TW411408B - Speed rate control method and equipment in computer numeric control curve path - Google Patents

Abstract

In the process of parametric curve computer numeric control, stepping rate is the deterministic factor of process quality. This invention proposes parametric curve interpolator with speed rate control and develops operation modes. The modes are constant rate interpolator and accelerate-decelerate interpolator. The operation mode of constant speed rate interpolator could maintain the parametric curve keeping speed rate at the constant value in the implementation process of interpolation. Furthermore, the operation mode will adapt the accelerate-decelerate design of parametric curve interpolator to achieve smoother accelerate-decelerate motions.

Description

五、發明説明（1) 發明背畺 發明領诚 f本發明係關於電腦數控（CNC)加工機，詳言之，係關 於具速率控制的參數化曲線插値器設計之電腦數控加工 機。）V. Description of the invention (1) The invention of the invention The invention of f. This invention relates to a computer numerical control (CNC) processing machine. In particular, it relates to a computer numerical control processing machine designed with a parameter-controlled curve inserter with rate control. )

J 相關技藝說明 傳統的CAD/CNC系統操作人員首先經由電腦辅助設計 (CAD)設計所需工件，如：模具、渦輪葉片、飛機模型等 的3-D曲線表示，其中曲線的表示在CAD系統中一般爲參 數化曲線的格式，並且由於一般的CNC系統僅提供直線與 圓的插値器，因此CAD尙必須將所設計的工件表面曲線分 段並傳送到CNC執行。當CNC系統的直線插値器接收到 工件表面曲線分段訊息後再以某些演算法則產生刀具運動 的內插點，而這些內插點即爲伺服驅動器的位置输入命 令。 經濟部中央標準局負工消f合作社印製 (請先閲請背面之注意事項再填寫本頁) 雖然傳統的曲線加工方式較爲簡單，但是在應用上仍 有些許缺點：α)爲使能更精確的表示曲線，因此必須將曲 線分段爲大量的區段並傳送於CAD與CNC之間，但是在 傳送大量的訊號時容易造成誤差，如：資料遺失與雜訊干 擾。（2)切割區段的不連續性會造成加工工件的表面精度惡 化° (3)因爲曲線區段直線化，速率在每一直線區段並非爲 順滑（smooth)變化，尤其是考慮CNC插値器的自動加減速 特性後更爲明顯。 傳統的加減速方式是將位置命令經過低通濾波器以產 本紙張尺度適用中园國家標準（C.N'S ) Λ4叱格（2Η)Χ2π〈，&gt;.ίί ) ； ~ 經濟部中央標隼局員工消费合作社印製 Α-ΙΓ 五、發明説明（2 ) 生較爲平滑的命令輸入。但是此法會使具有較大變化的命 令路徑產生徑向與弦高誤差，如加工曲線的起點與終點附 近。雖然Kim(D.I.Kim)提出使用參數的加減速方式以達到 參數化曲線加減速的目的，同時因爲是對參數進行加減速 的操作，因此內插點具有較小的徑向誤差，可以使內插點 的產生具有加減速的功能，但是在某些曲線上敢不能真正 達到速率加減速的目的，其原因是參數空間與曲線並非是 均勻對應。此外，當曲線之曲率半徑太小以至於進給速率 命令相形過大時，將造成明顯的位置命令誤差。 本發明鑑於習知之參數化曲線插値的過程中，曲線的 速率精度不易控制，而進給的速率是加工品質的決定性因 素，因此提出具速率控制的參數化曲線插値器的設計。 發明槪沭 本發明之目的爲準供一種具定速率插値器操作模式，· 可以使參數化曲線在插値的實現過程中，保持定値速率， 以確保加工品質之電腦數控曲線路徑速率控制方法及裝 置》 本發明之另一目的爲提供一種具加減速插値器操作模 式，利用參數式曲線插値器的加減速設計，以獲得更爲平 滑的加減速運動之電腦數控曲線路徑速率控制方法及裝 置。 本發明之電腦數控（CNC)曲線路徑速率控制方法，係 以等速率或加減速控制操作曲線路徑加工，包括下列步 踩· 本紙張尺度適用中國國家標準（CMS ) Λ4Μ1格（2!〇X21)7公兑） 2 156*5 ^~ — ίι 装 ^ ： 訂 (請先閱讀背vg之注意事項再填艿本頁) ΙΓ 411408 五、發明説明（3 ) (1) 參數化曲線插値器在接收由電腦輔助設計（CAD)所解譯 曲線的訊息後，以參數化曲線的參數迭代法（Iteration)產 生連續的內插點； (2) 僅考慮插値器產生的位置命令誤差之弦高誤差（chord height error)的影響，而不考慮徑间誤差（radial error); (3) 導出參數曲線公式（parametric curve formulation)之一次 近似參數迭代法則： (4) 設計具速率控制之參數迭代法則，將該表示之一次近似 參數迭代法則提出參數補償，經由補償量與曲線間的相 關性獲得更高精度的曲線速率控制： (5) 選擇在零點附近的補償値以獲得較爲可靠的參數迭代結 果；以及 (6) 將該獲得補償値之連續的內插點送入控制系統使刀具中 心沿著參數化曲線移動。 本發明之電腦數控（CNC)曲線路徑速率控制方法中所 使用之參數化曲線爲非等距B雲形線（NURBS)，而參數化 曲線插値器使用的參數迭代法，是以 Chou(J.J.Chou)和J Related Skills Description Traditional CAD / CNC system operators first design the required workpieces through computer-aided design (CAD), such as: 3-D curve representation of molds, turbine blades, aircraft models, etc., where the curve representation is in the CAD system Generally, it is a format of parameterized curves, and since general CNC systems only provide straight and circular inserters, CAD 尙 must segment the designed workpiece surface curve and transfer it to the CNC for execution. When the linear inserter of the CNC system receives the segmented information of the surface curve of the workpiece, it then uses some algorithms to generate interpolation points for the tool movement, and these interpolation points are the position input commands for the servo driver. Printed by the Central Bureau of Standards, Ministry of Economic Affairs, Cooperative Society (please read the notes on the back before filling this page) Although the traditional curve processing method is relatively simple, there are still some shortcomings in application: α) The curve is more accurately represented, so the curve must be segmented into a large number of sections and transmitted between CAD and CNC, but it is easy to cause errors when transmitting a large number of signals, such as data loss and noise interference. (2) The discontinuity of the cutting section will cause the surface accuracy of the processed workpiece to deteriorate. (3) Because the curve section is linear, the speed does not change smoothly in each linear section, especially considering the CNC insertion. The automatic acceleration and deceleration characteristics of the gearbox are more obvious. The traditional acceleration and deceleration method is to pass the position command through a low-pass filter to apply the China National Standard (CN'S) Λ4 叱 Grid (2Η) × 2π <, &gt; .ίί) to the paper size of the paper; ~ Central Standard of the Ministry of Economic Affairs Printed by the Consumer Cooperative of the Bureau A-ΙΓ V. Description of the invention (2) The command input is relatively smooth. However, this method will cause radial and chordal height errors for command paths with large changes, such as near the start and end points of the processing curve. Although Kim (DIKim) proposed the use of parameter acceleration and deceleration to achieve the purpose of parameterizing the curve acceleration and deceleration, and because it is the operation of the parameter acceleration and deceleration, the interpolation point has a small radial error, which can make the interpolation The generation of points has the function of acceleration and deceleration, but on some curves dare not really achieve the purpose of rate acceleration and deceleration, the reason is that the parameter space does not correspond to the curve uniformly. In addition, when the curvature radius of the curve is so small that the feed rate command is too large, it will cause obvious position command error. In view of the conventional process of parameterized curve interpolation, the present invention is difficult to control the rate accuracy of the curve, and the feed rate is a decisive factor for the processing quality. Therefore, the design of the parameterized curve inserter with rate control is proposed. Invention: The purpose of the present invention is to provide a mode of operation with a constant rate inserter, which can maintain the constant rate of the parameterized curve during the implementation of the interpolation, so as to ensure the processing rate of the computer numerical control curve path rate control method. And device "Another object of the present invention is to provide a computer numerical control curve path rate control method with an acceleration / deceleration inserter operation mode, which uses a parametric curve inserter's acceleration / deceleration design to obtain a smoother acceleration / deceleration motion. And device. The computer numerical control (CNC) curve path rate control method of the present invention is to operate the curve path processing at the same rate or acceleration / deceleration control, including the following steps: This paper size is applicable to the Chinese National Standard (CMS) Λ4M1 grid (2.0 × 21) 7 credits) 2 156 * 5 ^ ~ — ί ^: Order (please read the precautions on the back of vg before filling in this page) ΙΓ 411408 5. Description of the invention (3) (1) The parameterized curve inserter is in After receiving the information of the curve interpreted by computer-aided design (CAD), iterative method (Iteration) of the parameterized curve is used to generate continuous interpolation points; (2) Only the chord height of the position command error generated by the inserter is considered. The influence of chord height error, without taking into account the radial error; (3) Derive an approximate parameter iteration rule for the parametric curve formulation: (4) Design a parameter iteration rule with rate control , A parameter approximation rule of this representation is proposed to compensate the parameters, and the curve rate control with higher accuracy is obtained through the correlation between the compensation amount and the curve: (5) choose the compensation near zero to In a more reliable parameter iterative result; and (6) the obtained interpolation point Zhi continuous compensation of the control system into the center of the tool moves along a parametric curve. The parameterized curve used in the computer numerical control (CNC) curve path rate control method of the present invention is a non-equidistant B cloud line (NURBS), and the parameter iterative method used by the parameterized curve inserter is Chou (JJChou )with

Yang(D.C.H.Yang)所提出的一般化參數迭代法則爲基礎提 出進給速率控制的參數迭代方式° 本發明之電腦數控曲線路徑速率控制裝置’包括： 電腦，作輔助設計（CAD)之工作’該辅助設計工作包 括作參數化曲線格式及分段曲線： 電腦數控（CNC)機構’包括： 參數化曲線插値器’在接收該電腦所解譯之參數 ----Γ· I. 1---------士 κ _ _ _ f _ _ 丁 {請先閱讀背面之注意事項再填寫本頁) 經濟部中央標準局員工消費合作社印聚 本紙張尺度適用中國國家標準（CNS )八4故格（21〇&gt;&lt;2〔)7公兑） 3 15685 經濟部中央標隼局員工消费合作社印裝 Α7 Β7 五、發明説明（4 ) 曲線訊息後，以參數化曲線的點產生方式產生連續的 內插點： 控制器，接收該參數化曲線插値器所產生的連續 的內插點，送出控制加工信號； 刀具，接收該控制器送出之控制加工信號，中心 Ϊ* 沿著參數化曲線移動；以及 人機介面裝置，可讓操作者與該參數化曲線插値 器之間作人機溝通： 其中該參數化曲線插値器可對該參數化曲線作定速率 插値操作模式及加減速插値操作模式。 本發明之電腦數控曲線路徑速率控制之參數化曲線插 値器裝置，包括：定速率插値器，使參數化曲線路徑在插 値的實現過程中保持速率定値；加減速插値器，使該加工 曲線路徑獲得更爲平滑的加減速運動。 圖式之簡單說明 第1圖爲本發明實施例參數化曲線的加工系統方塊 圖。 第2圖爲刀具在兩內插點間以直線運動，插値器產生 位置命令誤差之示意圖- 第3圖爲補償量〜公式中，向量〇、曲線微分向量 與參數Μ、‘、1/, μ間的幾何關係。 第4圖爲形成相同實數値或共軛虛數値補償量之 情況β 第5圖爲本實施例應用之蝴蝶結曲線命令路徑》 本紙張尺度適用中國國家標準（CNS ) Α4規格（210X297公釐）4 15685 11. 1-I 裝 訂 - - (請先聞讀背面之注意事項再填寫本頁) 4. 經濟部中央標準局員工消費合作社印製 4^408 A- 1Γ 五、發明説明（5 ) 第 6圖爲一階近似（1 s t 〇 r d e r a p p r ο X i m a t i ο η)插値速率 命令結果曲線速率變動情形。 第7圖爲二階近似（2nd order approximation)插値速率 命令結果曲線速率變動情形。 第8圖爲本實施例定速率操作模式插値速率命令結果 曲線速率變動情形。 第9圖爲定速率操作模式中參數補償値計算結 果。 第10圖爲二次曲線加減速方式的速率差値變化1st階 近似之曲線情況。 第11圖爲二次曲線加減速方式的速率差値變化2nd階 近似之曲線情況》 第12圖爲二次曲線加減速方式的速率差値變化定速率 操作模式之曲線情況。 圖號說明 1電腦（CAD) 2電腦數控（CNC)機構 3參數化曲線插値器 4人機介面裝置 5控制器 6刀具 7參數曲線訊息 8工件輪廓曲線 9刀具運動路徑 (請先聞讀背面之注意事項再填{巧本頁) i—1 I - - - - - LI J L— . ^衣&quot;.— I —4— j -----. .........I - - I --·'. - I -II1 1ΓΙ ^^1---V-- 本紙張尺度適用中國國家標準（CNS ) Λ4叱格U丨0X2V?公兌） 5 15685 經濟部中央標準局員工消费合作社印製 4U408 Η' —______ 五'發明説明（6) 10徑向誤差 11弦高誤差 12內插點 較佳實施例之詳細說明 —般由於CAD系統所產生的曲線爲參數式曲線表示， 同時CAD系統也提供參數式曲線的相關參數資料傳輸格 式，因此在CAD/CNC系統的設計上可直接應用參數式曲 線的參數資訊作爲CAD/CNC系統間的加工資訊傳輸與CNC 的插値。本發明討論參數化曲線的加工系統如第1圖所示， 圖中1爲電腦，其作輔助設計（CAD)之工作，包括作參數 化曲線格式及分段曲線，2爲電腦數控（CNC)機構，其中參 數化曲線插値器3在接收由電腦1所解譯之參數曲線訊息 7後，以參數化曲線的點產生方式產生連續的內插點送入 控制器5使刀具6中心沿著參數化曲線移動，其中4爲人 機介面裝置，可讓操作者與CNC之間作溝通。常見的參數 化曲線爲：Bezier曲線、B雲形線（B Spline)、和NURBS (非 等距B雲形線）；本發明使用NURBS參數化曲線。 參數化曲線插値器3實現的過程，主要是進行參數化 曲線點的計算。一般較高曲線位置與速率精度的計算法則 需較複雜的計算方式與較大的計算量，此點在即時命令產 生的環境下較爲不利。因此計算法的選擇與設計必須考慮 曲線精度與計算時間的權衡·最常使用的計算法格式爲如 下的參數迭代方式： ^ «, + Δ(μ,) (請先閱讀背,6之注意事項再填」ΪΪ本頁) —-訂 本紙.张尺度適用中國國家標準（〔呢）六4規掊（210乂297公垃） 6 156«5 411438 A' ΙΓ 五、發明説明（7 ) 經濟部中央標準局員工消費合作社印製 (請先聞讀背面之注意事項再填寫本頁) 其中，《表示現在時序的參數，u,+l表示下一時序時的 參數，Δ(ί〇表示與現在時序相關的計算量。在參數化曲線 下，Mi表示曲線的參數，因此必須將該參數代入曲線的數 學表示式才能獲得該時序時的點。在參數化曲線插値器的 設計時，對於任意參數式曲線數學模型的應用，由於參數 化曲線中參數與曲線或幾何路徑間的關係並不明顯，不易 執行逆運算’即不容易由已知的曲線點反推相對應的參數 値，因此在參數的迭代法上不易對曲線速率有良好的控 制》在實際加工上，參數式曲線插値器會因爲不適當的參 數迭代法則造成插値結果曲線速率的誤差，曲線速率誤差 是指相鄰內插點間的移動速率與插値器的進給速率設定的 差値，當曲線速率的誤差越大時表示內插點間的移動不能 如進給速率所操作，往往會造成過大的位置誤差、過長的 加工時間與不良的加工工件表面。因此在參數化曲線插値 器的設計上，參數迭代法必須精確的控制曲線速率降低誤 差》除了曲線速率誤差，由於插値器產生刀具運動時的內 插點，而刀具在兩內插點間是以直線運動，因此插値器產 生的位置命令誤差一般可包含：徑向誤差（radial error)與 弦高誤差（chord height error)。徑向誤差、弦高誤差與曲 線間的關係可如第2圖所表示，其中8爲工件輪廓曲線* 9爲刀具運動路徑，10爲徑向誤差，U爲弦高誤差，12 爲內插點β 徑向誤差爲位置點與曲線間的最短距離，而弦高誤差 則爲兩位置點所形成的割線函與切割弧間的最大距離。在 本紙浪尺度適用中國國家標準（CNS ) Μ規格（210x ) 7 15685 經濟部中央標準局員工消費合作社印製 4： 五、發明説明（* ) 參數化曲線插値器的設計上，一般引起徑向誤差的原因爲 浮點數的圓切誤差（rounding error)，而引起弦高誤差的原 因爲不正確的進給速率所造成。由於在參數化曲線的表示 中，圓切誤差可利用精密電腦運算予以降低，而弦高誤差 往往會遠大於徑向誤差，因此在插値器的設計上％本發明 僅考慮弦高誤差的影響，並且弦高誤差應控制在一個基本 長度單位（BLU)以內。 參數式曲線的參數迭代法硏究上，在Bedi(S.Bedi),Ali (I.Ali),和QuaiUN.Quan)所使用的方法中，爲一常數値， 此時稱該迭代方式爲均勻（uniform)的參數迭代。此種方法 雖然簡單，但是參數的等間距選取並不能保證曲線位置命 令弦高誤差的邊界範圍與曲線速率的變化，因爲參數與曲 線點間的關係並非爲一致對應》Chou和Yang根據切削刀 具路徑與運動系統的動態特性提出精確的參數式曲線的參 數迭代方式，以同時控制系統的位置、速率與加速率，更 精密的原因是Chou和Yang的方法加入了參數與時間間的 動態關係考量· Kim討論參數化曲線中參數加減速的參數 迭代方式，經由參數加減速的方式以獲得具高精密度的位 置與順滑的速率加減速結果，但是由於參數與曲線間的關 係並非一致（uniform)對應，因此在速率上可能未有如預期 的加減速行爲。 由於插値器所產生的位置命令與曲線速率精度均會影 餐加工工件的品質；不精確的位置命令會造成精度不夠的 加工結果而曲線速率誤差會造成工時的延長與速率上的波Yang (DCHYang) proposed a generalized parameter iteration rule based on the iterative method of feed rate control. The computer numerically controlled curve path rate control device of the present invention 'includes: computer for CAD' work The auxiliary design work includes making the parameterized curve format and segmented curve: The computer numerical control (CNC) mechanism 'includes: the parameterized curve inserter' is receiving the parameters interpreted by the computer ---- Γ · I. 1-- ------- Shi κ _ _ _ f _ _ Ding {Please read the notes on the back before filling out this page) Printed on the paper by the Consumers' Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs This paper applies Chinese National Standards (CNS) 4 Old cases (21〇 &gt; &lt; 2 [) 7 credits) 3 15685 Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs A7 Β7 V. Description of the invention (4) The curve information is generated by parameterizing the points of the curve The method generates continuous interpolation points: the controller receives the continuous interpolation points generated by the parameterized curve interpolator and sends control processing signals; the tool receives the control processing signals sent by the controller, and the center Ϊ * along to parameterize Curve movement; and a human-machine interface device, which allows human-computer communication between the operator and the parameterized curve inserter: wherein the parameterized curve inserter can perform a constant-rate interpolation operation mode on the parameterized curve and Acceleration / deceleration insertion operation mode. The parameterized curve inserter device of the computer numerical control curve path rate control of the present invention includes: a constant rate inserter, which keeps the parameterized curve path at a fixed rate during the implementation of the interpolation; an acceleration / deceleration inserter, which makes the The machining curve path can obtain smoother acceleration and deceleration motion. Brief Description of the Drawings Fig. 1 is a block diagram of a processing system for a parameterized curve according to an embodiment of the present invention. Figure 2 is a schematic diagram of the tool moving in a straight line between the two interpolation points, and the inserter generates a position command error. Figure 3 is the compensation amount ~ In the formula, the vector 〇, the curve differential vector and the parameters M, ', 1 /, Geometric relationship between μ. Fig. 4 is the case where the same real number 値 or conjugate imaginary number 値 compensation amount is formed. Β Fig. 5 is the bow curve command path applied in this embodiment. The paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) 4 15685 11. 1-I Binding--(Please read the notes on the back before filling out this page) 4. Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs 4 ^ 408 A- 1Γ 5. Description of Invention (5) Section 6 The picture shows the first-order approximation (1 st 〇rderappr ο X imati ο η) interpolation rate command result curve rate change situation. Figure 7 shows the variation of the rate of the 2nd order approximation interpolation rate command result curve. Fig. 8 is a graph showing a situation in which the rate command curve of the constant rate operation mode is inserted in the present embodiment. Figure 9 shows the results of parameter compensation and calculation in the constant rate operation mode. Figure 10 is a curve approximation of the 1st order change in the rate difference of the quadratic curve acceleration / deceleration method. Fig. 11 is the 2nd order approximation of the rate difference of the quadratic curve acceleration and deceleration method. Fig. 12 is the curve of the rate difference and constant rate operation mode of the quadratic curve acceleration and deceleration method. Description of drawing number 1 computer (CAD) 2 computer numerical control (CNC) mechanism 3 parameterized curve inserter 4 human-machine interface device 5 controller 6 tool 7 parameter curve information 8 workpiece contour curve 9 tool movement path (please read the back first For the matters needing attention, please fill in (the clever page) i—1 I-----LI JL—. ^ 衣 &quot; .— I —4— j -----. ......... I --I-· '.-I -II1 1ΓΙ ^^ 1 --- V-- This paper size applies to Chinese National Standards (CNS) Λ4 叱 格 U 丨 0X2V? Official exchange) 5 15685 Employees of the Central Standards Bureau of the Ministry of Economic Affairs 4U408 printed by a consumer cooperative Η '—______ Five' Description of the invention (6) 10 Radial error 11 Chord height error 12 Interpolation point Detailed description of the preferred embodiment-Generally, the curve generated by the CAD system is a parametric curve representation, At the same time, the CAD system also provides the related parameter data transmission format of the parametric curve. Therefore, in the design of the CAD / CNC system, the parameter information of the parametric curve can be directly used as the processing information transmission between the CAD / CNC system and the CNC interpolation. The processing system for the parametric curve discussed in the present invention is shown in Fig. 1. In the figure, 1 is a computer, which is used for auxiliary design (CAD), including parametric curve format and segmented curve, and 2 is computer numerical control (CNC). Mechanism, in which the parametric curve inserter 3 receives the parametric curve information 7 interpreted by the computer 1 and generates continuous interpolation points in the parametric curve point generation mode and sends it to the controller 5 so that the center of the tool 6 is along Parametric curve movement, 4 of which are human-machine interface devices, allowing the operator to communicate with the CNC. Common parameterized curves are: Bezier curve, B Spline, and NURBS (non-equidistant B cloud line); the present invention uses NURBS parameterized curves. The process of implementing the parameterized curve inserter 3 is mainly to calculate the parameterized curve points. Generally, the calculation rule of higher curve position and rate accuracy requires more complicated calculation methods and larger calculation amount, which is disadvantageous in the environment where instant commands are generated. Therefore, the choice and design of the calculation method must consider the trade-off between the accuracy of the curve and the calculation time. The most commonly used calculation format is the following iterative method of parameters: ^ «, + Δ (μ,) (Please read the precautions of the back, 6 first. (Fill in this page again) —- The bound paper. The Zhang scale is applicable to the Chinese National Standard ([?] Sixty-four Regulations (210 乂 297 public garbage) 6 156 «5 411438 A 'ΙΓ 5. Explanation of the Invention (7) Ministry of Economic Affairs Printed by the Consumer Standards Cooperative of the Central Bureau of Standards (please read the precautions on the back before filling out this page), where "indicates the parameters of the current sequence, u, + l indicates the parameters of the next sequence, and Δ (ί〇 indicates the The amount of time-related calculations. Under the parameterized curve, Mi represents the parameters of the curve, so this parameter must be substituted into the mathematical expression of the curve to obtain the point in time. In the design of the parameterized curve inserter, for arbitrary The application of the parametric curve mathematical model, because the relationship between the parameters in the parametric curve and the curve or geometric path is not obvious, it is not easy to perform the inverse operation, that is, it is not easy to infer the corresponding parameters from the known curve points, because It is difficult to have good control of the curve rate in the iterative method of the parameter. "In actual processing, the parametric curve inserter will cause the error of the curve rate of the interpolation result due to the inappropriate parameter iteration rule. The curve rate error refers to the phase. The difference between the movement rate between adjacent interpolation points and the feed rate setting of the inserter. When the error of the curve rate is greater, it means that the movement between interpolation points cannot be operated as the feed rate, which often results in excessive positions. Errors, excessively long machining time, and poorly machined workpiece surfaces. Therefore, in the design of the parametric curve inserter, the parameter iterative method must accurately control the curve rate to reduce the error. In addition to the curve rate error, the tool movement caused by the inserter The interpolation point of the time, and the tool moves in a straight line between the two interpolation points, so the position command error generated by the inserter can generally include: radial error and chord height error. The relationship between the direction error, chord height error and the curve can be shown in Figure 2, where 8 is the workpiece contour curve * 9 is the tool movement path, and 10 is the radial direction U is the chord height error, 12 is the interpolation point β, the radial error is the shortest distance between the position point and the curve, and the chord height error is the maximum distance between the secant function and the cutting arc formed by the two position points. This paper scale is applicable to Chinese National Standards (CNS) M specifications (210x) 7 15685 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs 4: V. Description of the invention (*) The design of the parametric curve inserter generally causes radial The cause of the error is the rounding error of the floating-point number, and the cause of the chord height error is caused by the incorrect feed rate. Because in the representation of the parameterized curve, the round-cut error can be calculated by a precision computer It is reduced, and the string height error is often much larger than the radial error. Therefore, in the design of the inserter, the present invention only considers the influence of the string height error, and the string height error should be controlled within a basic length unit (BLU). The parametric iterative method of parametric curves is researched. In the methods used by Bedi (S. Bedi), Ali (I. Ali), and QuaiUN. Quan), it is a constant 値. At this time, the iteration method is called uniform. (Uniform) parameter iteration. Although this method is simple, the equidistant selection of parameters does not guarantee the change of the boundary range of the command position and the variation of the curve rate of the command string height because the relationship between the parameters and the curve points is not consistent. Chou and Yang according to the cutting tool path A precise parametric iterative method of the parametric curve is proposed with the dynamic characteristics of the motion system to control the system's position, rate, and acceleration simultaneously. The more precise reason is that Chou and Yang's method adds a dynamic relationship between parameters and time. Kim discusses the parameter iterative method of parameter acceleration and deceleration in the parameterized curve. The method of parameter acceleration and deceleration is used to obtain high-precision position and smooth rate acceleration and deceleration results, but the relationship between the parameters and the curve is not uniform Correspondingly, there may not be the expected acceleration and deceleration behavior in speed. Because the position command and curve rate accuracy produced by the inserter will affect the quality of the processed workpiece; inaccurate position commands will cause insufficient precision processing results, and the curve rate error will cause the extension of the working hours and the speed wave.

本紙張尺度適用中國國家標準（CNS ) Λ4ΐ.ί格（210 X 297公兑） 8 1368S (請先聞讀背面之注意事項再填寫本頁) 裝-------------•訂------i”---»--- 411408This paper size applies to Chinese National Standards (CNS) Λ4ΐ.ί grid (210 X 297 Kg) 8 1368S (please read the precautions on the back before filling this page) Packing ------------ -• Order ------ i ”---» --- 411408

經濟部中央標準局員工消费合作社印製 五、發明説明（9 ) 動會造成震動，影響加工工件的表面精度。因此在實現任 何的參數化曲線的過程中，如何設計參數的迭代過程產生 位置與曲線速率精度都能符合設計要求，亦即達成低位置 命令弦高誤差與低曲線速率誤差，是參數化曲線插値器實 現的重要關鍵》 在參數迭代的方法上，雖然Chou和Yang所提出的參 數迭代方法因爲具有參數與時間間的動態關係而使得曲線 速率變動的情況獲得改善，但是改善的幅度仍因泰勒展開 式的近似程度而受限制，同時也無法準確的控制曲線速 率。因此動機，本發明以Chou和Yang所提出的一般化參 數迭代法則爲基礎提出進給速率控制的參數迭代方式以準 確的控制插値器所產生的曲線速率。具速率控制的參數迭 代方法是在Chou和Yang原始的一階近似參數迭代法中加 入補正量，由於補正量考量參數與曲線速率間的近似關 係，因此可大幅降低曲線速率的波動。基於進給速率的控 制，參數式曲線插値器的內插點產生可依加工條件的要求 以定速率操作模式與加減速操作模式操作。定速率操作模 式是使插値器在曲線產生過程中維持相同的曲線速率以減 少因速率變動所引起的加工誤差。在加減速操作模式中， 由於速率控制的參數迭代方式可以獲得高精度的曲線速率 控制，因此在加減速的設計上可針對進給速率參數執行加 減速使曲線速率以相同的加減速方式進行並獲得真正的加 減速率結果，並且也可完全得知加減速時的速率變化》 (A)參數曲線公式（Parametric Curve Formulation)之導得： - - - -I - 1 - _ . _ ί ai^l—^ί —l^^i It—— V life ·ϋίι( ^^^^1 I (請先閱讀背面之注意事項再填艿本頁) 本紙張尺度適用中國國家標準（CNS ) ( 210X297公茄} 9 15685 4114G8 A7 B7 五、發明説明（ 10 在參數迭代方法的推導過程中，假定e(a)爲參數式曲線 點的表示式，其中《爲參數表示，並且爲時間ί的函數，即：Μ^)。定義 w(i.) = w, ； u(ti+x) = Μί+1則經由泰勒展開式可知： ’ du 珥+ — dt f \ \ d* uPrinted by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs. 5. Description of the invention (9) Motion will cause vibration and affect the surface accuracy of the processed workpiece. Therefore, in the process of implementing any parametric curve, how to design the iterative process of the parameters to produce position and curve rate accuracy can meet the design requirements, that is, to achieve a low position command string high error and low curve rate error, which is a parametric curve interpolation. Important key to implement implements "In the method of parametric iteration, although the parametric iteration method proposed by Chou and Yang has improved the curve rate variation situation due to the dynamic relationship between parameters and time, the improvement is still due to Taylor The degree of approximation of the expansion is limited, and the curve rate cannot be accurately controlled. For this reason, the present invention proposes a parameter iterative method of feed rate control based on the generalized parameter iteration rule proposed by Chou and Yang to accurately control the curve rate generated by the inserter. The iterative method with rate control is to add the correction amount to the original first-order approximate parameter iteration method of Chou and Yang. Because the correction amount considers the approximate relationship between the parameter and the curve rate, it can greatly reduce the fluctuation of the curve rate. Based on the control of the feed rate, the interpolation point generation of the parametric curve inserter can be operated in constant rate operation mode and acceleration / deceleration operation mode according to the requirements of the processing conditions. The fixed-rate operation mode is to maintain the same curve rate during the curve generation process of the inserter to reduce the processing error caused by the rate change. In the acceleration / deceleration operation mode, because the parameter iteration method of the rate control can obtain high-precision curve rate control, the acceleration / deceleration can be performed on the feed rate parameter in the design of the acceleration / deceleration so that the curve rate is performed in the same acceleration / deceleration mode. Get the real acceleration and deceleration rate results, and you can also fully understand the rate change during acceleration and deceleration "(A) The parametric curve formula (Parametric Curve Formulation) is derived:----I-1-_. _ Ί ai ^ l — ^ Ί —l ^^ i It—— V life · ϋίι (^^^^ 1 I (Please read the notes on the back before filling out this page) The paper size applies to the Chinese National Standard (CNS) (210X297 公 蛋} 9 15685 4114G8 A7 B7 V. Description of the invention (10 In the derivation of the parametric iteration method, it is assumed that e (a) is the expression of parametric curve points, where "is the parameter representation and is a function of time, ie, Μ ^). The definition w (i.) = W,; u (ti + x) = Μί + 1 can be known from Taylor's expansion: 'du 珥 + — dt f \ \ d * u

+H.O.T U) 由於曲線速率可表爲 &lt;C(w) ώ 碎)| du du {請先閱讀背面之注意事項再填寫本頁} 所以 dC(u) du u=ui (2) 對式（2)再進行一次微分可得 經濟部中央標隼局員工消費合作社印製 d2u _ -1 dt1 &lt;=(, ||&lt;λ^(μ) 2 1 ^ %). f d \ du dt 經由簡單的微分演算可知 f d 4)f \ ( d dC(u) V du f V ㈣一 ;u=h, du dt du dt du (3) (4) 將式（4)代入式（3)中可得， 本，氏張尺度適用中國國家標準（CNS &gt; A4規格（210 X 297公釐） 10 156S5 411408 A7 B7 五、發明説明（u ) f d 1斗)f V2(ut) l 1 du [ U=U} d2u dt1 (=t\ dC(u) 3 du du U^Ui (5) 同樣經由簡單的微分演算可知 f d dC(u) V du / u=ut dC(u) d2C(u) du du2 du+ HOT U) Since the curve rate can be expressed as &lt; C (w) FREE) | du du {Please read the notes on the back before filling this page} So dC (u) du u = ui (2) Contrast ( 2) Differentiate again to get the printed d2u _ -1 dt1 &lt; = (, || &lt; λ ^ (μ) 2 1 ^%). Fd \ du dt Differential calculus shows that fd 4) f \ (d dC (u) V du f V ㈣ 一; u = h, du dt du dt du (3) (4) Substituting equation (4) into equation (3) gives , The Zhang scale is applicable to the Chinese national standard (CNS &gt; A4 specification (210 X 297 mm) 10 156S5 411408 A7 B7 V. Description of the invention (u) fd 1 bucket) f V2 (ut) l 1 du [U = U} d2u dt1 (= t \ dC (u) 3 du du U ^ Ui (5) It is also known through simple differential calculations that fd dC (u) V du / u = ut dC (u) d2C (u) du du2 du

HI (6) 將式（6)代入式（5)中可得參數《的二次微分式爲 X n du du2 1 d2u w i=i, dC(u) 4 du (7) M JI- Γ . — 士'衣 ™I - ^&quot;&quot;&quot; 訂 (請先鬩讀背面之注意事項再填寫本頁) 經濟部中央標準局員工消費合作社印装 若曲線點產生間隔爲一個取樣時間*則 ^,&gt;1 ~ti = Z 將式（2)與（7)代入式（1)中並省略高次項，則可分別獲得一 次與二次近似的參數迭代法則如下： 一次近似的參數迭代法則： V(u)Ts - % dC(u) du U=Mi (8) 二次近似的參數迭代法則：HI (6) Substituting the formula (6) into the formula (5), the quadratic differential of the parameter "is X n du du2 1 d2u wi = i, dC (u) 4 du (7) M JI- Γ. — '' 衣 ™ I-^ &quot; &quot; &quot; Order (Please read the precautions on the back before filling out this page) Printed by the Consumer Cooperatives of the Central Standards Bureau, Ministry of Economic Affairs, if the curve point generation interval is a sampling time * then ^ , &gt; 1 ~ ti = Z Substituting equations (2) and (7) into equation (1) and omitting higher-order terms, the parameter iteration rules for the first and second approximations can be obtained as follows: The parameter iteration rules for the first approximation: V (u) Ts-% dC (u) du U = Mi (8) Parameter iteration rule for quadratic approximation:

Wi+i = «( + v(uty z Κι1 dC(u) td2C{uf du du2 . II碎) II ^ u=u IK(«) du 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） (9) 15685 411408 A7 B7 五、發明説明（ 12 其中，由於期望曲線速率爲進給速率設定値，因此在參數 式曲線插値器的實現上可以指定爲參數M = 時的進給速 率設定値》而在平面座標系統中，由於Wi + i = «(+ v (uty z Κι1 dC (u) td2C (uf du du2. II broken) II ^ u = u IK («) du This paper size applies to the Chinese National Standard (CNS) A4 specification (210X297) (9) 15685 411408 A7 B7 V. Description of the invention (12 Among them, since the expected curve rate is the feed rate setting 値, the implementation of the parametric curve inserter can be specified as the feed rate when the parameter M = Set 値》 and in the plane coordinate system, because

dC{u) du .吵)_ d^C^u) du du2 dCy(u) ’ du2 d2Cy{u) .du 一 L du2 J 所以 dC(u) du fdCx(u) 、du .dC (u) du. noisy) _ d ^ C ^ u) du du2 dCy (u) ’du2 d2Cy (u) .du a L du2 J so dC (u) du fdCx (u), du.

V du du2 J du dCx{u) d2Cx(u) ； dCy(u) d2Cy(u)' du du1 du du1 , (請先閲讀背面之注意事項再填寫本頁) 經濟部中央標準局負工消費合作社印裝 在應用上，式（9)的二次近似參數迭代法則相對於式（8)的 一次近似參數迭代法則具有較小的曲線速率誤差。 (B)具速率控制之參數迭代法則設計： 由上述中可知，式（8)與式（9)所表示的一次與二次近似 參數迭代法則是由曲線參數對時間的泰勒展開式中簡化高 階次項獲得，但在應用上，由於未知省略項對曲線的影響， 曲線速率精度往往受到限制。有鑑於此’本發明提出參數 補償的方法，經由補償量與曲線間的相關性獲得更高精度 的曲線速率控制&quot;設計的方法是在式（8)所表示的一次近似 參數迭代法中加入伞）的補償量’以修正參數的迭代，由 於是經由一次近似參數送代法進行補償，因此可以省去曲 線二次微分資訊的計算。經補償的參數迭代式爲： »i+l = Mi+1 本紙張尺度適用中國國家標率（CNS ) A4規格（210X297公釐} 15685 A7 B7 五、發明説明（ 其中V du du2 J du dCx {u) d2Cx (u); dCy (u) d2Cy (u) 'du du1 du du1, (Please read the notes on the back before filling out this page) The Central Standards Bureau of the Ministry of Economic Affairs, Consumer Cooperatives Printed in application, the iterative rule of the second approximation parameter of the formula (9) has a smaller curve rate error than the iterative rule of the first approximation parameter of the formula (8). (B) Parametric iteration rule design with rate control: As can be seen from the above, the first and second approximation parameter iteration rules represented by equations (8) and (9) are simplified by the higher order in the Taylor expansion of the curve parameters versus time. The secondary term is obtained, but in application, the curve rate accuracy is often limited due to the influence of unknown omitted terms on the curve. In view of this, the present invention proposes a method of parameter compensation, and obtains a more accurate curve rate control through the correlation between the compensation amount and the curve. The design method is to add it to an approximate parameter iterative method represented by equation (8) Umbrella) The compensation amount 'is used to iteratively modify the parameters. Since it is compensated through the first-order approximate parameter substitution method, the calculation of the curve's secondary differential information can be omitted. The compensated parameter iteration formula is: »i + l = Mi + 1 This paper size is applicable to China National Standard (CNS) A4 specification (210X297 mm) 15685 A7 B7 V. Description of the invention (where

Mi+i = Ui v(utyr, \\dC(u) du 爲求得參數迭代的補償量伞），本發明使用位置對參數 的一次泰勒展開式，並經由進給速率與曲線速率的要求求 解補償量。定義參數曲線表式爲，其中，c(«) cx(u) Cy{u\ G⑻與可分別表示參數a時的J軸與y軸的曲線位置 由於， «i+ι =«ί+ι +4Μί) 經由一次泰勒展開式的近似，Mi + i = Ui v (utyr, \\ dC (u) du is used to obtain the parametric iteration compensation parameter umbrella). The present invention uses a Taylor expansion of the position to the parameter and solves it through the requirements of the feed rate and the curve rate. The amount of compensation. The parameter curve table is defined as, where c («) cx (u) Cy {u \ G⑻ and the curve position of the J axis and the y axis when the parameter a can be expressed respectively, because« i + ι = «ί + ι + 4Μί) via a Taylor expansion approximation,

Cx(ui+l) = Cx(u'i+l) + dCx{\ Μί+1 du duCx (ui + l) = Cx (u'i + l) + dCx {\ Μί + 1 du du

Au&gt;) ----^_丨 — — — — ^1----iT------泉- (請先閲讀背面之注意事項再填寫本頁) 經濟部中央標準局貝工消費合作杜印製 爲使路徑運動時的速率能夠符合進給速率設定 値，，因此令 亦:如丨)-C办)]2 + [C&gt;,+1) - c&gt;,)f 〒! — 則可得如下之二次函式表示式Au &gt;) ---- ^ _ 丨 — — — — ^ 1 ---- iT ------ Quan-(Please read the precautions on the back before filling this page) Cooperative Du printing is to make the speed of the path in accordance with the feed rate setting 値, so let also: such as 丨) -C Office)] 2 + [C &gt;, + 1)-c &gt;,) f 〒! — You can get the following quadratic function expression

Us2 +Z-s + W = 0 其中， U = x\uM)\Y{^x)2 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） 13 15685 411408 ]Γ du 五、發明説明（14 ) Z = 2\DXX'{uMYDYr{^ W = DX1+DY2-i^(ui)T)1Us2 + Zs + W = 0 where U = x \ uM) \ Y {^ x) 2 The paper size is applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) 13 15685 411408] Γ du 5. Description of the invention ( 14) Z = 2 \ DXX '(uMYDYr {^ W = DX1 + DY2-i ^ (ui) T) 1

Dx=a(»;+i)-cx(«j) DY=Cy(u；^)-Cy^) ruj 並可求解補償量 &lt;叫）爲 ^1,2 («,)= \ρχ·χ {um)+dy-y (^t)]±y .r (»,„) - Dr- x’卜)-asr.r» /(«irt) +Ρ’(Η;+1)2 (10) 在式（10)中’由於補償量爲二次方程式的根値，因此必 須討論其根値的屬性並選擇適當的根値作爲速率控制參數 迭代法的補償値。定義 (請先閱讀背面之注意事項再填窍本頁) 經濟部中央標準局員工消費合作社印製Dx = a (»; + i) -cx (« j) DY = Cy (u; ^)-Cy ^) ruj and the compensation amount &lt; called) is ^ 1,2 («,) = \ ρχ · χ (um) + dy-y (^ t)] ± y .r (»,„)-Dr- x '卜) -asr.r »/ (« irt) + Ρ' (Η; +1) 2 ( 10) In formula (10), 'the compensation amount is the root of the quadratic equation, so the properties of the root must be discussed and an appropriate root should be selected as the compensation of the rate control parameter iteration method. Definition (please read the back first) Note: Please fill in this page again.) Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs

DD

CC

DX DY χ'(^} ^'(w；+1) 則式（10)可以改寫爲-(D.c'Ji./ilc'f -(v^yzf Tc- x&quot;dDX DY χ '(^) ^' (w; +1) The formula (10) can be rewritten as-(D.c'Ji. / Ilc'f-(v ^ yzf Tc- x &quot; d

PI (11) 本紙張尺度適用中國國家標準（CNS) A^uTTIioTT^r 14 15685 4114ϋ8 】Γ 五、發明説明（15 ) 其中，向量D、曲線微分向量亡與參數、《i+1間的幾何 關係可由第3圖表示，圖中Θ爲向量乃與曲線微分向量亡間 的夾角。在式（Π)中，由於 \CxD ；\\C'\\ -TslPI (11) This paper scale applies Chinese National Standard (CNS) A ^ uTTIioTT ^ r 14 15685 4114ϋ8] Γ 5. Description of the invention (15) Among them, the vector D, the curve differential vector and the parameters, "the geometry between i + 1 The relationship can be represented in Figure 3, where Θ is the vector and the angle between the vector and the curve's differential vector. In formula (Π), since \ CxD; \\ C '\\ -Tsl

Ic'lf-r,2 c z2 並且p|f&gt;〇，亡&gt;0 所以{P.f.^、.o2K}與Ic'lf-r, 2 c z2 and p | f &gt; 〇, annihilation &gt; 0 so {P.f. ^, .o2K} and

I 其中 方。 r2W- V2{u,)~ L·3 FI ^ d' ΤΛ ύη2Θ * sin2 Θ 同號 爲參數‘時曲線插値器產生的曲線速率平 y2M- sin2 θ 同號，因此補償 (請先閲讀背面之注意事項再瑱寫本頁 ^衣---- |，訂--- 經濟部中央標隼局員工消費合作社印製 量〜Μ會有下列三種情形： ⑴當 値 ζ sin2 Θ 時，補償量如Μ爲不同的實數 2 — ⑵當 ^ sin2 θ 値 時，補償量化(《,)爲相同的實數 本紙張尺度適用中國困家標隼（CN_S ) ,\4圯梠（2 Η) X 公垃）Ifi 15685 41ΗυΒ ΙΓ 五、發明説明（16 •sin2 ΘI which side. r2W- V2 {u,) ~ L · 3 FI ^ d 'ΤΛ ύη2Θ * sin2 Θ The curve rate produced by the curve inserter when the same number is the parameter' y2M- sin2 θ has the same number, so compensation (please read the first Note: Please write this page again ^ --------, order --- the amount printed by the staff consumer cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs will have the following three situations: ⑴ When 値 ζ sin2 Θ, the compensation amount is as follows: Μ is a different real number 2 — ⑵ When ^ sin2 θ ，, the compensation quantization (",) is the same real number. The paper scale is applicable to the Chinese family standard 隼 (CN_S), \ 4 圯 梠 (2 Η) X public trash) Ifi 15685 41ΗυΒ ΙΓ V. Description of the invention (16 • sin2 Θ

(3)當 値。 經過比較曲線插値器產生的曲線速率 D 與夾角0可知&lt; 厂2W- ts 時，補償里2 (“f)爲共輒虛數 進給琿率rh) sin2 θ 的正負號取決於向量Ζ)與曲 線微分向量Θ間的夾角Θ»因此可能形成相同實數値或共軛 虛數値補償量〜(Μ)的情況如第4圖所示。當C落在a，b附 近時，由於向量乃與曲線微分向量f近乎垂直，因此sinWsl 亦比較可能發生。換言之，相同實數 / β Ϋ _ 同時 V\u,)^ \ Ts •sin2 θ } 値或共軛虛數値補償量較可能發生在曲線曲率較大的點附 近。但在實際的應用上，相同實數値或共軛虛數値補償量 並不會發生，因爲基於位置命令精確度的考量，曲線參數 卜間並不允許有大曲率的曲線變化，同時在變化較爲 平緩的曲線應用上也不會發生相同實數値或共軛虛數値補 償量的情形。因此，補償量化〇/〇在實際的應用上一般爲不 同的實數値。由式（11)， (請先閲讀背面之注意事項再填窍本頁) 結濟部中央標华局員工消资合作杜印製 c\ 土 C' c b(3) When 値. After comparing the curve rate D and the included angle 0 generated by the curve inserter, it can be known that when the factory 2W-ts, the compensation 2 ("f) is the common imaginary feed rate rh) sin2 θ depends on the vector sign (Z) The angle Θ »with the curve differential vector Θ may therefore form the same real number 値 or conjugate imaginary number 値 compensation amount ~ (Μ) as shown in Figure 4. When C falls near a, b, because the vector is related to The curve differential vector f is almost vertical, so sinWsl is more likely to occur. In other words, the same real number / β Ϋ _ and V \ u,) ^ \ Ts • sin2 θ} 値 or conjugate imaginary number 値 compensation is more likely to occur when the curve curvature is more Near large points. However, in practical applications, the same real number 値 or conjugate imaginary number 値 compensation amount will not occur, because based on the accuracy of the position command, the curve parameter B is not allowed to change the curve with large curvature. At the same time, in the application of a curve with a relatively smooth change, the same real number 値 or conjugate imaginary number 値 compensation amount will not occur. Therefore, the compensation quantization 〇 / 〇 is generally a different real number 实际 in practical applications. By formula (11 ), (Please read the back first Please fill in this page again for further information) Printed by the Central Bureau of Standardization of the Ministry of Finance and Economic Cooperation of Employees c \ 土 C 'c b

Fll sin2 ΘFll sin2 Θ

本紙張尺度適用中國國家標準（CNS ) Λ4说格（：M〇_X 16 156u5 4ii4G8 五、發明説明（17 ) cos (m; ) T^f - Ipl + jD|j cos2 Θ 令 (厂w‘從 μ 當《,+1採用一階近似參數迭代方式時，# —般爲一相對小 値，因此經由泰勒展開式的近似可得知，μ 2_|p|pw _ 2.1得 cos θ IP' 即仏(%_)有一負補償値與在零點附近的補償値，並且該負補 償値遠離零點。由於補償値在此的目的是補償參數〜在曲 線速率上的不足，因此選擇在零點附近的補償値以獲得較 爲可靠的參數迭代結果，即 -[ΖΜΓ.(‘)遺·+7 ^,)^-(^,.)-7:)2 -[z)r-x'(a；+1)-DX-r'(«；+1] r(‘丨)2+r(‘)3j ‘ ^ ^^ ^~ ,ΜΊ ： —裝， _ ^ ^ .訂------^ (請先閱讀背面之注意事項再填寫本頁) 經濟部中央標準局貝工消費合作社印狀 在本節所討論的方法中，由於是基於插値曲線速率的不正 確而加入補償量，因此可獲得較高的曲線速率精確度。 在上述具速率控制的參數迭代法則中，由於可以精確 控制產生曲線的曲線速率，因此可應用於參數化曲線插値 器的設計，並且可依加工條件的不同而有不同的操作模 式。一般依加工條件的不同可將插値器的操作模式分爲U) 定速率操作模式與（2)加減速操作模式》定速率操作模式是 指在參數式曲線實現的過程中，插値器能產生固定曲線速 率的內插點。加減速操作模式則可應用在曲線運動開始與 本紙ft尺度適用中國國家標準（CNS ) Λ4ί·ί格（210X；；y7A尨 17 15685 411408 A7 B7 五、發明説明（ 18 終端的插値過程中以獲得較爲平緩的曲線速率變化。 (C)應用本實施例進給速率控制參數迭代法設計插値器，施 行加工例子之比較： (C.1)應用例 在系統的設定上，本發明所使用的系統是以C語言編 寫軟體插値程式並於個人電腦具Pentium 200MHz CPU的 系統上執行。在參數曲線的設定上，本發明採用2級數（2 degree)的NURBS參數化曲線模擬蝴蝶結曲線的命令路徑 如第5圖所示。其相關的NURBS參數設定爲： 控制點依序爲： 150 150 一 150 0 150 » 150 0 ·， -150 150 150 2.權重向量爲：F = [l 0_85 0.85 1 0.85 0.85 1] 1113,,· .節點向量爲：ί/: 0 0 0 &lt;請先閱讀背面之注意事項再填寫本頁) 經濟部中央標準局—工消費合作社印製 4 2 2 4 並且以下的參數迭代過程中，相關的參數設定爲： 1 .取樣時間：ί =0.01 sec。 2.進給速率：/^12^=2001^。 (C.2)定速率操作模式： 由於具速率控制之參數式曲線插値器設計可以精確的 控制插値結果的曲線速率，因此在曲線插値過程中可藉由 固定進給速率的給定以獲得固定曲線速率的插値結果。 參數式曲線插値器定速率操作模式模擬結果： 本紙張尺度適用中國國家標準（CNS ) A4規格（210 X 297公釐} 18 ί5685 4114G8 A7 ___B7 五、發明説明（） 19 在此將比較由不同參數迭代法設計之參數式曲線插値 器操作模式，均勻（uniform), —階近似（1st order approximation),二階近似（2nd order approximation),定速率 (constant feedra+te)間的插値結果曲線速率變動情形。 不同插値器操作模式的模擬插値曲線速率結果洳第6、 7、8圖所示|而定速率操作模式中參數補償値計算結果如 第9圖所示。 插値模擬結果總結如表1所示： 表1 : \測i 速度誤 差之均 平方 最大速 度波動 比 最大弦 尚誤差 以 80MHz CPU計 算時間 以 200MHz CPU計 算時間 模式\ Wee)2 mm //sec 只sec 均勻 5.483 xlO5 6.0797 0.1388 11 4 一階近似 2.7078 0.01373 0.01739 27 10 二階近似 0.01079 0,00942 0.01738 60 19 定速率 3.9642 xlG&quot;* 2.4909 xlO-6 0.01737 77 26 經濟部中央標準局員工消費合作社印製 (請先閲讀背面之注意事項再填寫本頁) 其中， 1. 曲線速率誤差的量測是指插値器所產生的曲線速率 與設計之進給速率間的差値。 2. 曲線速率變動率的計算公式爲 7, ，表示每一取樣時間的曲線速率變動率 K表示每一取樣時間插値器產生的曲線速率 本紙張尺度適用中國國家標準（CNS &gt; A4規格（210X297公釐） 19 15685 4U408 A7 _B7 五、發明説明（） 20 。爲進給速率設定 3.均勻Uniform)參數迭代方式時的參數間距爲取樣時 間大小。 經濟部中央標準局貞工消費合作社印製 (請先閲讀背面之注意事項再填寫本頁) 在模擬結果中明顯可知，由於速率控制的參數迭代方 式考慮曲線速率與補償値間的關係，定速率操作模式的插 値方式具有最小的曲線速率誤差與速率變動率。同時由於 是對1st階近似的參數迭代方式作楠償，因此可知經補償 後的1st階近似的速率精度獲得提昇，同時超越2nd階近 似的參數迭代所提供的速率精度•而均勻參數操作模式的 插値方式具有最大的曲線速率誤差與速率變動率，原因是 參數與曲線間並非是均勻分佈。在內插點間命令弦高誤差 的比較上，1st階近似，2nd階近似與定速率操作模式的命 令弦高誤差相差不大，原因是在本模擬所使用的蝴蝶結曲 線中曲線速率變化對內插點間命令弦高誤差的影響不大， 但是均勻操作模式命令弦高誤差明顯比其他的參數迭代方 式增加許多*而在每一內插點的計算時間比較上，由於均 与參數迭代方式產生內插點所需的時間僅是曲線內插點的 計算時間因此會最少，而在1st階近似與2nd階近似的比 較上，由於2nd階近似需要曲線二次辑分與高階的計算， 因此計算時間會比1st階近似多，而速率控制的參數迭代 方式雖然是以1st階近似爲基礎也不需進行曲線的二次微 分計算，但是需要計算額外一曲線內插點以及一些補償値 的計算過程，因此計算量會比2nd階近似稍高》雖然具速 率控制的參數迭代方式需要較其他參數迭代方式高出一些 本紙張尺度適用中國國家樣準（CNS } Α4規格（210X297公釐） 20 15685 411408 A7 B7 五、發明説明（） 21 的計算量，但是插値器的曲線速率精度卻比其他參數迭代 方式要高出許多，基於此高精度的曲線速率控制，控制器 或工件設計工程師可掌握更明確的加工過程：同時在與取 樣時間的比較上，定速率操作模式內插點計算時間所佔的 比例極小，因此計算時間在即時實現過程中爲可接受'總 結在曲線速率的變化程度比較上，參數式曲線插値器以定 速率操作模式具有最小的曲線速率誤差，其次是2nd瞎近 似的操作模式與1st階近似的操作模式，均勻參數操作模 式具有最大的曲線速率誤差。 (C.3)加減速操作模式： 經濟部中央標準局員工消費合作社印策 傳統的加減速方式是將位置命令經過低通濾波器以產 生較爲平滑的命令輸入。但是此法會使具有較大變化的命 令路徑產生徑向與弦高誤差，如加工曲線的起點與終點附 近。有鑑於此，Kim提出使用參數的加減速方式以達到參 數化曲線加減速的目的，同時因爲是對參數進行加減速的 操作，因此內插點具有較小的徑肉誤差。雖然Kim所提出 的參數加減速方式可以使內插點的產生具有加減速的功 能，但是在某些曲線上並不能真正達到速率加減速的目 的，其原因是參數空間與曲線並非是均勻對應。爲獲得曲 線真正的加減速以適當的控制速率在曲線運動中的變化， 本發明於此提出進給速率參數加減速應用的參數化曲線插 値器的加減速操作模式。 由於在具速率控制的參數迭代過程中’工件設計者可 以精確掌握速率的變化情形，因此可以用以作爲進給速率 156S5 (請先閲讀背面之注意事項再填寫本頁} 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） 411408 A7 __B7_ 五、發明説明（） 22 參數加減速的實現，並可精確掌握加減速時的加速率舆減 速率變化。具速率控制的參數迭代方式是爲控制參數的迭 代使插値器的曲線速率能符合進給速率的設定値^(*)，因 此在加減速的設計上可以將進給速率參數^(«0進行加減速 的操作。爾後再將經過加減速計算的進給速率參’數代 入進給速率控制的參數迭代公式以使曲線速率變化如預 期，如此可獲得更精確的加減速控制，也可獲得更精確的 加工結果》 相同的應用也可用在1st與2nd階近似的參數迭代法 則，或其他與進給速率相關的參數迭代法則。但是爲切確 掌握加減速時的加速率與減速率變化，參數迭代法必須使 插値器的曲線速率能精確的反應出進給速率設定，因此建 議使用本發明所提出之具速率控制之參數迭代方式實現參 數化曲線插値器的加減速操作模式。 參數式曲線插値器加減速操作模式模擬結果： 經濟部中央樣準局負工消費合作社印聚 (請先閲讀背面之注意事項再填寫本頁} 在參數式曲線插値器加減速操作模式的模擬中，由於 加速率與減速率是相同的過程，因此只比較參數式曲線插 値器在初始的加速率過程。在本節的模擬中將比較三種與 進給速率相關的參數迭代方式：第一（1st)階進似，第二（2nd) 階進似，與速率控制參數迭代方式應用於加減速過程中曲線 速率的變化情形，同時爲觀察參數迭代法則應用於不同加 減速方式的結果，本節將比較三種常用的加減速方式-線 性加減速，二次曲線加減速（parabolic)、與指數加減速。 由於二次曲線加減速方式爲平滑速率變化的加減速方式* 本紙張尺度適用中國國家標準（CNS ) A4規格（210X297公釐） 22 1S6S5 411408This paper size applies the Chinese National Standard (CNS) Λ4 grid (: M〇_X 16 156u5 4ii4G8 V. Description of the invention (17) cos (m;) T ^ f-Ipl + jD | j cos2 Θ Order (Factory w ' From μ, when “, + 1 uses a first-order approximate parameter iterative method, # — is generally a relatively small unitary, so it can be known from the Taylor expansion approximation that μ 2_ | p | pw _ 2.1 gives cos θ IP ', ie仏 (% _) has a negative compensation 値 and a compensation near zero, and the negative compensation 値 is far from zero. Since the purpose of compensation 此 here is to compensate for the parameter ~ the deficiency in the curve rate, so the compensation near zero is selected.値 to obtain more reliable parameter iteration results, namely-[ZΜΓ. (')' · + 7 ^,) ^-(^ ,.)-7:) 2-[z) r-x '(a; + 1) -DX-r '(«; + 1] r (' 丨) 2 + r (') 3j' ^ ^^ ^ ~, ΜΊ: —install, _ ^ ^. Order ------ ^ ( (Please read the notes on the back before filling this page.) Printed by the Central Standards Bureau of the Ministry of Economic Affairs, Shellfish Consumer Cooperatives. In the method discussed in this section, the compensation amount is added based on the incorrect interpolation curve rate, so you can get more High curve rate accuracy. In the parameter iteration rule of control, since the curve rate of the generated curve can be accurately controlled, it can be applied to the design of the parameterized curve inserter, and it can have different operation modes depending on the processing conditions. Generally, it depends on the processing conditions. The operation mode of the inserter can be divided into U) constant rate operation mode and (2) acceleration and deceleration operation mode. "Constant rate operation mode" refers to the fact that the inserter can generate a Insert point. Acceleration / deceleration operation mode can be applied to the beginning of the curve movement and the ft scale of this paper. Chinese national standard (CNS) Λ4ί · ί grid (210X; y7A 尨 17 15685 411408 A7 B7) V. Description of the invention Obtain a relatively gentle curve rate change. (C) Apply the iterative method of the feed rate control parameter of this embodiment to design the inserter and compare the processing examples: (C.1) The application example is in the system setting. The system used is a software plug-in program written in C language and executed on a personal computer system with a Pentium 200MHz CPU. In the setting of the parameter curve, the present invention uses a 2 degree NURBS parameterized curve to simulate the bow-tie curve The command path is shown in Figure 5. The related NURBS parameters are set as follows: The control points are: 150 150-150 0 150 »150 0 ·, -150 150 150 2. The weight vector is: F = [l 0_85 0.85 1 0.85 0.85 1] 1113 ,,.. The node vectors are: ί /: 0 0 0 &lt; Please read the notes on the back before filling out this page) Printed by the Central Standards Bureau of the Ministry of Economic Affairs—Industrial and Consumer Cooperatives 4 2 2 4 And with During the iterative process of parameters, the relevant parameters are set as follows: 1. Sampling time: ί = 0.01 sec. 2. Feed rate: / ^ 12 ^ = 2001 ^. (C.2) Constant rate operation mode: due to rate control The design of the parametric curve inserter can precisely control the curve rate of the interpolation result, so during the curve interpolation process, a fixed feed rate can be given to obtain a fixed curve rate interpolation result. Parametric curve interpolation The simulation results of the fixed-rate operation mode of the implement: This paper size applies to the Chinese National Standard (CNS) A4 (210 X 297 mm) 18 ί5685 4114G8 A7 ___B7 V. Description of the invention (19) Here we will compare the iterative design by different parameters The operation mode of the parametric curve interpolator, uniform, 1st order approximation, 2nd order approximation, constant feedra + te interpolation result curve rate changes. The results of the simulation interpolation curve rate of different plug-in operation modes are shown in Figures 6, 7, and 8 | The parameter compensation in the fixed-rate operation mode is shown in Figure 9. The calculation results are shown in Figure 9. The results are summarized in Table 1: Table 1: \ Measure i Speed error mean squared Maximum speed fluctuation ratio Maximum chord error Error with 80MHz CPU calculation time With 200MHz CPU calculation time mode Wee) 2 mm // sec only sec uniform 5.483 xlO5 6.0797 0.1388 11 4 First-order approximation 2.7078 0.01373 0.01739 27 10 Second-order approximation 0.01079 0,00942 0.01738 60 19 Constant rate 3.9642 xlG &quot; * 2.4909 xlO-6 0.01737 77 26 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs (please read the back first) Please pay attention to this page before filling in this page) Among them, 1. The measurement of the curve rate error refers to the difference between the curve rate produced by the inserter and the designed feed rate. 2. The formula for calculating the rate of change of the curve rate is 7, which represents the rate of change of the curve rate at each sampling time K represents the rate of the curve produced by the inserter at each sampling time. This paper's dimensions apply Chinese national standards (CNS &gt; A4 specifications ( 210X297 mm) 19 15685 4U408 A7 _B7 V. Description of the invention () 20. Setting the feed rate 3. Uniform Uniform) The parameter interval in the parameter iteration mode is the sampling time. Printed by Zhengong Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs (please read the notes on the back before filling this page). It is obvious from the simulation results that due to the iterative method of the rate control parameters, the relationship between the curve rate and the compensation rate is taken into account. The interpolation mode of the operation mode has the smallest curve rate error and rate change rate. At the same time, because the parameter iteration method of the 1st-order approximation is compensated, it can be seen that the rate accuracy of the 1st-order approximation after compensation is improved, and it exceeds the rate accuracy provided by the parameter iteration of the 2nd-order approximation. The interpolation method has the largest curve rate error and rate change rate, because the parameters and the curve are not uniformly distributed. In the comparison of the command string height error between interpolation points, the 1st order approximation and the 2nd order approximation are not significantly different from the command string height error of the constant rate operation mode, because the curve rate change in the bow curve used in this simulation is within. The effect of the command string height error between the interpolation points is not significant, but the command string height error of the uniform operation mode is significantly increased compared to other parameter iterative methods *, and the calculation time of each interpolation point is compared with the parameter iterative method. The time required for the interpolation point is only the calculation time of the curve interpolation point, so it will be the least. On the comparison of the 1st-order approximation and the 2nd-order approximation, the 2nd-order approximation requires the calculation of the second-order curve of the curve and the higher-order calculation, so the calculation Time will be more than the 1st-order approximation. Although the rate control parameter iteration method is based on the 1st-order approximation and does not require the second-order differential calculation of the curve, it needs to calculate an additional curve interpolation point and some calculations of the compensation 値, So the amount of calculation will be slightly higher than the 2nd order approximation "Although the parameter iteration method with rate control needs to be higher than the other parameter iteration methods The paper size applies to the Chinese National Standard (CNS) A4 (210X297 mm) 20 15685 411408 A7 B7 V. Description of the invention () 21 The amount of calculation, but the curve rate accuracy of the inserter is higher than the other parameter iterative methods Many, based on this high-precision curve rate control, the controller or workpiece design engineer can grasp a clearer process: At the same time, compared with the sampling time, the proportion of the calculation time of the interpolation point in the fixed-rate operation mode is very small, so The calculation time is acceptable in the real-time implementation process. To sum up the degree of change in the curve rate, the parametric curve inserter has the smallest curve rate error in the fixed rate operation mode, followed by the 2nd blind approximation operation mode and the 1st order. Approximate operation mode, uniform parameter operation mode has the largest curve rate error. (C.3) Acceleration and deceleration operation mode: The Central Consumers Bureau of the Ministry of Economic Affairs, the Consumer Cooperative Cooperative, printed the traditional acceleration and deceleration method by passing the position command through a low-pass filter To produce a smoother command input. However, this method will make the command path with large changes The radial and chord height errors of the diameter, such as near the start and end points of the processing curve. In view of this, Kim proposed the use of parameter acceleration and deceleration to achieve the purpose of parameterizing the curve acceleration and deceleration, and at the same time it is the operation of the parameter acceleration and deceleration Therefore, the interpolation point has a smaller diameter error. Although the parameter acceleration and deceleration method proposed by Kim can make the generation of the interpolation point have the function of acceleration and deceleration, the speed acceleration and deceleration cannot be really achieved on some curves. The reason is that the parameter space does not correspond to the curve uniformly. In order to obtain the true acceleration and deceleration of the curve in the curve movement at an appropriate control rate, the present invention proposes a parameterized curve interpolation for the application of the feed rate parameter acceleration and deceleration Acceleration / deceleration operation mode of the controller. During the iterative process of parameters with rate control, the workpiece designer can accurately grasp the change of the rate, so it can be used as the feed rate 156S5 (Please read the precautions on the back before filling this page } This paper size applies to China National Standard (CNS) A4 (210X297 mm) 411408 A7 __B7_ DESCRIPTION invention () parameter 22 achieved deceleration, acceleration and precise control of the rate at which geographical Save deceleration changes. The parameter iteration method with rate control is to control the parameter iteration so that the curve rate of the inserter can meet the setting of the feed rate 値 ^ (*), so the feed rate parameter ^ («0 Perform the acceleration and deceleration operations. Then the feed rate parameter calculated by the acceleration and deceleration is substituted into the parameter iteration formula of the feed rate control to make the curve rate change as expected. In this way, more accurate acceleration and deceleration control can be obtained. More Accurate Machining Results》 The same application can also be used in the parameter iteration laws of 1st and 2nd order approximations, or other parameter iteration laws related to the feed rate. However, to accurately grasp the changes in acceleration and deceleration rates during acceleration and deceleration, The parametric iteration method must make the curve rate of the inserter accurately reflect the setting of the feed rate. Therefore, it is recommended to use the parameter iterative method with rate control proposed by the present invention to implement the acceleration and deceleration operation mode of the parametric curve inserter. Simulation results of the acceleration and deceleration operation mode of the curved curve inserter: Printed by the Consumers Cooperatives of the Central Bureau of Standards, Ministry of Economic Affairs (please read the first Please fill in this page again for attention} In the simulation of the acceleration and deceleration operation mode of the parametric curve inserter, because the acceleration and deceleration rates are the same process, only the initial acceleration process of the parametric curve inserter is compared. The simulation in this section will compare three kinds of iterative methods related to the feed rate: the first (1st) step-like, the second (2nd) step-like, and the iterative method of the rate control parameter applied to the curve rate during acceleration and deceleration. Changes in the situation, and at the same time to observe the results of the parameter iteration rule applied to different acceleration and deceleration methods, this section will compare three commonly used acceleration and deceleration methods-linear acceleration and deceleration, quadratic curve acceleration and deceleration (parabolic), and exponential acceleration and deceleration. Because of the quadratic curve The acceleration / deceleration method is an acceleration / deceleration method that smooths the rate change. * This paper size applies to the Chinese National Standard (CNS) A4 specification (210X297 mm) 22 1S6S5 411408

五、發明説明（》) SJthtt較不同參數迭代方式應用於二次曲線加減速方式的 插M曲線速率模擬結果如第10, 11，12圖所示。參數迭代 於三種不同加減速方式時最大曲線速率差値列表 於表2中。 表2 :速率誤差 方式 線性 二次曲線 指數 迭代方 mm/ /sec mm/ /sec mm/ /sec 一階近似 6.0 3 χ 1〇'1 5.6 7 8 0 χ 10 5 1.6247 一階近似 5.4 0 1 8 χ ΙΟ'3 4.9210 xlO&quot;3 2.7 7 2 6 χ 10'2 定速率 5.5 8 93 xlO-6 4.6621 xlO^ 1.1 3 87 xlO-4 經濟部中央標準局員工消费合作社印製V. Explanation of the invention (") The simulation results of the interpolation curve rate of SJthtt applied to the quadratic curve acceleration / deceleration method with different parameter iterative methods are shown in Figures 10, 11, and 12. Parameter iterations The maximum curve rate difference between three different acceleration and deceleration modes is listed in Table 2. Table 2: Rate error method linear quadratic exponential iterative square mm / / sec mm / / sec mm / / sec first order approximation 6.0 3 χ 1〇'1 5.6 7 8 0 χ 10 5 1.6247 first order approximation 5.4 0 1 8 χ ΙΟ'3 4.9210 xlO &quot; 3 2.7 7 2 6 χ 10'2 Constant rate 5.5 8 93 xlO-6 4.6621 xlO ^ 1.1 3 87 xlO-4 Printed by the staff consumer cooperative of the Central Standards Bureau of the Ministry of Economic Affairs

L---‘ - !- fl·— ί^衣l· (請先閱讀背面之注意事項再填寫本頁J 在蝴蝶結曲線的加速率過程中，由於曲線曲率是由小 至大漸漸變化，因此在參數迭代時，其曲線速率的誤差會 漸漸增加如第10, 11，12圖中所示。但是在比較不同的參 數迭代法時，使用具速率控制的參數迭代方式明顯優於其 他與進給速率相關的參數迭代法。而在不同加減速方式的 比較上，指數式的加減速方式具有最大的曲線速率誤差， 二次曲線加減速方式的曲線速率變化較爲平滑且速率誤差 最小。因此總結上述的模擬結果可知，在加減速過程中， 當進給速率是以二次曲線的方式平滑變化時，則具速率控 制的參數迭代方式可以使插値器所產生的曲線速率具有高 精確度的二次曲線變化。換言之，當加減速之進給速率變 化曲線爲經過設計使參數化曲線插値器的插値結果具有所 設計的加速率與減速率變化時，經由具速率控制的參數迭 代方式所設計的參數式曲線插値器可使插値器的加速率與 減速率結果如設計’尤其是在高速進給速率曲線運動時》 本紙張尺度適用中國國家標準（CNS ) A4.UL格（210x2^7公|ί: ) 15685~ 經濟部中央標羋局員工消費合作社印製 4114G8 五、發明说明（24) 由上實施例及所作比較實例可知，本發明提出具速率 控制的參數式曲線插値器設計方式，並且依據曲線速率的 控制目的不同而有定速率操作模式與加減速操作模式等以 因應不同的加工條件。本發明所提出之速率控制參數迭代 方式因爲加入考慮參數與曲線速率關係的補償量I所以應 用在插値器的設計上可以獲得精確的曲線速率插値結果。 由於速率的變化會影響到加工工件的表面粗糙度，因此定 速率操作模式旨在參數化曲線實現過程中，相鄰內插點間 的移動速率維持定値。在參數化曲線插値器加減速操作模 式的討論上，由於本發明提出高精密度要求的速率控制參 數迭代方式，因此可應用於曲線速率加減速的控制，藉由 順滑變化的進給速率與精確的進給速率控制參數迭代方式 以使參數化曲線插値器的的插値結果曲線速率的加速率與 減速率變化可如預期。 在計算時間上，雖然本發明所提出之參數式曲線插値 方式需要較多的計算過程，但是其結果能更精確的控制曲 線路徑的位置與速率’使工件加工結果能更加的精確β在 電腦與處理器晶片速率越來越快，加工品質要求日益提高 的現在’本發明所提出之參數式曲線插値器設計同時提供 良好的位置及曲線速率精度》 ---.--^ Γ».--I. .士卜_hi ^__S___- T I_____户 (請先閱讀背面之注意事項再填寫本頁) 本紙張尺度過用中國國家標準（CNS ) A4«L格（210X297公兑） 24 15685L --- '-!-Fl · — ί ^ 衣 l · (Please read the notes on the back before filling out this page. J In the process of accelerating the bow curve, the curve ’s curvature gradually changes from small to large, so During parameter iteration, the error of the curve rate will gradually increase as shown in Figures 10, 11, and 12. However, when comparing different parameter iteration methods, using the parameter iteration method with rate control is significantly better than the other and feed. Iterative method of rate-related parameters. On the comparison of different acceleration and deceleration methods, the exponential acceleration and deceleration method has the largest curve rate error, and the curve rate change of the quadratic curve acceleration and deceleration method is smooth and the rate error is the smallest. The above simulation results show that during the acceleration and deceleration, when the feed rate is smoothly changed in the form of a quadratic curve, the parameter iterative method with rate control can make the curve rate produced by the inserter have high accuracy. Quadratic curve change. In other words, the feed rate change curve during acceleration and deceleration is designed so that the insertion result of the parameterized curve inserter has the designed acceleration. When the change with the deceleration rate, the parametric curve inserter designed by the parameter iterative method with rate control can make the inserter's acceleration and deceleration rate results as designed, especially when the high-speed feed rate curve moves. Paper size applies Chinese National Standard (CNS) A4.UL (210x2 ^ 7 公 | ί:) 15685 ~ Printed by the Consumer Cooperatives of the Central Standardization Bureau of the Ministry of Economic Affairs 4114G8 V. Description of the invention (24) From the above examples and comparisons It can be known from the examples that the present invention proposes a design method of a parametric curve inserter with rate control, and according to the control purpose of the curve rate, there are a constant rate operation mode and an acceleration / deceleration operation mode to respond to different processing conditions. The rate control parameter iterative method, because the compensation amount I that takes into account the relationship between the parameter and the curve rate, is added to the design of the inserter to obtain accurate curve rate interpolation results. Because the rate change will affect the surface roughness of the processed workpiece Therefore, the fixed-rate operation mode is designed to maintain the movement rate between adjacent interpolation points during the parameterization curve implementation process. In the discussion of the parameterized curve inserter acceleration / deceleration operation mode, the present invention proposes an iterative method of the rate control parameters required by high precision, so it can be applied to the control of the curve rate acceleration / deceleration, by smoothly changing the progression. The feed rate and precise feed rate control parameters are iterative to make the interpolation results of the parameterized curve inserter curve curve acceleration and deceleration rates change as expected. In terms of calculation time, although the parameters proposed by the present invention The curved curve interpolation method requires more calculation processes, but the results can more accurately control the position and speed of the curve path ', so that the workpiece processing results can be more accurate. The speed of the computer and processor chip is faster and faster, and the processing quality The increasingly demanding present 'parametric curve inserter design proposed by the present invention provides good position and curve rate accuracy at the same time》 ---.-- ^ Γ ».-- I.. 士卜 _hi ^ __ S ___- T I_____ households (please read the notes on the back before filling out this page) This paper has been used in China National Standard (CNS) A4 «L grid (210X297 credit) 24 15685

Claims (1)

4i：4G8 as C8 D8__ 六、申請專利範圍 1. 一種電腦數控（CNC)曲線路徑速率控制方法，係以等速 控制操作曲線路徑加工，包括下列步驟： (1) 參數化曲線插値器在接收由電腦辅助設計（CAD)所解 譯曲線的訊息後，以參數化曲線的參數迭代法 (Iteration)產生連續的內插點； 1 (2) 僅考慮插値器產生的位置命令誤差之弦高誤差（chord height error)的影響，而不考慮徑向誤差（radial error)； (3 )導出參數曲線公式（p a r a m e t r i c c u r v e f o r m u 1 a t i ο η)之一 次近似參數迭代法則； (4)設計具速率控制之參數迭代法則，將該表示之一次近 似參數迭代法則提出參數補償，經由補償量與曲線間 的相關性獲得更高精度的曲線速率控制； (5 &gt;選擇在零點附近的補償値以獲得較爲可靠的參數迭代 結果；以及 (6)將該獲得補償値之連續的內插點送入控制系統使刀具 中心沿著參數化曲線移動。 經濟部中央橾準局貝工消费合作社印製 ----------^------訂 (請先Μ讀背面之注意事項再球寫本頁) 2. 如申請專利範圍地1項之電腦數控曲線路徑速率控制方 法，其中所用之該參數化曲線爲非等距 B雲形線 (NURBS) · 3. 如申請專利範圍地1項之電腦數控曲線路徑速率控制方 法，其中參數化曲線插値器使用的參數迭代法，是以Cbou 和Yang所提出的一般化參數迭代法則爲基礎提出進給 速率控制的參數迭代方式》 本紙伕尺度逍用中國國家標準（CNS ) A4現格（210X297公釐） jj IJ685~ ABCD 經濟部中央梯準局男工消费合作社印策 々、申請專利範圍 4.—種電腦數控（CNC)曲線路徑速率控制方法，係以加減 速控制操作曲線路徑加工，包括下列步驟： (1) 參數化曲線插値器在接收由電腦輔助設計（CAD)所解 譯曲線的訊息後，以參數化曲線的參數迭代法 (Iteration)產生連續的內插點； &gt; (2) 僅考慮插値器產生的位置命令誤差之弦高誤差（chord height error)的影響，而不考慮徑向誤差（radial error)： (3) 導出參數曲線公式（parametric curve formulation)之一 次近似參數迭代法則： (4) 設計具速率控制之參數迭代法則，將該表示之一次近 似參數迭代法則提出參數補償，經由補償量與曲線間 的相關性獲得更高精度的曲線速率控制； (5) 選擇在零點附近的補償値以獲得較爲可靠的參數迭代 結果；以及 (6&gt;將該獲得補償値之連續的內插點送入控制系統使刀具 中心沿著參數化曲線移動》 5·如申請專利範圍地4項之電腦數控曲線路徑速率控制方 法，其中所用之該參數化曲線爲非等距 B雲形線 (NURBS)。 6.如申請專利範圍地4項之電腦數控曲線路徑速率控制方 法，其中參數化曲線插値器使用的參數迭代法，是以Chou 和Yang所提出的一般化參數迭代法則爲基礎提出進給 速率控制的參數迭代方式· &lt;請先閲讀背面之注意事項再填寫本頁) 裝· Ηπ 本紙張尺度逍用中國國家揉率（CNS )八4規^格（210X297公釐） 26 15685 4ίί4υ8 Β8 C8 D8 經濟部中央揉準局員工消f合作社印製 六、申請專利範圍 7. —種電腦數控曲線路徑速率控制裝置.，包括： 電腦，作輔助設計（CAD)用，該輔助設計工作包括參 數化曲線格式及分段曲線： 電腦數控（CNC)機構，包括： 參數化曲線插値器，在接收該電腦所解譯之參 數曲線訊息後，以參數化曲線的點產生方式產生連 續的內插點； 控制器，接收該參數化曲線插値器所產生的連 續的內插點，送出加工信號： 刀具，接收該控制器送出之控制加工信號，中 心沿著參數化曲線移動； 人機介面裝置，可讓操作者與該參數化曲線插 値器之間作人機溝通： 其中該參數化曲線插値器可對該參數化曲線作 定速率插値操作模式、加減速插値操作模式。 8. —種電腦數控曲線路徑速率控制之參數化曲線插値器裝 置，包栝： 定速率插値器，使參數化曲線路徑在插値的實現過 程中保持速率定値：以及 加減速插値器，使該加工曲線路徑獲得更爲平滑的 加減速運動。 ^^1 n I. (請先閲讀背面之注意事項再填寫本頁) 本紙張尺度遑用中國國家標準（CNS ) A4洗格（210X297公釐） 27 156854i: 4G8 as C8 D8__ VI. Patent application scope 1. A computer numerical control (CNC) curve path rate control method, which uses constant speed control to operate curve path processing, including the following steps: (1) Parameterized curve inserter is receiving After the information of the curve is interpreted by computer-aided design (CAD), continuous interpolation points are generated by the parameter iteration of the parameterized curve; 1 (2) Only the chord height of the position command error generated by the inserter is considered The influence of the error (chord height error), regardless of the radial error (radial error); (3) Derive a parametric curve formula (parametriccurveformu 1 ati ο η) an approximate parameter iterative rule; (4) design parameters with rate control Iterative rule, which proposes parameter compensation for an approximate parameter iterative rule of the representation, and obtains more accurate curve rate control through the correlation between the compensation amount and the curve; (5 &gt; choose a compensation near zero to obtain a more reliable Parameter iterative results of the; and (6) send the continuous interpolation points of the compensation to the control system to make the tool center along the Parametric curve movement. Printed by the Shellfish Consumer Cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs ------------ ^ ------ Order (please read the precautions on the back before writing this page) 2. For example, a computer numerically controlled curve path rate control method in the scope of patent application, where the parameterized curve used is a non-equidistant B cloud line (NURBS). Rate control method, in which the parameter iterative method used by the parametric curve inserter is based on the generalized parameter iterative rule proposed by Cbou and Yang. Iterative method of feed rate control is proposed. (CNS) A4 is now (210X297 mm) jj IJ685 ~ ABCD Printing Policy of Male Workers Consumer Cooperatives, Central Ladder Standard Bureau, Ministry of Economic Affairs, Patent Application Scope 4. A computer numerical control (CNC) curve path rate control method Deceleration control operation curve path processing includes the following steps: (1) After receiving the information of the curve interpreted by computer aided design (CAD), the parameterized curve inserter uses the parameter iterative method of the parameterized curve (Iterat ion) produces continuous interpolation points; &gt; (2) considers only the effect of chord height error of the position command error produced by the inserter, and does not consider the radial error: (3) Derive an approximate parameter iterative rule for the parametric curve formulation: (4) Design a parameter iterative rule with rate control, and propose a parameter iteration for the approximate parameter iterative rule for the expression, and then use the correlation between the compensation amount and the curve. Get more accurate curve rate control; (5) choose compensation near zero to get more reliable parameter iteration results; and (6 &gt; send the continuous interpolation point of the obtained compensation to the control system to make the tool The center moves along the parameterized curve. "5. For example, the computerized numerical control curve path rate control method of the 4 items in the scope of the patent application, wherein the parameterized curve used is a non-equidistant B cloud line (NURBS). 6. For example, the computer-controlled numerical control curve path rate control method of the 4 items in the patent scope, wherein the parameter iterative method used by the parameterized curve inserter is based on the generalized parameter iterative rule proposed by Chou and Yang. Controlled parameter iteration method &lt; Please read the notes on the back before filling in this page) Installation · Ηπ This paper size is free to use China National Kneading Rate (CNS) 8 4 rules ^ grid (210X297 mm) 26 15685 4ί4υ8 Β8 C8 D8 Printed by the staff of the Central Bureau of the Ministry of Economic Affairs, F. Cooperative, Co., Ltd. 6. Application for patent scope 7.-A kind of computer-controlled numerical control curve path rate control device, including: computer for auxiliary design (CAD), the auxiliary design includes parameterization Curve format and segmented curve: A computer numerical control (CNC) mechanism includes: a parametric curve inserter that generates continuous interpolation points by generating points of the parametric curve after receiving the parametric curve information interpreted by the computer ; The controller receives the continuous interpolation points generated by the parametric curve inserter and sends the processing signal: the tool receives the sent by the controller The processing signal is controlled, and the center moves along the parameterized curve. The human-machine interface device allows human-computer communication between the operator and the parameterized curve inserter: The parameterized curve inserter can be used for the parameterized curve. It is used for fixed-rate insertion operation mode and acceleration / deceleration insertion operation mode. 8. —A parameterized curve inserter device for computer numerically controlled curve path rate control, including: a constant rate inserter that keeps the parameterized curve path at a fixed rate during the implementation of the interpolation: and an acceleration / deceleration inserter , So that the processing curve path obtains a smoother acceleration and deceleration movement. ^^ 1 n I. (Please read the precautions on the back before filling out this page) This paper size is in accordance with Chinese National Standard (CNS) A4 wash case (210X297 mm) 27 15685