TWI326630B - - Google Patents

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TWI326630B
TWI326630B TW97110741A TW97110741A TWI326630B TW I326630 B TWI326630 B TW I326630B TW 97110741 A TW97110741 A TW 97110741A TW 97110741 A TW97110741 A TW 97110741A TW I326630 B TWI326630 B TW I326630B
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Taiwan
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axis
error
machine
sina
signals
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TW97110741A
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TW200940244A (en
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Univ Nat Formosa
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1326630 九、發明說明: 【發明所屬之技術領域】 生之誤差,以達高精度要求 本4月心'關方;-種檢測多轴加工機誤差之系統與方法係 以光學非接觸檢測模式檢測多轴加工機之線性轴丫與?轴j 與旋轉軸(A、B與C軸)運動時所產 之設計。 先前技術1326630 IX. Description of invention: [Technical field of invention] The error of birth, in order to meet the high precision requirements of this April's heart; - the system and method for detecting multi-axis machine error is detected by optical non-contact detection mode What is the linear axis of a multi-axis machine? The design produced when the axis j moves with the rotary axes (A, B, and C axes). Prior art

按’目前在產業界中,有愈來愈多的產品是應用多軸加工 機進行加工’當產品愈來愈微小,對產品尺寸的精準度也命來 愈高時’多軸加卫機的誤差就不可忽略了;尤其現今精密力^ 及精密量測之技術漸㈣起,精度的要求是奈米等級,是故多 軸加工機的檢測亦曰漸重要,必須有效的檢測多軸加工機之誤 差方能有效地提升產品之整個品質與良率。 工方向的加工 而三轴加工機 機具 上述之多軸加工機,是指具有三軸以上之加 ,一般有四軸、五軸與六軸等之加工機具; 是以三維空間中三個線性軸向為機具之加工運動方向分別為 x、Y與z三軸,因此三軸加工機對於加工形狀複雜之工件無法 進行製作》 多軸加工機的加工方向可以分為線性軸向與旋轉軸向其 中線性軸向與三軸加工機-樣分為Ζ三軸向;旋轉軸 °可刀為A、B與C軸’其中分別表示對χ軸旋轉方向 '對γ 轴旋轉方向與對ζ㈣轉方向;由於多軸加工機可以加工較複 5 1326630 雜之工件,所製作之成品更符合市場的要求’因此多轴加工機 已漸漸取代三軸加工機。 多軸加工機的檢測可分為三個部分,分別為線性轴檢測、 旋轉軸檢測與線性軸旋轉軸檢測;其中線性軸檢測與旋轉㈣ 測部分可㈣三軸加工機之檢測技術進行,檢測技術已十分成 熟,並已被國際標準化組織(IS〇)列入規範。 就目前應用於線性軸旋轉轴之檢測系統是以雙球球桿According to 'currently in the industry, there are more and more products that are processed by multi-axis processing machines'. When the products are getting smaller and smaller, the accuracy of the product size is also higher. The error can not be ignored; especially today's precision force ^ and precision measurement technology gradually (four), the accuracy requirement is the nano grade, so the detection of multi-axis processing machine is also becoming more and more important, must effectively detect multi-axis processing machine The error can effectively improve the overall quality and yield of the product. The multi-axis machining machine described above is a processing tool having three or more axes, generally four-axis, five-axis and six-axis, etc.; three linear axes in three-dimensional space The machining direction of the machine tool is three axes of x, Y and z, so the three-axis machining machine cannot manufacture the workpiece with complicated shape. The machining direction of the multi-axis machining machine can be divided into linear axis and rotation axis. The linear axial and three-axis machining machine - the sample is divided into three axes; the rotary axis ° can be the A, B and C axis 'which respectively indicate the direction of rotation of the axis of the axis θ to the direction of rotation of the γ axis and the direction of the opposite direction of the ζ (4); Since the multi-axis machine can process more than 5 1326630 miscellaneous workpieces, the finished products are more in line with the market requirements. Therefore, multi-axis machining machines have gradually replaced the three-axis machining machines. The detection of multi-axis machining machine can be divided into three parts, namely linear axis detection, rotary axis detection and linear axis rotation axis detection; wherein linear axis detection and rotation (four) measurement part can be carried out by (four) three-axis machining machine detection technology, detection The technology is very mature and has been included in the Code by the International Organization for Standardization (IS). The detection system currently applied to the linear axis rotation axis is a double ball club.

⑽咖㈣Bai.)為量測主體,將雙球球桿之前後設定於加工: 主軸與工作平面上,再由旋轉軸與線性軸分別進行旋轉運動盘 循圓運動,其運動方向相反,使雙_捍可料在以位置:、 藉由雙球球桿可量測加工機主軸與卫作平台間之相對位移’最 後對雙球球桿所量測得之數據進行分析,即可獲得線性㈣轉 軸之誤差。 然而’上述系統採用雙球球桿量測,僅可獲得單一% 再藉由公式的計算才可分離出其他軸向之誤差,精讀度 足,檢測效果有限。。 號源, 尚有不 緣此,本案發明人有鑒於上 扎里冽夕軸加工機誤差之技術 問題,特而研發一種用以光學 妾觸仏測模式,可簡易檢測出 夕軸加工機之線性軸(χ、γ與 轉軸(Α、Β與c軸)運動 時所產生之決差,以達高精度之要求。 【發明内容】 本發明主要目的在於提供—種『檢測多轴加 與H — 示、.此 //』可怎用方;乡軸加工機之檢測、校正與調校用;其系統 係結合雷射光源與二維光電式感測器等,為—光學非接觸式量測 系统’在量測時同時可獲得二組訊號,可有效的提升量測系統之 精確度。 斑本發明次要目的在於提供一種『檢測多轴加工機誤差之系統 Η方法』,採用具有高解析度之光學式儀器所架設之系統,使其 進行量測時,並不會受到磁場的干擾造成量測的誤差,且亦可應 用方、各種工作%合上’而達低成本、高精4度、體積小、攜帶方 便、架設簡易及檢測迅速等實質效益。 本發明為達上揭目的所設計之一種檢測多抽加工機誤差之 系統與方法,其系統係包含: 一雷射光源,具發射雷射光束,設立於旋轉平台; 光電式感測器’用來測得線性軸旋轉軸位移的變化量,以 供雷射光束照射在光電式感測器同位置上,再經由訊號處理後即 得到其誤差值。 而本發明對其檢測多轴加工機誤差方法,步驟如下: a. 將光電式感測器固定於待測加工機主軸上,並將雷射光源 固疋方;工作平台之旋轉平台上,其中旋轉平台架設於X軸 平移台與Y軸平移台上; b. 使雷射光源發射出一雷射光束,直接射入光電式感測 1326630 器,光電式感測器即可獲得雷射光束之位置; C·令待測加機之旋轉平台進行旋轉運動,χ軸平移台及Y 軸平移台以反方向進行循圓運動,上述之運動速度相等, 此運動模式是欲令雷射光源保持在同一位置,此時光電式 感測器可測得兩組線性軸旋轉軸之訊號; d.再令ζ轴移動L距離後再次進行量測可測得另兩組線 性轴旋轉軸之訊號;(10) Coffee (4) Bai.) For measuring the main body, the double-ball club is set before and after processing: the main shaft and the working plane, and then the rotating shaft and the linear shaft respectively perform a circular motion circular motion, and the moving direction is opposite, so that the double _ 捍 can be obtained in the position:, by the two-ball club can measure the relative displacement between the processing machine spindle and the guard platform The error of the shaft. However, the above system uses the double-ball cue measurement, only a single % can be obtained, and the other axial errors can be separated by the calculation of the formula. The intensive reading degree is sufficient, and the detection effect is limited. . The source of the source, there is still no such thing, the inventor of this case has developed a kind of optical contact measurement mode, which can easily detect the linearity of the Xi axis processing machine. The difference between the axes (χ, γ and the axis of rotation (Α, Β and c axis) is to meet the requirements of high precision. SUMMARY OF THE INVENTION The main object of the present invention is to provide a kind of "detecting multi-axis plus H- Show, how this can be used; the detection, correction and adjustment of the home shaft processing machine; its system is combined with laser light source and two-dimensional photoelectric sensor, etc., for optical non-contact measurement The system's two sets of signals can be obtained at the same time, which can effectively improve the accuracy of the measurement system. The second objective of the invention is to provide a system detection method for detecting multi-axis machine error, which has high resolution. The system built by the optical instrument makes it not subject to the measurement error caused by the interference of the magnetic field, and it can also be applied to the application and the various work% can be combined to achieve low cost and high precision. Degree, small size, carrier The present invention is a system and method for detecting the error of a multi-pulling machine designed for the purpose of the present invention. The system comprises: a laser source with a laser beam emitted, established in Rotating platform; photoelectric sensor 'measured to measure the displacement of the linear axis rotation axis displacement, so that the laser beam is irradiated on the same position of the photoelectric sensor, and then the error value is obtained after the signal processing. The method for detecting the error of the multi-axis processing machine of the invention is as follows: a. Fixing the photoelectric sensor on the main shaft of the processing machine to be tested, and fixing the laser light source; rotating the platform of the working platform, wherein the rotation The platform is mounted on the X-axis translation stage and the Y-axis translation stage; b. The laser light source emits a laser beam and directly enters the photoelectric sensing 1326630, and the photoelectric sensor can obtain the position of the laser beam. C. The rotating platform of the machine to be tested is rotated, and the yaw translation stage and the Y axis translation stage are circularly moved in the opposite direction. The above movement speed is equal, and the movement mode is to make the laser light Keeping in the same position, the photoelectric sensor can measure the signals of two sets of linear axis rotation axes; d. Let the ζ axis move the L distance and measure again to measure the signals of the other two sets of linear axis rotation axes. ;

e·藉由上it共四組訊號經計算後即可獲得線性軸旋轉轴之 误差。 【實施方式】 百先’請參閱圖-與圖二所示,本發明所設計之檢測多轴 加工機誤差之系統與方法’其所設計之結構技術,係包含: —雷射光源】,具發射雷射光束,為設立於工作平台之旋 平台10上; • —光電式感測器2’用來測得線性軸旋轉軸位移的變化量, 設切待測加1機主軸2G上,以供雷射光源」所產生的雷射光 束照射在光電式感測器2同位置上,再經由訊號處理後即㈣ 其誤差值。 再者,本發明所設計之『檢測多軸加工機誤差之系統與方 ^』,於上述結構之組裝與實際使用時’將光電式感測器2固定 方、待冽加工機主軸2〇上,益將雷射光源j固定於工作平台之旋 1326630 轉平台10上;其中,旋轉平台10架設於X軸平移台30與Υ 軸平移台40上,如圖一所示;使雷射光源1發射出一雷射光束, 直接射入光電式感測器2,光電式感測器2即可獲得雷射光束之 位置;令待測加工機之旋轉平台10進行旋轉運動,X軸平移台 30及Υ軸平移台40以反方向進行循圓運動,上述之運動速度 相等,此運動模式是欲令雷射光源1保持在同一位置,此時光 電式感測器2可測得兩組線性軸旋轉軸之訊號,分別可表示為: X1 = Ax+(sina)(cosG) (1) 鲁 yi=Ay+(sina)(sin9) (2) 其中,xl與yl為光電式感測器所測得之訊號,Δχ與Ay 為待測加工機對X與y軸向之誤差,a為待測加工機平台對z 軸之角度誤差,Θ為旋轉平台10之旋轉角度;令z軸移動L距 離後再次進行量測,可測得: x2=Ax+L(sina)(cos0) (3) y2=Ay+L(sina)(sin0) (4) φ 其中,x2與y2為光電式感測器所測得之訊號,L為ζ軸位 移之距離,由上述四個公式可計算得: a=sin-1 ((x2-x 1 )/(L-1 )(cos0)) (5.a) 或 a=sin-1 ((y2-y 1 )/(L-1 )(sin0)) (5 .b) Δχ= xl-(sina)(cos0) (6.a) 或 Δχ =x2—L(sina)(cos0) (6.b)e. The error of the linear axis rotation axis can be obtained by calculating the total four groups of signals on it. [Embodiment] Please refer to the figure- and FIG. 2, the system and method for detecting the error of the multi-axis machine designed by the present invention. The structural technology designed includes: - laser light source, with The laser beam is emitted on the rotating platform 10 of the working platform; • The photoelectric sensor 2' is used to measure the variation of the displacement of the linear axis rotating shaft, and is set to be 2G on the spindle to be tested, The laser beam generated by the laser source is irradiated to the same position of the photoelectric sensor 2, and then processed by the signal to be (4) its error value. Furthermore, the system and the method for detecting the error of the multi-axis machine tool designed by the present invention are used to fix the photoelectric sensor 2 and the spindle of the processing machine 2 in the assembly and actual use of the above structure. The laser source j is fixed on the rotating platform 1326630 of the working platform; wherein the rotating platform 10 is mounted on the X-axis translation stage 30 and the 轴-axis translation stage 40, as shown in FIG. 1; A laser beam is emitted and directly injected into the photoelectric sensor 2, and the photoelectric sensor 2 can obtain the position of the laser beam; the rotating platform 10 of the processing machine to be tested is rotated, and the X-axis translation stage 30 And the cymbal translation stage 40 performs a circular motion in the opposite direction, and the above motion speed is equal. The motion mode is to keep the laser light source 1 in the same position, and the photoelectric sensor 2 can measure two sets of linear axes. The signals of the rotating axes can be expressed as: X1 = Ax+(sina)(cosG) (1) Lu yi=Ay+(sina)(sin9) (2) where xl and yl are measured by photoelectric sensors The signal, Δχ and Ay are the error of the X and y axes of the machine to be tested, and a is the axis of the machine to be tested to the z axis. Degree error, Θ is the rotation angle of the rotating platform 10; let the z-axis move the L distance and measure again, can be measured: x2=Ax+L(sina)(cos0) (3) y2=Ay+L(sina) (sin0) (4) φ where x2 and y2 are the signals measured by the photoelectric sensor, and L is the distance of the ζ axis displacement, which can be calculated by the above four formulas: a=sin-1 ((x2- x 1 )/(L-1 )(cos0)) (5.a) or a=sin-1 ((y2-y 1 )/(L-1 )(sin0)) (5 .b) Δχ= xl- (sina)(cos0) (6.a) or Δχ =x2—L(sina)(cos0) (6.b)

Ay = y 1 -(sina)(sin0) (7.a) 1326630 或 △y = y2 -L(sina)(sinG) (7.b)。 據此’本發明所設計之『檢測多軸加工機誤差之系統與方 法』,運用雷射光源1與光電感測器2的系統架構,結合雷射光 源1與二維光電式感測器2搭配形成一光學非接觸式量測系 統,使之在進行量測時,透過二維光電式感測器2即可同時声 得二組訊號’可有效的提升檢測系統之精確度。 此外,本發明所設計之『檢測多軸加工機誤差之系統與方 法』’於進行檢測時,利用將雷射光源1固定於旋轉軸(旋轉平 台1 〇架設於X軸平移台30與Y軸平移台40 )上、光電感、、則养 2固定於線性軸(待測加工機主軸20)上,再依上述檢測步驟, 即可檢測多軸加工機之誤差。 值得一題的是,本發明所設計之『檢測多軸加工機誤差之 系統與方法』,採用具有高解析度之光學式儀器進行量測時並 不會受到磁場的干擾造成量測的誤差,且亦可以應用於各種工 作琢5上,而具有低成本、高精確度、體積小、攜帶方便、架 設簡易及檢測迅速等特性。 經由上述,本發明所設計之檢測多軸加工機誤差之系統與 方法,於上列詳細說明係針對一可行實施例為具體之代表,惟 。亥貝靶例亚非用以限制本發明之專利範圍,凡未脫離本發明之 技知神所為之等效實施或變更,均應包含於本發明訴求專利 之範圍中。 1326630 綜上所述,本發明所設計一種檢測多麵 與方法,不但在目前工業型態上韻創新 ^產之以 新穎性及進牛性之、土 ^ 且其應已充分符合 〜二 發明專利要件’麦依法提出申請,懇請 貝局核准本件發明專利申請案,以勵發明,至感德便。 【圖式簡單說明】 意圖 圖一係本發明之檢測多轴加工機誤差之立體系統架構示Ay = y 1 -(sina)(sin0) (7.a) 1326630 or Δy = y2 -L(sina)(sinG) (7.b). According to the "system and method for detecting multi-axis machining machine error" designed by the present invention, the system architecture of the laser light source 1 and the photo-inductor 2 is combined with the laser light source 1 and the two-dimensional photoelectric sensor 2 Together with the formation of an optical non-contact measuring system, the two-dimensional signal can be simultaneously transmitted through the two-dimensional photoelectric sensor 2 during the measurement, which can effectively improve the accuracy of the detection system. In addition, the "system and method for detecting multi-axis machining machine error" designed by the present invention uses the laser light source 1 to be fixed to the rotating shaft during the detection (the rotating platform 1 is erected on the X-axis translation stage 30 and the Y-axis) The translation stage 40), the optical inductance, and the maintenance 2 are fixed on the linear axis (the spindle 20 to be tested), and according to the above detection steps, the error of the multi-axis machining machine can be detected. It is worth noting that the system and method for detecting the error of a multi-axis machine designed by the present invention does not suffer from the measurement error caused by the interference of the magnetic field when the optical instrument with high resolution is used for measurement. It can also be applied to various work 琢5, and has the characteristics of low cost, high precision, small size, convenient carrying, simple erection and rapid detection. Through the above, the system and method for detecting the error of the multi-axis machine designed by the present invention are specifically represented in the above detailed description for a feasible embodiment. The singularity of the invention is intended to be limited to the scope of the invention, and equivalents or modifications of the invention are intended to be included within the scope of the invention. 1326630 In summary, the present invention is designed to detect a multi-faceted method and a method, which is not only novel in the current industrial type, but also novelty and inferiority, and which should fully comply with the second invention patent. The requirements of the 'Mc Law application, please ask the Bay Bureau to approve the invention patent application, in order to invent invention, to the sense of virtue. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a perspective view of a three-dimensional system architecture for detecting a multi-axis machine error of the present invention.

圖一係本發明之檢測多車由加 工機誤差之系統其側 示意圖。 【主要元件符號說明】 面架構 1 雷射光源 10 旋轉平台 2 光電式感測器 20 待測加工機主轴 30 X軸平移台 40 Y軸平移台BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a side elevational view of the system of the present invention for detecting errors in a multi-vehicle machine. [Main component symbol description] Surface structure 1 Laser light source 10 Rotary platform 2 Photoelectric sensor 20 Machine spindle to be tested 30 X-axis translation stage 40 Y-axis translation stage

Claims (1)

1326630 .- 年t月(日修(更)正替換頁 十、申請專利範圍: 丨 :-----^ ’ ’ 1. 一種檢測多軸加工機誤差之系統,係包含: 一雷射光源,具發射雷射光束,設立於旋轉平台; 一光電式感測器,用來測得線性軸旋轉軸位移的變化量,設 立於待測加工機主軸上,以供雷射光束照射在光電式感測器 同位置上,再經由訊號處理後而得到其誤差值。 2. 如申請專利範圍第1項所述之檢測多軸加工機誤差之系統, 其中上述旋轉平台係架設於X軸平移台與Y軸平移台上。 3. 一種檢測多軸加工機誤差之方法,其步驟如下: a. 將光電式感測器固定於待測加工機主軸上,並將雷射光源 固定於旋轉平台上,而旋轉平台架設於X軸平移台與Y軸平移 台上; b. 利用雷射光源發射出一雷射光束,直接射入光電式感測 器,透過光電式感測器即可獲得雷射光束之位置; c. 令待測加工機之旋轉平台進行旋轉運動,X軸平移台及Y 軸平移台以反方向進行循圓運動,上述之運動速度相等,使 雷射光源保持在同一位置,此時光電式感測器可測得兩組線 性軸旋轉軸之訊號,分別為: Xi=Ax+(sina)(cos0) (1) yi=Ay+(sina)(sin0) (2) 其中,xl與yl為光電式感測器所測得之訊號,Δχ與Ay為待 測加工機對X與y軸向之誤差,a為待測加工機平台對z軸之角 12 13266301326630 .- Year t month (Japanese repair (more) is replacing page ten, patent application scope: 丨:-----^ ' ' 1. A system for detecting multi-axis machine error, including: a laser source , with a laser beam emitted from the rotating platform, is set up on a rotating platform; a photoelectric sensor is used to measure the variation of the displacement of the linear axis of the rotating shaft, and is set on the main shaft of the processing machine to be tested for the laser beam to be irradiated in the photoelectric type The sensor is in the same position and then processed by the signal to obtain the error value. 2. The system for detecting the error of the multi-axis machine according to the first aspect of the patent application, wherein the rotating platform is erected on the X-axis translation stage With the Y-axis translation stage. 3. A method for detecting multi-axis machine error, the steps are as follows: a. Fix the photoelectric sensor to the spindle of the machine to be tested, and fix the laser source to the rotating platform. The rotating platform is mounted on the X-axis translation stage and the Y-axis translation stage; b. A laser beam is emitted by the laser light source, directly into the photoelectric sensor, and the laser is obtained through the photoelectric sensor. The position of the beam; c. The rotating platform of the machine rotates, and the X-axis translation stage and the Y-axis translation stage perform circular motion in the opposite direction. The above-mentioned movement speeds are equal, so that the laser light source is kept at the same position, and the photoelectric sensor can be measured at this time. The signals of the two sets of linear axis rotation axes are: Xi=Ax+(sina)(cos0) (1) yi=Ay+(sina)(sin0) (2) where xl and yl are measured by photoelectric sensors The signal, Δχ and Ay are the error of the X and y axes of the machine to be tested, and a is the angle of the platform of the machine to be tested to the z axis 12 1326630 R叙更)正替換頁 度誤差,θ為旋轉平台之旋轉角度; ------ d.再令ζ軸移動L距離後再次進行量測,即可測得另兩組線性 軸旋轉軸之訊號,分別為: ⑶ (4) x2=Ax+L(sina)(cos0) y2=Ay+L(sina)(sin0) 其中,x2與y2為光電式感測器所測得之訊號,L為ζ軸位移之 距離; e.藉由上述四組訊號經計算後即可獲得線性軸旋轉軸之誤 差。 4. 如申請專利範圍第3項所述之檢測多軸加工機誤差之方法, 其中上述四組訊號可計算得α,〇:為待測加工機平台對ζ轴 之角度誤差: a=sin'1((x2-xl)/(L-l)(cos0)) (5.a) 或 ci=sin-1((y2-yl)/(L-l)(sin0)) (5.b) 〇 5. 如申請專利範圍第3項所述之檢測多轴加工機誤差之方法, 其中上述四組訊號可計算得Δχ,Δχ為待測加工機對X軸向 之誤差: Δχ= xl-(sina)(cos9) (6.a) 或 Δχ =x2-L(sina)(cos0) (6.b)。 6. 如申請專利範圍第3項所述之檢測多軸加工機誤差之方法, 其中上述四組訊號可計算得Ay,Ay為待測加工機對y軸向 13 1326630 柃ϋ;; ^日修(更:)正替換頁 -TVM *«,3β·«ίΓ -· t I 丨《II _ I m -nr· ·Ί| , _ 之誤差: Ay = yl-(sina)(sin9) (7.a) 或 Ay = y2 -L(sina)(sin0) (7.b)。R 述) is replacing the page error, θ is the rotation angle of the rotating platform; ------ d. After the axis is moved by the L distance and then measured again, the other two sets of linear axis rotation axes can be measured. The signals are: (3) (4) x2=Ax+L(sina)(cos0) y2=Ay+L(sina)(sin0) where x2 and y2 are the signals measured by the photoelectric sensor, L The distance of the x-axis displacement; e. The error of the linear axis rotation axis can be obtained by calculating the above four groups of signals. 4. The method for detecting the error of the multi-axis machining machine described in the third paragraph of the patent application, wherein the above four groups of signals can be calculated as α, 〇: the angular error of the axis of the processing machine platform to be tested: a=sin' 1((x2-xl)/(Ll)(cos0)) (5.a) or ci=sin-1((y2-yl)/(Ll)(sin0)) (5.b) 〇5. If applying The method for detecting multi-axis machining machine error according to item 3 of the patent scope, wherein the four groups of signals can be calculated as Δχ, and Δχ is the error of the X-axis of the processing machine to be tested: Δχ= xl-(sina)(cos9) (6.a) or Δχ =x2-L(sina)(cos0) (6.b). 6. The method for detecting the error of the multi-axis machining machine described in claim 3, wherein the above four groups of signals can be calculated as Ay, and Ay is the processing machine to be y-axis 13 1326630 柃ϋ; (More:) Positive replacement page - TVM *«, 3β·«ίΓ -· t I 丨 "II _ I m -nr· ·Ί| , _ error: Ay = yl-(sina)(sin9) (7. a) or Ay = y2 -L(sina)(sin0) (7.b).
TW97110741A 2008-03-26 2008-03-26 System for detecting error of multi-axis processing machine and method thereof TW200940244A (en)

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