擠出機是塑膠成型機械中，將塑料強制送入成型模具中之重要設備。本研究針對同轉向嚙合型雙螺桿擠出機轉子之成形磨輪，建構其幾何數學模式及設計限制條件，分析磨輪安裝參數對接觸線長度以及磨輪厚度的影響。首先應用坐標轉換理論，由螺桿端截面之數學模式導出螺桿螺旋面方程。其次根據逆包絡理論，建立螺旋面與磨輪之接觸線條件方程，將螺桿螺旋面表示在磨輪坐標系並與接觸線條件方程聯立之後，導出磨輪之迴轉面數學模式。為了完整研磨出螺桿螺旋面，接觸線必須涵蓋整個螺旋面之範圍，據此條件得到刀具安裝參數之限制條件。最後，應用數值方法探討刀具安裝角對接觸線長度以及磨輪厚度的影響。數值計算結果顯示，磨輪刀具迴轉軸到螺桿軸垂直之距離固定時，磨輪有最大安裝角之限制，若安裝角大於此最大安裝角，則螺桿螺旋面無法經由成型磨輪包絡得到。此外，當磨輪厚度愈大，接觸線長度愈短；反之，磨輪厚度愈小，接觸線長度愈長。

This paper has investigated the design limitation of form grinding wheel for helical surface of twin screw extruder. The effects of varying assembly parameters on the length of contact and the thickness of grinding
wheel are studied. First, knowing the geometry of screw on the transverse plane, equations of helical surface of screw are derived based on the theories of coordinate transformation and gearing. Secondly, based on the
inverse envelope theory, the condition of contact between grind wheel and screw and the equation of grind wheel are created. On the condition that contact line should cover all the field of screw, the limitations for assembly parameters are investigated. Finally, the effects of varying parameters on the length of contact and the thickness of grind wheel are studied. According to the numerical results, the maximum value of assembly
angle should be limited if center distance keeps fixed. The increase in thickness of grinding wheel results in a decrease in length of contact line. The decrease in thickness of grinding wheel results in an increase in length of contact line.