Turning cutting force the faintness of uncertainty, gray is forecasted

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Summary: Forecast the uncertainty range of turning force for ration, be based on theory of symmetrical and ambiguous number, linear programming and gray theory, offerred power of a kind of cutting the faintness of uncertainty, gray forecasts a method, built the turning power that is used at getting evaluation data to survey a system with test and verify the effectiveness of this method. Forecast the comparative analysis with actual measurement result to make clear: To given cutting condition, calculating a value is a limits of alterable force, is not to use a of traditional method earning to define a point, actual measurement force falls in with minor opposite error forecast range inside. The uncertainty phenomenon that 1 foreword appears in treatment process already became an outstanding issue. Cutting force regards process feature as one of quantities, its uncertainty comes from a lot of process elements (include to be able to be quantified, difficult quantify element and can forecast, difficult forecast element) . If oversight is difficult,be quantified and difficult the impact that calculates an element, can think the uncertainty of cutting force basically results from approximately two respects: The effect that real power measures a system (temperature of the average in including demarcate method, drift to compensate method, software and round whole method, appearance that measure power the influence that wait) the influence that changes with process parameter (include cutting dosage the influence) of 3 element. The common estimation method to systematic uncertainty has probability distribution law, ambiguous estimation technique and least square method to wait, but the article that sees about machining a process uncertainty studies up to now or reportorial amount to are not much. To evaluate the uncertainty of cutting force, the consideration measures error of parameter of cutting of demarcate sum of errors, return to law and error compensation theory according to least square, investigator offerred TLSRM model, the uncertainty that this model generates forecasts a result is one is worth certainly and not be a limits; Change of consideration grinding parameter and oversight measure demarcate error effect of the system, be based on ambiguous theory and linear programming theory, concerned document put forward a faintness to forecast model GFPM, and uncertainty forecasts the grinding power that this model produces is and rather than of a limits as a result a certain value. Faintness forecasts model GFPM to use interval form to forecast and evaluate the uncertainty of grinding force, the angle that carries out from the project looks, want to decide than forecasting the drop is more significant. But the opposite error that model GFPM uncertainty forecasts is bigger still. To study this issue further, the author notices gray theory is good at the uncertainty at estimation random system, try to build a kind of faintness consequently, gray forecasts a method, apply its at turning force uncertainty is forecasted. For the means that place of test and verify offers, the author still built strength of a turning testing system. 2 turning force the faintness of uncertainty, gray forecasts principle turning in, advocate the experience maths model of cutting force can be conveyed in be Fz=Cz(ap)x(f)y(1) type, ap is cutting deepness (Mm) , f is feed (Mm/r) , x and Y are an index, cz is coefficient. To type (1) takes logarithm, can get Log(Fz)=log(Cz)+xlog(ap)+ylog(f)(2) to make: Y=log(Fz) , b0=log(Cz) , b1=x, x1=log(ap) , b2=y, x2=log(f) , era enters type (linear model is trenchant form is 2) Y=b0+b1X1+b2X2(3) defines type (the ambiguous form of 3) correspondence is the faintness that symmetrical triangle form chooses here subject spend function. The center that establishs triangular base and width are C and W respectively, symmetrical faintness counts expression to be Y(Xp)=[C(Xp) , w(Xp)] , a0=[C0, w0] , a1=[C1, w1] , a2=[C2, w2] . Trenchant variable is X1p=log(ap)p, x2p=log(f)p(p expresses experiment code, and P=1, 2, 3, ... , n) . To make the measured value of force falls in type (4) earning forecasts interval inside, the width Wi the sum that and symmetrization blurs counts is the smallest, ought to satisfy the following linear programming to concern: Program goal is Min of ∑ W(Xp) → .

(5) tie condition is type of C(Xp)-(1-h)W(Xp) (7) of ≥ of Log(Fz)p ≤ C(Xp)+(1-h)W(Xp)(6)log(Fz)p in, w(Xp)=W0+W1X1p+W2X2p, c(Xp)=C0+C1X1p+C2X2p, width Wi ≥ 0, and I=0 of suffix of 0(of central Ci ≥ , 1, 2) . Ambiguous and subject spend H to satisfy 0<h<1, log(Fz)p is the logarithm of actual measurement force to be worth. Considering feed 0<f<1, for computation of convenient process designing, often take X1p=log(10mf)p and take M ≥ 2. In addition, type (4) ～ (7) can popularize other cutting feature to measure logically (wait like cutting temperature) build a model. In seek a form (the ambiguous number Y(Xp)=[C(Xp) in 4) , after W(Xp)] , reassume antilogarithm, can gain turning strength of uncertainty forecast interval. The basis is given cutting parameter limits, arrangement surveys a test one group, experiment number is P=1, 2, ... , n. To P survey a test, measure real cutting force value; Type takes the place of corresponding cutting parameter in the meantime (4) ～ (7) , so that gain cutting strength,the faintness of uncertainty forecasts interval; Whether does the actual measurement value that inspects cutting force again fall in forecast range inside. Already some research make clear as a result, the faintness that above describes forecasts a model to have following features: It is better to should get forecast a result, the data example that builds a model is more, jump over satisfaction in the output of model of less than of limits of the data that build a model, but occupy in the number that build a model model output is more dissatisfactory beyond limits. And gray gather theory is good at at forecasting uncertainty, and the problem that can solve faintness to forecast a model to exist. Be based on type (4) , assume the output alignment of ambiguous model is: EY={Y(Xp)}={[Cp, wp]}={[Yu(p) , ys(p)]} among them Yu(p)=(Cp-Wp) , ys(p)=(Cp+Wp) , and P=1, 2, ... , n. Single out Q(q<n) the gray that data regards cutting force as uncertainty forecasts primitive data alignment, namely Yu0={Yu0(1) , yu0(2) , ... , yu0(j) , ... , yu0(q)}Ys0={Ys0(1) , ys0(2) , ... , ys0(j) , ... , ys0(q)} among them J=1, 2, ... , q<n. To alignment Yu0 and Ys0, their cumulative generate alignment to be defined respectively for Yu1={Yu1(1) , ... , yu1(j) , ... , yu1(q)}Ys1={Ys1(1) , ... , ys1(j) , ... , ys1(q)} among them J=1, 2, ... , q<n. Elemental Yu1(j) and Ys1(j) expression are Yk1(j)= ∑ Yk0(i)(8) among them J=1, 2, ... , q<n, k=u or S. To alignment Yu1 and Ys1, their Xiang Linping all generates cent to fasten a definition to be Zu1={Zu1(2) , ... , zu1(i) , ... , zu1(q)}(i=2, ... , q<n)Zs1={Zs1(2) , ... , zs1(i) , ... , zs1(q)} among them, elemental Zu1(i) and Zs1(i) can be conveyed for Zk1(i)=0.

5Yk1(i)+0.

5Yk1(i-1)(k=u or S) hypothesis list vector Y=[Yk0(2) , yk0(3) , ... , yk0(q)]T, and matrix B definition is B=[-Zk1(2) , 1; - Zk1(3) , 1; ... ; - Zk1(q) , the estimation value of the parameter A in 1](k=u or DYk1/dt+aYk1(t)=b of equation of S) gray differential and B is certainly: [A, type of B]T=(BTB)-1 BTY(9) basis (8) , have Yk1(0)=Yk0(1) . The solution of gray differential equation is Yk1(1)=Yk0(1)(10a)Yk1(i)=[Yk0(1)-b/a]exp[-a(i-1)]+b/a(10b) type in, i=2, 3, ... , q. Type (the imitate alignment Yk1 that 10) can use at begging Yk1. Accordingly, the imitate alignment Yk0 of Yk0 can be Yk0(1)=Yk0(1)(11a)Yk0(i)=Yk1(i)-Yk1(i-1)(11b) certainly among them I=2, 3, ... , q; K=u or S. I ≤ Q is used at the imitate of original series Yu0 and Ys0; I>q is used at cutting force uncertainty is forecasted. Produce the expected result of test of check of 3 cutting force expresses 1 testing system main component component explains 1 measure sensor resistance strain type voltage of resistance strain type of YD-4A of 2 signal amplifier magnifies 3 numbers measure an instrument 12 A/D change card 4 detect software uses C++ and MASM language development 5 collect parameter sampling frequency; Example 586 personal computer express 10006 computers of 500 ～ experiment of 2 turning force records No.

F(mm/r) of feed of cutting deepness Ap(mm) advocate cutting force Fz(N)120.

1439220.

2878320.

31129420.

41443520.

Condition of produce the expected result of test of check of 51756 cutting force blurs for test and verify, the effectiveness that gray forecasts a method, built cutting strength testing system, build model and evaluation data in order to get. The main component of testing system sees a table 1. Other experiment condition includes: Workpiece material 45 steel (normalizing processing, hardness HB187) , workpiece diameter 81mm; CA6140 lathe, 380r/min of main shaft rotate speed; Cutting speed 96m/min; Cutting tool of YT15 hard alloy. Cutting force experiment and detect be based on afore-mentioned cutting force check to check check condition and watch parameter of 2 rows cutting undertakes cutting force experiments, detect cutting force as a result the record is in watch 2 in. 4 forecast and the faintness of uncertainty returns to force of experiment evaluation cutting model basis type (4) ～ (7) , with the watch 2 in full data has cutting power uncertainty faintness builds a model (considering in the data that build a model faintness estimates poorer) beyond limits. To facilitate process designing is calculated, your M=2 and X1p=log(10mf)p. Watch 3 listed the faintness of uncertainty estimates cutting force result, corresponding ambiguous regression model is type of Y(Xp)=[logFz]p=A0+A1 [log(ap)]p+A2 [log(100f)]p in, a0=[1.

272603, 0.

1092808] , a1=[0.

8845206, 0] , a2=[0.

856115, 0] . Ambiguous and subject spend H=0.

5. Opposite error U(or S) definition estimate a value for =(- measured value) / measured value expresses 3 turning force uncertainty faintness estimates result No.

Faintness of actual measurement force estimates S(%)1439[415 of upper limit of floor level U(%) , 516]-5.

5+17.

52878[749, 932]-14.

7+6.

2031129[1063, 1324]-5.

8+17.

341443[1363, 1696]-5.

5+17.

551756[1646, 2047]-6.

35+16.

6 watches 4 turning force uncertainty is ambiguous, gray is forecasted (the partial information model that contains 3 data that build a model) No.

Actual measurement force is ambiguous, gray forecasts S(%)1439[415 of upper limit of floor level U(%) .

00, 516.

00]-5.

5+17.

52878[740.

10, 920.

80]-15.

7+4.

931129[1046.

6, 1303.

4]-7.

3+15.

441443[1480.

1, 1845.

1]+2.

6+27.

951756[2093.

2, 2611.

8]+19.

2+48.

7 watches 5 turning force uncertainty is ambiguous, gray is forecasted (the new information model that contains 4 data that build a model) No.

Actual measurement force is ambiguous, gray forecasts S(%)1439[415 of upper limit of floor level U(%) .

00, 516.

00]-5.

5+17.

52878[765.

60, 953.

30]-12.

8+8.

531129[1020.

6, 1270.

5]-9.

6+12.

541443[1360.

4, 1693.

2]-5.

7+17.

351756[1813.

5, 2256.

6]+3.

3+28.

5 watches 6 turning force uncertainty is ambiguous, gray is forecasted (the metabolic model that contains 3 data that build a model) No.

Actual measurement force is ambiguous, gray forecasts S(%)2878[749 of upper limit of floor level U(%) .

00, 932.

00]-14.

7+6.

231129[1056.

9, 1316.

4]-6.

4+16.

641443[1353.

4, 1684.

2]-6.

2+16.

751756[1733.

2, 2154.

6]-1.

3+22.

7 turning force the faintness of uncertainty, gray forecasts a choice to express 3 in No.

The data of 3 uses 1 ～ at faintness, gray is forecasted build a model, criterion turning force the faintness of uncertainty, if the watch is shown 4 times,gray forecasts a result, among them data No.

3 correspondence of 1 ～ at faintness, the imitate that gray builds modular data is worth (the data that build a model comes from faintness to estimate data No.

1 ～ 3) , and data No.

4 ～ 5 express faintness, gray establishs modular data range besides calculate a value. In addition, the parameter in gray differential equation is certainly [As, bs]=[-0.

3475, 590.

7376][au, bu]=[-0.

3466, 475.

3764] calculates a value for =(relative to error definition - measured value) / measured value chooses to express 3 medium data No.

1 ～ 4 use at faintness, gray is forecasted build a model, turning force uncertainty blurs, gray forecasts result rank to express 5, among them data No.

4 correspondence of 1 ～ at faintness, the imitate that gray builds modular data is worth (the data that build a model comes from faintness to estimate data No.

1 ～ 4) , and data No.

5 express faintness, gray establishs modular data range besides forecast. The parameter in gray differential equation is certainly [As, bs]=[-0.

2872, 674.

6824][au, bu]=[-0.

2874, 541.

5835] chooses to express 3 medium data No.

2 ～ 4 use at faintness, gray is forecasted build a model, criterion turning force uncertainty is ambiguous, gray forecasts result rank to express 6, among them data No.

4 correspondence of 2 ～ at faintness, the imitate that gray builds modular data is worth (the data that build a model comes from faintness to estimate data No.

2 ～ 4) , and data No.

5 express faintness, gray establishs modular data range besides calculate a value. The parameter in gray differential equation is certainly [As, bs]=[-0.

2464, 931.

306][au, bu]=[-0.

2473, 746.

3059]5 forecasts a result to analyse by the watch 4 data are knowable: Data No.

1 ～ the 3 better simulation that are primitive data (primitive data comes from a watch 3 in No.

1 ～ 3) , but forecast interval a little drift of towards the left; Although data No.

4 it is besides limits of the data that build a model, but its it is better to forecast and contain minor opposite error (+ 2.

6%) , namely actual measurement force falls in the left vicinity that calculates interval floor level; Data No.

Of 5 forecast poorer, namely actual measurement force falls in what calculate interval floor level left and contain bigger opposite error (+ 19.

2%) . By the watch 5 data are knowable: Data No.

1 ～ the 4 better simulation that are primitive data (primitive data comes from a watch 3 in data No.

1 ～ 4) ; Although data No.

5 it is besides limits of the data that build a model, but its it is better to forecast and contain minor opposite error (+ 3.

3%) , namely actual measurement force falls in the left vicinity that calculates interval floor level. By the watch 6 data are knowable: Data No.

2 ～ the 4 better simulation that are primitive data (primitive data comes from a watch 3 in data No.

2 ～ 4) ; Although data No.

5 it is to be besides limits of the data that build a model, but its it is better to forecast and contain minor opposite error (- 1.

3%) ; Actual measurement force falls in what calculate interval floor level on the right side of adjacent. Be based on afore-mentioned analysises knowable: Ambiguous, it is OK that gray forecasts a method better land imitate builds modular data, can occupy example in the number that build a model at the same time cutting strength is forecasted effectively besides limits uncertainty interval, true nevertheless forecast a drop effectively only bureau be confined to builds modular data that finally. Still can discover in addition: Express 6 medium metabolic models forecast result excel to express 4 medium partial information models, and express the partial information model of 4 excel expresses 5 medium new information models. The law of least square regression with convention, nerve network law and ambiguous regression method are apparently different, ambiguous, gray forecasts a law to need example of data of a few test to build a model only, forecast the uncertainty interval in the future effectively. The turning strength that 6 conclusion are building the test and verify in testing system the cutting power that offers uncertainty is ambiguous, the effectiveness that gray forecasts a method. Ambiguous, the comparison that gray calculates result and data of force of actual measurement cutting makes clear: What put forward forecast new method not only imitate of can better land builds modular data example, and still can forecast the other data beyond limits of the data that build a model to nod with minor opposite error (forecast prospective data to nod) namely. In addition, what differ apparently with the traditional method that build a model is: Ambiguous, gray forecasts a method to need a few test data example only in building a model, can reduce the cost that cutting experiments and workload greatly. CNC Milling CNC Machining