螺旋齒輪之齒面修整加工方法研究

沈正國(Cheng-Kuo Shen)

指導教授 ： 馮展華

國立中正大學/工學院/機械工程學系/碩士(2013年)

摘要

由於現代齒輪磨齒機的機械精度越來越好，標準漸開線螺旋齒輪很容易就能達到加工精度的要求，但螺旋齒輪被廣泛運用於各種產業機械，標準螺旋齒輪無法滿足多方面運用的需求，因此齒輪製造者常常對齒面進行修整，以改善齒面接觸狀況，減少齒面之間產生的邊界接觸而造成多餘的磨耗，導致齒輪壽命降低。本文針對以蝸桿式砂輪為刀具的螺旋齒輪創成法進行齒面修整方法研究，改善由於齒輪與蝸桿三維螺旋造型(結構)使螺旋齒輪在進行齒面修整時，隨螺旋角及修整量增加時所產生齒面的扭轉現象。
本文根據常用的CNC磨齒機台的機械自由度及西門子電子齒輪箱(Electronic Gear box)的功能推導出創成式磨齒機的數學模型，利用敏感度分析法建立齒面拓撲誤差敏感度矩陣，以矩陣的行列式值及標準差(Standard Deviation)判斷敏感度矩陣的秩(Rank)及相依的機械設定係數，再根據欲修整的齒面拓撲形狀，以奇異值分解法(Singular Value Decomposition)來求得機械設定係數的修整量，產生CNC磨齒機台的加工路徑，使標準漸開線螺旋齒輪經齒面修整後，產生Twist-free之齒面。

關鍵字

抑制齒面扭轉 ； 齒面修整 ； 敏感度分析 ； 西門子電子齒輪箱

並列摘要

The tooth form accuracy of the standard involute helical gear is relatively easy to achieve high grade due to increasing precision of the modern CNC gear grinding machine. However, helical gear is widely utilized in various industrial applications and the standard involute tooth form cannot satisfy the demand of versatile applications. Tooth surface modification is developed to improve the kinematical characteristics and to reduce the possibility of edge contact between the tooth surfaces in order to extend the service life of gear. The aim of this thesis is to develop a methodology to modify tooth surface topology based on the CNC generating gear grinder with worm grinding wheel. Hopefully, the tooth surface twist on the longitudinal crowned helical gear can be reduced or eliminated even in the case of large helical angle with big amount of crowning.
According to the Degree of Freedom (DOF) of modern CNC gear grinding machine and the Electronic Gear (EG) control module provided the Siemens, a mathematical model is developed to simulate the tooth surface generating grinding. The DOF of each CNC axis is modeled as 6 order polynomial or B-spline and a sensitivity analysis is done with respect to the coefficient of polynomials. The rank of sensitivity matrix and standard deviation are used to judge the number of independent variables and eliminate the dependent DOF from sensitivity matrix. Finally, the machine setting correction is calculated by the Singular Value Decomposition (SVD) to approaching the desired tooth topography. Several numerical examples are presented in this thesis to show the validation of the proposed methodology in twist-free tooth surface modification.

參考文獻

[1] Litvin, F. L., Zhang, J., and Handschuh, R. F., 1988, “Crowned spur gear: Methods for generation and tooth contact analysis － Part2: Generation of the pinion tooth surface by a surface of revolution, ” ASME Journal of Mechanisms, Transmissions and Automation in Design 110 343－347.

[2] Umeyama, M., 1995, “Effects of Surface Modification on the Transmission Error of a Helical Gear Pair and its Optimization, ”日本機械學會論文集(C編) 61卷582 號, pp.8－15.

[4] Iwase, Y., and Miyasaka, K., 1996, “Proposal of Modified Tooth Surface with Minimized Transmission Error of Helical Gear,” JSAE Journal Review 7 pp.191－212.

[5] Radzevich, S. P., 2003, “Design of shaving cutter for plunge shaving a topologically modified involute pinion ,” Journal of Mechanical Design, Transactions of the ASME Vol.125 (3), pp. 632－639.

[6] Radzevich, S. P., 2005, “Computation of parameters of a form grinding wheel for grinding of shaving cutter for plunge shaving of topologically modified involute pinion,” Journal of Manufacturing Science and Engineering, Transactions of the ASME Vol.127 (4), pp. 819－828.