CN107229800A - A kind of Optimization Design of roller line slideway auxiliary precision reliability - Google Patents

A kind of Optimization Design of roller line slideway auxiliary precision reliability Download PDF

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CN107229800A
CN107229800A CN201710422624.6A CN201710422624A CN107229800A CN 107229800 A CN107229800 A CN 107229800A CN 201710422624 A CN201710422624 A CN 201710422624A CN 107229800 A CN107229800 A CN 107229800A
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mrow
msub
mfrac
line slideway
slideway auxiliary
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CN107229800B (en
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王奇斌
马洪波
孔宪光
程涵
刘尧
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Xi'an Qigong Data Technology Co., Ltd
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Xidian Univ
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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/17Mechanical parametric or variational design
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00Details relating to CAD techniques
    • G06F2111/04Constraint-based CAD

Abstract

The present invention proposes a kind of Optimization Design of roller line slideway auxiliary precision reliability, it is intended to realizes the quantitative forecast to roller line slideway auxiliary precision reliability, and improves precision reliability.Realize that step is:Set up roller line slideway auxiliary accuracy loss model δV(S);Derive precision reliability limit state function δX(X);Set up precision reliability mathematical modeling RFM, average sensitivity model and variance sensitivity model;Choose stochastic variable xiWith stochastic variable xj;Set up the dimension constraint and Reliability Constraint of the sane Optimized model of multiple target;With stochastic variable xiAverage sensitivity minimum and stochastic variable xjThe minimum target of variance sensitivity, sets up the sane Optimized model F (x of roller line slideway auxiliary multiple targeti,xj);Optimizing is carried out to the sane Optimized model of roller line slideway auxiliary multiple target with most short ideal point method, stochastic variable x is obtainediWith stochastic variable xjOptimal solution.

Description

A kind of Optimization Design of roller line slideway auxiliary precision reliability
Technical field
The invention belongs to numerical control machine tool technique field, it is related to a kind of optimization design of roller line slideway auxiliary precision reliability Method, quantitative forecast and Optimal improvements available for roller line slideway auxiliary precision reliability.
Background technology
According to kinematic principle, so-called guide rail is exactly the device that moving link is tied to the only one of which free degree.This The individual free degree can be linear motion either gyration, and does the guide rail moved along a straight line and be referred to as line slideway.Roll straight Line guide rail is a kind of a kind of device for bearing to fix, guide movement and reduce its friction, for straight reciprocating motion occasion, is possessed The nominal load higher than linear bearing, while certain moment of torsion can be undertaken, high accuracy can be realized in high-load situations, this Linear motion.By design feature and frictional behavior, rolling linear guide includes rail plate, hydrostatic slideway and rolling guide again Deng.Wherein rolling linear guide is made up of guide rail, sliding block, rolling element and retainer etc., according to the difference of rolling element, is rolled Line slideway auxiliary includes roller line slideway auxiliary, needle roller linear guide rail pair and ball line slideway auxiliary again.Roller line slideway auxiliary Compared to ball line slideway auxiliary, its rigidity and bearing capacity are higher.Because roller line slideway auxiliary has positioning precision high, dynamic Confficient of static friction is small, the maintainable many merits such as good, and it has been widely used as the crucial of lathe and has been oriented to carrying field.
In recent years, lathe just constantly developed towards high speed, high-precision and long-life direction, and to roller line slideway The Performance And Reliability of this secondary key feature proposes higher requirement.Roller line slideway auxiliary reliability refers to guide rail It is secondary to complete in defined condition and in the time ability of predetermined function.Defined condition has installation shape of the guideway in equipment Formula, race and speed, load condition and working environment etc., the defined time be guideway running-in mileage in use or Person's running-in total time;Defined function refers to referring to linear rolling guide functional, precision, noise during running-in With vibration in tolerance interval, and occur without there is situations such as stuck, peeling and spot corrosion.In roller line slideway auxiliary During use, noise and vibration roller line slideway auxiliary is brought directly affect can also by roller line slideway auxiliary essence Retentivity is spent to embody.Precision is the important performance characteristic of roller line slideway auxiliary performance, and the height of precision directly affects lathe etc. The processing of equipment or running precision.The precision stability of roller line slideway auxiliary refers to roller line slideway auxiliary in the course of the work Keep the ability of original precision index.The low roller line slideway auxiliary of precision stability after a certain period of use time, guide rail, sliding block And deformation is come in contact between rolling element and is worn and torn, machine driving precision is influenceed, and then influence equipment operation or machining accuracy.Essence Degree reliability refers to that precision keeps stable probable value.So research and optimization to the precision reliability of roller line slideway auxiliary It is very necessary that design, which carries out further investigation,.
From the point of view of current disclosed data, the precision reliability optimization of the existing roller line slideway auxiliary of association area Research in terms of design method is more deficient, and some scholars obtain test data by ANSYS emulation, and apply corresponding reliability The method that theory is analyzed test data is studied the wear reliability of rail plate, but is due to that roller line is led The secondary structure secondary with rail plate of rail and abrasion mechanism are less identical, and this method considers inadequate to contact surface surface other factors Comprehensively, it is impossible to completely describe whole loss of significance process, the running-in only to the loss of significance starting stage weares and teares applicable, it is impossible to meet Lack the reliability consideration in the case of test data.And in the optimization design for roller line slideway auxiliary, be presently mainly It is excellent to roller line slideway auxiliary progress structure by analyzing experimental result by carrying out emulation experiment to roller line slideway auxiliary Change, so as to improve the rigidity of roller line slideway auxiliary.For example, the paper that Song Xianchun et al. is delivered at it " lead by high speed roller line Rail auxiliary structure optimization design and its performance test " (《Manufacturing technology and lathe》2015, (12):One kind is disclosed in 141-145) High speed roller line slideway auxiliary optimum structure design method, this method utilizes Multi-body Dynamics Theory combination numerical Analysis, By the kinematics simulation analysis to roller line slideway auxiliary, to roller in roller line slideway auxiliary, sliding block, integral structure layout and Its main structure parameters optimizes design, improves its force-bearing situation, improves its rigidity of structure.But this kind of method be not abundant Consider the dispersed and uncertainty of relevant parameter in actual condition, and roller line slideway auxiliary is as key function parts, The length that its precision stability is held time is vital for the reliability for improving Digit Control Machine Tool.
The content of the invention
It is an object of the invention to overcome the defect that above-mentioned prior art is present, there is provided a kind of roller line slideway auxiliary essence Spend the Optimization Design of reliability, it is intended to realize the quantitative forecast to roller line slideway auxiliary precision reliability, and improve rolling Post line slideway auxiliary precision reliability.
To achieve the above object, the technical scheme that the present invention takes comprises the following steps:
(1) roller line slideway auxiliary accuracy loss model δ is set upV(S):
(1.1) the elastic deformation amount δ of roller line slideway auxiliary is calculatedV1
(1.2) roller of roller line slideway auxiliary and the Wear prediction model δ in raceway contact face are set upV2(S);
(1.3) according to the elastic deformation amount δ of roller line slideway auxiliaryV1With the roller and raceway contact of roller line slideway auxiliary The Wear prediction model δ in faceV2(S) roller line slideway auxiliary accuracy loss model δ, is set upV(S);
(2) roller line slideway auxiliary precision reliability limit state function δ is derivedX(X):Utilize roller line slideway auxiliary Precision index U and roller line slideway auxiliary accuracy loss model δVDifference, calculate roller line slideway auxiliary precision reliability pole Limit function of state δX(X), δX(X)=U- δV(S), wherein, X represent basic random variables vector, can be from running parameter, material Chosen in parameter and geometric parameter;
(3) roller line slideway auxiliary precision reliability mathematical modeling R is set upFM
(3.1) by Taylor formula, to roller line slideway auxiliary precision reliability limit state function δX(X) deploy, Obtain precision reliability limit state function δX(X) retain to the Taylor expansions of quadratic term;
(3.2) average of each stochastic variable is substituted into precision reliability limit state function δ respectivelyX(X) Taylor exhibitions In open type, limit state function δ is obtainedX(X) equal value expression μg
(3.3) 2 Kronecker powers, 3 Kronecker of single order local derviation vector in Taylor expansions are calculated respectively Power and 4 Kronecker powers, while 2 Kronecker powers are multiplied with basic random variables vector X variance vectors, 3 times Kronecker powers and third moment multiplication of vectors, the vectorial phase of Fourth-order moment of 4 Kronecker powers and basic random variables vector X Multiply, obtain limit state function δX(X) variance expression formulaThird moment expression formula θgWith Fourth-order moment expression formula ηg
(3.4) by limit state function δX(X) equal value expression, variance expression formula, third moment expression formula and Fourth-order moment Expression formula substitutes into single failure mode formula of reliability based on HOMST, obtains reliability index expression formula βFM
(3.5) by reliability index expression formula βFMSubstitute into RFM=φ (βFM), obtain roller line slideway auxiliary precision reliability Mathematical modeling RFM
(4) by roller line slideway auxiliary precision reliability mathematical modeling RFMRespectively substitute into Fourth-order moment average sensitivity formula and Fourth-order moment variance sensitivity formula, obtains basic random variables vector X average sensitivity modelSubstantially with Machine variable vector X variance sensitivity model
(5) average and variance of the running parameter of roller line slideway auxiliary, material parameter and each stochastic variable are substituted into Average sensitivity model, the average sensitivity of each stochastic variable of each running-in location point of calculating roller line slideway auxiliary, is obtained To the average sensitivity curve of each stochastic variable, meanwhile, by the running parameter of roller line slideway auxiliary, material parameter and each random The average and variance of variable substitute into variance sensitivity model, calculate roller line slideway auxiliary each running-in location point it is each with The variance sensitivity of machine variable, obtains each variance of a random variable sensitivity curve;
(6) the random change corresponding to the farthest curve of deviation X-axis is chosen from the average sensitivity curve of each stochastic variable Measure xi, meanwhile, the stochastic variable deviateed corresponding to the farthest curve of X-axis is chosen from each variance of a random variable sensitivity curve xj
(7) stochastic variable x is chosen respectivelyiWith stochastic variable xjUpper and lower bound, obtain roller line slideway auxiliary multiple target The dimension constraint of sane Optimized model:
xi1≤xi≤xi2
xj1≤xj≤xj2
Wherein, xi1And xi2Respectively stochastic variable xiLower and upper limit, xj1And xj2Respectively stochastic variable xjLower limit And the upper limit;
(8) the target reliability degree R for giving task0Substitute into Reliability Constraint function FRg-1(R0)·σg, rolled The Reliability Constraint of the sane Optimized model of post line slideway auxiliary multiple target:
μg-1(R0)·σg≥0;
(9) with stochastic variable xiAverage on the influence of the reliability of roller line slideway auxiliary and with stochastic variable xjVariance Minimum target simultaneously is influenceed on the reliability of roller line slideway auxiliary, roller line slideway auxiliary multiple target is set up and steadily and surely optimizes mould Type F (xi,xj);
(10) stochastic variable x is calculated respectivelyiWith stochastic variable xjOptimal solution:
(10.1) in the range of dimension constraint and Reliability Constraint, using the optimizing algorithm of Non-Linear Programming, to roller The sane Optimized model F (x of line slideway auxiliary multiple targeti,xj) in each single-goal function carry out optimizing respectively, obtain two lists The corresponding ideal point of object functionWith
(10.2) two corresponding ideal points of single-goal function are judgedWithIt is whether identical, if so, then should Preferable point value is exactly stochastic variable xiWith stochastic variable xjOptimal solution, otherwise perform step (10.3);
(10.3) the sane Optimized model F (x of roller line slideway auxiliary multiple target are calculatedi,xj) and preferable point set Apart from mould, obtain evaluation function U (xi,xj):
(10.4) using the optimizing algorithm of Non-Linear Programming, to evaluation function U (xi,xj) optimizing is carried out, obtain the evaluation letter Number U (xi,xj) optimal solution obtain stochastic variable xiWith stochastic variable xjOptimal solution;
(11) average and variance of the running parameter of roller line slideway auxiliary, material parameter and each stochastic variable are substituted into Roller line slideway auxiliary precision reliability mathematical modeling, the precision of each running-in location point of calculating roller line slideway auxiliary is reliable Degree, obtains precision reliability curves;
(12) reliability curves, the stochastic variable x of roller line slideway auxiliary after optimization are obtainediAverage sensitivity curve with And variance sensitivity curve and stochastic variable xjAverage sensitivity curve and variance sensitivity curve:
(12.1) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xiOptimal solution, stochastic variable xjOptimal solution and other each stochastic variables average and variance, substitute into roller line slideway auxiliary Reliability Model, calculate rolling The precision reliability of each running-in location point of post line slideway auxiliary, the reliable of roller line slideway auxiliary is write music after being optimized Line;
(12.2) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xiOptimal solution, stochastic variable xjOptimal solution and other each stochastic variables average and variance substitute into average sensitivity model, roller line slideway is calculated respectively The stochastic variable x of each secondary running-in location pointiWith stochastic variable xjAverage sensitivity, roller line slideway after being optimized Secondary stochastic variable xiAverage sensitivity curve and stochastic variable xjAverage sensitivity curve;
(12.3) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xiOptimal solution, stochastic variable xjOptimal solution and other each stochastic variables average and variance substitute into variance sensitivity model, roller line slideway is calculated respectively The stochastic variable x of each secondary running-in location pointiWith stochastic variable xjVariance sensitivity, roller line slideway after being optimized Secondary stochastic variable xiVariance sensitivity curve and stochastic variable xjVariance sensitivity curve;
(13) by the reliability curves of roller line slideway auxiliary after optimization and the precision reliability curves of step (11), optimization The stochastic variable x of roller line slideway auxiliary afterwardsiAverage sensitivity curve and step (5) stochastic variable xiAverage sensitivity The stochastic variable x of roller line slideway auxiliary after curve, optimizationjAverage sensitivity curve and step (5) stochastic variable xjIt is equal It is worth the stochastic variable x of roller line slideway auxiliary after sensitivity curve, optimizationiVariance sensitivity curve and step (5) at random become Measure xiVariance sensitivity curve and optimization after roller line slideway auxiliary stochastic variable xjVariance sensitivity curve and step Suddenly (5) stochastic variable xjVariance sensitivity curve contrasted respectively, and judge optimization after roller line slideway auxiliary each song Whether line delays in correlation curve, if so, then completing the optimization design of roller line slideway auxiliary precision reliability, otherwise, uses Stochastic variable xiOptimal solution, respectively to stochastic variable xiUpper and lower bound is adjusted, while using stochastic variable xjIt is optimal Solution is respectively to stochastic variable xjUpper and lower bound be adjusted, and perform step (7)~step (13).
The present invention compared with prior art, has the following advantages that:
1st, the present invention is due to using roller line slideway auxiliary accuracy loss model δV(S), from two sides of elastic deformation and abrasion Face takes into full account the loss of significance process between roller line slideway auxiliary and track, and less with the hypothesis being related to, and as a result misses The less forth moment method of difference carries out fail-safe analysis to roller line slideway auxiliary loss of significance, establishes roller line slideway auxiliary essence Spend reliability mathematical modeling RFM, realize the quantitative forecast of roller line slideway auxiliary precision reliability.
2nd, the present invention takes into full account the uncertain factor of objective reality in roller line slideway auxiliary design, and reliability is set Meter is theoretical, Robust Optimal Design is theoretical and roller line slideway auxiliary accuracy loss model is combined, and establishes a kind of multiple target steady Strong Optimized model, thus can obtain meet the optimal solution of design requirement while, it is ensured that the reliability of the optimal solution and sane Property.
Brief description of the drawings
Fig. 1 is implementation process figure of the invention;
Fig. 2 is the roller line slideway auxiliary force analysis figure of the embodiment of the present invention;
Fig. 3 is increased with running-in mileage for each stochastic variable average sensitivity of roller line slideway auxiliary of the embodiment of the present invention Change curve;
Fig. 4 is increased with running-in mileage for each variance of random variable sensitivity of roller line slideway auxiliary of the embodiment of the present invention Change curve;
Fig. 5 is the roller line slideway auxiliary precision reliability R of the embodiment of the present inventionFMWith the increased change curve of running-in mileage Figure;
Fig. 6 is the roller line slideway auxiliary precision reliability R of the embodiment of the present inventionFMWith roller line slideway auxiliary essence after optimization Spend reliabilityContrast curve;
Fig. 7 is the roller line slideway auxiliary stochastic variable x of the embodiment of the present inventionαAverage sensitivity and optimization after roller it is straight The stochastic variable x of line guidewayαAverage Sensitivity comparison curve map;
Fig. 8 is the roller line slideway auxiliary stochastic variable x of the embodiment of the present inventionαVariance sensitivity and optimization after roller it is straight The stochastic variable x of line guidewayαVariance Sensitivity comparison curve map.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.
Reference picture 1, a kind of Optimization Design of roller line slideway auxiliary precision reliability, comprise the following steps:
Step 1, set up roller line slideway auxiliary accuracy loss model δV(S):Wanted when setting up guideway accuracy loss model From the aspect of elastic deformation and abrasion two, accuracy loss model δ is set upV(S) the step of, is as follows:
Step 1.1) calculate roller line slideway auxiliary elastic deformation amount δV1
Roller line slideway auxiliary is set by the used load F being carried in vertically downward on sliding block, what each roller was born Contact surface normal load is Qn, the angle of contact surface normal direction and vertical direction is α, and Z is the number that roller is often arranged on guide rail, Pretightning force F suffered by roller line slideway auxiliary0.Its stressing conditions is as shown in Figure 2.It can be obtained according to stress balance:
Using Palmgren empirical equations, normal direction contact load Q is considerednWith normal direction juxtaposition metamorphose δnContact and pre- Clamp force F0It is δ with initial deformation0Contact, calculates the elastic deformation amount δ for obtaining roller line slideway auxiliaryV1For:
Wherein, ν1And ν2The respectively Poisson's ratio of roller and raceway, E1And E2The respectively modulus of elasticity of roller and raceway;
Step 1.2) set up the roller of roller line slideway auxiliary and the Wear prediction model δ in raceway contact faceV2(S):According to Archard adhesive wears are theoretical, can obtain the volume wear W of rollerVCalculation formula:
Wherein, K is adhesive wear coefficient, and S is distance travelled, and H is the hardness of softer material, elastic creep rate
According to Hertz Elastic Contact Theories, the profile contacts area A of single-row roller can obtainpFor:
Wherein load W=Qn+F0/ 2Z=F/ (2Zcos α)+F0/ 2Z, R are roller radius;
So the roller of roller line slideway auxiliary and the Wear prediction model δ in raceway contact faceV2(S) it is:
Step 1.3) according to the elastic deformation amount δ of roller line slideway auxiliaryV1With the roller and raceway of roller line slideway auxiliary The Wear prediction model δ of contact surfaceV2(S) roller line slideway auxiliary accuracy loss model δ, is set upV(S):
Wherein, δV(S) it is total variation of the sliding block to guide rail bottom surface basis displacement deviation;
Step 2, derivation roller line slideway auxiliary precision reliability limit state function δX(X):Utilize roller line slideway Secondary precision index U and roller line slideway auxiliary accuracy loss model δVDifference, calculate roller line slideway auxiliary precision it is reliable Property limit state function δX(X), δX(X)=U- δV(S), wherein, X represents basic random variables vector, chooses plus load F, material Expect hardness H, roller diameter Da, roller effective diameter le, contact angle α and pretightning force F0.Because each stochastic variable obeys normal state Distribution, therefore the coefficient of skew of each stochastic variable is knowable to inspection information:CsX=(0,0,0,0,0,0)T, the kurtosis of each stochastic variable Coefficient is:CkX=(3,3,3,3,3,3)T
Step 3, set up roller line slideway auxiliary precision reliability mathematical modeling RFM
Step 3.1) by Taylor formula, to roller line slideway auxiliary precision reliability limit state function δX(X) open up Open, obtain precision reliability limit state function δX(X) retain to the Taylor expansions of quadratic term:
Step 3.2) average of each stochastic variable is substituted into precision reliability limit state function δ respectivelyX(X) Taylor In expansion, and each stochastic variable is relatively independent, obtains limit state function δX(X) equal value expression μg
Step 3.3) respectively calculate Taylor expansions in single order local derviation vector 2 Kronecker powers, 3 times Kronecker powers and 4 Kronecker powers, while by the variance vectors of 2 Kronecker powers and basic random variables vector X It is multiplied, 3 Kronecker powers and third moment multiplication of vectors, the Fourth-order moment of 4 Kronecker powers and basic random variables vector X Multiplication of vectors, obtains limit state function δX(X) variance expression formulaThird moment expression formula θgWith Fourth-order moment expression formula ηgPoint It is not:
Step 3.4) by limit state function δX(X) equal value expression, variance expression formula, third moment expression formula and quadravalence Square expression formula substitutes into single failure mode formula of reliability based on HOMST, obtains reliability index expression formula βFM, it is expressed Formula is:
Wherein, α3gFor the coefficient of skew expression formula of roller line slideway auxiliary precision reliability limit state function, it is expressed Formula isα4gFor the peak factor expression formula of roller line slideway auxiliary precision reliability limit state function, its table It is up to formulaβSMFor the Reliability Index of Second Moment of roller line slideway auxiliary precision reliability limit state function;
Step 3.5) by reliability index expression formula βFMSubstitute into RFM=φ (βFM), obtaining roller line slideway auxiliary precision can By degree mathematical modeling RFM
Step 4, by roller line slideway auxiliary precision reliability mathematical modeling RFMIt is public that the sensitivity of Fourth-order moment average is substituted into respectively Formula and Fourth-order moment variance sensitivity formula, Fourth-order moment average sensitivity formula and Fourth-order moment variance sensitivity formula, its expression formula Respectively:
Wherein,
Obtain basic random variables vector X average sensitivity modelWith basic random variables vector X's Variance sensitivity model
Step 5, the average sensitivity mould using computer application software MATLAB respectively to each basic random variables vector X TypeWith each basic random variables vector X variance sensitivity modelIt is programmed, and with shown in table 1 The major parameter of roller line slideway auxiliary calculated, can respectively obtain the embodiment of the present invention roller line slideway auxiliary it is each with The sensitivity of machine mean variable value with the increased change curve of running-in mileage and the roller line slideway auxiliary of the embodiment of the present invention it is each with Machine variable variance sensitivity is shown in accompanying drawing 3 and accompanying drawing 4 respectively with the increased change curve of running-in mileage:
The roller line slideway auxiliary guide rail major parameter table of table 1
Step 6, due to plus load F, pretightning force F0And material hardness H has uncertainty, therefore should be from stochastic variable Design parameter contact angle α, roller diameter DaWith effective length leMiddle selection need optimize stochastic variable.It is real from the present invention Each stochastic variable average sensitivity of roller line slideway auxiliary for applying example can be seen that with the increased change curve of running-in mileage Contact angle α average sensitivity increases with running-in mileage is increased to negative direction, i.e. essences of the contact angle α to roller line slideway auxiliary It is in negatively influencing to spend reliability, and influences increasing in motion process.And from the roller line slideway auxiliary of the embodiment of the present invention Each variance of random variable sensitivity is with the variance sensitivity that contact angle α is can be seen that in the increased change curve of running-in mileage It is increased to negative direction first increases and then decreases with running-in mileage, but contact angle α is in the precision reliability of roller line slideway auxiliary Negatively influencing, and be maximum in influence of the motion process compared with other stochastic variables, in summary, choose contact angle α and be used as needs The stochastic variable of optimization;
Step 7, selection stochastic variable xαUpper and lower bound, obtain the sane Optimized model of roller line slideway auxiliary multiple target Dimension constraint:
40≤xα≤50
Step 8, the target reliability degree R for giving task0=0.9 and running-in mileage S=618km substitutes into Reliability Constraint letter Number FRg-1(R0)·σg, obtain the Reliability Constraint of the sane Optimized model of roller line slideway auxiliary multiple target:
μg-1(0.9)·σg≥0;
Step 9, with stochastic variable xαAverage on the influence of the reliability of roller line slideway auxiliary and with stochastic variable xαSide Difference is on the reliability influence of roller line slideway auxiliary while minimum target, sets up roller line slideway auxiliary multiple target and steadily and surely optimize Model F (xα):
Step 10, calculating stochastic variable xαOptimal solution:
Step 10.1) in the range of dimension constraint and Reliability Constraint, it is utilized respectively in MATLAB Optimization Toolboxes Fmincon functions are solved, setting contact angle α initial value α0For 45, Optimized model F sane to roller line slideway auxiliary multiple target (xα) in each single-goal function carry out optimizing respectively, obtaining two corresponding ideal points of single-goal function is respectivelyWith
Step 10.2) due to two corresponding ideal points of single-goal functionWithDifference, then calculate roller line slideway The secondary sane Optimized model F (x of multiple targetα) and preferable point setApart from mould, obtain evaluation function U (xα):
Step 10.3) solved using the fmincon functions in MATLAB Optimization Toolboxes, to evaluation function U (xα) carry out Optimizing, obtains evaluation function U (xα) optimal solution obtain stochastic variable xαOptimal solution is 40.0034;
Step 11, using computer application software MATLAB to roller line slideway auxiliary precision reliability mathematical modeling RFMEnter Row programming, by the average and variance of the roller line slideway auxiliary major parameter of table 1, obtaining roller line slideway auxiliary kinematic accuracy can By degree RFMWith the increased change curve of running-in mileage, as shown in figure 5, the roller line slideway auxiliary of this example is in motion precision at initial stage Reliability is higher, and when running and mileage reaches 400km, precision reliability is begun to decline, when running and mileage reaches 800km, essence Degree reliability reaches 0.5;
Step 12, reliability curves, the stochastic variable x for obtaining roller line slideway auxiliary after optimizationαAverage sensitive write music Line and variance sensitivity curve:
Step 12.1) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xαOptimal solution other are each The average and variance of stochastic variable, substitute into the Reliability Model of roller line slideway auxiliary, using computer application software MATLAB, Calculate the precision reliability of each running-in location point of roller line slideway auxiliary, the precision of roller line slideway auxiliary after being optimized ReliabilityChange curve;
Step 12.2) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xαOptimal solution and other The average and variance of each stochastic variable substitute into average sensitivity model, and using computer application software MATLAB, rolling is calculated respectively The stochastic variable x of each running-in location point of post line slideway auxiliaryα, the stochastic variable x of roller line slideway auxiliary after being optimizedα Average sensitivity curve;
Step 12.3) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xαOptimal solution and other The average and variance of each stochastic variable substitute into variance sensitivity model, and using computer application software MATLAB, rolling is calculated respectively The stochastic variable x of each running-in location point of post line slideway auxiliaryα, the stochastic variable x of roller line slideway auxiliary after being optimizedα Variance sensitivity curve;
Shown in step 13, with reference to the accompanying drawings (6), by the reliability curves of roller line slideway auxiliary after optimization and step (11) Precision reliability curves are contrasted, it is found that the reliability curves of roller line slideway auxiliary after optimization decline and be substantially later than step (11) precision reliability curves, trend is more relaxed, and the precision reliability of identical running-in fare register is obviously improved;According to attached Scheme shown in (7), by the stochastic variable x of roller line slideway auxiliaryαAverage sensitivity curve and step (5) stochastic variable xα's Average sensitivity curve is contrasted, and finds the stochastic variable x of roller line slideway auxiliary after optimizationαAverage sensitivity curve under Drop is substantially later than the stochastic variable x of step (5)αAverage sensitivity curve, and trend more relaxes, contact angle α negatively influencing Reduce so that roller line slideway auxiliary precision reliability is not easy to failure;With reference to the accompanying drawings shown in (8), by roller line after optimization The stochastic variable x of guidewayαVariance sensitivity curve and step (5) stochastic variable xαVariance sensitivity curve contrasted, The stochastic variable x of roller line slideway auxiliary after optimizationαVariance sensitivity curve begin to decline and be substantially later than the random of step (5) Variable xαVariance sensitivity curve, and trend more relaxes, and contact angle α negatively influencing reduces so that roller line slideway auxiliary Precision reliability is not easy to failure.Stochastic variable xαOptimal solution can effectively improve precision reliability, reduction contact angle α's is equal It is worth sensitivity and variance sensitivity, completes the optimization design of roller line slideway auxiliary.

Claims (7)

1. a kind of Optimization Design of roller line slideway auxiliary precision reliability, it is characterised in that comprise the following steps:
(1) roller line slideway auxiliary accuracy loss model δ is set upV(S):
(1.1) the elastic deformation amount δ of roller line slideway auxiliary is calculatedV1
(1.2) roller of roller line slideway auxiliary and the Wear prediction model δ in raceway contact face are set upV2(S);
(1.3) according to the elastic deformation amount δ of roller line slideway auxiliaryV1Roller and raceway contact face with roller line slideway auxiliary Wear prediction model δV2(S) roller line slideway auxiliary accuracy loss model δ, is set upV(S);
(2) roller line slideway auxiliary precision reliability limit state function δ is derivedX(X):Utilize the precision of roller line slideway auxiliary Index U and roller line slideway auxiliary accuracy loss model δVDifference, calculate roller line slideway auxiliary precision reliability limit shape State function δX(X), δX(X)=U- δV(S), wherein, X represent basic random variables vector, can be from running parameter, material parameter Chosen with geometric parameter;
(3) roller line slideway auxiliary precision reliability mathematical modeling R is set upFM
(3.1) by Taylor formula, to roller line slideway auxiliary precision reliability limit state function δX(X) deploy, obtain essence Spend limit of reliability function of state δX(X) retain to the Taylor expansions of quadratic term;
(3.2) average of each stochastic variable is substituted into precision reliability limit state function δ respectivelyX(X) Taylor expansions In, obtain limit state function δX(X) equal value expression μg
(3.3) 2 Kronecker powers, the 3 Kronecker powers and 4 of single order local derviation vector in Taylor expansions are calculated respectively Secondary Kronecker powers, while 2 Kronecker powers are multiplied with basic random variables vector X variance vectors, 3 times Kronecker powers and third moment multiplication of vectors, the vectorial phase of Fourth-order moment of 4 Kronecker powers and basic random variables vector X Multiply, obtain limit state function δX(X) variance expression formulaThird moment expression formula θgWith Fourth-order moment expression formula ηg
(3.4) by limit state function δX(X) equal value expression, variance expression formula, third moment expression formula and Fourth-order moment expression formula Single failure mode formula of reliability based on HOMST is substituted into, reliability index expression formula β is obtainedFM
(3.5) by reliability index expression formula βFMSubstitute into RFM=φ (βFM), obtain roller line slideway auxiliary precision reliability mathematics Model RFM
(4) by roller line slideway auxiliary precision reliability mathematical modeling RFMFourth-order moment average sensitivity formula and quadravalence are substituted into respectively Square variance sensitivity formula, obtains basic random variables vector X average sensitivity modelBecome with essentially random Measure vector X variance sensitivity model
(5) average and variance of the running parameter of roller line slideway auxiliary, material parameter and each stochastic variable are substituted into average Sensitivity model, the average sensitivity of each stochastic variable of each running-in location point of calculating roller line slideway auxiliary obtains each The average sensitivity curve of stochastic variable, meanwhile, by the running parameter of roller line slideway auxiliary, material parameter and each stochastic variable Average and variance substitute into variance sensitivity model, calculate each of roller line slideway auxiliary each running-in location point and random become The variance sensitivity of amount, obtains each variance of a random variable sensitivity curve;
(6) the stochastic variable x corresponding to the farthest curve of deviation X-axis is chosen from the average sensitivity curve of each stochastic variablei, Meanwhile, the stochastic variable x deviateed corresponding to the farthest curve of X-axis is chosen from each variance of a random variable sensitivity curvej
(7) stochastic variable x is chosen respectivelyiWith stochastic variable xjUpper and lower bound, obtain roller line slideway auxiliary multiple target sane The dimension constraint of Optimized model:
xi1≤xi≤xi2
xj1≤xj≤xj2
Wherein, xi1And xi2Respectively stochastic variable xiLower and upper limit, xj1And xj2Respectively stochastic variable xjLower limit and upper Limit;
(8) the target reliability degree R for giving task0Substitute into Reliability Constraint function FRg-1(R0)·σg, obtain roller straight The Reliability Constraint of the sane Optimized model of line guideway multiple target:
μg-1(R0)·σg≥0;
(9) with stochastic variable xiAverage on the influence of the reliability of roller line slideway auxiliary and with stochastic variable xjVariance to rolling The reliability influence of post line slideway auxiliary is while minimum target, sets up the sane Optimized model F of roller line slideway auxiliary multiple target (xi,xj);
(10) stochastic variable x is calculated respectivelyiWith stochastic variable xjOptimal solution:
(10.1) in the range of dimension constraint and Reliability Constraint, using the optimizing algorithm of Non-Linear Programming, to roller line The sane Optimized model F (x of guideway multiple targeti,xj) in each single-goal function carry out optimizing respectively, obtain two single goals The corresponding ideal point of functionWith
(10.2) two corresponding ideal points of single-goal function are judgedWithIt is whether identical, if so, the then ideal Point value is exactly stochastic variable xiWith stochastic variable xjOptimal solution, otherwise perform step (10.3);
(10.3) the sane Optimized model F (x of roller line slideway auxiliary multiple target are calculatedi,xj) and preferable point setAway from From mould, evaluation function U (x are obtainedi,xj):
(10.4) using the optimizing algorithm of Non-Linear Programming, to evaluation function U (xi,xj) optimizing is carried out, obtain evaluation function U (xi,xj) optimal solution obtain stochastic variable xiWith stochastic variable xjOptimal solution;
(11) average and variance of the running parameter of roller line slideway auxiliary, material parameter and each stochastic variable are substituted into roller Line slideway auxiliary precision reliability mathematical modeling, calculates the precision reliability of each running-in location point of roller line slideway auxiliary, Obtain precision reliability curves;
(12) reliability curves, the stochastic variable x of roller line slideway auxiliary after optimization are obtainediAverage sensitivity curve and side Poor sensitivity curve and stochastic variable xjAverage sensitivity curve and variance sensitivity curve:
(12.1) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xiOptimal solution, stochastic variable xj's The average and variance of optimal solution and other each stochastic variables, substitute into the Reliability Model of roller line slideway auxiliary, calculate roller straight The precision reliability of each running-in location point of line guideway, the reliability curves of roller line slideway auxiliary after being optimized;
(12.2) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xiOptimal solution, stochastic variable xj's The average and variance of optimal solution and other each stochastic variables substitute into average sensitivity model, roller line slideway auxiliary are calculated respectively every The stochastic variable x of one running-in location pointiWith stochastic variable xjAverage sensitivity, roller line slideway auxiliary after being optimized Stochastic variable xiAverage sensitivity curve and stochastic variable xjAverage sensitivity curve;
(12.3) by the running parameter of roller line slideway auxiliary, material parameter, stochastic variable xiOptimal solution, stochastic variable xj's The average and variance of optimal solution and other each stochastic variables substitute into variance sensitivity model, roller line slideway auxiliary are calculated respectively every The stochastic variable x of one running-in location pointiWith stochastic variable xjVariance sensitivity, roller line slideway auxiliary after being optimized Stochastic variable xiVariance sensitivity curve and stochastic variable xjVariance sensitivity curve;
(13) it will be rolled after the reliability curves of roller line slideway auxiliary after optimization and the precision reliability curves of step (11), optimization The stochastic variable x of post line slideway auxiliaryiAverage sensitivity curve and step (5) stochastic variable xiAverage sensitivity curve, The stochastic variable x of roller line slideway auxiliary after optimizationjAverage sensitivity curve and step (5) stochastic variable xjAverage spirit The stochastic variable x of roller line slideway auxiliary after acuity curve, optimizationiVariance sensitivity curve and step (5) stochastic variable xi's The stochastic variable x of roller line slideway auxiliary after variance sensitivity curve and optimizationjVariance sensitivity curve and step (5) Stochastic variable xjVariance sensitivity curve contrasted respectively, and judge optimization after roller line slideway auxiliary each curve whether Delay in correlation curve, if so, the optimization design of roller line slideway auxiliary precision reliability is then completed, otherwise, using random change Measure xiOptimal solution, respectively to stochastic variable xiUpper and lower bound is adjusted, while using stochastic variable xjOptimal solution difference To stochastic variable xjUpper and lower bound be adjusted, and perform step (7)~step (13).
2. a kind of Optimization Design of roller line slideway auxiliary precision reliability according to claim 1, its feature exists In, the roller line slideway auxiliary precision reliability limit state function described in step (2), its expression formula is:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;delta;</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>U</mi> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>U</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>V</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>V</mi> <mn>2</mn> </mrow> </msub> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> <mo>)</mo> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>U</mi> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.36</mn> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>v</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>E</mi> <mn>1</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>v</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>E</mi> <mn>2</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mn>0.9</mn> </msup> <mo>(</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mi>F</mi> <mrow> <mn>2</mn> <mi>Z</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>0.9</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>F</mi> <mn>0</mn> </msub> <mrow> <mn>2</mn> <mi>Z</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>0.9</mn> </msup> </mrow> <msubsup> <mi>l</mi> <mi>e</mi> <mn>0.8</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;delta;</mi> <mrow> <mi>V</mi> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>D</mi> <mi>a</mi> </msub> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mrow> <mi>V</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>K</mi> <mi>S</mi> </mrow> <mrow> <mn>12</mn> <mi>H</mi> <mi>Z</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;pi;</mi> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>v</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>E</mi> <mn>1</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>v</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>E</mi> <mn>2</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mn>0.9</mn> </msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>F</mi> <mn>0</mn> </msub> <mrow> <mn>2</mn> <mi>Z</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mi>F</mi> <mrow> <mn>2</mn> <mi>Z</mi> <mi> </mi> <mi>cos</mi> <mi>&amp;alpha;</mi> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>D</mi> <mi>a</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mi>e</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, ν1And ν2The respectively Poisson's ratio of roller and raceway, E1And E2Respectively the modulus of elasticity of roller and raceway, F are outer Lotus is loaded, Z is carrying roller number, and K is adhesive wear coefficient, and S is running-in mileage and H is material hardness.
3. a kind of Optimization Design of roller line slideway auxiliary precision reliability according to claim 1, its feature exists In precision reliability limit state function δ described in step (3.1)X(X) retain to quadratic term Taylor expansions, specifically For:
<mrow> <msub> <mi>T</mi> <msub> <mi>&amp;delta;</mi> <mi>X</mi> </msub> </msub> <mo>=</mo> <msub> <mi>&amp;delta;</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mi>X</mi> </msub> <mo>)</mo> </mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;delta;</mi> <mi>X</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>X</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mi>X</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>&amp;delta;</mi> <mi>X</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>X</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msub> <mi>&amp;mu;</mi> <mi>X</mi> </msub> <mo>)</mo> </mrow> </mrow>
Wherein, μXFor the average of each stochastic variable,It is vectorial for single order local derviation in Taylor expansions,For Taylor exhibitions Second Order Partial derived vector in open type.
4. the Optimization Design of roller line slideway auxiliary precision reliability according to claim 1, it is characterised in that step Suddenly single failure mode formula of reliability based on HOMST described in (3.4), its expression formula is:
<mrow> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mo>(</mo> <mn>9</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>5</mn> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>9</mn> <mo>)</mo> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msqrt> </mfrac> </mrow>
Wherein, α3gFor the coefficient of skew expression formula of roller line slideway auxiliary precision reliability limit state function, its expression formula isα4gFor the peak factor expression formula of roller line slideway auxiliary precision reliability limit state function, its expression formula ForβSMFor the Reliability Index of Second Moment of roller line slideway auxiliary precision reliability limit state function.
5. the Optimization Design of roller line slideway auxiliary precision reliability according to claim 1, it is characterised in that step Suddenly Fourth-order moment average sensitivity formula described in (4) and Fourth-order moment variance sensitivity formula, its expression formula is respectively:
<mrow> <mfrac> <mrow> <msub> <mi>dR</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <msup> <mover> <mi>X</mi> <mo>&amp;OverBar;</mo> </mover> <mi>T</mi> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;mu;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;mu;</mi> <mi>g</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mover> <mi>X</mi> <mo>&amp;OverBar;</mo> </mover> <mi>T</mi> </msup> </mrow> </mfrac> </mrow>
<mrow> <mfrac> <mrow> <msub> <mi>dR</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
Wherein,
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mo>(</mo> <mn>9</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>5</mn> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>9</mn> <mo>)</mo> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msqrt> </mfrac> </mrow>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>F</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>12</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mfrac> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <msqrt> <mrow> <mo>(</mo> <mn>9</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>5</mn> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>9</mn> <mo>)</mo> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>&amp;lsqb;</mo> <mn>3</mn> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;CenterDot;</mo> </mrow>
<mfrac> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <mn>36</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>30</mn> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> <mn>2</mn> </msubsup> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>5</mn> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>9</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>4</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> </mrow> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mfrac> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>2</mn> <msqrt> <mrow> <mo>(</mo> <mn>9</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>5</mn> <msubsup> <mi>&amp;alpha;</mi> <mrow> <mn>3</mn> <mi>g</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mn>9</mn> <mo>)</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mn>4</mn> <mi>g</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </msqrt> </mrow> </mfrac>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>X</mi> </mrow> </mfrac> <mo>&amp;CircleTimes;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mrow> <mo>&amp;part;</mo> <mi>X</mi> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>S</mi> <mi>M</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;sigma;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>&amp;mu;</mi> <mi>g</mi> </msub> <msubsup> <mi>&amp;sigma;</mi> <mi>g</mi> <mn>2</mn> </msubsup> </mfrac> <mo>.</mo> </mrow>
6. the Optimization Design of roller line slideway auxiliary precision reliability according to claim 1, it is characterised in that step Suddenly the sane Optimized model F (x of roller line slideway auxiliary multiple target are set up described in (9)i,xj), its establishment step is:
(9.1) according to stochastic variable xiAverage sensitivity model, set up stochastic variable xiAverage to roller line slideway auxiliary Reliability influence object function f1(xi):
<mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>R</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>|</mo> <mo>;</mo> </mrow>
(9.2) according to stochastic variable xjVariance sensitivity model, set up stochastic variable xjVariance to roller line slideway auxiliary Reliability influence object function f2(xj):
<mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>R</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> </mrow>
(9.3) with stochastic variable xiAverage object function f is influenceed on the reliability of roller line slideway auxiliary1(xi) and random change Measure xjVariance object function f is influenceed on the reliability of roller line slideway auxiliary2(xj) while minimum target, sets up roller straight The sane Optimized model F (x of line guideway multiple targeti,xj):
<mrow> <mi>min</mi> <mi> </mi> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>R</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msub> </mrow> </mfrac> <mo>|</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>R</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>.</mo> </mrow>
7. the Optimization Design of roller line slideway auxiliary precision reliability according to claim 1, it is characterised in that step Suddenly evaluation function U (x described in (10.3)i,xj), its expression formula is:
<mrow> <mi>U</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>F</mi> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> <mo>-</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <mrow> <mi>j</mi> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> <mo>-</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>(</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> <mo>*</mo> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <mrow> <mi>j</mi> <mn>2</mn> </mrow> <mo>*</mo> </msubsup> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
WhereinFor the sane Optimized model F (x of roller line slideway auxiliary multiple targeti,xj) and preferable point set Close
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