An Instability Analysis Procedure for Three-Level Multi-Bearing Rotor-Foundation Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 753-762 ◽  
Author(s):  
N. F. Rieger ◽  
S. Zhou
Keyword(s):  
System Model ◽  
Complex Eigenvalue ◽  
Rigid Rotor ◽  
Turbine Generator ◽  
Instability Analysis ◽  
Rotor Systems ◽  
Flexible Foundations ◽  
Threshold Conditions ◽  
Flexible Supports ◽  
The Stability

A procedure for the instability analysis of three-level multi-span rotor systems is described. This procedure is based on a distributed mass-elastic representation of the rotor system in several eight-coefficient bearings. Each bearing is supported from an elastic foundation on damped, elastic pedestals. The foundation is represented as a general distributed mass-elastic structure on discrete supports, which may have different stiffnesses and damping properties in the horizontal and vertical directions. This system model is suited to studies of instability threshold conditions for multi-rotor turbomachines on either massive or flexible foundations. The instability condition is found by obtaining the eigenvalues of the system determinant, which is obtained by the transfer matrix method from the three-level system model. The stability determinant is solved for the lowest rotational speed at which the system damping becomes zero in the complex eigenvalue, and for the whirl frequency corresponding to the natural frequency of the unstable mode. An efficient algorithm for achieving this is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. A second example discusses a flexible rotor with four damped-elastic bearings. The third case compares the stability of a six-bearing 300 Mw turbine generator unit, using two different bearing types. These applications validate the computer program and various aspects of the analysis.

scholarly journals Smooth enlargement of human standing sway by instability due to weak reaction floor and noise

2016 ◽  
Vol 3 (1) ◽  
pp. 150570 ◽  
Author(s):  
Tetsuro Funato ◽  
Shinya Aoi ◽  
Nozomi Tomita ◽  
Kazuo Tsuchiya
Keyword(s):  
Nonlinear Control ◽  
Neurological Disorders ◽  
System Model ◽  
Quiet Standing ◽  
Body Sway ◽  
Intermittent Control ◽  
Dynamic Reaction ◽  
Weak Reaction ◽  
Integral Control ◽  
The Stability

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyses the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.

Optimization of Bearing Locations for Rotor Systems With Magnetic Bearings

1995 ◽  
Author(s):  
Sriram Srinivasan ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett
Keyword(s):  
Design Process ◽  
Magnetic Bearing ◽  
Rotating Machinery ◽  
Rotor Systems ◽  
Infinity Norm ◽  
Multi Stage ◽  
Scalar Measure ◽  
Bearing Design ◽  
The Stability ◽  
Practical Measure

This paper presents a method for quickly evaluating the effect of changes in bearing location on bearing design for stability of rotating machinery. This method is intended for use by rotating machinery designers to select the “best” bearing locations prior to the bearing design process. The purpose of the method is to improve the design process by separating the problem of determining the “best” bearing locations from that of determining the actual bearing design. The method is independent of the type of bearing employed. For each candidate bearing configuration, the method provides a scalar measure of the relative ability of bearings to meet stability specifications. Within certain limits, the stability specifications are defined by the designer. The scalar measure is used to rank the candidate bearing locations and thereby select the best one. The scalar measure is compared to a practical measure of magnetic bearing design such as the infinity norm of the controller for an example design of a multi-stage centrifugal compressor.

Dynamical properties about ultrasonic vibration assisted drilling of TiBw/TC4 composite

2020 ◽  
pp. 095440542096843
Author(s):  
Yong Feng ◽  
Haoxiang Wang ◽  
Min Zhang ◽  
Zihao Zhu ◽  
Xiaoyu Wang ◽  
...  
Keyword(s):  
Ultrasonic Vibration ◽  
Cutting Tools ◽  
System Model ◽  
Force Model ◽  
Drilling Process ◽  
Drilling Force ◽  
Dry Cutting ◽  
Analysis System ◽  
The Stability ◽  
Three Degree Of Freedom

TiBw / TC4 composite material was used as the machining object of Ultrasonic vibration assisted drilling (UVAD), the single directional three-degree-of-freedom dynamical system model was established. The dynamic signal test and analysis system was used for modal experiment to identify the parameters in the model. Under the condition of dry cutting, the drilling axial force and tool vibration in the drilling process are studied. The results showed that the maximum values of the predicted and measured axial drilling force were 412.5N and 439.6N respectively, and the error rate was 6.165%, which verified the reliability of the predicted axial drilling force model. For cutting tools, the average amplitudes of simulated vibration and measured vibration were 0.1124mm and 0.1151mm respectively, with a difference of 2.402%, and the overall trends were the same, which verifies the reliability of the dynamical model. Finally, the stability of drilling process was analyzed, and the frequency and amplitude of ultrasonic vibration were analyzed. The results show that in order to expand the unconditional stability region, it is more efficient to increase the amplitude than to increase the frequency.

Comparison Between Linear and Nonlinear Transient Analysis Techniques to Find the Stability of a Rigid Rotor

1999 ◽  
Vol 121 (1) ◽  
pp. 198-201 ◽  
Author(s):  
Ram Turaga ◽  
A. S. Sekhar ◽  
B. C. Majumdar
Keyword(s):  
Transient Analysis ◽  
Stability Limit ◽  
Journal Bearings ◽  
Quantitative Comparison ◽  
Rigid Rotor ◽  
Analysis Techniques ◽  
Analysis Technique ◽  
Nonlinear Transient ◽  
Nonlinear Transient Analysis ◽  
The Stability

The subsynchronous whirl stability limit of a rigid rotor supported on two symmetrical finite journal bearings has been studied using the linearised perturbation method and the nonlinear transient analysis technique. A quantitative comparison for journal bearings with different l/d ratios has been provided.

Threshold conditions for a family of epidemic dynamic models for malaria with distributed delays in a non-random environment

2018 ◽  
Vol 11 (06) ◽  
pp. 1850085 ◽  
Author(s):  
Divine Wanduku
Keyword(s):  
Incidence Rate ◽  
Dynamic Models ◽  
Family Type ◽  
Natural Immunity ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Reproduction Numbers ◽  
Threshold Conditions ◽  
Epidemic Dynamic ◽  
The Stability

A family of deterministic SEIRS epidemic dynamic models for malaria is presented. The family type is determined by a general functional response for the nonlinear incidence rate of the disease. Furthermore, the malaria models exhibit three random delays — the incubation periods of the plasmodium inside the female mosquito and human hosts, and also the period of effective acquired natural immunity against the disease. Insights about the effects of the delays and the nonlinear incidence rate of the disease on (1) eradication and (2) persistence of malaria in the human population are obtained via analyzing and interpreting the global asymptotic stability results of the disease-free and endemic equilibrium of the system. The basic reproduction numbers and other threshold values for malaria are calculated, and superior threshold conditions for the stability of the equilibria are found. Numerical simulation results are presented.

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Journal Bearings With Rectangular Dimples

2015 ◽  
Author(s):  
Ram Turaga
Keyword(s):  
Stability Analysis ◽  
Surface Texture ◽  
Transient Stability ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Pressure Curve ◽  
Rigid Rotor ◽  
Non Linear ◽  
The Stability ◽  
Transient Stability Analysis

The influence of deterministic surface texture on the sub-synchronous whirl stability of a rigid rotor has been studied. Non-linear transient stability analysis has been performed to study the stability of a rigid rotor supported on two symmetric journal bearings with a rectangular dimple of large aspect ratio. The surface texture parameters considered are dimple depth to minimum film thickness ratio and the location of the dimple on the bearing surface. Journal bearings of different Length to diameter ratios have been studied. The governing Reynolds equation for finite journal bearings with incompressible fluid has been solved using the Finite Element Method under isothermal conditions. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. When the dimple is located in the raising part of the pressure curve the positive rectangular dimple is seen to decrease the stability whereas the negative rectangular dimple is seen to improve the stability of the rigid rotor.

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