CN109409028A - Based on the reliability of gears analysis method for firmly believing reliability - Google Patents
Based on the reliability of gears analysis method for firmly believing reliability Download PDFInfo
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Abstract
The present invention provides a kind of based on the reliability of gears analysis method for firmly believing reliability, comprising the following steps: S1, establishes failure mechanism model；S2, the performance parameter p for determining gear train and performance parameter threshold values pth, obtain performance margin model；S3, judge performance parameter p and performance parameter threshold values pthThe distribution pattern of obedience, and S4, S5 and S6 are executed, correspondingly gear train firmly believes reliability expression for selection；S4, performance parameter p and performance parameter threshold values pthIt is all that gear train under uncertain variables firmly believes reliability expression；S5, performance parameter p are stochastic variable, performance parameter threshold values pthIt is that gear train under uncertain variables firmly believes reliability expression；S6, performance parameter p are uncertain variables, performance parameter threshold values pthIt is that gear train under stochastic variable firmly believes reliability expression；S7, calculating gear train firmly believe reliability.The reliability of firmly believing under different failure modes is calculated by this method, and has carried out the sensitivity analysis of parameter, it is significant to the raising of reliability of gears.
Description
Technical field
The invention belongs to the reliability Optimum Design fields of engineering goods, and in particular to a kind of based on the tooth for firmly believing reliability
Take turns analysis method for reliability.
Background technique
For different types of engineering goods, a gear drive often wherein very important ring.The knot of gear train
Structure is complex, and the operating condition in use process is changeable, therefore the fail-safe analysis of gear will receive the influence of several factors.It is existing
Gear reliability calculating in, usually regard the influence factors such as the design variable of gear, load and stress and intensity as clothes
From the stochastic variable of normal distribution or Weibull distribution, the Reliability Physics model that limit state equation establishes gear is reapplied,
To calculate gear reliability.These methods only considered influence of the stochastic uncertainty to reliability of parameter, and with data
Based on, reliability model is established using the method for statistics.However in actual application process, in addition to not knowing at random
Property, the reliability of gear train also recognizes probabilistic influence.Cognition uncertainty is the shortage due to people for knowledge
Caused by a kind of uncertainty, such as determine that the uncertainty that faces is exactly that cognition is not known when parameter distribution in data deficiencies
Property.
Nineteen ninety, Apostolakis G professor point out that other than stochastic uncertainty, cognition is uncertain in " science "
Property can also have an impact model.Then numerous considerations have been developed gradually and have recognized probabilistic analysis method for reliability, such as
Based on uncertain proposition, it is based on reliability, likelihood score measurement is based on interval metrics, and the reliability based on confidence factor measurement
Analysis method.However these methods have respective deficiency when calculating gear train reliability, as reliability index decays
Excessive velocities carry out quantitative calculating etc. without suitable mathematical system.In order to solve these problems, Zeng Zhiguo proposes that firmly believe can
By the concept of degree.
Firmly believe reliability using uncertain theory and chance theory as theoretical basis, it is contemplated that influence gear train reliability
Stochastic uncertainty and cognition it is uncertain.2010, Liu applied uncertain theory to the reliable of boolean's gear train for the first time
Property is analyzed, and then Zeng has been put forward for the first time in 2013 and has firmly believed reliability, initially gives the degree for firmly believing reliability later
Measure standards system.Chance theory was applied to firmly believe reliability analysis in 2015 by Wen and Kang for the first time.Zhang is into one later
Step has expanded the definition for firmly believing reliability, its intension of theory is made to enumerate probability theory and uncertain theory.Firmly believing that reliability is fixed
Amount calculates aspect, and what Zeng proposed a kind of gear train that independent component based on minimal cut set is constituted firmly believes reliability calculating
Method.Zu proposes a kind of method for obtaining using principle of maximum entropy and firmly believing reliability distribution.Zhang is based on the general of performance bounds
Thought has obtained the calculation expression that different situations lower tooth wheel system firmly believes reliability.Firmly believe that reliability is more applicable for Practical Project
In reliability calculating, especially in the case where not a large amount of reliability datas or the very unobtainable feelings of reliability data
Under condition, gear train can be calculated based on experience firmly believes reliability, to carry out reliability design and optimization to product.
Summary of the invention
For above situation, the present invention provide it is a kind of based on the reliability of gears analysis method for firmly believing reliability, pass through by
The part design parameter and influence factor of gear are described as uncertain distribution to consider that cognition is uncertain, and quantitative calculates tooth
Reliability is firmly believed under face contact fatigue and tooth root flexural fatigue, while having carried out the sensitivity analysis of parameter, and will make sure that can
It recognizes probabilistic reliability with parameter is not considered by degree and is compared, illustrate cognition uncertainty to reliability of gears
It influences, it is significant to the raising of reliability of gears.
The present invention provides a kind of based on the reliability of gears analysis method for firmly believing reliability, comprising the following steps:
S1, failure mechanism model under different failure modes is established；
S2, the performance parameter p for determining gear train and performance parameter threshold values pth, performance margin model is obtained, according to performance
Allowance model judges that gear train failure type, the gear train failure type include hoping small failure and the big failure of prestige；
S3, judge performance parameter p and performance parameter threshold values pthThe distribution pattern of obedience, if performance parameter p and performance ginseng
Number threshold values pthAll it is uncertain variables, and obeys uncertain distribution Φ (x) and Ψ (x) respectively, then step S4 is carried out, if performance
Parameter p is stochastic variable and obedience probability distribution Φ (x), performance parameter threshold values pthIt is uncertain variables and obeys uncertain distribution
Ψ (x) thens follow the steps S5, if performance parameter p is uncertain variables and obeys uncertain distribution Φ (x), performance parameter valve
Value pthIt is stochastic variable and obeys probability distribution Ψ (x), thens follow the steps S6；
If S4, gear train are to hope small failure, the reliability of firmly believing of gear train isIf gear train is to hope big failure, the reliability of firmly believing of gear train isAnd execute step S7；
If S5, gear train are to hope small failure, the reliability of firmly believing of gear train is
If gear train is to hope big failure, the reliability of firmly believing of gear train isAnd execute step
S7；
If S6, gear train are to hope small failure, the reliability of firmly believing of gear train isSuch as
Fruit gear train is to hope big failure, then the reliability of firmly believing of gear train isAnd
S7, reliability expression is firmly believed according under different distributions type, calculate gear train firmly believes reliability.
Further, the gear train firmly believe reliability calculating the following steps are included:
S71, judge performance parameter p or performance parameter threshold values pthWhen obeying uncertain distribution by parameter influenced type,
If performance parameter p or performance parameter threshold value pthBy effect of multiple parameters, then step S72 is carried out, if performance parameter p or performance
Parameter threshold pthIt is influenced by one-parameter, thens follow the steps S73；
S72, judge performance parameter p or performance parameter threshold value pthWhether can be obtained using the algorithm in uncertain theory
The analytic solutions that must do not know distribution carry out step S73 if analytic solutions can be obtained, if analytic solutions cannot be obtained,
Execute step S74；
S73, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate the reliability of firmly believing of gear train, walk
Rapid execute terminates；
S74, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate gear train using numerical integration algorithm
Firmly believe reliability.
Further, the step S74 numerical integration algorithm the following steps are included:
S741, performance parameter p or performance parameter threshold value p is acquiredthInverse function expression formula；
S742, the discretization on section is carried out to independent variable, and obtains corresponding inverse function value；
S743, performance parameter p or performance parameter threshold values p is acquiredthProbability distribution express formula；And
S744, will be discrete after inverse function value bring into step S743 determine probability distribution expression formula in, can according to firmly believing
By spending expression formula, calculate gear train firmly believes reliability.
Preferably, the failure mode includes face fatigue and root contact fatigue.
Preferably, as performance parameter threshold values pthIt is constant and gear train is to hope small failure, firmly believing for gear train is reliable
Degree is RB=Φ (pth), if gear train is to hope big failure, gear train firmly believes that reliability is RB=1- Φ (pth)。
The present invention provide it is a kind of based on the reliability of gears analysis method for firmly believing reliability, by the way that the part of gear is designed
Parameter and influence factor are described as uncertain distribution to consider that cognition is uncertain, and quantitative calculates face fatigue and tooth
Reliability is firmly believed under root flexural fatigue, while having carried out the sensitivity analysis of parameter, and be will make sure that reliability and do not considered to join
Number recognizes probabilistic reliability and is compared, and illustrates the uncertain influence to reliability of gears of cognition, this is conducive to
Improve the reliability of gear.
Detailed description of the invention
Fig. 1 is the flow chart of reliability of gears analysis method of the present invention；
Fig. 2 is that the gear train of reliability of gears analysis method of the present invention firmly believes reliability calculating flow chart；
Fig. 3 is the numerical integration algorithm flow chart of reliability of gears analysis method of the present invention；
Fig. 4 is gear train reliability of the present invention with Z in contact stressHMean μ and standard deviation α situation of change signal
Figure；
Fig. 5 is gear train reliability of the present invention with K in contact stressAParameter a, b situation of change schematic diagram；
Fig. 6 is gear train reliability of the present invention with σ in contact fatigue strengthHLimMean μ and standard deviation α variation feelings
Condition schematic diagram；
Fig. 7 is gear train reliability of the present invention with K in Dedenda's bending stressAParameter a, b situation of change schematic diagram；
And
Fig. 8 is gear train reliability of the present invention with σ in tooth root bending allowable stressHLimMean μ and standard deviation α change
Change situation schematic diagram.
Specific embodiment
By the technology contents of the detailed present invention, structure feature, reach purpose and efficacy, below with reference to Figure of description
It is described in detail.
In the present invention, uncertain theory includes uncertainty measure, uncertain variables, uncertain distribution, uncertain operation method
It is then theoretical with chance.
Uncertainty measure of the invention: setting Γ is a nonempty set, and L is a α σ algebra on Γ, then the element in L
Λ is referred to as event, triple (Γ, L, M) is referred to as an Instable Space, uncertainty measure M is that one of L to [0,1] is full
It is enough the set function of lower four axioms:
Axiom 1: for complete or collected works Γ, there is M (Γ)=1；
Axiom 2: for any one occurrence Λ, there is M { Λ }+M { ΛC}=1；
Axiom 3: the sequence of events Λ denumerable for a column1,Λ2,Λ3..., have
A series of axiom 4: to Instable Space (Γk,Lk,Mk), k=1,2 ..., note product σ algebra is L=L1×L2
× ..., for any LkIn arbitrarily choose Λk, the product uncertainty measure M on product α σ algebra meets
Uncertain variables of the invention: setting ξ is the function that set of real numbers R is arrived from Instable Space (Γ, L, M), if
For arbitrary Borel set B, { ξ ∈ B }=γ ∈ Γ | ξ (γ) ∈ B } it is an event, then claiming ξ is one not true
Determine variable.
Uncertain distribution of the invention: uncertain distribution Φ's is defined as: Φ (x)=M { ξ≤x }, wherein ξ is indicated not true
Determine variable, x is any real number, two kinds of common uncertain distributions are as follows:
1, linear distribution ξ~L (a, b) is not known
2, normal distribution ξ~N (e, σ) is not known
Uncertain algorithm of the invention: ξ1,ξ2,…,ξnUncertain variables are independent from each other, and stringent clothes respectively
From the uncertain distribution Φ of canonical1,Φ2,…,Φn.If f is a strictly increasing function, ξ=f1(ξ1,ξ2,…,ξn)
In the presence of inverse uncertain distribution are as follows:
Chance of the invention is theoretical: chance theory can regard the cross theory of probability theory and uncertain theory as, it
Substantially estimate is to be intersected by probability measure and uncertainty measure and obtained, and can define uncertain random change on chance measure
Amount: if for any Borel set B, from probability space (Γ, L, M) arrive uncertain variables set M { ξ (w) ∈ B } about w
Function ξ be all it is measurable, then claiming ξ is a uncertain stochastic variable.
In the present invention, performance margin indicates the distance between performance parameter and performance parameter threshold value, in a gear train
In, the failure of performance bounds and gear train has close connection, defines the performance parameter that p is gear train, pthIt is to cause
Gear train can then be failed and be expressed as following two type by the performance parameter threshold value of gear train failure:
1, small failure STB is hoped: as p >=pthWhen, gear train failure；
2, big failure GTB is hoped: as p≤pthWhen, gear train failure；
Then performance margin indicates are as follows:It is defined according to gear train it can be seen that working as m≤0
When, gear train fails.
The present invention provide it is a kind of based on the reliability of gears analysis method for firmly believing reliability, as shown in Figure 1, include following step
It is rapid:
S1, failure mechanism model under different failure modes is established；
S2, the performance parameter p for determining gear train and performance parameter threshold values pth, performance margin model is obtained, according to performance
Allowance model judges that gear train failure type, gear train failure type include hoping small failure and the big failure of prestige；
S3, judge performance parameter p and performance parameter threshold values pthThe distribution pattern of obedience, if performance parameter p and performance ginseng
Number threshold values pthAll it is uncertain variables, and obeys uncertain distribution Φ (x) and Ψ (x) respectively, then step S4 is carried out, if performance
Parameter p is stochastic variable and obedience probability distribution Φ (x), performance parameter threshold values pthIt is uncertain variables and obeys uncertain distribution
Ψ (x) thens follow the steps S5, if performance parameter p is uncertain variables and obeys uncertain distribution Φ (x), performance parameter valve
Value pthIt is stochastic variable and obeys probability distribution Ψ (x), thens follow the steps S6；
If S4, gear train are to hope small failure, the reliability of firmly believing of gear train isIf gear train is to hope big failure, the reliability of firmly believing of gear train isAnd execute step S7；
If S5, gear train are to hope small failure, the reliability of firmly believing of gear train isIf gear train is to hope big failure, the reliability of firmly believing of gear train isAnd execute step S7；
If S6, gear train are to hope small failure, the reliability of firmly believing of gear train isSuch as
Fruit gear train is to hope big failure, then the reliability of firmly believing of gear train isAnd
S7, reliability expression is firmly believed according under different distributions type, calculate gear train firmly believes reliability.
As shown in Fig. 2, gear train firmly believe reliability calculating the following steps are included:
S71, judge performance parameter p or performance parameter threshold values pthWhen obeying uncertain distribution by parameter influenced type,
If performance parameter p or performance parameter threshold value pthBy effect of multiple parameters, then step S72 is carried out, if performance parameter p or performance
Parameter threshold pthIt is influenced by one-parameter, thens follow the steps S73；
S72, judge performance parameter p or performance parameter threshold value pthWhether can be obtained using the algorithm in uncertain theory
The analytic solutions that must do not know distribution carry out step S73 if analytic solutions can be obtained, if analytic solutions cannot be obtained,
Execute step S74；
S73, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate the reliability of firmly believing of gear train, walk
Rapid execute terminates；
S74, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate gear train using numerical integration algorithm
Firmly believe reliability.
As shown in figure 3, numerical integration algorithm the following steps are included:
S741, performance parameter p or performance parameter threshold value p is acquiredthInverse function expression formula；
S742, the discretization on section is carried out to independent variable, and obtains corresponding inverse function value；
S743, performance parameter p or performance parameter threshold values p is acquiredthProbability distribution express formula；And
S744, will be discrete after inverse function value bring into step S743 determine probability distribution expression formula in, can according to firmly believing
By spending expression formula, calculate gear train firmly believes reliability.
It is of the invention specific steps are as follows:
The present invention provides a kind of based on the reliability of gears analysis method for firmly believing reliability, comprising the following steps:
S1, failure mechanism model under different failure modes is established；
S2, the performance parameter p for determining gear train and performance parameter threshold values pth, performance margin model is obtained, according to performance
Allowance model judges that gear train failure type, gear train failure type include hoping small failure and the big failure of prestige；
S3, judge performance parameter p and performance parameter threshold values pthThe distribution pattern of obedience, if performance parameter p and performance ginseng
Number threshold values pthAll it is uncertain variables, and obeys uncertain distribution Φ (x) and Ψ (x) respectively, then step S4 is carried out, if performance
Parameter p is stochastic variable and obedience probability distribution Φ (x), performance parameter threshold values pthIt is uncertain variables and obeys uncertain distribution
Ψ (x) thens follow the steps S5, if performance parameter p is uncertain variables and obeys uncertain distribution Φ (x), performance parameter valve
Value pthIt is stochastic variable and obeys probability distribution Ψ (x), thens follow the steps S6；
If S4, gear train are to hope small failure, the reliability of firmly believing of gear train isIf gear train is to hope big failure, the reliability of firmly believing of gear train isAnd execute step S7；
If S5, gear train are to hope small failure, the reliability of firmly believing of gear train is
If gear train is to hope big failure, the reliability of firmly believing of gear train isAnd execute step
S7；
If S6, gear train are to hope small failure, the reliability of firmly believing of gear train isSuch as
Fruit gear train is to hope big failure, then the reliability of firmly believing of gear train isAnd
S7, reliability expression is firmly believed according under different distributions type, calculate gear train firmly believes reliability.
Specifically, gear train firmly believe reliability calculating the following steps are included:
S71, judge performance parameter p or performance parameter threshold values pthWhen obeying uncertain distribution by parameter influenced type,
If performance parameter p or performance parameter threshold value pthBy effect of multiple parameters, then step S72 is carried out, if performance parameter p or performance
Parameter threshold pthIt is influenced by one-parameter, thens follow the steps S73；
S72, judge performance parameter p or performance parameter threshold value pthWhether can be obtained using the algorithm in uncertain theory
The analytic solutions that must do not know distribution carry out step S73 if analytic solutions can be obtained, if analytic solutions cannot be obtained,
Execute step S74；
S73, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate the reliability of firmly believing of gear train, walk
Rapid execute terminates；
S74, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate gear train using numerical integration algorithm
Firmly believe reliability.
Specifically, when including multiple obedience probability distribution, i.e. p=f in performance parameter p1(ξ1,ξ2,…ξn), wherein ξ1,
ξ2,…ξnIt is independent uncertain variables and obeys the uncertain distribution Φ of canonical1,Φ2,…Φn, f1For strictly increasing function；Property
It can parameter threshold pthIn comprising it is multiple obey probability distribution parameters, i.e. pth=f2(ξ′1,ξ′2,…ξ′n), wherein ξ '1,ξ
′2,…ξ′nIt is independent stochastic variable and obeys different types of probability distribution Ψ1,Ψ2,…Ψn, while performance parameter p and property
It can parameter threshold pthThe analytic solutions of uncertain distribution cannot be obtained using the algorithm in uncertain theory, then numerical integration
Algorithm the following steps are included:
S741, the inverse function expression formula for acquiring performance parameter p:
S742, the discretization on section [0,1] is carried out to the α in above formula, and obtains corresponding inverse function value, inverse function
Value is the discrete value of y in integral expression；
S743, performance parameter threshold values p is acquiredth=f2(ξ′1,ξ′2,…ξ′n) probability distribution Ψ (y) expression formula；And
S744, by integral expressionIt is expressed asWherein Φ
(y) discrete value is above-mentioned α value, then will be discrete after y bring into obtain corresponding Ψ ' (y), finally with the method for numerical value product
Point.
In the present invention, failure mode includes face fatigue and root contact fatigue.
Face fatigue of the invention firmly believes that reliability calculating and Parameter sensitivity are analyzed as follows:
Gear Contact stress expression formula are as follows:
In formula, ZHIndicate that Area Node coefficient, calculation expression areWherein
αtIndicate end face pressure angle of graduated circle, βbIndicate Base spiral angle, α 'tIndicate the end face angle of engagement；KAIndicate coefficient of utilization；ZEIt indicates
Coefficient of elasticity；ZβIndicate spiral ascent；ZεIndicate Superposition degree modulus；KVIndicate dynamic load factor；KHβIndicate load distribution along width system
Number；KHαIndicate load share between teeth；U indicates gear ratio；d1Indicate pinion gear reference diameter；B indicates the facewidth；FtIt indicates
Nominal tangential force in end face on reference circle.
The contact fatigue strength expression formula of gear are as follows:
σHP=σHLimZNZLZRZX
In formula, σHLimIndicate the contact fatigue strength limit of experiment gear, it is assumed that Normal Distribution；ZNIndicate life factor；ZL
Indicate lubricating oil coefficient；ZXIndicate size factor；ZRIndicate roughness value.
The distribution or definite value that each parameter is obeyed by taking the gear parameter under specific operating condition as an example, in expression formula are as shown in the table:
For face fatigue, the performance parameter p of selection is Gear Contact stress σH, performance parameter threshold values PthFor gear
Contact fatigue strength σHP, Gear Contact stress σHGreater than the contact fatigue strength σ of gearHPWhen gear train fail, therefore tooth
Wheel system is to hope small failure, since performance parameter p at this time is by effect of multiple parameters, and the parsing of the uncertain distribution of performance parameter p
Solution can not obtain, and be calculated using the method for numerical integration, then gear train reliability result is as shown in the table:
| Distribution situation | Reliability RB |
| ZH~N (μ=2.5, σ=0.11), KA~L (0.9,1.1) | 0.8304 |
| ZH=2.5, KA~L (0.9,1.1) | 0.9171 |
| ZH~N (μ=2.5, σ=0.11), KA=1 | 0.8926 |
| ZH=2.5, KA=1 | 0.9389 |
As can be seen from the table: (1) only considering ZHIt is probabilistic to firmly believe that reliability is less than only consideration KAUncertainty is really
Believe reliability, illustrates contact fatigue lower gear reliability, parameter Z in contact stressHUncertain influence degree be greater than parameter KA
Uncertain influence degree；(2) when considering that the cognition in performance parameter p is uncertain, by ZHAnd KAIt is assumed to be 1 He of definite value
It is 0.9389 with the reliability result that Monte Carlo simulation is calculated when 1.25, it can greater than probabilistic firmly believe is considered
By spending calculated result, illustrate that gear train reliability can reduce to a certain extent when considering that cognition is uncertain.
The uncertainty of contact stress has node region coefficient ZHWith coefficient of utilization KATwo parameters determine, wherein ZHIt obeys
Uncertain normal distribution, KAIt obeys and does not know linear distribution, and contact fatigue strength Normal Distribution.
The parameter σ in contact fatigue strengthHLim~N (1035,562), contact stress KAThe feelings of parameter in~L (0.9,1.1)
Under condition, gear train reliability is with Z in contact stressHMean μ and standard deviation α situation of change, as shown in figure 4, contacting
Fatigue, Z in contact stressHMean μ reliability, which is affected, is firmly believed to gear train, change more obvious, and ZHStandard deviation
It is smaller that α firmly believes that reliability influences to gear train, and mean μ is when section (1,1.6) nearby changes, the variation of gear train reliability
Smaller, approximation shows linear change, and mean μ when after value 1.6, firmly believe that reliability changes greatly and show by gear train
Nonlinear change.
The Z in contact stressHIn the case where~N (μ=2.5, σ=0.11), gear train reliability is with K in contact stressA
Parameter a, b situation of change, as shown in figure 5, working as KAUncertainty distribution siding-to-siding block length when increasing, i.e. parameter uncertainty
When increase, gear train reliability is reduced, and when with the mean value of uncertain linear distribution close to 0.9, gear train is firmly believed reliably
Growth trend is presented in degree.
The parameter K in contact stressA~L (0.9,1.1), ZHIn the case where~N (μ=2.5, σ=0.11), gear train
Reliability is with σ in contact fatigue strengthHLimMean μ and standard deviation α situation of change, as shown in fig. 6, firmly believing reliability with connecing
The mean μ of touching intensity changes greatly, approximately linear, and standard deviation α is smaller to the influence for firmly believing reliability.
Tooth root flexural fatigue of the invention firmly believes that reliability calculating and Parameter sensitivity are analyzed as follows.
Dedenda's bending stress expression formula are as follows:
In formula, KFβIndicate the Longitudinal Load Distribution Factors of bending strength；KFαIndicate the load distribution among teeth system of bending strength
Number；mnIndicate normal module；YFαIndicate form factor；YSαIndicate tooth top Stress Correction Coefficient；YεIndicate Superposition degree modulus, YβTable
Show spiral ascent；KAIndicate coefficient of utilization；KVIndicate dynamic load factor；B indicates the facewidth；FtIndicate the name in end face on reference circle
Adopted tangential force.
Stress expression formula forever is permitted in tooth root bending are as follows:
σFP=σFLimYSTYNTYδrelTYX
In formula, σFLimIndicate the bending fatigue limit of gear, it is assumed that Normal Distribution；YSTIndicate Stress Correction Coefficient；
YNTIndicate life factor；YδrelTIt indicates relative to root fillet sensitivity coefficient；YXIndicate size factor.
The distribution or definite value that each parameter is obeyed by taking the gear parameter under specific operating condition as an example, in expression formula are as shown in the table:
For tooth root flexural fatigue, the performance parameter p of selection is Dedenda's bending stress σF, performance parameter threshold values PthFor tooth root
Stress σ forever is permitted in bendingFP, tooth bending stress σFPermitted stress σ forever greater than tooth root bendingFPWhen gear train fail, therefore gear train
System is to hope small failure, and since performance parameter p at this time is influenced by one-parameter, the uncertain distribution of performance parameter p can be solved directly
Out.
It firmly believes that reliability result is 0.9983 by gear train is calculated, does not consider cognition in performance parameter p not
Certainty, i.e., by KAWhen being assumed to be definite value 1, the reliability result being calculated with Monte Carlo simulation is 0.9990, greater than examining
Considered cognition it is probabilistic firmly believe reliability as a result, illustrate consider Gear System Parameters cognition uncertainty when, gear train
System reliability can reduce.
Dedenda's bending stress σFThere is coefficient of utilization KAIt determines, and KAUncertain linear distribution is obeyed, stress forever is permitted in tooth root bending
σFPNormal Distribution.
Gear train reliability is with K in Dedenda's bending stressAParameter a, b situation of change, as shown in fig. 7, working as tooth root
K in bending stressADistributed area length increase when, i.e., parameter uncertainty increase when, gear train reliability reduce, with
The mean value of uncertain linear distribution from 1.1 be changed to 0.9 when, gear train firmly believes that reliability is presented and first increases becoming of reducing afterwards
Gesture.
Gear train reliability is with σ in tooth root bending allowable stressHLimMean μ and standard deviation α situation of change, such as scheme
Shown in 8, tooth root is bent σ in allowable stressHLimMean μ reliability influence degree is similar to be firmly believed to gear train with standard deviation α,
The influence of mean μ is bigger.
The present invention provides a kind of based on the reliability of gears analysis method for firmly believing reliability, calculates gear on this basis
Gear train under contact fatigue and tooth root flexural fatigue firmly believes reliability, is as a result less than the gear considered when cognition is uncertain
System dependability, while as the result is shown for the gear train reliability under Gear Contact fatigue, contact stress interior joint region
Coefficient ZHUncertain influence degree be greater than coefficient of utilization KAUncertain influence degree, therefore in practical projects, to production
Product carry out that cognition probabilistic influence cannot be ignored when fail-safe analysis, and should consider coefficient of region Z emphaticallyHIt is uncertain
Property influence.
By the Parameter Sensitivity Analysis to Gear Contact fatigue and tooth root flexural fatigue, find to connect contact fatigue
Touch stress interior joint coefficient of region ZHMean μ reliability, which is affected, is firmly believed to gear train, and standard deviation α is to firmly believe can
Smaller, contact fatigue strength limit σ in contact strength is influenced by degreeHLimMean μ reliability, which is affected, is firmly believed to gear train,
And standard deviation α on firmly believe reliability influence it is smaller；For flexural fatigue, tooth root bending is permitted tooth root bending in stress forever and is permitted stress forever
σFLimMean value firmly believe that reliability influence is similar with standard deviation on gear train, either contact fatigue is still bent tired
Labor, when the uncertainty of parameter is bigger, gear train reliability just will receive bigger influence, and reliability is caused further to drop
It is low.
The present invention provide it is a kind of based on the reliability of gears analysis method for firmly believing reliability, by the way that the part of gear is designed
Parameter and influence factor are described as uncertain distribution to consider that cognition is uncertain, and quantitative calculates face fatigue and tooth
Reliability is firmly believed under root flexural fatigue, while having carried out the sensitivity analysis of parameter, and be will make sure that reliability and do not considered to join
Number recognizes probabilistic reliability and is compared, and illustrates the uncertain influence to reliability of gears of cognition, can to gear
Raising by property is of great significance.
The above is the preferred embodiment of the application, is not limited the scope of protection of the present invention with this, it is noted that right
For those skilled in the art, under the premise of not departing from this technology principle, can also make it is several improvement and
Retouching, these improvements and modifications also should be regarded as the protection scope of the application.
Claims (5)
1. a kind of based on the reliability of gears analysis method for firmly believing reliability, which comprises the following steps:
S1, failure mechanism model under different failure modes is established；
S2, the performance parameter p for determining gear train and performance parameter threshold values pth, performance margin model is obtained, according to performance margin
Model judges that gear train failure type, the gear train failure type include hoping small failure and the big failure of prestige；
S3, judge performance parameter p and performance parameter threshold values pthThe distribution pattern of obedience, if performance parameter p and performance parameter valve
Value pthAll it is uncertain variables, and obeys uncertain distribution Φ (x) and Ψ (x) respectively, then carries out step S4；If performance parameter
P is stochastic variable and obedience probability distribution Φ (x), performance parameter threshold values pthIt is uncertain variables and obeys uncertain distribution Ψ
(x), S5 is thened follow the steps, if performance parameter p is uncertain variables and obeys uncertain distribution Φ (x), performance parameter threshold values
pthIt is stochastic variable and obeys probability distribution Ψ (x), thens follow the steps S6；
If S4, gear train are to hope small failure, the reliability of firmly believing of gear train is
If gear train is to hope big failure, the reliability of firmly believing of gear train isAnd it executes
Step S7；
If S5, gear train are to hope small failure, the reliability of firmly believing of gear train isIf
Gear train is to hope big failure, then the reliability of firmly believing of gear train isAnd execute step S7；
If S6, gear train are to hope small failure, the reliability of firmly believing of gear train isIf tooth
Wheel system is to hope big failure, then the reliability of firmly believing of gear train isAnd
S7, reliability expression is firmly believed according under different distributions type, calculate gear train firmly believes reliability.
2. according to claim 1 based on the reliability of gears analysis method for firmly believing reliability, which is characterized in that the tooth
Wheel system firmly believe reliability calculating the following steps are included:
S71, judge performance parameter p or performance parameter threshold values pthWhen obeying uncertain distribution by parameter influenced type, if
Performance parameter p or performance parameter threshold value pthBy effect of multiple parameters, then step S72 is carried out, if performance parameter p or performance parameter
Threshold value pthIt is influenced by one-parameter, thens follow the steps S73；
S72, judge performance parameter p or performance parameter threshold value pthWhether can be obtained not using the algorithm in uncertain theory
It determines that the analytic solutions of distribution carry out step S73 if analytic solutions can be obtained, if analytic solutions cannot be obtained, executes
Step S74；
S73, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate the reliability of firmly believing of gear train, step is held
Row terminates；
S74, reliability expression is firmly believed according to what is determined in above-mentioned steps, calculate gear train really using numerical integration algorithm
Believe reliability.
3. according to claim 2 based on the reliability of gears analysis method for firmly believing reliability, which is characterized in that the step
Rapid S74 numerical integration algorithm the following steps are included:
S741, performance parameter p or performance parameter threshold value p is acquiredthInverse function expression formula；
S742, the discretization on section is carried out to independent variable, and obtains corresponding inverse function value；
S743, performance parameter p or performance parameter threshold values p is acquiredthProbability distribution express formula；And
S744, will be discrete after inverse function value bring into the probability distribution expression formula that step S743 is determined, according to firmly believing reliability
Expression formula, calculate gear train firmly believes reliability.
4. according to claim 2 based on the reliability of gears analysis method for firmly believing reliability, which is characterized in that the mistake
Effect mode includes face fatigue and root contact fatigue.
5. according to claim 2 based on the reliability of gears analysis method for firmly believing reliability, which is characterized in that work as performance
Parameter threshold pthIt is constant and gear train is to hope small failure, gear train firmly believes that reliability is RB=Φ (pth), if tooth
Wheel system is to hope big failure, then gear train firmly believes that reliability is RB=1- Φ (pth)。
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