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資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 Journal of Materials Processing Technology xxx (2005) xxxxxxFuzzy control strategy for an adaptive force control in end-millingU. Zuperl, F. Cus, M. MilfelnerFaculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, SloveniaAbstractThis paper discusses the application of fuzzy adaptive control strategy to the problem of cutting force control in high speed end-millingoperations. The research is concerned with integrating adaptive control with a standard computer numerical controller (CNC) for optimising ametal-cuttingprocess.Itisdesignedtoadaptivelymaximisethefeed-ratesubjecttoallowablecuttingforceonthetool,whichisverybeneficialfor a time consuming complex shape machining. The purpose is to present a reliable, robust neural controller aimed at adaptively adjustingfeed-rate to prevent excessive tool wear, tool breakage and maintain a high chip removal rate. Numerous simulations and experiments areconducted to confirm the efficiency of this architecture. 2005 Elsevier B.V. All rights reserved.Keywords: End-milling; Adaptive force control; Fuzzy1. IntroductionA remaining drawback of modern CNC systems is thatthemachiningparameters,suchasfeed-rate,speedanddepthof cut, are programmed off-line. The machining parametersare usually selected before machining according to program-mersexperienceandmachininghandbooks.Topreventdam-age and to avoid machining failure the operating conditionsare usually set extremely conservative.Asaresult,manyCNCsystemsareinefficientandrunun-dertheoperatingconditionsthatarefarfromoptimalcriteria.Even if the machining parameters are optimised off-line byan optimisation algorithm 5 they cannot be adjusted duringthe machining process.Toensurethequalityofmachiningproducts,toreducethemachining costs and increase the machining efficiency, it isnecessary to adjust the machining parameters in real-time, tosatisfy the optimal machining criteria. For this reason, adap-tive control (AC), which provides on-line adjustment of theoperatingconditions,isbeingstudiedwithinterest3.InourAC system, the feed-rate is adjusted on-line in order to main-tain a constant cutting force in spite of variations in cuttingconditions. In this paper, a simple fuzzy control strategy isdeveloped in the intelligent system and some experimentalCorresponding author. Tel.: +386 2 220 7623; fax: +386 2 220 7990.E-mail address: uros.zuperluni-mb.si (U. Zuperl).simulations with the fuzzy control strategy are carried out.The results demonstrate the ability of the proposed system toeffectively regulate peak forces for cutting conditions com-monly encountered in end-milling operations.Force control algorithms have been developed and eval-uated by numerous researchers. Among the most commonis the fixed gain proportional integral (PI) controller origi-nally proposed for milling by 4. Kim et al. 4 proposedan adjustable gain PI controller where the gain of the con-troller is adjusted in response to variations in cutting con-ditions. The purely adaptive model reference adaptive con-troller (MRAC) approach was originally investigated by Cusand Balic 2. These controllers were simulated and evalu-ated and physically implemented by 1. Both studies foundall three-parameter adaptive controller to perform better thanthe fixed gain PI controller. As regards fuzzy control sys-tems, an introductory survey of pioneering activities is givenby Huang and Lin 3, and a more systematic view is pre-sented by in 4. Comparisons of fuzzy with proportional in-tegral derivative (PID) control and stability analysis of fuzzysystems and supervisory fuzzy control are addressed in Ref.3.Much work has been done on the adaptive cutting forcecontrol for milling 2. However, most of the previous workhas simplified the problem of milling into one-dimensionalmotion. In this contribution, we will consider force controlfor three-dimensional milling.0924-0136/$ see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2005.02.1432U. Zuperl et al. / Journal of Materials Processing Technology xxx (2005) xxxxxxThe paper is organised as follows. Section 2 briefly de-scribes the overall force control strategy. Section 3 coversthe CNC machining process model. Section 5 describes thesimulation/experiments and implementation method of pro-posedcontrolscheme.Finally,Sections6and7presentexper-imentalresults,conclusions,andrecommendationsforfutureresearch.2. Adaptive fuzzy controller structureA new on-line control scheme which is called adaptivefuzzy control (AFC) (Fig. 1) is developed by using the fuzzysettheory.Thebasicideaofthisapproachistoincorporatetheexperience of a human operator in design of the controller.The control strategies are formulated as a number of ruleswhich are simple to carry out manually but difficult to im-plement by using conventional algorithm. Based on this newcontrol strategy, very complicated process can be controlledmoreeasilyandaccuratelycomparedtostandardapproaches.The objective of fuzzy control is keeping the metal removalrate (MRR) as high as possible and maintaining cutting forceas close as possible to a given reference value. Furthermore,the amount of computation task and time can be reduced ascompared to classical or modern control theory. Schematiccontrol rules are constructed by using real experimental data.Fuzzy adaptive control ensures continuous optimising feedrate control that is automatically adjusted to each particularcutting situation. When spindle loads are low, the system in-creasescuttingfeedsaboveandbeyondpre-programmedfeedrates, resulting in considerable reductions in cycle times andproduction costs. When spindle loads are high the feed ratesare lowered, safeguarding machine tools from damage frombreakage. When system detects extreme forces, it automati-cally stops the machine to protect the cutting tool. It reducestheneedforconstantoperatorsupervision.Sequenceofstepsfor on-line optimisation of the milling process are presentedbelow.1. Thepre-programmedfeedratesaresenttoCNCcontrollerof the milling machine.2. The measured cutting forces are sent to the fuzzy con-troller.3. Fuzzy controller uses the entered rules to find (adjust) theoptimal feed-rates and sends it back to the machine.4. Steps1and3arerepeateduntilterminationofmachining.The adaptive force controller adjusts the feed-rate by as-signingafeed-rateoverridepercentagetotheCNCcontrolleron a four-axis Heller, based on a measured peak force. Theactual feed-rate is the product of the feed-rate override per-centage and the programmed feed-rate. If the feed-rate opti-misation models were perfect, the optimised feed-rate wouldalways be equal to the reference peak force. In this case thecorrect override percentage would be 100%. In order for thecontroller to regulate peak force, force information must beavailable to the control algorithm at every controller sam-ple time. A data acquisition software (Labview) is used toprovide this information.2.1. Structure of a fuzzy controllerIn fuzzy process control, expertise is encapsulated intoa system in terms of linguistic descriptions of knowledgeabout human operating criteria, and knowledge about theinputoutput relationships. The algorithm is based on theoperators knowledge, but it also includes control theory,throughtheerrorderivative,takingintoconsiderationthedy-namics of the process. Thus, the controller has as its inputs,the cutting force error ?F and its first difference ?2F, andas outputs, the variation in feed rate ?f. The fuzzy controlvariables fuzzification (see Fig. 2) as well as the creationof the rules base were taken from the expert operator. Thecutting force error and first difference of the error are calcu-lated, at each sampling instant k, as: ?F(k)=FrefF(k) and?2F(k)=?F(k)?F(k1), where F is measured cuttingforce and Frefis force set point.Fig. 1. Comparison of actual and model feed-rate.U. Zuperl et al. / Journal of Materials Processing Technology xxx (2005) xxxxxx3Fig. 2. Structure of a fuzzy controller.3. CNC machining process modelA CNC machining process model simulator is used toevaluate the controller design before conducting experimen-tal tests. The process model consists of a neural force modeland feed drive model. The neural model estimates cuttingforces based on cutting conditions and cut geometry as de-scribed by Zuperl 1. The feed drive model simulates themachine response to changes in commanded feed-rate. Thefeed drive model was determined experimentally by examin-ing step changes in the commanded velocity. The best modelfit was found to be a second-order system with a natural fre-quency of 3Hz and a settling time of 0.4s. Comparison ofexperimentalandsimulationresultsofavelocitystepchangefrom 7 to 22mm/s is shown on Fig. 3.The feed drive and neural force model are combined toform the CNC machining process model. Model input is thecommanded feed-rate and the output is the X, Y resultant cut-ting force. The cut geometry is defined in the neural forcemodel. The simulator is verified by comparison of experi-mental and model simulation results. A variety of cuts withfeed-rate changes were made for validation.The experimental and simulation resultant force for a stepchange in feed-rate from 0.05 to 2mm/tooth is presented inFig. 4. The experimental results correlate well with modelresults in terms of average and peak force. The experimentalFig. 3. Comparison of actual and model federate.4U. Zuperl et al. / Journal of Materials Processing Technology xxx (2005) xxxxxxFig. 4. Structure of a fuzzy controller.results correlate well with model results in terms of averageand peak force.The obvious discrepancy may be due to inaccuracies inthe neural model, and unmodeled system dynamics.3.1. Cutting force modelingTo realise the on-line modelling of cutting forces, a stan-dardBPneuralnetwork(NN)isproposedbasedonthepopu-lar back propagation leering rule. During preliminary exper-iments it proved to be sufficiently capable of extracting theforce model directly from experimental machining data. It isused to simulate the cutting process.TheNNformodellingneedsfourinputneuronsformillingfederate (f), cutting speed (vc) axial depth of cut (AD) and ra-dial depth of cut (RD). The output from the NN are cuttingforce components, therefore two output neurons are neces-sary.ThedetailedtopologyoftheusedNNwithoptimaltrain-ing parameters and mathematical principle of the neuron isalsoshowninFig.5.BestNNconfigurationcontains5,3and7 hidden neurons in hidden layers.3.2. Topology of neural network and its adaptation tomodeling problemThe effect of topology is also studied by considering dif-ferent cases. The topologies are varied by varying the num-ber of neurons in hidden layers. To evaluate the individualeffects of training parameters on the performance of neuralnetwork 40 different networks were trained, tested and anal-ysed. The network performances were evaluated using fourdifferent criteria 5: ETstMax, ETst, ETrn, and ETrnMaxand the number of training cycles. The number of neurons inthe input and output layers are determined by the number ofinput and output parameters. From the results the followingconclusions can be drawn.U. Zuperl et al. / Journal of Materials Processing Technology xxx (2005) xxxxxx5Fig. 5. Structure of a fuzzy controller. Learning rates below 0.3 give acceptable prediction errorswhile learning rates must be between 0.01 and 0.2 to min-imise the number of training cycles. To minimise the estimation errors, momentum rates be-tween0.001and0.005aregood.However,themomentumrate should not exceed 0.004 if the number of training cy-cles is also to be minimised. The optimum number of hidden layer nodes is 3 or 6. Net-works with between 2 and 12 hidden layer nodes, otherthan3or6,alsoperformedfairlywellbutresultedinhighertraining cycles. Networks that employ the sine function require the lowestnumber of training cycles followed by the ArcTangent,while those that employ the hyperbolic tangent require thehighest number of training cycles.4. Data acquisition system and experimentalequipmentThe data acquisition equipment used in this acquisitionsystem consists of dynamometer, fixture module, hardwareand software module as shown in Fig. 1. The cutting forceswere measured with a piezoelectric dynamometer (Kistler9255) mounted between the workpiece and the machiningtable. When the tool is cutting the workpiece, the force willbe applied to the dynamometer through the tool. The piezo-electric quartz in the dynamometer will be strained and anelectric charge will be generated. The electric charge is thentransmitted to the multi-channel charge amplifier throughthe connecting cable. The charge is then amplified using themulti-channel charge amplifier. In the multi-channel chargeamplifier, different parameters can be adjusted so that the re-quired resolution can be achieved. Essentially, at the outputof the amplifier, the voltage will correspond to the force de-pendingontheparameterssetinthechargeamplifier.Thein-terfacehardwaremoduleconsistsofaconnectingplanblock,analogue signal conditioning modules and a 16 channel A/Dinterface board (PC-MIO-16E-4). In the A/D board, the ana-logue signal will be transformed into a digital signal so thatthe LabVIEW software is able to read and receive the data.The voltages will then be converted into forces in X, Y and Zdirections using the LabVIEW program. With this program,the three axis force components can be obtained simulta-neously, and can be displayed on the screen for analysingforce changes. The ball-end-milling cutter with interchange-able cutting inserts of type R216-16B20-040 with two cut-ting edges, of 16mm diameter and 10helix angle was se-lected for machining. The cutting inserts R216-1603 M-Mwith 12rake angle were selected. The cutting insert ma-terial is P30-50 coated with TiC/TiN, designated GC 4040in P10-P20 coated with TiC/TiN, designated GC 1025. Thecoolant RENUS FFM was used for cooling. The fuzzy con-trolisoperatedbytheintelligentcontrollermodule(Labview)and the modified feed-rates are send to the CNC. Communi-cation between the force control software and the NC ma-chine controller is enabled through memory sharing. Thefeed-rate override percentage variable DNCFRO is avail-able to the force control software for assignment at a rateof 1kHz.5. Simulations and fuzzy control milling experimentTo examine the stability and robustness of the adaptivefuzzy control strategy, the system is first examined by sim-ulation using Simulink and Labview fuzzy Toolset. Thenthe system is verified by various experiments on a CNCmilling machine (type HELLER BEA1) for Ck 45 and Ck45 (XM) steel workpiece with variation of cutting depth(Fig. 6).The ball-end-milling cutter (R216-16B20-040) with twocutting edges, of 16mm diameter and 10helix angle wasselected for experiments. Cutting conditions are: milling6U. Zuperl et al. / Journal of Materials Processing Technology xxx (2005) xxxxxxFig. 6. Workpiece profile.widthRD=3mm,millingdepthAD=2mmandcuttingspeedvc= 80m/min.The parameters for fuzzy control are the same as for theexperiments for the traditional system performance.To use the fuzzy control structure on Fig. 1 and to opti-mise the feed-rate, the desired cutting force is Fref=280N,pre-programmed feed is 0.08mm/teeth and its allowable ad-justing rate is 0150%.Fig. 7 is the response of the cutting force and the feed-ratewhen the cutting depth is changed. It shows the experimentalresult where the feed-rate is adjusted on-line to maintain thecutting force at the maximum desired value.Simulated control response to a step change in axial depthis presented in Fig. 8. The simulation represents a 16mm,two-flute cutter, at 2000rpm, encountering a step change inaxial depth from 3 to 4.2mm. The step change occurs at2s and the controller returns the peak forces to the refer-ence peak force within 0.5s. In this research the stabilityof fuzzy controller is evaluated by simulation. Test simula-tions with small and large step changes in process gain arerun to ensure system stability over a range of cutting con-ditions. Small process gain changes are simulated with anaxial depth change from 3 to 4.2mm at a spindle speed of2000rpm. Large gain changes are simulated with an axialdepth change from 3 to 6mm at 2000rpm. The system re-mains stable in all simulation tests, with little degradation inperformance.Fig. 7. Experimental results with variable cutting depth. Response of MRR, resulting cutting force, feed-rate. (a) Conventional milling and (b) milling withadaptive fuzzy control.U. Zuperl et al. / Journal of Materials Processing Technology xxx (2005) xxxxxx7Fig. 8. Simulated fuzzy control response to a step change in axial depth.6. Results and discussionIn the first experiment using constant feed rates (conven-tionalcutting,Fig.7a)theMRRreachesitspropervalueonlyin the last step.However, in second test (Fig. 7b), machining the samepiece but using fuzzy control, the average MRR achieved ismuch more close to the proper MRR.Comparing Fig. 7a and b, the cutting force for the neuralcontrol milling system is maintained at about 240N, and thefeed-rate of the adaptive milling system is close to that of thetraditionalCNCmillingsystemfrompointCtopointD.FrompointAtopointCthefeed-rateoftheadaptivemillingsystemis higher than for the classical CNC system, so the millingefficiency of the adaptive milling system is improved.The experimental results show that the MRR can be im-proved by up to 27%. As compared to most of the exist-ing end-milling control systems, the proposed fuzzy controlsystem has the following advantages 3: 1. multi-parameteradjustment; 2. insensitive to changes in workpiece geome-try,cuttergeometry,andworkpiecematerial;3.cost-efficientand easy to implement; 4. mathematically modeling-free.The simulation results show that the milling process withthe designed fuzzy controller has a high robustness, stabil-ity, and also higher machining efficiency than standard con-trollers.Experiment has shown that fuzzy controllers have impor-tant advantages over conventional controllers. The main ad-vantageisthatafuzzycontrollerrespondsquicklytocomplexsensory inputs while the executing speed of sophisticatedcontrol algorithms in a conventional controller is severelylimited.Current research has shown that fuzzy controller has im-portant advantages over conventional controllers. The firstadvantage is that a fuzzy controller can efficiently utilisea much larger amount of sensory information in planningand executing a control action than an industrial controllercan.Thesecondadvantageisthatafuzzycontrollerrespondsquickly to complex sensory inputs while the executing speedof sophisticated control algorithms in a conventional con-troller is severely limited.7. ConclusionThe purpose of this contribution is to present a reliable,robust fuzzy force controller aimed at adaptively adjustingfeed-rate to prevent excessive tool wear, tool breakage andmaintain a high chip removal rate.The results of the intelligent milling experiments withadaptive control strategy show that the fuzzy controller hashigh robustness and global stability. The approach was suc-cessfully applied to an experimental milling centre Heller.The proposed architecture for on-line determining of op-timal cutting conditions is applied to ball-end-milling in thispaper, but it is obvious that the system can be extended toother machines to improve cutting efficiency.References1 J. Balic, A new NC machine tool controller for step-by-step milling,Int. J. Adv. Manuf. Technol. 8 (2000) 399403.2 F. Cus, J. Balic, Optimization of cutting process by GA approach,Robot. Comput. Integr. Manuf. 19 (2003) 113121.3 S.J. Huang, C.C. Lin, A self-organising fuzzy logic controller for acoordinate machine, Int. J. Adv. Manuf. Technol. 19 (2002) 736742.4 M.K. Kim, M.W. Cho, K. Kim, Application of the fuzzy controlstrategy to adaptive force control of non-minimum phase end millingoperations, Int. J. Machine Tools Adv. Manuf. Technol. 15 (1999)791795.5 U. Zuperl, F. Cus, Optimizat