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A new method and instrument for measuring circular motion error of NC machine tools H.L. Liua,b,*, H.M. Shia, B. Lia, X. Lia aNational CNC Control System Research Center, Mechanical Department, Huazhong University of Science and Technology, Wuhan 430074, China bZhanjiang Ocean University, Zhanjiang, Guangdong 524025, China Received 31 August 2004; accepted 13 January 2005 Available online 16 February 2005 Abstract A new method andinstrument formeasuring circular motionerror of numerical control (NC) machine tools are described inthis paper. The instrument consists of a linear displacement transducer bar with two balls at each end and a high accuracy rotary encoder. The radius variations are detected by the transducer and the rotation angle of the bar is measured by the rotary encoder while the machine is moving in a circular path. The measuring area is circular except for a small area around the center of the disc. The bar can be expanded and contracted along its axis for different application. The instrument has a compact structure and can be installed on a machine tool simply and quickly. It is shownby the experimental results that the instrument hasgood repeatability andhighprecision ofmeasuring circular motiontrajectories. The instrument can be widely used especially in the error-compensation and error-source project in the industrial application. q 2005 Elsevier Ltd. All rights reserved. Keywords: NC machine tool; Motion error; Measurement instrument; Circular measurement 1. Introduction In recent years, the precision machining process has attracted much attention from numerous investigators. One of its important tasks for error-compensation and error source diagnosis is to map the volumetric errors of a machine tool 1. Current techniques have the ability to measure parametric error function for each of the machines axes, for instance, the positioning and linear motion accuracy. However, it is still diffi cult to measure precisely the circular motion error let alone a more general motion trajectory. Several devices and methods are usually used to measure the trajectory accuracy of circular motions, and described as follows: (1) A test bar and a one-dimensional probe 2. (2) A disk (or a ring gage) and a two-dimensional probe 3. (3) The double ball bar system (DBB) consists of a fl exural bar at each end and two magnetic balls constrained by special sockets with a spherical surface. The deviation of the relative distance between balls is measured using the fl exural bar while the machine moves in circular motion 4,5. (4) The double-bar linkage and two rotary encoders are set at the root end of the link separately to detect the rotation angles of the links 6,7. (5) The KGM circular test system 8. The above-mentioned instruments and methods have really used to assess the trajectory accuracy of circular motion and some usefully results have been gained. There exist some problems to some extent in their practical applications as those pointed out by several researchers 1,6. In (1) and (2), there is limitation by its own stranded disk accuracy. High accuracy can be obtained by (3) but only in the radius direction. Although circular motion errors along x axis and y axis in XY plane (two-dimensional error) can be got in (4), the instrument is very complicated and will be made hardly. KGM circular test system, also called cross-grid encoder, has an excellent performance, but it is very costly and the biggest measuring zone is merely a circular of about radius 120 mm. 0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.01.012 International Journal of Machine Tools fax: C86 27 87545256. E-mail address: huanlao_liu (H.L. Liu). A new method and instrument for measuring the circular motion error of NC machine tools is presented in this paper. When the machine is stopped at points along the circular path where radius and angle information can be gained and commanded and actual points can be compared, errors of x and y axis can be measured which is a two-dimensional error. Moreover, this method is simple and convenient in practical application, while the instrument is of a compact structure with low cost. 2. Outline of the measurement instrument A schematic diagram of the presented prototype measurement instrument is shown in Fig. 1. This instrument consists of a linear transducer bar with two balls at each end of the bar similar to DBB and a rotary encoder, which is set at root end of ball 1 to detect rotation angles of the bar. Ball 2 is connected to machine tool spindle by ball holder. The base of the instrument is fi xed on table of an NC machine tool to be measured, for example, xy stage of the machine center. The rotation plane of the linear transducer bar is parallel to xy plane of the machine table and perpendicular to the rotation axis of the spindle. The measuring coordinate frame can be set as that the rotation axis of the encoder on the root of ball 1 is defi ned as the z- axis, which is parallel to the rotation axis of the spindle denoted as Z. The x and y axes are set to be parallel respectively to the machine tool and denoted as X, Y, so the xy plane is located on the rotation plane of the linear transducer bar. Fig. 2 is a photograph of the prototype measurement instrument. 3. Principle of the measurement method In order to avoid the velocity lag of the axis servo, which always cause the actual point dropping behind the commanded point in machine moving, machine must be programmed to move in such a way that a point P(xi,yi) is moved along a circle and stopped at an actual point P(Xi,Yi) after a few seconds, while the position data of this point got by the linear transducer and rotary encoder are transferred to a personal computer. The resolution of the linear transducer is 0.1 mm. The type of the rotary encoder made in HEIDENHAIN is ROD 280, which can send out 18000 sine wave pulses. The signals are transferred to a personal computer through IK220 interpolator which can equally divided one original sine wave pulse into maximum 4096 square pulses. Therefore, the periphery resolution of the angle signal is less than 0.1 mm. Motion error of point P(xi,yi) can be expressed as: EXiZxiKXi(1) EYiZyiKYi(2) In which, the coordinates of the actual point P(Xi,Yi) in the circular path is given as: XiZRicosqi(3) YiZRisinqi(4) RiZRCDRi(5) where, R is rotation radius of the moving circle which is the distance between the two balls, qiis rotation angle of the linear transducer bar which is measured by the rotary encoder, and DR is radius variations of the actual path which is obtained by the linear transducer. In order to eliminate Fig. 1. Schematic diagram of the prototype measurement. Fig. 2. Photograph of the measurement instrument. H.L. Liu et al. / International Journal of Machine Tools 1;2;.;N K1: (8) where i indicates measured points in a full revolution. Following equations can be obtained by the least square method: 4r;a;b Z X NK1 iZ0 r CDR2Kr2? Zmin(9) v4r;a;b vr Z0(10) v4r;a;b va Z0(11) v4r;a;b vb Z0(12) The offset distance a and b can be obtained: a Z 1 N X NK1 iZ0 Xi(13) b Z 1 N X NK1 iZ0 Yi(14) r Z 1 N X NK1 iZ0 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffi ffiffi ffiffi ffiffi ffiffi ffiffi ffi XiKa2CYiKb2 q (15) To remove the effects of the center-offset error, Eqs. (1) and (2) can be revised as: ExiZxiKXiKa(16) EyiZyiKYiKb(17) From Eqs. (16) and (17), the circular error in a given point can be got. 5. Results In this section, some measurement results with the prototype instrument are demonstrated and discussed. The NC machine tool used in these experiments is a new vertical machiningcenter.Afeedrate,40 mm/min,wasusedinorder to measure the center-offset error accurately. Measurement processisseparated intotwo steps.Theoneistomeasurethe center-offset error, in which more than 1000 points can be measured at equal interval in one full revolution without stopping when the machine was commanded to move in a circular path. The other is circular motion error measure- ment, in which the machine tool can be stopped in a commanded point and total 36 point in one full revolution can be got. Results of measuring center-offset error is shown inFig.4,whereradiusis156.2780 mmandthecirclemarked with the dotted line is the moving path which is the machine tool commanded to move. The circle marked with centerline is the raw date error trace before the center-offset error is compensated. The circle marked with solid line is error trace after the center-offset error is compensated. From above results, some conclusions can be drawn: (1) The instrument can be used to measure the circular motion error. (2) The center-offset error has great effect on the measure- ment results. (3) The method of center-offset error compensation is correct. (4) The circular motion error can be obtained through comparing coordinate magnitude between commanded Fig. 3. The schematic diagram for center-offset error. H.L. Liu et al. / International Journal of Machine Tools & Manufacture 45 (2005) 134713511349 andactualpointafterthecenter-offseterror compensation. Then following experiments will only show results after center-offset error compensation. Experimental results of three times at the same location are shown in Fig. 5, where the feed rate is 40 mm/min and the radius is 156.2780 mm. It is demonstrated that the instrument is of very good repeatability and the magnitude is less than G1 mm. Some similar results of circular motion error also can be observed in the paper 2. As a further verifi cation, the results of the circular motion error measurement can be compared with that of KGM measurement system. Because of the limitation of the working range of the KGM, the connecting link on the instrument is changed. The measurement radius is 110.230 mm. In Fig. 6, the results of error trace measure- ment is compared using the instrument in three times with that of KGM measurement system. Two of results match one another very well, and difference value is less than G2 mm. Therefore, it is confi rmed that the measurement results with the instrument presented in this paper are suffi ciently accurate and reliable. 6. Conclusions A new method and instrument to measure the circular motion error of NC machine tools is developed and presented. The major feature can be summarized as follows: The developed instrument is of simple and compact structure yet provides larger working range. To install the instrument for measuring is simple and quick. The measurement operation is easy and convenient in practical applications. The proposed method is suitable to measure while the machine is commanded to stop at points along a circular path so that the commanded and actual points could be compared. Itis confi rmed by experimental results that the instrument is of high precision and repeatability. The proposed method will fi nd widely use to enhance the accuracy of NC machine tools, especially for error compensation and error source project in industrial application. Acknowledgements The research was supported by the national advanced technological plan projector (2002AA423260). The authors also would like to express their thanks to the HEIDENHAIN CO. for the free use of the KGM measurement system. References 1 R. Ramesh, M.A. Mannnan, A.N. Poo, Error compensation in machine toolsa review. Part I: geometric, cutting-force induced and fi xture-dependent errors, International Journal of Machine Tools and Manufacture 40 (2000) 12351256. 2 S. Hong, Y. Shin, H. Lee, An effi cient method for identifi cation of motion error sources from circular test results in NC machines, Fig. 4. Measuring results of center-offset. Fig. 5. The diagram of the repeatability results. Fig. 6. The diagram of the comparison accuracy re