mitedwhennon-linearcutsarerequired.Theotherapproachistousecross-couplingcontrolinwhichaxial-feedbackinformationissharedbetweenthemovingaxes.Thecross-couplingcontrollerisusedinadditiontotheconventionalaxialservocontroller.Ateachsamplingtime,thecross-couplingcontrollercalculatesthecurrentcontourerrorandgeneratesacommandthatmovesthetooltowardtheclosestpointonthedesiredtoolpath.Thiscontrolstrategyofth:J.Tu.Keywords:machinetool,cross-couplingcontroller,non-orthogonal,RMTIntroductionCurrentlymanufacturingindustrieshavetwoprimarymethodsforproducingmediumandhighvolumemachinedparts:dedicatedmachiningsystems(DMSs)andflexiblemanufacturingsystems(FMSs)thatincludeCNCmachines.TheDMSisanidealsolutionwhenthepartdesignisfixedandmassproductionisrequiredtoreducecost.Ontheotherhand,theFMSisidealwhentherequiredquantitiesarenotsohighandmanymodificationsinthepartdesignareforeseen.Incontrasttothesetwoextremes,Korendescribesaninnovativeapproachofcustomizedmanufacturingcalledreconfigurablemanufacturingsystems(RMS).Themainadvantageofthisnewapproachisthecustomizedflexibilityinthesystemtoproducea"partfamily"withlowerinvestmentcostthanFMS.AtypicalRMSincludesbothconventionalCNCmachinesandanewtypeofmachinecalledtheReconfigurableMachineTool.TheEngineeringResearchCenter(ERC)forReconfigurableMachiningSystems(RMS)attheUniversityofMichiganwithitsindustrialpartnershasdesignedanexperimentalReconfigurableMachineTool(RMT)。ThismachineallowsERCresearcherstovalidatemanyofthenewconceptsandmachinetooldesignmethodologiesthathavebeenalreadydevelopedinthecenter.TherearemanytypesofRMTs.Thispaperdescribesanarch-typenon-orthogonalmulti-axisRMTmachine。TheeconomicjustificationofRMTsisgiveninsectionofthispaper.Acontouringmotionrequiresthatthecuttingtoolmovesalongadesiredtrajectory.Typically,computerizedcontrolsystemsformachinetoolsgeneratecoordinatedmovementsoftheseparatelydrivenaxesofmotioninordertotraceapredeterminedpathofthecuttingtoolrelativetotheworkpiece.Toreducethecontouringerror,whichisdefinedasthedistancebetweenthepredeterminedandtheactualpath,therehavebeentwomaincontrolstrategies.Thefirstapproachistousefeedforwardcontrolinordertoreduceaxialtrackingerrors.however,theyarelimitedwhennon-linearcutsarerequired.Theotherapproachistousecross-couplingcontrolinwhichaxial-feedbackinformationissharedbetweenthemovingaxes.Thecross-couplingcontrollerisusedinadditiontotheconventionalaxialservocontroller.Ateachsamplingtime,thecross-couplingcontrollercalculatesthecurrentcontourerrorandgeneratesacommandthatmovesthetooltowardtheclosestpointonthedesiredtoolpath.Thiscontrolstrategyofth向右边线种行动当行不是影响时和行。然而,行绝不会通过仅仅变化横越行。这观察意义是:水平主轴位置代表系统较好稳定。.稳定地区随着增加取样时期变得小。带有NS-CC-FF控制系统有WP,WI,和WZ最大稳定地区。这因为交叉耦合控制之间冲突被Z路线运动onl被深度减少移去事实误差。S-CC和S-CC-FF控制中交叉耦合控制之间冲突能在被领进来Eqs转移功能中被看见。()和()。关于形状误差子系统,这仅仅包括X和Y路线,仅仅应该包含与诸如X和Y路线有关变量前,Ey,Xr,和Yr。然而,这子系统也包含一个Ez期间。将这Ez术语充当一场干扰到形状子系统。同样,子系统深度误差,这仅仅包括Y和Z路线,应该镇静自若与Y和Z路线有关条款。再一次,子系统术语深度包含前将充当一场干扰到这子系统。不同于Eq中Z路线转移功能。(),在Eq中一个。()包含前馈期间Kff。这Kff把干扰减少到在S-CC-FF一种较好性能中比S-CC控制导致系统。考虑到NS-CC-FF控制转移功能领进来Eq。(),关于形状误差子系统仅仅术语深度包含与X和Y路线和子系统有关误差包含补偿干扰期间前馈期间Kff。换句话说,从交叉耦合控制深度交叉耦合形状干扰期间控制使用前馈期间被移去。从干扰期间同时把控制深度交叉耦合到交叉耦合控制被仅仅活动Z路线被深度纠正移去形状误差。总来说,NS-CC-FF控制系统使用性能被期待在所提出控制中间最好,而仿真结果支持这分析。仿真结果用于仿真简化RMT轴模型每一路线参数能在附录A中找到。交叉耦合控制参数被选择这样系统将在在以前段中被定义稳定地区之内操作。这些参数自从优化控制以来不是最理想,不是本文一个目。对于比较目,所有交叉耦合控制参数在整个仿真中被保持同样。期望工具路径是在倾斜XS平面上一个通报运动到一场干扰,而每一控制反应将加以比较。数字,和描述仿真结果。一个通报中一个形状误差数字一个展览结果在S平面上切削。没有干扰所有三个所提出CC控制(汇聚到数字)上一条线中给比分离控制较好结果。数字b显示深度结果没有干扰误差控制。在这种情况下,很明显对称CC控制(S-CC)有糟糕性能。数字a和b显示仿真结果Y路线方向(机器)列中一场步骤干扰。结果趋势在作用于Y路线干扰面前类似于图.那些,S-CC-FF和NS-CC-FF控制之间性能区别作为是无意义被领进来。数字a和b朝着Z路线方向(主轴路线)显示仿真结果因为一场步骤干扰。数字个一个展览因为一形状误差所有三个CC控制操作比分离控制更好,但是NS-CC-FF控制提出最好性能。NS-CC-FF控制形状误差被Z路线中干扰不是影响,而S-CC-FF形状误差阴谋计划有一次突然跳跃。同样地,对于深度误差,当五月在图中被看见b时,NS-CC-FF控制显示比S-CC控制较好性能。为了总结结果,我们可能结束NS-CC-FF控制性能是在所有环境方面较高那所有仿真结果展览,正在设计阶段如所预料。结论在文中被描述了交叉耦合控制概念性设计过程允许对RMT控制问题进行洞察力和较好理解。在传统上,使用一台直角CNC机器要求四或者度自由某种机器过程,可能由有自由仅仅三度一台新机器类型,可构成机床(RMT)执行。RMT配置不利是当形状削减在X--S平面中是需要时,一种新类型误差—可能深度误差。这误差,适当地不控制,严重可能影响机器表面表面结束。为了深度减少结果误差,我们介绍三个类型交叉耦合控制并且发现所有三对一个合理范围参数是稳定。再可重组角度(或者工具定位角度)一个增加形状和深度误差和稳定减少该地区。进而,我们也发现所有三种类型交叉耦合(CC)控制在相当大程度上减少形状和深度误差。显示,对于非直角拱形类型RMT控制,非对称交叉耦合喂食前方(NS-CC-FF)控制有三个CC控制最好性能。对称交叉耦合(S-CC)控制在深度方面充分地解决对非直角RMTs是典型误差问题一个误差。S-CC-FF控制是边际地可接受,但是当一场干扰(诸如一种切削力)被运用于Z路线时会有问题。仅仅NS-CC-FF控制深度减少在相当大程度上两形状和误差。进而,稳定分析显示NS-CC-FF控制对各式各样参数是比其它控制稳定。我们主要结论,因此,NS-CC-FF控制充分地适合拱形类型RMT。然而,我们不能说明它是所有类型RMT一个一般结论。:J.Tu.Keywords:machinetool,cross-couplingcontroller,non-orthognal,RMTIntroductionCurrentlymanufacturingindustrieshavetwoprimarymethodsforproducingmediumandhighvolumemachinedparts:dedicatedmachiningsystems(DMSs)andflexiblemanufacturingsystems(FMSs)thatincludeCNCmachines.TheDMSisanidealsolutionwhenthepartdesignisfixedandmassproductionisrequiredtoreducecost.Ontheotherhand,theFMSisidealwhentherequire附录ControlofaNon-OrthogonalReconfigurableMachineToolReuvenKatzJohnYookYoramKorenReceived:January,;revised:September,AbstractComputerizedcontrolsystemsformachinetoolsmustgeneratecoordinatedmovementsoftheseparatelydrivenaxesofmotioninordertotraceaccuratelyapredeterminedpathofthecuttingtoolrelativetotheworkpiece.However,sincethedynamicpropertiesoftheindividualmachineaxesarenotexactlyequal,undesiredcontourerrorsaregenerated.Thecontourerrorisdefinedasthedistancebetweenthepredeterminedandactualpathofthecuttingtool.Thecross-couplingcontroller(CCC)strategywasintroducedtoeffectivelydecreasethecontourerrorsinconventional,orthogonalmachinetools.Thispaper,however,dealswithanewclassofmachinesthathavenon-orthogonalaxesofmotionandcalledreconfigurablemachinetools(RMTs).Thesemachinesmaybeincludedinlarge-scalereconfigurablemachiningsystems(RMSs).Whentheaxesofthemachinearenon-orthogonal,themovementbetweentheaxesistightlycoupledandtheimportanceofcoordinatedmovementamongtheaxesbecomesevengreater.Inthecaseofanon-orthogonalRMT,inadditiontothecontourerror,anothermachiningerrorcalledin-deptherrorisalsogeneratedduetothenon-orthogonalnatureofthemachine.Thefocusofthisstudyisontheconceptualdesignofanewtypeofcross-couplingcontrollerforanon-orthogonalmachinetoolthatdecreasesboththecontourandthein-depthmachiningerrors.Varioustypesofcross-couplingcontrollers,symmetricandnon-symmetric,withandwithoutfeedforward,aresuggestedandstudied.Thestabilityofthecontrolsystemisinvestigated,andsimulationisusedtocomparethedifferenttypesofcontrollers.Weshowthatbyusingcross-couplingcontrollersthereductionofmachiningerrorsaresignificantlyreducedincomparisonwiththeconventionalde-coupledcontroller.Furthermore,itisshownthatthenon-symmetriccross-couplingfeedforward(NS-CC-FF)controllerdemonstratesthebestresultsandistheleadingconceptfornon-orthogonalmachinetools.ASMEContributedbytheDynamicSystems,Measurement,andControlDivisionofTHEAMERICANSOCIETYOFMECHANICALENGINEERSforpublicationintheASMEJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROL.ManuscriptreceivedbytheASMEDynamicSystemsandControlDivisionJanuary,;finalrevisionSeptember,.AssociateEditor:J.Tu.Keywords:machinetool,cross-couplingcontroller,non-orthogonal,RMTIntroductionCurrentlymanufacturingindustrieshavetwoprimarymethodsforproducingmediumandhighvolumemachinedparts:dedicatedmachiningsystems(DMSs)andflexiblemanufacturingsystems(FMSs)thatincludeCNCmachines.TheDMSisanidealsolutionwhenthepartdesignisfixedandmassproductionisrequiredtoreducecost.Ontheotherhand,theFMSisidealwhentherequiredquantitiesarenotsohighandmanymodificationsinthepartdesignareforeseen.Incontrasttothesetwoextremes,Korendescribesaninnovativeapproachofcustomizedmanufacturingcalledreconfigurablemanufacturingsystems(RMS).Themainadvantageofthisnewapproachisthecustomizedflexibilityinthesystemtoproducea"partfamily"withlowerinvestmentcostthanFMS.AtypicalRMSincludesbothconventionalCNCmachinesandanewtypeofmachinecalledtheReconfigurableMachineTool.TheEngineeringResearchCenter(ERC)forReconfigurableMachiningSystems(RMS)attheUniversityofMichiganwithitsindustrialpartnershasdesignedanexperimentalReconfigurableMachineTool(RMT)。ThismachineallowsERCresearcherstovalidatemanyofthenewconceptsandmachinetooldesignmethodologiesthathavebeenalreadydevelopedinthecenter.TherearemanytypesofRMTs.Thispaperdescribesanarch-typenon-orthogonalmulti-axisRMTmachine。TheeconomicjustificationofRMTsisgiveninsectionofthispaper.Acontouringmotionrequiresthatthecuttingtoolmovesalongadesiredtrajectory.Typically,computerizedcontrolsystemsformachinetoolsgeneratecoordinatedmovementsoftheseparatelydrivenaxesofmotioninordertotraceapredeterminedpathofthecuttingtoolrelativetotheworkpiece.Toredu 附录ControlofaNon-OrthogonalReconfigurableMachineToolReuvenKatzJohnYookYoramKorenReceived:January3,2003;revised:September16,2003AbstractComputerizedcontrolsystemsformachinetoolsmustgeneratecoordinatedmovementsoftheseparatelydrivenaxesofmotioninordertotraceaccuratelyapredeterminedpathofthecuttingtoolrelativetotheworkpiece.However,sincethedynamicproperti