本文關(guān)鍵詞： NURBS 五軸數(shù)控加工 插補(bǔ)算法 刀軸矢量 軌跡光順　出處：《合肥工業(yè)大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：隨著自由曲面在工業(yè)領(lǐng)域中的應(yīng)用日趨廣泛,自由曲面零件的五軸加工技術(shù)受到了越來越多的關(guān)注。NURBS由于其具備較強(qiáng)的形狀控制能力,已經(jīng)被ISO確定為描述工業(yè)產(chǎn)品幾何形狀的唯一數(shù)學(xué)方法。與在CAD(Computer Aided Design)中的廣泛應(yīng)用相比,NURBS在CAM(Computer-Aided Manufacturing)領(lǐng)域則相對滯后。NURBS技術(shù)在數(shù)控加工領(lǐng)域的應(yīng)用,符合五軸加工技術(shù)高速高精度的發(fā)展趨勢,有利于提高數(shù)控加工技術(shù)的整體水平。我國的五軸數(shù)控技術(shù)仍然落后于發(fā)達(dá)國家,國外的高檔數(shù)控系統(tǒng)已較成熟地融入了五軸NURBS插補(bǔ)功能,但仍然對我國實(shí)行出口限制和技術(shù)封鎖。因此,持續(xù)開展包括NURBS技術(shù)在內(nèi)的數(shù)控關(guān)鍵技術(shù)研究,對于我國裝備制造業(yè)的轉(zhuǎn)型升級具有重要的戰(zhàn)略意義�；谏鲜霰尘�,本文針對自由曲面五軸加工的離散刀位軌跡,開展了刀具路徑的NURBS擬合與插補(bǔ)技術(shù)研究。主要研究以下幾個(gè)方面的內(nèi)容:第一,研究了NURBS曲線曲面的擬合方法。針對有序的密集數(shù)據(jù)點(diǎn)列,為滿足擬合精度并有效壓縮曲線數(shù)據(jù)量,提出了一種基于曲率優(yōu)勢點(diǎn)的NURBS曲線擬合方法。先計(jì)算離散數(shù)據(jù)點(diǎn)列的曲率,再遴選出曲率優(yōu)勢點(diǎn)作為型值點(diǎn)擬合初始曲線并計(jì)算擬合偏差,在偏差超過允許值的局部增加型值點(diǎn)重新擬合曲線,直至所得的NURBS曲線滿足精度要求。在此基礎(chǔ)上,采取最小公用節(jié)點(diǎn)矢量法解決了曲線簇間的相容性問題,獲得了曲面的控制網(wǎng)絡(luò)和二維節(jié)點(diǎn)矢量參數(shù),最終完成了NURBS曲面重構(gòu)與實(shí)體造型。第二,研究了NURBS曲線直接插補(bǔ)技術(shù)。為避免復(fù)雜的求導(dǎo)運(yùn)算,提出了一種基于遞歸特性的NURBS曲線實(shí)時(shí)插補(bǔ)算法。先采用Simpson數(shù)值方法計(jì)算出曲線長度,再確定速度極小值點(diǎn)并作為節(jié)點(diǎn)將原曲線劃分為若干子曲線,分別進(jìn)行加減速規(guī)劃。在速度規(guī)劃階段,探索出了一種由曲線兩端同時(shí)插補(bǔ)至減速點(diǎn)的相向插補(bǔ)方法,結(jié)合插補(bǔ)周期和進(jìn)給速度計(jì)算各周期內(nèi)的精度約束步長。為獲取期望插補(bǔ)步長,依據(jù)所推導(dǎo)出的插補(bǔ)弦長與參數(shù)增量間的近似線性關(guān)系,通過必要的迭代計(jì)算,最終獲得了各插補(bǔ)點(diǎn)的參數(shù)值。第三,研究了五軸加工線性刀路的雙NURBS光順技術(shù),具體分為光順擬合和光順插補(bǔ)兩個(gè)方面。首先采用前述的曲線擬合方法,對五軸加工的離散刀位數(shù)據(jù),分別擬合出刀尖點(diǎn)和刀軸點(diǎn)的NURBS曲線,完成對線性刀路的雙NURBS光順描述。在此基礎(chǔ)上,為有效控制插補(bǔ)過程中的刀軸方向偏差,提出了一種分區(qū)間參數(shù)同步的雙NURBS曲線插補(bǔ)算法。以刀尖點(diǎn)曲線的插補(bǔ)進(jìn)度為準(zhǔn),使刀軸點(diǎn)曲線的插補(bǔ)參數(shù)在對應(yīng)子區(qū)間內(nèi)保持線性同步,確保兩個(gè)插補(bǔ)點(diǎn)的間距保持不變,進(jìn)而實(shí)現(xiàn)對刀具運(yùn)動(dòng)的光順插補(bǔ)。此外,借鑒剛體空間螺旋運(yùn)動(dòng)的表述方法,研究了采用對偶四元數(shù)方法描述刀具的位置和姿態(tài),綜合了五軸加工過程中刀具的平移運(yùn)動(dòng)和旋轉(zhuǎn)運(yùn)動(dòng),獲得了等距雙NURBS刀具路徑。第四,研究了五軸加工后置處理相關(guān)技術(shù)。首先總結(jié)了五軸機(jī)床旋轉(zhuǎn)軸的實(shí)現(xiàn)方式,并以A-C雙轉(zhuǎn)臺(tái)機(jī)床為例,建立了運(yùn)動(dòng)學(xué)模型并求解。對于旋轉(zhuǎn)軸的多解選擇問題,根據(jù)刀軸的最大轉(zhuǎn)角與旋轉(zhuǎn)軸極限行程間的關(guān)系,確定首行刀位對應(yīng)的非依賴軸選解區(qū)間,所選解兼顧了旋轉(zhuǎn)軸極限行程和運(yùn)動(dòng)的連續(xù)性。對于旋轉(zhuǎn)軸所致的非線性誤差,建立了誤差計(jì)算模型,并通過插入中間刀位點(diǎn)法有效控制了非線性誤差。對于指令進(jìn)給速度規(guī)劃問題,基于速度和加速度約束以及工件坐標(biāo)系與機(jī)床坐標(biāo)系的映射關(guān)系,反算出編程進(jìn)給率,最終獲得了平滑的刀尖進(jìn)給速度。最后開發(fā)了后置處理程序,生成符合上述約束條件的數(shù)控代碼,并在VERICUT中進(jìn)行了仿真加工驗(yàn)證。第五,在理論分析的基礎(chǔ)上進(jìn)行了所提算法的實(shí)驗(yàn)研究。在開放式數(shù)控實(shí)驗(yàn)平臺(tái)上,進(jìn)行遞歸特性插補(bǔ)法和Taylor級數(shù)展開法的NURBS曲線插補(bǔ)實(shí)驗(yàn),分析比較實(shí)驗(yàn)數(shù)據(jù),驗(yàn)證本算法在計(jì)算效率和插補(bǔ)精度方面的優(yōu)勢。在五軸義齒加工中心平臺(tái)上,進(jìn)行雙NURBS曲線插補(bǔ)加工實(shí)驗(yàn),驗(yàn)證該算法加工零件的表面質(zhì)量。
[Abstract]:With the application of free surface in the industrial field more and more widely, five axis machining technology of free-form surface parts has attracted more and more attention to.NURBS because of its strong ability of shape control, ISO has been identified as the only mathematical methods describe the shape of industrial products. And in the CAD (Computer Aided Design) compared with the widely application. NURBS CAM (Computer-Aided Manufacturing) in the field is lagging behind the application of.NURBS technology in the field of NC machining, in line with the development trend of five axis machining technology of high speed and high precision, is conducive to improve the overall level of CNC technology. Five axis CNC technology in China still lags behind the developed countries, high-end CNC system has been more mature abroad in five axis NURBS interpolation function, but still subject to export restrictions and technology blockade against our country. Therefore, sustainable development of NC technology, including NURBS Research on the key technology, has important strategic significance for the transformation and upgrading of equipment manufacturing industry in China. Based on the above background, this paper path discrete cutter with free-form surface for five axis machining, the tool path NURBS fitting and interpolation technology research. The main research contents of the following aspects: first, research on the NURBS curve fitting method the surface. For dense data points and orderly column, in order to meet the fitting precision and effective compression curve data, put forward the NURBS curve fitting method based on curvature advantage point. First calculate the discrete data points of curvature, and then select the dominant point curvature as data points fitting initial curve and calculate the error of fitting. The local increase in type deviation exceeds the allowable value of re fitting curve, NURBS curve and income to meet the accuracy requirements. On this basis, taking the minimum utility node vector method The problem of compatibility curve between clusters, the surface of the control network and the two-dimensional node vector parameters, the final completion of the surface reconstruction and modeling of entity NURBS. Second, NURBS curve direct interpolation. In order to avoid the complicated derivation, proposes a real-time interpolation algorithm of NURBS curve characteristics based on recursion. Using the Simpson numerical method to calculate the length of the curve, and then determine the point as a node of the original curve is divided into several sub minimum speed curve, respectively. The speed acceleration and deceleration in the planning stage, to explore a curve both ends to the deceleration point interpolation to calculate the interpolation method, the precision constraint step cycle with the interpolation cycle and feed speed. In order to obtain the desired interpolation step, an approximate linear relationship between the interpolation length and parameter increment according to the derived the necessary through iterative calculation, finally The parameters of each interpolation point value. Third, the study of double linear NURBS five axis machining tool path fairing technology, specifically divided into smooth fitting and smoothing interpolation in two aspects. Firstly, using the curve fitting method on the five axis machining, discrete cutter location data, were fitted by NURBS curve knife the knife tip point and axis point, to complete the double NURBS on the linear tool path fairing is described. On this basis, in order to effectively control the interpolation of knife axis deviation, put forward double NURBS curve interpolation algorithm for synchronous partition parameters. With the progress of the interpolation curve as the standard, the interpolation parameters point curve of the cutter shaft to maintain linear synchronous in the corresponding sub interval, to ensure that the distance between the two interpolation points remain unchanged, and thus the realization of tool motion smoothing interpolation. In addition, from the expression method of rigid space spiral motion, was studied by dual four element method. The attitude and position of the tool, the translational motion and rotational motion of the cutter for five axis machining process, the dual NURBS tool path. On the fourth, five axis machining post-processing technology. Firstly summarizes the realization of five axis machine tool's axis of rotation, and the A-C double turntable machine tool as an example, the establishment of the kinematics model and solve for the axis of rotation of multiple solutions problem, according to the relationship between the maximum angle of the cutter shaft and the rotary shaft limit travel between the first axis to determine the non dependent tool corresponding to the selected solution interval, the selected solutions of both continuous rotation limit travel and movement. The nonlinear error of the axis of rotation due to the error of the calculation model, is established, and by inserting a middle knife site method to effectively control the nonlinear error. For the instruction of feed rate planning, speed and acceleration constraints and the workpiece coordinate system and machine tool based on Sat Mapping coordinates, calculate the feed rate, finally get the tip smooth feeding speed. Finally, the development of post processing program of NC code generation, with the above constraints, and the machining simulation in VERICUT. Fifth, on the basis of theoretical analysis and experimental study was carried out by the proposed algorithm. In the open NC experimental platform, NURBS curve interpolation experiment recursive feature interpolation method and Taylor series method, comparative analysis of experimental data, verify the advantages of this algorithm in computational efficiency and accuracy of the interpolation. In five axis denture processing center platform, double NURBS curve interpolation processing experiment, verify the surface quality of the algorithm parts of the processing.

【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.7;TG659

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