TW201816531A - Numerically controlled machine tool with spatial positional error compensation - Google Patents
Numerically controlled machine tool with spatial positional error compensation Download PDFInfo
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- B23Q15/00—Automatic control or regulation of feed movement, cutting velocity or position of tool or work
- B23Q15/007—Automatic control or regulation of feed movement, cutting velocity or position of tool or work while the tool acts upon the workpiece
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本發明是有關於一種具有空間位置誤差補償功能的數值控制工具機,尤其是有關於一種即時補償空間加工位置誤差的數值控制工具機。The invention relates to a numerical control machine tool with a function of compensating for spatial position error, and more particularly to a numerical control machine tool for instantly compensating for a spatial processing position error.
1890年,阿貝博士(Ernst Karl Abbé, 1840~1905)在德國卡爾蔡司(Carl Zeiss)工廠工作時,對量測儀器設計提出了指導性的原則: “在位移量測儀上,該感測位置裝置的量測軸線須與該量測探頭的運動軸線一致,否則會因運動軸的角度誤差產生量測位置誤差”,這種誤差即稱之為阿貝誤差(Abbe error),此原則亦稱之阿貝原則(Abbe Principle)。阿貝原則已被公認為精密機械的設計準則,可應用於工具機、量測儀器、精密定位平台等。In 1890, when Dr. Ernst Karl Abbé (1840 ~ 1905) worked at the Carl Zeiss factory in Germany, he proposed guiding principles for the design of measuring instruments: "On a displacement measuring instrument, the sensing The measurement axis of the position device must be consistent with the movement axis of the measurement probe, otherwise the measurement position error will be caused by the angular error of the movement axis. "This kind of error is called Abbe error, and this principle is also Called the Abbe Principle. The Abbe principle has been recognized as a design criterion for precision machinery, which can be applied to machine tools, measuring instruments, precision positioning platforms, etc.
數值控制工具機為工業界普遍使用中的精密加工設備。任何多軸的數值控制工具機都是由基本的線性運動軸為基底加上旋轉軸所搭建出來的。數值控制工具機的線性移動台是利用裝置於線性移動台下方對應其移動軸的位移感測器來測量線性移動台實際位移量,達到精密定位的功能。但是,一般的線性移動台由於結構設計的限制,其位移感測器,所裝設的量測軸線無法和其在空間加工點的運動軸線同軸,亦即一般數值控制工具機的結構設計是不符合阿貝原則的,各軸移動台位置感測器的感測點和刀具的空間加工點之間仍存在一個空間位置的偏位,俗稱阿貝偏位(Abbe offset)。由於各軸移動時具有三種角度誤差(Angular errors),在國際標準規範ISO230-1中分別定義為:俯仰(Pitch)、搖擺(Yaw)及滾動(Roll),每一種角度誤差將由於阿貝偏位造成實際空間加工點位置和三軸位置感測器所顯示的位置值不同,亦即所謂的空間位置誤差,影響數值控制工具機的加工精度甚巨。Numerically controlled machine tools are precision machining equipment commonly used in industry. Any multi-axis numerically-controlled machine tool is constructed by using a basic linear motion axis as a base and a rotary axis. The numerically controlled machine tool's linear moving stage uses a displacement sensor installed under the linear moving stage and corresponding to its moving axis to measure the actual displacement of the linear moving stage to achieve precise positioning. However, due to the structural design limitation of a general linear mobile station, the displacement axis of the displacement sensor cannot be coaxial with its movement axis at the spatial processing point, that is, the structural design of a general numerical control machine is not In accordance with Abbe's principle, there is still a spatial position deviation between the sensing point of each axis mobile stage position sensor and the spatial processing point of the tool, which is commonly known as Abbe offset. As each axis moves with three types of Angular errors, they are defined in the international standard ISO230-1 as: Pitch, Yaw, and Roll. Each angle error will be due to Abbe's deviation. The position causes the actual spatial processing point position to be different from the position value displayed by the three-axis position sensor, which is the so-called spatial position error, which affects the machining accuracy of the numerical control machine tool.
習知的工具機空間位置誤差補償法係先行經校正並儲存對應的空間位置誤差值而建立位置誤差表,再以軟體修正指定的位移量做位置誤差補償,此即所謂的前饋誤差補償(Feed-forward error compensation), 如US 4945501、US5021941、US7171320 B2、US6430465B2、US6164117 A。前饋誤差補償法只有感測並回饋位置資訊,且需要大量的記憶空間以建立誤差表,此誤差表並非即時資料,當操作環境變化時此誤差值會隨著變化,故只能補償先前校正過的空間位置誤差。The conventional machine tool space position error compensation method is to first correct and store the corresponding space position error value to establish a position error table, and then use software to modify the specified displacement amount for position error compensation. This is the so-called feedforward error compensation ( Feed-forward error compensation), such as US 4945501, US5021941, US7171320 B2, US6430465B2, US6164117 A. The feedforward error compensation method only senses and returns position information, and requires a lot of memory space to create an error table. This error table is not real-time data. This error value will change as the operating environment changes, so it can only compensate the previous correction. Passed spatial position error.
本發明提供了一種適用於工具機的即時空間位誤差補償方法,以解決先前技術所需解決的課題。更詳細的說,是提供一種因三軸移動平台的角度誤差而產生一空間加工位置誤差的補償方法。The invention provides an instant space error compensation method suitable for a machine tool, so as to solve the problem to be solved by the prior art. In more detail, it is to provide a method for compensating a spatial processing position error due to an angular error of a three-axis moving platform.
根據本發明一實施例,其揭露了一種工具機包括刀具、主軸、三軸移動平台、三軸感測位置裝置、三軸角度感測模組、誤差補償單元以及控制器。移動平台有三個,分別用以夾持一加工工件或是承載主軸與刀具,且沿X軸、Y軸或Z軸運動。各軸感測位置裝置設置於各軸移動平台下方,用以感測各軸移動平台所在位置,而發出各軸移動平台位置資訊。各軸角度感測模組緊鄰於各軸移動平台,用以感測各軸移動平台的俯仰、搖擺與滾動三種轉動角度,而產生各軸角度誤差資訊。誤差補償單元電性連接三軸角度感測模組及三軸感測位置裝置,用以接收各軸感測位置資訊及角度誤差資訊而產生一空間加工位置誤差補償資訊。控制器電性連接主軸、三軸移動平台、三軸感測位置裝置、以及誤差補償單元,用以根據誤差補償單元所產生的加工位置誤差補償資訊操作三軸移動平台而將加工工件進行空間位置誤差補償切削加工。According to an embodiment of the present invention, it is disclosed that a machine tool includes a cutter, a main shaft, a three-axis moving platform, a three-axis sensing position device, a three-axis angle sensing module, an error compensation unit, and a controller. There are three moving platforms, which are respectively used to hold a processing workpiece or carry a spindle and a tool, and move along the X axis, Y axis, or Z axis. Each axis sensing position device is arranged below each axis moving platform, and is used for sensing the position of each axis moving platform, and transmitting position information of each axis moving platform. Each axis angle sensing module is next to each axis moving platform, and is used to sense the three rotation angles of each axis moving platform, such as pitch, sway and roll, to generate the error information of each axis angle. The error compensation unit is electrically connected to the three-axis angle sensing module and the three-axis sensing position device, and is used for receiving the position sensing information and the angle error information of each axis to generate a space processing position error compensation information. The controller is electrically connected to the main shaft, the three-axis moving platform, the three-axis sensing position device, and the error compensation unit, and is used for operating the three-axis moving platform to spatially process the workpiece according to the processing position error compensation information generated by the error compensation unit. Error-compensated cutting.
在本發明一實施例中,角度感測模組可為一光學感測模組,但不以此為限。該三軸角度感測模組包含X軸移動平台角度感測模組、Y軸移動平台角度感測模組以及Z軸移動平台角度感測模組。X軸移動平台角度感測模組緊鄰於該軸移動平台,用以感測X軸移動平台的三種轉動角度,包括:以X軸為轉軸的滾動角度、以Y軸為轉軸的俯仰角度、以及以Z軸為轉軸的搖擺角度,而產生X軸移動平台的三種轉動角度誤差資訊。Y軸移動平台角度感測模組緊鄰於該移動平台,用以感測Y軸移動平台的三種轉動角度,包括:以X軸為轉軸的俯仰角度、以Y軸為轉軸的滾動角度、以及以Z軸為轉軸的搖擺角度,而產生Y軸移動平台的三種轉動角度誤差資訊。Z軸移動平台角度感測模組緊鄰於該移動平台,用以感測Z軸移動平台的三種轉動角度,包括:以X軸為轉軸的俯仰角度、以Y軸為轉軸的搖擺角度、以Z軸為轉軸的滾動角度,而產生Z軸移動平台的三種轉動角度誤差資訊。In an embodiment of the present invention, the angle sensing module may be an optical sensing module, but is not limited thereto. The three-axis angle sensing module includes an X-axis moving platform angle sensing module, a Y-axis moving platform angle sensing module, and a Z-axis moving platform angle sensing module. The X-axis moving platform angle sensing module is next to the axis-moving platform and is used to sense the three rotation angles of the X-axis moving platform, including: the rolling angle with the X axis as the rotation axis Pitch angle with Y axis as the rotation axis And the swing angle with the Z axis as the rotation axis , And three kinds of rotation angle error information of the X-axis moving platform are generated. The Y-axis moving platform angle sensing module is next to the moving platform and is used to sense the three rotation angles of the Y-axis moving platform, including: the pitch angle with the X axis as the rotation axis Rolling angle with Y axis as rotation axis And the swing angle with the Z axis as the rotation axis , And three kinds of rotation angle error information of the Y-axis moving platform are generated. The Z-axis moving platform angle sensing module is next to the moving platform and is used to sense the three rotation angles of the Z-axis moving platform, including: the pitch angle with the X axis as the rotation axis Swing angle with Y axis as the rotation axis , Rolling angle with Z axis as rotation axis , And three kinds of rotation angle error information of the Z-axis moving platform are generated.
在本發明一實施例中,誤差補償單元用以接收X軸、Y軸、以及Z軸移動平台的共計9種轉動角度誤差資訊以及該三軸感測位置資訊而產生刀具在空間加工位置的誤差補償資訊。In an embodiment of the present invention, the error compensation unit is configured to receive a total of nine types of rotation angle error information of the X-axis, Y-axis, and Z-axis moving platforms and the three-axis sensing position information to generate an error of the tool in the space processing position. Compensation information.
在本發明一實施例中,該X軸移動平台的三種轉動角度誤差資訊造成刀具空間加工位置誤差資訊有三個方向分量,包含X方向位置誤差分量為、Y方向位置誤差分量為,以及Z方向位置誤差分量為,分別滿足 ,為該X軸移動平台感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離,為該X軸感測位置裝置的感測點與該刀具之間平行Y軸的最短直線距離。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(1)]。,為該X軸移動平台感測位置裝置的感測點與該刀具之間平行X軸的最短直線距離。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(2)]。。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(3)]。In an embodiment of the present invention, the three-dimensional rotation angle error information of the X-axis moving platform causes the tool space processing position error information to have three direction components, including the X-direction position error component as , Y-direction position error component is , And the position error component in the Z direction is , Respectively , Is the shortest linear distance between the sensing point of the X-axis moving platform sensing position device and the tool in parallel with the Z-axis, The shortest linear distance between the sensing point of the X-axis position sensing device and the tool in parallel with the Y-axis. Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula 1)]. , The shortest straight line distance between the sensing point of the X-axis moving platform sensing position device and the tool in parallel with the X-axis. Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (2)]. . Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (3)].
在本發明一實施例中,該Y軸移動平台的三種轉動角度誤差資訊造成刀具空間加工位置誤差資訊有三個方向分量,包含X方向位置誤差為分量、Y方向位置誤差分量為,以及Z方向位置誤差為,分別滿足 ,為該Y軸移動平台感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離,為該Y軸移動平台感測位置裝置的感測點與該刀具之間平行Y軸的最短直線距離。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(4)]。,為該Y軸移動平台感測位置裝置的感測點與該刀具之間平行X軸的最短直線距離。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(5)]。。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(6)]。In an embodiment of the present invention, the three types of rotation angle error information of the Y-axis moving platform cause the tool space processing position error information to have three directional components, including the X-direction position error as Component, Y-direction position error component is , And the position error in the Z direction is , Respectively , The shortest straight line distance between the sensing point of the Y-axis moving platform sensing position device and the tool in parallel with the Z-axis, The shortest linear distance between the sensing point of the Y-axis moving platform sensing position device and the tool in parallel with the Y-axis. Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (4)]. , The shortest linear distance between the sensing point of the Y-axis moving platform sensing position device and the tool parallel to the X-axis. Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (5)]. . Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (6)].
在本發明一實施例中,該Z軸移動平台的三種轉動角度誤差資訊造成刀具空間加工位置誤差資訊有三個方向分量,包含X方向位置誤差為分量、Y方向位置誤差分量為,以及Z方向位置誤差為,分別滿足 ,為該Z軸移動平台感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離,為該Z軸移動平台感測位置裝置的感測點與該刀具之間平行Y軸的最短直線距離。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(7)]。,為該Z軸移動平台感測位置裝置的感測點與該刀具之間平行X軸的最短直線距離。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(8)]。。一般工具機各軸的轉動角度均很小,上式也可簡化為:[公式(9)]。In an embodiment of the present invention, the three rotation angle error information of the Z-axis moving platform causes the tool space processing position error information to have three directional components, including the X-direction position error as Component, Y-direction position error component is , And the position error in the Z direction is , Respectively , The shortest linear distance between the sensing point of the Z-axis moving platform sensing position device and the tool in parallel with the Z-axis, The shortest linear distance between the sensing point of the Z-axis moving platform sensing position device and the tool in parallel with the Y axis. Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (7)]. , The shortest linear distance between the sensing point of the Z-axis moving platform sensing position device and the tool in parallel with the X-axis. Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (8)]. . Generally, the rotation angle of each axis of the machine tool is very small, and the above formula can also be simplified to: [Formula (9)].
在本發明一實施例中,角度感測模組為一光學感測模組。In an embodiment of the invention, the angle sensing module is an optical sensing module.
本發明實施例的工具機誤差補償單元可依據角度感測模組感測移動平台而推導X軸、Y軸及Z軸的空間三正交方向的關於定位誤差的誤差資訊[公式(1)至公式(9)],且控制器可根據誤差資訊即時補償,使得控制器可準確地調整承載加工工件的移動平台與加工工件的刀具之間的空間相對關係而對加工工件進行加工,而可增加工具機控制器的加工精度。The machine tool error compensation unit according to the embodiment of the present invention can derive the error information about the positioning error of the three orthogonal directions of the X-axis, Y-axis, and Z-axis according to the sensing platform of the angle sensing module [formula (1) to [Formula (9)], and the controller can compensate in real time according to the error information, so that the controller can accurately adjust the spatial relative relationship between the mobile platform carrying the processing workpiece and the tool processing the workpiece to process the processing workpiece, which can increase the Machining accuracy of machine tool controllers.
請參照圖1及圖2,圖1係繪示依照本發明一實施例的具有阿貝誤差補償的數值控制工具機立體示意圖。圖2係繪示圖1的工具機在加工一工件時X軸移動平台有角度誤差的側視圖。如圖1及圖2所示,本實施例的工具機100包括刀具110、三軸移動平台(120a、120b、120c)、X軸感測位置裝置130、三軸角度感測模組140、誤差補償單元150、控制器160以及主軸170。Please refer to FIG. 1 and FIG. 2, which are three-dimensional schematic diagrams of a numerical control machine tool with Abbe error compensation according to an embodiment of the present invention. FIG. 2 is a side view showing an angular error of the X-axis moving platform when the machine tool of FIG. 1 processes a workpiece. As shown in FIG. 1 and FIG. 2, the machine tool 100 of this embodiment includes a tool 110, a three-axis moving platform (120a, 120b, 120c), an X-axis sensing position device 130, a three-axis angle sensing module 140, and an error. The compensation unit 150, the controller 160, and the main shaft 170.
三軸移動平台包括X軸移動平台120a、Y軸移動平台120b以及Z軸移動平台120c。X軸移動平台120a與Y軸移動平台120b設置於刀具110的下方,X軸移動平台120a用以夾持一加工工件200且沿X軸運動;Y軸移動平台120b用以承載X軸移動平台120a且沿Y軸運動;Z軸移動平台120a用以承載主軸170與刀具110,且沿Z軸運動,使得刀具110對加工工件200進行切削加工。進一步的說,移動平台(120a、120b、120c)及刀具110可受到控制器160的操控而啟動以進行對加工工件200的切削。The three-axis moving platform includes an X-axis moving platform 120a, a Y-axis moving platform 120b, and a Z-axis moving platform 120c. The X-axis moving platform 120a and the Y-axis moving platform 120b are disposed below the tool 110. The X-axis moving platform 120a is used to hold a workpiece 200 and move along the X-axis; the Y-axis moving platform 120b is used to carry the X-axis moving platform 120a And moves along the Y axis; the Z-axis moving platform 120a is used to carry the main shaft 170 and the tool 110, and moves along the Z axis, so that the tool 110 performs cutting processing on the workpiece 200. Further, the mobile platform (120a, 120b, 120c) and the tool 110 can be controlled by the controller 160 to be activated to perform cutting on the workpiece 200 to be processed.
X軸移動平台120a的X軸移動平台感測位置裝置130a設置於該移動平台下方,X軸移動平台感測位置裝置130a的感測點132a用以感測刀具110所在的X軸位置,而發出X軸感測位置資訊。在本實施例中,X軸位置感測點132a與刀具110端部之間平行Z軸的最短直線距離(Lxz )為圖2中的感測點132a到點D1的距離,其中刀具110的端部也就是指刀具110的用以切削加工工件200的加工位置,感測點132a在Z方向的高度為已知的固定值,D1點為X軸移動平台120a無俯仰角轉動時加工工件的200理想加工位置,可由Z軸移動平台的感測位置裝置所發出的Z軸感測位置得知。另一方面,X軸移動平台120a可沿一X軸滑軌122a及一X軸滾珠導螺桿124a移動,其中X軸滑軌122a及X軸滾珠導螺桿124a與作為X軸移動平台感測位置裝置130a的感測軸體大致平行。The X-axis moving platform sensing position device 130a of the X-axis moving platform 120a is disposed below the moving platform. The sensing point 132a of the X-axis moving platform sensing position device 130a is used to sense the X-axis position of the tool 110, and is issued. X-axis senses position information. In this embodiment, the shortest straight line distance (L xz ) between the X-axis position sensing point 132 a and the end of the tool 110 parallel to the Z axis is the distance from the sensing point 132 a to the point D1 in FIG. 2, where The end part refers to the machining position of the tool 110 for cutting and processing the workpiece 200. The height of the sensing point 132a in the Z direction is a known fixed value, and the point D1 is the machining position of the workpiece when the X-axis moving platform 120a rotates without a pitch angle. The 200 ideal processing position can be known from the Z-axis sensing position issued by the sensing position device of the Z-axis moving platform. On the other hand, the X-axis moving platform 120a can be moved along an X-axis slide rail 122a and an X-axis ball guide screw 124a, wherein the X-axis slide rail 122a and the X-axis ball guide screw 124a and the position sensing device as the X-axis mobile platform The sensing axis of 130a is substantially parallel.
然而,雖然X軸滑軌122a及X軸滾珠導螺桿124a與X軸移動平台感測位置裝置130a大致平行,但X軸移動平台120a與X軸移動平台感測位置裝置130a之間仍可能存在沿X軸、Y軸或Z軸轉動的角度的誤差。也就是指,X軸移動平台120a具有俯仰角、搖擺角、滾動角的角度誤差。However, although the X-axis slide rail 122a and the X-axis ball guide screw 124a are approximately parallel to the X-axis moving platform sensing position device 130a, there may still be a distance between the X-axis moving platform 120a and the X-axis moving platform sensing position device 130a. X, Y or Z rotation angle error. That is, the X-axis moving platform 120a has an angular error of a pitch angle, a roll angle, and a roll angle.
如上所述,本實施例的工具機100的Y軸移動平台120b與Z軸移動平台120c均各自具有俯仰角、搖擺角、滾動角的角度誤差。As described above, the Y-axis moving platform 120b and the Z-axis moving platform 120c of the machine tool 100 of this embodiment each have an angular error of a pitch angle, a roll angle, and a roll angle.
因此,本實施例的工具機100還設置一個三軸角度感測模組140來感測前述各軸移動平台的三種角度誤差,此三軸角度感測模組140包括X軸角度感測模組144、Y軸角度感測模組142、以及Z軸角度感測模組146。詳細來說,如圖1所示,X軸角度感測模組144緊鄰X軸移動平台120a、Y軸角度感測模組142緊鄰Y軸移動平台120b、以及Z軸角度感測模組146緊鄰Z軸移動平台120c。如圖2所示,X軸移動平台120a以Y軸為轉軸的俯仰角度(x),而產生一Y軸轉動俯仰角度誤差資訊。如圖3所示,X軸移動平台120a以Z軸為轉軸的搖擺角度(x),而產生一Z軸轉動搖擺角度誤差資訊。如圖3所示,X軸移動平台120a以X軸為轉軸的滾動角度(x),而產生一X軸轉動滾動角度誤差資訊。經由圖2及圖3的教示,可輕易得知的是,Y軸移動平台120b以X軸為轉軸的俯仰角度,而產生一X軸轉動俯仰角度誤差資訊,以Y軸為轉軸的滾動角度,而產生一Y軸轉動滾動角度誤差資訊,並以Z軸為轉軸的搖擺角度,而產生一Z軸轉動搖擺角度誤差資訊;以及,Z軸移動平台120c以X軸為轉軸的俯仰角度,而產生一X軸轉動俯仰角度誤差資訊,並以Y軸為轉軸的搖擺角度,而產生一Y軸轉動搖擺角度誤差資訊,並以Z軸為轉軸的滾動角度,而產生一Z軸轉動滾動角度誤差資訊。在本實施例中,X軸移動平台120a角度感測模組144、Y軸移動平台120b角度感測模組142以及Z軸移動平台120c角度感測模組146的至少其中之一可由半導體雷射(LD)、四象限光感測器(QPD)、及光學元件組合而成,藉由光學自動視準儀原理而量測移動平台的俯仰與搖擺轉動角度,而產生誤差資訊。Therefore, the machine tool 100 of this embodiment is further provided with a three-axis angle sensing module 140 to sense the three angle errors of the aforementioned moving platforms of each axis. The three-axis angle sensing module 140 includes an X-axis angle sensing module. 144, a Y-axis angle sensing module 142, and a Z-axis angle sensing module 146. In detail, as shown in FIG. 1, the X-axis angle sensing module 144 is located next to the X-axis moving platform 120a, the Y-axis angle sensing module 142 is located next to the Y-axis moving platform 120b, and the Z-axis angle sensing module 146 is next to Z-axis moving platform 120c. As shown in FIG. 2, the pitch angle of the X-axis moving platform 120 a with the Y-axis as the rotation axis (x), and a Y-axis rotation pitch angle error information is generated. As shown in FIG. 3, the swing angle of the X-axis moving platform 120a with the Z-axis as the rotation axis (x), and a Z-axis rotation swing angle error information is generated. As shown in FIG. 3, the rolling angle of the X-axis moving platform 120a with the X-axis as the rotation axis (x), and an X-axis rotation and rolling angle error information is generated. According to the teachings in FIG. 2 and FIG. 3, it can be easily known that the pitch angle of the Y-axis moving platform 120 b with the X-axis as the rotation axis , And generate an X-axis rotation pitch angle error information, the Y-axis is the rolling angle of the rotation axis , And generate a Y-axis rotation and rolling angle error information, and the Z-axis is the swing angle of the rotation axis , And a Z-axis rotation swing angle error information is generated; and, the Z-axis moving platform 120c uses the X-axis as the rotation angle of the pitch angle , And generates an X-axis rotation pitch angle error information, and the Y-axis is the swing angle of the rotation axis , And produce a Y-axis rotation swing angle error information, and take the Z-axis as the rolling angle of the rotation axis , And produce a Z-axis rotation and rolling angle error information. In this embodiment, at least one of the X-axis moving platform 120a angle sensing module 144, the Y-axis moving platform 120b angle sensing module 142, and the Z-axis moving platform 120c angle sensing module 146 may be semiconductor lasers. (LD), four-quadrant light sensor (QPD), and optical components are combined to measure the pitch and swing angles of the mobile platform through the principle of an optical automatic collimator, which generates error information.
進一步的說,該X軸移動平台沿X方向加工位置誤差資訊為,也可稱為X方向的定位誤差,也就是指刀具110的端部112(加工點)和感測裝置130a的感測點132a在X 軸方向的相對位移,X軸加工位置定位誤差資訊滿足 。如圖3所示,為該X軸移動平台感測裝置130a的感測點132a與該刀具110的端部112(加工點)之間平行Z軸的最短直線距離。同理,為該X軸感測位置裝置130a的感測點132a與該刀具110的端部112(加工點)之間平行Y軸的最短直線距離。Further, the processing position error information of the X-axis moving platform in the X direction is , Can also be referred to as the X-direction positioning error, which means the relative displacement of the end 112 (processing point) of the tool 110 and the sensing point 132a of the sensing device 130a in the X-axis direction, and the positioning error information of the X-axis processing position Satisfy . As shown in Figure 3, The shortest linear distance between the sensing point 132a of the X-axis moving platform sensing device 130a and the end 112 (processing point) of the tool 110 parallel to the Z axis. Similarly, The shortest linear distance between the sensing point 132a of the X-axis sensing position device 130a and the end 112 (processing point) of the tool 110 is parallel to the Y-axis.
由於與(x)的角度很小,故,在一些實施例中,X軸加工位置定位誤差資訊為,其滿足。due to versus The angle of (x) is small. Therefore, in some embodiments, the positioning error information of the X-axis machining position is Which satisfies .
同理,該X軸移動平台沿Y方向加工位置誤差資訊為,也可稱為Y方向的位置誤差,也就是指刀具110的端部112(加工點)和感測裝置130a的感測點132a在Y方向的相對位移,X軸移動平台沿Y方向位置誤差資訊滿足 。如圖3所示,為該X軸移動平台感測位置裝置130a的感測點132a與該刀具110的端部112(加工點)之間平行X軸的最短直線距離。Similarly, the position error information of the X-axis moving platform in the Y direction is , Can also be referred to as the Y-direction position error, that is, the relative displacement of the end portion 112 (processing point) of the tool 110 and the sensing point 132a of the sensing device 130a in the Y direction, and the position error of the X-axis moving platform in the Y direction Information Satisfy . As shown in Figure 3, The shortest linear distance between the sensing point 132a of the X-axis moving platform sensing position device 130a and the end 112 (processing point) of the tool 110 parallel to the X-axis.
由於與(x)的角度很小,故,在一些實施例中,X軸移動平台沿Y方向位置誤差資訊,其滿足。due to versus The angle of (x) is small. Therefore, in some embodiments, the position error information of the X-axis moving platform in the Y direction Which satisfies .
同理,該X軸移動平台沿Z方向加工位置誤差資訊為,也可稱為Z方向的位置誤差,也就是指刀具110的端部112(加工點)和X軸移動平台感測位置裝置130a的感測點132a在Z方向的相對位移,X軸移動平台沿Z方向位置誤差資訊滿足 。由於與(x)的角度很小,故,在一些實施例中,X軸移動平台沿Z方向位置誤差資訊,其滿足。Similarly, the position error information of the X-axis moving platform in the Z direction is , Which can also be referred to as the position error in the Z direction, that is, the relative displacement of the sensing point 132a of the end position 112 (processing point) of the tool 110 and the X-axis moving platform 130a in the Z direction, and the X-axis moving platform Position error information in the Z direction Satisfy . due to versus The angle of (x) is small. Therefore, in some embodiments, the position error information of the X-axis moving platform in the Z direction Which satisfies .
同理,該Y軸移動平台沿X方向加工位置誤差資訊為,也可稱為該Y軸移動平台在X方向的位置誤差,其滿足 。如圖4所示,為該Y軸移動平台感測位置裝置130b的感測點132b與該刀具110的端部112(加工點)之間平行Z軸的最短直線距離。為該Y軸移動平台感測位置裝置130b的感測點132b與該刀具110的端部112(加工點)之間平行Y軸的最短直線距離。Similarly, the position error information of the Y-axis moving platform in the X direction is , Also known as the position error of the Y-axis moving platform in the X direction, which satisfies . As shown in Figure 4, The shortest linear distance between the sensing point 132b of the Y-axis moving platform sensing position device 130b and the end 112 (processing point) of the tool 110 parallel to the Z axis. The shortest linear distance between the sensing point 132b of the Y-axis moving platform sensing position device 130b and the end 112 (processing point) of the tool 110 in parallel with the Y-axis.
由於與(y)的角度很小,故,在一些實施例中,Y軸移動平台沿X方向位置誤差資訊,其滿足。due to versus The angle of (y) is small. Therefore, in some embodiments, the position error information of the Y-axis moving platform in the X direction Which satisfies .
同理,該Y軸移動平台沿Y方向加工位置誤差資訊為,也可稱為Y軸移動平台的定位誤差,其滿足 。如圖4所示,該Y軸移動平台感測位置裝置130b的感測點132b與該刀具110的端部112(加工點)之間平行X軸的最短直線距離。Similarly, the position error information of the Y-axis moving platform in the Y direction is , Also known as the positioning error of the Y-axis moving platform, which satisfies . As shown in Figure 4, The shortest linear distance between the sensing point 132b of the Y-axis moving platform sensing position device 130b and the end 112 (processing point) of the tool 110 parallel to the X-axis.
由於與的角度很小,故,在一些實施例中,Y軸移動平台加工位置定位誤差資訊為,其滿足。due to versus The angle is very small. Therefore, in some embodiments, the positioning error information of the processing position of the Y-axis moving platform is Which satisfies .
同理,該Y軸移動平台沿Z方向加工位置誤差資訊為,也可稱為Y軸移動平台在Z方向的位置誤差,其滿足 。由於與的角度很小,故,在一些實施例中,Y軸移動平台沿Z方向加工位置誤差資訊為,其滿足。Similarly, the position error information of the Y-axis moving platform in the Z direction is , Also known as the position error of the Y-axis moving platform in the Z direction, which satisfies . due to versus The angle is very small. Therefore, in some embodiments, the position error information of the Y-axis moving platform in the Z direction is Which satisfies .
同理,該Z軸移動平台沿X方向加工位置誤差資訊為,也可稱為該Z軸移動平台在X方向的位置誤差,其滿足 。如圖4所示,為該Z軸移動平台感測位置裝置130c的感測點132c與該刀具110的端部112(加工點)之間平行Z軸的最短直線距離。為該Z軸移動平台感測位置裝置130c的感測點132c與該刀具110的端部112(加工點)之間平行Y軸的最短直線距離。Similarly, the position error information of the Z-axis moving platform in the X direction is , Also known as the position error of the Z-axis moving platform in the X direction, which satisfies . As shown in Figure 4, The shortest linear distance between the sensing point 132c of the Z-axis moving platform sensing position device 130c and the end 112 (processing point) of the tool 110 parallel to the Z axis. The shortest linear distance between the sensing point 132c of the Z-axis moving platform sensing position device 130c and the end 112 (processing point) of the tool 110 in parallel to the Y-axis.
由於與(z)的角度很小,故,在一些實施例中,Z軸移動平台沿X方向位置誤差資訊,其滿足。due to versus The angle of (z) is small, so in some embodiments, the position error information of the Z-axis moving platform in the X direction Which satisfies .
同理,該Z軸移動平台沿Y方向加工位置誤差資訊為,也可稱為該Z軸移動平台在Y方向的位置誤差,其滿足 。如圖4所示,該Z軸移動平台感測位置裝置130c的感測點132c與該刀具110的端部112(加工點)之間平行X軸的最短直線距離。Similarly, the position error information of the Z-axis moving platform in the Y direction is , Also known as the position error of the Z-axis moving platform in the Y direction, which satisfies . As shown in Figure 4, The shortest linear distance between the sensing point 132c of the Z-axis moving platform sensing position device 130c and the end 112 (processing point) of the tool 110 in the parallel X-axis.
由於與的角度很小,故,在一些實施例中,Z軸移動平台在Y方向的加工位置誤差資訊為,其滿足。due to versus The angle is very small. Therefore, in some embodiments, the processing position error information of the Z-axis moving platform in the Y direction is Which satisfies .
同理,該Z軸移動平台沿Z方向加工位置誤差資訊為,也可稱為Z軸移動平台在Z方向的定位誤差,其滿足 。由於與的角度很小,故,在一些實施例中,Z軸移動平台加工位置定位誤差資訊為,其滿足。Similarly, the position error information of the Z-axis moving platform in the Z direction is , Also known as the positioning error of the Z-axis moving platform in the Z direction, which satisfies . due to versus The angle is very small. Therefore, in some embodiments, the positioning error information of the processing position of the Z-axis moving platform is Which satisfies .
在本發明一實施例中,三軸移動平台在X軸加工位置誤差資訊為、及,在Y軸加工位置誤差資訊為、及,及在Z軸加工位置誤差資訊為、及,可為阿貝誤差資訊,但不以此為限。In an embodiment of the present invention, the error information of the three-axis moving platform in the X-axis processing position is , and , The machining position error information in the Y axis is , and , And the error information of the machining position in the Z axis is , and , Can be Abbe error information, but not limited to this.
誤差補償單元150電性連接三軸移動平台角度感測模組140(包括142、144、146)及三軸移動平台感測位置裝置(包括130a、130b、130c),用以接收感測各軸位置資訊及角度誤差資訊而產生一空間加工位置誤差補償資訊,由於加工工件200設置於X軸移動平台120a的軸心O上,加工位置資訊即為關於加工工件200的位置資訊。進一步的說,誤差補償單元150用以接收該X軸移動平台120a的俯仰、偏擺與滾動(,(x),)三轉動角度誤差資訊、該Y軸移動平台120b的俯仰、偏擺與滾動(,(y),)三轉動角度誤差資訊、該Z軸移動平台120c的俯仰、偏擺與滾動(,(z),)三轉動角度誤差資訊以及該三軸移動平台感測位置資訊而產生該三軸移動平台空間加工位置誤差資訊。因此,誤差補償單元150可根據三軸移動平台感測位置裝置(包括130a、130b、130c)提供關於刀具110的端部112的與三軸移動平台感測位置裝置的感測點(包括132a、132b、132c)最短直線距離的感測資訊(舉例來說,如圖2所示,X軸移動平台感測位置裝置130a所感測到的加工工件200的加工位置為D1)以及關於三軸移動平台傾斜產生的角度誤差的誤差資訊而將感測位置資訊即時補償空間位置誤差資訊後產生關於X軸移動平台120a上的加工工件200的空間加工點的位置資訊(舉例來說,如圖2所示,X軸移動平台感測位置資訊所提供的關於加工工件200的加工位置應為D2)。電性連接主軸170、三軸移動平台(包括120a、120b、120c)、三軸移動平台感測位置裝置(包括130a、130b、130c)以及誤差補償單元150的控制器160可根據三軸移動平台位置資訊以及空間加工位置誤差資訊操作三軸移動平台而將設置於X軸移動平台120a上的加工工件200進行精確的空間位置誤差補償切削加工。The error compensation unit 150 is electrically connected to the three-axis mobile platform angle sensing module 140 (including 142, 144, and 146) and the three-axis mobile platform sensing position device (including 130a, 130b, and 130c) to receive and sense each axis The position information and the angle error information generate a spatial processing position error compensation information. Since the processing workpiece 200 is disposed on the axis O of the X-axis moving platform 120a, the processing position information is the position information about the processing workpiece 200. Further, the error compensation unit 150 is configured to receive the pitch, yaw, and roll of the X-axis moving platform 120a ( , (x), ) Three rotation angle error information, pitch, yaw and roll of the Y-axis moving platform 120b ( , (y), ) Three rotation angle error information, pitch, yaw and roll of the Z-axis moving platform 120c ( , (z), ) Three-rotation angle error information and the three-axis mobile platform sensing position information to generate the three-axis mobile platform space processing position error information. Therefore, the error compensation unit 150 may provide the sensing point of the end portion 112 of the tool 110 with the three-axis moving platform sensing position device (including 132a, 130a, 130b, and 130c) 132b, 132c) Sensing information of the shortest linear distance (for example, as shown in FIG. 2, the processing position of the processing workpiece 200 sensed by the X-axis moving platform sensing position device 130a is D1) and the three-axis moving platform The error information of the angular error generated by the tilt, and the position information of the spatial position error information will be compensated in real time by sensing the position information. For example, as shown in FIG. The processing position provided by the X-axis moving platform sensing position information on the processing workpiece 200 should be D2). The controller 160 which is electrically connected to the main shaft 170, the three-axis mobile platform (including 120a, 120b, 120c), the three-axis mobile platform sensing position device (including 130a, 130b, 130c) and the error compensation unit 150 can be based on the three-axis mobile platform The position information and the spatial processing position error information operate the three-axis moving platform to perform precise spatial position error compensation cutting processing on the processing workpiece 200 provided on the X-axis moving platform 120a.
舉例來說,當X軸移動平台120a感測位置裝置感測到X軸移動平台120a上的加工工件200在X軸上的位置為X',加上X軸移動平台的轉動角度所造成的刀具加工點空間位置誤差資訊,即為誤差補償單元150發出的空間位置誤差資訊中關於X軸方向的空間位置資訊,控制器160可根據前述的位置資訊即時準確地補償X軸移動平台120a上的加工工件200在X軸上的空間位置誤差,同理,誤差補償單元150也可發出關於Y軸及Z軸的空間位置誤差資訊而使控制器160可根據前述的空間位置誤差資訊即時準確地補償X軸移動平台120a上的加工工件200在Y軸及Z軸上的位置。For example, when the X-axis moving platform 120a sensing position device senses that the position of the processing workpiece 200 on the X-axis moving platform 120a on the X-axis is X ', plus the tool caused by the rotation angle of the X-axis moving platform Spatial position error information of processing point That is, the spatial position information about the X-axis direction in the spatial position error information issued by the error compensation unit 150, and the controller 160 can accurately and accurately compensate the processed workpiece 200 on the X-axis moving platform 120a on the X axis according to the aforementioned position information. In the same way, the error compensation unit 150 can also send the spatial position error information about the Y-axis and the Z-axis so that the controller 160 can compensate the X-axis mobile platform 120a on the basis of the aforementioned spatial position error information immediately and accurately. The position of the workpiece 200 on the Y-axis and the Z-axis is processed.
詳細而言,三軸角度感測模組140的X軸移動平台角度感測模組144、Y軸移動平台角度感測模組142以及Z軸移動平台角度感測模組146可即時地量測各對應的移動平台(包括120a、120b、120c)在各位置時關於俯仰、搖擺及滾動的轉動角度在X方向的誤差資訊(包括、、)、在Y方向的誤差資訊(包括、、)、在Z方向的誤差資訊(包括、、),整體而言即為前述的九種轉動角度誤差資訊。九種轉動角度誤差資訊經由介面卡進入誤差補償單元150後,誤差補償單元150可參考接收的各軸感測位置資訊而即時計算出運動指令的加工點三正交方向的空間誤差值,而控制器160可即時的根據位置資訊進行操控三軸移動平台(包括120a、120b、120c),使得實際加工位置相較傳統只設有感測位置裝置(包括130a、130b、130c)的工具機100更為準確。在本實施例中,前述的介面卡可為網路卡的數位傳輸、類比/數位轉換卡(A/D converter)或USB,但不以此為限。In detail, the X-axis mobile platform angle sensor module 144, the Y-axis mobile platform angle sensor module 142, and the Z-axis mobile platform angle sensor module 146 of the three-axis angle sensor module 140 can measure in real time. Error information of each corresponding mobile platform (including 120a, 120b, 120c) in the X direction about the rotation angles of pitch, roll and roll at each position (including , , ), Error information in the Y direction (including , , ), Error information in the Z direction (including , , ), As a whole, it is the aforementioned nine kinds of rotation angle error information. After the nine kinds of rotation angle error information enter the error compensation unit 150 through the interface card, the error compensation unit 150 can refer to the received position information of each axis to calculate the spatial error value of the machining instruction's three orthogonal directions in real time, and control The device 160 can control the three-axis mobile platform (including 120a, 120b, 120c) according to the position information in real time, which makes the actual processing position more than the traditional machine tool 100 which only has a position sensing device (including 130a, 130b, 130c). For accuracy. In this embodiment, the aforementioned interface card may be a digital transmission of a network card, an analog / digital converter (A / D converter), or a USB, but is not limited thereto.
由上述本發明實施例可知,應用本發明具有以下優點。本發明的工具機誤差補償單元可依據三軸角度感測模組與三軸移動平台感測位置裝置而推導X軸、Y軸及Z軸的三正交方向的關於空間加工位置誤差的誤差資訊,且控制器可根據空間位置誤差資訊即時補償,使得控制器可準確地調整承載加工工件的移動平台與加工加工工件的刀具之間的空間相對關係而對加工工件進行加工,而可增加工具機的加工精度。It can be known from the foregoing embodiments of the present invention that the application of the present invention has the following advantages. The machine tool error compensation unit of the present invention can derive error information about spatial processing position errors in the three orthogonal directions of the X-axis, Y-axis, and Z-axis according to the three-axis angle sensing module and the three-axis mobile platform sensing position device. And the controller can compensate in real time according to the spatial position error information, so that the controller can accurately adjust the spatial relative relationship between the mobile platform carrying the processing workpiece and the tool processing the processing workpiece to process the processing workpiece, and can increase the machine tool Processing accuracy.
雖然本發明已以實施方式揭露如上,然其並非用以限定本發明,任何熟習此技藝者,在不脫離本發明之精神和範圍內,當可作各種之更動與潤飾,因此本發明之保護範圍當視後附之申請專利範圍所界定者為準。Although the present invention has been disclosed in the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make various modifications and retouches without departing from the spirit and scope of the present invention. Therefore, the protection of the present invention The scope shall be determined by the scope of the attached patent application.
100‧‧‧工具機100‧‧‧tool machine
110‧‧‧刀具110‧‧‧tool
112‧‧‧刀具端部112‧‧‧Tool end
120a‧‧‧X軸移動平台120a‧‧‧X-axis moving platform
120b‧‧‧Y軸移動平台120b‧‧‧Y-axis moving platform
120c‧‧‧Z軸移動平台120c‧‧‧Z axis moving platform
122a‧‧‧X軸移動平台滑軌122a‧‧‧X-axis mobile platform slide
124a‧‧‧X軸移動平台滾珠導螺桿124a‧‧‧X-axis mobile platform ball guide screw
130a‧‧‧X軸移動平台感測位置裝置130a‧‧‧X-axis moving platform position sensing device
130b‧‧‧Y軸移動平台感測位置裝置130b‧‧‧Y-axis moving platform sensing position device
130c‧‧‧Z軸移動平台感測位置裝置130c‧‧‧Z-axis mobile platform position sensing device
132a‧‧‧X軸移動平台感測位置裝置感測點132a‧‧‧X-axis moving platform sensing position device sensing point
132b‧‧‧Y軸移動平台感測位置裝置感測點132b‧‧‧Y-axis moving platform sensing position device sensing point
132c‧‧‧Z軸移動平台感測位置裝置感測點132c‧‧‧Z-axis moving platform sensing position device sensing point
140‧‧‧三軸角度感測模組140‧‧‧Three-axis angle sensing module
142‧‧‧Y軸角度感測模組142‧‧‧Y-axis angle sensing module
144‧‧‧X軸角度感測模組144‧‧‧X-axis angle sensing module
146‧‧‧Z軸角度感測模組146‧‧‧Z-axis angle sensing module
150‧‧‧誤差補償單元150‧‧‧ Error Compensation Unit
160‧‧‧控制器160‧‧‧controller
170‧‧‧主軸170‧‧‧ Spindle
200‧‧‧加工工件200‧‧‧Processed workpiece
Lxx‧‧‧X軸移動平台的感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離The shortest linear distance between the sensing point of the sensing position device of the Lxx‧‧‧ X-axis moving platform and the tool parallel to the Z axis
Lxy‧‧‧X軸感測位置裝置的感測點與該刀具之間平行Y軸的最短直線距離The shortest linear distance between the sensing point of the Lxy‧‧‧X-axis position sensing device and the tool in parallel with the Y-axis
Lxz‧‧‧X軸感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離The shortest linear distance between the sensing point of the Lxz‧‧‧ X-axis position sensing device and the tool in parallel with the Z axis
Lyx‧‧‧Y軸移動平台感測位置裝置的感測點與該刀具之間平行X軸的最短直線距離The shortest linear distance between the sensing point of the Lyx‧‧Y-axis moving platform sensing position device and the tool parallel to the X-axis
Lyy‧‧‧Y軸移動平台感測位置裝置的感測點與該刀具之間平行Y軸的最短直線距離The shortest linear distance between the sensing point of the Lyy‧‧Y-axis moving platform sensing position device and the tool in parallel with the Y-axis
Lyz‧‧‧Y軸移動平台感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離The shortest linear distance between the sensing point of the Lyz‧‧Y-axis moving platform sensing position device and the tool in parallel with the Z axis
Lzx‧‧‧Z軸移動平台感測位置裝置的感測點與該刀具之間平行X軸的最短直線距離The shortest linear distance between the sensing point of the Lzx‧‧‧Z-axis moving platform sensing position device and the tool in parallel to the X axis
Lzy‧‧‧Z軸移動平台感測位置裝置的感測點與該刀具之間平行Y軸的最短直線距離The shortest linear distance between the sensing point of the Lzy‧‧‧Z-axis moving platform sensing position device and the tool in parallel with the Y-axis
Lzz‧‧‧Z軸移動平台感測位置裝置的感測點與該刀具之間平行Z軸的最短直線距離The shortest linear distance between the sensing point of the Lzz‧‧Z-axis moving platform sensing position device and the tool parallel to the Z-axis
O‧‧‧軸心O‧‧‧Axis
D1‧‧‧X軸移動平台理想加工位置D1‧‧‧X-axis moving platform ideal processing position
D2‧‧‧X軸移動平台實際加工位置D2‧‧‧ X-axis mobile platform actual machining position
θx(x)‧‧‧X軸移動平台以X軸為轉軸的轉動角度θ x (x) ‧‧‧ Rotation angle of X-axis moving platform with X axis as rotation axis
θy(x)‧‧‧X軸移動平台以Y軸為轉軸的轉動角度θ y (x) ‧‧‧ Rotation angle of X-axis moving platform with Y-axis as rotation axis
θZ(x)‧‧‧X軸移動平台以Z軸為轉軸的轉動角度θ Z (x) ‧‧‧ Rotation angle of X-axis moving platform with Z axis as rotation axis
為讓本發明之敘述和其他目的、特徵、優點與實施例能更明顯易懂,所附圖式之說明如下: 圖1係繪示依照本發明一實施例的具有阿貝誤差補償的數值控制工具機的立體示意圖。 圖2係繪示圖1的工具機在加工一工件時X軸移動平台有角度誤差的側視圖。 圖3係繪示圖1的工具機在加工一工件時X軸移動平台有阿貝偏位的立體圖。 圖4係繪示圖1的工具機在加工一工件時X軸、Y軸及Z軸移動平台有阿貝偏位的立體圖。In order to make the description and other objects, features, advantages, and embodiments of the present invention more comprehensible, the description of the drawings is as follows: FIG. 1 illustrates numerical control with Abbe error compensation according to an embodiment of the present invention Schematic illustration of a machine tool. FIG. 2 is a side view showing an angular error of the X-axis moving platform when the machine tool of FIG. 1 processes a workpiece. FIG. 3 is a perspective view showing that the X-axis moving platform has an Abbe deflection when the machine tool of FIG. 1 processes a workpiece. FIG. 4 is a perspective view showing that the X-axis, Y-axis, and Z-axis moving platform of the machine tool of FIG. 1 has an Abbe deflection when processing a workpiece.
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