一種新的測量數(shù)控制機(jī)床圓形運(yùn)動(dòng)誤差的方法和器械外文文獻(xiàn)翻譯、中英文翻譯

A new method and instrument for measuring circular motionerror of NC machine toolsAbstractA new method and instrument for measuring circular motion error of numerical control (NC) machine tools are described in this 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 shown by the experimental results that the instrument has good repeatability and high precision of measuring circular motion trajectories. The instrument can be widely used especially in the error-compensation and error-source project in the industrial application.1. IntroductionIn recent years, the precision machining process has attracted much attention from numerous investigators. One of its important tasks for error-compensation and errorsource 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 difficult 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 flexural 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 flexural 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 practicalapplications 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.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 instrumentA 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 endof 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 fixed 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 andperpendicular 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 defined as the zaxis, 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 thexy plane is located on the rotation plane of the linear transducer bar.Fig. 1. Schematic diagram of the prototype measurement.3. Principle of the measurement methodIn 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 beprogrammed 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: （1） （2）In which, the coordinates of the actual point P(Xi,Yi) in the circular path is given as: （3） （4） （5）where, R is rotation radius of the moving circle which is the distance between the two balls, qi is rotation angle of the linear transducer bar which is measured by the rotaryencoder, and DR is radius variations of the actual path which is obtained by the linear transducer. In order to eliminate motion vibration in measuring process, machine is programmed to move at low speed. Because the connected link attached to the linear transducer bar can be changed, the actual working range can be defined as: （6）where r is distance from the measuring point to the original o of the measuring coordinate, Rmin and Rmax are minimum and maximum length of the linear transducer bar respectively. Rmin, which has been confirmed by experimental, isless than 80 mm. Rmax should not more than 500 mm.Therefore, the whole working range is of annulus form around the original o whose inner radius is 80 mm and outerradius is 500 mm.4. Center-offset error compensationIn practice, the center point of the ball 1, on the xoy plane denoted by O may not be coincided with the center of the circular motion which the machine tool is commaned moving. This will cause center-offset error, as shown in Fig. 3. On considering the error characteristics of DR, centeroffset error e can be expressed as: （7）where a, b are the offset distance associated with the x- and y-axis respectively. An equation can be obtained: （8）where i indicates measured points in a full revolution. Following equations can be obtained by the least square method: （9） （10） （11） （12）Fig. 3. The schematic diagram for center-offset error.The offset distance a and b can be obtained: （13） （14） （15）To remove the effects of the center-offset error, Eqs. (1) and (2) can be revised as: （16） （17）From Eqs. (16) and (17), the circular error in a given point can be got.5. ResultsIn 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 machining center. A feed rate, 40 mm/min, was used in order to measure the center-offset error accurately. Measurement process is separated into two steps. The one is to measure the 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 measurement, 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 in Fig. 4, where radius is 156.2780 mmand the circle marked 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 measurement 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 and actual point after the center-offset errorcompensation.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 verification, 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 measurement 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 confirmed that the measurement results with the instrument presented in this paper are sufficiently accurate and reliable.Fig. 4. Measuring results of center-offset.Fig.4. The diagram of the repeatability results. Fig.5. The diagram of the comparison accuracy results.6. ConclusionsA 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. he 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. It is confirmed by experimental results that the instrument is of high precision and repeatability. The proposed method will find widely use to enhance the accuracy of NC machine tools, especially for error compensation and error source project in industrial application.References1 R. Ramesh, M.A. Mannnan, A.N. Poo, Error compensation in machine toolsa review. Part I: geometric, cutting-force induced and fixture-dependent errors, International Journal of Machine Tools and Manufacture 40 (2000) 12351256.2 S. Hong, Y. Shin, H. Lee, An efficient method for identification of motion error sources from circular test results in NC machines, International Journal of Machine Tools and Manufacture 37 (3) (1997)327340.3 W. Knapp, Test of the three-dimensional uncertainty of machine tools and measuring machines and its relation to the machine errors, Annals CIRP 32 (1) (1983) 459464.4 J.B. Bryan, A simple method for testing measuring machines and machine tools, part 1: principles and application, Precision Engineering 4 (2) (1982) 6169.5 J.B. Bryan, A simple method for testing measuring machines and machine tools, part 2: construction, Precision Engineering 4 (3) (1982) 125138.6 H. Qiu, Y. Li, Y. Li, A new method and device for motion accuracy measurement of NC machine tools. Part 1: principle and equipment, International Journal of Machine Tools and Manufacture 41 (2001) 521534.7 H. Qiu, Y. Li, Y. Li, A new method and device for motion accuracy measurement of NC machine tools. Part 2: device error identification and trajectory measurement of general planar motions, International Journal of Machine Tools and Manufacture 41 (2001) 535554.8 HEIDENHAIN, Measuring System for Machine Tool Inspection and Acceptance Testing December 2002, Germany.一種新的測量數(shù)控制機(jī)床圓形運(yùn)動(dòng)誤差的方法和器械摘要本文描述的是一種新的測量數(shù)控機(jī)床圓形運(yùn)動(dòng)誤差的的方法和器械。該器械由在每個(gè)末端的二個(gè)球狀物和一個(gè)具有高精確旋轉(zhuǎn)性編碼器的線性位移傳感器條組成。半徑的變化由傳感器測得，而且當(dāng)機(jī)器移動(dòng)到一條圓形的軌道時(shí)，傳感器的旋轉(zhuǎn)角度由旋轉(zhuǎn)編碼器測得。 測定的區(qū)域除了圓盤中心周圍的一個(gè)小的區(qū)域外都是圓形的。 傳感器能夠擴(kuò)張而且由于不同的應(yīng)用還能沿著它的軸收縮。該器械結(jié)構(gòu)緊湊且能簡單、快速地安裝在機(jī)床上。 實(shí)驗(yàn)結(jié)果顯示該器械在測量圓形運(yùn)動(dòng)軌道上具有很好的重復(fù)性和很高的精密度。 本器械具有廣泛地應(yīng)用，尤其是在工業(yè)的誤差補(bǔ)償和誤差來源上。 關(guān)鍵詞: 數(shù)控機(jī)床; 運(yùn)動(dòng)誤差; 測量工具; 圓形測量法1、緒論 近年來，精加工方法已經(jīng)吸引了許多研究人員的注意。 它的一個(gè)重要工作就是根據(jù)誤差補(bǔ)償和誤差來源的診斷繪制出機(jī)床的測定體積誤差的圖形 1?，F(xiàn)在的技術(shù)能夠?yàn)槊恳徊繖C(jī)器的軸測量參數(shù)的誤差函數(shù)，例如定位和線性運(yùn)動(dòng)的精確性。 然而，它仍然難以精確地測量一個(gè)比較普通的圓形運(yùn)動(dòng)軌道的誤差。 一些裝置和方法通常被用來測量圓形運(yùn)動(dòng)的軌道準(zhǔn)確性,描述如下： (1) 一根測試傳感器條和直線探針 2。(2) 一個(gè)磁盤片 (或一個(gè)圓形計(jì)量器) 和二維探針 3。(3) 由在每個(gè)末端的曲形傳感器條和二個(gè)被球形表面的特殊孔固定的磁性球組成的雙球形傳感器條系統(tǒng) (DBB) 。當(dāng)機(jī)器運(yùn)動(dòng)到圓形運(yùn)動(dòng)的時(shí)候，球之間的背離距離被曲形傳感器條 測量出來 4和5。(4) 復(fù)縱線聯(lián)接和二個(gè)旋轉(zhuǎn)編碼器在分離鏈接的根端部被分開，以便于探測鏈接的旋轉(zhuǎn)角度6和7。(5) KGM 圓形測試系統(tǒng) 8。上述的器械和方法已經(jīng)被用于估算圓形運(yùn)動(dòng)軌道的準(zhǔn)確性，并且已經(jīng)獲得了一些成果。 但是正如一些研究員所指出的它在實(shí)際應(yīng)用方面還存在一些問題 1和6 。而且在(1)和(2）上, 磁盤片的準(zhǔn)確性還有局限性。在(3)上，只有在半徑方向才能獲得高精確性。 雖然(4)能夠獲得沿X-Y平面的x軸和y軸上的圓形運(yùn)動(dòng)誤差(二維誤差)，但是該器械非常復(fù)雜，而且很難制造。KGM 圓形測試系統(tǒng),也被稱為十字柵格編碼器,它具有優(yōu)良的性能, 但是它非常昂貴，而且最大測量區(qū)域只是一個(gè)大約半徑120mm的圓形。本文介紹的是一種新的測量數(shù)控機(jī)床圓形運(yùn)動(dòng)誤差的的方法和器械。 當(dāng)機(jī)器停在能獲得并掌握半徑和角度的圓形軌道上的不同的點(diǎn)上時(shí)，x 軸和 y 軸的二維誤差就能被測量出來。 而且，這一個(gè)方法在實(shí)際應(yīng)用中既簡單又方便，并且該器械成本低，結(jié)構(gòu)緊湊。2、測量器械的外形圖1是測量器械原型的示意圖。它由一個(gè)與DDB相似的在末端有二個(gè)球的線性傳感器條和一個(gè)放置在球1根部以探測旋轉(zhuǎn)角度的旋轉(zhuǎn)編碼器組成, 球2通過支架連接到機(jī)床上。機(jī)器的底部有規(guī)則地固定在數(shù)控機(jī)床的工作臺(tái)上，例如以機(jī)器中心的X-Y平面為基準(zhǔn)。線性傳感器的旋轉(zhuǎn)平面平行于機(jī)床工作臺(tái)的X-Y平面，垂直于心軸的旋轉(zhuǎn)軸。測量相同結(jié)構(gòu)時(shí)，若球1根部編碼器的旋轉(zhuǎn)軸被定為Z軸，那么與該軸平行的心軸就是Z方向。而X軸、Y軸則分別與機(jī)床平行，并且就是X方向、Y方向，因此X-Y平面就在線性傳感器上。圖1 原型測量示意圖3、測量方法的原理機(jī)器移動(dòng)時(shí)實(shí)際點(diǎn)的位置總是比要求的落后，因此為了要避免軸的伺服系統(tǒng)的速度延遲, 機(jī)器必須按這樣的程序移動(dòng)：點(diǎn)P(xi,yi) 沿著一個(gè)圓周移動(dòng)并且在數(shù)秒之后停在真實(shí)的點(diǎn) P(Xi,Yi)上，同時(shí)把線性傳感器和旋轉(zhuǎn)編碼器得到的該點(diǎn)的位置數(shù)據(jù)傳到計(jì)算機(jī)上。該線性傳感器的精度是0.1 m。在HEIDENHAIN制造的該類型的旋轉(zhuǎn)編碼器為ROD 280,它能發(fā)出18000個(gè)正弦脈沖波。信號(hào)通過能在最多為4096的平方個(gè)脈沖波中區(qū)分出原始的正弦脈沖的IK220分類機(jī)傳到計(jì)算機(jī)上。因此，角度