| 摘要: | 隨著工業 4.0 的推進，擺線齒輪需求量迅速增加，精密加工技術與方法也隨之提升並逐漸普及。與此同時，隨著擺線盤加工精度的提高，精度檢測方法的重要性愈加凸顯。本研究旨在建立一套針對擺線齒輪盤加工精度的評估方法，用以辨識加工過程中的系統誤差，進而提升加工精度。
本方法基於量銷法，利用模擬量銷圓與齒廓接觸於兩點的特性，分析相同銷徑下各齒空處量銷圓心所形成的幾何特徵，以評估對應的誤差。具體而言，本方法可準確評估擺線盤的中心誤差、節距誤差、成型磨對稱軸線誤差，並結合設計的理想曲線數據進行輪廓比較分析，進一步量化進刀誤差。
為實現本方法，研究採用 B-Spline 曲線擬合量測點數據，利用牛頓法計算不同銷徑下的量銷中心，並通過最小平方圓法求取平均中心以減少隨機誤差。結合最小平方法與 Powell 法，進一步計算節距誤差與成型磨對稱軸線誤差，最後根據設計理想曲線數據評估進刀誤差。
在驗證演算法性能時，本研究針對多種誤差類型進行測試，包括輪廓誤差、中心誤差、節距誤差、進刀誤差與成型磨對稱軸線誤差，並生成理想與偏差輪廓進行分析。結果顯示，輪廓誤差對測量精度有顯著影響，例如當輪廓誤差為 ±5μm 時，量測誤差約為 10μm，證實演算法性能與輪廓數據精度密切相關。此外，針對不同加工水準機台製作的擺線盤數據進行分析，驗證結果符合預期。
研究結果表明，所開發的演算法能有效評估擺線盤加工誤差，準確診斷加工精度問題，為後續加工控制與改進提供可靠依據。本方法對於提升加工精度及確保機台穩定運行具有重要意義。
;With the progress of Industry 4.0, the demand for cycloidal gears is increasing rapidly, and precision machining technologies and methods are being upgraded and becoming more popular as a result. At the same time, with the improvement of the machining precision of the cycloidal gear disc, the importance of the precision inspection method becomes more and more important. The purpose of this study is to establish a set of evaluation methods for the machining precision of cycloidal gear discs, which can be used to identify the systematic errors in the machining process, and then to improve the machining precision.
The method is based on the pin gauging method, which makes use of the simulation of the characteristics of the pin circle in contact with the tooth profile at two points, and analyses the geometrical characteristics of the pin circle at each tooth space under the same pin diameter to assess the corresponding errors. Specifically, this method can accurately assess the centre error, pitch error and symmetric axis error of the profile grinding of the cycloidal disc, and further quantify the feed error by combining it with a comparative profile analysis of the ideal curve data of the design.
In order to implement this method, the B-Spline curve is used to fit the measured point data, and Newton′s method is used to calculate the pin centres at different pin diameters, and the least square circle method is used to find the mean centre in order to reduce the random errors. Combining the least square method and the Powell method, the pitch error and the symmetric axis error of the profile grinding were further calculated, and finally the feeding error was evaluated based on the designed ideal curve data.
In verifying the performance of the algorithm, this study tests several types of errors, including contour error, centre error, pitch error, feed error and symmetric axis error of the profile mill, and generates ideal and deviated contours for analysis. The results show that the contour error has a significant effect on the measurement accuracy, for example, when the contour error is ±5μm, the measurement error is about 10μm, which confirms that the performance of the algorithm is closely related to the accuracy of the contour data. In addition, the analysis of the cycloidal disc data produced by machines with different machining levels confirms that the results are as expected.
The results show that the developed algorithm can effectively evaluate the machining error of the cycloidal disc, accurately diagnose the machining precision problems, and provide a reliable basis for the subsequent machining control and improvement. This method is of great significance for improving the machining accuracy and ensuring the stable operation of the machine.
In verifying the performance of the algorithm, this study tests several types of errors, including contour error, center error, pitch error, feed error, and symmetric axis error of the profile mill. Ideal and deviated contours are generated for analysis. The results indicate that contour error significantly impacts measurement accuracy, with an error of ±5 μm resulting in a measurement error of approximately 10 μm. This validates the algorithm′s performance correlation with contour data accuracy.Additionally, an analysis of cycloidal disc data generated by machines with varying machining levels substantiates the expected outcomes.
The findings demonstrate that the developed algorithm can effectively evaluate the machining error of the cycloidal disc, accurately diagnose machining precision problems, and provide a reliable basis for subsequent machining control and improvement. This method is of great significance for improving machining accuracy and ensuring the stable operation of the machine. |
