تحلیل لنگش و پایداری روتورهای با قطر متغیر ساخته شده از مواد هدفمند تحت اثر نیروی محوری و گشتاور پیچشی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان، ایران

2 گروه مکانیک، واحد خمینی شهر، دانشگاه آزاد اسلامی، خمینی شهر، اصفهان، ایران

چکیده

در این پژوهش تحلیل های لنگش و پایداری برای روتورهای ساخته شده از مواد مدرج تابعی تحت نیروی محوری و گشتاور پیچشی بررسی شده اند. روتور بر اساس تئوری تیر تیموشنکو و با در نظر گرفتن اثرات ژیروسکوپیک مدلسازی شده است. قطر روتور و خواص مکانیکی آن در راستای طولی به صورت پیوسته تغییر می کنند و در هر تکیه گاه آن دو فنر انتقالی
و دو فنر پیچشی در نظر گرفته شده اند که قادر به مدلسازی تمامی شرایط مرزی می باشند. با استفاده از قوانین نیوتن معادلات حاکم و شرایط مرزی استخراج شده و با استفاده از روش عددی تفاضلات مربعی حل شده اند. پس از اثبات همگرایی و صحت تحلیل عددی ارائه شده، تاثیر پارامترهای مختلف مانند توان پروفیل، سرعت دورانی، مقدار و جهت نیروی محوری و گشتاور پیچشی بر روی فرکانس های پیشرو و پسرو روتور و پایداری آن بررسی شده اند. نتایج عددی نشان می دهند که افزایش توان در معادله ی تغییرات خواص، وجود نیروی محوری فشاری و گشتاور پیچشی منجر به کاهش تمامی فرکانس های پیشرو و پسرو و سرع تهای بحرانی روتور می گردند و اعمال نیروی محوری کششی نیز باعث افزایش تمامی فرکانس های پیشرو و پسرو وسرعت های بحرانی روتور می شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Whirling and Stability Analyses of FG-rotors with Variable Diameter Subjected to Axial Load and Torsional Torque

نویسندگان [English]

  • K. Torabi 1
  • H. Afshari 2
1 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran
چکیده [English]

In this paper, whirling and stability analyses of a rotor made of functionally graded
materials are investigated. The rotor is modeled based on Timoshenko beam theory and gyroscopic
effects are considered. Diameter and mechanical properties of the rotor are considered to be variable
in longitudinal direction and the rotor is considered to be subjected to axial load and torsional torque.
In order to generalization of the modeling of bearings, each of them is replaced with four springs; two
translational and two rotational acting on two perpendicular directions. Using Newton’s second law,
the set of governing equations and external boundary conditions are derived and solved numerically
using differential quadrature method (DQM). Convergence and accuracy of the presented solution are
confirmed and effect of various parameters including power index, angular velocity of spin, value and
sign of applied axial load and torsional torque on the forward and backward frequencies and stability
of the rotor are investigated. Numerical results show that all forward and backward frequencies and
therefore critical speeds decrease by increase in power law, applying axial pressure load and torsional
torque and increase by applying axial tension force.

کلیدواژه‌ها [English]

  • Non-uniform rotor
  • Whirling
  • Functionally graded materials
  • Differential quadrature method

مراجع

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نشریه مهندسی مکانیک امیرکبیر
دوره 49، شماره 4
اسفند 1396
صفحه 759-772

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