以齒輪幾何量測點資料進行虛擬單齒腹檢測技術之研究

Study on the Pseudo Single Flank Test by Measured Tooth Geometry Data

林禎祥(Chen-Hsiang Lin)

指導教授 ： 馮展華

國立中正大學/工學院/機械工程學系/博士(2014年)

摘要

齒輪在傳動方面至今佔有不可取代的地位，本文主要是在齒輪的運動誤差上的研究與分析，作者以數值齒印接觸分析建立虛擬單齒腹量測系統，將齒輪量測儀上量出的齒輪點資料或使用理論齒面點資料，以曲面擬合的方式呈現後，在虛擬單齒腹量測系統中只需要齒面的點位置即可計算運動誤差及接觸齒印。虛擬單齒腹量測系統中的B-spline是非常彈性的，可以擬合出各種齒形。數值齒印接觸分析是多齒接觸的，所提出的模擬計算架構是非常適合平行運算的。最小轉角法以及改良的四元素法是用來計算運動誤差與接觸齒印。本研究虛擬單齒腹量測系統會以商業齒輪接觸軟體與真實單齒腹量測結果進行驗證。
虛擬單齒腹量測系統模擬取得面齒輪在齒輪箱內運轉的運動誤差，其模擬裝配包含了標準裝配以及各項誤差的裝配值。進而以快速傅利葉對運動誤差做頻譜分析，將各軸及齒輪的影響拆解出來，並進行分析。本文建立了齒面擬合系統，以B-spline曲面進行齒面擬合，在B-spline各項參數選取法中選擇誤差最小、最適合齒面擬合的方法。量出齒面的三維點資料後，將資料放入虛擬單齒腹量測系統進行模擬，以利取代夾治具製作不方便、齒輪箱不好放置的單齒腹測試機。虛擬單齒腹量測系統所模擬出來的運動誤差結果，再與三次元量測儀上的各項量測數據做比對，完成一套封迴路的檢測方法，最後以齒輪量測儀進行齒面量測再加上虛擬單齒腹量測系統即可對齒輪箱的裝配誤差進行分析。

關鍵字

快速傅利葉轉換 ； 運動誤差 ； 單齒腹量測 ； 曲面擬合 ； 齒輪量測

並列摘要

A numerical tooth contact analysis (NTCA) technique was developed to simulate the single flank test by the gear geometry data measured on a gear measuring center. The proposed NTCA uses only the position vector to calculate continuous transmission error (CTE) and the corresponding contact pattern. The proposed NTCA is very flexible since the tooth surface is measured from real gear and reconstructed as a B-Spline free form surface, no mathematical model for specified gear type is required. The calculation speed of NTCA is fast for the multiple tooth contact since the structure of the proposed numerical algorithm is suitable for the parallel computing. The least rotation angle (LRA) method and the improved quad-tree (QT) search algorithm were used to determine the CTE and the tooth contact pattern. The validation of the proposed NTCA is verified by comparing the contact pattern and CTE of test gear to the theoretical TCA results generated by the commercial TCA software.
The CTE of a gear train is typically measured using a single-flank tester (SFT) or calculated using numerical tooth contact analysis (NTCA). The CTE curve is transformed from the time domain to the frequency domain by using the fast Fourier transform (FFT) to further study the kinematical characteristics of the gear train. However, the result of the FFT is unstable because of signal noise and leakage to the sideband of the spectrum. In this paper, we propose a signal processing technique with a direct function fit (DFF) to improve the assessment accuracy of kinematical characteristics of the gear train. A special filter is also developed to reduce signal noise in the NTCA. Several numerical examples are presented to show the validity of the DFF. Compared with the frequency spectrum determined using the FFT, the frequency spectrum obtained using the DFF is clear-cut and without any sideband, and the kinematical characteristics are more consistent with the geometric data obtained on a gear measuring center.

並列關鍵字

Fast Fourier transform ； Single flank test ； Transmission error ； Direct function fit ； surface fit

參考文獻

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