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تأثیر لقی تکیه گاه های یاتاقان غلتشی بر پایداری روتور با بکارگیری روش اجزای محدود غیرخطی
سجادپور، مهدی Sajjadpour, Mehdi
The Effect of the Clearance of the Rolling Bearing Supports on the Stability of the Rotor Using Nonlinear Finite Element Method
Sajjadpour, Mehdi | 2022
205
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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 57395 (45)
- University: Sharif University of Technology
- Department: Aerospace Engineering
- Advisor(s): Hosseini Kordkhili, Ali
- Abstract:
- Rotating shafts are widely used in various industries, especially aerospace industries such as engines, compressors and turbines. Due to the sensitivity of these shafts, considerable efforts have been made by researchers to investigate their dynamic behavior. In this thesis, the finite element numerical method has been used to analyze and investigate rotating shafts using a pipe elbow element. This element has four nodes and six degrees of freedom in each node, that is, three degrees for translation and three degrees for rotation relative to the general coordinate system and has a circular cross section. In the linear part of the dynamic formulation of the finite element for rotating axes in the presence of rotation effects, using the kinetic energy and the obtained potential and the mass, stiffness, gyroscopic and centrifugal terms that appear as volume integrals in the Lagrange equation, using a method The reduced numerical integration is obtained using the Newton-Cotes formula, and then the linear Newmark method is used to solve the dynamic linear equation. In the non-linear part, using the governing equilibrium equations of solids based on the Lagrangian point of view, the formulation of the finite elements for the geometrical non-linear dynamic analysis of rotating rotors has been derived. While deriving the equations of the finite elements governing the problem, in order to reduce the linearization errors of the nonlinear equations resulting from the principle of virtual displacement, a new linearization method is used. Using this linearization method corrects the linear and non-linear stiffness matrices as well as the vector of internal forces and the mass matrix. In order to use this formulation to analyze non-linear problems of rotating axes, inertial, Coriolis and centrifugal forces are also included in the virtual work equation and during the numerical solution process, a repeated design in each development of the solution based on the modified Newton-Raphson method to obtain Equilibrium is achieved. Finally, a finite element formulation for the nonlinear dynamic analysis of the rotor is obtained empirically, and the nonlinear Newmark method is used to solve this equation. After deriving the formulation of the dynamic finite elements of rotating shafts, these formulas are applied in a developed code and using that some sample problems that were previously experimentally, analytically or numerically by other researchers and using other conventional elements such as beam element and solid element was dissolved, analyzed and compared with the obtained results. Also, the effects of the support and clearance on the dynamic behavior of the rotor have been investigated. The obtained results indicate the accuracy and correctness of the present formulation, while compared to numerical solutions and similar finite elements, the number of elements is much less and the computational cost is very low
- Keywords:
- Nonlinear Finite Element Method ; Rotating Shafts ; Dynamic Behavior ; BackLash ; Pipe Elbow Element ; Support Effects ; Rolling Bearing ; Rotor Stability
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