【摘要】：數(shù)控加工精度與加減速運動控制、插補(bǔ)算法密切相關(guān),插補(bǔ)算法直接影響控制器的性能。%!(#曲線加工過程中,用小直線段逼近曲線加工時,直線距離短,造成速度波動大,加工誤差難以控制。因此,樣條曲線插補(bǔ)技術(shù)是實現(xiàn)高速高精數(shù)控加工的關(guān)鍵因素。同時,隨著近年來微電子技術(shù)的發(fā)展,嵌入式數(shù)控系統(tǒng)由于體積小、運算速度快、穩(wěn)定性高等優(yōu)點具有廣泛的應(yīng)用前景。本文以2#.3 0嵌入式數(shù)控控制器為基本開發(fā)平臺,開發(fā)了一種高性能樣條曲線插補(bǔ)算法,具有重要的應(yīng)用價值。本文首先研究了樣條曲線的數(shù)學(xué)模型,通過對數(shù)學(xué)模型的研究,給出了采用插值法求取樣條曲線的公式。為了更好的應(yīng)用于嵌入式系統(tǒng),便于編程,本文還給出了%!(#曲線求取的矩陣表示形式。為了驗證算法的正確,利用4開發(fā)了圖形顯示的組件,并進(jìn)行插值仿真。其次,是對刀位點進(jìn)行了處理,目前由0,生產(chǎn)的刀位點直接是孤立的、毫無聯(lián)系的一組數(shù)據(jù)點。將數(shù)據(jù)刀位點進(jìn)行分類,通過識別與剔除,保留了在設(shè)置精度范圍內(nèi),擬合樣條曲線需要的基本數(shù)據(jù)點,去除了不必要的誤差點與冗余點,簡化了求取條件。同時,考慮到數(shù)控系統(tǒng)計算的實時性與最大的承受能力,給出了樣條曲線分段的方法,保證樣條曲線分段前后圖形一致。利用上述算法,對樣條曲線進(jìn)行仿真分析,驗證了算法的可行性。第三,在上述技術(shù)的基礎(chǔ)上給出了利用泰勒級數(shù)展開原理求取節(jié)點增量實現(xiàn)樣條曲線實時插補(bǔ)的方法。通過比較齊次坐標(biāo)與系數(shù)矩陣的插補(bǔ)方式,給出了齊次坐標(biāo)插補(bǔ)算法與齊次坐標(biāo)表示式。根據(jù)速度、加速度與加工精度的要求,給出了弓高誤差的計算方式與控制因素。通過設(shè)計直線型加減速算法,達(dá)到最終的到位檢測。最后將上述算法移植到2#.30控制器上,搭建測試平臺,在相同的測試條件下,通過對比圓弧直線插補(bǔ)與樣條曲線插補(bǔ)的速度圖形,驗證了算法的高效性與穩(wěn)定性。
[Abstract]:NC machining accuracy and acceleration and deceleration motion control, interpolation algorithm is closely related, interpolation algorithm directly affect the performance of the controller. Processing error is difficult to control. Therefore, spline curve interpolation technology is a key factor to achieve high-speed and high-precision NC machining. At the same time, with the development of microelectronics technology in recent years, embedded numerical control system has a wide application prospect because of its small size, fast operation speed and high stability. In this paper, a high performance spline interpolation algorithm is developed on the platform of 2#3.30 embedded NC controller, which has important application value. In this paper, the mathematical model of spline curve is studied at first. Through the study of mathematical model, the formula of using interpolation method to obtain the sampling spline curve is given. In order to be better applied in embedded system and easy to program, the matrix representation of # curve is also given in this paper. In order to verify the correctness of the algorithm, a graphic display component is developed using 4, and the interpolation simulation is carried out. Secondly, the knife site is treated, and the knife site produced by 0 is directly isolated and unrelated to a set of data points. The data knife sites are classified, and by identifying and eliminating, the basic data points needed for fitting spline curves are retained in the range of setting accuracy, and unnecessary error points and redundant points are removed, and the conditions for obtaining the data points are simplified. At the same time, considering the real time and the maximum bearing capacity of the numerical control system, the method of spline curve segmentation is given to ensure that the spline curve segmentation is consistent with each other. The feasibility of the algorithm is verified by the simulation analysis of the spline curve. Thirdly, on the basis of the above techniques, a method for real-time interpolation of spline curves by using Taylor series expansion principle to obtain node increments is presented. By comparing the interpolation method of homogeneous coordinate and coefficient matrix, the interpolation algorithm of homogeneous coordinate and the expression of homogeneous coordinate are given. According to the requirements of velocity, acceleration and machining accuracy, the calculation method and control factors of bow height error are given. Through the design of linear acceleration and deceleration algorithm to achieve the final detection in place. Finally, the algorithm is transplanted to the 2#.30 controller, and the test platform is built. Under the same test conditions, the efficiency and stability of the algorithm are verified by comparing the velocity figures of the arc-line interpolation and spline curve interpolation.
【學(xué)位授予單位】：廣州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TG659

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