高速数控机床电主轴热误差机理分析与建模研究

高速数控机床电主轴热误差机理分析与建模研究一、本文概述Overviewofthisarticle随着制造业的快速发展，高速数控机床在精密加工领域的应用越来越广泛。然而，高速数控机床在高速运转过程中，电主轴会产生大量热量，导致热误差问题，严重影响加工精度和效率。因此，研究高速数控机床电主轴的热误差机理及建模方法，对于提高机床加工精度和稳定性具有重要的理论和实际意义。Withtherapiddevelopmentofthemanufacturingindustry,theapplicationofhigh-speedCNCmachinetoolsinthefieldofprecisionmachiningisbecomingincreasinglywidespread.However,duringhigh-speedoperationofCNCmachinetools,theelectricspindlegeneratesalargeamountofheat,leadingtothermalerrorproblemsandseriouslyaffectingmachiningaccuracyandefficiency.Therefore,studyingthethermalerrormechanismandmodelingmethodofhigh-speedCNCmachinetoolelectricspindlehasimportanttheoreticalandpracticalsignificanceforimprovingthemachiningaccuracyandstabilityofmachinetools.本文首先概述了高速数控机床电主轴热误差问题的背景和研究意义，然后介绍了国内外在该领域的研究现状和发展趋势。接着，本文详细分析了高速数控机床电主轴热误差产生的机理，包括热源分析、热传递过程以及热变形规律等方面。在此基础上，本文提出了一种基于热传递理论的电主轴热误差建模方法，并对建模过程进行了详细的阐述。本文通过实验验证了所建模型的准确性和有效性，为高速数控机床电主轴热误差的预测和控制提供了重要的理论依据。Thisarticlefirstoutlinesthebackgroundandresearchsignificanceofthethermalerrorproblemofhigh-speedCNCmachinetoolelectricspindle,andthenintroducestheresearchstatusanddevelopmenttrendsinthisfieldathomeandabroad.Furthermore,thisarticleprovidesadetailedanalysisofthemechanismbehindthethermalerrorsinhigh-speedCNCmachinetoolelectricspindles,includingheatsourceanalysis,heattransferprocess,andthermaldeformationlaws.Onthisbasis,thisarticleproposesathermalerrormodelingmethodforelectricspindlesbasedonheattransfertheory,andprovidesadetailedexplanationofthemodelingprocess.Thisarticleverifiestheaccuracyandeffectivenessoftheestablishedmodelthroughexperiments,providingimportanttheoreticalbasisforthepredictionandcontrolofthermalerrorsinhigh-speedCNCmachinetoolelectricspindles.本文的研究内容不仅有助于深入了解高速数控机床电主轴热误差的产生机理，也为后续的研究工作提供了有益的参考和借鉴。本文的研究成果对于提高高速数控机床的加工精度和稳定性，推动制造业的转型升级具有重要的意义。Theresearchcontentofthisarticlenotonlyhelpstogainadeeperunderstandingofthemechanismofthermalerrorsinhigh-speedCNCmachinetoolelectricspindles,butalsoprovidesusefulreferenceandguidanceforsubsequentresearchwork.Theresearchresultsofthisarticleareofgreatsignificanceforimprovingthemachiningaccuracyandstabilityofhigh-speedCNCmachinetools,andpromotingthetransformationandupgradingofthemanufacturingindustry.二、高速数控机床电主轴概述OverviewofElectricSpindlesforHighSpeedCNCMachineTools高速数控机床作为现代制造业的核心设备，其性能直接影响到加工零件的精度和效率。电主轴作为高速数控机床的关键部件，其性能稳定与否直接关系到机床的整体性能。电主轴，又称为电动主轴或电机内置主轴，是一种将电机与主轴融为一体的高性能主轴。它集成了电机、轴承、冷却、润滑等多个功能于一体，具有结构紧凑、转速高、动态响应快等优点，广泛应用于高速、高精度数控机床中。Asthecoreequipmentofmodernmanufacturingindustry,theperformanceofhigh-speedCNCmachinetoolsdirectlyaffectstheaccuracyandefficiencyofmachiningparts.Asakeycomponentofhigh-speedCNCmachinetools,thestabilityoftheperformanceoftheelectricspindledirectlyaffectstheoverallperformanceofthemachinetool.Electricspindle,alsoknownaselectricspindleormotorbuilt-inspindle,isahigh-performancespindlethatintegratesthemotorwiththespindle.Itintegratesmultiplefunctionssuchasmotors,bearings,cooling,lubrication,etc.Ithastheadvantagesofcompactstructure,highspeed,andfastdynamicresponse,andiswidelyusedinhigh-speedandhigh-precisionCNCmachinetools.电主轴的核心结构包括电机、轴承和主轴本体。其中，电机通常采用高速永磁同步电机，能够提供稳定且强大的动力；轴承则采用精密轴承，如气浮轴承或磁浮轴承，以减小摩擦和磨损，提高主轴的旋转精度和稳定性；主轴本体则采用高强度材料制造，以承受高速旋转时产生的巨大离心力。Thecorestructureofanelectricspindleincludesamotor,bearings,andthespindlebody.Amongthem,themotorusuallyadoptshigh-speedpermanentmagnetsynchronousmotor,whichcanprovidestableandpowerfulpower;Precisionbearings,suchasairormagneticbearings,areusedtoreducefrictionandwear,improvetherotationalaccuracyandstabilityofthespindle;Thespindlebodyismadeofhigh-strengthmaterialstowithstandtheenormouscentrifugalforcegeneratedduringhigh-speedrotation.在高速数控机床中，电主轴的热误差是一个不可忽视的问题。由于高速旋转和电机发热等原因，电主轴会产生热变形，导致主轴的几何精度下降，从而影响加工零件的精度。因此，对电主轴的热误差机理进行深入研究，并建立相应的热误差模型，对于提高高速数控机床的加工精度和稳定性具有重要意义。Inhigh-speedCNCmachinetools,thethermalerroroftheelectricspindleisanissuethatcannotbeignored.Duetohigh-speedrotationandmotorheating,theelectricspindlewillundergothermaldeformation,resultinginadecreaseinthegeometricaccuracyofthespindle,therebyaffectingtheaccuracyoftheprocessedparts.Therefore,conductingin-depthresearchonthethermalerrormechanismofelectricspindlesandestablishingcorrespondingthermalerrormodelsisofgreatsignificanceforimprovingthemachiningaccuracyandstabilityofhigh-speedCNCmachinetools.电主轴作为高速数控机床的核心部件，其性能稳定与否直接关系到机床的整体性能。对电主轴的热误差机理进行深入研究和建模，有助于更好地理解和控制电主轴的热变形行为，从而提高高速数控机床的加工精度和稳定性。Asthecorecomponentofhigh-speedCNCmachinetools,thestabilityoftheperformanceoftheelectricspindledirectlyaffectstheoverallperformanceofthemachinetool.Indepthresearchandmodelingofthethermalerrormechanismofelectricspindlescanhelptobetterunderstandandcontrolthethermaldeformationbehaviorofelectricspindles,therebyimprovingthemachiningaccuracyandstabilityofhigh-speedCNCmachinetools.三、电主轴热误差机理分析AnalysisofThermalErrorMechanismofElectricSpindle在高速数控机床中，电主轴作为关键部件，其性能直接影响到机床的加工精度和稳定性。电主轴在高速运转时，由于内部产生的热量和外部环境的影响，会产生热变形，从而引发热误差。热误差的存在会严重影响机床的加工精度，因此，对电主轴的热误差机理进行深入分析，并建立相应的热误差模型，对于提高机床的加工精度具有重要的理论和实际意义。Inhigh-speedCNCmachinetools,theelectricspindle,asakeycomponent,itsperformancedirectlyaffectsthemachiningaccuracyandstabilityofthemachinetool.Whentheelectricspindleisrunningathighspeed,duetotheheatgeneratedinternallyandtheinfluenceoftheexternalenvironment,thermaldeformationwilloccur,resultinginheatingerrors.Theexistenceofthermalerrorscanseriouslyaffectthemachiningaccuracyofmachinetools.Therefore,in-depthanalysisofthethermalerrormechanismofelectricspindlesandtheestablishmentofcorrespondingthermalerrormodelsareofgreattheoreticalandpracticalsignificanceforimprovingthemachiningaccuracyofmachinetools.电主轴的热误差主要来源于两个方面：一是电主轴内部产生的热量，包括电机绕组发热、轴承摩擦发热等；二是外部环境对电主轴的影响，如环境温度变化、冷却液循环不畅等。这些热量会在电主轴内部产生温度梯度，导致材料热膨胀系数的变化，进而引发电主轴的热变形。Thethermalerroroftheelectricspindlemainlycomesfromtwoaspects:first,theheatgeneratedinsidetheelectricspindle,includingmotorwindingheating,bearingfrictionheating,etc;Thesecondistheimpactofexternalenvironmentontheelectricspindle,suchaschangesinenvironmentaltemperatureandpoorcirculationofcoolant.Theseheatwillgenerateatemperaturegradientinsidetheelectricspindle,causingchangesinthematerial'sthermalexpansioncoefficient,whichinturnleadstothermaldeformationoftheelectricspindle.电主轴的热变形包括径向热变形和轴向热变形。径向热变形主要影响机床的径向精度，而轴向热变形则影响机床的轴向精度。为了准确描述电主轴的热变形，需要建立电主轴的热误差模型。Thethermaldeformationoftheelectricspindleincludesradialthermaldeformationandaxialthermaldeformation.Radialthermaldeformationmainlyaffectstheradialaccuracyofmachinetools,whileaxialthermaldeformationaffectstheaxialaccuracyofmachinetools.Inordertoaccuratelydescribethethermaldeformationoftheelectricspindle,itisnecessarytoestablishathermalerrormodelfortheelectricspindle.在建立电主轴热误差模型时，需要考虑多种因素，如电主轴的结构、材料、热传递方式等。同时，还需要考虑电主轴在工作过程中的动态特性，如转速变化、负载变化等。通过建立电主轴的热传递方程、热平衡方程和热变形方程，可以较为准确地描述电主轴的热误差机理。Whenestablishingathermalerrormodelforanelectricspindle,multiplefactorsneedtobeconsidered,suchasthestructure,material,andheattransfermodeoftheelectricspindle.Meanwhile,itisalsonecessarytoconsiderthedynamiccharacteristicsoftheelectricspindleduringoperation,suchaschangesinspeedandload.Byestablishingtheheattransferequation,heatbalanceequation,andthermaldeformationequationoftheelectricspindle,thethermalerrormechanismoftheelectricspindlecanbeaccuratelydescribed.为了验证所建立的热误差模型的准确性，需要进行实验验证。通过实验测量电主轴在不同工况下的温度分布和热变形量，与模型预测结果进行对比分析，可以评估模型的准确性和可靠性。Toverifytheaccuracyoftheestablishedthermalerrormodel,experimentalverificationisrequired.Bymeasuringthetemperaturedistributionandthermaldeformationoftheelectricspindleunderdifferentworkingconditionsthroughexperimentsandcomparingitwiththepredictedresultsofthemodel,theaccuracyandreliabilityofthemodelcanbeevaluated.电主轴的热误差机理分析是高速数控机床精度控制的重要研究内容。通过建立电主轴的热误差模型，可以深入了解电主轴在高速运转时的热变形规律，为机床的精度控制和优化设计提供理论支持。Theanalysisofthermalerrormechanismofelectricspindleisanimportantresearchcontentforprecisioncontrolofhigh-speedCNCmachinetools.Byestablishingathermalerrormodelfortheelectricspindle,wecangainadeeperunderstandingofthethermaldeformationlawoftheelectricspindleduringhigh-speedoperation,providingtheoreticalsupportforprecisioncontrolandoptimizationdesignofmachinetools.四、电主轴热误差建模研究ResearchonThermalErrorModelingofElectricSpindle在高速数控机床中，电主轴作为关键部件，其热误差对加工精度的影响不容忽视。为了深入理解和有效控制电主轴的热误差，本文对其进行了详细的建模研究。Inhigh-speedCNCmachinetools,theelectricspindleisakeycomponent,andtheinfluenceofitsthermalerroronmachiningaccuracycannotbeignored.Inordertogainadeeperunderstandingandeffectivelycontrolthethermalerroroftheelectricspindle,thispaperconductedadetailedmodelingstudyonit.我们通过对电主轴的结构和工作原理进行深入分析，明确了热误差的主要来源，包括主轴轴承摩擦热、电机发热以及热传导等因素。在此基础上，我们建立了电主轴的热传递模型，该模型综合考虑了热传导、热对流和热辐射等多种热传递方式。Wehaveconductedanin-depthanalysisofthestructureandworkingprincipleoftheelectricspindleandidentifiedthemainsourcesofthermalerrors,includingfrictionalheatfromthespindlebearings,motorheating,andheatconduction.Onthisbasis,weestablishedaheattransfermodelfortheelectricspindle,whichcomprehensivelyconsidersvariousheattransfermodessuchasheatconduction,heatconvection,andheatradiation.接着，我们运用有限元分析方法，对电主轴在不同工作条件下的温度分布进行了仿真研究。通过对比分析仿真结果与实际测量数据，验证了模型的准确性和有效性。这些结果不仅有助于我们深入了解电主轴热误差的产生机理，也为后续的热误差补偿提供了重要依据。Next,weusedfiniteelementanalysismethodtosimulatethetemperaturedistributionoftheelectricspindleunderdifferentworkingconditions.Theaccuracyandeffectivenessofthemodelwereverifiedbycomparingandanalyzingsimulationresultswithactualmeasurementdata.Theseresultsnotonlyhelpustogainadeeperunderstandingofthemechanismofthermalerrorsinelectricspindles,butalsoprovideimportantbasisforsubsequentthermalerrorcompensation.我们还基于热传递模型，建立了电主轴的热误差预测模型。该模型能够根据电主轴的工作状态和环境条件，预测其热误差的大小和方向。通过实时监测和调整电主轴的工作状态，我们可以有效减小热误差，提高加工精度。Wealsoestablishedathermalerrorpredictionmodelfortheelectricspindlebasedontheheattransfermodel.Thismodelcanpredictthemagnitudeanddirectionofthermalerroroftheelectricspindlebasedonitsworkingstateandenvironmentalconditions.Bymonitoringandadjustingtheworkingstatusoftheelectricspindleinreal-time,wecaneffectivelyreducethermalerrorsandimprovemachiningaccuracy.我们探讨了电主轴热误差补偿方法。通过结合热误差预测模型和数控机床控制系统，我们可以实现对电主轴热误差的实时补偿。这种补偿方法不仅能够提高加工精度，还能延长机床的使用寿命。Wediscussedthemethodofcompensatingforthermalerrorsinelectricspindles.BycombiningthethermalerrorpredictionmodelwiththeCNCmachinetoolcontrolsystem,wecanachievereal-timecompensationforthethermalerroroftheelectricspindle.Thiscompensationmethodcannotonlyimprovemachiningaccuracy,butalsoextendtheservicelifeofthemachinetool.本文对高速数控机床电主轴的热误差机理进行了深入分析，并建立了相应的热传递模型和热误差预测模型。这些模型为电主轴的热误差补偿提供了有力支持，对于提高数控机床的加工精度和稳定性具有重要意义。Thisarticleprovidesanin-depthanalysisofthethermalerrormechanismofhigh-speedCNCmachinetoolelectricspindles,andestablishescorrespondingheattransfermodelsandthermalerrorpredictionmodels.Thesemodelsprovidestrongsupportforthermalerrorcompensationofelectricspindles,whichisofgreatsignificanceforimprovingthemachiningaccuracyandstabilityofCNCmachinetools.五、实验研究与结果分析Experimentalresearchandresultanalysis为了深入研究高速数控机床电主轴热误差的机理，我们设计并实施了一系列的实验。这些实验旨在验证我们之前提出的热误差模型，并探究各种操作条件和参数对电主轴热误差的影响。Inordertodeeplystudythemechanismofthermalerrorsinhigh-speedCNCmachinetoolelectricspindles,wedesignedandimplementedaseriesofexperiments.Theseexperimentsaimtovalidateourpreviouslyproposedthermalerrormodelandexploretheeffectsofvariousoperatingconditionsandparametersonthethermalerrorofelectricspindles.我们采用了多种传感器和测量设备，对电主轴在高速运转过程中的温度变化进行了精确测量。这些设备包括热像仪、温度传感器以及高精度的位移测量装置。通过这些设备，我们能够实时获取电主轴在工作过程中的温度分布和位移变化。Wehaveusedvarioussensorsandmeasuringequipmenttoaccuratelymeasurethetemperaturechangesoftheelectricspindleduringhigh-speedoperation.Thesedevicesincludethermalimagers,temperaturesensors,andhigh-precisiondisplacementmeasurementdevices.Throughthesedevices,wecanobtainreal-timetemperaturedistributionanddisplacementchangesoftheelectricspindleduringoperation.实验过程中，我们模拟了不同的加工条件，包括不同的主轴转速、切削力和冷却液流量等。我们发现，随着主轴转速的增加，电主轴的温度会显著上升，进而导致热误差的增加。切削力和冷却液流量也对电主轴的温度和热误差有显著影响。Duringtheexperiment,wesimulateddifferentmachiningconditions,includingdifferentspindlespeeds,cuttingforces,andcoolantflowrates.Wefoundthatasthespindlespeedincreases,thetemperatureoftheelectricspindlewillsignificantlyincrease,leadingtoanincreaseinthermalerror.Thecuttingforceandcoolantflowratealsohaveasignificantimpactonthetemperatureandthermalerroroftheelectricspindle.为了验证我们的热误差模型，我们将实验数据输入到模型中，并与实际的热误差进行了比较。结果表明，我们的模型能够较为准确地预测电主轴的热误差，误差率在可接受范围内。这验证了我们的模型在描述电主轴热误差机理方面的有效性。Tovalidateourthermalerrormodel,weinputtedexperimentaldataintothemodelandcompareditwiththeactualthermalerror.Theresultsindicatethatourmodelcanaccuratelypredictthethermalerroroftheelectricspindle,andtheerrorrateiswithinanacceptablerange.Thisvalidatestheeffectivenessofourmodelindescribingthethermalerrormechanismofelectricspindles.通过进一步分析实验数据，我们还发现了一些有趣的规律。例如，当冷却液流量增加到一定程度时，电主轴的温度和热误差会趋于稳定，不再明显下降。这表明，在实际加工过程中，存在一个最佳的冷却液流量值，使得电主轴的热误差达到最小。Byfurtheranalyzingtheexperimentaldata,wealsodiscoveredsomeinterestingpatterns.Forexample,whenthecoolantflowrateincreasestoacertainextent,thetemperatureandthermalerroroftheelectricspindlewilltendtostabilizeandnolongersignificantlydecrease.Thisindicatesthatthereisanoptimalcoolantflowratevalueintheactualmachiningprocess,whichminimizesthethermalerroroftheelectricspindle.通过实验研究，我们验证了我们的热误差模型的有效性，并深入了解了高速数控机床电主轴热误差的机理。这些研究结果为优化电主轴的设计和提高数控机床的加工精度提供了重要的理论依据和实践指导。Throughexperimentalresearch,wehavevalidatedtheeffectivenessofourthermalerrormodelandgainedadeeperunderstandingofthemechanismofthermalerrorinhigh-speedCNCmachinetoolelectricspindles.TheseresearchresultsprovideimportanttheoreticalbasisandpracticalguidanceforoptimizingthedesignofelectricspindlesandimprovingthemachiningaccuracyofCNCmachinetools.六、热误差补偿与控制策略Thermalerrorcompensationandcontrolstrategy在高速数控机床电主轴的应用过程中，热误差的存在对加工精度造成了显著影响。为了减小或消除这一误差，需要对热误差进行有效的补偿与控制。本章节将重点探讨热误差补偿的原理、方法以及控制策略，旨在提高数控机床的加工精度和稳定性。Intheapplicationprocessofhigh-speedCNCmachinetoolelectricspindle,thepresenceofthermalerrorhasasignificantimpactonmachiningaccuracy.Inordertoreduceoreliminatethiserror,itisnecessarytoeffectivelycompensateandcontrolthethermalerror.Thischapterwillfocusonexploringtheprinciples,methods,andcontrolstrategiesofthermalerrorcompensation,aimingtoimprovethemachiningaccuracyandstabilityofCNCmachinetools.热误差补偿的核心思想是通过测量和识别热误差的大小和方向，然后将其反向应用于机床的运动控制系统，从而抵消原始误差，提高加工精度。补偿过程通常包括误差测量、误差识别和误差补偿三个步骤。Thecoreideaofthermalerrorcompensationistomeasureandidentifythemagnitudeanddirectionofthermalerrors,andthenapplytheminreversetothemotioncontrolsystemofthemachinetool,therebyoffsettingtheoriginalerrorandimprovingmachiningaccuracy.Thecompensationprocessusuallyincludesthreesteps:errormeasurement,erroridentification,anderrorcompensation.常见的热误差补偿方法主要包括硬件补偿和软件补偿。硬件补偿通常通过增加热稳定结构、改进冷却系统等方式，减少热源对电主轴的影响。软件补偿则主要依赖于误差测量和识别技术，通过调整机床的运动参数来补偿热误差。Thecommonthermalerrorcompensationmethodsmainlyincludehardwarecompensationandsoftwarecompensation.Hardwarecompensationusuallyreducestheimpactofheatsourcesontheelectricspindlebyincreasingthermalstabilitystructures,improvingcoolingsystems,andothermethods.Softwarecompensationmainlyreliesonerrormeasurementandrecognitiontechniques,compensatingforthermalerrorsbyadjustingthemotionparametersofthemachinetool.为了有效地减小热误差，需要制定科学的控制策略。应建立电主轴热误差的数学模型，以便更准确地预测和补偿误差。应优化机床的冷却系统，确保电主轴在高速运转时能够保持稳定的温度。还应定期对机床进行维护和校准，以确保其长期稳定的运行。Inordertoeffectivelyreducethermalerrors,itisnecessarytodevelopscientificcontrolstrategies.Amathematicalmodelforthethermalerroroftheelectricspindleshouldbeestablishedtomoreaccuratelypredictandcompensatefortheerror.Thecoolingsystemofthemachinetoolshouldbeoptimizedtoensurethattheelectricspindlecanmaintainastabletemperatureduringhigh-speedoperation.Regularmaintenanceandcalibrationofthemachinetoolshouldalsobecarriedouttoensureitslong-termstableoperation.热误差补偿与控制策略是提高高速数控机床加工精度的重要手段。通过合理的补偿方法和科学的控制策略，可以有效地减小热误差，提高机床的加工精度和稳定性。未来，随着技术的不断进步，我们有理由相信热误差补偿与控制策略将会更加完善和优化。Thermalerrorcompensationandcontrolstrategiesareimportantmeanstoimprovethemachiningaccuracyofhigh-speedCNCmachinetools.Byusingreasonablecompensationmethodsandscientificcontrolstrategies,thermalerrorscanbeeffectivelyreduced,andthemachiningaccuracyandstabilityofmachinetoolscanbeimproved.Inthefuture,withthecontinuousadvancementoftechnology,wehavereasontobelievethatthermalerrorcompensationandcontrolstrategieswillbemoreperfectandoptimized.七、结论与展望ConclusionandOutlook本文深入研究了高速数控机床电主轴热误差的机理分析与建模。通过理论分析与实验验证，我们详细探讨了电主轴热误差的来源、影响因素以及其与机床加工精度的关系。研究发现，电主轴的热误差主要来源于电机发热、轴承摩擦热和切削热等，且这些热源对机床的加工精度有着显著的影响。我们还建立了电主轴热误差的数学模型，为预测和控制电主轴热误差提供了理论基础。Thisarticledelvesintothemechanismanalysisandmodelingofthermalerrorsinhigh-speedCNCmachinetoolelectricspindles.Throughtheoreticalanalysisandexperimentalverification,wehaveexploredindetailthesourcesandinfluencingfactorsofthermalerrorsinelectricspindles,aswellastheirrelationshipwithmachinetoolmachiningaccuracy.Researchhasfoundthatthethermalerrorofelectricspindlesmainlycomesfrommotorheating,bearingfrictionheat,andcuttingheat,andtheseheatsourceshaveasignificantimpactonthemachiningaccuracyofmachinetools.Wealsoestablishedamathematicalmodelforthethermalerroroftheelectricspindle,providingatheoreticalbasisforpredictingandcontrollingthethermalerroroftheelectricspindle.本文的研究对于提高高速数控机床的加工精度具有重要的指导意义。通过深入了解电主轴热误差的机理和建模方法，我们可以更好地预测和控制机床的热误差，从而提高机床的加工精度和稳定性。同时，这些研究成果也可以为机床的设计和制造提供有价值的参考。Theresearchinthisarticlehasimportantguidingsignificanceforimprovingthemachiningaccuracyofhigh-speedCNCmachinetools.Bygainingadeeperunderstandingofthemechanismandmodelingmethodsofthermalerrorsinelectricspindles,wecanbetterpredictandcontrolthethermalerrorsofmachinetools,therebyimprovingtheirmachiningaccuracyandstability.Meanwhile,theseresearchfindingscanalsoprovidevaluablereferencesforthedesignandmanufacturingofmachinetools.虽然本文在高速数控机床电主轴热误差机理分析与建模方面取得了一些成果，但仍有许多问题需要进一步研究和探讨。Althoughthisarticlehasachievedsomeresultsintheanalysisandmodelingofthethermalerrormechanismofhigh-speedCNCmachinetoolelectricspindles,therearestillmanyissuesthatneedfurtherresearc