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Int J Adv Manuf Technol (2001) 17:6496532001 Springer-Verlag London LimitedReal-Time Prediction of Workpiece Errors for a CNC TurningCentre, Part 1. Measurement and IdentificationX. LiDepartment of Manufacturing Engineering, City University of Hong Kong, Hong KongThis paper analyses the error sources of the workpiece in barturning, which mainly derive from the geometric error ofmachine tools, i.e. the thermally induced error, the errorarising from machineworkpiecetool system deflection inducedby the cutting forces. A simple and low-cost compact measuringsystem combining a fine touch sensor and Q-setter of machinetools (FTSFQ) is developed, and applied to measure the work-piece dimensions. An identification method for workpiece errorsis also presented. The workpiece errors which are composedof the geometric error, thermal error, and cutting force errorcan be identified according to the measurement results of eachstep. The model of the geometric error of a two-axis CNCturning centre is established rapidly based on the measurementresults by using an FTSFQ setter and coordinate measuringmachine (CMM). Experimental results show that the geometricerror can be compensated by modified NC commands in barturning.Keywords: Dimension measure; Error identification; Geo-metric error; Turning1. IntroductionIn recent years, ultraprecision machining has made remarkableprogress. Some special lathes have been able to make ultra-precision machining, to less than a submicron and nanomicrontolerances a possibility. A common second approach is thatthe grinding is used to achieve a high level of dimensionalaccuracy after turning. However, the condition of the cuttingtool (diamond) and workpiece (aluminium) have restricted theapplication of ultraprecision lathes. The second approachincreases the number of machine tools and machining processesused 1, which results in an increase in the manufacturing cost.At present, most CNC lathes are equipped with a positioningresolution of 1 mm. Various machining errors in finish turning,however, degrade the accuracy to a level of approximatelyCorrespondence and offprint requests to: Dr Xiaoli Li, Department ofManufacturing Engineering, City University of Hong Kong, HongKong. E-mail: lixiaoliF10 mm, so that when turning carbon steel, a machining errorpredictably arises in excess of 2030 mm. For improving mach-ining accuracy, the method of careful design and manufacturehas been extensively used in some CNC lathes. However, themanufacturing cost based on the above method will rapidlyincrease when the accuracy requirements of the machine toolsystem are increased beyond a certain level. For further improv-ing machine accuracy cost-effectively, real-time error predictionand compensation based on sensing, modelling and controltechniques have been widely studied 2, so ultraprecision andfinish tuning can be performed on one CNC lathe.The positioning resolution of the cutting tools and workpieceis reduced so that it cannot maintain high accuracy duringmachining because of the cutting-force-induced deflection ofthe machineworkpiecetool system, and the thermally inducederror, etc. In general, a positioning device using a piezo-eletricactuator is used to improve the working accuracy, but themethod introduces some problems, such as, the feedback strat-egy, and the accuracy of sensors, which add to the manufactur-ing cost of the products. However, if the workpiece error canbe measured by using a measuring instrument, or predicted byusing a modelling, the turning program produced by modifiedNC commands can be executed satisfactorily on a CNCmachine tool. Thus, a CNC turning centre can compensate forthe normal machining error, i.e. the machine tool can machinea product with a high level of accuracy using modified NCcommands, in real time.The workpiece error derives from the error in the relativemovement between the cutting tool and the ideal workpiece.For a two-axis turning centre, this relative error varies as thecondition of the cutting progresses, e.g. the thermal deflectionof the machine tool is time variant, which results in differentthermal errors. According to the various characters of the errorsources of the workpiece, the workpiece errors can be classifiedas geometric error, thermally induced error, and cutting-force-induced error. The main affecting factors include the positionerrors of the components of the machine tool and the angularerrors of the machine structure, i.e. the geometric error. Thethermally induced errors of the machine tool (i.e. the thermalerror), and the deflection of the machining system (includingthe machine tools, workpiece, and cutting tools) arising fromcutting forces, are called the cutting-force error.650 X. LiThis paper analyses the workpiece error sources in turning.The errors of a machined workpiece are mainly composed ofthe geometric error of the machine tools, the thermally inducederror, and the error arising from machineworkpiecetool sys-tem deflection induced by the cutting forces. A simple andlow-cost measuring instrument for the workpiece dimensions,which combines a fine touch sensor and machine tool Q-setter(FTSFQ), is described, and applied to measure the workpieceerror. A new method for identifying the geometric error, thethermal error, and the cutting-force error is also presented fora two-axis turning centre. Finally, the modelling of the geo-metric error of a CNC turning centre is presented, based onthe measurement results using the FTSFQ and CMM. Thegeometric error can be compensated by the modified NCcommand method.2. Error Sources in TurningThe machine tool system is composed of the drive servo, themachine tool structure, the workpiece and the cutting process.The major error sources derive from the machine tool (thermalerrors, geometric errors, and forced vibrations), the control(drive servo dynamics and programming errors) and the cuttingprocess (machine tool and cutting tool deflection, workpiecedeflection, tool wear, and chatter) 3.Errors derived from the machine tool include thermal errors(machine thermal error and workpiece thermal errors), geo-metric errors, and forced vibrations, which dominate machiningaccuracy. The thermal errors and geometric errors are thedominant factors with respect to machining accuracy in finecutting. However, machine tool errors can be decoupled fromthe other error sources and compensated 4. The error derivedfrom forced vibration can be reduced through balanced dynamiccomponents and vibration isolation 3.The errors derived from the controller/drive dynamics arerelated to the cutting force disturbances and the inertia of thedrive and the machine table. These errors can be reduced byan interpolator with a deceleration function 5 or by anadvanced feed drive controller 6, these errors, reduced byusing the above methods, are small when compared with othererror sources.Owing to the demand for high productivity, high feedratesand large depths of cut are required, which result in largecutting forces. Therefore, the cutting-force induced deflectionsof the machine tool (spindle), tool holder, workpiece, andcutting tool make significant contributions to machining accu-racy during the cutting process. In addition, tool wear andmachine tool chatter are also important error sources in thecutting process. However, these effects are neglected here soas to focus on the main error sources.In short, the error of a machined workpiece, i.e. the totalmachining error (dTot), is composed mainly of the geometricerrors of the machine tool(s) (dG), the thermally induced error(dT), and the error (dF) arising from the deflection of themachineworkpiecetool system induced by the cutting forces.Hence,dTot dG+ dT+ dF(1)In the next section, we present a novel compact measuringinstrument and a new analytical approach for measuring andidentifying workpiece errors in turning.3. A Compact Measurement SystemContact sensors, such as touch trigger probes, have been usedto measure workpiece dimensions in machining. In machiningpractice, the measuring instrument is attached to one of themachines axes to measure a surface on the workpiece. ATP7M or MP3 associated with the PH10M range of motorisedprobe heads or a PH6M fixed head have been used widely inthe automated CNC inspection environment owing to their highlevel of reliability and accuracy and integral autojoint. Thoughthe probeheads are of adequate accuracy (unidirectionalrepeatability at stylus tip (high sensitivity): 0.25 mm; pre-travelvariation 360 (high sensitivity): 60.25 mm), and versatile inapplication, they have clear drawbacks, including complexityof construction, high price ($4988), and the need for carefulmaintenance.To overcome these drawbacks of touch trigger probes,Ostafiev et al. 7 presented a novel technique of contactprobing for designing a fine touch sensor. The cutting toolitself is used as a contact probe. The sensor is capable ofyielding measurement accuracy comparable to that of the besttouch trigger probe in use. Moreover, the principle of operationand construction of the sensor is extremely simple, the cost ofthe sensor is low, and the maintenance is very easy. In thispaper, this sensor will be used to measure the diameter of aworkpiece associated with the Q-setter.A touch sensor is mounted on a CNC turning centre. Whenwe manually bring the tool nose into contact with it, aninterrupt signal is generated for the NC unit to stop an axis.Moreover, it can write in an offset and a workpiece coordinateshift automatically. This function facilitates set-up when replac-ing a tool, and this convenient function is called the “QuickTool Setter” or “Q-setter”. Based on the above principle, wecan operate a switch, which is controlled by fine touch sensor,between the Q-setter and NC unit. When the tool tip touchesthe workpiece surface, the fine touch sensor can send a controlsignal to the switch, to turn it to the “off” state. See Fig. 1,the fine touch sensor replaces the Q-setter function, to stop anaxis and write in an offset and a workpiece coordinate shiftautomatically. Therefore, the fine touch sensor associated withFig. 1. Flow diagram of a fine touch sensor fixed on a CNC controller.Real-Time Prediction of Workpiece Errors. Part 1 651a Q-setter (FTSFQ) can be used to inspect the diameter of theworkpiece, the method is shown in Fig. 2.When the cutting tool tip touches the workpiece surface, a“beep” sound is heard and the switching “OFF” signal appearsand the axis stops automatically, as far the Q-setter. A new“tool offset” XT-Wis obtained by the NC unit (display of CNC).Before touching the workpiece surface, the cutting tool tiptouches the Q-setter, and the “tool offset” XT-Qis obtained.Thus, the on-machine workpiece diameter Don-machineis givenby the following Eq.:Don-machine= 2 H + uXT-Qu - uXT-Wu (2)whereXT-Qis the tool offset when the cutting tool contactsthe Q-setterXT-Wis the “tool offset” when the cutting toolcontacts the workpiece surfaceH is the distance from the centre of the Q-setter to the centreof the spindle in the x-axis direction and is provided by themachine tool manufacturer, for the Seiki-Seicos L II Turningcentre, it is 85.356 mm.Ostafiev and Venuvinod 8 tested the measurement accuracyof the fine touch sensor, performing on-machine inspection ofturned parts, and found that the method was capable of achiev-ing a measurement accuracy of the order of 0.01 mm undershop floor conditions. However, the measurement accuracy ofthe fine touch sensor together with the Q-setter obtained anaccuracy of about mm because the results of the measurementsystem are displayed by the CNC system, and the readingsaccuracy of the CNC system is up to 1 mm.4. Identification of Workpiece ErrorsFrom the above analysis of error sources of the workpiece,the total error dTotof machined parts is mainly composed ofthe following errors in a turning operation:I dGthe geometric errors of machine tools.I dTthe thermally induced error.Fig. 2. Inspection for the diameter of a workpiece by using the finetouch sensor with the Q-setter of a machine tool.I dFthe cutting force induced error.To analyse the error sources of a machined workpiece,Liu & Venuvinod 9 used Fig. 3 to illustrate the relationshipamongst dimensions associated with different error componentsin turning.In Fig. 3, Ddesis the desired dimension of the workpiece;Domwis the dimension obtained by on-machine measurementusing FTSFQ immediately after the machining operation; Domcis the dimension obtained by on-machine measurement usingFTSFQ after the machine has cooled down; and Dppis thedimension obtained by post-process process measurement usinga CMM after the workpiece has been removed from themachine.When the workpiece has been machined, and removed fromthe machine tool system, it is then sent for inspection of thedimensions using a CMM. This procedure is called post-processinspection, by which we obtain it Dppvalue. As the positioningerror of the CMM is very much smaller than the desiredmeasurement accuracy, the total error isdTot= (Dpp- Ddes)/2 (3)The dimension Domwis obtained through on-machinemeasurement using FTSFQ immediately after machining, i.e.the machine is still in the same thermal state as at thetime of machining. The measurement is made with the samepositioning error as that which existed during machining.Hence, the positioning error in this state would be equal to(dG1dT), i.e.(Dpp- Domw)/2 = dG+ dT(4)When the machine has completely cooled down, i.e. withoutthermal error, the dimension Domccan be obtained by on-machine measurement using FTSFQ. The measurement has apositioning error equal to the geometric error of the machineat the location of measurement. Hence, the positioning errorin this state would be equal to (dG), i.e.(Dpp- Domc)/2 = dG(5)Combining Eqs (4) and (5), the thermally induced error dTis(Domc- Domw)/2 = dT(6)Hence, taking Eqs (1), (3), and (4) into account, the cutting-force-induced error owning to the deflection of the machineworkpiecetool system dFis(Domw- Ddes)/2 = dF(7)Fig. 3. The relationships among dimensions.652 X. LiSo far, the machining error is composed of the geometricerror, the thermal error, and the cutting-force-induced error andcan be identified using the above procedure. The thermal errorand the force-induced error modellings is addressed in Li10. Here, the geometric error of machine tool is measuredand modelled.5. Modelling of Geometric ErrorThe geometric error of a workpiece is mainly affected by theoffset of the spindle, and the linear error and the angular errorsof the cross-slide for a two-axis CNC turning centre. Here,only the geometric error of workpiece in the x-axis directionis taken into account for a bar workpiece. This is expressedby the following formula.dG= d(s) - e(x) hT-Q- dx(x) (8)whered(s) is the spindle offset along the x-axis directione(x) is the angular error (yaw) of the cross-slidein the x, y-planedx(x) is the linear displacement error of the cross-slide along the x-axis directionThe spindle offset is a constant value independent of thethe machining position. The angular error term and the linearerror term are functions of the cross-slide position x.In this paper, the FTSFQ is mounted on a Hitachi Seiiki,HITEC-TURN 20SII two-axis turning centre. The FTSFQ cali-bration instrument was developed to measure rapidly the dimen-sion of the workpiece in the x-axis direction on the two-axisCNC turning centre when the machine has completely cooleddown, i.e. without the effect of thermal error. The geometricerror can be computed by using Eq. (5) according to themeasured results. First, the diameter of a precision ground testbar is measured at 10 positions, 20 mm apart, by a CMM,their values Dppi(i = 1, 2, . . ., 10) are recorded. Then, thetest bar is mounted on the spindle, and its diameter is alsomeasured at 10 positions, 20 mm apart, by the FTSFQ. Themeasurement arrangement is shown in Fig. 4, the readings areDomcl(i = 1, 2, . . ., 10). Thus, the geometric error at eachpoint along the x-axis for the bar workpiece are computedas follows:dGi= (Dppi- DGi)/2 (9)From starting point B to point A, the results are shown inFig. 5 for diameters of 30, 45, 60, and 75 mm. The workpieceFig. 4. Diagram of the geometric error measurement of the workpieceusing FTSFQ.Fig. 5. Geometric errors of the workpiece along the z-axis.geometric errors in the z-axis direction are the same. Theworkpiece geometric errors, however, increase along the x-axisdirection, as shown in Fig. 6. These average geometric errorsare 27.1036, 29.0636, 210.7764, 212.5955 (mm) for dia-meters 30, 45, 60, and 75 mm, respectively. Hence, the geo-metric errors of the two-axis CNC turning centre can becalculated by the following Eq.:dG(x) =- 0.121x - 3.519 (10)where x is the diameter of the workpiece (mm), dG(x)(mm)is the geometric error of the workpiece.6. Compensation of Geometric ErrorTo compensate for the geometric error in the direction of thedepth of cut, the tool path can be shifted in accordance withthe error. The NC commands in turning are modified, at aminimum resolution 1 mm, in the direction of the depth of cut.The calculated geometric error exceeded 1 mm according tothe equation (10), as illustrated in Fig 7.Figure 8 shows that the workpiece errors include the geo-metric error, the thermal error and the cutting force error. Thetool path determined by the calculated geometric error, andthe workpiece error are compensated for by the modified NCcommand method. In this example, we used a cutting speedof 4 m s21, a feedrate of 0.2 mm rev21, a depth of cut ofFig. 6. The average geometric error for the different diameters.Real-Time Prediction of Workpiece Errors. Part 1 653Fig. 7. Compensation of geometric error.Fig. 8. Compensation of geometric error by a modified NC command.1 mm (cutting length 100 mm), a diameter of 40 mm, mildsteel workpieces, and DNMG 1506 04 QM tools. The work-piece error was measured using our FTSFQ