【摘要】：數(shù)控加工中,在實(shí)時插補(bǔ)階段——將CAM軟件仿真生成的刀位軌跡即G代碼導(dǎo)入到CNC系統(tǒng)中,通常用小線段表達(dá)刀位軌跡。然而,小線段生成的刀位軌跡只能達(dá)到位置(C0)連續(xù),不利于后續(xù)的速度規(guī)劃,需要對其進(jìn)行樣條曲線的光滑擬合。采用Akima樣條曲線對刀位點(diǎn)進(jìn)行擬合,不僅在曲線形態(tài)上呈現(xiàn)G1及以上連續(xù),與實(shí)際加工輪廓有著良好的吻合度,而且對實(shí)時加工中刀具的加減速運(yùn)動起到一定的良好控制效果,便于加工過程的順利進(jìn)行。本文主要針對數(shù)控加工的刀位軌跡生成以及Akima曲線在擬合算法上的改進(jìn)及其評價指標(biāo)進(jìn)行研究,主要包括以下幾個方面:對于不同的數(shù)控加工方式,會生成疏密程度截然不同的刀位軌跡。通過不同類型輪廓的三維實(shí)體模型選擇針對性好的加工方式,綜合考慮加工余量、步距等內(nèi)在因素與切削速度、過(欠)切現(xiàn)象等外在因素,生成相對較好的刀位軌跡,以利于后續(xù)的刀位軌跡的樣條擬合。針對Akima樣條擬合算法理論,本文在對刀位點(diǎn)進(jìn)行參數(shù)化方面,采用弧長參數(shù)化替代已有的節(jié)點(diǎn)參數(shù)化,提出弧長參數(shù)化Akima樣條的遞推式擬合算法。其擬合流程主要分為兩個部分:一是對Akima曲線的約束分段,即利用雙弦與弦切誤差測試設(shè)置的誤差閾值,判斷Akima曲線段與對應(yīng)弦長的弦誤差,以此對刀位點(diǎn)和Akima曲線進(jìn)行約束與分段;二是對約束刀位點(diǎn)的遞推式擬合,即當(dāng)已知刀位點(diǎn)的個數(shù)不小于三時,保留并延用相鄰曲線段之間共有約束刀位點(diǎn)的切矢,在相鄰的約束刀位點(diǎn)之間利用弧長參數(shù)化依此進(jìn)行Akima曲線的遞推式擬合。同時通過實(shí)例對比分析了無約束的節(jié)點(diǎn)參數(shù)化Akima曲線與約束刀位點(diǎn)的弧長參數(shù)化Akima曲線的擬合狀態(tài),驗(yàn)證本文提出算法的有效性�；趦煞N參數(shù)化的Akima曲線,對刀位點(diǎn)生成的不同小線段弦長和轉(zhuǎn)角進(jìn)行四種類型的劃分。在此基礎(chǔ)上,為了獲取曲線的節(jié)點(diǎn)切矢信息,確定以曲線最大弦誤差、最大曲率值以及曲率變化率三個評價指標(biāo)作為判斷Akima曲線形態(tài)優(yōu)劣的標(biāo)準(zhǔn)。在處理不同類型的小線段時,加入NURBS曲線的刀位點(diǎn)擬合,比較三種曲線在不同情況下的擬合性能,建立兩種Akima參數(shù)曲線與NURBS曲線的最適處理小線段類型的對應(yīng)關(guān)系。通過MatLab仿真實(shí)驗(yàn)與分析,進(jìn)行實(shí)體輪廓的整體擬合對比三種曲線的擬合效果,以進(jìn)一步驗(yàn)證弧長參數(shù)化的Akima算法,在對刀位點(diǎn)進(jìn)行適當(dāng)約束時,能得到光順性較好的擬合曲線,更優(yōu)的曲線形態(tài)評價指標(biāo)值,進(jìn)而提升了小線段(初始刀位軌跡)的Akima曲線擬合性能。
[Abstract]:In NC machining, in the real-time interpolation stage, the tool path (G code) generated by CAM software simulation is imported into the CNC system, and the tool path is usually expressed by small line segments. However, the tool path generated by the small line segment can only reach the position (C _ 0) continuous, which is not conducive to the subsequent speed planning, so it is necessary to smooth fitting the spline curve. The Akima spline curve is used to fit the tool position, which not only shows G1 or more continuity in the shape of the curve, but also has a good agreement with the actual machining contour, and also has a good control effect on the acceleration and deceleration movement of the tool in real-time machining. It is convenient for the processing process to proceed smoothly. In this paper, the tool path generation of NC machining and the improvement of Akima curve in fitting algorithm and its evaluation index are studied, including the following aspects: for different NC machining methods, A tool path with a very different degree of density will be generated. According to the three-dimensional solid model of different types of contours, a relatively good tool path can be generated by selecting the targeted machining mode, considering the internal factors such as machining allowance, step distance, cutting speed, over-cutting phenomenon and other external factors, and so on. In order to facilitate the subsequent tool path spline fitting. In view of the theory of Akima spline fitting algorithm, in this paper, arc length parameterization is used to replace the existing node parameterization, and a recursive fitting algorithm of arc length parameterized Akima spline is proposed in the aspect of parameterization of tool points. The fitting flow is divided into two parts: one is the restriction segmentation of Akima curve, that is, using the error threshold set by double chord and chord tangent error test to judge the chord error of Akima curve segment and corresponding chord length. The tool point and Akima curve are constrained and segmented. The second is the recursive fitting of the constrained tool points, that is, when the number of known tool sites is not less than 03:00, the tangential vectors of the constrained knife sites shared between adjacent curve segments are preserved and extended. The arc length parametrization is used to fit the Akima curve between adjacent constrained tool points. At the same time, the fitting state of the unconstrained node parameterized Akima curve and the arc length parameterized Akima curve of the constrained tool point is compared with an example, and the validity of the proposed algorithm is verified in this paper. Based on two parameterized Akima curves, four types of chord length and rotation angle are divided into four types. On the basis of this, in order to obtain the node tangent vector information of the curve, the maximum chord error, the maximum curvature value and the curvature change rate of the curve are selected as the criteria for judging the shape of the Akima curve in terms of the maximum chord error, the maximum curvature value and the curvature change rate. When dealing with different types of line segments, the tool point fitting of the NURBS curve is added to compare the fitting performance of the three curves under different conditions, and the corresponding relationship between the two Akima parameter curves and the optimal treatment line segment type of the NURBS curve is established. Through the MatLab simulation experiment and analysis, the whole fitting of solid contour is compared with the fitting effect of three kinds of curves, in order to further verify the arc length parameterized Akima algorithm, when the tool point is properly constrained, the fitting curve with good smoothness can be obtained. The better curve shape evaluation index value improves the Akima curve fitting performance of small line segment (initial tool path).
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TG659

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