| 年度 | 95 |
|---|---|
| 計劃編號 | NSC95-2221-E-159-010- |
| 研究學門 | 機構與傳動 |
| 中文計劃名稱 | 飛刀創成之蝸輪與ZK型蝸桿之接觸特性研究(3/3) |
| 執行期限 | 2006-08-01～2007-07-31 |
| 主持人 | 蔡忠杓 |
| 職稱 | |
| 預算 | 1748000 |
| 中文摘要 | 蝸桿蝸輪組(Worm Gear Set)具有高傳動減速比，低噪音及結構緊湊等特點，是工 業上常用的空間交錯軸(Crossed Axes)傳動機構。增加蝸桿蝸輪組之接觸比(Contact Ratio)除了可以提高其定位精度與穩定度外，同時亦可使蝸桿蝸輪組傳遞更大的負 荷。本專題係研究非對偶創成之非 90°交錯角蝸桿蝸輪組，其蝸桿是使用錐狀盤形磨 輪來加以研磨之單包絡 ZK 型蝸桿，並且以飛刀(Fly Cutter)配合非 90°之交錯角之創 成機構來切製蝸輪。此種方式將可增加蝸桿蝸輪組之接觸比，使得蝸桿蝸輪組能傳 遞更高的負載。 在本專題研究計畫中，依據齒輪原理(Theory of Gearing)並利用錐狀盤形磨輪 (Conical-Shaped Grinding Wheel)來推導出單包絡 ZK 型蝸桿之齒面數學模式，並以飛 刀來推導蝸輪之齒面數學模式，再配合微分幾何原理(Differential Geometry)及數值方 法，探討此蝸輪之齒面過切問題，以了解刀具設計參數之改變對其滾削之蝸輪齒面 的影響，並應用齒面接觸分析(Tooth Contact Analysis)技術，分析此蝸桿蝸輪組在具 有裝配偏差時，其傳動誤差(Transmission Errors)及接觸比，而此蝸桿蝸輪組之接觸齒 印則係利用齒面外形法(Tooth Surface Topology Method)求得。最後，本專題研究計畫 使用有限單元法進行此蝸桿蝸輪組在負載下之齒面接觸分析(Loaded Tooth Contact Analysis)。 本專題研究計畫為三年期之研究計畫，計畫之第一年(93 年 8 月至 94 年 7 月)， 係利用錐狀盤形之磨輪，配合切削單包絡 ZK 型蝸桿之加工機構，再應用齒輪原理 及微分幾何的觀念，推導單包絡 ZK 型蝸桿之齒面數學模式。其次再利用軌跡法， 由飛刀之運動方式來定義切製蝸輪所需之蝸桿型滾刀(Worm-Type Hob Cutter)外形， 再配合滾削蝸輪之機構，推導由飛刀所創成之蝸輪的齒面數學模式。通常在壓力角 較小的情況下，被創成之蝸輪齒面很容易產生過切(Undercutting)現象，造成齒根應 力集中以及接觸齒面過小。因此，本計畫利用所建立之齒面數學模式，推導蝸輪齒 面發生過切之條件式，以計算出蝸輪齒面上的過切線，並探討在不同設計參數下齒 面的過切狀況，以供選取適當之刀具參數及加工條件。 本專題研究計畫之第二年(94 年 8 月至 95 年 7 月) ，則將 ZK 型蝸桿之齒面數學 模式與由飛刀創成之蝸輪齒面的數學模式經由座標轉換，建立包含組裝誤差在內的 非對偶創成且非 90°交錯角之蝸桿蝸輪組在實際接觸嚙合時的數學模式，利用此嚙合 模型所發展的齒面接觸分析電腦軟體，即可探討蝸桿蝸輪組在不同的裝配狀況與設 計參數下的傳動誤差及接觸點之分佈。此外，亦利用自行發展的齒輪組接觸比之分 析軟體，來計算此蝸桿蝸輪組在不同的裝配狀況與設計參數下的接觸比。 本專題研究計畫之第三年(95 年 8 月至 96 年 7 月)，則利用齒面接觸外形法來求 解並預測非對偶創成之非 90°交錯角蝸桿蝸輪組之接觸橢圓，亦即假設齒面為剛體的 情況下，以齒面幾何外形為基礎，來預測在不同的齒輪設計參數下，兩齒面的接觸齒 印大小與位置。齒面接觸外形法係假設齒面為剛體的條件下進行齒面接觸分析，然而 在實際的蝸桿蝸輪組嚙合時，齒面的接觸狀況十分複雜，為了得到更真實的結果，將 利用有限單元法(Finite Element Method)來探討負載下兩齒面的接觸情況。由第一年所 推導的齒面數學模式，建立一對接觸齒的實體模型(Solid Model)，再將三維齒面做網 格分割以及設定適當的負載、齒面摩擦力、材料性質及邊界條件...等，然後利用國科 會補助之經費承租 ABAQUS 有限單元應力分析軟體，來模擬齒輪組在負載下的齒面 應力分佈與齒面變形，以得到較接近於實際具有負載嚙合狀態下的齒面接觸分析結 果。 |
| 英文摘要 | Due to high transmission ratios, low noise and compact structures, the worm gear set is widely used in gear-reduction mechanisms for transmitting torques between crossed axes. Increasing the contact ratio of a worm gear set not only improves the orientation precision and transmission stability, but also increases the loading capacity of the worm gear set. In this research project, the worm gear set is composed of the ZK type worm and the worm gear generated by a fly cutter with a non-ninety-degree crossing angle. The proposed approach can increases the contact ratio of a worm gear set, and it makes the worm gear set providing a higher loading ability. In this research project, the mathematical models of the ZK-type worm and the worm gear generated by a fly cutter have been developed based on the worm gear drive generation mechanism and the theory of gear meshing. According to the developed gear tooth mathematical model, the tooth undercutting of the worm gear set can be analyzed. In this research project, the tooth contact analysis technology has been utilized to the investigations on transmission errors and contact ratios of the worm gear set under ideal and error assembly conditions. The contact ellipses of the worm gear set can be obtained by applying the contact surface topology method. Finally, the contact stress contours on the tooth surfaces and the tooth deformation have been investigated by employing the finite element stress analysis software. The proposed research project is a three-year project. In the first year, based on the conical-shaped grinding wheel and the practical cutting mechanism, the mathematical model of the ZK-type worm surface can be derived according the theory of gearing and differential geometry. Furthermore, the mathematical model of the worm gear surface generated by a fly cutter is developed by considering the profiles of cutting tools and the machine-tool settings. Usually, tooth undercutting occurs under some certain conditions such as small pressure angle, which consequently results in stress concentration near the tooth fillets. On the basis of the developed mathematical model of the tooth surface, the condition of tooth undercutting can be obtained and the undercutting line on the tooth surface can be calculated and plotted. Tooth undercutting under various combinations of design parameters was studied. In the second year of the research project, a mathematical model for the worm gear, generated by a fly cutter, meshed with the ZK type worm with a non-ninety-degree crossing angle was set up firstly. Additionally, the assembly errors were considered in the mathematical model of this worm gear sets. Owing to non-conjugate contact for the ZK-type worm and worm gear generated by a fly cutter, the proposed worm gear sets exhibit point contact instead of line contact. Tooth contact analysis (TCA) was adopted to determine the bearing contacts and transmission errors of the worm gear sets. Moreover, the effects of assembly conditions and design parameters on the transmission errors and the contact ratios were also studied. In the third year of the research project, the directions and dimensions of the contact ellipses of the worm gear set can be determined by applying the contact surface topology method. The influences of design parameters on the dimension of contact ellipses were also investigated. The tooth surface was assumed to be rigid when the contact ellipses were determined by contact surface topology method. However, in practical applications, the worm gear set is under load during transmissions. To obtain more realistic simulation results, loaded tooth contact analysis (LTCA) was performed by employing the finite element stress analysis software on the workstation. An automatic meshes generation program for the three-dimensional tooth surface was developed based on the mathematical model proposed in the first year. Furthermore, the contact stress contours on the tooth surfaces and the tooth deformation were investigated. The results obtained from LTCA are more realistic and helpful than those obtained from TCA. |
| 中文關鍵字 | ZK 型蝸桿 |
| 英文關鍵字 | |
| 檔案 | 飛刀創成之蝸輪與ZK型蝸桿之接觸特性研究(3/3)(3,505,303 bytes) |