喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== ORIGINAL ARTICLEAn experimental investigation of spindle rotary erroron high-speed machining centerLan Jin&Zhaoyang Yan&Liming Xie&Weidong Gou&Linhu TangReceived: 21 February 2013 /Accepted: 22 August 2013 /Published online: 8 September 2013#Springer-Verlag London 2013Abstract A method is described in this paper for measuringthe spindle rotation error and a technique for separating theeccentric error caused by setup error of the master cylinder.The system consists of two non-contact capacitance sensorsused to measure the radial displacement of the rotating mastercylinder and an LMS Test.Lab used to collect the measure-ment data. LMS Test.Lab offers a complete engineering solu-tion for rotating machinery. Based on our experimental re-search, it indicates that this system can be used to measuringthe spindle rotary error at different speeds. It is also verifiedthe feasibility of the error separation methods developed inthis paper.Keywords High-speedspindlerotaryerror.Experimentalsetup.Measurement.Separatetheseerrors1 IntroductionOne of the significant parameter of spindle unit is rotationprecision of spindle. It not only influences the machiningprecision of machine tool but also geometrical shape andsurface roughness of workpiece. Spindle rotary error is avariation, of which the actual axis of the spindle relative toideal axis in the measurement plane within the specified. Thevariation is small; spindle rotary precision is high; conversely,the lower the rotary precision. Thus, the identification of thespindlerotationerrorshasbecomeveryimportant.Sucherrorscause degradation in surface finish, roundness, feature size,and feature location. In an earlier work, Tlustry and Bryanet al. 1, 2 proposed a method for measuring spindle errormotions with a master ball while machining and generated abasecircle for better visualizing the motion ofaxisofrotation.After this, many machine tool testing methods were adoptedin many international standards such as American NationalStandards Institute (ANSI) and ISO, and ANSI especiallydrew up the standard for the test of the spindle 3.With the development of high-speed and high-precisionmachine tools, the high-speed rotation and the built-in motoralsointroducelargeamountsofheatandrotatingmassintothesystem, requiring precisely regulated cooling, lubrication, andbalancing. As a result, the thermal and mechanical behaviorsof high-speed motorized spindles have become very difficultto predict for spindle designers and users 4. The measure-ment and evaluation of rotation error of tool spindle is moreimportant for evaluating the performance of high-speed CNC(computer numerical control) machine tools. However, theanalysis of spindle rotation errors can not only predict thequality of the machined part but also be used to evaluate themachine tool precision for purchasing and maintenance pur-poses.Insomespindlemeasurementsystems510,aprecisesphere or cylinder and multiple probes are used to inspect thespindle axis rotary error for the case of a rotating-sensitivedirection. It is desirable to separate out unnecessary data, suchas the roundness error and the eccentricity error of a precisesphere or cylinder, when the principle of the spindle errormeasurement and means cannot be fundamentally changed.Thus, many error separation methods have been developed toL. Jin (*):L. XieSchool of Mechanical & Electronical Engineering,Lanzhou University of Technology,Lan gongping 287#, Qilihe district, Lanzhou 730050,Gansu Province, Chinae-mail: lan_Z. YanCAMA (Luo Yang) Electromechanic Co.,LTD, Luoyang 471003, ChinaW. GouQinghai No.1 CNC Machine Tool Co.,Ltd, Xining 810018, ChinaL. TangLanzhou Institute of Technology,Lanzhou 730050, ChinaInt J Adv Manuf Technol (2014) 70:327334DOI 10.1007/s00170-013-5270-9separateouttheroundnesserrorfromthereferenceartifactandfrom the spindle error. He et al. 11 proposed a mathematicalmodel for the rotary motion of an electromagnetic spindle andseparateditintomanycircularmotions with differentfrequen-cies and then solved the rotary motion equations for thecircular motions. Wan and Liu 12 presented a method whichused the phase difference between several sensors along withFourier expansions and computations to eliminate the influ-enceoftheeccentricityandformerrorsinordertomeasuretherotational error precisely. Gao et al. 13 reported the angularthree-probe method for roundness and spindle error measure-ment. Compared with the conventional displacement three-probe method, the angular three-probe method was moresuitable for detecting the multi-degree-of-freedom compo-nents of spindle error and roundness.Many new concepts of spindle error measurement havebeen provided 1417, but the influence of eccentricity, themain component of the measuring signal, was ignored. Anymethod of spindle error measurement must be capable ofseparating the eccentricity error. The frequency-domain meth-od is normally used to separate out the error signal. After thepros and cons of two Fourier transforms, the spindle error canbe separated out from the measured signal by filtering tech-nology. While measuring the rotatingerror atdifferent speeds,the types and parameters of the filter need to be changedconstantly so that the most suitable filter can be found to dealwith the measured signal. In addition, more complex pro-grams are often written to change the filter. This is complexand difficult work.In this paper, an effective method of the spindle errormeasurement and separating out the eccentricity error is de-scribed in detail and the corresponding experimental resultsare reported, specifically at an electrospindle maximum speedof 15,000 rpm and 25 kW (continuous service)/30 kW(30 min), with which an asynchronous electric motor that isintegrated into the spindle structure between the front and rearceramic bearings was used.2 Measurement principle2.1 Sensor distributionThe installation of the sensor X and Yis shown in Fig. 1. TwoMICRO-EPSILON eddyNCDT 3010sensors,which is a non-contacting displacement measuring system operating on theeddy current principle, with 0.1 m of static repeatability,made in Germany and used for measuring targets made ofelectrically conductive materials that may be either ferromag-netic or non-ferromagnetic, are mounted in orthogonal direc-tions on a mounting bracket which is installed on the spindlehousing. The sensors X and Y are maintained at the samedistance of their surface to the master cylinder, according tothe JB/T10801.2-2007 standards 18, as shown in Fig 1.Before measuring the radial displacement of the rotating spin-dle, the initial distances of the sensor to the cylinder should besubtracted to simulate the sensors contacting the master cyl-inder in order to obtain the actual signal of the rotation error.2.2 Error analysisAccuracy of spindle error measurement is affected by theinherent error, the random error, and the external error. Theinherent error in the spindle includes the spindle-shank,shank-collet, and collet-tool interfaces 19. The random erroris that the rise in temperature will affect the bearing contactload and will also induce thermal growth. While high-bearingtemperature is one of the primary factors for bearing failure,spindle thermal growth affects the accuracy of machined parts20, especially the spindle speed of 12,000 r/min or more,bearing temperature could rise rapidly and cause shaft-bending deformation, resulting in inaccurate measurement,such as the temperature of bearing, the external error includessensor offset, eccentricity error of the master cylinder, theform error of the target surface installed in the spindle.Inherent error cannot measure the spindle rotation error di-rectly by using the sensors, but the rotation error could bemeasured indirectly through the master cylinder installed inthe spindle and used this to substitute for a cutting tool. Thisprocedure will inevitably combine the roundness error andeccentricity error of the master cylinder or of the master ball.In order to facilitate the measurement processing, the spindlerotation error can be simplified into radial error motion andaxial error motion 21. Therefore, it is necessary to findeffective methods to separate out these errors.In this experiment, spindle thermal growth is monitored atambient temperature 25 C; thermal growth is normalaccording to the JB/T10801.2-2007 standards 18.2.3 Mathematical models2.3.1 Calculation of eccentricity and initial phase angleTheartifactmustbeconsideredfirstbecauseithaseccentricityand roundness errors. Initially, a simulation is carried out toanalyzethechangeofmeasurementdatabasedoneccentricity.The eccentricity e is expressed as the distance between theorigin point of the reference coordinate system and the centerof the rotating axis O 19. The eccentricity of the mastercylinderandtheinitialphaseangleofthesensorscanbetestedby the method described in Fig. 2(a).As shown in Fig. 2(b), a dial gauge is used to measure themaster cylinder in a static and low-speed state. Point A shownin Fig. 2(c) is the initial position of the dial gauge. The valuesof points B, C, D, and E measured by the dial gauge are m,emax, n, and emin.328Int J Adv Manuf Technol (2014) 70:327334Fig. 1 Distribution sensorsFig. 2 Calculation ofeccentricityand initial phase angleInt J Adv Manuf Technol (2014) 70:327334329The eccentricity can be expressed as:e emax emin=21where e is the eccentricity of the master cylinder.In the triangle OGF shown in Fig. 2(b)OG eOF m n=2Therefore, the initial phase of the sensor X is: arcsinOF=OG arcsinm n=2e?22.3.2 Construction of the error modelThe measurement ofthe spindle error isdirectlyinfluencedbythe out-of-roundness of the master cylinder and theFig. 3 Schematic diagram of themeasurementFig. 4 Spindle errormeasurement system330Int J Adv Manuf Technol (2014) 70:327334eccentricity of the master cylinder. Specifically, the eccentricerror is present in the measuring signals, and it decreases theprecision of the measuredspindle error, especiallyinthe high-precision measurements. Therefore, several attempts havebeenmadetoseparatetheseerrors.Generally,Fourieranalysisis used to calculate the influence of eccentricity of the mastercylinder on the machine spindle for measured data sets. Theintegration scheme is used to calculate appropriate Fouriercoefficients for the eccentricity or once-around, or fundamen-tal frequency of the gauge data. These Fourier coefficients arethen used to reconstruct the once-around. The once-aroundwaveform can then be subtracted from the entire data set sothat only the second order and higher harmonics of the errorTable 1 The dependency of speed with respect to unbalancingSpindle speed (rpm)Rotary error (mm)X-axisY-axismaxminmaxmin1,00026.423.224.817.92,00028.724.422.222.13,00021.519.322.023.94,00020.823.322.220.15,00023.724.829.422.76,00027.828.830.723.37,00033.147.940.120.28,00014.325.238.823.19,00022.936.341.424.510,00022.134.444.326.111,00026.240.149.826.513,00027.241.147.150.414,00032.845.630.447.315,00042.447.141.750.1Fig. 6 Rotation-sensitive directional error motions at 15,000 rpmabcdX-axis eccentricity error signalsX-axis rotation errorY-axis eccentricity error signalsY-axis rotation errorFig. 5 a Eccentricity error signals ex, b rotation error x(x=x(t)ex), c eccentricity error signals ey, and d rotation error y(y=x(t)ey)Int J Adv Manuf Technol (2014) 70:327334331are included. However, Fourier analysis can introduce somenew errors affecting the results of measurement. Therefore,the best method is to calculate the eccentricity error first andonly then to remove it from the gauge data.The two sensors are used to measure the spindle error asshown in Fig. 3. As the measuring signal includes both therotation error and the shape error, the mathematical modelmust be constructed to remove them. The measuring signalobtained via the sensors can be deduced from the schematicdiagram shown in Fig. 4.The location designated by the point O in Fig. 3 representsthe center of the spindle. Point O1 is the center of the mastercylinder. R is the radius of the master cylinder. In a frame ofreference, in which the spindle is stationary and the sensorsmove, r is the radius of the trace of the sensor motion. TheinitialpositionofsensorXisatpointA,asshowninFig.3,theinitial phase of which is . After rotating through angle , thesensor X moves to point B. The length of BC is the errorcausedbyaneccentric mountingofthe mastercylinder.Ifx(t)represents the output of the sensor X, x the spindle error ofdirection x, exthe eccentricity error of direction x, and the shape error at the angular velocity, these variables arerelated in the following expression as:x t x ex 3With the use ofa high-accuracy mastercylinder, the round-ness error can be considered to be negligible. Therefore,Eq. 3 can be simplified to Eq. 4 as follows:x t x ex4ThedistanceLxfromthespindlecentertothesurfaceofthemaster cylinder is:LxffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 esin ?2q ecos 5The radius r of the trace of the sensor motion can then beobtained as:r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 esin2q ecos6Therefore, the eccentricity error excan be expressed as:ex Lxr7Since the sensors X and Yare aligned at an angle of 90 asshown in Fig. 3, output y(t) of the sensor Y can be describedby the following equations:LyffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 esin 90?2q ecos 90?8ey Lyr9y t y ey102.3.3 Evaluation of the rotation errorAfter removing the eccentricity error, the results of the X andYerror motions can be used to produce an errormotion plotfor a given rotation-sensitive direction. The calculation ofD(t), the motion error, is performed from Eq. 11 below:D t r0 xt sin t yt cos t11where rois the radius of an arbitrarily chosen base circle, xandyare the measurederror motions, isthe rotationrateofthe sensors, and t is the measuring time. To evaluate the errormotion value, a least-squares fit of the data is performed toposition the error motion on a least-squares center. The totalradial error is determined to be the maximum value of thespindle error less the minimum value with respect to the least-squares center. The position (a, b) of the least-squares centerand the radius D of the least squares are calculated in confor-mity with the ANSI Standard B89.3.4 M as follows:a 2Xk1nxk12b 2Xk1nyk13D 2Xk1ndk14Where a and b correspond to the X and Y locations of theleast-squares circle center, respectively, n is the number ofdiscrete data points, and xkand ykcorrespond to the values ofthe ithdata points in the X and Y direction, respectively 11.The distance DKfrom the position (a, b) to the position(xk, yk) can be expressed as:Dkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixka2 ykb2q15Therefore, the spindle error is:f DkmaxDkmin16332Int J Adv Manuf Technol (2014) 70:3273343 Experimental measurement3.1 Measuring system3.1.1 Total systemFigure 4 shows the measuring system for a rotating spindleinstalled inthe testing platform. A precision mastercylinderismounted on the tool position of the spindle. The roundness ofthe master cylinder has an accuracy of better than 0.001 m.The device for mounting the two sensors is shown in Fig. 4.The sensor-mounting device not only supports the sensors butalso keeps the sensors at the same cross sectional circle of themaster cylinder. With the sensor-mounting bracket, the mea-surement signals can minimize the setup error of the sensors.During measurement, sensor signals are acquired by anLMS Test.lab collector where the signals are pretreated andthen transferred into the receiving computer for furtheranalysis.3.2 Test resultsThe dependency of speed with respect to unbalancing is listedin Table 1. The critical speed of this spindle is of 7,000 r/min.After using the error separation model described in theprevious section to remove the setup error of the mastercylinder, the rotating error and the setup eccentricity of themaster cylinder are subtracted from the measured data. Thevariations in the output are as depicted in Fig. 5The least-squares method was used for each revolution,which has removed the setup error associated with the mastercylinder. The lateral spindle error is 0.005 mm at 15,000 rpmas shown in Fig. 6.To demonstrate the feasibility of the proposed spindle-measuring system and the error separation method, experi-ments on a high-speed horizontal machining center with dif-ferent spindle speeds. A trace of the rotating master cylinderwas measured by the method proposed previously in thisstudy. The least-squares method was used for each revolution,and the setup eccentricity of the master cylinder wassubtracted from the measured data. The overall test resultsare summarized in Table 2.Table 2 summarizes the measured rotation error at differentspeeds. The maximum error of the spindle rotation, as shownin Table 2, is 7,000 rpm, which may fall into the resonanceregion. The general trend of rotation errors is indicated inFig. 7. It can be seen that the rotation error increases as thespeed increases with the exception of the region around7,000 rpm.The rotation static error of this spindle is 4 m, while thetest result is 5 m. Measured rotation errors are very close totheir real values. These measurement results confirm the fea-sibility of the proposed spindle-measuring system.4 ConclusionThispaperdescribestheprincipleofanewdevicedeterminingspindle rotation error using a method of error separation at15,000 rpm. The results of our measuring experiments usingthe system proposed above, along with appropriate signalprocessing techniques, demonstrate that the new device formeasuringthe rotationerror ofa high-speedspindle isfeasibleTable 2 The overall test results of the spindle error measurementsSpindle Speed(r/min)1,0003,0005,0007,0009,00010,00012,00013,00014,00015,000Rotary error (mm)4.624.644.685.184.934.744.784.864.89510003000500070009000 10000120001300014000 150004.555.5spindle speed (r/min)rotary error (mm)Fig. 7 The trend of rotary errorsInt J Adv Manuf Technol (2014) 70:327334333and that the mathematical model of error separation can ef-fectively isolate the eccentricity error caused by setup error.Compared with filtering for error separation, use of the meth-od of error separation described in this paper can obviate theundesirableremovalofsomecomponentsofthesignalswhichwe would otherwise need.References1. Tlustry J (1959) System and methods for testing machine tools.Microtechnic 13:1622. 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