CN107741324A - A kind of housing washer fault section diagnosis method - Google Patents

A kind of housing washer fault section diagnosis method Download PDF

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CN107741324A
CN107741324A CN201710954465.4A CN201710954465A CN107741324A CN 107741324 A CN107741324 A CN 107741324A CN 201710954465 A CN201710954465 A CN 201710954465A CN 107741324 A CN107741324 A CN 107741324A
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outer ring
angle position
msup
vibration acceleration
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CN107741324B (en
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崔玲丽
黄金凤
张飞斌
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Beijing University of Technology
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Beijing University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis

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Abstract

The present invention relates to a kind of housing washer fault section diagnosis method.This method initially sets up rolling bearing arrangement non-linear dynamic model, and the dynamic differential equation group of bearing arrangement is derived by lagrange equation of the second kind.Based on system dynamics differential equation group, bearing arrangement when simulating different faults Angle Position horizontally and vertically vibration acceleration signal.Then by emulation data, linear relation of the outer ring fault angle position with the flat synchronous root-mean-square value that hangs down is gone out using least square fitting.Next measures the level diagnosis reference data of the disconnected bearing arrangement of follow-up, and calculates the flat synchronous root-mean-square value that hangs down of level diagnosis reference data, relational expressions of the outer ring failure Angle Position θ of bearing arrangement with putting down vertical synchronous root-mean-square value so that it is determined that follow-up breaks.The Angle Position θ for being diagnosed outer ring failure is finally then made a definite diagnosis out by outer ring failure Angle Position positioning moded.What the present invention realized bearing outer ring failure is accurately positioned diagnosis, has important theory significance and application value.

Description

A kind of housing washer fault section diagnosis method
Technical field
The invention belongs to rolling bearing fault diagnosis field, and in particular to a kind of housing washer fault section diagnosis side Method.
Background technology
Rolling bearing is one of most commonly used parts in the equipment such as rotating machinery, and is easiest to zero of damage Part.When it produces failure, whole equipment will be induced and produce failure, therefore, rolling bearing fault diagnosis research is set for maintenance Standby normal operation is very crucial.Bearing failure diagnosis research at present is concentrated mainly on bearing fault quantitative Diagnosis, bearing fault Pattern-recognition etc..Level diagnosis research for bearing outer ring failure does not almost have, but the failure of different Angle Positions can Different producing causes, such as manufacture, assembling and working condition etc. can be correspond to.In addition, in other factorses identical situation Under, the failure of different Angle Positions may correspond to different residual lifes, such as defect Angle Position closer to the axle at carrying center The residual life held is often shorter.Further, realize that bearing outer ring fault section diagnosis will be helpful to after tearing machine open faster arrange Abort situation is found, while contributes to the maintenance and maintenance work of bearing, improves operating efficiency.Therefore solve it is how quick, The problem of predicting bearing outer ring failure Angle Position exactly has weight to bearing failure diagnosis and bearing residual life estimation The theory significance and engineering application value wanted.
VR refers to Ping-vertical synchronous root-mean-square value, is one for being realized the level diagnosis of bearing outer ring by inventor and being proposed Kind New Set, its detailed algorithm and application technology will illustrate in present invention and embodiment.
The content of the invention
In order to quickly and accurately predict the Angle Position of housing washer failure, the present invention is dug based on study mechanism The VR indexs excavated propose a kind of housing washer fault section diagnosis method, while have been opened up newly for bearing fault technology Developing direction.
To achieve the above object, technical scheme is as follows：
A kind of housing washer fault section diagnosis method, including step in detail below：
Step 1 establishes rolling bearing arrangement non-linear dynamic model and its differential equation group,
The global absolute rectangular coordinate system of bearing arrangement is established, as reference, horizontal direction to be set towards power intake For x-axis, and level is positive direction to the right, and vertical direction is set as into y-axis, and is positive direction vertically downward, and bearing inner race represents For particle m1, bearing outer ring is expressed as particle m2, the horizontal direction displacement and vertical direction displacement of bearing inner race are expressed as x1 And y1, the horizontal direction displacement and vertical direction displacement of bearing outer ring are expressed as x2And y2, bearing outer ring is by horizontal direction Spring-damper 1 and the spring-damper of vertical direction 2 are supported, and the rigidity and damped coefficient of spring-damper 1 are expressed as k1And c1, the rigidity and damped coefficient of spring-damper 2 are expressed as k2And c2, it is θ by outer ring fault angle positional representation, base In above-mentioned institute's established model, the dynamic differential equation group of bearing arrangement is derived by lagrange equation of the second kind；
Step 2 establishes the flat functional relation hung down between synchronous root-mean-square value and outer ring failure Angle Position, sets outer ring failure The constant interval of Angle Position is [240 °, 300 °], and the constant interval is carried out into 7 deciles, then obtains 7 ascending outer rings events Hinder Angle Position θ1,θ2…θj…θ7, j represents the numbering of outer ring failure Angle Position, the integer between value 1~7；By being pushed away in step 1 The each failure Angle Position θ of bearing system dynamics Systems of Ordinary Differential Equations ledjCorresponding horizontal direction emulates vibration acceleration Signal ax,jWith vertical direction emulation vibration acceleration signal ay,j, then calculate the flat vertical synchronous square of each fault angle position correspondence Root：
In above formula, N is emulation data points, wherein, with θjFor independent variable, VRjIt is linear by least square method for dependent variable Fit outer ring failure Angle Position θ and VR values relational expression：
θ=270 ± k (VR-VR4) (2)
Step 3 measures the level diagnosis reference data of the disconnected bearing arrangement of follow-up,
So that towards power intake, as reference, horizontal setting is to the right 0 °, and vibration acceleration sensor 1 is arranged on into follow-up 90 ° of positions of the bearing block of disconnected bearing arrangement, vibration acceleration sensor 2 is arranged on to the bearing block of the disconnected bearing arrangement of follow-up 180 ° of positions, outer ring failure Angle Position is measured at 270 ° by vibration acceleration sensor 1 and vibration acceleration sensor 2 respectively Vertical vibration acceleration signal a 'yWith horizontal direction vibration acceleration signal a 'x, then calculate determining for the disconnected bearing arrangement of follow-up Position diagnosis benchmark VR values:
By the VR in VR' replacement formulas (2)4, obtain outer ring failure Angle Position θ and the pass of VR values of the disconnected bearing arrangement of follow-up It is formula：
θ=270 ± k (VR-VR ') (4)
Step 3 outer ring failure Angle Position positioning mode then,
So that towards power intake, as reference, horizontal setting is to the right 0 °, and vibration acceleration sensor 1 is arranged on into follow-up 90 ° of positions of the bearing block of disconnected bearing arrangement, vibration acceleration sensor 2 is arranged on to the bearing block of the disconnected bearing arrangement of follow-up 180 ° of positions, measure the Vertical Square for being diagnosed faulty bearings respectively by vibration acceleration sensor 1 and vibration acceleration sensor 2 To vibration acceleration signal a "yWith horizontal direction vibration acceleration signal a "x, and calculate the VR values for being diagnosed faulty bearings：
A " is drawn respectivelyxWith a "yTime domain beamformer, observe oscillogram in failure impact prime direction, as a "xWaveform Failure impact prime direction in figure is just and a "yFailure impact prime direction in oscillogram for it is negative when, then the outer ring failure It can determine that as positioned at 270 ° of left side, that is, the failure Angle Position being diagnosed can be identified as：
θd=270-k (VR "-VR ') (6)
As a "xFailure impact prime direction in oscillogram is negative and a "yFailure impact prime direction in oscillogram is negative When, then the outer ring failure can determine that as positioned at 270 ° of right side, that is, the failure Angle Position being diagnosed can be identified as：
θd=270+k (VR "-VR ') (7)
The beneficial effects of the invention are as follows：A kind of housing washer fault section diagnosis method is proposed, is establishing follow-up The outer ring failure Angle Position θ of disconnected bearing arrangement with after the functional relation of VR values, by outer ring failure Angle Position positioning mode then The Angle Position for being diagnosed outer ring failure can be made a definite diagnosis out, there is important actual application value.
The present invention is further illustrated with example for lower mask body combination accompanying drawing.
Brief description of the drawings
The workflow diagram of Fig. 1 present invention
Fig. 2 rolling bearing arrangement non-linear dynamic model schematic diagrames
Fig. 3 outer rings failure Angle Position θ and the variation relation figure for putting down the synchronous root-mean-square value that hangs down
Fig. 4 is the horizontally and vertically vibration acceleration signal of faulty bearings system to be diagnosed
Embodiment
The diagnostic method of the present invention is described in detail with embodiment for lower mask body combination accompanying drawing, but the guarantor of the present invention Shield scope is not limited to the embodiment.
As shown in figure 1, it is a kind of workflow diagram of housing washer fault section diagnosis method of the present invention.Specifically Implementation process is as follows：
Step 1 establishes rolling bearing arrangement non-linear dynamic model and its differential equation group,
The global absolute rectangular coordinate system of bearing arrangement is established, as reference, horizontal direction to be set towards power intake For x-axis, and level is positive direction to the right, and vertical direction is set as into y-axis, and is positive direction vertically downward, and bearing inner race represents For particle m1, bearing outer ring is expressed as particle m2, the horizontal direction displacement and vertical direction displacement of bearing inner race are expressed as x1 And y1, the horizontal direction displacement and vertical direction displacement of bearing outer ring are expressed as x2And y2, bearing outer ring is by horizontal direction Spring-damper 1 and the spring-damper of vertical direction 2 are supported, and the rigidity and damped coefficient of spring-damper 1 are expressed as k1And c1, the rigidity and damped coefficient of spring-damper 2 are expressed as k2And c2, it is θ by outer ring fault angle positional representation, it is complete Bearing arrangement non-linear dynamic model after is as shown in Figure 2；Based on above-mentioned institute's established model, by lagrange equation of the second kind Derive the dynamic differential equation group of bearing arrangement；
Step 2 establishes the flat functional relation hung down between synchronous root-mean-square value and outer ring failure Angle Position, and the present invention uses NSK6308 bearings are as specific embodiment, bearing ball quantity Nb=8, ball bearing radius rb=7.54mm, outer raceway radius Ro= 40.04mm, the failure angular spread of selection is Δ φf=1 °, failure depth h=0.04mm, sample frequency Fs=65536Hz, if The constant interval for determining outer ring failure Angle Position is [240 °, 300 °], by the constant interval carry out 7 deciles, then obtain 7 by it is small to Big outer ring failure Angle Position θ1,θ2…θj…θ7, j represents the numbering of outer ring failure Angle Position, the integer between value 1~7, By each failure Angle Position θ of the bearing system dynamics Systems of Ordinary Differential Equations derived in step 1jCorresponding horizontal direction emulation Vibration acceleration signal ax,jWith vertical direction emulation vibration acceleration signal ay,j, then calculate the flat of each fault angle position correspondence Hang down synchronous root-mean-square value：
According to formula (1) and known parameters, each failure Angle Position θ can be calculatedjCorresponding VR values are respectively VR1= 0.5649, VR2=0.3384, VR3=0.1648, VR4=0.01165, VR5=0.1638, VR6=0.3615, VR7= 0.5943.With θjFor independent variable, VRjFor dependent variable, outer ring fault angle position θ and VR values are gone out by least-squares algorithm linear fitting Relational expression：
The change curve of outer ring fault angle position θ and VR values is as shown in Figure 3 in the present embodiment determined by formula 2.
Step 3 measures the level diagnosis reference data of the disconnected bearing arrangement of follow-up,
So that towards power intake, as reference, horizontal setting is to the right 0 °, and vibration acceleration sensor 1 is arranged on into follow-up 90 ° of positions of the bearing block of disconnected bearing arrangement, vibration acceleration sensor 2 is arranged on to the bearing block of the disconnected bearing arrangement of follow-up 180 ° of positions, outer ring failure Angle Position is measured at 270 ° by vibration acceleration sensor 1 and vibration acceleration sensor 2 respectively Vertical vibration acceleration signal a 'yWith horizontal direction vibration acceleration signal a 'x, then calculate determining for the disconnected bearing arrangement of follow-up Position diagnosis benchmark VR values:
By the VR in VR'=0.497 replacement formulas (2)4, obtain follow-up break bearing arrangement outer ring failure Angle Position θ with The relational expression of VR values is：
θ=270 ± 50 (VR-0.497) (4)
Step 3 outer ring failure Angle Position positioning mode then,
So that towards power intake, as reference, horizontal setting is to the right 0 °, and vibration acceleration sensor 1 is arranged on into follow-up 90 ° of positions of the bearing block of disconnected bearing arrangement, vibration acceleration sensor 2 is arranged on to the bearing block of the disconnected bearing arrangement of follow-up 180 ° of positions, measure the Vertical Square for being diagnosed faulty bearings respectively by vibration acceleration sensor 1 and vibration acceleration sensor 2 To vibration acceleration signal a "yWith horizontal direction vibration acceleration signal a "x, and calculate the VR values for being diagnosed faulty bearings：
A " is drawn respectivelyxWith a "yTime domain beamformer, as shown in figure 4, observation oscillogram in failure impact prime direction Understand, a "xIn failure impact prime direction be negative and a "yIn failure impact prime direction be also negative, so in the present embodiment Outer ring failure can determine that as positioned at 270 ° of right side, that is, the failure Angle Position being diagnosed can be diagnosed as：
Thus embodiment is understood, after the physics and geometric parameter of bearing arrangement are given, is proposed by the inventive method Formula only needs this parameter of VR to predict corresponding failure Angle Position.Absolutely proved the inventive method significance and Application value.

Claims (1)

  1. A kind of 1. housing washer fault section diagnosis method, it is characterised in that：This method includes step in detail below,
    Step 1 establishes rolling bearing arrangement non-linear dynamic model and its differential equation group,
    The global absolute rectangular coordinate system of bearing arrangement is established, as reference, horizontal direction is set as into x towards power intake Axle, and level is positive direction to the right, and vertical direction is set as into y-axis, and be positive direction vertically downward, bearing inner race is expressed as matter Point m1, bearing outer ring is expressed as particle m2, the horizontal direction displacement and vertical direction displacement of bearing inner race are expressed as x1With y1, the horizontal direction displacement and vertical direction displacement of bearing outer ring are expressed as x2And y2, bearing outer ring by horizontal direction bullet Spring damper 1 and the spring-damper of vertical direction 2 support, and the rigidity and damped coefficient of spring-damper 1 are expressed as k1 And c1, the rigidity and damped coefficient of spring-damper 2 are expressed as k2And c2, it is θ by outer ring fault angle positional representation, is based on Above-mentioned institute's established model, the dynamic differential equation group of bearing arrangement is derived by lagrange equation of the second kind；
    Step 2 establishes the flat functional relation hung down between synchronous root-mean-square value and outer ring failure Angle Position,
    The constant interval of outer ring failure Angle Position is set as [240 °, 300 °], the constant interval is subjected to 7 deciles, then obtains 7 Ascending outer ring failure Angle Position θ1,θ2…θj…θ7, j represents the numbering of outer ring failure Angle Position, between value 1~7 Integer；By each failure Angle Position θ of the bearing system dynamics Systems of Ordinary Differential Equations derived in step 1jCorresponding level side To emulation vibration acceleration signal ax,jWith vertical direction emulation vibration acceleration signal ay,j, then calculate each failure Angle Position pair The flat synchronous root-mean-square value that hangs down answered：
    <mrow> <msub> <mi>VR</mi> <mi>j</mi> </msub> <mo>=</mo> <msqrt> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </msqrt> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...7</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    In above formula, N is emulation data points, wherein, with θjFor independent variable, VRjFor dependent variable, by least-squares algorithm linear fitting Go out outer ring fault angle position θ and VR values relational expression：
    θ=270 ± k (VR-VR4) (2)
    Step 3 measures the level diagnosis reference data of the disconnected bearing arrangement of follow-up,
    So that towards power intake, as reference, horizontal setting is to the right 0 °, and vibration acceleration sensor 1 is arranged on into follow-up off-axis 90 ° of positions of the bearing block of system are held, vibration acceleration sensor 2 is arranged on to 180 ° of the bearing block of the disconnected bearing arrangement of follow-up Position, it is vertical at 270 ° that outer ring failure Angle Position is measured by vibration acceleration sensor 1 and vibration acceleration sensor 2 respectively Direction vibration acceleration signal a 'yWith horizontal direction vibration acceleration signal a 'x, then calculate follow-up break bearing arrangement positioning examine Disconnected benchmark VR values:
    <mrow> <msup> <mi>VR</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <msqrt> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mi>x</mi> <mo>&amp;prime;</mo> </msubsup> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mi>y</mi> <mo>&amp;prime;</mo> </msubsup> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    By the VR in VR' replacement formulas (2)4, obtain the outer ring failure Angle Position θ and the relational expression of VR values of the disconnected bearing arrangement of follow-up：
    θ=270 ± k (VR-VR ') (4)
    Step 3 outer ring failure Angle Position positioning mode then,
    So that towards power intake, as reference, horizontal setting is to the right 0 °, and vibration acceleration sensor 1 is arranged on into follow-up off-axis 90 ° of positions of the bearing block of system are held, vibration acceleration sensor 2 is arranged on to 180 ° of the bearing block of the disconnected bearing arrangement of follow-up Position, measured respectively by vibration acceleration sensor 1 and vibration acceleration sensor 2 and be diagnosed the vertical direction of faulty bearings and shake Dynamic acceleration signal a "yWith horizontal direction vibration acceleration signal a "x, and calculate the VR values for being diagnosed faulty bearings：
    <mrow> <msup> <mi>VR</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msqrt> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mi>x</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mi>y</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    A " is drawn respectivelyxWith a "yTime domain beamformer, observe oscillogram in failure impact prime direction, as a "xIn oscillogram Failure impact prime direction for just and a "yWhen failure impact prime direction in oscillogram is negative, then the outer ring failure can be sentenced It is set to positioned at 270 ° of left side, that is, the failure Angle Position being diagnosed can be identified as：
    θd=270-k (VR "-VR ') (6)
    As a "xFailure impact prime direction in oscillogram is negative and a "yWhen failure impact prime direction in oscillogram is negative, Then the outer ring failure can determine that as positioned at 270 ° of right side, that is, the failure Angle Position being diagnosed can be identified as：
    θd=270+k (VR "-VR ') (7).
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CN109211566A (en) * 2018-08-21 2019-01-15 北京工业大学 A kind of housing washer defect two dimension Quantitative Diagnosis method
CN109992926A (en) * 2019-04-23 2019-07-09 清华大学 Bearing outer ring defect Angle Position quantitative estimation method
CN110146290A (en) * 2019-05-29 2019-08-20 清华大学 A kind of housing washer defect location diagnostic method based on positioning universal laws
CN110146290B (en) * 2019-05-29 2020-08-18 清华大学 Rolling bearing outer ring defect positioning diagnosis method based on universal positioning rule
CN111046502A (en) * 2019-11-13 2020-04-21 长江大学 Method and device for calculating stiffness of soil spring of pipeline crossing fault
CN111046502B (en) * 2019-11-13 2023-08-25 长江大学 Soil spring stiffness calculation method and device for pipeline crossing fault
CN112267979A (en) * 2020-10-26 2021-01-26 积成电子股份有限公司 Early warning method and system for judging failure of yaw bearing
CN113029570A (en) * 2021-04-01 2021-06-25 温州大学 Harmonic bearing fault sample generation model and diagnosis method
CN114235414A (en) * 2021-12-28 2022-03-25 频率探索智能科技江苏有限公司 Signal processing method suitable for outer ring defect positioning diagnosis
CN114235414B (en) * 2021-12-28 2023-08-04 频率探索智能科技江苏有限公司 Signal processing method suitable for outer ring defect positioning diagnosis
CN114486261A (en) * 2022-01-21 2022-05-13 沈阳科网通信息技术有限公司 Bearing outer ring fault positioning method based on synchronous root-mean-square ratio
CN114486261B (en) * 2022-01-21 2022-09-23 沈阳科网通信息技术有限公司 Bearing outer ring fault positioning method based on synchronous root-mean-square ratio

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