平行與序列式多軸運動平台之精密軌跡追蹤

Abstract

本論文考慮精密追蹤對現代製造機器的重要，因此提出序列式與平行式機構對精密軌跡追蹤的論題。 精密軌跡追蹤一直是序列式工具機提升加工品質的特徵性質。然而傳統的軌跡控制只侷限於軌跡追蹤，卻忽略切削動態對軌跡的影響性。而卓越的輪廓與表面加工品質，須整合多方面的研究。因此論文第一部分提出一個完整的CNC工具機輪廓誤差的系統，此系統含括軌跡規劃、軌跡路徑、切削過程與工具機結構。在研究中，運用敲擊法及系統辨識法，分別求得工具機結構的主軸參數及x-y平台的轉移函數，以切削實驗驗證平台轉移函數的準確性，並發展軌跡控制法與切削動態系統的結合，以模擬預測真實切削輪廓時，工件的輪廓精度、誤差值及切削力，並分析傳統研究的不足。 平行機構由於機構特徵因素，要精密追蹤輪廓幾乎困難。因此本論文第二部份提出一台具有Z、α及β三自由度的三軸油壓平行機構的輪廓誤差控制方法。在研究輪廓誤差控制中，由於三自由度的單位不同，無法計算輪廓誤差進而進行軌跡控制。因此在研究中，首先定出飛行軌跡的控制點，運用逆向運動學解出三軸位置量，再以三軸位置運用即時插補器插補出一條在Ｌ1、Ｌ2及L3三軸座標系統的軌跡，此軌跡可完全替代Z、α及β座標系的軌跡，再結合多軸交叉偶合預補償方法(MCCPM)控制輪廓誤差。此方法不但可以進行輪廓控制，亦可減少解前向解的時間。 論文第三部分創造一台具有三自由度（Z-α-β）AC伺服馬達的三軸平台，此機構經過精密設計，將奇異曲面排除在工作空間之外。因此在這部份提出兩種不同的軌跡追蹤模式，一是在軸空間中運用MCCPM追蹤軌跡，此方法不需解前向解，因此可解省計算的時間，並可應用於精密加工和固定進給速度的場合。另一種是直接於Z-α-β座標系統的軌跡追蹤，此方法需解前向運動解，而MCCPM因為是速度控制模式則無法應用，但CCS仍然可以。此方法可運用於不需固定進給速度且注重方向運動的軌跡追蹤。

Precision Tracking is important for modern manufacturing machines. This dissertation addressed the topic of precision tracking for machines of both serial and parallel mechanism. For machine tools, which are of serial mechanism, precision tracking is one of their advantageous features contributing to the quality of manufacturing, yet the conventional tracking control is limited to tracking itself, no perspective of cutting is considered. Machining quality is the outcome of both of these processes. The first part of this dissertation proposes the contour errors of a complete CNC machine system. A system model is developed to cover all groups of functions, including trajectory planning, trajectory tracking, cutting process and machine structure. In this study, the parameters of CNC tools structure are determined by impulse method and it is utilized system identification to calculate transfer function of x-y table, which is verified accuracy by cutting experiment. Analysis result reveals the limitations of traditional studies. The second part dealt with motion platform of hydraulic parallel mechanism. Parallel mechanisms could be hardly used in contour tracking because of their mechanism features. This study proposes a link-space real time contour tracking for a 3 DOF (Z、α and β) hydraulic parallel mechanism. The essence of this approach is to convert control points of command trajectory to link space by inverse kinematics. A real-time interpolator was created and the multi-axis cross-coupled pre-compensation control (MCCPM) was constructed for link-space contour tracking. It was shown that a contour-accurate trajectory tracking could be performed which was impossible in the original Z-α-β space. The third part created a ac-electric motion platform of parallel mechanism with no obstacle of singular surface. This part evaluated two different approaches of trajectory tracking, one with forward kinematics, another without forward kinematics. The approach without forward kinematics has the advantage that all proven trajectory tracking schemes can be implemented in its frame. For the application requiring precision trajectory and constant feeding speed, the approach without forward kinematics offered a good platform. For the approach with forward kinematics, no MCCPM is possible, but CCS is still possible. For applications which require only motion with orientation, but no constant speed requirement, the approach with forward kinematics is a good tracking structure.