具轉角平滑化之創新五軸插補器設計

本文主要是開發創新五軸插補器以生成平滑的進給率曲線和刀具中心點軌跡之命令，所提出的方法可依據各驅動軸的最大速度、加速度、急衝度以刀尖點的最大進給速度，並在給定轉角輪廓誤差的條件下進行插補器加減速規劃。首先，基於齊次轉換矩陣推導了五軸工具機的順逆向運動學方程式，以建立驅動軸與刀具姿態之間的相對關係，接著計算插補程序所需資訊，而核心技術包含速度限制公式與轉角平滑化，速度限制公式調整最大速度以確保切線和軸向的速度符合限制，轉角平滑化功能藉由考量刀具和運動軸方向上的急衝度、加速度以及速度來產生平滑的運動軌跡，以解決多線段相接時向量改變導致轉角速度不連續的問題，同時確保轉角輪廓誤差在給定的範圍。最後，搭配海德漢iTNC530控制器的五軸雕刻機上進行實驗，並經由相同的參數設定，將所發展的方法與海德漢控制器所輸出的五軸插補點進行比較，以分析所提出方法之優缺點。

This developed novel five-axis interpolator can generate a smooth feedrate profile and tool center point (TCP) trajectory. The proposed method can provide maximum feedrate of TCP according to each drive’s maximum velocity, acceleration and jerk; according to the setting of corner profile tolerance to carry out the interpolator’s acceleration and deceleration feedrate scheduling. First, the generalized forward and inverse kinematics equations of five-axis machine tools are derived to establish the relative relationship between drives and tool posture based on the homogeneous transformation matrix. Next, the information required for the interpolation process is calculated. The core technology includes TCP feedrate constraint formula and kinematic corner smoothing. The TCP feedrate constraint formula regulates the maximum speed to ensure that the tangential and axial speeds meet the limits. The kinematic corner smoothing algorithm considers the jerk, acceleration and velocity of TCP and motion axes to produce a smooth motion trajectory that could solve the problem of corner speed discontinuity and ensure the corner tolerance at the same time. Finally, an experiment was carried out on a five-axis engraving machine equipped with a Heidenhain iTNC530 controller, and the same parameter settings were used to compare with the five-axis interpolation points output from the Heidenhain controller and then the pros and cons of the proposed method were analyzed.