Stability Analysis of a Cracked Rotor With Several Degrees of Freedom

2009 ◽  
Author(s):  
Roberto Ricci ◽  
Paolo Pennacchi
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Analytical Models ◽  
Cracked Rotor ◽  
Common Notion ◽  
Rotating Shafts ◽  
Stiffness Variation ◽  
The Stability ◽  
First Time ◽  
Breathing Mechanism

It is a common notion in literature that cracks in horizontal rotating shafts can cause instability of the system. Actually the stiffness variation due to the breathing mechanism may cause parametric excitation to the rotor system. This phenomenon has been investigated by means of both analytical models and simulation, but the studies are related to simple Jeffcott’s rotors. In this paper the method normally used to investigate the stability of cracked rotors, i.e. Floquet’s theory, is applied for the first time to a model of a real rotor with several degrees of freedom, considering also the bearings and the foundation. Huge calculation resources have been necessary and this may explain why this analysis was not performed before. The results are very different from those obtained by means of simple Jeffcott’s rotor.

Stability analysis of mechanisms having unpowered degrees of freedom

Robotica ◽  
1989 ◽  
Vol 7 (4) ◽  
pp. 349-357 ◽  
Author(s):  
B. Borovac ◽  
M. Vukobratović ◽  
D. Stokić
Keyword(s):  
Stability Analysis ◽  
Decomposition Method ◽  
Degrees Of Freedom ◽  
Complete System ◽  
Dynamic Effect ◽  
Numerical Example ◽  
Spatial Mechanisms ◽  
The Stability ◽  
First Time ◽  
Lyapunov Vector

SUMMARYThe stability analysis of active spatial mechanisms comprising both powered and unpowered joints is carried out for the first time using aggregation-decomposition method via Lyapunov vector functions. This method has already been used for analysis of mechanisms with all powered joints. To extend the application of the method to the stability analysis of mechanisms containing unpowered joints we developed modelling of special subsystem consisting of one powered and one unpowered joint. Then, we consider the stability of the complete system without neglecting any dynamic effect. The stability analysis is demonstrated by a numerical example of a particular biped system.

Stability Analysis of Monument: A Case Study–Safdarjung Tomb

2010 ◽  
Vol 133-134 ◽  
pp. 403-410
Author(s):  
Adil Ahmad ◽  
Khalid Moin
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Seismic Load ◽  
New Delhi ◽  
Archaeological Survey ◽  
Central Dome ◽  
Lateral Forces ◽  
Shear Beam ◽  
The Stability ◽  
Lumped Masses

Present study deals with the stability analysis of an existing historical monument “Safdarjung Tomb” under Seismic Load. The tomb is situated at New Delhi, India. The building is classified as protected monument by the Archaeological Survey of India (ASI). This is a ground plus two storey masonry structure with a central dome. The basic seismic parameters have been evaluated using Bureau of Indian Standards (BIS) Codal method. Distribution of lateral forces is carried out to individual piers and walls using Rigidity Approach. The seismic performance of the building is studied under the gravity and earthquake loads. The building is modeled as a two-degree-of-freedom shear-beam system. The piers, which are located parallel to the direction of earthquake shaking are assumed to provide spring action. The mass of the walls and slabs are lumped at the storey levels. The lumped masses are assumed to be connected to each other through massless springs. The degree of each mass in horizontal direction is considered, neglecting the vertical translational and rotational degrees of freedom. Stiffness of the walls parallel to longitudinal and transverse directions of the building has been computed separately which was used for computation of lateral forces in each direction. The forces so evaluated are used in pier analysis to evaluate stress induced in various elements. The majority of the structural elements were found safe and the overall structure is stable. The stresses due to shear and bending are within permissible limit

A new tuning procedure for nonlinear PID global regulators with bounded torques for rigid robots

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1926-1947 ◽  
Author(s):  
Jorge Orrante-Sakanassi ◽  
Víctor Santibánez ◽  
Víctor M. Hernández-Guzmán
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Experimental Tests ◽  
Pid Controllers ◽  
Stability Conditions ◽  
Proportional Integral Derivative ◽  
Global Regulators ◽  
The Stability ◽  
First Time

SUMMARYIn this paper we propose new tuning conditions for three saturated nonlinear proportional-integral-derivative (PID) global regulators with bounded torques for robot manipulators, which have been presented previously in the literature. The motivation of this work relies on the fact that the tuning conditions presented previously in the literature for assuring global asymptotic stability are so restrictive that it had been impossible, until now, to carry out experimental tests. New tuning criteria of unsaturated PID controllers for robot manipulators with stability conditions more relaxed than those presented previously in the literature have been proposed recently in some works by the authors. This was achieved by setting the stability conditions as expressions that have to be satisfied at each joint instead of general conditions for the whole robot. Based on this idea, we now obtain stability conditions for saturated global PID controllers which are so relaxed that they have allowed to perform, by the first time, experimental tests using controller gains which completely satisfy the proposed stability conditions. The results of such experiments are presented in this paper, where we have used a two-degrees-of-freedom robot manipulator.

scholarly journals Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

1997 ◽  
Vol 3 (4) ◽  
pp. 329-371
Author(s):  
Henryk Flashner ◽  
Ramesh S. Guttalu
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Mapping Method ◽  
Periodic Systems ◽  
Resonance Problem ◽  
Point Mapping ◽  
Analytical Stability ◽  
Functional Relations ◽  
Ground Resonance ◽  
The Stability

Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

A modified stability analysis method of landfills dependent on gas pressure

2020 ◽  
pp. 0734242X2094447
Author(s):  
Chao Liu ◽  
Jianyong Shi ◽  
Yaru Lv ◽  
Guojian Shao
Keyword(s):  
Stability Analysis ◽  
Slope Failure ◽  
Gas Pressure ◽  
Analytical Models ◽  
Analysis Method ◽  
Triggering Mechanism ◽  
Liner System ◽  
Leachate Level ◽  
The Stability ◽  
Gp Model

Excessive gas pressure (GP) in landfills is a potential triggering mechanism for slope failure, which is rarely considered in analytical models. This paper presents a modified analytical model for landfill stability dependent on GP. A two-layered GP model is established to describe the GP above and below the leachate level. The distribution of GP is then used to calculate the factor of safety (FS) using a modified wedge stability analysis method. It is found that the lack of consideration of the GP in landfill stability analysis leads to serious overestimation of the FS. In addition, the GP gas pressure within the landfill accelerates the critical interface of a multilayer liner system shifting from one to another. A new estimation criterion for FS is proposed. The proposed criterion can directly estimate the stability of the landfill by the field-tested pore pressure. Finally, the proposed method is applied to estimate the slope failure of Xiaping landfill in Shenzhen, and the results verify the proposed method.

Stability Analysis of a Free-Standing Block With Friction on a Moving Foundation

2001 ◽  
Author(s):  
Anna Sinopoli ◽  
Alessio Ageno
Keyword(s):  
Stability Analysis ◽  
Dynamic Response ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Unilateral Constraints ◽  
Free Standing ◽  
Time Intervals ◽  
Analysis And Evaluation ◽  
The Stability ◽  
Scientific Purpose

Abstract The problem analyzed here concerns the dynamic response of a bidimensional polygonal rigid body simply supported on a harmonically moving rigid ground. The immediate scientific purpose of the paper is to obtain and analyze the dynamic response by using a variational formulation, recently proposed by one of the authors [1], where the dynamics is described as a differential inclusion. This formulation allows us to determine the instantaneous accelerations of the system by means of a mechanical model with friction and unilateral constraints, which does not reduce the degrees of freedom or impose an “a priori” choice of the mechanism activated during the motion. By treating the friction coefficient as a stability parameter, it has been possible to obtain different kind of responses, ranging from rocking to sliding-rocking, and compare them with those obtained in the literature. Sliding-rocking motions obtained so far have exhibited not only harmonic but also interesting and more complex behaviors with chaotic features. The search for theoretical and numerical instruments able to identify and classify these more complex motions was first performed in the case of rocking, characterized by a smaller number of degrees of freedom. A technique was then implemented for calculating Lyapunov’s exponents also during the time intervals of the impacts. The introduction and evaluation of these exponents can also permit us to perform the stability analysis with respect to overturning, by limiting the analysis and evaluation to the first impact that the system undergoes by starting at rest: in fact, large values of Lyapunov’s exponents before the first impact are connected with overturning during the motion which follows. This circumstance can make it easier to carry out the stability analysis with respect to overturning, as a function of the amplitude and frequency of the excitation.

scholarly journals Chatter Suppression and Stability Analysis of Rotary Ultrasonic Milling Titanium Alloy Thin-walled Workpiece

2021 ◽  
Author(s):  
Lianjun Sun ◽  
Kan Zheng ◽  
Wenhe Liao
Keyword(s):  
Titanium Alloy ◽  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Machined Surface ◽  
Thin Walled Structures ◽  
Chatter Suppression ◽  
Ultrasonic Milling ◽  
Thin Walled ◽  
The Stability ◽  
Rotary Ultrasonic Milling

Abstract Titanium alloy and its thin-walled structures are widely used in the aerospace field. Aiming at the processing chatter and difficult-to-machine problem of titanium alloy thin-walled workpieces, rotary ultrasonic milling technology (RUM) is employed to restrict machining vibration in this paper. Firstly, the titanium alloy web with low stiffness is equivalent to a mass-spring-damping system with three degrees of freedom for describing its dynamic characteristics. Then, a novel stability analysis method is proposed for RUM thin-walled workpiece (RUM-tww) through defining an ultrasonic function angle. Furthermore, RUM-tww stability lobe diagrams (SLDs) are achieved based on the semi-discrete method (SDM). The simulation results show that the milling stability of titanium alloy webs is improved effectively under the effect of ultrasonic vibration energy. Compared with conventional milling thin-walled workpiece (CM-tww), the stability region of RUM-tww is increased by 80.32% within the spindle speed from 1000r/min to 5000r/min. Finally, milling experiments are carried out to verify the validity and rationality of SLDs via analyzing chatter marks, cutter marks and flatness on the machined surface. The experimental results are in good agreement with the theoretical prediction.

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