螺杆转子成形磨削用砂轮廓形的包络-像素设计方法

Envelope-Pixel Design for Generating Grinding Wheel Profile in Forming Screw Rotor

针对双螺杆压缩机核心部件螺杆转子的高效高精制造问题,提出一种基于包络-像素法的螺杆转子成形磨削用砂轮廓形的设计方法,能够在图形空间高效完成螺杆转子成形磨削用砂轮廓形的设计。该方法结合计算机图形学与啮合原理相关理论,建立了螺杆转子与砂轮之间包络运动形成的扫掠面模型,基于Bresenham算法用指定的颜色点亮最佳逼近像素点,通过边界跟踪方法依次分段提取边界像素点,得到精准的成形砂轮廓形数据。通过与传统解析包络法的对比以及实际磨削试验,结果表明,包络-像素法与解析包络法生成的成形砂轮廓形偏差在±0.003 mm,加工转子误差在±0.01 mm,可以满足实际工业应用。另外,包络-像素法可避免传统啮合运动共轭曲面的接触线计算中存在求解非线性方程复杂、异常解和人工干预等不足,为计算机图形学技术在螺旋面刀具廓形设计应用提供新思路,亦适用于齿轮、蜗杆、铣刀等类似共轭产品的设计。

Focusing on high efficiency and high precision manufacturing of screw rotor,which is the core component of the twin-screw compressor,a design scheme based on the envelope-pixel method to generate a grinding wheel profile for forming screw rotor is proposed,which can efficiently complete the design of grinding wheel profile in a graphic space.The enveloping surface of the conjugate motion between the screw rotor and the forming wheel is established with the computer graphics and the meshing theory.Then a specified color is used to light the best approximation pixels of the enveloping surface with Bresenham algorithm,and the boundary pixels of the enveloping surface are captured by boundary tracking for the accurate data of grinding wheel profile.Grinding experiment shows that the deviation between different grinding wheel profiles generated by the envelope-pixel method and the traditional analytical envelope method gets±0.003 mm,and the error of machined rotor in the envelope-pixel method gets±0.01 mm,which meets the requirement of industrial applications.The envelope-pixel method can avoid the shortcomings of solving nonlinear equations,abnormal solutions and manual intervention in the traditional calculation of the contact lines of meshing motion conjugate surfaces.Additionally,this method can also provide a new idea for the application of the computer graphics in design of helical tool,and can be applied to design of other similarly conjugated products,such as gears,worms and milling cutters.