CN106355039B - Rolling bearing fatigue life and reliability degree calculation method based on independent contact pair - Google Patents
Rolling bearing fatigue life and reliability degree calculation method based on independent contact pair Download PDFInfo
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Abstract
Rolling bearing fatigue life and reliability degree calculation method based on independent contact pair, in calculating process, first by the clearance of rolling bearing and inner geometry parameter, the stress distribution under the different contact conditions between rolling element and different raceways is calculated according to Lundberg-Palmgren formula.The fatigue characteristic of different raceways is considered by the contact stress between different raceways, the fatigue life of different raceways under calculating demand reliability, further choose the service life that shorter raceway service life in service life is complete bearing, return again to new reliability of the mathematic(al) expectation longer raceway under the shorter service life, so that it is determined that reliability of the complete bearing under the service life, the fatigue life being further scaled under demand reliability.
Description
Technical field
The invention belongs to the technical fields of rolling bearing fatigue life and reliability calculating, are related to the tired longevity of rolling bearing
Life calculates and the assessment calculation method of fatigue life reliability.
Background technique
Rolling bearing is important mechanical basic part, and the service life has an important influence host.The service life of rolling bearing
Refer to total revolution before the material of any part of Bearing inner first appears fatigue equivalent (or under a certain given constant rotational speed
Operating hours number).The fatigue life discreteness of rolling bearing is more significant, the identical structure of a batch, identical size, identical material
The rolling bearing of material, identical heat treatment condition and identical processing method, service life difference is also very huge, thus actually answers
With the rated life time of middle general provision rolling bearing.The rated life time of rolling bearing refers to the identical bearing of a collection of model, identical
Operating condition under, wherein the 90% total revolution (L that can be operated before fatigue equivalent10) or can operate under given rotating speed total
Work hours (Lh10), 90% here refers to the reliability of this batch of bearing.
The reliability demand of different applications, rolling bearing is different.It is some to be related to great personal safety as well as the property safety
Occasion, such as aerospace field, manned vehicle etc., the reliability of rolling bearing require high；And some simple application fields
It closes, such as curtain bearing, toy bearing, is then not required to too high reliability.Reliability requires difference, then its fatigue life calculated
Also there were significant differences, and reliability requirement is higher, then its mathematic(al) expectation is shorter.Therefore, it is possible to think the fatigue reliability of rolling bearing
Degree refers to the reliability under the fatigue life that certain is determined, the fatigue life of rolling bearing then refers to determining Fatigue Reliability premise
Under fatigue life, thus, the two is closely coupled, interdependence.The result of current engineering practice and scientific research all shows
The fatigue life of rolling bearing obeys Weibull (W.Weibull) distribution.
In existing international standard and scientific research, rolling bearing calculation methods of fatigue reliability has two major classes type: 1,
Based on bearing dynamic load rating calculation method.The rolling bearing fatigue that this method is carried out according to the dynamic load rating information of product
The simplification algorithm that service life calculates, its advantage is that calculating process is relatively simple, but accuracy is insufficient, in order to ensure reliability, often
Largely sacrifice the remaining life of rolling bearing；2, the calculation method based on Lundberg-Palmgren formula.This method root
According to external applied load size, connecing between each rolling element and raceway is calculated by the clearance and interior geometry parameter of rolling bearing
Stress is touched, the L of every raceway is calculated separately10It is service life, then reliable using a whole set of bearing of method compromise acquisition of statistical disposition again
Service life when degree is 90%, i.e. L10.This method is more accurate relative to first method, but its fussy degree also accordingly increases
Add.
Summary of the invention
The object of the present invention is to provide rolling bearing fatigue lifes and reliability degree calculation method based on independent contact pair.Meter
During calculation, first by the clearance of rolling bearing and inner geometry parameter, calculates and roll according to Lundberg-Palmgren formula
The stress distribution under different contact conditions between body and different raceways.Different rollings are considered by the contact stress between different raceways
The fatigue characteristic in road calculates the fatigue life of the different raceways under demand reliability, further chooses shorter raceway longevity in service life
Life is the service life of complete bearing, new reliability of the mathematic(al) expectation longer raceway under the shorter service life is returned again to, thus really
Fixed reliability of the complete bearing under the service life, the fatigue life being further scaled under demand reliability.
It is repeatedly and tediously long to avoid, centripetal point contact ball bearing is only chosen in the present invention and centripetal line contact roller bearing is
The calculation method of example explanation, the fatigue life and reliability of thrust point contact ball bearing and thrust line contact roller bearing can foundation
Method proposed by the present invention is analogized.
To achieve the above object, used technical solution is: rolling bearing fatigue life based on independent contact pair with
Reliability degree calculation method, comprising the following steps:
(1) theoretical according to Lundberg-Palmgren, the contact fatigue life between rolling element and raceway can be estimated according to following formula
It calculates:
In formula (1), QcFor contact rating load, Q is applied load；
(2) during one's term of military service, the speed between two lassos has larger difference to rolling bearing, and one is swivel ferrule, another
A low speed lasso or fixed lasso are non-rotating rings；
For spot contact bearing,
In formula (2), QcμFor swivel ferrule contact rating load, QeμFor swivel ferrule applied load；QcvIt is connect for fixed lasso
Touch rated load, QevFor fixed lasso applied load；Subscript μ refers to swivel ferrule, and subscript ν refers to non-rotating rings；
It is similar to indicate for line contact bearing are as follows:
The meaning of symbology in formula (3) is identical as formula (2)；
(3) contact rating load is only and contact type, material are related with heat treatment situation, with rolling element and inside/outside circle it
Between contact unrelated, thus the inside and outside circle contact rating load of point contact may be expressed as:
The inside and outside circle contact rating load of line contact may be expressed as:
In formula (4) and (5), when inner ring Calculation of Contact Stress, uses upper symbol, i.e., is "-" number on molecule, is on denominator
"+"；Upper symbol is used when the Calculation of Contact Stress of outer ring, i.e., is "+" number on molecule, is "-" on denominator, and f is ditch curvature number；α is
Contact angle；D is rolling element diameter；Z is rolling element number；γ may be expressed as:
In formula (6), dmFor bearing pitch diameter；
(4) since applied load acts on, contact stress is generated between rolling element and inside and outside circle, due to the raceway of Internal and external cycle
Diameter, the influence of curvature direction, contact stress caused by applied load differ；
For spot contact bearing,
For line contact bearing,
In formula (7) and formula (8), j refers to j-th of rolling element, QjRefer to that the contact stress of j-th of rolling element, Z are total rolling element
Number；
(5) formula (4) and formula (7) are substituted into formula (2), formula (5) and formula (8) substitute into formula (3), can acquire respectively inner and outer ring raceway and connect
The touching secondary service life when demand reliability is R；It is assumed that tired longevity of the Contact Pair in demand reliability R between outer ring and rolling element
Life is LRO, fatigue life of the Contact Pair in demand reliability R is L between inner ring and rolling elementRI, since a Contact Pair is sent out
Raw failure then can determine that a whole set of bearing failure, thus need to choose shorter mathematic(al) expectation as the benchmark service life of subsequent calculating,
The calculating benchmark of complete bearing life when i.e. reliability requirement is R are as follows:
L=Min [LRI,LRO] (9)
(6) for the raceway of longer life, since its demand service life is reduced, then its reliability will also be increase accordingly, that is, be existed
Its reliability will increase under one shorter requirements for life；
It is assumed that LRI>LRO, then the reliability of interior rollaway nest is promoted, i.e., its reliability becomes R from RI；Similarly, it is assumed that LRO>LRI, then
The reliability of outer rollaway nest is promoted, i.e., its reliability becomes R from RO；That is:
In formula (10), the subscript I/O in formula refers to inner ring or outer ring；LSMathematic(al) expectation when for probability of survival being S, L10I
Indicate fatigue life when inner ring raceway/rolling element Contact Pair reliability is 90%；L10OIndicate outer ring raceway/rolling element contact
Fatigue life when secondary reliability is 90%.
(7) as previously mentioned, the then complete bearing failure of any Contact Pair element failure, then for the reliability of complete bearing,
More accurate using series connection reliability description, reliability R ' of a whole set of bearing at service life L can be described as:
R '=R × RI/O (11)
Formula (11) indicates the new reliability R ' of complete bearing for demand reliability R and the interior R lasted a long timeIOr outer ROMeter
The product of reliability is calculated, interior rollaway nest mathematic(al) expectation is longer, selects RI, outer rollaway nest lasts a long time, and selects RO, RIOr ROValue by
Formula (10) determines；
(8) different from demand reliability R by the reliability R ' obtained after calculating, then need to return calculating demand reliability
Mathematic(al) expectation under R, this calculating process can solve Different Reliability, i.e., different survivals according to the Slope relationship of Weibull distribution
Different fatigue service life under probability, relationship can be described as:
In formula (12), S is the corresponding probability of survival of demand reliability R, and S ' is then practical reliable under the calculating corresponding service life
Spend the corresponding probability of survival of R ', LSMathematic(al) expectation when for probability of survival being S, LS' mathematic(al) expectation when be probability of survival being S ',
It requires to be 90% according to reliability, then formula (12) can simplify are as follows:
The medicine have the advantages that in the present invention, rolling bearing fatigue life and reliability degree calculation method exist
It is expanded on the basis of Lundberg-Palmgren formula, i.e., the distribution of rolling bearing internal load is calculated first, using need
The reliability asked calculates separately the service life of inside and outside raceway, then just carries out the new method proposed in this patent.
In the present invention, rolling bearing no longer goes to consider as a whole, but be split as interior rollaway nest rolling element contact
Secondary, outer rollaway nest two different units of rolling element Contact Pair go to calculate its fatigue life and reliability, any cell failure is then a whole set of
Bearing failure.
The rolling bearing fatigue life and reliability degree calculation method based on independent contact pair proposed according to the present invention, with not
Most short life with Contact Pair is basic as the calculating of complete bearing life, can ensure the reliability of calculating.
The rolling bearing fatigue life and reliability degree calculation method based on independent contact pair proposed according to the present invention calculates
Fatigue life out is noticeably greater than original method, this is solved in current engineering practice, and actual life is much larger than mathematic(al) expectation, but
The case where being theoretically unsound.
Detailed description of the invention
Fig. 1 is the Contact Pair of radial ball bearing；
Fig. 2 is the Contact Pair of radial roller bearing；
Fig. 3 is that the supporting region load of radial ball bearing is distributed；
Fig. 4 is that the supporting region load of radial roller bearing is distributed.
Specific embodiment
Rolling bearing fatigue life and reliability degree calculation method proposed by the present invention based on independent contact pair, existing pass
It still can be used as current methods in material, lubrication, working environment clean conditions equivalent life correction factor, in this patent
It does not repeat again.
The step of rolling bearing fatigue life and reliability degree calculation method based on independent contact pair, is as follows:
(1) theoretical according to Lundberg-Palmgren, the contact fatigue life between rolling element and raceway can be estimated according to following formula
It calculates:
In formula (1), QcFor contact rating load, Q is applied load.Due between different types of rolling element and raceway
Contact condition is different, and fatigue life is also variant, thus separately shown.
(2) rolling bearing during one's term of military service, fix by a general lasso, the rotation of another lasso.Also there is a small amount of Internal and external cycle
The operating condition rotated, but the speed between two swivel ferrules has larger difference, thus low speed circle is assumed to non-rotating rings.
For spot contact bearing,
In formula (2), QcμFor swivel ferrule contact rating load, QeμFor swivel ferrule applied load；QcvIt is connect for fixed lasso
Touch rated load, QevFor fixed lasso applied load；Subscript μ refers to swivel ferrule, and subscript ν refers to non-rotating rings；Point contact
In bearing, the contact stress state between steel ball and the contact condition and single steel ball and inner and outer ring raceway of Internal and external cycle is shown in attached drawing 1.
For line contact bearing, similar can indicate are as follows:
The meaning of symbology in formula (3) is identical as formula (2)；In line contact bearing, contact shape of the roller with Internal and external cycle
Contact stress state between state and single roller and inner and outer ring raceway is shown in attached drawing 2.
(3) contact rating load is only and the initial factors such as contact type, material and heat treatment situation are related, with rolling element with
Contact unrelated between inside/outside circle, thus the inside and outside circle contact rating load of point contact may be expressed as:
The inside and outside circle contact rating load of line contact may be expressed as:
In formula (4) and (5), when inner ring Calculation of Contact Stress, uses upper symbol, i.e., is "-" number on molecule, is on denominator
"+"；Upper symbol is used when the Calculation of Contact Stress of outer ring, i.e., is "+" number on molecule, is "-" on denominator.F is ditch curvature number；α is
Contact angle；D is rolling element diameter；Z is rolling element number；γ may be expressed as:
In formula (6), dmFor bearing pitch diameter.
(4) since applied load acts on, contact stress is generated between rolling element and inside and outside circle.Due to the raceway of Internal and external cycle
Diameter, the influence of the factors such as curvature direction, contact stress caused by applied load differ.
For spot contact bearing,
In spot contact bearing, the internal load distribution of complete bearing and supporting region are shown in attached drawing 3.
For line contact bearing,
In line contact bearing, the internal load distribution of complete bearing and supporting region are shown in attached drawing 4.In formula (7) and formula (8), j
Refer to j-th of rolling element, QjRefer to the contact stress of j-th of rolling element；
Above 4 steps are consistent with the existing calculation method based on Lundberg-Palmgren formula, it is therefore intended that first
Find out the load distribution of Bearing inner.Following steps are new method proposed by the present invention.
(5) formula (4) and formula (7) are substituted into formula (2), formula (5) and formula (8) substitute into formula (3), can acquire respectively inner and outer ring raceway and connect
The touching secondary service life when reliability is R.It is assumed that the fatigue life between outer ring and rolling element when Contact Pair reliability R is LRO, interior
Fatigue life between circle and rolling element when Contact Pair reliability R is LRI, due to Contact Pair occur failure then can determine that it is whole
Bearing failure is covered, thus needs to choose service life of the shorter mathematic(al) expectation as complete bearing, i.e., the calculating of complete bearing life
Benchmark are as follows:
L=Min [LRI,LRO] (9)
(6) for the raceway of longer life, since its demand service life is reduced, then its reliability will also be increase accordingly, that is, be existed
Its reliability will increase under one shorter requirements for life.
It is assumed that LRI>LRO, then the reliability of interior rollaway nest is promoted, i.e., its reliability becomes R from RI；Same reason, it is assumed that LRO
>LRI, then the reliability of outer rollaway nest is promoted, i.e., its reliability becomes R from RO；That is:
In formula (10), ζ is failure probability, and the subscript I/O in formula refers to inner ring or outer ring；LSWhen for probability of survival being S
Mathematic(al) expectation, reliability R is 1- ζ at this time；Formula (10) derives from Weibull distribution expression formula.
(7) as previously mentioned, the then complete bearing failure of any Contact Pair element failure, then for the reliability of complete bearing,
More accurate using series connection reliability description, reliability R ' of a whole set of bearing at service life L can be described as:
R '=R × RI/O (11)
Formula (11) indicates the new reliability R ' of complete bearing for demand reliability R and certain raceway (the interior R lasted a long timeI
Or outer RO) calculating reliability product, interior rollaway nest mathematic(al) expectation is longer, selects RI, outer rollaway nest lasts a long time, and selects RO。RI
Or ROValue by formula (10) determine.
(8) different from demand reliability R by the reliability R ' obtained after calculating, then need to return calculating demand reliability
Mathematic(al) expectation under R.This calculating process can solve Different Reliability (i.e. different survivals according to the Slope relationship of Weibull distribution
Probability) under the different fatigue service life, relationship can be described as:
In formula (12), S is the corresponding probability of survival of demand reliability R, and S ' is then practical reliable under the calculating corresponding service life
Spend the corresponding probability of survival of R '.LSMathematic(al) expectation when for probability of survival being S, LS' mathematic(al) expectation when be probability of survival being S '.
It requires to be 90% according to reliability, then formula (12) can simplify are as follows:
Rolling bearing fatigue life and reliability calculating based on independent contact pair is described in detail below in conjunction with specific example
The specific implementation step of method, it should be noted that this embodiment be exemplary type example, rather than for limit it is of the invention
Range is extremely applied.
In order to preferably realize comparison, this example select two in T.A.Harris works " rolling bearing analysis " about
The calculated examples of the fatigue life and reliability of deep groove ball bearing and cylinder roller bearing, selection bearing identical with the example,
Identical internal structure parameter and identical application conditions, more clearly to show method proposed by the present invention, more
Clearly compare the difference between new method and existing calculation method；It is calculated to simplify, what is be more clear shows new calculating
Method is not introduced into life adjustment factor in following example, as existing method, cleans shape about material, lubrication, working environment
State equivalent life correction factor can also calculation method incorporated in the present invention.
Embodiment 1:
6209 deep groove ball bearings, steel ball number Z are 9, and steel ball size D is 12.7mm, bearing pitch diameter dmIt is interior for 65mm
The ditch coefficient of curvature f of outer ringi=fo=0.52, radial internal clearance 0.015mm.Under the Radial Loads of 8900N, inner ring
It is rotated with the speed of 1800RPM, calculates the L of two raceways10Service life, and calculate the practical reliability of the life conditions.
(1) from formula (6):
(2) inside and outside circle contact rating load is acquired by formula (4) respectively
In formula (15) and formula (16), since clear swivel ferrule is inner ring, non-rotating rings are outer ring, thus use Qci
Instead of Qcμ, QcoInstead of Qcv。
(3) according to the external applied load of the radial internal clearance of the bearing, interior geometry parameter and receiving, using Approach by inchmeal
The load such as table 1 that method or solution by iterative method Bearing inner 8 different rolling elements are born:
The distribution of 1 6209 Bearing inner load of table
(4) since swivel ferrule is inner ring, therefore the data in table 1, which are substituted into formula (7), to be obtained:
In formula (17), QeiWith Q in formula (7)eμSymbol meaning is identical, and being also due to clear swivel ferrule is inner ring, because
And change subscript.
(5) outer ring is retainer plate, therefore the data in table 1, which are substituted into formula (7), to be obtained:
In formula (18), QeoWith Q in formula (7)evSymbol meaning is identical, and being also due to clearly fixed lasso is outer ring, because
And change subscript.
(6) by formula (3), the L of inside and outside circle can be obtained10It is respectively as follows:
In formula (19), L10IIndicate fatigue life when inner ring raceway/rolling element Contact Pair reliability is 90%；L10OIt indicates
Fatigue life when outer ring raceway/rolling element Contact Pair reliability is 90%.
(7) by formula (19), the L of inside and outside circle10Difference, and have a long way to go, weak link is inner ring, and inner ring/rolling element connects
The set bearing has failed after the secondary failure of touching, that is to say, that the L of the set bearing10oMore than L10iPart be it is meaningless, this meaning
Taste under this operating condition the reliability of outer ring be more than 90%.
(8) by formula (19), under the application conditions, the outer ring service life only needs to reach 23.2 × 106, by formula (10), can obtain
Under the requirements for life, outer ring reliability are as follows:
(9) by formula (11), a whole set of bearing life is 23.2 × 106Practical reliability when r can be described as:
R '=0.9 × 0.987=0.89 (21)
(10) by formula (12), reverse goes out calculating fatigue life when reliability is 90% are as follows:
L10=23.0 × 106 (22)
(11) in existing calculation method, the calculating process of preceding 4 step is consistent with calculating process of the invention.But its calculating is whole
When the service life of body bearing, the probability of direct equivalent each element, by the service life Integrative expression of complete bearing are as follows:
(12) each Contact Pair service life is substituted into formula 16, when the complete bearing reliability that can acquire existing method calculating is 90%
Fatigue life are as follows:
L10=20.9 × 106 (24)
Contrast (19) and formula (20) are it is found that aobvious using calculation method calculated race bearing fatigue life of the invention
It writes and improves 10%, the calculating fatigue life of deep groove ball bearing is often substantially less than mathematic(al) expectation in practical application, and the present invention more connects
Closely and practical application.
Embodiment 2:
N209 cylinder roller bearing, roller number Z are 14, and roller diameter D is 10mm, bearing pitch diameter dmFor 65mm,
Roller effective length 29.6mm, under the Radial Loads of 4450N, bearing is that modified line contacts and inner ring rotates, and calculates two
The L of raceway10Service life, and calculate the practical reliability of the life conditions.
(1) from formula (6)
(2) inside and outside circle contact rating load is acquired by formula (4) respectively
(3) successive approximation approach can be used or solution by iterative method Bearing inner 3 different rolling elements (referring to fig. 2) are born
Load such as table 2:
The distribution of 1 6209 Bearing inner load of table
(4) since swivel ferrule is inner ring, therefore the data in table 2, which are substituted into formula (7), to be obtained:
(5) outer ring is retainer plate, therefore the data in table 2, which are substituted into formula (7), to be obtained:
(6) by formula (3), the L of inside and outside circle can be obtained10It is respectively as follows:
(7) by formula (9), the L of inside and outside circle10Difference, and having a long way to go, weak link is inner ring, i.e. the set bearing
L10More than LIPart be it is meaningless, also mean that the reliability of the outer ring under this operating condition far more than 90%.
(8) by formula (10), under the application conditions, outer ring requirements for life is 1155 × 106, then outer ring reliability are as follows:
RO=0.98 (31)
(9) by formula (11), a whole set of bearing life is 1155 × 106Practical reliability when r can be described as:
R '=0.9 × 0.98=0.882 (32)
(10) by formula (12), reverse goes out calculating fatigue life when reliability is 90% are as follows:
L10=9.88 × 108 (33)
(11) in existing calculation method, the calculating process of preceding 4 step is consistent with calculating process of the invention.But its calculating is whole
When the service life of body bearing, the probability of direct equivalent each element, by the service life Integrative expression of complete bearing are as follows:
(12) each Contact Pair service life is substituted into formula 16, when the complete bearing reliability that can acquire existing method calculating is 90%
Fatigue life are as follows:
L10=9.85 × 108 (35)
Contrast (33) and formula (35) using calculation method calculated race bearing fatigue life of the invention it is found that mentioned
High by 0.03%, the calculating fatigue life of cylindrical bearing and mathematic(al) expectation degree of closeness are higher in practical application, this is also anti-from side
Reflect the correctness of calculation method of the invention.
Claims (1)
1. rolling bearing fatigue life and reliability degree calculation method based on independent contact pair, it is characterised in that: including following step
It is rapid:
(1) theoretical according to Lundberg-Palmgren, the contact fatigue life between rolling element and raceway can be estimated according to following formula:
In formula (1), QcFor contact rating load, Q is applied load；
(2) during one's term of military service, the speed between two lassos has larger difference to rolling bearing, and one is swivel ferrule, another is low
Fast lasso or fixed lasso are non-rotating rings；
For spot contact bearing,
In formula (2), QcμFor swivel ferrule contact rating load, QeμFor swivel ferrule applied load；QcvVolume is contacted for fixed lasso
Constant load, QevFor fixed lasso applied load；Subscript μ refers to swivel ferrule, and subscript ν refers to non-rotating rings；
It is similar to indicate for line contact bearing are as follows:
The meaning of symbology in formula (3) is identical as formula (2)；
(3) contact rating load is only and contact type, material are related with heat treatment situation, indirectly with rolling element and inside/outside circle
Touch unrelated, thus the inside and outside circle contact rating load of point contact may be expressed as:
The inside and outside circle contact rating load of line contact may be expressed as:
In formula (4) and (5), when inner ring Calculation of Contact Stress, uses upper symbol, i.e., is "-" number on molecule, is "+" on denominator；Outside
Upper symbol is used when enclosing Calculation of Contact Stress, i.e., is "+" number on molecule, is "-" on denominator, f is ditch curvature number；α is contact angle；
D is rolling element diameter；Z is rolling element number；γ may be expressed as:
In formula (6), dmFor bearing pitch diameter；
(4) since applied load acts on, contact stress is generated between rolling element and inside and outside circle, due to the raceway diameter of Internal and external cycle,
The influence of curvature direction, contact stress caused by applied load differ；
For spot contact bearing,
For line contact bearing,
In formula (7) and formula (8), j refers to j-th of rolling element, QjRefer to that the contact stress of j-th of rolling element, Z are total rolling element number；
(5) formula (4) and formula (7) are substituted into formula (2), formula (5) and formula (8) substitute into formula (3), can acquire inner and outer ring raceway Contact Pair respectively
Service life when demand reliability is R；It is assumed that fatigue life of the Contact Pair in demand reliability R is between outer ring and rolling element
LRO, fatigue life of the Contact Pair in demand reliability R is L between inner ring and rolling elementRI, since a Contact Pair is lost
Effect then can determine that a whole set of bearing failure, thus need to choose shorter mathematic(al) expectation as the benchmark service life of subsequent calculating
Calculating benchmark by spending complete bearing life when requirement is R are as follows:
L=Min [LRI,LRO] (9)
(6) for the raceway of longer life, since its demand service life is reduced, then its reliability will also be increase accordingly, i.e., at one
Its reliability will increase under shorter requirements for life；
It is assumed that LRI>LRO, then the reliability of interior rollaway nest is promoted, i.e., its reliability becomes R from RI；Similarly, it is assumed that LRO>LRI, then outer rolling
The reliability in road is promoted, i.e., its reliability becomes R from RO；And:
In formula (10), the subscript I/O in formula refers to inner ring or outer ring；LSMathematic(al) expectation when for probability of survival being S, L10IIn expression
Enclose fatigue life when raceway/rolling element Contact Pair reliability is 90%；L10OIndicate that outer ring raceway/rolling element Contact Pair is reliable
Fatigue life when degree is 90%；
(7) as previously mentioned, the then complete bearing failure of any Contact Pair element failure uses then for the reliability of complete bearing
Reliability of connecting description is more accurate, and reliability R ' of a whole set of bearing at service life L can be described as:
R '=R × RI/O (11)
Formula (11) indicates the new reliability R ' of complete bearing for demand reliability R and the interior R lasted a long timeIOr outer ROCalculating can
By the product of degree, interior rollaway nest mathematic(al) expectation is longer, selects RI, outer rollaway nest lasts a long time, and selects RO, RIOr ROValue by formula
(10) it determines；
(8) different from demand reliability R by the reliability R ' obtained after calculating, then it needs to return under calculating demand reliability R
Mathematic(al) expectation, this calculating process can solve Different Reliability according to the Slope relationship of Weibull distribution, i.e., it is different survive it is general
Different fatigue service life under rate, relationship can be described as:
In formula (12), S is the corresponding probability of survival of demand reliability R, and S ' is then the practical reliability R ' calculated under the corresponding service life
Corresponding probability of survival, LSMathematic(al) expectation when for probability of survival being S, LS' mathematic(al) expectation when be probability of survival being S ', it rolls
Its L of the more demands of the Calculation of Fatigue Life of bearing10Service life requires to be 90% according to reliability, then formula (12) can simplify are as follows:
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| CN201610917636.1A CN106355039B (en) | 2016-10-21 | 2016-10-21 | Rolling bearing fatigue life and reliability degree calculation method based on independent contact pair |
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| CN201610917636.1A CN106355039B (en) | 2016-10-21 | 2016-10-21 | Rolling bearing fatigue life and reliability degree calculation method based on independent contact pair |
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| CN106355039B true CN106355039B (en) | 2019-04-26 |
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| CN201610917636.1A Active CN106355039B (en) | 2016-10-21 | 2016-10-21 | Rolling bearing fatigue life and reliability degree calculation method based on independent contact pair |
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102472317A (en) * | 2009-08-14 | 2012-05-23 | 谢夫勒科技有限两合公司 | Rolling bearing |
| CN103328947A (en) * | 2011-01-17 | 2013-09-25 | Ntn株式会社 | Life estimation device and life estimation method for rolling bearing |
| CN104471366A (en) * | 2012-07-12 | 2015-03-25 | Ntn株式会社 | Device for estimating service life and method for estimating service life of rolling bearing |
-
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102472317A (en) * | 2009-08-14 | 2012-05-23 | 谢夫勒科技有限两合公司 | Rolling bearing |
| CN103328947A (en) * | 2011-01-17 | 2013-09-25 | Ntn株式会社 | Life estimation device and life estimation method for rolling bearing |
| CN104471366A (en) * | 2012-07-12 | 2015-03-25 | Ntn株式会社 | Device for estimating service life and method for estimating service life of rolling bearing |
Non-Patent Citations (3)
| Title |
|---|
| Forecasting Method for Product Reliability Along with Performance Data;Xintao xia;《Journal of Failure Analysis and Prevention》;20121031;第12卷(第5期);第532–540页 |
| Spatio-temporal characteristics of friction torque of rolling bearing for space applications;Xintao Xia等;《Mechanic Automation and Control Engineering (MACE)》;20110818;第6087-6090页 |
| 汽车轮毂轴承可靠性分析;徐兴振等;《汽车维修》;20141231;第43-44页 |
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