雙螺桿壓縮機廣泛應用於機械及製冷等產業，具備高穩定性及高效能等特性，機體內由一對相互嚙合之公、母螺桿轉子組成，齒形設計直接影響其接觸行為，進而決定壓縮機之振動與傳動性能。本研究旨在建立雙螺桿壓縮機多體動力學分析方法，探討不同齒形對壓縮機振動與傳動性能之影響。 首先以齒形點資料求取曲率半徑，並以赫茲接觸理論計算轉子間接觸剛性，再依理論內壓縮模型求得工作腔壓力隨嚙合轉角之變化，並可計算轉子所受氣體負載分力及扭矩。接著分別建立不考慮與考慮氣體負載之多體動力學模型，針對三種齒形進行動載模擬，其中BSR424與XSR424規格相近，僅齒形參數些許不同，可觀察齒形設計本身之影響，XSR426尺寸與額定功率較高，可作機型放大之參考，並以接觸力峰對峰值、嚙合頻振幅及傳動誤差峰對峰值來比較其振動與傳動性能。結果顯示兩種條件下三組齒形優劣順序一致，均為BSR424最佳、XSR426次之及XSR424最差。 在此基礎上，以XSR424齒形為優化對象，以齒直角齒條刀創成法搭配Levenberg–Marquardt (LM)法進行齒形擬合，並依均勻設計法規劃參數組合，便可求得兩種模型之傳動誤差峰對峰值及比功率，再以熵權法計算加權值，以此計算出綜合指標，並結合ISIGHT建立近似模型，誤差約1.66%，即可探討齒形參數對綜合指標之影響。結果顯示低壓側齒直角齒條壓力角影響最大，為-27.5%，低壓側節線長次之，為24.3%，其餘參數影響有限。 優化結果顯示，不考慮氣體負載時，接觸力峰對峰值、嚙合頻振幅及傳動誤差峰對峰值分別降低60.8%、67.0%及64.6%，且比功率維持一樣，考慮氣體負載時改善幅度較小但方向一致，顯示優化齒形可在維持效能的前提下有效改善振動與傳動性能。;Twin-screw compressors are widely used in mechanical and refrigeration industries due to their high stability and efficiency. The compressor body consists of a pair of intermeshing male and female screw rotors， and the tooth profile design directly affects the contact behavior between the rotors， which in turn determines the compressor′s vibration and transmission performance. This study aims to establish a multibody dynamics analysis method for twin-screw compressors to investigate the effects of different tooth profiles on compressor vibration and transmission performance. First， the radius of curvature was obtained from the tooth profile point data， and Hertzian contact theory was used to calculate the contact stiffness between the rotors. The variation of working chamber pressure with the meshing angle was then obtained based on a theoretical internal compression model， from which the gas load force components and torque acting on the rotors could be calculated. Next， multibody dynamics models with and without gas loading were established， and dynamic load simulations were performed for three tooth profiles. Among them， BSR424 and XSR424 have similar specifications， differing only slightly in tooth profile parameters， allowing the effect of the tooth profile design itself to be observed， while XSR426 has a larger size and higher rated power， serving as a reference for scaling up the machine model. The peak-to-peak contact force， meshing frequency amplitude， and peak-to-peak transmission error were used to compare vibration and transmission performance. The results showed that the ranking of the three tooth profiles was consistent under both conditions， with BSR424 performing best， followed by XSR426， and XSR424 performing worst. Building on this， the XSR424 tooth profile was selected as the optimization target. A rack-cutter generation method combined with the Levenberg–Marquardt (LM) method was used for tooth profile fitting， and a uniform design method was employed to plan parameter combinations， from which the peak-to-peak transmission error and specific power of the two models could be obtained. The entropy weight method was then used to calculate the weighting values， from which a comprehensive index could be derived. Combined with ISIGHT to establish an approximation model with an error of approximately 1.66%， the influence of tooth profile parameters on the comprehensive index could then be investigated. The results showed that the pressure angle of the rack cutter on the low-pressure side had the greatest influence， at −27.5%， followed by the pitch line length on the low-pressure side， at 24.3%， while the remaining parameters had limited influence. The optimization results showed that， without gas loading， the peak-to-peak contact force， meshing frequency amplitude， and peak-to-peak transmission error were reduced by 60.8%， 67.0%， and 64.6%， respectively， while the specific power remained unchanged. With gas loading， the improvement was smaller but in the same direction， indicating that the optimized tooth profile can effectively improve vibration and transmission performance while maintaining efficiency.
