球头铣刀多轴铣削加工的切削刃微元点轨迹模型

Modelling of tooth element trajectory in multi-axis ball-end milling

切削刃微元点轨迹是描述瞬时未变形切削厚度的基础,瞬时未变形切削厚度是铣削力预测的关键.为此,针对球头铣刀多轴铣削加工过程,建立利用位置矢量来准确描述切削刃微元点的轨迹模型.首先,通过建立工件和刀具瞬时坐标系的空间变换模型来描述刀具的位置和位姿;然后,在此基础上结合球头铣刀切削刃的几何特点建立切削刃微元点的空间位置矢量,并进一步推导描述切削刃微元点轨迹的矢量形式;最后,利用C++编程语言和OpenGL图形接口实现切削刃微元点轨迹仿真,并通过对比分析仿真结果与跟踪球头铣刀1∶1三维模型上标记点的位置数据,验证了切削刃微元点轨迹模型的正确性.

The tooth element trajectory is the basis to calculate the undeformed chip thickness which plays an important role in the accurate prediction of multi-axis ball-end milling.The purpose of this paper is to present a novel model describing the tooth element trajectory of ball-end cutter with its position vector in multi-axis milling.First,the transformation model between workpiece and cutter coordinate systems is given to analyze the position and posture of cutter in multi-axis milling.Then,the position vector of tooth element in cutter coordinate system is modelled based on the geometry analysis of ball-end milling cutter.The position and posture trajectories of a cutter are also analyzed in detail.Combing all above-mentioned research,the model of tooth element trajectory is given as a vector in the workpiece coordinate system.Finally,the simulation of tooth element trajectory based on the given model is implemented with the C＋＋ programming language and OpenGL SDK.Comparisons of the simulation results and the position data of the points marked on the geometric model of a cutter show the validity of the given model in this paper.