First, the friction mechanism in the interference fit can be analysed independently and then easily transformed into an equivalent viscous coefficient. As in elementary rotordynamics, the spin speed of the system is as sumed to be. It evolved out of lectures delivered at different universities over the last two decades. Dynamic behaviour of the laval rotor with a transverse crack92008. Two types of rotor models are discussed in this chapter. Zhivotov yuzhnoye state design office dniepropetrovsk, ukraina abstractthe dynamics of the rotor with a moment unbalance was examined for the first time relatively to a rotor with a solid shaft in resilient supports. The rotating damping matrix, also depends upon the rotational velocities. Madyn 2000 for rotor dynamics by delta js 1,580 views. The jeffcott rotor model with linear viscous internal damping is selected as the overall model of the system for two main reasons. Pdf the behaviour of the jeffcott rotor under a vibrating base of. Muszynskas model is used to express the seal force with multiple parameters.
This background will be helpful in the identification of rotor bearing system parameters and its use i. Introduction to dynamics of rotorbearing systems includes numerous examples, from a singledegreeoffreedom system to complicated industrial rotating machinery, which serve to illustrate fundamental dynamic behaviors. The gyroscopic matrix, which depends on the rotational velocity or velocities of the analysis model. The xlrotor computation engine integrates with microsoft excel to increase versatility, enhance automation capabilities, and reduce valuable time spent building and generating reports. Rajiv tiwari, department of mechanical engineering, iit guwahati. Darpe 8 studied dynamics of a jeffcott rotor with slant crack. Sometimes the intricacies of these equations overshadow their simpler physical meaning. The analytical imbalance response of jeffcott rotor. This model, historically referred to as a jeffcott or laval model, is a single.
Complex modal analysis of rotating machinery rotor dynamics is a subset of vibration analysis that deals with the dynamic characteristics of spinning machines. Turbopump rotor dynamics because of high power density and low damping in rocket turbopumps, these machines exhibit in their most extreme form a variety of vibration effects, which are either absent or masked by normal damping mechanisms in other turbo machines. The nonlinear coupling vibration and bifurcation of a highspeed centrifugal compressor with a labyrinth seal and two airfilm journal bearings are presented in this paper. Turbopump rotor dynamics because of high power density and low damping in rocket turbopumps, these machines exhibit in their most extreme form a variety of vibration effects, which are either absent or masked by normal damping mechanisms in. This site is a gateway to technical literature on rotordynamics, including an online database of over 26,000 technical papers presented at conferences related to rotordynamics worldwide since 1974. This document introduced dynamic behavior of a rotor of a disc rotor laval having a transverse crack in the elastic axis. In the present work, a modified jeffcott rotor with linear viscous damping and cubic stiffness excited by harmonic forcing. The third revised and enlarged edition of the book presents an indepth study of the dynamic behaviour of rotating and reciprocating machinery. Pdf the whirl motion of the jeffcott rotor was investigated. The study shows that the frequency of vibration decreases as the distance of the crack from free end increases. A jeffcott rotor with three blades is used and the contacts are described by. A rotor system is modeled as a massless, elastic shaft supported by two nonflexible bearings.
It modifies the apparant stiffness of the model and can produce unstable. It also misses the experimental verification of these numerical models. Dynamics of a jeffcott rotor with slant crack sciencedirect. Dynamics of a jeffcott rotor with slant crack request pdf. In bearing design, the emphasis is on the lubrication, such as minimum film thickness, power loss, temperature rise, peak film pressure, and flow rate. Additionally, often a single frequency force can excite rotor. Hot spot stability analysis with the rotor dynamics software madyn 2000 duration. Murphy is the author of xlrotor, one of the most widely used computer programs for rotordynamic analysis. Regular and chaotic dynamics of a discontinuously nonlinear. Conditions are studied under which the rotor undergoes either forward synchronous whirling or selfexcited backward whirling motions with continuous stator contact. It is the most valuable tool available for anyone working on modeling rotating machinery at the machine design stage or performing further analytical and experimental research on rotating machine dynamics. Introduction to rotordynamics mathias legrand mcgill university structural dynamics and vibration laboratory october 27, 2009. The shaft mass may be included in this analysis by placing yi. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage.
Study of the dynamics of rotorbearing using matlab and. A simple rotating machine the rotating machinery equivalent to the single springmassdamper system is a lumped mass on a massless, elastic shaft. The analysis of a smart jeffcott rotor with direct velocity. So, in this paper in the study of the dynamic behavior of rotors, we are interested in. Below natural frequency the solution was found to be stationary. Objectives of rotordynamics analysis the springmass model synchronous and nonsynchronous whirl analysis of the jeffcott rotor some damping definition. Introduction to rotordynamics analysis machinery vibration.
Figure 8 shows the undamped, steady state, unbalance response of the rotor in figure 5 with an asymmetry along the zaxis a single spring at the twothirds point of the shaft and, in contrast to figure 7, it shows response peaks at both. Jeffcott rotor a jeffcott rotor is the simplest model used in the literature to study the behaviour of a flexible shaft carrying a rigid rotor. In this setup, the bearings are rigid and frictionless. This work is a part of the performance and life enhancement of the t53 engine industrial application project.
Rotordynamics project gutenberg selfpublishing ebooks. An electromechanical rotor model was derived by combining the jeffcott rotor. The study of flexural behaviour of jeffcott was carried out by many authors. In rotor design, the emphasis is on dynamics such as the positions of critical speeds, rotor response due to excitations, and rotor stability. The purpose of this book is to give a basic understanding of rotor dynamics phenomena with the help of simple rotor models and subsequently, the modern analysis methods for real life rotor systems. Rao publication right here, you will certainly get some advantages not to choose the book shop. Nonlinear vibration analysis for a jeffcott rotor with seal. A jeffcott rotor with three blades is used and the contacts are described by large displacement beam theory. Rotordynamics is the preeminent guide to rotordynamic theory and practice. The present research aims at clearly comprehending the dynamics of a vertical jeffcott rotor with a very flexible shaft whose compliance far exceeds that of the support bearings where the often. 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.
Lateral vibration analysis vibration, dynamics and noise. Rotordynamics, critical speed, and stability analysis. Rajiv tiwari,department of mechanical engineering,iit guwahati. The rotor system is rotating with a constant rotational speed, see figure 2 figure 2 a jeffcott. Rotor dynamic laboratory description the rotor dynamics spin laboratory at nasa glenn is designed such as it has the capabilities to spin a subscale test article rotor disk with a maximum outside diameter of 23. The simulating model in this stage provides numerical study of vibration response of the t53 engine incorporated in the orenda aerospace corporation 1. Chapter 1 describes the classical analytical techniques used by engineers for troubleshooting vibration problems. Nonlinear dynamics of a jeffcott rotor with torsional. This paper attempts to compensate for this by explaining the dynamic behavior of spinning rotors without writing any equations. The analysis of the lateral and torsional motion of spinning rotors is replete with applications of newtons and eulers equations. Dynamics of a rubbing jeffcott rotor with three blades. For airfilm journal bearings, the model proposed by zhang et al. Lateral vibration of a shaft rotor is due to instability, unbalance, or other forces acting on the rotor.
The dynamics of a modified jeffcott rotor is studied, including rotor torsional deformation and rotor stator contact. Rotor dynamics is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. Jeffcott rotor, lagrangian, fluid film bearings, whirl orbits. A flexibility matrix for such a rotor is derived based on fracture mechanics concepts and then used in the simple jeffcott rotor model limiting only to lateral and axial degrees of freedom for analysing the response of such rotor to only unbalance excitation. Additionally, often a singlefrequency force can excite rotor. The method was also applied to a modified jeffcott rotor model see figure 2 supported on bearings, with clearances see appendix a which was also published as a paper in nonlinear dynamics, 17. Electromechanical interaction in rotordynamics of cage. In such systems rich dynamics have been found for frequencies above the natural frequency. The case with double zero real part of eigenvalues is analyzed by means of the theory of center manifold and ndimension hopf bifurcation.
A disk with a known mass unbalance is placed in the middle. The problem is characterized by generally nonsymmetric system matrices whose elements depend upon the rotor speed. This background will be helpful in the identification of rotorbearing system parameters and its use i. The rotary shaft and disk are modeled as a rigid jeffcott rotor. By downloading and install the online rotor dynamics, by j. Pdf rotor dynamics without equations semantic scholar. The model has two degrees of freedom and it consists of a lumped mass located at the middle of a flexible shaft rotating at a constant rotational speed. Data collection and analysis software development for rotor. The singlemass jeff cott rotor was first addressed by h.
Thus the jeffcott rotor equation is same as a single degree of freedom mass system in. Application notes static and dynamic balancing of rigid. A jeffcott rotor model is often used to explain the whirling effect. This paper deals with a jeffcott rotor with slant crack.
A numerical study on vibration control of a nonlinear. The purpose of this course is to give a basic understanding of the rotor dynamics phenomena with the help of simple rotor models and subsequently the modern analysis methods for real. Pdf dynamics of a rubbing jeffcott rotor with three blades. Nonetheless, a rubbing jeffcott rotor with three blades has been developed by aidanpaa and lindkvist 15. The concepts in the text are reinforced by parametric studies and numerous illustrative examples and figures. The jeffcott rotor model is obviously an oversimplification of realworld rotors but it nevertheless assists an. The bifurcations and stability of periodic motions on the bifurcation tree are discussed. Dynamics of rotors and foundations, erwin kramer, springerverlag berlin heidelberg 1993 vibration analysis of rotors, chongwon lee, center for noise and vibration control novic, korea, 1993, springer rotordynamics of automotive turbochargerslinear and nonlinear rotordynamics bearing design rotor. In this paper, a bifurcation tree of period1 to period8 motions in a nonlinear jeffcott rotor system is obtained through the discrete mapping method. Apr 30, 2014 hot spot stability analysis with the rotor dynamics software madyn 2000 duration. Stability of the jeffcott rotor with local rubbing.