CN113295417B - Bearing fault characteristic frequency calculation method and device - Google Patents

Bearing fault characteristic frequency calculation method and device Download PDF

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CN113295417B
CN113295417B CN202110558775.0A CN202110558775A CN113295417B CN 113295417 B CN113295417 B CN 113295417B CN 202110558775 A CN202110558775 A CN 202110558775A CN 113295417 B CN113295417 B CN 113295417B
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bearing
diameter
characteristic frequency
fault characteristic
formula
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刘育玮
吴建军
程玉强
杨述明
胡润生
崔孟瑜
戚元杰
邓凌志
石业辉
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National University of Defense Technology
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    • 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
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Abstract

The invention discloses a bearing fault characteristic frequency calculation method and device. The method comprises the following steps: s1, carrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation; s2, reconstructing the inner diameter and the outer diameter of the bearing, S3, calculating the fault characteristic frequency of the bearing according to the corresponding relation in the step S1 according to the numerical value of the inner diameter and the outer diameter of the bearing after reconstruction. The method can solve the bearing fault characteristic frequency by analogy with the planetary gear system, has small calculated amount and is convenient for engineering realization.

Description

Bearing fault characteristic frequency calculation method and device
Technical Field
The invention relates to the technical field of bearing fault detection, in particular to a bearing fault characteristic frequency calculation method and device.
Background
The bearing is an important component of various rotor machines and plays a vital role in connecting the rotor and the support. However, due to the harsh operating conditions, failures often occur. In a rotating machine, the failure rate of a bearing reaches 70%, and detection of a bearing failure is extremely important in order to ensure normal operation of machine components. The rub-in between the rolling bodies and local bearing faults can generate a pulse signal. The frequency of which corresponds to the type of bearing failure and is referred to as the failure signature frequency.
Currently, the calculation formula of the bearing fault characteristic frequency is the bearing fault characteristic frequency calculated according to the geometric parameters and the rotating frequency of the bearing. However, for some bearings, the calculation formula of the diameter of the bearing pitch circle is different from the pitch diameter of the actual bearing; another way of calculation is to assume that the bearing is rolling purely, but in practice the bearing is not rolling purely.
Disclosure of Invention
The invention aims to provide a bearing fault characteristic frequency calculation method and a bearing fault characteristic frequency calculation device to overcome the defects in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a bearing fault characteristic frequency calculation method comprises the following steps:
s1, carrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation;
s2, reconstructing the inner diameter and the outer diameter of the bearing;
and S3, calculating the fault characteristic frequency of the bearing according to the reconstructed numerical values of the inner diameter and the outer diameter of the bearing and the corresponding relation in the step S1.
Further, the step S1 specifically includes,
s10, calculating fault characteristic frequency in the planetary gearbox;
fmesh＝fcarrierZring(1) (ii) a In the formula (f)meshIs the gear mesh frequency; f. ofcarrierThe rotational frequency of the planet carrier; zringThe number of teeth of the gear ring;
Figure GDA0003529551410000011
in the formula (f)planet1Is the failure characteristic frequency of the planet gear; f. ofplanet2Fault characteristic frequencies are provided for both sides of the planetary gear; zplanetIs the number of planet gear teeth;
Figure GDA0003529551410000012
in the formula (f)sun1Is sun gear fault signature frequency; f. ofsun2The special diagnosis frequency of the local fault of the sun wheel; z is a linear or branched membersunThe number of sun gear teeth; n is a radical of hydrogenplanetThe number of planet wheels;
Figure GDA0003529551410000021
in the formula (f)ring1Is the gear ring fault characteristic frequency; f. ofring2The local fault diagnosis frequency of the gear ring is obtained;
s11, converting the expression (4) according to the relation of the expression (1) to obtain fring2＝fcarrier(5)；
S12, a calculation formula of the planetary gear is as follows:
Figure GDA0003529551410000022
in the formula, f is the input rotation frequency of the planetary gearbox;
the planetary gear system is similar to a bearing in analogy, according to the mechanical design knowledge, the reference circle diameter is the modulus X tooth number, and the following are obtained:
d is mxz (7), wherein d is the reference circle diameter, m is the modulus, and Z is the number of teeth;
in the planetary gear system, the module of the gears which are meshed with each other is certain to be the same, and the formula (7) is respectively taken into the formulas (2), (3) and (6);
Figure GDA0003529551410000023
in the formula, dringThe diameter of the reference circle of the gear ring; dplanetThe diameter of the reference circle of the planet gear;
Figure GDA0003529551410000024
in the formula (d)sunThe diameter of the reference circle of the sun wheel;
Figure GDA0003529551410000025
s13, analogy between the planetary gear train and the bearing, according to the above mentioned guidance:
fo＝fring,fi＝fsun,fb＝fplanet(11) in the formula: f. ofoIs the bearing outer ring fault characteristic frequency; f. ofiIs the bearing inner ring fault characteristic frequency; f. ofbFor rolling of bearingsBody fault signature frequency.
Further, the inner and outer diameters of the bearing in the step S2 are calculated according to the following formula;
Dr＝(Do+Di)/2；
Figure GDA0003529551410000026
in the formula, DrThe reconstructed bearing pitch circle diameter; doThe diameter of the bearing outer ring is the original diameter; diIs the original diameter of the bearing inner ring Dr,oIs the reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling body
Further, in step S3, the bearing fault characteristic frequency calculation formula obtained by analogy with the planetary gear train is as follows:
the bearing retainer fault characteristic frequency calculation formula is as follows:
Figure GDA0003529551410000031
the bearing outer ring fault characteristic frequency calculation formula is as follows: f. ofo＝fcarrier·NbIn the formula, NbThe number of the rolling bodies is;
the bearing rolling element fault characteristic frequency calculation formula is as follows:
Figure GDA0003529551410000032
the bearing inner ring fault characteristic frequency calculation formula is as follows:
Figure GDA0003529551410000033
the invention also provides a device for realizing the bearing fault characteristic frequency calculation method, which comprises the following steps:
the analog analysis module is used for carrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation;
the reconstruction module is used for reconstructing the inner and outer diameters of the bearing, and the reconstruction formula is as follows;
Dr＝(Do+Di)/2；
Figure GDA0003529551410000034
in the formula, DrThe reconstructed bearing pitch circle diameter; doThe diameter of the bearing outer ring is the original diameter; diIs the original diameter of the bearing inner ring Dr,oThe reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling body;
and a calculating module, configured to calculate a fault characteristic frequency of the bearing according to the reconstructed numerical values of the inner and outer diameters of the bearing and the corresponding relationship in step S1.
Further, the analogy analysis module comprises:
the second calculation module is used for calculating the fault characteristic frequency in the planetary gearbox;
a transformation module for transforming the expression (4) according to the relation of the expression (1) to obtain fring2＝fcarrier；
A first analog module for analog-comparing the planetary gear train with the bearing;
a second analogy module for analogy between the planetary gear train and the bearing to obtain fo＝fring,fi＝fsun,fb＝fplanet。
Further, the first calculation module comprises a bearing retainer fault characteristic frequency calculation module, a bearing outer ring fault characteristic frequency calculation module, a bearing rolling body fault characteristic frequency calculation module and a bearing inner ring fault characteristic frequency calculation module.
Compared with the prior art, the invention has the advantages that: aiming at the rolling bearing with the contact angle of zero, the method can calculate the fault characteristic frequency more conveniently, compared with the traditional method, the method can solve the fault characteristic frequency of the bearing by simulating a planetary gear train, has small calculation amount and is convenient for engineering realization.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a bearing fault characteristic frequency calculation method of the present invention.
Fig. 2 is a sectional view of a bearing of the present invention.
Fig. 3 is a schematic view of the structure of the bearing of the present invention.
In the figure, D, diameter of rolling element, D, diameter of bearing pitch circle, Z, number of rolling elements, alpha, contact angle, omegatAngular velocity of rotation of bearing, omegabAngular velocity of rolling element, omegacAnd the rolling bodies revolve.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention will be more clearly and clearly defined.
Referring to fig. 1 to 3, the present embodiment discloses a method for calculating a bearing fault characteristic frequency, which is implemented by the following steps:
step 1, carrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation;
in this embodiment, the characteristic frequency of a fault in the planetary gear box is:
fmesh＝fcarrierZring (1)；
in the formula (f)meshIs the gear mesh frequency; f. ofcarrierThe rotational frequency of the planet carrier; zringThe number of teeth of the ring gear.
Figure GDA0003529551410000041
In the formula (f)planet1Is the failure characteristic frequency of the planet gear; f. ofplanet2Fault characteristic frequencies are provided for both sides of the planetary gear; z is a linear or branched memberplanetThe number of planet gear teeth.
Figure GDA0003529551410000042
In the formula (f)sun1Is sun gear fault signature frequency; f. ofsun2The special diagnosis frequency of the local fault of the sun wheel; zsunThe number of sun gear teeth; n is a radical ofplanetThe number of the planet wheels.
Figure GDA0003529551410000043
In the formula (f)ring1Is the gear ring fault characteristic frequency; f. ofring2The special diagnosis frequency of the local fault of the gear ring.
And (4) transforming the relation of the formula (1) to obtain:
fring2＝fcarrier (5)；
from the calculation formula of the planetary gear:
Figure GDA0003529551410000051
where f is the rotational frequency of the input to the planetary gearbox.
The planetary gear system is similar to a bearing, and according to mechanical design knowledge, the reference circle diameter is the modulus X, namely the tooth number:
d＝m×Z (7)；
wherein d is the reference circle diameter; m is a modulus; z is the number of teeth.
Since the gear modules of the planetary gear system, which mesh with each other, are necessarily the same, the expressions (7) are respectively taken into the expressions (2), (3) and (6) to obtain:
Figure GDA0003529551410000052
in the formula (d)ringThe diameter of the reference circle of the gear ring; dplanetIs the pitch circle diameter of the planet gear.
Figure GDA0003529551410000053
In the formula (d)sunThe diameter of the pitch circle of the sun wheel.
Figure GDA0003529551410000054
Analogy between planetary gear train and bearing, according to the above-mentioned guidance:
fo＝fring,fi＝fsun,fb＝fplanet (11)；
and 2, reconstructing the inner diameter and the outer diameter of the bearing, wherein the size of the inner ring and the outer ring of the bearing is deviated from the size proportion of the sun gear and the gear ring in the planetary gear train, so that the deduced fault characteristic frequency calculation formula is not applicable to calculation by directly substituting the formula into the calculation formula. Therefore, when the fault characteristic frequency of the bearing is calculated by using the formula, the sizes of the inner diameter and the outer diameter of the bearing need to be reconstructed once.
The reconstruction method is as follows:
Dr＝(Do+Di)/2 (12)；
in the formula, DrThe reconstructed bearing pitch circle diameter; doThe diameter of the bearing outer ring is the original diameter; diThe diameter of the bearing inner ring is the original diameter;
Dr,o＝Dr+d
Dr,i＝Dr-d (13)；
in the formula, Dr,oIs the reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling element.
The present embodiment adopts an NSK626 bearing (deep groove ball bearing), the structure of which is shown in fig. 2, and the specific geometric parameters of which are shown in table 1 below.
Table 1 example bearing geometry
Figure GDA0003529551410000061
The reconstructed bearing inner diameter is 9.02mm, and the bearing outer diameter is 15.98 mm.
And 3, calculating the fault characteristic frequency of the bearing by using a method of simulating a planetary gear train according to the reconstructed value of the inner diameter and the outer diameter of the bearing.
The bearing retainer fault characteristic frequency calculation formula is as follows:
Figure GDA0003529551410000062
the bearing outer ring fault characteristic frequency calculation formula is as follows: f. ofo＝fcarrier·NbIn the formula, NbThe number of the rolling bodies is;
the bearing rolling element fault characteristic frequency calculation formula is as follows:
Figure GDA0003529551410000063
the bearing inner ring fault characteristic frequency calculation formula is as follows:
Figure GDA0003529551410000064
in this embodiment, when the rotational speed of the bearing is 1810rpm, the bearing frequency (fr) is 30.17 Hz. The results of calculating the fault characteristic frequency of the bearing are shown in table 2:
TABLE 2 bearing failure frequency of the examples
Figure GDA0003529551410000065
The invention also provides a device for realizing the bearing fault characteristic frequency calculation method, which comprises the following steps: analog analysis module for connecting the shaftCarrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation; the reconstruction module is used for reconstructing the inner and outer diameters of the bearing, and the reconstruction formula is as follows; dr＝(Do+Di)/2；
Figure GDA0003529551410000066
In the formula, DrThe reconstructed bearing pitch circle diameter; doThe diameter of the bearing outer ring is the original diameter; diIs the original diameter of the bearing inner ring Dr,oIs the reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling body; and a calculating module, configured to calculate a fault characteristic frequency of the bearing according to the reconstructed values of the inner and outer diameters of the bearing and the corresponding relationship in step S1.
The analogy analysis module comprises: the second calculation module is used for calculating the fault characteristic frequency in the planetary gearbox; a transformation module for transforming the expression (4) according to the relation of the expression (1) to obtain fring2＝fcarrier(ii) a A first analog module for analog-analogizing the planetary gear train and the bearing; a second analogy module for analogy between the planetary gear train and the bearing to obtain fo＝fring,fi＝fsun,fb＝fplanet。
The first calculation module comprises a bearing retainer fault characteristic frequency calculation module, a bearing outer ring fault characteristic frequency calculation module, a bearing rolling body fault characteristic frequency calculation module and a bearing inner ring fault characteristic frequency calculation module.
According to the bearing fault characteristic frequency calculation method and system, the bearing is compared with a planetary gear system to derive the bearing fault characteristic frequency calculation formula, compared with the traditional bearing fault characteristic frequency calculation, the bearing fault characteristic frequency is calculated by numerically reconstructing the sizes of the inner ring and the outer ring of the bearing and calculating the fault characteristic frequency of the bearing through another thought, the calculated amount is small, and engineering implementation is facilitated.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, various changes or modifications may be made by the patentees within the scope of the appended claims, and within the scope of the invention, as long as they do not exceed the scope of the invention described in the claims.

Claims (4)

1. A bearing fault characteristic frequency calculation method is characterized by comprising the following steps:
s1, carrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation;
s2, reconstructing the inner diameter and the outer diameter of the bearing;
s3, calculating the fault characteristic frequency of the bearing according to the reconstructed numerical value of the inner diameter and the outer diameter of the bearing and the corresponding relation in the step S1;
the step S1 specifically includes the steps of,
s10, calculating fault characteristic frequency in the planetary gearbox;
fmesh＝fcarrierZring(1) (ii) a In the formula (f)meshIs the gear mesh frequency; f. ofcarrierThe rotational frequency of the planet carrier; zringThe number of teeth of the gear ring;
Figure FDA0003542512710000011
in the formula, fplanet1Is the failure characteristic frequency of the planet gear; f. ofplanet2Fault characteristic frequencies are provided for both sides of the planetary gear; zplanetIs the number of planet gear teeth;
Figure FDA0003542512710000012
in the formula (f)sun1Is sun gear fault signature frequency; f. ofsun2The special diagnosis frequency of the local fault of the sun wheel; zsunThe number of sun gear teeth; n is a radical ofplanetThe number of the planet wheels is;
Figure FDA0003542512710000013
in the formula (f)ring1Is the gear ring fault characteristic frequency; f. ofring2The local fault diagnosis frequency of the gear ring is obtained;
s11, converting the expression (4) according to the relation of the expression (1) to obtain fring2＝fcarrier (5)；
S12, a calculation formula of the planetary gear is as follows:
Figure FDA0003542512710000014
in the formula, f is the input rotation frequency of the planetary gearbox;
the planetary gear system is similar to a bearing in analogy, according to the mechanical design knowledge, the reference circle diameter is the modulus X tooth number, and the following are obtained:
d ═ m × Z (7), where d' is the reference circle diameter, m is the modulus, and Z is the number of teeth;
in the planetary gear system, the module of the gears which are meshed with each other is certain to be the same, and the formula (7) is respectively taken into the formulas (2), (3) and (6);
Figure FDA0003542512710000015
in the formula (d)ringThe diameter of the reference circle of the gear ring; dplanetThe diameter of the reference circle of the planet gear;
Figure FDA0003542512710000016
in the formula (d)sunThe diameter of the reference circle of the sun wheel;
Figure FDA0003542512710000021
s13, analogy of the planetary gear train and the bearing, according to the above guidance:
fo＝fring1，fi＝fsun，fb＝fplanet(11) in the formula: f. ofoFor bearing outer ring fault characteristic frequency；fiIs the bearing inner ring fault characteristic frequency; f. ofbThe fault characteristic frequency of the bearing rolling body is shown;
in the step S2, the inner and outer diameters of the bearing are calculated according to the following formula;
Dr＝(Do+Di)/2；
Figure FDA0003542512710000022
in the formula, DrThe reconstructed bearing pitch circle diameter; doThe diameter of the bearing outer ring is the original diameter; diIs the original diameter of the bearing inner ring Dr,oIs the reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling body;
in step S3, the calculation formula of the characteristic frequency of the bearing fault obtained from the planetary gear train analogy is as follows:
the bearing retainer fault characteristic frequency calculation formula is as follows:
Figure FDA0003542512710000023
the bearing outer ring fault characteristic frequency calculation formula is as follows: f. ofo＝fcarrier′·NbIn the formula, NbThe number of the rolling bodies is;
the bearing rolling element fault characteristic frequency calculation formula is as follows:
Figure FDA0003542512710000024
the bearing inner ring fault characteristic frequency calculation formula is as follows:
Figure FDA0003542512710000025
in the formula, Dr,oIs the reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling element.
2. An apparatus for implementing the bearing fault characteristic frequency calculation method according to claim 1, comprising:
the analog analysis module is used for carrying out analog analysis on the fault characteristic frequency of the bearing and the fault characteristic frequency of the planetary gear train to obtain a corresponding relation;
the reconstruction module is used for reconstructing the inner and outer diameters of the bearing, and the reconstruction formula is as follows;
Dr＝(Do+Di)/2；
Figure FDA0003542512710000026
in the formula, DrThe reconstructed bearing pitch circle diameter; doThe diameter of the bearing outer ring is the original diameter; diIs the original diameter of the bearing inner ring Dr,oIs the reconstructed bearing outer ring diameter; dr,iIs the reconstructed bearing inner ring diameter; d is the diameter of the bearing rolling body;
and a first calculating module, configured to calculate a fault characteristic frequency of the bearing according to the reconstructed numerical values of the inner diameter and the outer diameter of the bearing and according to the corresponding relationship in step S1.
3. The apparatus of claim 2, wherein the analogy analysis module comprises:
the second calculation module is used for calculating the fault characteristic frequency in the planetary gearbox;
a transformation module for transforming the expression (4) according to the relation of the expression (1) to obtain fring2＝fcarrier；
A first analog module for analog-comparing the planetary gear train with the bearing;
a second analogy module for analogy between the planetary gear train and the bearing to obtain fo＝fring1，fi＝fsun，fb＝fplanet。
4. The apparatus of claim 2, wherein the first calculation module comprises a bearing cage fault characteristic frequency calculation module, a bearing outer ring fault characteristic frequency calculation module, a bearing rolling element fault characteristic frequency calculation module, and a bearing inner ring fault characteristic frequency calculation module.
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