CN104794366A - Full-factor experiment analysis method for oil nozzle abrasive flow machining - Google Patents
Full-factor experiment analysis method for oil nozzle abrasive flow machining Download PDFInfo
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Abstract
The invention relates to a full-factor experiment analysis method for oil nozzle abrasive flow machining. The method comprises the specific steps that firstly, a selected model is fitted, wherein 1, the total effect in an analysis of variance table is checked; 2, the unfit phenomenon in the analysis of variance table is checked; 3, curve items in the analysis of variance table are checked; 4, fitted total effect correlation coefficients R2 and corrected total effect correlation coefficients are checked; 5, an s value or an s2 value is analyzed; 6, the significance of all effects is checked; secondly, a residual error is diagnosed; thirdly, whether the model needs to be improved is judged; fourthly, the model is analyzed and interpreted; fifthly, whether a target is achieved is judged. The method improves a fit-analysis abrasive flow machining mathematic model, a regression equation with the abrasive physical property as the principal thing is elicited, the quality of abrasive flow machining is controlled in a quantitative mode, and the method has certain academic significance and engineering value.
Description
Technical field
The present invention relates to a kind of atomizer abrasive Flow Machining total divisor test analysis method, belong to abrasive Flow Machining technical field.
Background technology
Abrasive Flow Machining is a kind of up-to-date machining process, it is the surface flowing through the required processing of workpiece with abrasive medium (being mixed with the flowable potpourri of one of abrasive particle) under stress, carry out deburring, deburring, angle rounding, to reduce percent ripple and the roughness of surface of the work, reach precision machined smooth finish.This method is at the complicated manual finishing of needs or complex-shaped workpiece, and the unmanageable position of additive method is best alternative job operation.This method also can be applicable to satisfied not with cylinder, vibrations and other processing in enormous quantities or adds the workpiece wanting injured man-hour.And the delamination of regeneration after effectively obtaining removing electric discharge processing or laser beam processing and previous operation finished surface the unrelieved stress that remains.
Summary of the invention
The object of the present invention is to provide a kind of atomizer abrasive Flow Machining total divisor test analysis method, to be researched and analysed for abrasive Flow Machining method better, providing better foundation for using this technology.
To achieve these goals, technical scheme of the present invention is as follows.
A kind of atomizer abrasive Flow Machining total divisor test analysis method, its concrete steps are as follows:
The first step, model is selected in matching: specifically comprise:
(1) the total effect in analysis of variance table is seen: H
0: model is invalid
h
1model is effective: if the p-value < 0.05 of the recurrence item of correspondence, then show to refuse null hypothesis, namely can judge that this model is effective on the whole, if the recurrence item p-value > 0.05 of correspondence, then show to refuse null hypothesis, namely can decision model in general invalid.
(2) see that phenomenon is intended in the mistake in analysis of variance table: this hypothesis checked is: H
0intend without losing
h
1lose plan: in ANOVA analysis result, if lose the p-value > 0.05 intending item correspondence, explanation cannot refuse null hypothesis, namely can judge that plan phenomenon do not lost by this model; Otherwise, illustrate that selected model may miss out critical item, should consider to re-establish model; Losing the basis intending item correspondence is: the difference between first calculated revision test, it can be used as the estimation of test error; The item of disappearance is compared with it with caused error sum of squares, can conclusion be obtained through F inspection.After, will be judged as in analysis result that inapparent item is all classified as stochastic error, whether significantly recalculate mistake plan item.
(3) the bending item in analysis of variance table is seen: this hypothesis checked is: H
0: without bending
h
1: have bending; In ANOVA analysis result, if the p-value > 0.05 of bending item correspondence, then show to refuse null hypothesis, namely can judge that this model does not have buckling phenomenon; Otherwise, illustrate that data are case of bending, and in model, do not have quadratic term, quadratic term should be filled; The foundation that bending item calculates is: calculate the difference between revision test, by its estimation as test error, first three observed readings are got to independent variable, get the embodiment data that high level, low-level and central point are corresponding respectively, then remove linear term, obtain the quadratic sum of quadratic term; Whether quadratic sum and the embodiment error of quadratic term compare, by F test and judge model in bending.
(4) total effect coefficient R of matching
2(i.e. R-Sq) and the total effect coefficient R revised
2 adji.e. (R-Sq (adj)).
Can be obtained by the square rooting matrix formula in Regression Analysis Result:
SS
Total＝SS
Model+SS
Error(1)
By considering SS
modelat SS
totalin shared ratio, define R quadratic term (R-Square, i.e. R-Sq):
Obviously, this numerical value is more better close to 1.Easily find out, he has another kind of literary style:
If also regard independent variable as stochastic variable, the related coefficient between them can be derived.And R-Sq be just exactly related coefficient square.Therefore, its definition understands very well.For the situation that independent variable is more, define by identical way, can be understood as " the polynary coefficient of determination ", still represent SS
modelat SS
totalin ratio.Such as, but also have a shortcoming: when independent variable number increases, the independent variable that only increase by is new, whether the effect of this independent variable no matter increased is remarkable, R
2(R-Sq) all can increase, thus evaluate whether should increase this independent variable enter regression equation time, use R
2just be not worth.For this reason, the R revised is introduced
2i.e. R
2 adj, its definition is:
In formula, n is test total degree; P is all effect items (comprising constant term) in regression equation.Coefficient R
2 adj(R-Sq (adj)) is the impact not considering that in regression equation, item number is how many, thus can the quality of judgment models more accurately, R
2 adjclose to 1, numerical value more illustrates that model is better, in actual application, be usually at least greater than 1, be thus easy to draw, R owing to comprising item number p in model
2 adjalways than R
2smaller.Therefore, judge that the quality of two models can judge from R-Sq (adj) and the degree of closeness of R-Sq, the difference of the two is less, illustrates that model is better.In analytic process, originally selected model comprises whole factor usually, i.e. " full model ", usually those inapparent factors are deleted after again model being modified, be referred to as " deleting model ", if delete after the effect inapparent factor leaves out, the value of R-Sq (adj) and R-Sq closer to, illustrate and delete that model is improved than initial model.
(5) to s value or s
2analysis: assuming that the error of observed reading and theoretical model is with 0 for average, with σ
2for distributing just very much of variance.In analysis of variance table, the numerical value σ just of the average deviation quadratic sum (adjMS) that residual error error is corresponding
2unbiased estimator, be designated as square error MSE, and its square root s can be exported by some software after computation in the lump, can think that s value is the estimation of σ.Generally, predicted value being added and subtracted 2 times of s, is namely the fiducial interval of 95% of predicted value.The less explanation model of s value is better obviously.
(6) conspicuousness of every effect: in the most beginning of result of calculation, estimates, in regression coefficient y, to list every effect and assay.By point other inspection to each, can show that some is significant and some is inapparent, it is noted herein that: for a significant higher order term of effect, its lower term comprised is the remarkable item of effect necessarily.Such as, if second order interaction item AC is the remarkable item of effect, then main effect item A and main effect item C also should comprise in a model.
For the analysis of the conspicuousness of every effect, MINITAB software also exports some relational graphs, helps to verify conclusions further.Mainly Pareto effect figure and normal state effect figure.
Judge that the conspicuousness of factorial effect is very intuitively with Pareto effect figure, but it there is an important shortcoming, when that is exactly the t inspection carrying out each effect, first use s
2estimate σ
2come, and usual s
2might not be reliable.By the effect of each factor by lining up sequence from small to large, these effect points are marked in normal probability plot, Here it is normal state effect figure.Usually can think in most factor, to only have a few factors to be effect significant factor, i.e. the sparse principle of so-called effect.Therefore, after the point group those being positioned at middle effect fits to straight line, judge which factor is the significant factor of effect with this straight line as observation standard, observation principle is judged as the remarkable item of effect away from the factor of this straight line, and the factor near this straight line is judged to be effect remarkable item.
Just complete the initial analysis to data in sum, namely complete the task of the first step " model is selected in matching ".
Second step: residual error is diagnosed:
Residual error diagnosis specifically comprises four steps, observes four figures that computing machine exports automatically respectively.
(1) scatter diagram being transverse axis with observed reading order in observation residual plot, observe in scatter diagram, whether each point descends random fluctuation on the horizontal axis.
(2) scatter diagram being transverse axis with response variable match value in observation residual plot, observe in figure, whether residual error remains equal variance, if residual error does not keep equal variance, this figure there will be " funnel-form " or " horn-like ".
(3) observe the test of normality figure of residual error, judge whether residual error distributes by normal distribution law.
(4) observing in residual error take independent variable as the scatter diagram of transverse axis, mainly sees in figure whether there is warp tendency.When loose point is obviously U-shaped or anti-U-shaped bending, this illustrates response variable y, only gets linear term and does not meet the demands, also lack quadratic term or cube item in model, should increase quadratic term or cube item of x, will make models fitting better effects if this independent variable x.
Four figure of residual error diagnosis are all normal then representative models is normal.
3rd step: judgment models is the need of improvement.
The main task of this step is the result according to the first step and second step, and by numerical analysis and residual plot two aspect judgment models the need of improvement, and how model should improve.If model needs to improve the increase should carrying out quadratic term or cube item according to residual plot, in addition, based on the conspicuousness according to each effect, not remarkable item in model is deleted, in a word, find in model, there is the place needing amendment, just return the initial first step.
Through the modification and perfection repeatedly (sometimes only namely obtaining satisfied model through once revising) of first three step, finally determine that is satisfied with a model, this model selected carries out next step and analyzes.
4th step: analysis interpretation model.Mainly contain the content of following three aspects, the requirement of this three aspect, generally can automatically provide in computer software.
(4) each factor main effect figure and interaction figure.Those Summing Factor interaction items selected by confirming further from main effect figure and interaction figure whether really the main effect of remarkable and those factors unchecked and interaction whether genuine remarkable, thus more specifically confirm selected model more intuitively.
(5) contour map, response surface design figure is exported.Contour map and response surface design figure can help to confirm further each independent variable and he they between mutual item be how to affect response variable result.If target is hoped little (hope large or hope order), so how independent variable is arranged, can response variable minimum (maximum or closest with target) be made? in MINITAB software, contour map and the surface chart of every two independents variable combination all can be provided by software automatically.
(6) optimization is realized.Large according to the prestige of particular problem, hope little or hope that order numerically obtains the optimum value in whole scope of embodiments, this numerical value can be provided automatically by MINITAB software.Although the object of embodiment design is selection variables in the factor design stage, in fact, in the first step that DOE analyzes, just can judge which variable is which variable is inapparent significantly, on the basis using these information, optimum value can be obtained." response variable optimizer " that computing machine provides can provide optimum setting automatically.As long as usually set optimal objective again after selected response variable.
5th step: judge whether target reaches: mainly by the desired value of analyses and prediction compared with former embodiment target.If from target still away from, then should consider to arrange new round embodiment, if substantially reach target, then should set demonstration test to guarantee to produce can obtain Expected Results according to top condition in the future.
This beneficial effect of the invention is: carry out total divisor experimental study by principal element abrasive concentration, Abrasive Particle Size, abrasive material viscosity three being affected to abrasive Flow lapping liquid performance, further investigated abrasive media physical attribute on the impact of abrasive Flow Machining non-rectilinear surface quality, and obtains one group of optimal parameter combination; By collecting embodiment data, arranging, statistical study, heuristic data inherent law, perfect plan analyzes abrasive Flow Machining mathematical model, derive based on the regression equation of abrasive material physical attribute, realize the fixing quantity to abrasive Flow Machining quality, this research has certain academic significance and construction value.
Accompanying drawing explanation
Fig. 1 is institute's using method process flow diagram in the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described, better to understand the present invention.
Embodiment 1
Total divisor design of experiment analysis method of the present invention is the Typical Representative in test design method, is characterized in the combination of the whole levels considering the factor, and total divisor analysis of experiments process generally comprises five large steps, and analysis process as shown in Figure 1.Its concrete steps are as follows:
The first step, model is selected in matching:
" model is selected in matching " refers to according to embodiment object, and a selected mathematical model, this mathematical model generally includes the reciprocation between whole factor and each factor comprised in process of the test, i.e. " full model ".But under normal circumstances, three rank and above reciprocation do not need to consider." full model " mentioned here mainly refers to the second order interaction between each factor main effect and each factor.By analyzing selected model, usually can show which factorial effect is remarkable, which factorial effect is remarkable, when carrying out that model is selected in matching next time, usually only considers the remarkable item of effect, specifically comprises:
1. see the total effect in analysis of variance table: H
0: model is invalid
h
1model is effective: if the p-value < 0.05 of the recurrence item of correspondence, then show to refuse null hypothesis, namely can judge that this model is effective on the whole, if the recurrence item p-value > 0.05 of correspondence, then show to refuse null hypothesis, namely can decision model in general invalid.The reason causing this situation common may be as follows:
(1) embodiment error is too large.First the concept of F statistic is introduced for analyzing the excessive reason of embodiment error, when carrying out ANOVA inspection, by every deviation square compared with stochastic error quadratic sum, the ratio of the two and F statistic.If too large as denominator, then F will be made to diminish, namely stochastic error quadratic sum too conference cause the conclusion that can not get " effect is remarkable ".Certainly, measuring system not accurately also can cause error excessive, at this moment will improve the precision of measuring system, improve measuring system.
(2) test design miss out key factor.Miss out key factor must cause test findings error to increase.
(3) be likely selected cover half type existing problems itself, such as plan lost by model, or data have stronger bending, and model at this moment also can be caused nonsensical.Analysis interpretation will be carried out below to this two problems.
2. see that phenomenon is intended in the mistake in analysis of variance table: this hypothesis checked is: H
0intend without losing
h
1lose plan: in ANOVA analysis result, if lose the p-value > 0.05 intending item correspondence, explanation cannot refuse null hypothesis, namely can judge that plan phenomenon do not lost by this model; Otherwise, illustrate that selected model may miss out critical item, should consider to re-establish model.Losing the basis intending item correspondence is: the difference between first calculated revision test, it can be used as the estimation of test error; The item of disappearance is compared with it with the error sum of squares that (such as three rank and above interaction item) cause, can conclusion be obtained through F inspection.After, will be judged as in analysis result that inapparent item is all classified as stochastic error, whether significantly recalculate mistake plan item.
3. see the bending item in analysis of variance table: this hypothesis checked is: H
0: without bending
h
1: have bending; In ANOVA analysis result, if the p-value > 0.05 of bending item correspondence, then show to refuse null hypothesis, namely can judge that this model does not have buckling phenomenon; Otherwise, illustrate that data are case of bending, and in model, do not have quadratic term, quadratic term should be filled.The foundation that bending item calculates is: calculate the difference between revision test, by its estimation as test error, first three observed readings are got to independent variable, get the embodiment data that high level, low-level and central point are corresponding respectively, then remove linear term, obtain the quadratic sum of quadratic term; Whether quadratic sum and the embodiment error of quadratic term compare, by F test and judge model in bending.
4. total effect coefficient R of matching
2(i.e. R-Sq) and the total effect coefficient R revised
2 adji.e. (R-Sq (adj)).
Can be obtained by the square rooting matrix formula in Regression Analysis Result:
SS
Total＝SS
Model+SS
Error(1)
By considering SS
modelat SS
totalin shared ratio, define R quadratic term (R-Square, i.e. R-Sq):
Obviously, this numerical value is more better close to 1.Easily find out, he has another kind of literary style:
If also regard independent variable as stochastic variable, the related coefficient between them can be derived.And R-Sq be just exactly related coefficient square.Therefore, its definition understands very well.For the situation that independent variable is more, define by identical way, can be understood as " the polynary coefficient of determination ", still represent SS
modelat SS
totalin ratio.Such as, but also have a shortcoming: when independent variable number increases, the independent variable that only increase by is new, whether the effect of this independent variable no matter increased is remarkable, R
2(R-Sq) all can increase, thus evaluate whether should increase this independent variable enter regression equation time, use R
2just be not worth.For this reason, the R revised is introduced
2i.e. R
2 adj, its definition is:
In formula, n is test total degree; P is all effect items (comprising constant term) in regression equation.Coefficient R
2 adj(R-Sq (adj)) is the impact not considering that in regression equation, item number is how many, thus can the quality of judgment models more accurately, R
2 adjclose to 1, numerical value more illustrates that model is better, in actual application, be usually at least greater than 1, be thus easy to draw, R owing to comprising item number p in model
2 adjalways than R
2smaller.Therefore, judge that the quality of two models can judge from R-Sq (adj) and the degree of closeness of R-Sq, the difference of the two is less, illustrates that model is better.In analytic process, originally selected model comprises whole factor usually, i.e. " full model ", usually those inapparent factors are deleted after again model being modified, be referred to as " deleting model ", if delete after the effect inapparent factor leaves out, the value of R-Sq (adj) and R-Sq closer to, illustrate and delete that model is improved than initial model.
5. couple s value or s
2analysis: assuming that the error of observed reading and theoretical model is with 0 for average, with σ
2for distributing just very much of variance.In analysis of variance table, the numerical value σ just of the average deviation quadratic sum (adjMS) that residual error error is corresponding
2unbiased estimator, be designated as square error MSE, and its square root s can be exported by some software after computation in the lump, can think that s value is the estimation of σ.Generally, predicted value being added and subtracted 2 times of s, is namely the fiducial interval of 95% of predicted value.The less explanation model of s value is better obviously.
6. the conspicuousness of every effect: in the most beginning of result of calculation, estimates, in regression coefficient y, to list every effect and assay.By point other inspection to each, can show that some is significant and some is inapparent, it is noted herein that: for a significant higher order term of effect, its lower term comprised is the remarkable item of effect necessarily.Such as, if second order interaction item AC is the remarkable item of effect, then main effect item A and main effect item C also should comprise in a model.
For the analysis of the conspicuousness of every effect, MINITAB software also exports some relational graphs, helps to verify conclusions further.Mainly Pareto effect figure and normal state effect figure.
Judge that the conspicuousness of factorial effect is very intuitively with Pareto effect figure, but it there is an important shortcoming, when that is exactly the t inspection carrying out each effect, first use s
2estimate σ
2come, and usual s
2might not be reliable.By the effect of each factor by lining up sequence from small to large, these effect points are marked in normal probability plot, Here it is normal state effect figure.Usually can think in most factor, to only have a few factors to be effect significant factor, i.e. the sparse principle of so-called effect.Therefore, after the point group those being positioned at middle effect fits to straight line, judge which factor is the significant factor of effect with this straight line as observation standard, observation principle is judged as the remarkable item of effect away from the factor of this straight line, and the factor near this straight line is judged to be effect remarkable item.
Just complete the initial analysis to data in sum, namely complete the task of the first step " model is selected in matching ".
Second step: residual error is diagnosed:
Residual error diagnosis specifically comprises four steps, observes four figures that computing machine exports automatically respectively.
(1) scatter diagram being transverse axis with observed reading order in observation residual plot, observe in scatter diagram, whether each point descends random fluctuation on the horizontal axis.
(2) scatter diagram being transverse axis with response variable match value in observation residual plot, observe in figure, whether residual error remains equal variance, if residual error does not keep equal variance, this figure there will be " funnel-form " or " horn-like ".
(3) observe the test of normality figure of residual error, judge whether residual error distributes by normal distribution law.
(4) observing in residual error take independent variable as the scatter diagram of transverse axis, mainly sees in figure whether there is warp tendency.When loose point is obviously U-shaped or anti-U-shaped bending, this illustrates response variable y, only gets linear term and does not meet the demands, also lack quadratic term or cube item in model, should increase quadratic term or cube item of x, will make models fitting better effects if this independent variable x.
Four figure of residual error diagnosis are all normal then representative models is normal.
3rd step: judgment models is the need of improvement.
The main task of this step is the result according to the first step and second step, and by numerical analysis and residual plot two aspect judgment models the need of improvement, and how model should improve.If model needs to improve the increase should carrying out quadratic term or cube item according to residual plot, in addition, based on the conspicuousness according to each effect, not remarkable item in model is deleted, in a word, find in model, there is the place needing amendment, just return the initial first step.
Through the modification and perfection repeatedly (sometimes only namely obtaining satisfied model through once revising) of first three step, finally determine that is satisfied with a model, this model selected carries out next step and analyzes.
4th step: analysis interpretation model.Mainly contain the content of following three aspects, the requirement of this three aspect, generally can automatically provide in computer software.
(7) each factor main effect figure and interaction figure.Those Summing Factor interaction items selected by confirming further from main effect figure and interaction figure whether really the main effect of remarkable and those factors unchecked and interaction whether genuine remarkable, thus more specifically confirm selected model more intuitively.
(8) contour map, response surface design figure is exported.Contour map and response surface design figure can help to confirm further each independent variable and he they between mutual item be how to affect response variable result.If target is hoped little (hope large or hope order), so how independent variable is arranged, can response variable minimum (maximum or closest with target) be made? in MINITAB software, contour map and the surface chart of every two independents variable combination all can be provided by software automatically.
(9) optimization is realized.Large according to the prestige of particular problem, hope little or hope that order numerically obtains the optimum value in whole scope of embodiments, this numerical value can be provided automatically by MINITAB software.Although the object of embodiment design is selection variables in the factor design stage, in fact, in the first step that DOE analyzes, just can judge which variable is which variable is inapparent significantly, on the basis using these information, optimum value can be obtained." response variable optimizer " that computing machine provides can provide optimum setting automatically.As long as usually set optimal objective again after selected response variable.
5th step: judge whether target reaches: mainly by the desired value of analyses and prediction compared with former embodiment target.If from target still away from, then should consider to arrange new round embodiment, if substantially reach target, then should set demonstration test to guarantee to produce can obtain Expected Results according to top condition in the future.
Embodiment 2: atomizer abrasive Flow Machining total divisor is tested
The factor affecting abrasive Flow lapping liquid performance mainly contains abrasive concentration, Abrasive Particle Size and abrasive material viscosity three physical attributes.The present embodiment for parameter with abrasive concentration, Abrasive Particle Size and abrasive material viscosity, take atomizer as processing object, carries out total divisor experimental study.Mainly for research abrasive concentration, Abrasive Particle Size, abrasive material viscosity how to affect atomizer inside surface A FM crudy, and then guidance configures the lapping liquid having more construction value, use it for the abrasive Flow Machining of non-straight spool, realize the quality control of non-straight spool abrasive Flow Machining.
On the basis of theoretical analysis and experimental study, choose the level of above three parameters, concrete condition is as shown in table 1.
Table 1 atomizer AFM machined parameters and varying level value
First the surface roughness Ra choosing the little internal surface of hole of atomizer is response variable, the factor given according to table 1 and level carry out total divisor test design, by MINITAB factor Software Create total divisor embodiment design table (note: for the ease of representing in MINITAB software, viscosity grade level uses 1 respectively, 0 ,-1 represent).Then choose 12 atomizer parts according to embodiment design table, and complete abrasive Flow Machining test according to testing program, the embodiment data (surface roughness Ra) obtained are inserted in embodiment design table.Total divisor test design table and the test findings of atomizer AFM processing are as shown in table 2.
Table 2 atomizer AFM total divisor test design table
The first seven in table 2 is classified as the form that MINITAB generates automatically, rear row are the numerical value of the surface roughness Ra carrying out testing the aperture of 12 atomizers of rear acquisition according to total divisor test design table, and inserted in MINITAB test design form, next total divisor analysis of experiments is carried out to test findings.
Test findings ANOVA analyzes, and concrete steps are as follows:
The first step: model is selected in matching.First whole alternate item is listed in model.Here comprise abrasive concentration, abrasive size, abrasive material viscosity and second order interaction item abrasive concentration * Abrasive Particle Size, wear particle concentration * abrasive material viscosity, Abrasive Particle Size * abrasive material viscosity between them, notice that this analysis does not comprise third-order interaction effect item.Analyzed selected model by MINITAB software, its result of calculation is as shown in following table 3 and table 4:
The estimation effect of table 3 surfaceness and be
The variance analysis of table 4 surfaceness
Can clearly find out from table 4 surfaceness analysis of variance table (analysis of variance table), in main effect item, p-value is 0.013, be less than 0.05, it is significant, effective for showing the total effect of selected model, and in a bending hurdle, p-value is 0.909, its value is obviously greater than 0.05, and display response variable does not have obvious warp tendency.In mistake plan one hurdle, p-value is 0.955, and its value is obviously greater than 0.05, and the selected model of display does not significantly lose plan to response variable (surfaceness).
Can also see in surfaceness analysis of variance table, the p-value that abrasive concentration is corresponding is 0.009, and the p-value that Abrasive Particle Size is corresponding is 0.011, and the p-value of both correspondence is all less than 0.05; P-value corresponding to abrasive material viscosity is 0.947, and its value is far longer than 0.05; Abrasive concentration is 0.029 with the interactive corresponding p-value of Abrasive Particle Size, and its value is less than 0.05; The p-value that abrasive concentration is corresponding with the reciprocation of abrasive material viscosity is 0.869, and the p-value that Abrasive Particle Size is corresponding with the reciprocation of abrasive material viscosity is 0.206, and the p-value of both correspondence is obviously greater than 0.05.Can be judged by the p-value of above every correspondence, abrasive concentration and Abrasive Particle Size and the reciprocation of the two are the Be very effective item affecting atomizer abrasive Flow Machining.From Pareto figure and the factor normal state effect figure can verify this point equally.
Second step: residual error is diagnosed: observing residual error for observed reading order is whether the scatter diagram of transverse axis is normal.By observing, each point descends random fluctuation at random on the horizontal axis, and without abnormal lifting trend, this figure is normal.Observe residual error whether normal for response variable match value scatter diagram.By observing, the variances such as residual error maintenance, this figure is normal.If variances such as residual error do not keep, this figure there will be " funnel-form " or " horn-like ".Whether the Normal distribution test figure observing residual error is normal.By observing, residual error Normal Distribution can be found out.Comparatively speaking the results contrast of scatter diagram display is coarse, can directly carry out normality inspection to residual error and then obtain assay more accurately.Observe residual error whether normal for the scatter diagram of each independent variable, whether high spot reviews has warp tendency.By observing, do not see there is warp tendency.
3rd step: whether judgment models will be improved.
Find out from residual error diagnosis, model is effective, just in the every effect of inspection, finds that not all independent variable is all active effects item.In three independent variable main effects, factors A (abrasive concentration), factor B (Abrasive Particle Size) effect significantly, factor C (abrasive material viscosity) effect is not remarkable, in three second order interaction items between them, only AB (wear particle concentration * Abrasive Particle Size) is remarkable, and all the other two interaction items are not remarkable.Therefore, model of fit is modified, the remarkable item in selected diagnostic result, again selected model of fit.
The new first step: model is selected in matching.
The inapparent item of effect is deleted for master pattern, re-starts computational analysis.This model again selected comprises factors A (abrasive concentration), factor B (Abrasive Particle Size) and the interaction item AB of the two (abrasive concentration * Abrasive Particle Size).For current selected model, still analyze by the method introduced above and step.Obtain data as shown in table 5 and table 6.
The estimation effect of table 5 surface roughness Ra and coefficient
The variance analysis of table 6 surface roughness Ra
Can be obtained by analysis of variance table, the p-value of main effect item and the mutual item of second order is that 0.001 and 0.010 its value is less than 0.05 and is less than, can judgment models effective, and numerical value is less than the p-value 0.013 of the main effect item in master mould.In this test, the p-value of song error is 0.902, and its value is large more than critical value 0.05, shows that model linear hypothesis is set up substantially.Whether comparison model improves to some extent before and after deleting again below.The estimator two models being calculated R-Sq and R-Sq (adj) and the standard deviation obtained is aggregated into table, and model deletes that the contrast of front and back numerical value is in table 7.
Table 7 full model with delete modelling effect comparison sheet
As can be seen from Table 7, after carrying out model optimization, the numerical value that R-Sq is corresponding has reduction by a small margin, in this test, be reduced to 0.8951 by 0.9336, then see whether the R-Sq (adj) of correction increases, and in this test, R-Sq (adj) brings up to 0.8352 by 0.8173, it can thus be appreciated that model delete the numerical value of rear R-Sq and R-Sq (adj) closer to, illustrate leave out those effects significantly Xiang Xianghou model be really improved.And the reduction of s also demonstrates model obtains optimization, the regression effect of system is better.
New two steps, residual error is diagnosed.
Residual error diagnosis is still carried out according to four steps of regulation.
(1) observe the scatter diagram of residual error for observed reading order, in this test, this figure is normal.
(2) observe residual error for the scatter diagram of response variable match value, can find out the variances such as residual error remains by this figure, this figure is without exception.
(3) observe the standardized normal effect figure of residual error, visible residual error meets normal distribution.
(4) observe residual error for the scatter diagram being transverse axis with each independent variable, in observation figure, whether there is warp tendency.By observing, all there is not warp tendency in this three width figure.Residual error is normal to the scatter diagram become separately.
New three steps: whether judgment models will be improved.
By above-mentioned analysis, assert that model does not need to be optimized again, according to the numerical value that result of calculation provides, the encode regression equation finally determined can be write out.
The estimation effect of table 8 surface roughness Ra and coefficient (after optimizing)
Coefficient in formula 5 is by the estimation effect of table 8 surface roughness Ra and coefficient table gained, and 0.6508 ,-0.1015,0.096 and-0.0712 is respectively constant, coefficient corresponding to A (abrasive concentration), B (Abrasive Particle Size) and AB (abrasive concentration * Abrasive Particle Size).
in the central value 8%, 2 of 8 height two concentration levels represented selected in the present embodiment be difference 2% between varying level.
in like manner, 8 represent 8 μm, and be the central value of the selected Abrasive Particle Size height of this test two levels, 2 is also the difference 2 μm between varying level.
The numerical value of the surfaceness that can obtain under can calculating the embodiment condition of different abrasive concentration and different Abrasive Particle Size by this regression equation.
4th step: analysis interpretation model.
For selected model, export more graphical information by MINITAB software, and carry out detailed analysis interpretation.
(1) export the main effect figure of each factor, interaction figure, and provide significant explanation.Factors A (abrasive concentration) and factor B (Abrasive Particle Size), impact for response variable (surface roughness Ra) is significant really, and factor C (abrasive material viscosity) impact on response variable is inapparent really.And it can also be seen that, for making the value of surface roughness Ra less, abrasive concentration should be allowed large as far as possible, and Abrasive Particle Size is little as far as possible.The impact of reciprocation on response variable (surface roughness Ra) of factors A (abrasive concentration) and factor B (Abrasive Particle Size) is significant (two bar line is very not parallel) really, and the impact of other interactions on response variable (surface roughness Ra) is inapparent (two bar line is almost parallel) really.
(2) level line, response surface design figure etc. is exported.The main effect of abrasive concentration and Abrasive Particle Size and interaction are that very significant (level line is very bending for the impact of response variable really, it is very serious that curved surface departs from plane), for making surfaceness value less, Abrasive Particle Size should be allowed to reduce, and abrasive concentration is larger as far as possible.
(3) optimization is realized.In this test, response variable is surfaceness, belongs to the optimization to " hoping little " characteristic model.Arranged by MINITAB software.At this moment, in target (goal) setting to optimum, get and minimize, in setting window, only need fill in " upper end " and " target " two, and " lower end " is left blank.Get " upper end "=0.8 μm (this value achieves in the test done), get " target "=0.4 μm (this value fails to reach in the test done, and is the target wanting to reach).Usually reach optimum problem and be converted into solving response variable Y and solve a Possibility-Satisfactory Degree d (0≤d≤1) craving for function and reach maximum problem, what this craved for function specifically arranges computer-chronograph according to " hope large ", " hoping little ", " prestige order " three kinds of different situations Lookup protocols, its details need not be bothered about, after Computer Automatic Search, the minimum result of calculated value can be obtained.
When factors A (abrasive concentration) gets 10% (maximal value), factor B (Abrasive Particle Size) is got 6 μm (minimum value), and surfaceness will reach average minimum 0.5345 μm.Here also output d value, function value is craved in the representative of d value, and when result is more close to target setting, d value more levels off to 1, this routine result d=0.68875, and this is 4 μm according to minimum value ideal, and when the setting of minimum value is not identical, the result of d also can be different.
Observe initial embodiment result can see, in the 6th embodiment, (abrasive concentration is 10%, Abrasive Particle Size is 6 μm), surfaceness reaches 0.496, the optimal value why calculated is not as good as the result obtained, this is because embodiment always has error existence, have contingency in the result of No. 6 embodiment, numerical value is less than normal.
5th step: judge whether target reaches
Judge in the present embodiment that roughness reaches target, test can be terminated.Demonstration test is done on the parameter level best of breed basis that next will obtain in analysis, guarantees that such parameter combinations can obtain minimum surfaceness in reality processing, guarantee that it may be used for Instructing manufacture.
Next, in optimum factor level, several times demonstration test is done at place, and the corresponding Output rusults of test calculated each time should drop within the scope of what kind of, and the mean value calculating m test drops within the scope of what, if the mean value of m test drops within the scope of precalculated average, then represent that model is correct, all are normal, predict the outcome credible.
The determination mode of estimation range is predicted by MINITAB software, inputs the value of main gene in hurdle successively, just can obtain predicted value and forecast interval in " factor ".The match value standard deviation at match value, predicted value place can be obtained, the fiducial interval of the regression result at predicted value place, the fiducial interval of the single predicted value at predicted value place, calculate following numerical value (table 9) by Computer Analysis:
Table 9
What 95% fiducial interval showed is the fiducial interval that regression equation is put, this due to regression equation coefficient be estimate based on sample observations, it will inevitably have error, and the error of regression coefficient will inevitably cause the error of predicted value on regression equation.Can be understood as this interval, according to the fiducial range arranging 95% of the unlimited theoretical average that will obtain that reruns down repeatedly of this independent variable, this value can write on final report as the forecast of the result improved.
Based on the fiducial interval of the point that what 95% forecast interval showed is on above-mentioned regression equation, add that the variance that observed reading has is σ
2fluctuation and the fiducial interval provided.Here suppose that the variance fluctuated is the constant σ not relying on independent variable position
2, and obtained its unbiased estimator MSE, here, forecast interval is the scope that will will fall into when being used as one-time authentication test, can for when doing demonstration test.If obtain 95% fiducial interval of m (such as m=3 or m=5) observed reading, then can only write macro instruction under MINITAB condition, or directly use hand computation.The mean value of m observed reading 95% fiducial interval, its computing formula is:
In formula, n is the total degree of test: p is the item number (constant term will count) comprised in final mask; M is the number of times of demonstration test.SE of Fits is the standard error of the match value exported when regression equation predicted value; MSE is the MS item of the error exported in analysis of variance table, namely σ
2unbiased estimator.During certain m=1.This fiducial interval is exactly 95%PI; When m is tending towards infinity, this fiducial interval is exactly 95%CI; When needing 95% fiducial interval obtaining m (such as m=3 or m=5) observed reading, as long as bring the numerical value of corresponding m into.
Four demonstration tests are done, so n=12, p=3, m=4, SEs of Fit=0.040583, MSE=0.0032940 (see ANOVA table) in formula for this test supposition.The t fractile looking into 8 degree of freedom can obtain SEs of Fit
The formula of variation radius is as follows:
0.00569 of variation radius calculation
Therefore known, 95% fiducial interval of the mean value of four observed readings is
The above is the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.
Claims (1)
1. an atomizer abrasive Flow Machining total divisor test analysis method, is characterized in that: concrete steps are as follows:
The first step, model is selected in matching: specifically comprise:
(1) the total effect in analysis of variance table is seen: H
0: model is invalid
h
1model is effective: if the p-value < 0.05 of the recurrence item of correspondence, then show to refuse null hypothesis, namely can judge that this model is effective on the whole, if the recurrence item p-value > 0.05 of correspondence, then show to refuse null hypothesis, namely can decision model in general invalid;
(2) see that phenomenon is intended in the mistake in analysis of variance table: this hypothesis checked is: H
0intend without losing
h
1lose plan: in the results of analysis of variance, if lose the p-value > 0.05 intending item correspondence, explanation cannot refuse null hypothesis, namely can judge that plan phenomenon do not lost by this model; Otherwise, illustrate that selected model may miss out critical item, should consider to re-establish model; Losing the basis intending item correspondence is: the difference between first calculated revision test, it can be used as the estimation of test error; The item of disappearance is compared with it with caused error sum of squares, can conclusion be obtained through F inspection; After, will be judged as in analysis result that inapparent item is all classified as stochastic error, whether significantly recalculate mistake plan item;
(3) the bending item in analysis of variance table is seen: this hypothesis checked is: H
0: without bending
h
1: have bending; In ANOVA analysis result, if the p-value > 0.05 of bending item correspondence, then show to refuse null hypothesis, namely can judge that this model does not have buckling phenomenon; Otherwise, illustrate that data are case of bending, and in model, do not have quadratic term, quadratic term should be filled; The foundation that bending item calculates is: calculate the difference between revision test, by its estimation as test error, first three observed readings are got to independent variable, get the embodiment data that high level, low-level and central point are corresponding respectively, then remove linear term, obtain the quadratic sum of quadratic term; Whether quadratic sum and the embodiment error of quadratic term compare, by F test and judge model in bending;
(4) total effect coefficient R of matching
2and the total effect coefficient R revised
2adj;
(5) to s value or s
2analysis: assuming that the error of observed reading and theoretical model is with 0 for average, with σ
2for distributing just very much of variance; In analysis of variance table, the numerical value σ just of the average deviation quadratic sum that residual error error is corresponding
2unbiased estimator, be designated as square error MSE, and its square root s can be exported by some software after computation in the lump, can think that s value is the estimation of σ; Generally, predicted value being added and subtracted 2 times of s, is namely the fiducial interval of 95% of predicted value; The less explanation model of s value is better;
(6) conspicuousness of every effect: in the most beginning of result of calculation, estimates, in regression coefficient y, to list every effect and assay; By point other inspection to each, can show that some is significant and some is inapparent, it is noted herein that: for a significant higher order term of effect, its lower term comprised necessarily remarkable item of effect; For the analysis of the conspicuousness of every effect, MINITAB software also exports some relational graphs, helps to verify conclusions further; Mainly Pareto effect figure and normal state effect figure;
Second step: residual error is diagnosed: residual error diagnosis specifically comprises four steps, observe four figures that computing machine exports automatically respectively:
(1) scatter diagram being transverse axis with observed reading order in observation residual plot, observe in scatter diagram, whether each point descends random fluctuation on the horizontal axis;
(2) scatter diagram being transverse axis with response variable match value in observation residual plot, observe in figure, whether residual error remains equal variance, if residual error does not keep equal variance, this figure there will be " funnel-form " or " horn-like ";
(3) observe the test of normality figure of residual error, judge whether residual error distributes by normal distribution law;
(4) observing in residual error take independent variable as the scatter diagram of transverse axis, mainly sees in figure whether there is warp tendency; When loose point is obviously U-shaped or anti-U-shaped bending, this illustrates response variable y, only gets linear term and does not meet the demands, also lack quadratic term or cube item in model, should increase quadratic term or cube item of x, will make models fitting better effects if this independent variable x;
Four figure of residual error diagnosis are all normal then representative models is normal;
3rd step: judgment models is the need of improvement:
The main task of this step is the result according to the first step and second step, and by numerical analysis and residual plot two aspect judgment models the need of improvement, and how model should improve; If model needs to improve the increase should carrying out quadratic term or cube item according to residual plot, in addition, based on the conspicuousness according to each effect, not remarkable item in model is deleted, in a word, find in model, there is the place needing amendment, just return the initial first step;
Through the modification and perfection repeatedly of first three step, finally determine that is satisfied with a model, this model selected carries out next step and analyzes;
4th step: analysis interpretation model: the content mainly containing following three aspects, the requirement of this three aspect, generally can automatically provide in computer software:
(1) each factor main effect figure and interaction figure: those Summing Factor interaction items selected by confirming further from main effect figure and interaction figure whether really the main effect of remarkable and those factors unchecked and interaction whether genuine remarkable, thus more specifically confirm selected model more intuitively;
(2) export contour map, response surface design figure: contour map and response surface design figure can help to confirm further each independent variable and he they between mutual item be how to affect response variable result;
(3) realize optimization: large according to the prestige of particular problem, hope little or hope that order numerically obtains the optimum value in whole scope of embodiments, this numerical value can be provided automatically by MINITAB software; Although the object of embodiment design is selection variables in the factor design stage, in fact, in the first step that DOE analyzes, just can judge which variable is which variable is inapparent significantly, on the basis using these information, optimum value can be obtained; " response variable optimizer " that computing machine provides can provide optimum setting automatically; As long as usually set optimal objective again after selected response variable;
5th step: judge whether target reaches: mainly by the desired value of analyses and prediction compared with former embodiment target; If from target still away from, then should consider to arrange new round embodiment, if substantially reach target, then should set demonstration test to guarantee to produce can obtain Expected Results according to top condition in the future.
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