Introduction to finite element analysis fea or finite. Variation of maximum real part with the spin speed 31 figure 3. Displaced position of the shaft cross section 21 figure 3. Numerical examples and solutions finite elements in analysis and design, vol. Twist2 twist2 is a torsional vibration analysis code that can perform stability analysis and steady state forced response analysis using the nite element method. However, the co element shape functions have been employed recently as well. Behera department of mechanical engineering, national institute of technology,rourkela. A shaft finite element for analysis of viscoelastic tapered. The program was used to perform analysis by determining the campbell diagrams, critical speeds, and. Finite element analysis for vibration characteristic on. An engineering application of the hp version of the finite. Based on the work of archer 1963, 1965, ruhl and booker 1972 used cubic hermitianshape functions to formulate.
Finite element fe analysis helps find correction factors that make more costeffective, simplified analyses as accurate as possible. Finite element methods for rotor dynamics request pdf. Books on rotor dynamics finite element analysis fea. Shaft finite elements for rotor dynamics analysis journal of. Study of modal behaviour of viscoelastic rotors using finite element method page i list of figures s. Types of finite element analysis finite element analysis. The development of finite element formulations for use in rotor dynamics analysis has been the subject of many recent publications.
Nelson and mcvaugh 16 extended this to include gyroscopic effects. Pdf history of rotating machinery dynamics pp 269297 cite as. Design optimization based on finite element analysis provides an efficient methodology to meet the desired objectives related to structural elements. Vaugh 1 first used the finite element method and derived various property matrices. In the formulation of rotor elements, except for gears, the rotor dynamics program rotvib. These are used to simulate behavior of rotational structures that enable the function of various types of machinery. Pdf a conical beam finite element for rotor dynamics. Dynamic analysis of a spindlebearing system based on finite. Applications of rotor dynamics are associated with important energy industry machinery, such as generators and wind turbines, as well as airplane engines and propellers. The objective of this study was to develop a finite element program for the dynamic analysis of geared rotor systems and to study the effect of bearing flexibility, which is usually neglected in simpler gear dynamics models, on the dynamics of the system.
Modeling a rotor whose cross section varies can be done using uniform stepped cylindrical elements, but the number of elements required for the converged results is enormous. It is used mainly for problems for which no exact solution, expressible in some mathematical form, is available. Lateral vibration of a shaft rotor is due to instability, unbalance, or other forces acting on the rotor. A multibody formula for three dimensional brick finite. The wing is modified by attaching ribs and spars in order to increase the strength of the wing. The finite element analysis of the gas turbine blade was done sequentially i. Request pdf finite element methods for rotor dynamics the finite element method for rotors was first developed by ruhl and booker 29.
Application of fuzzy random finite element method on rotor. On the finite element modeling of turbo machinery rotors. Design optimisation and analysis of a quadrotor arm using. A shaft finite element for analysis of viscoelastic. At its most basic level, rotor dynamics is concerned with one or more. A tapered beam finite element for rotor dynamic analysis. Finite element methods for rotor dynamics springerlink. The structural analysis of quad rotor frame is important since it has to withstand the forces due to aerodynamics and gravitational force due to the mounted weights. Finite element modeling of thick rotor deep rotor requires the use of the timoshenko element, which takes care of shear deformation.
In using the finite element method, we have seen that gyroscopic moments responsible for the variation of the natural frequency as a function of the speed of rotation or of the circulatory forces which make the movement unstable from a certain speed in the purely linear frame. Further modeling of doubly tapered rotors and rotors with sharp changes in taper angle. Finite element analysis of a rotor supported with hydrodynamic journal bearings a project report submitted in partial requirements for the degree of batchelor of technology in mechanical engineering by a ranjit kumar 111me0303 under the guidance of prof. A linearly tapered beam finite element incorporating shear deformation and rotary inertia for vibration analysis. Lateral analysis also called rotordynamics analysis simulates the rotating system, calculates the critical speeds, predicts vibration amplitudes, and provides recommendations to reduce vibration risks. The materials used for aircraft wings are mostly metallic alloys. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. Zienkiewiczthe finite element method in engineering science. Whirl speed and stability analysis a revolution in rotor. An advancedmultileveliterativesubstructuring method the dualprimal finite element tearing and interconnecting fetidp method pioneered by farhat et al. This background will be helpful in the identification of rotorbearing system parameters and its use in futuristic modelbased condition monitoring. Finite element analysis fea and computational fluid dynamics cfd human vibration. The purpose of this paper is to present the development and application of a numerical formulation for the structural dynamics and aeroelastic analysis of new generation helicopter and tiltrotor rotor blades.
Rotor dynamics is very important for responses prediction of rotating machineries. The neumann stochastic finite element method based on neumann expansion combined with newmark. As such, it is a numerical rather than an analytical method. For more than a century, we have had a firm grasp on rotor dynamics involving rigid bodies with regular shapes, such as cylinders and shafts. The acronym, dyrobes, denotes dynamics of rotor bearing systems. Dec 16, 2019 finite element modeling of thick rotor deep rotor requires the use of the timoshenko element, which takes care of shear deformation. In the past 20 years, a lot of literatures were focused on numerical simulation of rotor systems, and dynamic models can be divided into three kinds. Dynamic analysis of a spindlebearing system based on.
Finite element modeling rotor shaft rolling bearings system. However, to achieve an equally solid understanding of the. Study of modal behaviour of viscoelastic rotors using. In using the finite element method, we have seen that. Solution procedures and sample results for comprehensive rotor dynamics program for design purposes are presented. The study of the dynamic behavior of geared rotor systems usually requires that torsional and transverse vibratlon modes be coupled in the model, a problem not present for studies of for rotors without gears. Floquet transformations for modal analysis of bladed rotor structures, j. Finite element analysis, rotor bearing system, perturbation scheme, critical speeds, damping, fluid film bearings. In the present paper natural frequencies of the gas turbine unit rotor with varying bearings stiffness are analyzed for axisymmetrical model. A threedimensional beam element is used for the discretization of the rotor. Basic concepts the finite element method fem, or finite element analysis fea, is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces. This background will be helpful in the identification of rotor bearing system parameters and its use in futuristic modelbased condition monitoring.
These works have included the effects of rotatory inertia, gyroscopic moments, axial load, internal damping, and shear deformation. These are used to simulate behavior of rotational structures that enable the function of various types of machineryfrom. This approach provides flexibility factors for reinforced piping joints, adjustment factors for calculating forces transmitted by reciprocating compressors to their foundations, and the rotor stiffening effect. Harmonic response analysis is a technique used to determine the steadystate response of a linear structure to loads that vary sinusoidally harmonically with time and is used to predict the sustained. A conical beam finite element for rotor dynamics analysis. The disc and the bearings are assumed to be rigid, with deformable shaft, the material is isotropic. Computational techniques of rotor dynamics with the finite element method explores the application of practical finite element method fembased computational techniques and stateoftheart engineering software.
Komzsikcomputational techniques of rotor dynamics with finite element method. Users reference manual, 450, intes publication, stuttgart 2014. Rotor dynamics is the key in design and maintenance of all rotating machinery, which. The effects of axial torque were included by zorzi and nelson 37 and nelson 15 gave rotor dynamics elements with the timoshenko beam theory. The finite element method for rotors was first developed by ruhl and booker 29. The field is the domain of interest and most often represents a physical structure. For rotor dynamics studies, the flnlte element method seems. Using ansys software, a finiteelement model for a gear rotor system on flexible bearing has been developed, with martix element, beam element and mass. Dynamic reduction in rotor dynamics by the finite element. Kahraman1 dynamic analysis of geared rotors by finite elements. Developed for the working engineer, dyrobes offers complete rotordynamic analysis, vibration analysis, bearing performance and balancing calculations based in finite element analysis.
Design and finite element analysis of aircraft wing using. Kahraman1 dynamic analysis of geared rotors by finite. Dynamic analysis of geared rotors by finite elements ahmet kahraman, h. Request pdf dynamic strength and shock response analysis of a diesel crankshaft based on finite element and multibody dynamics the strength analysis of a 16 vengine crankshaft was carried. On finite element methods for nonlinear dynamic response klausjurgen bathe massachusetts institute of technology cambridge, ma 029, u. Abstractthe hp hybrid finite element method is used in this paper for the dynamic analysis of a symmetrical onboard rotor on mobile dimensionally stable supports. Shaft finite elements for rotor dynamics analysis citeseerx. Dynamic analysis of geared rotors by finite elements. The program was used to perform analysis by determining the campbell diagrams, critical speeds, and unbalance response. Rotordynamics, also known as rotor dynamics, is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. These works have included the effects of rotatory inertia. I would like to know some good reference books dealing with rotor dynamics. Design and thermal analysis by using finite element method. A conical element for finite element rotor dynamics.
Critical speed and dynamic response of fuzzy stochastic rotor systems are described by the proposed method. Complex modal analysis of a vertical rotor by finite elements method agostini, c. Apdl program based on finite element method has been developed for obtaining full analysis of rotor dynamic in order to investigate the behaviour of spindlebearing dynamic. A finite element structural dynamics model of a beam with an arbitrary moving basepart ii. A problem oriented user environment uidl was created to make input parameters entry, specification of the analysis and results evaluation easy. An engineering application of the hp version of the. Study of modal behaviour of viscoelastic rotors using finite. On the finite element modeling of turbo machinery rotors in. We use finite element analysis to precisely model turbine components and determine the root cause of component issues and to evaluate the remaining life shells, rotors, valves and other integral parts subject to high thermal stress factors. Dynamic stability of a rotor blade using finite element. Abstract in this paper we briefly focus on the nonlinear analysis of solids and structures when these undergo large deformations, possibly over long time durations, and perhaps subjected to fluid. Lateral vibration analysis vibration, dynamics and noise. Gear rotor systems are widely used in many automotive, aerospace and marine applications.
Dynamic analysis of gear rotor systems is essential in describing noise and durability characteristics. In design and finite element analysis of aircraft wing using ribs and spars, an aircraft wing is designed and modeled in 3d modeling software proengineer. Introduction equations of motion structural analysis case studies references history and scientists history and scientists 7 27 1869 ankine r on the centrifugal force on rotating shafts steam turbines notion of critical speed 1895 oppl f, 1905 belluzo, stodola notion of supercritical speed 1919 effcott j the lateral vibration of loaded shafts in the neighborhod. Remaining life finite element analysis mda turbines. Purpose the purpose of this paper is to present the development and application of a numerical formulation for the structural dynamics and aeroelastic analysis of new generation helicopter and tiltrotor rotor blades. Boundary value problems are also called field problems. These are characterized by a curvilinear elastic axis, typically. Pdf a conical beam finite element for rotor dynamics analysis. The dyrobes difference combining power with ease of use dyrobes is a complete rotordynamics software tool that is powerful and versatile, yet easy to learn. Apdl program based on finite element method has been developed for obtaining full analysis of rotordynamic in order to investigate the behaviour of spindlebearing dynamic. The use of dynamic reduction of finite element matrices in rotor dynamics analysis is shown to offer advantages of computational efficiency and modeling accuracy. This program has been developed for the analysis of free and forced vibrations lateral, torsional, and axial of multishaft and multibranch flexible rotorbearingsupport systems.
Kao 1979 journal of sound and vibration 66, 119140. This paper is devoted to finite element analysis of rotors and casings vibration analysis for various gas turbine units. The finite element method fem, or finite element analysis fea, is a computational technique used to obtain approximate solutions of boundary value problems in engineering. Study of the dynamics of rotorbearing using matlab and. Rotordynamic analyses using finite element method a thesis. Today the finite element method fem is the standard method in mechancal engineering to determine static and. The reported finite element models on the rotor dynamics analysis use the c shape functions to generate the element structural matrices and load vectors. Fe finite element fem finite element model mac modal assurance criterion cmp correlated mode pair comac coordinate modal assurance criterion frac frequency response assurance criterion symbols magnitude 2 p2 euclidean norm. Dynamic strength and shock response analysis of a diesel. These are characterized by a curvilinear elastic axis, typically with the presence of tip sweep and anhedral angles. Study of the dynamics of rotorbearing using matlab and finite elements.
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