平移式滾子從動件圓柱形凸輪之設計與分析

相較於盤形凸輪，圓柱形凸輪具有能改變空間中運動傳遞方向的優點，因此圓柱形凸輪非常適用於非平行輸入/輸出軸間的運動轉換。由於圓柱形凸輪輪廓與從動件輪廓可視為一組相互嚙合的共軛齒型，因此本文利用由Litvin所提出的共軛曲面法來計算圓柱形凸輪輪廓，並藉由微分幾何之理論來探討凸輪輪廓的曲面特性。　　首先，本研究利用共軛曲面法求得每一瞬間圓柱形凸輪和滾子從動件的接觸線段，而所有接觸線段所形成的直紋曲面即為圓柱形凸輪的輪廓面。本研究結果發現離凸輪旋轉中心軸越近之接觸點的壓力角越大，而過大的壓力角不利於圓柱形凸輪將力量傳遞至從動件。因此，圓柱形凸輪之內徑不宜過小。另外，本文亦提及兩種加工刀具相對於圓柱形凸輪之配置，兩種刀具配置皆會造成輪廓誤差，適當地選擇加工方式將有助於同時滿足精度與成本的考量。此外，此研究同時分析輪廓曲面之曲率並檢測過切現象，並且探討各個設計參數對過切現象的影響。最後，本文利用赫茲接觸應力理論分析接觸點之最大接觸應力，以及計算圓柱形凸輪之輸入扭矩。根據本研究結果發現，在空間容許的考量下，應盡可能設計較大尺寸的圓柱形凸輪，否則小尺寸的凸輪將對加工誤差、力量的傳遞、過大的接觸應力以及過切現象等皆有不良的影響。本文中所提及的設計與分析圓柱形凸輪機構之理論可適用於其他的空間凸輪機構。

關鍵字

共軛曲面；空間凸輪；圓柱形凸輪

並列摘要

Compared with disc-cam mechanisms, cylindrical cam mechanisms have the advantage of shifting the direction of spatial motion transmission. Hence, cylindrical cam mechanisms is quite adequate for realizing the input-output transmission of two non-parallel joint axes. Since the surface of cylindrical cam and that of follower can be regarded as a set of conjugate gear tooth profiles, this research employs the theory of conjugate surface proposed by Litvin for calculating the cylindrical cam profile and apply theory of differential geometry for investigating the characteristics of cam profile. First, this research applies theory of conjugate surface for locating the contact line between the cylindrical cam and the follower at every instant. These contact lines in space form a ruled surface which is the cylindrical cam profile. The research indicates that the pressure angle is larger for the contact points closer to the axis of cam rotation. The force transmission may deteriorate sharply due to larger pressure angles. Therefore, it is recommended to avoid designing the cylindrical cam with smaller inner diameter. In addition, this work addresses two arrangements of the cutting tool for manufacturing cylindrical cams. Both of two arrangements of the cutting tool may result in the deviation of the cam profile at a certain level. Appropriately choosing the way of manufacture may help meet the trade-off between precision and cost. Moreover, the curvature of surface of cylindrical cam profile is analyzed for detecting the undercutting phenomenon. The impacts of design parameters on the undercutting phenomenon are included in this work as well. Finally, we adopt the contact stress theory developed by Hertz for analyzing the maximum contact stress of contact points and calculate the input torque used for driving cylindrical cam mechanisms. In conclusion, the inner diameters of cylindrical cams, subjected to available space, should be designed as larger as possible. Otherwise, a smaller cam size may lead to considerable deviations of cam profile, inefficient force transmission, larger contact stress and undesired undercutting. The present method for designing and analyzing cylindrical cams mechanisms can be comprehensively applicable to other types of spatial cam mechanisms as well.

並列關鍵字

conjugate surface ； spatial cam ； cylindrical cam

參考文獻

[1] Chen, F.A.,Mechanics and Design of Cam Mechanisms, Pergamon, New York, 1982.

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[2] Kim, H. R.,and Newcombe, W. R., “The Effect of Cam Profile Errors and System Flexibility on Cam Mechanism Output,” Mechanism and Machine Theory, Vol. 17, No. 1, 1982, pp. 52-72.