CNC控制器之Nurbs曲線插補技術發展

NURBS interpolation algorithm for CNC controller

曾聖戎(Sheng-Jung Tzeng)

指導教授 ： 賴景義

國立中央大學/工學院/機械工程學系/碩士(2006年)

摘要

隨著CNC工具機設備的進步，傳統以線段插補的路徑規劃方式已不能滿足高速度、高精度的要求，取而代之的是以Nurbs曲線做為路徑規劃，進行切削。本研究的目的，是以可變進給速率的方式，在對Nurbs曲線進行插補的過程中，依照曲率變化的狀況，規劃出能滿足要求的速度、加速度、急衝度限制，且為高精度的加工路徑。

由於工具機進行加工時必須考慮機器的性能，又需避免因急衝度過大使機器產生震動，因此在各位置點之速度決定上，必須以急衝度、加速度控制及精度作為速度規劃的主要考量。本文先依照曲線的曲率變化，在滿足弦長誤差的限制下，對整條曲線之路徑點進行估算，並使最大加速度與最大急衝度在允許限制內；接著由輸出結果中找出有速度變化趨勢的點作為斷點，此處「有速度變化趨勢」是指加速度等於零之段落的起點或終點，將該點視為斷點；接著再以斷點為指標，進行第二階段的即時插補。由於以斷點作為速度的指標，因此即時插補所要考量的條件相當簡單，計算上花費的時間很短，可以滿足加工即時性。

CNC加工路徑多半具有相當的複雜度，不能以單一條Nurbs曲線表示，因此加工路徑必須劃分為多條曲線組成。本研究針對多條曲線情況考量加工路徑規劃，包含預視線數的計算、曲線間不同連續性的處理、加工道次終點、以及短曲線的規劃，透過另外的處理動作使多曲線規劃路徑的速度仍能保持一定連續性。

本研究在以上限制的條件下進行NC路徑點與速度規劃，並進行電腦模擬，模擬結果顯示，輸出路徑的弦長誤差、速度、加速度和急衝度，均能夠滿足預設的規格與限制條件。本文也將顯示多種曲線之運動軌跡，說明本曲線插補方法的特性，並驗證其可行性。

關鍵字

Nurbs曲線 ； 進給速度控制 ； 曲線插補

並列摘要

The control of the maximum acceleration and jerk in the trajectory planning of the CNC controller is very important because it affects the smoothness of the machined surface substantially. We proposed a parametric interpolator composed of a look-ahead stage and a real-time sampling stage for jerk-limited acceleration planning. A pre-sampling process was implemented in the look-ahead stage to identify the segment points, where the acceleration changed across zero. A check of the acceleration and jerk was implemented and the feedrate was modified accordingly. In addition, a backtracking process was carried out during the deceleration stage to ensure that the modified feedrate was satisfied. In the real-time sampling stage, an acceleration profile based on constant jerk was implemented for each region between two segment points. With this algorithm, we ensured that both the chord error and the maximum acceleration and jerk were within the allowable limits. Also, it kept the similarity of the speed profiles for adjacent cutting paths in zigzag machining.

In addition, we discussed the problem for the NC paths of multiple curves and provided solutions for each of them. Several computer simulations were also presented to demonstrate the feasibility of the proposed approach.

並列關鍵字

Nurbs interpolator ； feedrate control

參考文獻

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