بررسي تحليلي قفل‌شدگي تشديد در سيستم هاي ناميزان دوار و اثر يك ناميزاني دوار آزاد بر رفتار سيستم

Analytical study of resonant capture in rotating unbalanced systems and effect of a free unbalanced disk on system behavior

در سيستم هاي دوار با پايه‌ي الاستيك، ناميزاني سيستم باعث ارتعاشات پايه مي‌شود. اين ارتعاشات نيز موجب اعمال يك گشتاور نوساني به روتور و نوساني‌شدن سرعت دوران مي‌شود. بنابراين يك سازوكار انعكاسي شكل مي‌گيرد كه مي‌تواند رفتاري غيرخطي با طيف متفاوتي از پاسخ ها را به نمايش بگذارد. در مجاورت فركانس طبيعي، ارتعاشات بزرگ پايه موجب افزايش چشمگير توان مصرفي مي‌شود و از افزايش سرعت روتور جلوگيري مي كند. در اين حالت ممكن است سيستم توان كافي براي گذر از تشديد را نداشته و دچار قفل‌شدگي تشديد شود. در اين نوشتار پيشنهاد شده است به‌منظور ايجاد اغتشاش در شكل‌گيري سازوكار قفل‌شدگي، يك ناميزاني آزاد به سيستم اضافه شود. براي بررسي كارايي اين روش، معادلات ديناميكي سيستم استخراج شده و به روش هارمونيك بالانس و روش عددي حل شده‌ است. نتايج به دست آمده نشان مي دهد با افزودن يك ناميزاني آزاد، مي توان محدوده‌ي قفل‌شدگي و امكان گذر از آن را بهبود داد.

Vibration problems in rotating machines can be extremely frustrating and may lead to great damages, reduced reliability, and unpleasant side-effects. Unbalanced rotating masses are a main source of machine vibrations. In an unbalanced rotating system with elastic supports, mass center displacements induce an oscillatory force into the support and cause base vibrations. On the other hand, base vibrations introduce an oscillatory torque to the rotor and cause velocity oscillations. In this way, a reciprocal action forms a complex set of nonlinear equations which depend on actuating torque, giving a wide range of harmonic, periodic and chaotic solutions. Close to the system natural frequency, base’s high amplitude vibrations result in considerable power waste and prevent rotor acceleration. In such a case, system may suffer power shortage and remain in resonance. This phenomenon is named resonant capture. In this article, it is proposed to interrupt capture mechanism by adding a free unbalanced mass to the system. It is predicted that system base vibrations force the added mass to rotate or vibrate, and the reacting forces will affect the base motions. This may delay the capture mechanism and provide enough time for the system to accelerate and escape the capture region. To evaluate the efficiency of the proposed method, an unbalanced rotating system with elastic supports is considered. The nonlinear governing equations of motion are derived and using harmonic balance method, capture region is defined. Numerical results are provided to assess the validity of obtained solutions. Then a free rotating unbalanced disk is added to the system. Using harmonic balance method and numerical solutions, effect of the added free unbalanced disk on the capture range is discussed. Numerical results are provided for different unbalanced added discs and different initial conditions. Obtained results show that the added unbalanced mass can improve the system capability to narrow the capture region and escape it.