乾式螺桿真空泵以一對同步嚙合之圓錐螺旋轉子壓縮輸送氣體，壓縮腔內無需潤滑油，適用於半導體、製藥及化學等對污染敏感之製程。本論文轉子為圓錐形，截面沿軸向連續變化，造成質量分布不對稱，產生動態不平衡合力偶，導致軸承振動、加速磨損及噪音。傳統作法於轉子幾何確定後以移除材料修正，卻在平衡與結構或密封性能間產生取捨。本論文探討於輪廓設計階段即解決不平衡問題，並將此法與傳統質量移除法於同一轉子模型下、以相同合力偶指標及多體動力學模型直接比較。目標轉子為鑄鐵結構，質量14.5 kg，軸向長度191.25 mm，轉速3000 rpm。轉子幾何以五段二維截面定義，再映射為三維螺旋曲面。本論文發展並驗證兩種平衡方法：方法A為雙平面質量移除法，於兩修正平面設計膠囊形凹槽陣列，深度由力矩平衡方程式求得；方法B為輪廓最佳化法，將節距律設計為三段曲線，並以多目標差分進化演算法對六項幾何參數最佳化，同時最大化流道面積並最小化密封線長度與動態不平衡量。結果顯示，方法A移除189.3 g材料（占總質量1.30%），使合力偶降低99.65%（289倍），平衡品質由G2.5提升至優於G0.4；方法B於零材料移除下使合力偶降低99.999996%（達7.4個數量級），流道面積增益6.28%，密封線僅增加0.81%。多體動力學模擬證實：方法A使軸承徑向力振幅降低41.9%，方法B於進氣平面降低38.8%。實務上，轉子輪廓已定型時應採用質量移除法；於初期設計階段，若排量增益足以補償未完全修正之排氣平面不平衡，則應採用輪廓最佳化法;Dry screw vacuum pumps use a pair of synchronized， intermeshing conical screw rotors to compress and move gas without oil in the compression chamber， making them suitable for semiconductor， pharmaceutical， and chemical processes sensitive to contamination. The rotor in this thesis is conical， with a cross-section that varies continuously along its axis， producing an asymmetric mass distribution and a dynamic-unbalance couple that vibrates bearings， accelerates wear， and increases noise. The conventional approach corrects this by removing material after the rotor geometry is fixed， trading off balance against structural or sealing performance. This thesis investigates resolving the unbalance during profile design itself， directly comparing this approach with conventional mass removal on the same rotor model using a shared resultant-couple metric and the same multibody-dynamics model. The target rotor is cast iron， with a mass of 14.5 kg， axial length of 191.25 mm， and operating speed of 3000 rpm. The rotor geometry is defined by a five-segment two-dimensional cross-section， then mapped into a three-dimensional helical surface. Two balancing methods are developed and verified: Method A， two-plane mass removal， sizes capsule-shaped groove arrays at two correction planes， with depths obtained from moment-balance equations; Method B， lead-curve profile optimization， redesigns the pitch law as three connected segments and applies a multi-objective differential-evolution algorithm to optimize six geometric parameters， while maximizing flow area and minimizing sealing-line length and dynamic unbalance. Results show Method A removes 189.3 g of material (1.30% of total mass)， reducing the resultant couple by 99.65% and raising the balance quality grade from G2.5 to better than G0.4; Method B， with zero material removed， reduces the resultant couple by 99.999996% (over 7.4 orders of magnitude)， gaining 6.28% in flow area against only a 0.81% increase in sealing line. Multibody-dynamics simulation confirms these results: Method A reduces bearing radial-force amplitude by 41.9%， and Method B reduces it by 38.8% at the suction plane. In practice， mass removal should be used when the rotor profile is already fixed， while profile optimization should be applied during early design when the capacity gain justifies an incompletely corrected discharge-plane unbalance
