目前市面上看到的擺線齒輪，一般製造方式為滾齒切削後在進行研磨，用擠製製程加工擺線齒輪為新的研究領域，雖然製造時間比較短，但是也存在尺寸、精度不易控制的缺點，對實際生產造成了諸多困擾。
為了解決擠製後成品的精度問題，許多人會用分析軟體先進行模擬，分析產品加工後的狀況再加以修正，以利減少廢料產生。但是模擬後產品的輸出圖檔呈現出不規則的三角網格，讓量測者不知該如何著手，目前也沒有一套對這方面完整的量測方式，所以本論文提出DEFORM 3D三角網格齒形誤差評估與補償，以改善此種情況。本論文首先設立了多個數學模型，將擺線齒輪各項物理量及其做動、修形方式均以算式表示。然後藉助這些數學模型，本文會詳細說明經由模擬，胚料（Workpiece）擠製成齒輪樣品後，要如何運用本論文建立的DEFORM 3D三角網格齒形誤差評估與補償，從樣品中提取出單一截面上的數據點並計算其與理論數值的誤差量，再利用敏感度矩陣算出下模(Bottom Die)單齒的左右齒面補償量，從而進行後續的補償修正處理。
之後還建立了一套全新的冷擠製模擬分析流程，特別改良擠製模具中下模的設計更加適用於實際生產製造。本文亦將充分介紹這套流程的設定細節及其實驗結果，以驗證本論文提出的齒輪量測與補償方式的可行性。

At present, the common manufacturing method of cycloidal gears seen on the market is grinding after hobbing. The extrusion processing of cycloidal gears is a new research field. Although the manufacturing time is relatively short, it also has the disadvantage of difficult to control the size and accuracy, which has caused many troubles to the actual production.
To solve the problem of the precision of extruded products, many people will use analysis software to simulate and analyze the situation of products after processing, and then amend it to reduce waste generation. But after simulation, the output drawings of the products show irregular triangular mesh, which makes the surveyors not know how to start. At present, there is no complete measurement method for this aspect. So this paper proposes DEFORM 3D triangular mesh tooth profile error evaluation and compensation to improve this situation. This paper first established several mathematical models, the cycloid gear and do the physical move, modification way equation is expressed. Then, with the help of these mathematical models, this paper will explain in detail how to use DEFORM 3D triangular mesh to evaluate and compensate tooth profile errors after extruding gear samples with simulated Workpiece, extract data points on a single cross-section from the samples and calculate their errors with theoretical values, so as to benefit further. The compensation of the left and right tooth surfaces of the lower die is calculated by the sensitivity matrix, and then the compensation correction is carried out subsequently.
After that, a new cold extrusion simulation analysis process was established, especially the improved design of the lower and middle die of the extrusion die was more suitable for actual production and manufacturing. To verify the feasibility of the gear measurement and compensation method proposed in this paper, the details of the process setting and the experimental results will also be fully introduced in this paper.

[1] F. L. Litvin and P.-H. Feng, "Computerized design and generation of cycloidal gearings," Mechanism and Machine Theory, vol. 31, no. 7, pp. 891-911, 1996.
[2] J.-H. Shin and S.-M. Kwon, "On the lobe profile design in a cycloid reducer using instant velocity center," Mechanism and Machine Theory, vol. 41, no. 5, pp. 596-616, 2006.
[3] Z.-H. Fong and C.-W. Tsay, "Study on the undercutting of internal cycloidal gear with small tooth difference," JOURNAL-CHINESE SOCIETY OF MECHANICAL ENGINEERS, vol. 21, no. 4, pp. 359-368, 2000.
[4] J. Blanche and D. Yang, "Cycloid drives with machining tolerances," Journal of mechanisms, transmissions, and automation in design, vol. 111, no. 3, pp. 337-344, 1989.
[5] B. Chen, H. Zhong, J. Liu, C. Li, and T. Fang, "Generation and investigation of a new cycloid drive with double contact," Mechanism and Machine Theory, vol. 49, pp. 270-283, 2012.
[6] H.-S. Yan and T.-S. Lai, "Geometry design of an elementary planetary gear train with cylindrical tooth-profiles," Mechanism and machine theory, vol. 37, no. 8, pp. 757-767, 2002.
[7] M. Sramek and A. Kaufman, "Fast ray-tracing of rectilinear volume data using distance transforms," IEEE Transactions on visualization and computer graphics, vol. 6, no. 3, pp. 236-252, 2000.
[8] J. Amanatides and A. Woo, "A fast voxel traversal algorithm for ray tracing," in Eurographics, 1987, vol. 87, no. 3, pp. 3-10.
[9] T.-S. Lai, “Design and machining of the epicycloid planet gear of cycloid drives,” The International Journal of Advanced Manufacturing Technology, Volume 28, Issue7–8,pp 665–670, 2006.
[10] T.-X. Li, X.-Z. Deng, J.-B. Li, J.-J. Yang, “Automatic feedback correction and deviation analysis for tooth surface of spiral bevel and hypoid gear,”Journal of Aerospace Power, 2011-05.
[11] H. Chen, “Error-sensitivity analysis of hourglass worm gearing with spherical meshing elements,” Mechanism and Machine Theory , Vol. 70, pp 91-105, 2013
[12] A. Rahmani-Hanzaki, P.V.M. Rao, S.-K. Saha, “Kinematic and sensitivity analysis and optimization of planar rack-and-pinion steering linkages,” Mechanism and Machine Theory, Vol. 44,pp 42-56,2009
[13] B. Majidi,J. Milimonfared, “Modeling, Design, and Sensitivity Analysis of a Continuous Magnetic Gear Using Finite-Element Method,” Electric Power Components and Systems, Vol. 44,pp1028-1039, 2016
[14] J. G. Blanche, D. C. H. Yang, “Cycloid Drives With Machining Tolerances,” Journal of Mechanisms, Transmissions, and Automation in Design, Volume 111, Issue 3,pp 337–344, 1989.
[15] K. Biernacki, “Selection of the optimum tooth profile for plastic cycloidal gears,”Proceedings of the Institution of Mechanical Engineers, Volume 228, Issue 18,pp 3395–3404, 2014.
[16] Fang, S., Liu, Y., Wang, H., Taguchi, T., and Takeda, R., “Compensation Method for the Alignment Angle Error of a Gear Axis in Profile Deviation Measurement,” Measurement Science and Technology, Vol. 24, No. 5, Paper No. 055008, 2013.
[17] Fang, S., Liu, Y., Wang, H., Taguchi, T., and Takeda, R., “Research on the Compensation Method for the Measruuement Error of Cycloidal Gear Tooth Flank,” International Journal of Precision Engineering and Manufacturing, Volume 15,Issue 10,pp 2065–2069, 2014.
[18] 胡建軍，李小平，2011，DEFORM-3D塑性成形CAE應用教程，北京大學出版社，河北，中國。
[19] Altinbalik, T., Ayer, Ö., “Finite element analysis of gear like form by using lateral and forward extrusion,” TEM Journal, Vol. 3, No. 2, 2014.
[20] Y.-M. Hwang, J.-M. Chen, “Surface permeation and die design during rod extrusion processes,” The International Journal of Advanced Manufacturing Technology, Vol. 69, Issue1-4, pp 397–403, 2013.
[21] K. Abrinia, M. Makaremi, “An analytical solution for the spread extrusion of shaped sections,” The International Journal of Advanced Manufacturing Technology, Vol. 41, Issue7-8, pp 670–676, 2009.
[22] C. H. Cao, L. Hua, S. L. Liu, “Flange forming with combined blanking and extrusion process on sheet metals by FEM and experiments,” The International Journal of Advanced Manufacturing Technology, Vol. 45, Issue3-4, pp 234–244, 2009.