[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】数控机床控制器对于虚拟加工CAM系统轮廓特性的测量与评价-外文文献

Int J Adv Manuf Technol (2000) 16:2712762000 Springer-Verlag London LimitedContouring Performance Measurement and Evaluation of NCMachine Controller for Virtual Machining CAM SystemS.-H. Suh1and E.-S. Lee21Department of Industrial Engineering, Computer Automated Manufacturing Laboratory, Pohang, Korea; and2Department of MechanicalEngineering, Chungbuk University, Chungju, KoreaTo realise a virtual machining CAM system the machine toolaccuracy together with the controller behaviour should beincorporated in the CAM system. For such a purpose a ball-bar method is presented for measuring and verifying thecircular positioning, contouring, and performance evaluationof a CNC controller. A parameter adjustment method for theenhancement of CNC controller errors was also proposed.First, a mathematical representation of the error patterns wasdefined, and transformed into contouring forms. By comparingthe measured data with the defined controller error patterns,an analysis method was developed based on the “weightedresidual method”. The algorithms developed in this study wereimplemented in a software for extracting the error patterns ofan NC controller from the measured contouring data using aball-bar. The software is also able to suggest the parameteradjustment required to enhance the NC controller perform-ance optimally.Keywords: Ball-bar; Circular interpolation or contouring test;Extra sum of squares; NC controller; Virtual machining CAMsystem; Weighted residual method1. IntroductionTo realise a virtual machining CAM system, prediction ofthe machined surface is a crucial task. With a contemporaryCAD/CAM system, where the tool path is generated andverified based purely on the geometric operation, the geometricaccuracy of the machined part cannot be guaranteed. Thedegree of accuracy is dependent on how much the real pheno-mena are precisely reflected in the prediction model. For sucha purpose we present a ball-bar method for measuring andverifying the circular positioning, contouring, and performanceevaluation of a CNC controller.Correspondence and offprint requests to: Dr Suk-Hwan Suh,Department of Industrial Engineering, POSTECH, San 31 Hyoja-Dong,Nam-gu, Pohang, Korea 780-784. E-mail: shsKpostech.ac.krTo measure the accuracy standard of an NC macchine, apositioning test of the machine table and spindle under no-load conditions is typically used. One of the most efficientmethods for testing spindle positioning accuracy is based on acontouring test. Years ago, a precise standard disk was usedwith a dial gauge for comparing the circular path with thespindle path 1. Recently, a new method using a ball-bar wasdeveloped and used for testing the contouring performance2,3. A ball-bar consists of two accurate steel balls and anLVDT (Linear Variable Displacement Transformer), as shownin Fig. 1. The length between the base and the spindle ball ismeasured by an LVDT and is compared with the coordinatesdisplayed on the NC machine controller. Ball-bar tests are usedin many areas for checking the performances of NC machinetools, because of their simplicity speed. The ball-bar systemcan be used to test, not only NC machine performance, butalso the control characteristics of robots, the accuracy ofCMMs, etc. 4.In general, the contouring data include much information tobe analysed. There are two major groups of error sources inNC machine tools, as shown in Fig. 2. One is geometric errors,due to the moving mechanism such as, straightness, rolling,yawing, and squareness error; and the other is due to controlFig. 1. Ball-bar set-up in a CNC milling machine.272 S.-H. Suh and E.-S. LeeFig. 2. 5-axis (X, Y, Z, A, C) vertical spindle type CNC millingmachine.errors, such as, interpolation errors, hysteresis, servo mismatch,master slave change over, and scale mismatch. The geometricerrors can be measured using such devices as laser interfer-ometer and a ball bar. Much work has been carried out inmeasuring the geometric errors the machine tools, e.g. 46,and commercial software is available, e.g. 78.However, there have not been many attempts at measuringthe controller error separately because of the complicatedcharacteristics of the NC controller interfaced with the machinetool motion. Some workers have studied the definition ofcontrol errors and tried to formulate the error patterns intonumerical forms 911. However, they defined and formulatedonly a limited number of errors. Further, previous researcherswere mainly concerned with measurement and experimentalmethodology, and analytical investigation of the ball-barmeasurement method has not been made. Some field engineersdo not like the no-load condition of the ball-bar test. However,they use the ball-bar test frequently because of its simplicityin testing NC machines at the final assembly stage.In this paper, a method to separate the NC controller errorsfrom the ball-bar measurement is studied using a statisticalmethod. For this purpose, the controller characteristics areanalysed with the definition of error patterns as analytic equ-ation. The control error patterns can be plotted in a 2Dcontouring form, called “masks” in this paper. The methodproposed in this study was verified using a simulation tech-nique, and the performance evaluation software was testedusing the various control parameters of the NC machine. Thedifference between the analytical method using the ball-barunder no-load conditions and the machining result using a testpiece will also be shown.2. Ball-Bar Measuring TheoryA ball-bar consists of a base ball, which is fixed, and a movingball. The centre coordinate of the base ball can be set asO(0, 0, 0) and the coordinate of the moving ball as P(X, Y,Z). Figure 3 shows the measuring length using a ball-barbetween the base ball and the moving positions for a circularFig. 3. Measuring points by a ball-bar on a circular path with a tiltingangle a .path. The distance R between the base and the moving ball isas follows:R2= X2+ Y2+ Z2(1)When the spindle is commanded to move to a pointP(X, Y, Z), the real position of the spindle (with error) willbe P9(X9, Y9, Z9). Therefore, the positioning error of the spindle,(DX, DY, DZ), can be expressed as follows;DX = X9 - X, DY = Y9 - Y, DZ = Z9 - ZC = (DX, DY, DZ) (2)DR = (XDX + YDY + ZDZ)/Rwhere C is the error vector and DR is the length error alongthe ball-bar direction. Equation (2) shows the relation betweenthe positioning error vector of the spindle and the measuringdata using a ball-bar. The ball-bar measuring data, DR, aroundthe circular points can be plotted in polar coordinate to amagnified scale for showing the contouring characteristic ofthe NC machine.3. Error Patterns of NC Controller3.1 Backlash (Positive, Negative)“Backlash” is a positioning error that occurs when the spindleapproach direction is reversed, and, in general, it is due to thetolerance of the ball lead screw or guide way. Sometimes,backlash appears as a result of an excessive backlash compen-sating adjustment of the NC controller. Backlash is not afunction of feedrate, in general. In the 2D case, e.g. the ball-bar path, the error vector of the “backlash mask” is expressedas follows:C= (a, b, 0) (3)where a and b are the magnitudes of the backlash steps in theX- and Y-directions. The Z-component of the error vector willbe zero because the ball-bar moves only on the 2D plane. Anexample of positive backlash is shown in Fig. 4(a). TheContouring Performance Measurement 273backlash error vector in the ball-bar direction for a movingangle u around the circular path is:DR =Sa2R cos u +b2R sin uD/R (4)3.2 MasterSlave ChangeoverFor 2D movement, there exists a leading axis (master) and afollowing axis (slave). In a circular interpolation path, stepsappear at every 45 , as shown in Fig. 4. This is called “masterslave changeover” and is due to the change of feedrate in thedifferent axes at a given position. For this reason, the “masterslave changeover” error increases proportionally to the feedrate.The “masterslave changeover” error can be expressed as fol-lows:C=Sa cosp4+b sinp4, - a sinp4+ b cosp4,0D(5)where a is the magnitude of the masterslave changeover stepat angles 45 and 225 , and b is at 135 and 315 . Using theerror vector, the length error in the ball-bar direction is:DR =FaR cosSu +p4D+ bR sinSu +p4DG/R (6)3.3 Servo Mismatch“Servo mismatch” appears owing to the different velocities ofthe spindle in the two axes. This results in different gainvalues, showing as a distorted circle on the ball-bar measuringFig. 4. NC controller error masks.data. The velocity difference is a maximum at every 45 ,sothat it appears as two tilted ellipses for both rotating directions,clockwise (CW) and counter clockwise (CCW), as shown inFig. 4(c).Therefore, the magnitude of the “servo-mismatch” is pro-portional to the feedrate. The “servo-mismatch” error vectorfor the two rotating directions is expressed as follows:C=S-VXKSX, -VYKSY,0DVX= 7 F sin u, VY= 7 F cos u (7)where F is the circumference speed of the spindle and VxandVyare the feedrates of the X and Y axes and Ksxand Ksyarethe position loop gains of the X- and Y-axes. The upper signis for the CCW and the lower is for the CW direction. Fromthe error vector, the length error in the ball-bar direction canbe derived as follows:DR =F2sin 2 uS KSX7 KSYKSX KSYD(8)4. Quantitative Analysis of Error Patterns4.1 Weighted Residual MethodThe controller error patterns have been defined previously.Now, it is required to separate the error patterns from the ball-bar measuring data. For this purpose, a statistical technique,the “weighted residual method” 12 is used to derive themagnitude of each pattern. The measured ball-bar data can beexpressed as follows:DR(u) =Ol1ai DRi(u)(i = 1, 2, %, l) (9)where l is the total number of error patterns, DR(u) is themeasured error using a ball-bar and DRi(u) is the ith errorpattern number. The term aiis a weighting factor and showsthe magnitude of the error pattern. The difference between themeasured error and the summation of the error patterns will be:e(u) = DR(u) -Oli=1ai Ri(u) (10)The above equation shows the residual. Therefore, the weight-ing factor aican be determined as the minimum residual,which gives the magnitude of each error pattern. The terme(u) in Eq. (10) can be minimised using double integrationas follows:E2p0e(u)Fi(u) -u = 0(i = 1, 2, %, l) (11)where Fi(u) is the independent weighting function. Increasingthe number l, results in decreasing the residual e(u). Theweighting function can be replaced as the error pattern itself,Ri(u), in this case. Thus, Eq. (11) can be represented as follows:274 S.-H. Suh and E.-S. LeeE2p0HDR(u) -Oli=1aiDRiRi(u)JDRi(u) -u = 0 (12)Olklikak= mi(i, k = 1, 2, %, l)lik=E2p0DRk(u) DRi(u) -umi=E2p0DR(u) DRi(u) -u (13)The one-dimensional multilinear Eq. (13) can be solved usingDolittles method 12 for l to be a non-singular form.4.2 Method of Extra Sum of SquaresThe weighting factor aidoes not represent the absolute magni-tude of the error pattern, but only the ratio of the error patternRi(u). For this problem, the concept of “extra sum of squares”is used in this paper. This method is used for determining theeffect of a particular error pattern with the calculation of thesum of squares after removing or adding the particular errorpattern. At first, the original equation for the regression(reduced model) is defined as:y = a0+ a1x1(14)This equation is changed by adding an extra variable x2(fullmodel) as follows:y = a0+ a1x1+ a2x2(15)Therefore, the marginal effect of adding the variable (x2)ofthe full model is:SSR(x1ux2) = SSE(x1) - SSE(x1, x2) (16)where SSE(x1) means the sum of squares of the reduced modeland SSE(x1, x2) means the sum of squares of the full model.Equation (16) can be modified as follows:SSEFRi=E2p0SDR(u) -SOlk=1akDRk(u) - aiDRi(u)DD2-uSSEFall =E2p0SDR(u) -SOlk=1akDRk(u)DD2-uSSRFRi= SSEFRi- SSEFallMSRFRi= SSRFRi/(n - 1) - (n - l - 1) (17)where n is the number of data items for the calculation. SSEFRirepresents the sum of squares, except the ith error pattern, andSSEFall represents the sum of squares for all error patterns.SSRFRirepresents the extra sum of squares except the ith errorpattern and MSRFRirepresents the mean squares of SSRFRi.Therefore, the absolute magnitude of the error pattern can berepresented by the extra sum of squares using the weightingfactor ai.5. Evaluation of NC Controller ErrorUseful software for evaluating the NC controller was developedbased on the presented algorithm, called NC controller per-formance evaluation software (NCPES). The NCPES was testedusing an NC milling machine with a HEIDENHAIN TNC 407controller. The ball-bar length used in this study was 100 mmand it measures points continuously on the X, Y-plane. Thecontouring feedrate was 1000 mm min- 1and the sampling ratewas 15.625/s.Figure 5 shows the evaluation results using a ball-bar withthe NCPES. The ball-bar is not able to measure the axialpositioning error. Therefore, the position error must be adjustedfrom the ball-bar data as shown in Fig. 5(b). The magnitudeof the position error in the X-axis was measured at the sameball-bar working using a laser interferometer, as shown inFig. 6. The adjusting value was taken as an average of theforward and the backward measurement of the laser interfer-ometer. The positioning error in the Y-axis was ignored in thismachine. In Fig. 5, the weighting factors (bottom left, non-dimensional) and the values of the extra sum of squares(MSRFRi) are shown (top left, mm2) for “backlash”, “masterslave changeover” and “servo-mismatch” error patterns. TheMSRFRivalues are the order of effects for the controllererror patterns.From the evaluation result, it is shown that the “servo-mismatch” error is dominant in this controller. The evaluationtechnique proposed in this study shows a good agreement withthe measurement data.Fig. 5. Evaluation and comparison of results with measurement. (a)Before adjustment. (b) After adjustment.Contouring Performance Measurement 275Fig. 6. Position error measurement in the X-axis.The software developed in this study, NCPES, was alsoverified using a simulation method. Figure 7 shows an examplefor the combined controller error patterns, comparing the simul-ation with the evaluation result. The ball-bar simulation datafor error patterns (“back lash”, “masterslave changeover”,“servo mismatch”) were constructed using random numbers forthe weighting factors. The evaluation result coincides with thesimulation data exactly, validating the evaluation accuracy ofour method.The ball-bar evaluation results were compared withan actual experiment using a circular test piece for the round-ness measurement shown in Fig. 8. The “masterslavechangeover” error clearly appeared on the test piece, comparedwith the ball-bar measurement. This seems to be due to themachining force of the tool in the radial direction of thecircular workpiece, which causes an increase in the “masterslave changeover” effect.6. ConclusionWe have addressed the identification of the NC controllererror. Previous research has been mainly concerned with thegeometric accuracy of the machine tool. By developing astatistics based analysis method, we can readily decouple thecontroller error sources from the measured data.To check the validity of our method, the ball-bar evaluationresults were compared with an actual manufacturing experimentusing various test pieces. These experimental results will beFig. 7. Verification of the evaluation algorithm using a simulationmethod.Fig. 8. The comparison of the ball-bar measurement and the test piecemachining (clockwise). (a) Ball-bar measurement under no-load con-dition. (b) Roundness measurement after machining. (c) Machinedtest piece.useful in identifying the machining effects under differentconditions, such as friction effects, feedrate, manufacturingforce, etc. Through the experiments, we found the correlationbetween the NC control parameters and the quantitative valuesof the controller error patterns, which can be used for adjustingthe parameters of the NC machine in different geometricconditions.The method presented will be useful for the NC controllermanufacturer to determine the exact error sources quickly.Also, the results can be used to verify the overall NC controllerperformance after assembling the controller with the machinetool. Further, by incorporating the method in a VMCS (virtualmachining CAM system), the machined surface can be pre-cisely predicted off-line.276 S.-H. Suh and E.-S. LeeAcknowledgementThis research was carried out under the KoreaFrance Inter-national Collaborative Research Program funded by KOSEF(Korea Science and Engineering Foundation) contract number966-1007-001-2.References1. M. Burdekin and J. Park, “CONTISURE A computer