CN108470082A - A kind of aerospace hydraulic pump accelerated life test modeling method based on index-antipower law - Google Patents
A kind of aerospace hydraulic pump accelerated life test modeling method based on index-antipower law Download PDFInfo
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Abstract
The present invention proposes a kind of aerospace hydraulic pump accelerated life test model based on index antipower law, is applied to aerospace hydraulic pump reliability field.It is not simple power function relationship that the model discloses wear extent in the rotor valve plate unit interval with pressure, rotating speed by quantitative calculating, on this basis, it is proposed that a kind of index antipower law accelerated life model based on the physics of failure.Model describes the service life distribution of squeeze pump using accumulation Weibull distribution, and the conversion relationship of service life and load is described using index inverse power law model.Emulation and the experimental results showed that：Compared with tradition is based on the antipower law accelerated life model of statistics experience, index antipower law accelerated life model proposed by the present invention can react the physics of failure characteristic of aerospace hydraulic pump deeper into ground, have higher estimated accuracy.
Description
Technical field
The invention belongs to aerospace hydraulic pump reliability fields, and in particular to a kind of hydraulic air based on index-antipower law
Pump accelerated life test modeling method.
Background technology
Axial plunger pump provides high-voltage oil liquid for plane hydraulic system and flies the control systems such as rudder face and undercarriage to drive.Plunger
Failure of pump can cause aerial mission that can not normally complete, or even cause the major accident of fatal crass, therefore, for airplane hydraulic pressure
The requirement for pumping life and reliability is higher and higher.With the continuous improvement in design of hydraulic pump service life, life appraisal is carried out to it
Difficulty and cost are also increasing.Therefore often use the method for accelerated life test with the compression test time in engineering.
In accelerated life test, by applying the load harsher than normal running conditions to hydraulic pump, make hydraulic pump that event faster occur
Hinder, then estimates the service life of hydraulic pump under normal load by statistical method.
Accelerated life test is, by reinforcing the method for stress, to accelerate production under the premise of not changing product failure mechanism
Product failure shortens test period, the method for predicting product life characteristics under normal stress effect in a relatively short period of time.No
Change the premise that failure mechanism is accelerated life test, the environmental stress or working stress that reinforcement product is born are to be accelerated
The necessary means of life test.Accelerated life test is to shorten test period by reinforcing stress, but if stress is excessive, is changed
The failure mechanism of product is become, then accelerated life test just loses meaning.If stress is less than normal, test period can be caused to contract
Short to be not obvious, accelerated life test is unable to get best effect.How the actual condition of combination product, determination do not change production
Product failure mechanism and the accelerated life test section that can play preferable acceleration are always the problem for perplexing designer.
The chife failure models of aircraft axial plunger pump include the abrasion of internal component, inlet port insufficient pressure, rotor
Bearing fault etc..According to statistics, the abrasion of internal component is the most important fault mode of aircraft axial plunger pump.The work of hydraulic pump
It is an important factor for influencing internal component abrasion to make pressure and rotating speed, and higher rotating speed can directly accelerate the mill of internal component
Damage, and higher operating pressure can make the lubricant effect of internal component be deteriorated, to aggravate its abrasion.Therefore pump rotating speed and
Pressure can be as the accelerating load of hydraulic pump accelerated life test.
Ideally, the accelerated life test of hydraulic pump should be based on the failure physical model of hydraulic pump.However, due to
Axial plunger pump failure mechanism is excessively complicated, also lacks a kind of accelerated life model based on the physics of failure at present.Hydraulic pump
Failure procedure is mainly determined that accelerated life model will not only consider to directly contribute hydraulic pressure by the lubrication and abrasion state of internal component
The factor for pumping performance degradation, it is also contemplated that the influence of a variety of coupling factors.
The reference of external product accelerated life test can be retrieved at present, but has focused largely on grinding for statistical method
Study carefully, the content about acceleration model is considerably less.Closing policy is taken to China's the relevant technologies in view of foreign countries, we are to external aviation
How hydraulic pump accelerated life test model, which is established, is had no way of learning, China is also rigid to the research of aerospace hydraulic pump accelerated life test
Ground zero, up to the present there has been no the aerospace hydraulic pump accelerated life test models for being suitable for engineer application in China.
Invention content
The present invention is based on the analyses to abrasion of hydraulic pump failure procedure, it is proposed that a kind of by the physics of failure and engineering experience phase
In conjunction with accelerated life model.In the accelerated life model proposed, it is believed that accumulation is obeyed in the distribution of basic service life of hydraulic pump
Weibull distribution, and its service life-load conversion relationship is a kind of index-power law relation.
A kind of aerospace hydraulic pump accelerated life test modeling method based on index-antipower law proposed by the present invention, specifically
Step is：
Step 1: Hydraulic pump fault mechanism and wear process analysis；
Step 2: the relation derivation of rotor valve plate spacing and the operating pressure of pump, rotating speed；
Step 3: the accelerated life model based on index-antipower law；
Step 4: accelerated life model error analysis.
The advantages and positive effects of the present invention are：
(1) it on the basis of detailed analysis aerospace hydraulic pump friction and wear failure mechanism, is disclosed and is turned by quantitative calculating
Wear extent and pressure, rotating speed in the sub- valve plate unit interval are not simple power function relationships, on this basis, it is proposed that one
The kind index based on the physics of failure-antipower law accelerated life model.
(2) model describes the service life distribution of squeeze pump using accumulation Weibull distribution, is described using index-inverse power law model
The conversion relationship in service life and load.It is proposed by the present invention compared with tradition is based on the antipower law accelerated life model of statistics experience
Index-antipower law accelerated life model can react the physics of failure characteristic of aerospace hydraulic pump deeper into ground, have higher estimation
Precision.
Description of the drawings
Fig. 1 is two-dimentional diamond shape Abrasive model；
Fig. 2 is the abrasion condition at any on valve plate；
Fig. 3 is the depth of abrasive grain insertion rotor and valve plate；
Fig. 4 is valve plate geometric dimension；
Fig. 5 is accelerated life test device；
Fig. 6 is accelerated life test principle；
Fig. 7 is reliability curve and probability density of failure curve under declared working condition；
Fig. 8 is flow chart of the method for the present invention.
Specific implementation mode
Below in conjunction with drawings and examples, the present invention is described in further detail.
The present invention is a kind of aerospace hydraulic pump accelerated life test modeling method based on index-antipower law, flow such as Fig. 8
It is shown, including following steps：
Step 1: Hydraulic pump fault mechanism and wear process analysis.
The inside of plunger pump has three pairs of main frictions secondary：Rotor and valve plate, plunger and plunger hole and swash plate and cunning
Boots.The secondary abrasion of above-mentioned three pairs of frictions can cause the increase of leakage rate, and the output flow of pump is caused to cannot be satisfied requirement.Theory meter
It calculates and experiment shows to leak in the leakage of aerospace hydraulic pump in the highest flight caused by rotor-flow mill damage.Therefore exist
In engineering, the wear condition of hydraulic air pump rotor valve plate is usually monitored with leakage rate.
During hydraulic pump works, the surface of rotor and valve plate is not to be in direct contact, but by one layer of very thin profit
Lubricating oil film separates.However, hydraulic oil is not pure, wherein certain density hard particles are left floating, these particulate matter meetings
The surface of rotor and valve plate is caused to wear.The valve plate to break down is put into observed under electron microscope, can with
A-circle-by-a-circle cut is observed on flow table surface, this illustrates that the hard particles object in the abrasion mainly fluid of valve plate causes
's.
Studies have shown that the degree of wear caused by particle is mainly influenced by the distance of desirable particle size and two surfaces.
According to the two-dimentional diamond shape Abrasive model of Williams and Hyncica, as shown in Figure 1, working as D/h≤1/cos βdWhen, mill
Grain is freely rotated in fluid, does not cause to wear to rotor and plane valving surface；As D/h ＞ 1/cos βdWhen, abrasive grain is in rotor
It is rotated between two surface of valve plate, reaches an equilbrium position, while wearing two surfaces.Wherein, D is that abrasive grain is maximum straight
Diameter, h are two surface spacing, βdFor abrasive grain shape angle.
As shown in Fig. 2, considering on valve plate that a bit (x, y), oil film thickness is h (x, y), area dxdy, is discussed (x, y)
Abrasion condition of the contained abrasive grain to valve plate in place's fluid.
As shown in figure 3, according to geometrical relationship and the relative hardness of rotor and valve plate, single abrasive grain is embedded in rotor and matches
The depth of flow table is respectively：
Wherein, ΔAIt is embedded in rotor surface depth, Δ for abrasive grainBFor abrasive grain be embedded in plane valving surface depth, H be valve plate and
Rotor surface hardness ratio.
Accordingly single abrasive grain grooving cross-sectional area caused by rotor and valve plate is：
Single abrasive grain wear volume caused by rotor and valve plate is respectively in certain time：
Wherein, f is the coefficient of waste, and ω is hydraulic pressure revolution speed, and r is the corresponding radius of point (x, y).
All abrasive grains wear volume caused by rotor and valve plate is respectively in the region (x, y) in certain time：
Wherein, k (D) is the corresponding concentration of abrasive grain that size is D.
So certain time internal rotor and flow mill damage total volume are
Wherein, Ω indicates all regions needed to be considered on rotor and valve plate.
Formula (5) is arranged and can be obtained, rotor caused by abrasive grain-valve plate contact surface Volume Loss v in the unit interval,
Meet following relational expression：
This illustrates the rotational speed omega of rotor caused by abrasive grain in the unit interval-valve plate contact surface Volume Loss v and pump at just
Than directly proportional to the cube of rotor valve plate spacing h.
For accelerated life model, it is most concerned with the operating pressure of unit interval Volume Loss and pump, rotating speed
Relationship, so deriving rotor-valve plate spacing h and the rotational speed omega of pump and the work of pump according to simplified Reynolds equation in next step
Make pressure PdAnalytical expression.
Step 2: the relation derivation of rotor valve plate spacing and the operating pressure of pump, rotating speed.
The spacing h of rotor valve plate can be acquired by the Reynolds equation simplified under cylindrical coordinates.Under cylindrical coordinates, Reynolds side
Journey can be reduced to：
Wherein, p is oil film dynamic pressure distribution, and μ is fluid dynamic viscosity, and ω is hydraulic pressure revolution speed, and r is radial coordinate, θ
For azimuthal coordinate.
The geometric dimension of valve plate is as shown in figure 4, radius is r on valve platerCircumferentially spaced about 120 ° take three ginsengs
Examination point, then the oil film thickness on valve plate at any point (x, y) function of these three permanent datums can be expressed as：
Wherein, h1 h2 h3Three refer to point coordinates respectively.
The average distance of rotor valve plate can be expressed as：
Under cylindrical coordinates, any point (x, y) can be expressed as on valve plate
Formula (10) is substituted into formula (8), can be obtained
Partial derivative about θ is asked to formula (11), can be obtained
Formula (12) is substituted into formula (7), and equal sign both sides integrate r, r is the cylindrical coordinates of conversion, can be obtained：
Wherein, C1For undetermined constant, need according to Boundary Condition for Solving.
For simplified expression, enable
After arrangement
Formula (15) equal sign both sides integrate r, can obtain：
Wherein, C2For undetermined constant.
According to the boundary condition of oil sealing band in oil-discharging cavity, have
Wherein, PSFor oil suction cavity pressure, PdFor oil extraction cavity pressure, r1For inner seal band outer radius, r2It is outside inner seal band half
Diameter.
Formula (16) is substituted into boundary condition (17), then is had
Undetermined coefficient C can be solved according to above equation1And C2：
Wherein,
The pressure distribution that internal oil sealing takes is integrated, and support force of the interior oil sealing band to rotor can be obtained
Wherein, θ2-θ1For oil distribution casing window angle.
Similar, according to the boundary condition of oil sealing band outside oil-discharging cavity, have
Wherein, r3For external seal band inside radius, r4For external seal band outer radius.
Then outer oil sealing band is to the support force of rotor
Wherein, undetermined coefficient is
Wherein,
Rotor is pressed to the gross pressure of valve plate to be with approximate calculation
According to the condition of rotor stability, gross pressure should be equal with total support force, i.e.,
Fp=Fsi+Fso (28)
By formula (21), (24), (27) substitute into formula (28), and simplify to equation, only retain following variable：It is average
Oil film thicknessPump work pressure Pd, revolution speed ω.Other parameters are considered as constant merging treatment, change
After letter：
(C01Pd+C02ω+1)M(h0)=ln { N (h0)} (29)
Wherein, C01, C02It is constant, M (h0), N (h0) it is about h0Rational polynominal.Formula (29) under normal conditions without
The method of method parsing solves, but it reflects pressure, rotating speed and two surface spacing and meets certain exponential relationship, i.e.,
H=aPbωcexp{dP+eω} (30)
Wherein, a, b, c, d, e are undetermined parameters, and ω is rotor speed, and P is hydraulic pump works pressure.
Step 3: the accelerated life model based on index-antipower law.
Traditional hydraulic pump accelerated life test generally uses inverse power law model as accelerated life model (power-law
Model, abbreviation PL model)：
V=aPbωc (31)
Wherein, a, b, c are undetermined parameters, and ω is rotor speed, and P is hydraulic pump works pressure.
In conjunction with formula (6) and (30) it is found that rotor-valve plate spacing and pressure rotating speed are not simple power function relationships,
So being different from traditional inverse power law model, a kind of new index-inverse power law model (exponential-power-law is proposed
Model, abbreviation EPL model)：
V=aPbωcexp{dP+eω} (32)
Wherein, a, b, c, d, e are undetermined parameters, and ω is rotor speed, and P is hydraulic pump works pressure.
The hydraulic pump acceleration model based on accumulation Weibull distribution and index-antipower law is derived below.One completely adds
Fast life model should convert relationship including the service life between the distribution of the basic service life of product under certain loads and different loads.
Four basic assumptions：
(1) service life of hydraulic pump obeys following Weibull distributions under any load S (P, ω)：
Wherein, F (t) is probability of malfunction, and t is the out-of-service time, and η is characterized the service life, and m is form parameter.
(2) the form parameter m of Weibull distributions is constant under any load S (P, ω).
(3) characteristics life η is in different loads Si(Pi, ωi) and Sj(Pj, ωj) between can be converted by following relationship：
(4) product remaining life is only related with current accumulated damage and current load, unrelated with progressive damage mode.
N sample of selection carries out accelerated life test, j-th of sample experience under varying stress loading spectrumLoad history, the corresponding cumulative failure time is Wherein there is n1A product failure, there is n2A product proceeds to experiment
End failure not yet.
Fault sample ZjCumulative failure density be：
For truncated sample YjAccumulation reliability be：
WhereinFor history loadTo current loadThe equivalent conversion time, τJ, 0=0,
The maximum likelihood function of mixed-weibull distribution is：
Wherein, n1For fault sample number；n2For truncated sample number, n=n1+n2.Parameter to be estimated is
Rated load S0(P0, ω0) under reliability function be：
Fault probability function under rated load is：
Mean down time, (MTTF) was
Step 4: accelerated life model error analysis；
The error of Maximum-likelihood estimation is evaluated usually using Fisher information matrix, defining Fisher information matrix is：
Each single item in Fisher information matrix is that logarithm maximum likelihood function is micro- for respectively parameter Second Order Partial to be estimated respectively
The mathematic expectaion divided.About the symmetrical item of leading diagonal it is equal in Fisher information matrix, so needing to calculate 6+5 altogether
The mathematic expectaion of+4+3+2+1=21 second order partial differentials.
By Fisher information matrix, error of estimate variance can be further calculated.Reliability function R0Estimation
Error variance is
Wherein
Mean down time TMTTFEstimation error variance be
Wherein
A kind of aerospace hydraulic pump accelerated life test model based on index-antipower law of the present invention is applied to aviation liquid
Press pump reliability field.The model discloses wear extent in the rotor valve plate unit interval and pressure by quantitative calculating, turns
Speed is not simple power function relationship, on this basis, it is proposed that a kind of index based on the physics of failure-antipower law accelerated aging
Model.Model using accumulation Weibull distribution describe squeeze pump service life distribution, using index-inverse power law model describe the service life with
The conversion relationship of load.Emulation and the experimental results showed that：Compared with tradition is based on the antipower law accelerated life model of statistics experience,
Index proposed by the present invention-antipower law accelerated life model can react the physics of failure characteristic of aerospace hydraulic pump, tool deeper into ground
There is higher estimated accuracy.
Embodiment
Pass through practical accelerated life test data verification accelerated life model proposed by the present invention.Experimental subjects flies for certain type
The Electric Motor Driven Pump (Electric Motor Driven Pump, EMP) of machine.Accelerated life test device is as shown in figure 5, examination
It is as shown in Figure 6 to test principle.The operating pressure pumped using pressure sensor monitoring utilizes the shell oil return of flow sensor monitoring pump
Flow.Select pressure and rotating speed as accelerated stress, the rated pressure of pump is 21MPa, and rated speed 4000r/min passes through
The operating pressure for loading throttle valve adjustment pump passes through the rotating speed of speed regulating motor control pump.The failure criteria of pump is super for return flow
Mark.
According to experiment of knowing the real situation as a result, not changing failure mechanism under the premise of, the limit stress that can apply is pressure
28MPa rotating speeds 6000r/min.According to the regulation of national military standard, aircraft hydraulic pumps life test should use varying load to compose, accelerated aging
Test load spectrum is as shown in table 1, is recycled according to 8 stages shown in table 1, and experiment truncated time is 300 hours.Share 8
A sample, experiment the result is that there is 7 sample failures, 1 test sample truncation and is cut at each test sample specific out-of-service time
The tail time is as shown in table 2.
1 accelerated life test loading spectrum of table
2 accelerated life test result of table
According to experimental result shown in loading spectrum shown in table 1 and table 2, Maximum-likelihood estimation, parameter estimation result are carried out
As shown in table 3.
3 accelerated life test parameter estimation result of table
According to the parameter estimation result of table 3, the event of (pressure 21MPa, rotating speed 4000r/min) is calculated under declared working condition
Hinder probability density curve and reliability curve is as shown in Figure 7.
The Fisher information matrix of EPL models is：
The Fisher information matrix of PL models is：
Mean down time TMTTFAnd its estimation error variance AVar (TMTTF) as shown in table 4.
4 mean down time of table and its estimation error variance
From table 4, it can be seen that estimation error variance AVar (T of the EPL models to the mean down timeMTTF) it is less than PL moulds
Type illustrates that EPL models have higher estimated accuracy.
Claims (1)
1. a kind of aerospace hydraulic pump accelerated life test modeling method based on index-antipower law, including following steps：
Step 1: Hydraulic pump fault mechanism and wear process analysis；
As D/h≤1/cos βdWhen, abrasive grain is freely rotated in fluid, does not cause to wear to rotor and plane valving surface；Work as D/
H ＞ 1/cos βdWhen, abrasive grain rotates between two surface of rotor and valve plate, reaches an equilbrium position, while wearing two
Surface；Wherein, D is abrasive grain maximum gauge, and h is two surface spacing, βdFor abrasive grain shape angle；
On establishing flow table a bit (x, y), oil film thickness is h (x, y), area dxdy, single abrasive grain insertion rotor and valve plate
Depth be respectively：
Wherein, ΔAIt is embedded in rotor surface depth, Δ for abrasive grainBIt is embedded in plane valving surface depth for abrasive grain, H is valve plate and rotor
Case hardness ratio；
Accordingly single abrasive grain grooving cross-sectional area caused by rotor and valve plate is：
Single abrasive grain wear volume caused by rotor and valve plate is respectively in certain time：
Wherein, f is the coefficient of waste, and ω is hydraulic pressure revolution speed, and r is the corresponding radius of point (x, y)；
All abrasive grains wear volume caused by rotor and valve plate is respectively in the region (x, y) in certain time：
Wherein, k (D) is the corresponding concentration of abrasive grain that size is D；
So certain time internal rotor and flow mill damage total volume are
Wherein, Ω indicates all regions needed to be considered on rotor and valve plate；
Formula (5) is arranged and can be obtained, rotor caused by abrasive grain-valve plate contact surface Volume Loss v in the unit interval meets
Following relational expression：
Step 2: the relation derivation of rotor valve plate spacing and the operating pressure of pump, rotating speed；
The spacing h of rotor valve plate is acquired by the Reynolds equation simplified under cylindrical coordinates, and under cylindrical coordinates, Reynolds equation simplifies
For：
Wherein, p is oil film dynamic pressure distribution, and μ is fluid dynamic viscosity, and ω is hydraulic pressure revolution speed, and r is radial coordinate, and θ is side
Parallactic angle coordinate；
Radius is r on valve platerCircumferentially spaced about 120 ° take three reference points, then on valve plate at any point (x, y)
Oil film thickness is expressed as the function of these three permanent datums：
Wherein, h1 h2 h3Three refer to point coordinates respectively；
The average distance of rotor valve plate is expressed as：
Under cylindrical coordinates, any point (x, y) is expressed as on valve plate
Formula (10) is substituted into formula (8), can be obtained
Partial derivative about θ is asked to formula (11), can be obtained
Formula (12) is substituted into formula (7), and equal sign both sides integrate r, r is the cylindrical coordinates of conversion, can be obtained：
Wherein, C1For undetermined constant；
It enables
After arrangement
Formula (15) equal sign both sides integrate r, can obtain：
Wherein, C2For undetermined constant；
According to the boundary condition of oil sealing band in oil-discharging cavity, have
Wherein, PSFor oil suction cavity pressure, PdFor oil extraction cavity pressure, r1For inner seal band outer radius, r2For inner seal band outer radius；It will
Formula (16) substitutes into boundary condition (17), then has
Solve undetermined coefficient C1And C2：
Wherein,
The pressure distribution that internal oil sealing takes is integrated, and support force of the interior oil sealing band to rotor can be obtained
Wherein, θ2-θ1For oil distribution casing window angle；
According to the boundary condition of oil sealing band outside oil-discharging cavity, have
Wherein, r3For external seal band inside radius, r4For external seal band outer radius；
Then outer oil sealing band is to the support force of rotor
Wherein, undetermined coefficient is
Wherein,
The gross pressure approximate calculation that rotor is pressed to valve plate is
According to the condition of rotor stability, gross pressure should be equal with total support force, i.e.,
Fp=Fsi+Fso (28)
By formula (21), (24), (27) substitute into formula (28), and simplify to equation, only retain following variable：Average oil film
ThicknessPump work pressure Pd, revolution speed ω；Other parameters are considered as constant merging treatment, after abbreviation
：
(C01Pd+C02ω+1)M(h0)=ln { N (h0)} (29)
Wherein, C01, C02It is constant, M (h0), N (h0) it is about h0Rational polynominal；Formula (29) reflect pressure, rotating speed and
Two surface spacing meet：
H=aPbωcexp{dP+eω} (30)
Wherein, a, b, c, d, e are undetermined parameters, and ω is rotor speed, and P is hydraulic pump works pressure；
Step 3: the accelerated life model based on index-antipower law；
If index-inverse power law model is：
V=aPbωcexp{dP+eω} (32)
Wherein, a, b, c, d, e are undetermined parameters, and ω is rotor speed, and P is hydraulic pump works pressure；
If four basic assumptions are：
(1) service life of hydraulic pump obeys following Weibull distributions under any load S (P, ω)：
Wherein, F (t) is probability of malfunction, and t is the out-of-service time, and η is characterized the service life, and m is form parameter；
(2) the form parameter m of Weibull distributions is constant under any load S (P, ω)；
(3) characteristics life η is in different loads Si(Pi, ωi) and Sj(Pj, ωj) between by following relationship convert：
(4) product remaining life is only related with current accumulated damage and current load, unrelated with progressive damage mode；
N sample of selection carries out accelerated life test, j-th of sample experience under varying stress loading spectrumLoad history, the corresponding cumulative failure time is Wherein there is n1A product failure, there is n2A product proceeds to experiment
End failure not yet；
Fault sample ZjCumulative failure density be：
For truncated sample YjAccumulation reliability be：
WhereinFor history loadTo current loadThe equivalent conversion time, τJ, 0=0,
The maximum likelihood function of mixed-weibull distribution is：
Wherein, n1For fault sample number；n2For truncated sample number, n=n1+n2；Parameter to be estimated isIt is specified
Load S0(P0, ω0) under reliability function be：
Fault probability function under rated load is：
Mean down time is：
Step 4: accelerated life model error analysis；
If Fisher information matrix is：
Reliability function R0Estimation error variance be
Wherein
Mean down time TMTTFEstimation error variance be
Wherein
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