滾齒凸輪接觸特性、製造與組裝之研究

Abstract

由於滾齒凸輪具備高速運轉及可以提供精密分度之特性而廣泛應用於各項自動化之應用案例中。以往對於滾齒凸輪之創成機制及在理想狀況下製造組裝特性已有深入的研究。然而，在實際之製造組裝條件之下，各項誤差之產生實在無法避免，致使理想狀況之線接觸條件不復存在；使得凸輪曲面與凸輪轉子之間的接觸條件轉變成為點接觸。基於實際之點接觸條件，本論文之研究針對分度式滾齒凸輪機構之接觸特性、製造之過切條件及組裝性質。 凸輪機構使用之夀命週期決定於實際的接觸應力。當二個曲面體受負荷作用而做彈性接觸時，二接觸面之間將衍生出接觸橢圓區域。而其伴隨而生之接觸應力將可能造成接觸曲面之損壞，而其形成之接觸橢圓亦將影響曲面之間的潤滑特性。本論文將就滾齒凸輪機構之接觸特性，包括凸輪接觸曲面之主軸曲率、主軸方向，接觸橢圓及接觸赫茲應力等，在點接觸之條件下，利用齒輪原理做有系統之研究。 共軛運動機構之接觸曲面若發生過切，將嚴重影響其運動及動態特性。以往對凸輪機構過切條件之研究，多係針對單一的個別案例。本論文提出無因次化過切條件之數學模型，據此可決定避免過切發生其設計參數之可行區間。此分析結果可提供設計工程師對各項設計條件進行整體評估時，直接而方便的決定避免過切發生的可行設計區間。 本論文中在個人電腦上發展一套自動整合商用套裝分析軟體Mathematica與多功能最佳化分析軟體MOST之最佳化設計流程。在此一設計流程中，設計者可以根據設計參數之實際條件，完成連續及離散型設計參數之最佳化設計。 最後，製造誤差造成對凸輪組裝性能改變的最小變異條件的組裝概念，被用來達成穩健公差設計。此一公差演算規則是依據實體組裝模型、齒面接觸分析技巧及矩陣原理而建立，可以直接以解析法則求得穩健條件之公差配置。此一穩健公差設計之方法並不限於凸輪機構，更而可以方便整合於各類型機構之公差設計。期盼本論文之研究結果將有助於工業界提高滾齒凸輪機構之製造及組裝之精度及品質。

Roller gear cams are widely used in the industry for indexing. Compared with conventional indexing cams, roller gear cams require less space and provide accurate, high-speed motions. To date, most studies have been devoted to develop generation models based on the ideal condition of line contact between the cylindrical type of cutters and cam surfaces. However, due to manufacturing and assembly errors, contacts of a roller gear cam become point contacts rather than line contacts. The bearing contact, the undercutting condition and the assembly tolerance were studied based on the realistic of point contact model in this study. The capability of a cam mechanism for an acceptable lifecycle deeply depends on the stress distribution in the practical contact. When two elastic bodies with curved surface transmit loads from one to the other at the point or line contact, contact area can be developed, and accompanied by compressive contact stress, which may effect the lubrication property, even more, may cause fatigue damages on both of the engaged surfaces. For the idea to study of bearing contact properties, the principal directions and curvatures of the cam surface, the contact ellipse and the Hertzian contact stress are studied in sequence based on gearing theory. Undercutting is very detrimental to the kinematic and dynamic performance. Up to now, most studies on the undercutting condition of the roller gear cam were case by case. A mathematical model for the surface profile of the roller gear cams in dimensionless space is proposed. According to this model, the conditions for non-undercutting are generated with procedure to determine the feasible condition region that is free from undercutting is developed in the dimensionless space. This result can be employed with the design approach to determine the feasible region of design parameters. An integrity and robustness of optimization approach is developed that made engineers take account of all aspect of design, possibly and easily. The studies in this thesis can help engineers to improve the design and manufacturing with higher accuracy and quality of roller gear cam mechanisms. Finally, the concept of the robust assemble condition under the minimum variations caused by manufacturing errors is used to achieve the robust tolerance design. The tolerance algorithm is constructed based on the 3-D assembly model, the tooth contact analysis (TCA) technique and the condition number for the theory of matrix. The investigated results demonstrated in, but not limit to, understanding of the assembly nature of the roller gear cam, and can be easily employed for other type of tolerance design. The results are most helpful to the design and manufacturing of the roller gear cam mechanisms with high accuracy and quality.