor.
In summary, a flowchart of the method for identifying the fault position of the outer ring of the bearing is shown in fig. 10.
Examples of the production of,
First, signal acquisition
(1) And (3) installing a signal acquisition mechanism, fixing the signal acquisition mechanism provided by the method at the position of the bearing to be detected 15, enabling the central section of the mechanism to be superposed with the radial central section of the bearing to be detected, and fixing the position of the machine body 11 by using a fixing bolt 1.
(2) And unlocking the locking knob 3, driving the left sliding block 4 to move up and down in the left sliding groove 2 through the servo motor, enabling the left non-contact vibration sensor 12 to be superposed with the central horizontal line of the bearing to be detected, and then locking the progress position of the locking knob 3.
(3) And unlocking the locking knob 10, driving the right sliding block 9 to move up and down in the right sliding groove 8 through the servo motor, enabling the right non-contact vibration sensor 14 to be overlapped with the central horizontal line of the bearing to be detected, and then locking the progress position of the locking knob 10.
(4) And unlocking the locking knob 5, driving the upper side sliding block 6 to move up and down in the upper sliding groove 7 through the servo motor, enabling the upper side non-contact type vibration sensor 13 to be superposed with the central horizontal line of the bearing to be detected, and then locking the progress position of the locking knob 5.
(5) And (3) running the bearing to be tested to enable the bearing to be in a stable running state, and then acquiring three groups of synchronous vibration signals through three non-contact vibration sensors. And importing three groups of data into excel, wherein the first column is a vibration signal acquired by a left non-contact vibration sensor, the second column is a vibration signal acquired by a right non-contact vibration sensor, the third column is a vibration signal acquired by an upper non-contact vibration sensor, and the file is named as 'experimental data x ls'.
Second, kinetic analysis
(1) Login MATLAB interface
The program was run in a MATLAB application to complete the kinetic simulation analysis. First, open the folder in which the file "bearing.m" is located, and open the file "bearing.m".
(2) Inputting bearing parameters
Relevant parameters of the bearing to be tested need to be input in the file, namely NN is the number of the bearing rolling bodies, DW is the diameter of the bearing pitch circle, dr is the diameter of the bearing rolling bodies, fr is the rotation frequency, mi is the mass of the inner ring of the bearing, and mo is the mass of the outer ring of the bearing.
(3) Running program
And simulating the fault of the bearing to be tested through a program to obtain vibration signals of the bearing fault at different positions. And (4) performing synchronous root mean square processing on the simulation signal, and then processing data according to the equations (7), (8) and (9) to obtain a positioning index HHVSRMS. In the right working area of MATLAB, the sequence "o"
Indicating the location of the fault and the series "hhv" indicates the location indicator HHVSRMS.
(4) Fitting a mapping curve
And fitting a corresponding relation between the obtained fault position and the positioning index HHVSRMS to obtain a corresponding relation fitting formula. Select "application" on the top side of MATLAB, then select Curve fixing. And taking the positioning index HHVSRMS as an x coordinate and the fault position as a y coordinate, namely selecting 'hhv' for the x value and 'o' for the y value. Function selection "Rational" function number degree selection "2", Denominator degree selection "1", fitting out a function
Figure BDA0003482085460000101
In the formula, p 1 ＝-15.8，p 2 ＝-13，p 3 ＝28.3，p 4 ＝0.64。
Thirdly, identifying fault positions of bearing outer rings
(1) Inputting fitting parameters
Opening a 'weichi.m' file in a corresponding folder, and obtaining relevant parameters, p, of the fitting relational expression according to simulation 1 、p 2 、p 3 、p 4 And inputting the data into a program.
(2) Inputting measured data
The file "experimental data. xls" is placed in the same folder as the program, and the eighth line of code in the program is changed to "x ═ xlsread ('experimental data. xlsx')". And operating the program to identify the fault position of the bearing.
(3) Outputting the result
The output result is shown as "fault position 302.7472". The fault position of the bearing to be tested is set to be 300 degrees, the error between the test result and the preset result is small, and the feasibility of the method for identifying the fault position of the outer ring of the bearing is verified within the acceptable range.

Claims (3)

1. The bearing outer ring fault positioning method based on the synchronous root-mean-square ratio is characterized by comprising the following steps of:
1) establishing a bearing nonlinear contact dynamic model, inputting bearing system parameters and bearing simulation fault parameters into the bearing nonlinear contact dynamic model, and outputting a simulation vibration signal of a fault point position;
2) taking three measuring points, obtaining vibration signals of the positions of the three measuring points according to the simulated vibration signals of the positions of the fault points in the step 1) and the attenuation parameters of the bearing system, carrying out synchronous root mean square processing on the vibration signals of the positions of the three measuring points, providing a bearing fault positioning index curve based on the synchronous root mean square processing, and fitting a relational expression between the bearing fault positioning index curve and the positions of the fault points;
considering that a certain distance exists between a bearing fault position and a measuring point, a certain attenuation inevitably exists in a vibration signal in a transmission process, the attenuation process is similar to exponential attenuation, so that a vibration attenuation factor is introduced into a bearing dynamic system, and the attenuated vibration signal is expressed as:
Figure FDA0003770930940000011
in the formula, s l For the damped vibration signal, s is the vibration signal generated at the fault position, i.e. s is the sum of the x vibration signal vector and the y vibration signal vector, l is the distance between the bearing fault point and the measuring point, r 0 Is the radius of the vibration source, f 0 Is the system vibration source frequency xi 0 Is a geometric attenuation coefficient, alpha 0 Is the energy attenuation coefficient;
due to the existence of attenuation, when the outer ring of the bearing has a fault, the vibration signals obtained at different measuring points have differences, the fault position is identified by analyzing the mapping relation between the vibration signals at the different measuring points and the fault position of the bearing, and three measuring points x are taken from the outer ring of the bearing 1 、x 2 、y 1 ，s x1 、s x2 、s y1 Respectively representing the vibration signals of the three measuring points, and firstly, carrying out synchronous root mean square processing on the vibration signals of the three measuring points to obtain an SRMS y1 、SRMS x1 、SRMS x2 And a bearing fault location index HHVSRMS is provided on the basis that:
Figure FDA0003770930940000021
DSRMS＝ΔSRMS 1 /ΔSRMS 2 (8)
Figure FDA0003770930940000022
the HHVSRMS curves are obtained according to the equations (7), (8) and (9), and it is known that HHVSRMS is monotonously symmetrical in two intervals of about 270 DEG, and only one of them is considered
Figure FDA0003770930940000023
The corresponding relation between the HHVSRMS and the fault angle position is adopted, the relation between the HHVSRMS and the fault angle position is fitted according to the corresponding relation, the fault angle is identified, then whether the fault is on the left side or the right side of 270 degrees is judged according to the value of the intermediate parameter DSRMS, and the final fault position is obtained, wherein the relation between the HHVSRMS and the fault angle position is as follows:
Figure FDA0003770930940000024
Figure FDA0003770930940000025
formula (10) is a fault angle
Figure FDA0003770930940000026
Time HHVSRMS value and fault angle location
Figure FDA0003770930940000027
Corresponding relation of (1), wherein p 1 、p 2 、p 3 、p 4 Is a trimming coefficient, f represents an intermediate quantity angle calculated by the formula (10);
3) collecting actual signals of three measuring points on a bearing with faults;
4) inputting the actual signals acquired in the step 3) into the relational expression between the bearing fault positioning index curve and the fault angle position established in the step 2) to obtain a specific fault angle position.
2. The synchronous RMS (root mean square) ratio-based bearing outer ring fault location method according to claim 1, wherein in step 1), the bearing local fault is described based on a geometric boundary fault model theory pair, and the expression of the bearing nonlinear contact dynamic model is as follows:
Figure FDA0003770930940000031
wherein m is the bearing mass, c and k are the damping and rigidity of the bearing system, Z is the number of balls in the bearing, and x and y are the vibration signal vectors in the horizontal and vertical directions,
Figure FDA0003770930940000032
The included angle between the connecting line between the observation ball and the circle center and the horizontal direction is observed;
for the outer ring fault passing fault depth H, the included angle of the defect width relative to the circle center of the bearing
Figure FDA0003770930940000033
And angle of defect position
Figure FDA0003770930940000034
Three parameters are described, then the fault depth of the jth ball passing through the outer ring defect
Figure FDA0003770930940000035
Comprises the following steps:
Figure FDA0003770930940000036
Figure FDA0003770930940000037
wherein r is 1 Radius of outer ring raceway r b Is the ball radius; from the geometrical relationship of the bearing system, the elastic deformation of the jth ball
Figure FDA0003770930940000038
Expressed as:
Figure FDA0003770930940000039
wherein, c r Radial play of bearing, the contact load according to Hertz contact theory
Figure FDA00037709309400000310
Expressed as:
Figure FDA00037709309400000311
wherein K represents the hertzian contact stiffness.
3. The method for locating the bearing outer ring fault based on the synchronous RMS ratio as claimed in claim 1, wherein in step 3), a bearing fault signal collecting mechanism is used to collect the actual signals of three measuring points on the faulty bearing, the bearing fault signal collecting mechanism includes a doorframe-type body (11), two side frames and one upper frame of the body (11) are respectively provided with a long hole, a slide block is movably connected to the frame outside each long hole, three surfaces of the three slide blocks close to each other are respectively fixedly connected with a non-contact vibration sensor, when collecting the actual signals, the bearing is placed in the middle diameter of the body (11), and the three non-contact vibration sensors collect the fault vibration signals of the three measuring points of the faulty bearing.
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