CN107229800B - A kind of optimum design method of roller line slideway auxiliary precision reliability - Google Patents
A kind of optimum design method of roller line slideway auxiliary precision reliability Download PDFInfo
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Abstract
The invention proposes a kind of optimum design methods of roller line slideway auxiliary precision reliability, it is intended to realize the quantitative forecast to roller line slideway auxiliary precision reliability, and improve precision reliability.Realize step are as follows: establish roller line slideway auxiliary accuracy loss model δV(S)；Derive precision reliability limit state function δX(X)；Establish precision reliability mathematical model RFM, mean value sensitivity model and variance sensitivity model；Choose stochastic variable xiWith stochastic variable xj；Establish the dimension constraint and Reliability Constraint of the steady Optimized model of multiple target；With stochastic variable xiMean value sensitivity minimum and stochastic variable xjThe minimum target of variance sensitivity establishes the steady Optimized model F (x of roller line slideway auxiliary multiple targeti,xj)；Optimizing is carried out to the steady Optimized model of roller line slideway auxiliary multiple target with most short ideal point method, obtains stochastic variable xiWith stochastic variable xjOptimal solution.
Description
Technical Field
The invention belongs to the technical field of numerical control machines, and relates to an optimization design method for precision reliability of a roller linear guide rail pair, which can be used for quantitative prediction and optimization improvement of the precision reliability of the roller linear guide rail pair.
Background
According to the kinematic principle, the guide rail is a device for constraining a moving member to only one degree of freedom. The degree of freedom may be linear or rotational, and the guide rail that moves linearly is referred to as a linear guide rail. The rolling linear guide rail is a device for bearing, fixing, guiding and moving and reducing friction thereof, is used in the linear reciprocating motion occasion, has higher rated load than a linear bearing, can bear certain torque, and can realize high-precision linear motion under the condition of high load. According to the structural characteristics and the friction characteristics, the rolling linear guide rail comprises a sliding guide rail, a static pressure guide rail, a rolling guide rail and the like. The rolling linear guide rail pair comprises a roller linear guide rail pair, a roller pin linear guide rail pair and a ball linear guide rail pair according to the difference of the rolling bodies. Compared with a ball linear guide rail pair, the roller linear guide rail pair has higher rigidity and bearing capacity. The roller linear guide rail pair has the advantages of high positioning precision, small dynamic and static friction coefficient, good maintainability and the like, and is widely used in the key guide bearing field of machine tools.
In recent years, machine tools are continuously developing towards high speed, high precision and long service life, and higher requirements are put on the performance and reliability of a key functional component of the roller linear guide rail pair. The reliability of the roller linear guide rail pair refers to the capability of the guide rail pair to complete a specified function under specified conditions and within specified time. The specified conditions comprise the installation form, running and speed, loading condition, working environment and the like of the guide rail pair on the equipment, and the specified time is the running-in mileage or the total running-in time of the guide rail pair in the using process; the specified function means that the finger rolling linear guide rail pair has good performance in the running-in process, the precision, the noise and the vibration are within an acceptable range, and the situations of blocking, peeling, pitting and the like do not occur. In the use process of the roller linear guide rail pair, the direct influence of noise and vibration on the roller linear guide rail pair can also be reflected by the precision maintenance performance of the roller linear guide rail pair. The precision is an important performance parameter of the roller linear guide rail pair, and the machining or running precision of equipment such as a machine tool is directly influenced by the precision. The precision retentivity of the roller linear guide rail pair refers to the capability of the roller linear guide rail pair for maintaining the original precision index in the working process. After the roller linear guide rail pair with low precision retentivity is used for a certain time, contact deformation and abrasion occur among the guide rail, the sliding block and the rolling body, the mechanical transmission precision is influenced, and further the equipment operation or processing precision is influenced. Accuracy reliability refers to the probability value that accuracy remains stable. Therefore, it is necessary to deeply study the precision reliability and the optimized design of the roller linear guide rail pair.
From the present published data, the research on the precision reliability optimization design method of the existing roller linear guide rail pair in the related field is deficient, some scholars obtain test data through ANSYS simulation and research the wear reliability of the sliding guide rail by applying a method for analyzing the test data by using a corresponding reliability theory, but the structures and wear mechanisms of the roller linear guide rail pair and the sliding guide rail pair are not very same, and the method is not comprehensive enough to consider other factors on the surface of a contact surface, cannot completely describe the whole precision loss process, is only suitable for running-in wear at the initial stage of precision loss, and cannot meet the reliability research under the condition of lacking of the test data. In the optimization design of the roller linear guide rail pair, at present, a simulation experiment is mainly carried out on the roller linear guide rail pair, and the structure of the roller linear guide rail pair is optimized by analyzing an experiment result, so that the rigidity of the roller linear guide rail pair is improved. For example, Song-Shi-Chun et al in its published paper "high-speed roller linear guide pair structure optimization design and its performance test" ("manufacturing technology and machine tool" (2015, (12): 141-145)) disclose a high-speed roller linear guide pair structure optimization design method, which utilizes multi-body dynamics theory in combination with numerical calculation analysis, and through motion simulation analysis of the roller linear guide pair, optimizes the roller, slider, overall structure layout and its main structural parameters in the roller linear guide pair, improves its stress condition, and increases its structural rigidity. However, the method does not fully consider the dispersion and uncertainty of relevant parameters in actual working conditions, and the roller linear guide rail pair is used as a key functional part, so that the length of the precision retentivity maintaining time is crucial to the improvement of the reliability of the numerical control machine tool.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an optimal design method for precision reliability of a roller linear guide rail pair, which aims to realize quantitative prediction of the precision reliability of the roller linear guide rail pair and improve the precision reliability of the roller linear guide rail pair.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) establishing precision loss model delta of roller linear guide rail pairV(S)：
(1.1) calculating the elastic deformation delta of the roller linear guide pairV1；
(1.2) establishing a wear prediction model delta of the roller and raceway contact surface of the roller linear guide rail pairV2(S)；
(1.3) according to the elastic deformation delta of the roller linear guide pairV1And a roller and raceway contact surface wear prediction model delta of the roller linear guide rail pairV2(S) establishing a precision loss model delta of the roller linear guide rail pairV(S)；
(2) Deducing precision reliability limit state function delta of roller linear guide pairX(X): precision index U of roller linear guide rail pair and precision loss model delta of roller linear guide rail pairVCalculating the accuracy reliability limit state function delta of the roller linear guide pairX(X)，δX(X)＝U-δV(S), wherein X represents a basic random variable vector, which can be selected from working parameters, material parameters and geometric parameters;
(3) establishing a roller linear guide pair precision reliability mathematical model RFM：
(3.1) performing precision reliability limit state function delta on the roller linear guide rail pair through a Taylor formulaX(X) expanding to obtain a precision reliability limit state function deltaX(X) Taylor expansion retained to quadratic term;
(3.2) substituting the mean values of the random variables into the extreme state function delta of the accuracy and reliabilityX(X) the Taylor expansion of the (X) to obtain the limit state function deltaXMean expression of (X) < mu >g；
(3.3) respectively calculating 2 times of Kronecker power, 3 times of Kronecker power and 4 times of Kronecker power of a first-order partial derivative vector in the Taylor expansion formula, simultaneously multiplying the 2 times of Kronecker power with a variance vector of a basic random variable vector X, multiplying the 3 times of Kronecker power with a third-order moment vector, multiplying the 4 times of Kronecker power with a fourth-order moment vector of the basic random variable vector X to obtain a limit state function deltaX(X) expression of varianceThird moment expression thetagAnd fourth order moment expression ηg；
(3.4) applying a limit state function deltaXSubstituting the mean expression, the variance expression, the third moment expression and the fourth moment expression of (X) into a single failure mode reliability calculation formula based on HOST to obtain a reliability index expression betaFM；
(3.5) expressing the reliability index by the expression betaFMSubstitution into RFM＝φ(βFM) To obtain a roller linear guide pair precision reliability mathematical model RFM；
(4) Mathematical model R for precision reliability of roller linear guide rail pairFMRespectively substituting into the fourth moment mean value sensitivity formula and the fourth moment variance sensitivity formula to obtain a mean value sensitivity model of the basic random variable vector XVariance sensitivity model of sum basic random variable vector X
(5) Substituting the working parameters, the material parameters and the mean and variance of all the random variables of the roller linear guide rail pair into a mean sensitivity model, calculating the mean sensitivity of all the random variables of each running-in position point of the roller linear guide rail pair to obtain a mean sensitivity curve of all the random variables, simultaneously substituting the working parameters, the material parameters and the mean and variance of all the random variables of the roller linear guide rail pair into a variance sensitivity model, calculating the variance sensitivity of all the random variables of each running-in position point of the roller linear guide rail pair to obtain a variance sensitivity curve of all the random variables;
(6) selecting the random variable X corresponding to the curve farthest from the X axis from the mean sensitivity curves of the random variablesiAt the same time, the random variable X corresponding to the curve farthest from the X axis is selected from the variance sensitivity curves of the random variablesj；
(7) Respectively selecting random variables xiAnd a random variable xjThe upper limit and the lower limit of the linear roller guide rail pair are obtained, and the size constraint of the multi-objective robust optimization model is obtained:
xi1≤xi≤xi2
xj1≤xj≤xj2
wherein x isi1And xi2Are respectively random variables xiLower and upper limits of (2), xj1And xj2Are respectively random variables xjLower and upper limits of (d);
(8) target reliability R given to task0Substituting a reliability constraint function FR＝μg-φ-1(R0)·σgAnd obtaining the reliability constraint of the roller linear guide rail pair multi-target steady optimization model:
μg-φ-1(R0)·σg≥0；
(9) with a random variable xiThe mean value of (A) has influence on the reliability of the roller linear guide pair and is represented by a random variable xjThe influence of the variance on the reliability of the roller linear guide rail pair is minimized at the same time as a target, and a multi-target robust optimization model F (x) of the roller linear guide rail pair is establishedi,xj)；
(10) Separately calculating random variables xiAnd a random variable xjThe optimal solution of (2):
(10.1) in the range of size constraint and reliability constraint, utilizing an optimization algorithm of nonlinear programming to carry out a multi-objective robust optimization model F (x) on the roller linear guide rail pairi,xj) Each single objective function in the system is respectively optimized to obtainIdeal points corresponding to two single objective functionsAnd
(10.2) judging the corresponding ideal points of the two single objective functionsAndif the two are the same, the ideal point value is a random variable xiAnd a random variable xjOtherwise, executing step (10.3);
(10.3) calculating a roller linear guide rail pair multi-objective robust optimization model F (x)i,xj) Set with ideal pointsTo obtain an evaluation function U (x)i,xj)：
(10.4) optimization algorithm using non-linear programming to evaluate function U (x)i,xj) Optimizing to obtain the evaluation function U (x)i,xj) The optimal solution of (a) yields a random variable xiAnd a random variable xjThe optimal solution of (2);
(11) substituting the working parameters, the material parameters and the mean value and the variance of each random variable of the roller linear guide rail pair into a roller linear guide rail pair precision reliability mathematical model, and calculating the precision reliability of each running-in position point of the roller linear guide rail pair to obtain a precision reliability curve;
(12) obtaining the reliability curve and the random variable x of the optimized roller linear guide rail pairiMean sensitivity curve and variance sensitivity curve of (1) and random variable xjMean sensitivity curve and variance sensitivity curve of (1):
(12.1) adjusting the operating parameters of the roller linear guide rail pair,Material parameter, random variable xiOptimal solution of, random variable xjSubstituting the optimal solution and the mean value and variance of other random variables into a reliability model of the roller linear guide rail pair, and calculating the precision reliability of each running-in position point of the roller linear guide rail pair to obtain a reliability curve of the optimized roller linear guide rail pair;
(12.2) setting the working parameters, material parameters and random variable x of the roller linear guide rail pairiOptimal solution of, random variable xjThe optimal solution and the mean value and variance of other random variables are substituted into a mean value sensitivity model to respectively calculate the random variable x of each running-in position point of the roller linear guide rail pairiAnd a random variable xjObtaining the random variable x of the optimized roller linear guide rail pairiMean sensitivity curve and random variable xjThe mean sensitivity curve of (a);
(12.3) setting the working parameters, material parameters and random variable x of the roller linear guide rail pairiOptimal solution of, random variable xjThe optimal solution and the mean value and variance of other random variables are substituted into a variance sensitivity model to respectively calculate the random variable x of each running-in position point of the roller linear guide rail pairiAnd a random variable xjThe variance sensitivity of the roller linear guide rail pair is obtained, and the random variable x of the roller linear guide rail pair after optimization is obtainediVariance sensitivity curve and random variable xjA variance sensitivity curve of (a);
(13) the reliability curve of the optimized roller linear guide rail pair, the precision reliability curve of the step (11) and the random variable x of the optimized roller linear guide rail pairiThe mean sensitivity curve of (5) and the random variable x of step (5)iMean sensitivity curve, random variable x of optimized roller linear guide pairjThe mean sensitivity curve of (5) and the random variable x of step (5)jMean sensitivity curve, random variable x of optimized roller linear guide pairiVariance sensitivity curve of (5) and random variable x of step (5)iVariance sensitivity curve of (1) and random variable x of roller linear guide pair after optimizationjVariance sensitivity curve of (5) and random variation of step (5)Quantity xjRespectively comparing the variance sensitivity curves, judging whether each curve of the optimized roller linear guide rail pair is slower than the comparison curve, if so, finishing the optimization design of the precision reliability of the roller linear guide rail pair, otherwise, adopting a random variable xiRespectively to the random variable xiThe upper limit and the lower limit are adjusted, and a random variable x is adoptedjRespectively to the random variable xjAnd (4) adjusting the upper limit and the lower limit, and executing the step (7) to the step (13).
Compared with the prior art, the invention has the following advantages:
1. the invention adopts a roller linear guide pair precision loss model deltaV(S), the precision loss process between the roller linear guide rail pair and the track is fully considered from the two aspects of elastic deformation and abrasion, the reliability analysis is carried out on the precision loss of the roller linear guide rail pair by using a four-order moment method with less related assumptions and smaller result errors, and a precision reliability mathematical model R of the roller linear guide rail pair is establishedFMAnd the quantitative prediction of the precision reliability of the roller linear guide rail pair is realized.
2. The invention fully considers the uncertainty factors objectively existing in the design of the roller linear guide rail pair, combines the reliability design theory, the steady optimization design theory and the precision loss model of the roller linear guide rail pair, and establishes a multi-objective steady optimization model, thereby ensuring the reliability and the robustness of the optimal solution while obtaining the optimal solution meeting the design requirements.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram illustrating a force analysis of a roller linear guide pair according to an embodiment of the present invention;
FIG. 3 is a graph of the sensitivity of the mean value of random variables of a roller linear guide pair as a function of the increase of the running-in mileage according to an embodiment of the present invention;
FIG. 4 is a graph of the variance sensitivity of each random variable of a roller linear guide pair as a function of the increase of the running-in mileage according to an embodiment of the present invention;
FIG. 5 shows a roller according to an embodiment of the present inventionPrecision reliability R of column linear guide pairFMA variation curve graph with the increase of the running-in mileage;
FIG. 6 shows the accuracy reliability R of the roller linear guide pair according to the embodiment of the present inventionFMAnd the precision reliability of the rear roller linear guide rail pair is optimizedA comparative graph of (a);
FIG. 7 shows a random variable x of a roller linear guide pair according to an embodiment of the present inventionαAverage value sensitivity of and random variable x of optimized roller linear guide rail pairαThe mean sensitivity contrast plot of (a);
FIG. 8 shows a random variable x of a roller linear guide pair according to an embodiment of the present inventionαVariance sensitivity of the roller linear guide pair and random variable x of the optimized roller linear guide pairαVariance sensitivity versus plot of (a).
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the optimal design method for precision reliability of the roller linear guide rail pair comprises the following steps:
step 1, establishing a precision loss model delta of the roller linear guide rail pairV(S): when the precision loss model of the guide rail pair is established, the precision loss model delta is established by considering the two aspects of elastic deformation and abrasionVThe step of (S) is as follows:
step 1.1) calculating the elastic deformation delta of the roller linear guide rail pairV1：
Setting the action load F loaded on the slide block vertically downwards to the roller linear guide rail pair, and the normal load of the contact surface born by each roller to be QnThe included angle between the normal direction of the contact surface and the vertical direction is alpha, Z is the number of each row of rollers on the guide rail, and the pre-tightening force F borne by the roller linear guide rail pair0. The stress condition is shown in figure 2. According to the stress balance, the following results are obtained:
adopting Palmgren empirical formula, comprehensively considering normal contact load QnNormal contact deformation deltanRelation and pretension force F0And initial deformation of δ0Connecting, calculating to obtain the elastic deformation delta of the roller linear guide rail pairV1Comprises the following steps:
wherein, v1V and v2Poisson's ratio of the rollers and raceways, respectively, E1And E2The elastic modulus of the roller and the raceway respectively;
step 1.2) establishing a wear prediction model delta of the roller and raceway contact surface of the roller linear guide rail pairV2(S): the volume abrasion W of the roller can be obtained according to Archard's adhesive abrasion theoryVCalculating the formula:
wherein K is the adhesive wear coefficient, S is the operating mileage, H is the hardness of the softer material, the elastic creep rate
According to the Hertz elastic contact theory, the contour contact area A of the single-row roller can be obtainedpComprises the following steps:
wherein the load W is Qn+F0/2Z＝F/(2Zcosα)+F02Z, R is the roller radius;
so that the wear prediction model delta of the roller and raceway contact surface of the roller linear guide rail pairV2(S) is:
step 1.3) according to the elastic deformation delta of the roller linear guide rail pairV1And a roller and raceway contact surface wear prediction model delta of the roller linear guide rail pairV2(S) establishing a precision loss model delta of the roller linear guide rail pairV(S)：
Wherein, deltaV(S) is the total variation of the displacement deviation of the sliding block to the bottom surface reference of the guide rail;
step 2, deducing a precision reliability limit state function delta of the roller linear guide rail pairX(X): precision index U of roller linear guide rail pair and precision loss model delta of roller linear guide rail pairVCalculating the accuracy reliability limit state function delta of the roller linear guide pairX(X)，δX(X)＝U-δV(S), wherein X represents a basic random variable vector, and the applied load F, the material hardness H and the roller diameter D are selectedaEffective diameter of rollereContact angle alpha and pretightening force F0. Because each random variable obeys normal distribution, the skewness coefficient of each random variable is known by looking up data as follows: csX＝(0,0,0,0,0,0)TThe kurtosis coefficient of each random variable is: ckX＝(3,3,3,3,3,3)T；
Step 3, establishing a roller linear guide rail pair precision reliability mathematical model RFM：
Step 3.1) carrying out precision reliability limit state function delta on the roller linear guide rail pair through a Taylor formulaX(X) expanding to obtain a precision reliability limit state function deltaX(X) Taylor expansion retained to quadratic term:
step 3.2) substituting the mean value of each random variable into the limit state function delta of precision reliabilityXIn the Taylor expansion of (X), and each randomly variesThe quantities are relatively independent to obtain a limit state function deltaXMean expression of (X) < mu >g：
Step 3.3) respectively calculating 2 times of Kronecker power, 3 times of Kronecker power and 4 times of Kronecker power of a first-order partial derivative vector in the Taylor expansion formula, simultaneously multiplying the 2 times of Kronecker power and a variance vector of a basic random variable vector X, multiplying the 3 times of Kronecker power and a third-order moment vector, multiplying the 4 times of Kronecker power and a fourth-order moment vector of the basic random variable vector X to obtain a limit state function deltaX(X) expression of varianceThird moment expression thetagAnd fourth order moment expression ηgRespectively as follows:
step 3.4) applying the extreme State function deltaXSubstituting the mean expression, the variance expression, the third moment expression and the fourth moment expression of (X) into a single failure mode reliability calculation formula based on HOST to obtain a reliability index expression betaFMThe expression is as follows:
wherein alpha is3gThe expression of the skewness coefficient is the extreme state function of the precision reliability of the roller linear guide rail pairα4gThe expression is the peak coefficient expression of the precision reliability limit state function of the roller linear guide rail pair, and the expression isβSMThe second moment reliability index is a precision reliability limit state function of the roller linear guide rail pair;
step 3.5) expressing the reliability index by the expression betaFMSubstitution into RFM＝φ(βFM) To obtain a roller linear guide pair precision reliability mathematical model RFM；
Step 4, a roller linear guide rail pair precision reliability mathematical model RFMRespectively substituting into a fourth moment mean value sensitivity formula, a fourth moment variance sensitivity formula, a fourth moment mean value sensitivity formula and a fourth moment variance sensitivity formula, wherein the expressions are respectively as follows:
wherein,
obtaining a mean sensitivity model of a basic random variable vector XVariance sensitivity model of sum basic random variable vector X
Step 5, adopting computer application software MATLAB to respectively carry out mean value sensitivity model on each basic random variable vector XAnd variance sensitivity model of each basic random variable vector XProgramming is carried out, and main parameters of the roller linear guide rail pair shown in table 1 are calculated, so that a change curve graph of the mean sensitivity of each random variable of the roller linear guide rail pair of the embodiment of the invention along with the increase of the running-in mileage and a change curve graph of the variance sensitivity of each random variable of the roller linear guide rail pair of the embodiment of the invention along with the increase of the running-in mileage can be respectively obtained, and the change curve graphs are respectively shown in an attached figure 3 and an attached figure 4:
TABLE 1 roller Linear guide auxiliary guide rail main parameter table
Step 6, due to the external load F and the pretightening force F0And material hardness H, so the contact angle alpha and the roller diameter D are designed parameters from random variablesaAnd an effective length leTo select the random variables to be optimized. As can be seen from the change curve graph of the mean value sensitivity of each random variable of the roller linear guide rail pair increasing along with the running mileage, the mean value sensitivity of the contact angle alpha increases towards the negative direction along with the increase of the running mileage, namely the contact angle alphaThe precision reliability of the roller linear guide rail pair is negatively influenced, and the influence is increasingly large in the motion process. In addition, as can be seen from the variation curve graph of the variance sensitivity of each random variable of the roller linear guide rail pair increasing along with the running-in mileage, the variance sensitivity of the contact angle alpha increases first and then decreases along with the increase of the running-in mileage in a negative direction, but the contact angle alpha has a negative influence on the accuracy reliability of the roller linear guide rail pair, and the influence of the contact angle alpha on the movement process is the largest compared with the influence of other random variables, and in conclusion, the contact angle alpha is selected as the random variable to be optimized;
step 7, selecting a random variable xαThe upper limit and the lower limit of the linear roller guide rail pair are obtained, and the size constraint of the multi-objective robust optimization model is obtained:
40≤xα≤50
step 8, giving target reliability R to the task0Substituting the running mileage S618 km into the reliability constraint function FR＝μg-φ-1(R0)·σgAnd obtaining the reliability constraint of the roller linear guide rail pair multi-target steady optimization model:
μg-φ-1(0.9)·σg≥0；
step 9, random variable xαThe mean value of (A) has influence on the reliability of the roller linear guide pair and is represented by a random variable xαThe influence of the variance on the reliability of the roller linear guide rail pair is minimized at the same time as a target, and a multi-target robust optimization model F (x) of the roller linear guide rail pair is establishedα)：
Step 10, calculating a random variable xαOptimal solution:
step 10.1) in the range of size constraint and reliability constraint, respectively utilizing fmincon function in MATLAB optimization toolbox to solve, and setting an initial value alpha of the contact angle alpha045, a multi-objective robust optimization model F (x) for the roller linear guide rail pairα) Each single objective function in the system is respectively optimized to obtain twoThe ideal points corresponding to the single objective function are respectivelyAnd
step 10.2) ideal points corresponding to two single objective functionsAndotherwise, calculating a multi-objective robust optimization model F (x) of the roller linear guide rail pairα) Set with ideal pointsTo obtain an evaluation function U (x)α)：
Step 10.3) solving by using fmincon function in MATLAB optimization toolbox, and carrying out evaluation on the function U (x)α) Optimizing to obtain the evaluation function U (x)α) The optimal solution of (a) yields a random variable xαThe optimal solution is 40.0034;
step 11, adopting computer application software MATLAB to carry out precision reliability mathematical model R on the roller linear guide rail pairFMProgramming is carried out, and the motion precision reliability R of the roller linear guide rail pair is obtained through the mean value and the variance of the main parameters of the roller linear guide rail pair shown in the table 1FMAlong with the variation curve of the running-in mileage, as shown in fig. 5, the roller linear guide rail pair of the embodiment has high precision reliability in the initial stage of movement, when the running and mileage reaches 400km, the precision reliability begins to decline, and when the running and mileage reaches 800km, the precision reliability reaches 0.5;
step 12, obtaining a reliability curve and a random variable x of the optimized roller linear guide rail pairαMean sensitivity curve ofLine and variance sensitivity curves:
step 12.1) working parameters, material parameters and random variables x of the roller linear guide rail pairαThe mean value and the variance of other random variables are substituted into a reliability model of the roller linear guide rail pair, and the precision reliability of each running-in position point of the roller linear guide rail pair is calculated by adopting computer application software MATLAB to obtain the precision reliability of the optimized roller linear guide rail pairA change curve;
step 12.2) working parameters, material parameters and random variables x of the roller linear guide rail pairαSubstituting the optimal solution and the mean value and variance of other random variables into a mean value sensitivity model, and respectively calculating the random variable x of each running-in position point of the roller linear guide rail pair by adopting computer application software MATLABαObtaining the random variable x of the optimized roller linear guide rail pairαThe mean sensitivity curve of (a);
step 12.3) working parameters, material parameters and random variables x of the roller linear guide rail pairαSubstituting the optimal solution and the mean value and variance of other random variables into a variance sensitivity model, and respectively calculating the random variable x of each running-in position point of the roller linear guide rail pair by adopting computer application software MATLABαObtaining the random variable x of the optimized roller linear guide rail pairαA variance sensitivity curve of (a);
step 13, comparing the reliability curve of the optimized roller linear guide rail pair with the precision reliability curve of the step (11) according to the graph shown in the attached figure (6), and finding that the reliability curve of the optimized roller linear guide rail pair is obviously later than the precision reliability curve of the step (11), the trend is mild, and the precision reliability is obviously improved when the running-in mileage is the same; according to the attached figure (7), the random variable x of the roller linear guide rail pairαThe mean sensitivity curve of (5) and the random variable x of step (5)αComparing the mean sensitivity curves to find out the random variable x of the optimized roller linear guide rail pairαMean value ofRandom variable x with sensitivity curve dropping significantly later than in step (5)αThe average value sensitivity curve is mild in trend, and the negative influence of the contact angle alpha is reduced, so that the precision reliability of the roller linear guide rail pair is not easy to lose efficacy; according to the figure (8), the random variable x of the roller linear guide rail pair after optimizationαVariance sensitivity curve of (5) and random variable x of step (5)αComparing the variance sensitivity curves, and optimizing the random variable x of the roller linear guide rail pairαThe sensitivity to variance curve of (5) begins to decline significantly later than the random variable x of step (5)αThe variance sensitivity curve has a moderate trend, and the negative influence of the contact angle alpha is reduced, so that the precision reliability of the roller linear guide rail pair is not easy to lose efficacy. Random variable xαThe optimal solution can effectively improve the precision reliability, reduce the mean sensitivity and the variance sensitivity of the contact angle alpha and complete the optimal design of the roller linear guide rail pair.
Claims (7)
1. An optimization design method for precision reliability of a roller linear guide rail pair is characterized by comprising the following steps:
(1) establishing precision loss model delta of roller linear guide rail pairV(S)：
(1.1) calculating the elastic deformation delta of the roller linear guide pairV1；
(1.2) establishing a wear prediction model delta of the roller and raceway contact surface of the roller linear guide rail pairV2(S)；
(1.3) according to the elastic deformation delta of the roller linear guide pairV1And a roller and raceway contact surface wear prediction model delta of the roller linear guide rail pairV2(S) establishing a precision loss model delta of the roller linear guide rail pairV(S)；
(2) Deducing precision reliability limit state function delta of roller linear guide pairX(X): precision index U of roller linear guide rail pair and precision loss model delta of roller linear guide rail pairVCalculating the accuracy reliability limit state function delta of the roller linear guide pairX(X)，δX(X)＝U-δV(S), wherein X represents a basic random variable vectorIt can be selected from working parameters, material parameters and geometric parameters;
(3) establishing a roller linear guide pair precision reliability mathematical model RFM：
(3.1) performing precision reliability limit state function delta on the roller linear guide rail pair through a Taylor formulaX(X) expanding to obtain a precision reliability limit state function deltaX(X) Taylor expansion retained to quadratic term;
(3.2) substituting the mean values of the random variables into the extreme state function delta of the accuracy and reliabilityX(X) the Taylor expansion of the (X) to obtain the limit state function deltaXMean expression of (X) < mu >g；
(3.3) respectively calculating 2 times of Kronecker power, 3 times of Kronecker power and 4 times of Kronecker power of a first-order partial derivative vector in the Taylor expansion formula, simultaneously multiplying the 2 times of Kronecker power with a variance vector of a basic random variable vector X, multiplying the 3 times of Kronecker power with a third-order moment vector, multiplying the 4 times of Kronecker power with a fourth-order moment vector of the basic random variable vector X to obtain a limit state function deltaX(X) expression of varianceThird moment expression thetagAnd fourth order moment expression ηg；
(3.4) applying a limit state function deltaXSubstituting the mean expression, the variance expression, the third moment expression and the fourth moment expression of (X) into a single failure mode reliability calculation formula based on HOST to obtain a reliability index expression betaFM；
(3.5) expressing the reliability index by the expression betaFMSubstitution into RFM＝φ(βFM) To obtain a roller linear guide pair precision reliability mathematical model RFM；
(4) Mathematical model R for precision reliability of roller linear guide rail pairFMRespectively substituting into the fourth moment mean value sensitivity formula and the fourth moment variance sensitivity formula to obtain a mean value sensitivity model of the basic random variable vector XVariance sensitivity model of sum basic random variable vector X
(5) Substituting the working parameters, the material parameters and the mean and variance of all the random variables of the roller linear guide rail pair into a mean sensitivity model, calculating the mean sensitivity of all the random variables of each running-in position point of the roller linear guide rail pair to obtain a mean sensitivity curve of all the random variables, simultaneously substituting the working parameters, the material parameters and the mean and variance of all the random variables of the roller linear guide rail pair into a variance sensitivity model, calculating the variance sensitivity of all the random variables of each running-in position point of the roller linear guide rail pair to obtain a variance sensitivity curve of all the random variables;
(6) selecting the random variable X corresponding to the curve farthest from the X axis from the mean sensitivity curves of the random variablesiAt the same time, the random variable X corresponding to the curve farthest from the X axis is selected from the variance sensitivity curves of the random variablesj；
(7) Respectively selecting random variables xiAnd a random variable xjThe upper limit and the lower limit of the linear roller guide rail pair are obtained, and the size constraint of the multi-objective robust optimization model is obtained:
xi1≤xi≤xi2
xj1≤xj≤xj2
wherein x isi1And xi2Are respectively random variables xiLower and upper limits of (2), xj1And xj2Are respectively random variables xjLower and upper limits of (d);
(8) target reliability R given to task0Substituting a reliability constraint function FR＝μg-φ-1(R0)·σgAnd obtaining the reliability constraint of the roller linear guide rail pair multi-target steady optimization model:
μg-φ-1(R0)·σg≥0；
(9) with a random variable xiThe mean value of (A) has influence on the reliability of the roller linear guide pair and is represented by a random variable xjThe influence of the variance on the reliability of the roller linear guide rail pair is minimized at the same time as a target, and a multi-target robust optimization model F (x) of the roller linear guide rail pair is establishedi,xj)；
(10) Separately calculating random variables xiAnd a random variable xjThe optimal solution of (2):
(10.1) in the range of size constraint and reliability constraint, utilizing an optimization algorithm of nonlinear programming to carry out a multi-objective robust optimization model F (x) on the roller linear guide rail pairi,xj) Each single objective function in the system is optimized to obtain the corresponding ideal point of the two single objective functionsAnd
(10.2) judging the corresponding ideal points of the two single objective functionsAndif the two are the same, the ideal point value is a random variable xiAnd a random variable xjOtherwise, executing step (10.3);
(10.3) calculating a roller linear guide rail pair multi-objective robust optimization model F (x)i,xj) Set with ideal pointsTo obtain an evaluation function U (x)i,xj)：
(10.4) optimization algorithm using non-linear programming to evaluate function U (x)i,xj) Optimizing to obtain the evaluation function U (x)i,xj) The optimal solution of (a) yields a random variable xiAnd a random variable xjThe optimal solution of (2);
(11) substituting the working parameters, the material parameters and the mean value and the variance of each random variable of the roller linear guide rail pair into a roller linear guide rail pair precision reliability mathematical model, and calculating the precision reliability of each running-in position point of the roller linear guide rail pair to obtain a precision reliability curve;
(12) obtaining the reliability curve and the random variable x of the optimized roller linear guide rail pairiMean sensitivity curve and variance sensitivity curve of (1) and random variable xjMean sensitivity curve and variance sensitivity curve of (1):
(12.1) setting the working parameters, material parameters and random variable x of the roller linear guide rail pairiOptimal solution of, random variable xjSubstituting the optimal solution and the mean value and variance of other random variables into a reliability model of the roller linear guide rail pair, and calculating the precision reliability of each running-in position point of the roller linear guide rail pair to obtain a reliability curve of the optimized roller linear guide rail pair;
(12.2) setting the working parameters, material parameters and random variable x of the roller linear guide rail pairiOptimal solution of, random variable xjThe optimal solution and the mean value and variance of other random variables are substituted into a mean value sensitivity model to respectively calculate the random variable x of each running-in position point of the roller linear guide rail pairiAnd a random variable xjObtaining the random variable x of the optimized roller linear guide rail pairiMean sensitivity curve and random variable xjThe mean sensitivity curve of (a);
(12.3) setting the working parameters, material parameters and random variable x of the roller linear guide rail pairiOptimal solution of, random variable xjThe optimal solution and the mean value and variance of other random variables are substituted into a variance sensitivity model to respectively calculate the random variable x of each running-in position point of the roller linear guide rail pairiAnd a random variable xjThe variance sensitivity of the roller linear guide rail pair is obtained, and the random variable x of the roller linear guide rail pair after optimization is obtainediVariance sensitivity curve and random variable xjA variance sensitivity curve of (a);
(13) the reliability curve of the optimized roller linear guide rail pair, the precision reliability curve of the step (11) and the random variable x of the optimized roller linear guide rail pairiThe mean sensitivity curve of (5) and the random variable x of step (5)iMean sensitivity curve, random variable x of optimized roller linear guide pairjThe mean sensitivity curve of (5) and the random variable x of step (5)jMean sensitivity curve, random variable x of optimized roller linear guide pairiVariance sensitivity curve of (5) and random variable x of step (5)iVariance sensitivity curve of (1) and random variable x of roller linear guide pair after optimizationjVariance sensitivity curve of (5) and random variable x of step (5)jRespectively comparing the variance sensitivity curves, judging whether each curve of the optimized roller linear guide rail pair is slower than the comparison curve, if so, finishing the optimization design of the precision reliability of the roller linear guide rail pair, otherwise, adopting a random variable xiRespectively to the random variable xiThe upper limit and the lower limit are adjusted, and a random variable x is adoptedjRespectively to the random variable xjAnd (4) adjusting the upper limit and the lower limit, and executing the step (7) to the step (13).
2. The method for optimally designing the precision reliability of the roller linear guide pair according to claim 1, wherein the precision reliability limit state function of the roller linear guide pair in the step (2) is expressed as:
wherein, v1V and v2Poisson's ratio of the rollers and raceways, respectively, E1And E2Respectively the elastic modulus of the roller and the raceway, F the external load, Z the number of the bearing rollers, K the adhesive wear coefficient, S the running-in mileage, H the material hardness, DaIs the diameter of the roller, /)eIs the effective length of the roller, alpha is the rollerContact angle with raceway, F0Is a pre-tightening force.
3. The method for optimally designing the precision reliability of the roller linear guide rail pair according to claim 1, wherein the precision reliability limit state function delta in the step (3.1)X(X) Taylor expansion retained to quadratic term, specifically:
wherein, muXIs the mean value of each of the random variables,for the first order partial derivative vector in the Taylor expansion,is the second order partial derivative vector in the Taylor expansion.
4. The method for optimally designing the precision reliability of the roller linear guide pair according to claim 1, wherein the HOST-based single failure mode reliability calculation formula in the step (3.4) is expressed as follows:
wherein alpha is3gThe expression of the skewness coefficient is the extreme state function of the precision reliability of the roller linear guide rail pairα4gThe expression is the peak coefficient expression of the precision reliability limit state function of the roller linear guide rail pair, and the expression isβSMThe second moment reliability index is the extreme state function of the precision reliability of the roller linear guide rail pair.
5. The optimal design method for precision reliability of the roller linear guide pair as claimed in claim 1, wherein the expressions of the fourth-order moment mean sensitivity formula and the fourth-order moment variance sensitivity formula in the step (4) are respectively:
wherein,
6. the method for optimally designing the precision and reliability of the roller linear guide pair according to claim 1, wherein the step (9) is implemented by establishing a multi-objective robust optimization model F (x) of the roller linear guide pairi,xj) The establishing steps are as follows:
(9.1) according toRandom variable xiThe mean sensitivity model of (1) to establish a random variable xiThe mean value of (a) influences the target function f on the reliability of the roller linear guide rail pair1(xi)：
(9.2) according to the random variable xjThe variance sensitivity model of (1) to establish a random variable xjThe variance of (a) influences the objective function f on the reliability of the roller linear guide rail pair2(xj)：
(9.3) with a random variable xiThe mean value of (a) influences the target function f on the reliability of the roller linear guide rail pair1(xi) And a random variable xjThe variance of (a) influences the objective function f on the reliability of the roller linear guide rail pair2(xj) Meanwhile, establishing a roller linear guide rail pair multi-target steady optimization model F (x) by taking the minimum as a targeti,xj)：
7. The method for optimizing the accuracy and reliability of a roller linear guide pair according to claim 1, wherein the evaluation function U (x) in step (10.3)i,xj) The expression is as follows:
whereinMulti-objective robust optimization model F (x) for roller linear guide rail pairi,xj) Andset of ideal points
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