Cutting tool tatty slants analysis of least square regression and build a model

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In process of metallic cutting treatment, of cutting tool wear away with damaged it is the main factor that affects quality of the surface that be mixed by precision of treatment spare parts, serious cutting tool wears away to still can cause cutting flutter, attaint machine tool, knife and tool and workpiece. Normally, of cutting tool wear away on the two contacts division that produces in cutting tool and workpiece. Below higher cutting temperature, face of the knife before cutting tool is cutting bits to shed what outdated arises to be being mixed to pressure grind the conference below action appears rub caustic, face of the knife before calling wears away (crescent moon wears away depression) ; The surface already machined with workpiece on face of the knife after the cutting tool when cutting is machined grind after the generation on knife face wears away belt, the face of the knife after be that say wears away. In machining process and academic experiment research actually, main later knife face wears away the wear extent VB on the belt is worth those who measure cutting tool to wear away degree. Cutting cutting tool wears away the mechanism of generation is more complex, influencing factor is more, build an accurate and applicable analysis model very hard, accordingly, use more undertake analyse and building a model by experimental data, commonly used method has use least square to plan to close build explicit model, or use artificial nerve network to undertake study training building concealed type model. These methods are put in a few defect severally, classical least square regression plans to add up to a method to overcome variable multiple dependency hard, and the explanatory sex to the model needs artificial nerve network, in addition, these methods do not have variable to choose a function. The article considers to use slant PLSR(Partial Least-squares Regression) of least square regression is academic, wear away to cutting process cutting tool the method that experimental data has analyse and building a model. This method can undertake variable is chosen, overcome the multiple dependency between variable effectively, build relatively ideal cutting tool tatty multivariate recursive model, still have better solubility. 1 slant principle of least square regression is summarized those who consider algorithm is run-of-mill, of will much because variable is right much independent variable slant principle of least square regression and algorithm, make as follows summarize. Because of,be opposite variable Y: With independent variable X: Concern to study the statistic between Y and X, it is above all in independent variable X, extract advocate composition T1(T1 is X1, x2, ... , the linear of Xp combines) , in the meantime, because variable Y is medium,be in, extract advocate composition U1(u1 is Y1, y2, ... , the linear of Yq combines) . Slant analysis of least square regression is extracting these two advocate when composition, be like below two requirements: T1 and U1 should as far as possible the earth extracts them the mutation information in respective primary variable system; The relevant degree of T1 and U1 can be achieved the biggest. These two ask to make clear, t1 and U1 should as far as possible good land is integrated their respective primary variable system, in the meantime, independent variable advocate because of,composition T1 is opposite variable advocate the explanatory sex of composition U1 can be achieved again the biggest. Be in the first advocate after composition T1 and U1 are come out by extraction, carry out the regression of the X regression to T1 and Y to T1 respectively. If return to equation to had achieved satisfactory precision, algorithmic stop; Otherwise, the leftover information after be being explained the leftover information after using X to be explained by T1 and Y by T1 undertakes the 2nd round advocate composition extraction. Relapse so, till the precision that arrives at a requirement continuously. If extracted M finally in all to X advocate composition T1, t2, ... , t M, slant least square regression will is opposite through carrying out Yk T1, t2, ... , the regression of Tm, express as finally Yk about former variable X1, x2, ... , the recursive equation of Xp, among them, k ＝ 1, 2, ... , q. According to afore-mentioned principles, slant the algorithm that least square returns to but reduce is as follows measure. standardization of X of primitive observation data, Y, the E0 of independent variable matrix after getting standardizing and because of variable matrix F0. Beg main shaft Wi, Ci and advocate composition Ti, Ui, use following iteration algorithm (to simplify for the purpose of, skip suffix I) : Take U to list Yj for some, e=E0, f=F0; To E data piece: WT= UTE/uTu WTnew=wTold/ | | Wold | | T=Ew/wTw is right F data piece: CT=tTF/tTt CTnew=cTold/ | | Cnew | | U=Fc/cTc examination is astringent, if be in D.

Pace calculative T is worth or contented computation precision asks, turn I.

, otherwise, turn to B.

; PT=tTx/tTt PTnew=rTold/ | | Pnew | | Tnew=told/ | | Told | | WTnew=wTold/ | | Pold | | Computational incomplete differs Eres and Fres: Eres=E-tpTFres=F-trT makes E=Eres, f=Fres. Return B.

Pace, undertake main shaft is mixed falling one round advocate the computation of composition; If be being calculated M the algorithm after composition is stopped, have E0=t1p1T+t2p2T+ ... + TmpmTF0=t1r1T+t2r2T+ ... + TmrmT because T1, t2, ... , tm all can express to be E01, e02, ... , the linear of E0m is combined, because this can get Y*=F0 the recursive equation form about Xj*=E0j: Y*=a1x1*+a2x2*+ ... + the Fm in Amxm*+Fm type is differred for incomplete. According to standardization go against a process, y* reductive for Y. Express V(m/min) Fr(mm/min) A(mm) 1 350 300 2 of serial number of cutting experiment condition.

0 2 250 300 2.

0 3 150 300 2.

0 4 350 150 2.

0 5 250 150 2.

0 6 150 150 2.

0 7 325 240 1.

0 8 325 120 1.

Of 02 tests data and its analysis and data of the test that build a model getting tatty of cutting process cutting tool to concern data is the test has on numerical control lathe and obtain, cutting tool material is hard alloy (Sandvik Coromat Co.

TNMG16-04-08-QM) , workpiece is makings of P20 mould steel bar, by installation the Kistler trends on tool carrier measures power instrument to measure treatment in real time in the process 3 to cutting component of force, cutting component of force is handled by intelligent cutting module and protect existence hard disk to go up, every cutting is certain the journey (namely after feed is apart from S) , of cutting tool wear away to value VB determines by cutting tool microscope and be recorded. Below different cutting condition, had test of much group cutting. Experimental condition is shown like right watch. Below the cutting condition that shows in right watch, had turning test, the experiment is measured so that cutting component of force is worth Fx, Fy, Fz, the graph is shown 1 times all be worth a curve to cutting component of force for X, VB is like knife face wear extent after the graph shows a picture 2 times measured value of Fx of 1 cutting component of force pursues 2 hind knife face wears away PLSR analysis and variable choose tatty of measured value cutting tool to machine a process in cutting in, because element of tatty of influence cutting tool is more, the filtration of independent variable should undertake above all when building a model. PLSR method is used to undertake variable is chosen in this research. With F of cutting speed V, feed, 3 to cutting component of force all be worth ratio of Fx, Fy and Fz, component of force 8 variable such as Ryx=Fx/Fx, Rzx=Fz/Fx and cutting deepness A serve as independent variable, make variable value umbriferous VIP index and factor analysis, reach VIP index pursues (graph 3) and graph of factor load Ai (graph 4) . Graph the VIP graph of 3 variable pursues graph of VIP of graph of 4 factor load and Ai graph show, speed of variable F(feed) with deepness of variable A(cutting) VIP value and A2 of load factor coefficient and A8 are opposite at wanting for other variable small much, because this is in the model, negligible. This one result is right the import that in machining a process actually, online to cutting tool tatty real time estimates it is very important to be had with monitoring, because be in treatment process, cutting deepness can produce change as the change of the profile of workpiece or mental allowance, and feed is crash because the long attune of handlers also won't maintain,spend a likelihood for constant. According to afore-mentioned analysises, when building a model but purify variable F and variable A. More thorough cutting is mechanical wear away with cutting tool mechanism analysis makes clear, after introducing cutting force ratio, negligible cutting deepness and feed are affected to cutting tool tatty. Accordingly, PLSR analyses be photograph be identical as a result to the analysis of experimental data and theory, this shows PLSR wears away to cutting tool the analysis of influencing factor has the explanation that agrees with cutting theory. Can think, with Fx of component of force of cutting speed V, cutting, Fy, Fz all Ryx of value, ratio and RRzx serve as independent variable, wear away with cutting tool because of,VB* value is variable, building model and online forecast to cutting tool tatty is better choice. Accordingly, the experimental data below the cutting requirement that model of tatty of cutting process cutting tool can represent to be PLS of tatty of VB*=aa1V*+a2Fx*+a3Fy*+a4Fz*+a5Ryx*+a6Rzx* cutting tool to return to a model to be listed to expressing 1, according to afore-mentioned analysises, serve as independent variable with V, Fx, Fy, Fz, Ryx, Rzx, because of,VB * serves as variable, undertake least square returns to iteration computation slanting, get VB*=0.

065V*+0.

036Fx*+0.

363Fy*+0.

151Fz*+0.

261Ryx*+0.

4Rzx* (1) goes against what VB* presses standardization the process, beg a VB namely. 3 data desired result and online forecast imitate use desired result of the data that build a model by type (1) is denotive tatty of cutting process cutting tool slants least square returns to a model, the experimental data below the cutting requirement that covers with data to establishing modular institute undertakes desired result is calculated, get the computation of VB is worth is opposite, graph 5 gave out computation is worth VB ' be worth VB contrast with actual measurement come loose bit of graph. Can see, most computation value and actual measurement value are be identical. Graph the desired result result of data of test of 5 pairs of parts pursues online forecast imitate is result of imitate of 6 online forecast examine model (the circumstance that whether 1) applies to independent variable new measured value, use the independent variable data that measures below new disparate test requirement, imitate is actual in cutting process circumstance of tatty of online estimation cutting tool. VB of imitate estimation result ' be worth VB contrast with actual measurement come loose bit of graphic representation at graph 6. Pursue knowable by this, what fall to proposing the cutting requirement that did not cover when the model is new measure example place, by type (the it is better to return to a model to still can be obtained estimation that 1) gives out forecasts a value. 4 conclusion slant PLSR of least square regression is the statistical regression method that by data example has one kind building a model. The analysis that this method can use at wear extent of the cutting tool in cutting process and build a model, imitate is online the forecast of online real time that forecast makes clear to this method machines applicable condition of the cutting tool in the process at cutting. Use slant when least square returns to a method, after if choose appropriate variable,be being combined, because of,make variable and independent variable the first advocate when better linear dependency is being shown between composition, slant model of least square regression can obtain taller precision and reliability, and the expression of PLSR model is understood simply, to cutting each element is right in the process the influence of the wear extent of cutting tool has very strong explanation sense, can announce because of,go out the underlying concern between variable and independent variable, pass graphic representation, can be analysed clearly and choose proper independent variable, this is the characteristic that other undertakes building modular method is likened to hard by data; Measure a consideration from the consideration that advocates model and forecast, PLSR builds a model to be able to use direct numeration, also can use iteration algorithm, its computation volume is minor, the computational amount that forecast has after building a model is very small more, this is online to considering to grow real time further the port with build model and model to amend algorithm to have very principal. The place on put together is narrated, slant method of least square regression is sex of a kind of simple and reliable, explanation hidebound of strong, computation establishs modular method, of condition of the cutting tool in applying at cutting process build model, analysis and forecast, can achieve more satisfactory result. CNC Milling CNC Machining