CN114264477A - Method for diagnosing rolling bearing defects - Google Patents
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Abstract
The invention discloses a method for diagnosing defects of a rolling bearing, which comprises the following steps: s1, acquiring a parameter set of the defect; s2, classifying the interaction of the ball and the defect into five types; s3, solving the central displacement of the ball when passing through the bearing raceway, and establishing a bearing defect model; s4, establishing a multi-body dynamic model of the rolling bearing, S5, establishing ten-degree-of-freedom dynamic equations, and solving the dynamic equations by using a fourth-order Runge Kutta method to obtain vibration displacement, vibration speed and vibration acceleration of the balls during movement; s6, respectively calculating envelope spectrums of vibration displacement, vibration speed and vibration acceleration, and respectively obtaining vibration characteristics of five degrees of freedom of the inner ring and the outer ring of the bearing under the defect; and S7, diagnosing the size of the defect according to the vibration characteristics. Through carrying out concrete classification to the mutual action when the ball passes through the defect, and then carry out subsequent vibration characteristic analysis again, diagnose defect size and position, can improve diagnostic precision.
Description
Technical Field
The invention relates to the technical field of bearing maintenance, in particular to a diagnosis method for defects of a rolling bearing.
Background
The rolling bearing is the most widely used part in various mechanical equipment, and the good running state of the rolling bearing is directly related to the safe running of the whole equipment. According to relevant statistics, about 30% of rotating machine failures are caused by bearing failures, and about 90% of rolling bearing failures are caused by outer and inner ring failures. Poor installation, untimely maintenance, fatigue of the surface of the bearing raceway and the like can cause bearing defects. Therefore, the bearing fault diagnosis technology has very important significance for finding out the fault as early as possible, avoiding the generation of catastrophic accidents and ensuring the normal, safe and orderly operation of equipment.
At present, deep groove ball bearings are mostly selected during defect analysis of rolling bearings, defects are simplified into a two-dimensional form in the center of a raceway, and the defect diagnosis is inaccurate due to the fact that the defects are far from the actual situation.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the bearing defect diagnosis method aims to solve the technical problems that bearing defect diagnosis is not comprehensive and accuracy is low in the prior art. The invention provides a method for diagnosing defects of a rolling bearing, which can improve the precision of defect diagnosis by classifying the contact form of a ball passing through the defects and then establishing a multi-body dynamic model of the bearing.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for diagnosing a rolling bearing defect, comprising the steps of: s1, acquiring a parameter set of the defect; s2, classifying the interaction of the ball and the defect into five types according to the parameter set and the motion path of the ball in the bearing; s3, solving the central displacement of the ball when passing through the bearing raceway according to the interaction between the ball and the defect, and establishing a bearing defect model; s4, establishing a multi-body dynamic model of the rolling bearing by taking the bearing defect model as a basis, and deducing a mass matrix, a damping matrix and a rigidity matrix of the multi-body dynamic model; s5, establishing a dynamic equation with ten degrees of freedom, and solving the dynamic equation by using a fourth-order Runge Kutta method to obtain vibration displacement, vibration speed and vibration acceleration of the balls during movement; s6, performing Fourier transform on the vibration displacement, the vibration speed and the vibration acceleration, respectively calculating envelope spectrums of the vibration displacement, the vibration speed and the vibration acceleration, and respectively obtaining vibration characteristics of five degrees of freedom of the inner ring and the outer ring of the bearing under the defect; and S7, diagnosing the size of the defect according to the vibration characteristics.
According to the method, the interaction (namely the contact form) of the balls passing through the defects is specifically classified, the multi-body dynamic model is established according to different types, the subsequent vibration characteristic analysis is further carried out, the sizes and the positions of the defects are diagnosed, and the diagnosis precision can be improved.
Further, the parameter set of the defect includes a defect depth hmaxCircumferential size of defect Δ ψdAxial size of defect Δ ψ'dCircumferential position of defect psidThe axial position β 'and the contact angle α' of the defect.
Further, in step S2, the basis for classifying the interaction of the balls with the defects into five categories is: whether the ball has impact characteristics with the two side edges and the bottom of the defect in the axial direction when passing through the defect.
Further, when the ball passes through the defect,
if the ball contacts with the two side edges in the axial direction of the defect and the bearing does not contact with the bottom of the defect, the relationship between the ball and the defect satisfies:
and is
Wherein the content of the first and second substances,
the axial dimension of the defect is the axial dimension of the defect when the ball is simultaneously contacted with the bottom of the defect and the two axial side edges of the defect,
the circumferential size of the defect is the circumferential size of the defect when the ball is simultaneously contacted with the bottom of the defect and the two circumferential side edges of the defect;
if the ball contacts with one side edge of the defect in the axial direction and the ball contacts with the bottom of the defect, the relation between the ball and the defect satisfies:
and is
If the ball and the two side edges of the defect axis are parallelAll do not contact, and the ball contacts with defect bottom, then the relation between ball and the defect satisfies:
and is
If the ball contacts with one side edge of the axial direction of the defect and the ball does not contact with the bottom of the defect, the relation between the ball and the defect satisfies:
and is
Wherein R isgroRadius of curvature of bearing raceway, RoThe radius of the bearing raceway at the defect position;
if the ball is not contacted with the two side edges of the defect in the axial direction, and the ball is not contacted with the bottom of the defect, the relation between the ball and the defect is satisfied:
and is
Further, in step S3, the step of solving the central displacement of the ball when passing through the bearing raceway specifically includes: s31, calculating the radial displacement delta of the ball center when passing through the defectdrjAnd axial displacement deltadzj(ii) a S32, according to radial displacement deltadrjAnd axial displacement deltadzjThe central displacement of the ball when passing through the bearing raceway is solved.
Further, the calculation process of step S32 includes:
establishing a bearing vibration displacement equation:
x(t)＝[xin xout]＝[xi yi zi θix θiy xo yo zo θox θoy]，
wherein x isinRepresenting the displacement, x, of the inner race of the bearingoutIndicating the displacement, x, of the outer race of the bearingi、yiAnd ziRespectively representing the displacement components, theta, of the bearing inner race in the xyz directionixAnd thetaiyRespectively representing angular displacement of the bearing inner ring in the xy direction; x is the number ofo、yoAnd zoRespectively representing the displacement components, theta, of the outer race of the bearing in the xyz directionoxAnd thetaoyRespectively representing the angular displacement of the bearing outer ring in the xy direction;
deriving radial displacement delta of the central displacement of the balls as they pass the bearing racewaysrjAnd axial displacement deltazj：
δrj(t)＝δx(t)cosψcj(t)+δy(t)sinψcj(t)-0.5cd-δdrj(t)，
δzj(t)＝δz(t)+0.5dm[θx(t)sinψcj(t)-θy(t)cosψcj(t)]-δdzj(t)，
Wherein the content of the first and second substances,
δx(t)＝xi(t)-xo(t)，δy(t)＝yi(t)-yo(t)，δz(t)＝zi(t)-zo(t)，
θx(t)＝θix(t)-θox(t)，θy(t)＝θiy(t)-θoy(t)，
wherein t represents time,. phicjRepresenting the angle between the ball entry defect and the ball ejection defect, cdIndicating radial clearance of the bearing, dmIndicating the bearing pitch circle diameter.
Further, the mass matrix, the damping matrix and the stiffness matrix of the multi-body dynamic model are respectively as follows:
M＝diag[mi mi mi Iix Iiy mo mo mo Iox Ioy]，
wherein m isiAnd moRespectively representing the mass of the inner and outer rings of the bearing, IixAnd IiyRespectively representing the moment of inertia of the inner ring of the bearing in the xy direction, IoxAnd IoyRespectively representing the rotational inertia of the bearing outer ring in the xy direction;
C＝diag[0 0 0 0 0 cox coy coz coθx coθy]，
wherein, cox，coyAnd cozRespectively, the support damping of the bearing outer ring in the xyz direction, coθxAnd coθyRespectively showing the support damping of the bearing outer ring in the x-axis rotating direction and the y-axis rotating direction;
K＝diag[0 0 0 0 0 kox koy koz koθx koθy]，
wherein k isox，koyAnd kozRespectively, the support stiffness, k, of the bearing outer ring in the xyz directionoθxAnd koθyThe support stiffness of the bearing outer ring in the x-axis rotation direction and the y-axis rotation direction is respectively shown.
Further, the kinetic equations for the ten degrees of freedom are expressed as:
wherein the content of the first and second substances,
an equation of the vibration velocity is expressed,
represents the vibration acceleration equation, [ F ]ex Fey Fez Mex Mey 0 0 0 0 0]TRepresenting the external exciting force to which the bearing is subjected, FS(t) represents the stiffness force of the contact between the balls and the bearing raceways, FC(t) represents the damping force between the balls and the bearing raceways; the four-step Rungestota method can be used for calculating x (t) to express the vibration displacement equation,
equation expressing the vibration velocity
Representing the vibration acceleration equation.
The method for diagnosing the defects of the rolling bearing has the advantages that the diagnosis precision can be improved by specifically classifying the interaction (namely the contact form) of the balls passing through the defects, establishing the multi-body dynamic model according to different types, further carrying out subsequent vibration characteristic analysis, and diagnosing the sizes and positions of the defects. The invention not only can broaden the dimension of bearing defect vibration signal analysis, but also can carry out quantitative diagnosis on the size of the bearing defect; the contact form of the ball and the raceway defect is refined and classified to be used as an auxiliary analysis means for analyzing vibration characteristics, so that the defect diagnosis precision is improved; meanwhile, the influence of the single axial load and the composite load on the vibration characteristics of the defective bearing can be analyzed, and the method has important practical application value.
Drawings
The invention is further illustrated with reference to the following figures and examples.
Fig. 1 is a flowchart of a method for diagnosing a rolling bearing defect of the present invention.
Figure 2 is a radial and axial schematic view of the ball of the present invention at the defect.
Figure 3 is a schematic illustration of a ball pass defect of the present invention under the type.
Figure 4 is a top view of a ball pass defect of the present invention under the type.
FIG. 5 is a multi-body dynamic model of a bearing of the present invention.
Fig. 6 is a vibration characteristic diagram of five degrees of freedom of the bearing outer ring of the present invention.
Fig. 7 is a partially enlarged view of fig. 6(b) of the present invention.
FIG. 8 is a graph comparing vibration characteristics for different circumferential defect sizes of the present invention.
Fig. 9 is a vibration characteristic diagram of different stress situations of the bearing of the invention.
FIG. 10 is a vibration signature envelope spectrum for a bearing of the present invention subjected to only axial forces.
FIG. 11 is an envelope spectrum of the vibrational characteristics of a bearing of the present invention subjected to axial-radial compound forces.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and are therefore not to be considered limiting of the invention. Furthermore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
A rolling bearing is a precise mechanical element that reduces friction loss by changing sliding friction between a running shaft and a shaft seat into rolling friction. The rolling bearing generally comprises an inner ring, an outer ring, a ball and a bearing seat, wherein the inner ring is used for being matched with a shaft and rotating together with the shaft; the outer ring is matched with the bearing seat to play a supporting role; the rolling bodies are uniformly distributed between the inner ring and the outer ring by the aid of the retainer. The inner ring and the outer ring are both provided with roller paths so that the balls can roll.
As shown in fig. 1, the method for diagnosing a rolling bearing defect specifically includes the following steps.
And S1, acquiring a parameter set of the defect.
It should be noted that the parameter set of the defect includes a defect depth hmaxCircumferential size of defect Δ ψdAxial size of defect Δ ψ'dCircumferential position of defect psidThe axial position β 'and the contact angle α' of the defect. These six parameter values can be measured by corresponding sensors, which can be fastened to the bearing block. Referring to fig. 2 and fig. 3, fig. 2(a) is a radial view of the bearing, fig. 2(b) is an axial view of the bearing, the defect on the raceway may be, for example, a pit, a three-dimensional coordinate system is established for the bearing, a horizontal direction on a radial plane of the bearing is an x-axis, a vertical direction is a y-axis, an axial direction of the bearing is a z-axis, and a center point of the bearing is denoted as O. Circumferential dimension of defect Δ ψdThe values are expressed in degrees, understood as the angle occupied by the width of the defect in the circumferential direction of the bearing, the axial dimension Δ ψ of the defect'dThe values of the angles are indicated, and it is understood that the angle occupied by the arc length of the defect in the axial direction of the bearing and the circumferential position psi of the defectdThe angle value is expressed, the included angle between the central line of the defect in the circumferential direction of the bearing and the x axis can be understood, the included angle between the central line of the defect in the axial direction of the bearing and the y axis can be understood, the contact angle alpha 'represents the angle value, the connecting line of the tangent point of the ball circumference and the raceway circumference and the ball center point is marked as E, and the contact angle alpha' is the included angle between the connecting line E and the y axis.
And S2, classifying the interaction of the ball and the defect into five types according to the parameter set and the motion path of the ball in the bearing.
It should be noted that the contact manner between the balls and the defects when the balls move in the bearing raceways can be classified into five categories, i.e., the interaction between the balls and the defects can be classified into five categories. Specifically, the classification is based on: whether the ball has impact characteristics with the two side edges and the bottom of the defect in the axial direction when passing through the defect.
The type one is as follows: if the ball contacts with the two side edges in the axial direction of the defect and the bearing does not contact with the bottom of the defect, the relationship between the ball and the defect satisfies:
and is
Wherein the content of the first and second substances,
the axial dimension of the defect is the axial dimension of the defect when the ball is simultaneously contacted with the bottom of the defect and the two axial side edges of the defect,
the circumferential dimension of the defect is the circumferential dimension of the defect when the ball is simultaneously contacted with the bottom of the defect and the two circumferential side edges of the defect.
Type two: if the ball contacts with one side edge of the defect in the axial direction and the ball contacts with the bottom of the defect, the relation between the ball and the defect satisfies:
and is
Type three: if the ball is not contacted with the two side edges of the defect in the axial direction and the ball is contacted with the bottom of the defect, the relation between the ball and the defect is satisfied:
and is
Type four: if the ball contacts with one side edge of the axial direction of the defect and the ball does not contact with the bottom of the defect, the relation between the ball and the defect satisfies:
and is
Wherein R isgroRadius of curvature of bearing raceway, RoThe radius of the bearing raceway at the defect.
Type five: if the ball is not contacted with the two side edges of the defect in the axial direction, and the ball is not contacted with the bottom of the defect, the relation between the ball and the defect is satisfied:
and is
The five types represent five different states of the ball when passing through the defect. When the subsequent defect diagnosis is carried out, the type of the ball passing through the defect can be judged firstly, and the diagnosis precision can be improved when the specific analysis diagnosis is carried out.
And S3, solving the central displacement of the ball when passing through the bearing raceway according to the interaction between the ball and the defect, and establishing a bearing defect model.
In step S2, the interaction between the ball and the defect is classified into five types, each of which can calculate the central displacement of the ball when passing through the bearing raceway, and a bearing defect model can be built according to the parameter set of the defect, the interaction between the ball and the defect, and the central displacement of the ball when passing through the bearing raceway.
The method specifically comprises the following steps: s31, calculating rollRadial displacement delta of bead center as it passes through defectdrjAnd axial displacement deltadzj. S32, according to radial displacement deltadrjAnd axial displacement deltadzjAnd solving the central displacement of the ball when passing through the bearing raceway.
The following describes the solving process in detail by taking type one as an example.
Referring to fig. 3 and 4, the angle ψ of the balls between the entry defect and the ejection defectcjCan be expressed as:
thus, the depth of the defect follows the angle psicjThe varying relationship can be expressed as:
wherein, hamaxIndicating the depth of contact of the ball with the two axial edges of the defect.
Referring to fig. 3 and 4, the displacement change of the center of the ball when the ball passes through the defect can be represented as la1a1”(i.e., the distance between a1 and a 1'), la1a1”The component in the x direction is the radial displacement delta of the ball center as it passes through the defectdrj，la1a1”The component in the y-direction is the axial displacement delta of the ball center as it passes through the defectdzjAnd r is the radius of the ball, and can be obtained according to the cosine theorem:
thereby, the radial displacement δ can be obtaineddrjAnd axial displacement deltadzj：
Obtaining the radial displacement deltadrjAnd axial displacement deltadzjThe centre displacement of the ball as it passes through the bearing raceway can then be derived (where centre displacement includes both the displacement of the ball as it passes through a defect and the displacement of the ball as it passes through a normal raceway). Firstly, establishing a bearing vibration displacement equation:
x(t)＝[xin xout]＝[xi yi zi θix θiy xo yo zo θox θoy]，
wherein x isinRepresenting the displacement, x, of the inner race of the bearingoutIndicating the displacement, x, of the outer race of the bearingi、yiAnd ziRespectively representing the displacement components, theta, of the bearing inner race in the xyz directionixAnd thetaiyRespectively representing angular displacement of the bearing inner ring in the xy direction; x is the number ofo、yoAnd zoRespectively representing the displacement components, theta, of the outer race of the bearing in the xyz directionoxAnd thetaoyRespectively, the angular displacement of the bearing outer race in the xy direction.
Radial displacement delta of the center displacement of the balls as they pass the bearing racewaysrjAnd axial displacement deltazjCan be expressed as:
δrj(t)＝δx(t)cosψcj(t)+δy(t)sinψcj(t)-0.5cd-δdrj(t)，
wherein t represents time,. phicjIndicating ball entry and ejection defectsAngle of (c) betweendDenotes the bearing radial clearance, is constant, dmThe pitch circle diameter of the bearing is shown as a constant.
Wherein the content of the first and second substances,
δx(t)＝xi(t)-xo(t)，δy(t)＝yi(t)-yo(t)，δz(t)＝zi(t)-zo(t)，
θx(t)＝θix(t)-θox(t)，θy(t)＝θiy(t)-θoy(t)，
wherein x isi(t) is xiFunction of time t, yi(t) is yiFunction of time t, zi(t) is ziFunction of time t, thetaix(t) is θixFunction of time t, thetaiy(t) is θiyFunction of variation with time t, xo(t) is xoFunction of time t, yo(t) is yoFunction of time t, zo(t) is zoFunction of time t, thetaox(t) is θoxFunction of time t, thetaoy(t) is θoyAs a function of time t.
Thus, a variation model of the center displacement of the ball when passing through the bearing raceway, which is an important component of the bearing defect model, can be obtained.
And S4, establishing a multi-body dynamic model of the rolling bearing by taking the bearing defect model as a basis, and deducing a mass matrix, a damping matrix and a rigidity matrix of the multi-body dynamic model.
It should be noted that the bearing defect model is an important basis for establishing a multi-body dynamic model.
Referring to fig. 5, the mass matrix of the multi-body kinetic model can be represented as:
wherein m isiAnd moRespectively representing the mass of the inner and outer rings of the bearing, IixAnd IiyRespectively representing the moment of inertia of the inner ring of the bearing in the xy direction, IoxAnd IoyRespectively, the moment of inertia of the bearing outer ring in the xy direction.
The damping matrix of the multi-body dynamics model can be expressed as:
wherein, cox，coyAnd cozRespectively, the support damping of the bearing outer ring in the xyz direction, coθxAnd coθyThe support damping of the bearing outer ring in the x-axis and y-axis rotational directions is shown respectively. Since the bearing inner ring is movable while the bearing outer ring is stationary, the damping of the bearing inner ring is considered to be 0.
The stiffness matrix of the multi-body kinetic model can be expressed as:
wherein k isox，koyAnd kozRespectively, the support stiffness, k, of the bearing outer ring in the xyz directionoθxAnd koθyThe support stiffness of the bearing outer ring in the x-axis rotation direction and the y-axis rotation direction is respectively shown. Since the bearing inner ring is movable while the bearing outer ring is fixed, the rigidity of the bearing inner ring is considered to be 0.
And S5, establishing a dynamic equation with ten degrees of freedom, and solving the dynamic equation by using a fourth-order Runge Kutta method to obtain the vibration displacement, the vibration speed and the vibration acceleration of the ball during movement.
It is understood that the ten-degree-of-freedom dynamic equations can be established from the bearing vibration displacement equation x (t), the mass matrix, the damping matrix, and the stiffness matrix in step S3. The kinetic equation can be expressed as:
wherein the content of the first and second substances,
an equation of the vibration velocity is expressed,
expressing a vibration acceleration equation, the vibration velocity equation being the first derivative of the vibration displacement equation, the vibration acceleration equation being the second derivative of the vibration displacement equation, [ F ]ex Fey Fez MexMey 0 0 0 0 0]TRepresenting the external exciting force to which the bearing is subjected, FS(t) represents the stiffness force of the contact between the balls and the bearing raceways, FC(t) represents the damping force between the balls and the bearing raceways.
The dynamic equation is input into simulation software, parameters such as solving initial values and solving time step lengths are set, and vibration displacement, vibration speed and vibration acceleration can be solved by applying a four-order Runge Kutta method. When the ball passes through the same defect, the characteristics that vibration displacement, vibration speed and vibration acceleration showed are different, and vibration signal change can be reflected earlier, more obviously to vibration speed and vibration acceleration, and to low frequency vibration trouble, vibration displacement can more obviously reflect vibration signal change, consequently, this embodiment adopts the mode that three kinds of vibration characteristics combined together, the vibration change of analysis ball that can be more comprehensive to more accurate prediction and diagnosis defect size.
And S6, performing Fourier transform on the vibration displacement, the vibration speed and the vibration acceleration, respectively calculating envelope spectrums of the vibration displacement, the vibration speed and the vibration acceleration, and respectively obtaining the vibration characteristics of the bearing inner ring and the bearing outer ring with five degrees of freedom under the defects.
It should be noted that the timestamps corresponding to the vibration displacement, the vibration velocity, and the vibration acceleration are the same, fourier transform is performed on the vibration displacement, the vibration velocity, and the vibration acceleration, a time domain signal can be converted into a frequency domain signal, and the vibration change can be more obviously seen. And respectively calculating envelope spectrums of vibration displacement, vibration speed and vibration acceleration, and respectively obtaining vibration characteristics of five degrees of freedom of the inner ring and the outer ring of the bearing under the defect.
For example, referring to the drawings, fig. 6(a) to 6(e) show the vibration characteristics of the bearing outer ring with five degrees of freedom, i.e., x-direction, y-direction, z-direction, θxDirection and thetayAnd (4) direction. As can be seen from the figure, in the y-direction, the z-direction and θxThe envelope spectrum of the vibration acceleration in the direction is more obvious, and in one period, the y direction, the z direction and the theta directionxThe envelope spectrum of the directions has two peaks and the time interval between the two peaks is very close, which indicates that the ball has experienced two impacts (in-defect and out-defect) during this time period, indicating that there is a defect.
And S7, diagnosing the size of the defect according to the vibration characteristics.
Fig. 7 is a partially enlarged view of fig. 6(B), in which the abscissa of the graph has a time interval of 0.065 sec to 0.085 sec, the left ordinate of the graph indicates the vibration acceleration, the right ordinate of the graph indicates the ball center displacement, the curve a indicates the vibration acceleration amplitude variation curve, and the curve B indicates the ball center displacement variation curve. It can be seen from fig. 7 that when the center displacement of the ball is suddenly changed, the ball entering or ejecting defect is indicated, and at the same time, the vibration acceleration is suddenly changed twice, which corresponds to the ball entering and ejecting defect, and the vibration acceleration amplitude change is larger when the ball is ejected from the defect than when the ball enters the defect. The edge of the defect can be determined according to the two impacts, and the position and the size of the defect can be determined according to the time difference of the two impacts and the rotating speed and the phase position of the rotor (which can be measured by a key phase sensor).
FIG. 8 shows three different sizes of defect circumferential dimension Δ ψdThe simulated vibration characteristics of (2) can find that the ball is impacted twice when passing through the defects with different sizes. When the balls enter the defect, the circumferential dimension delta psi of the defectdThe larger the amplitude, the more pronounced the amplitude; when the ball is ejected from the defect, the circumferential dimension delta psi of the defectdThe amplitude is most pronounced at 2 °. When the ball passes through the defects with different sizes, the circumferential dimension delta psi of the defectsdThe smaller the difference in amplitude of the two impacts. The defect size and the circumferential position of the defect can be quantitatively diagnosed by determining the time difference of the impact of the ball entering and ejecting the defect and the rotating speed of the primary bearing during operation.
In addition, the present embodiment also simulates the effect of the load on the vibration signal. Referring to fig. 9, the vibration acceleration amplitude of the bearing subjected to only axial force is significantly smaller than that of the bearing subjected to the axial-radial combined load. When defects exist, the stress condition of the bearing also becomes complex, and the defect diagnosis can be carried out through vibration characteristic analysis as shown in fig. 9. Referring to fig. 10 and 11, fig. 10 and 11 show envelope spectrums of vibration acceleration under two different load conditions, and comparing the two graphs, when the bearing is subjected to a composite load, the envelope spectrums not only have characteristic frequencies and harmonic characteristics of raceway defects, but also have half-frequencies of the characteristic frequencies, such as frequency components of 1.5 times, 2.5 times, and the like, which indicates that the vibration characteristics of the bearing under different stress conditions can be used as a basis for fault analysis of bearing defects.
In conclusion, the diagnosis method for the defects of the rolling bearing can not only widen the dimension of vibration signal analysis of the defects of the bearing, but also carry out quantitative diagnosis on the sizes of the defects of the bearing; the contact form of the ball and the raceway defect is refined and classified to be used as an auxiliary analysis means for analyzing vibration characteristics, so that the defect diagnosis precision is improved; meanwhile, the influence of the single axial load and the composite load on the vibration characteristics of the defective bearing can be analyzed, and the method has important practical application value.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the contents of the specification, and must be determined by the scope of the claims.
Claims (8)
1. A method for diagnosing a rolling bearing defect, comprising the steps of:
s1, acquiring a parameter set of the defect;
s2, classifying the interaction of the ball and the defect into five types according to the parameter set and the motion path of the ball in the bearing;
s3, solving the central displacement of the ball when passing through the bearing raceway according to the interaction between the ball and the defect, and establishing a bearing defect model;
s4, establishing a multi-body dynamic model of the rolling bearing by taking the bearing defect model as a basis, and deducing a mass matrix, a damping matrix and a rigidity matrix of the multi-body dynamic model;
s5, establishing a dynamic equation with ten degrees of freedom, and solving the dynamic equation by using a fourth-order Runge Kutta method to obtain vibration displacement, vibration speed and vibration acceleration of the balls during movement;
s6, performing Fourier transform on the vibration displacement, the vibration speed and the vibration acceleration, respectively calculating envelope spectrums of the vibration displacement, the vibration speed and the vibration acceleration, and respectively obtaining vibration characteristics of five degrees of freedom of the inner ring and the outer ring of the bearing under the defect;
and S7, diagnosing the size of the defect according to the vibration characteristics.
2. Method for diagnosing rolling bearing defects according to claim 1, characterized in that said set of parameters of defects comprises a defect depth hmaxCircumferential size of defect Δ ψdAxial size of defect Δ ψ'dCircumferential position of defect psidThe axial position β 'and the contact angle α' of the defect.
3. A method for diagnosing a defect in a rolling bearing according to claim 2, wherein in step S2, the interaction of the balls with the defect is classified into five groups based on: whether the ball has impact characteristics with the two side edges and the bottom of the defect in the axial direction when passing through the defect.
4. A method for diagnosing a rolling bearing defect as set forth in claim 3, wherein when the ball passes through the defect,
if the ball contacts with the two side edges in the axial direction of the defect and the bearing does not contact with the bottom of the defect, the relationship between the ball and the defect satisfies:
and is
Wherein the content of the first and second substances,
the axial dimension of the defect is the axial dimension of the defect when the ball is simultaneously contacted with the bottom of the defect and the two axial side edges of the defect,
the circumferential size of the defect is the circumferential size of the defect when the ball is simultaneously contacted with the bottom of the defect and the two circumferential side edges of the defect;
if the ball contacts with one side edge of the defect in the axial direction and the ball contacts with the bottom of the defect, the relation between the ball and the defect satisfies:
and is
If the ball is not contacted with the two side edges of the defect in the axial direction and the ball is contacted with the bottom of the defect, the relation between the ball and the defect is satisfied:
and is
If the ball is in the axial direction of the defectAnd the ball is not contacted with the bottom of the defect, then the relation between the ball and the defect is satisfied:
and is
Wherein R isgroRadius of curvature of bearing raceway, RoThe radius of the bearing raceway at the defect position;
if the ball is not contacted with the two side edges of the defect in the axial direction, and the ball is not contacted with the bottom of the defect, the relation between the ball and the defect is satisfied:
and is
5. The method for diagnosing a defect in a rolling bearing according to claim 1, wherein the step S3 of solving the central displacement of the ball when passing through the bearing raceway specifically comprises:
s31, calculating the radial displacement delta of the ball center when passing through the defectdrjAnd axial displacement deltadzj；
S32, according to radial displacement deltadrjAnd axial displacement deltadzjThe central displacement of the ball when passing through the bearing raceway is solved.
6. The method for diagnosing a rolling bearing defect of claim 5, wherein the calculation process of the step S32 includes:
establishing a bearing vibration displacement equation:
x(t)＝[xin xout]＝[xi yi zi θix θiy xo yo zo θox θoy]，
wherein x isinRepresenting the displacement, x, of the inner race of the bearingoutIndicating the displacement, x, of the outer race of the bearingi、yiAnd ziRespectively representing the displacement components, theta, of the bearing inner race in the xyz directionixAnd thetaiyRespectively representing angular displacement of the bearing inner ring in the xy direction; x is the number ofo、yoAnd zoRespectively representing the displacement components, theta, of the outer race of the bearing in the xyz directionoxAnd thetaoyRespectively representing the angular displacement of the bearing outer ring in the xy direction;
deriving radial displacement delta of the central displacement of the balls as they pass the bearing racewaysrjAnd axial displacement deltazj：
δrj(t)＝δx(t)cosψcj(t)+δy(t)sinψcj(t)-0.5cd-δdrj(t)，
δzj(t)＝δz(t)+0.5dm[θx(t)sinψcj(t)-θy(t)cosψcj(t)]-δdzj(t)，
Wherein the content of the first and second substances,
δx(t)＝xi(t)-xo(t)，δy(t)＝yi(t)-yo(t)，δz(t)＝zi(t)-zo(t)，
θx(t)＝θix(t)-θox(t)，θy(t)＝θiy(t)-θoy(t)，
wherein t represents time,. phicjRepresenting the angle between the ball entry defect and the ball ejection defect, cdIndicating radial clearance of the bearing, dmIndicating the bearing pitch circle diameter.
7. The method for diagnosing a rolling bearing defect of claim 6, wherein the mass matrix, the damping matrix and the stiffness matrix of the multi-body dynamic model are respectively:
M＝diag[mi mi mi Iix Iiy mo mo mo Iox Ioy]，
wherein m isiAnd moRespectively representing the mass of the inner and outer rings of the bearing, IixAnd IiyRespectively representing the moment of inertia of the inner ring of the bearing in the xy direction, IoxAnd IoyRespectively representing the rotational inertia of the bearing outer ring in the xy direction;
C＝diag[0 0 0 0 0 cox coy coz coθx coθy]，
wherein, cox，coyAnd cozRespectively, the support damping of the bearing outer ring in the xyz direction, coθxAnd coθyRespectively showing the support damping of the bearing outer ring in the x-axis rotating direction and the y-axis rotating direction;
K＝diag[0 0 0 0 0 kox koy koz koθx koθy]，
wherein k isox，koyAnd kozRespectively, the support stiffness, k, of the bearing outer ring in the xyz directionoθxAnd koθyThe support stiffness of the bearing outer ring in the x-axis rotation direction and the y-axis rotation direction is respectively shown.
8. The method for diagnosing a rolling bearing defect of claim 7, wherein the ten degrees of freedom kinetic equation is expressed as:
wherein the content of the first and second substances,
an equation of the vibration velocity is expressed,
represents the vibration acceleration equation, [ F ]ex Fey Fez Mex Mey 0 0 0 0 0]TRepresenting the external exciting force to which the bearing is subjected, FS(t) representsRigidity of contact between the balls and the bearing raceways, FC(t) represents the damping force between the balls and the bearing raceways;
the four-step Rungestota method can be used for calculating x (t) to express the vibration displacement equation,
equation expressing the vibration velocity
Representing the vibration acceleration equation.
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|---|---|---|---|---|
| CN103712785A (en) * | 2013-09-12 | 2014-04-09 | 西安交通大学 | Rolling bearing-rotor system damage vibration response quantitative calculation method |
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2021
- 2021-12-20 CN CN202111563330.8A patent/CN114264477A/en not_active Withdrawn
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|---|---|---|---|---|
| CN103712785A (en) * | 2013-09-12 | 2014-04-09 | 西安交通大学 | Rolling bearing-rotor system damage vibration response quantitative calculation method |
| CN107704695A (en) * | 2017-10-13 | 2018-02-16 | 北京工业大学 | A kind of full-scale quantitative Diagnosis method of housing washer defect |
| KR20210111642A (en) * | 2020-03-03 | 2021-09-13 | 주식회사 일진글로벌 | Diagnosis method for wheel bearing |
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