Dynamic Modelling and Diagnosis of Transverse Crack and Rotor/Stator Rub in a Flexible Rotor System

2019 ◽  
Author(s):  
Rajiv Kumar Vashisht ◽  
Qingjin Peng
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Dynamic Modelling ◽  
Vibration Response ◽  
Transverse Cracks ◽  
Transient Vibration ◽  
Premature Failure ◽  
Multiple Faults ◽  
Integer Multiple ◽  
High Harmonics

Abstract Due to unbalance present in a rotating machinery, fluctuating stresses are generated leading to the formation of transverse cracks in rotors. The cracks propagate with the passage of time and increase the amplitude of vibration. High vibration amplitudes can give rise to rotor/stator rubs. During the rubbing phase, the crack propagation gets enhanced due to inter-connected nature of these faults. If left unattended, these faults can cause the premature failure of machine components. Hence, there is a need to develop fault detection mechanisms based on the vibration response so that these faults can be diagnosed during initial stages. The effect of gravity and the presence of cracks significantly changes vibration characteristics of the rotor, which is thoroughly investigated in this research for a two-degrees-of-freedom Jeffcott rotor. It has been observed that during rubbing, high harmonics are excited. These harmonics are integer multiple of the rotor spin frequency. Similar type of the response is also observed due to the presence of a transverse rotor crack. It is difficult to distinguish the type of faults based on the steady state dynamic response only. Instead of working only on a steady state vibration response, the transient vibration response during coasting up of the rotor is considered. During coasting up of the rotor, high harmonics are excited for both the crack as well as rotor/stator rubbing. The excitation of higher harmonics starts at much earlier in the spectrogram of the vertical response for the cracked rotor compared to that of rubbing. This fact is used in the development of a fault diagnosis technique based on Short Time Fourier Transform of the vibration response. The proposed technique can efficiently distinguish different types of faults even if multiple faults coexist.

Effect of Bladed Packets on Transient Vibration Localization Behaviors of Mistuned Whole Bladed Disk System

2021 ◽  
Author(s):  
Xuanen Kan
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Vibration Characteristics ◽  
Vibration Response ◽  
Vibration Energy ◽  
Disk System ◽  
Transient Vibration ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Alternative Approach

Abstract The multi-packets whole bladed disks are usually used in the turbo-machineries. The most different characteristic of the multi-packets whole bladed disk is that some blades are connected by lacing forming a bladed packet, and several bladed packets are assembled to form a multi-packets whole bladed disk system. Mistuning of blades is an attractive vibration subject due to vibration localization problems that vibration energy focuses on some blades. The vibration localization characteristics of steady state of bladed disk are mainly discussed in previous studies, and few works focus on the transient vibration localization behaviors of the multi-packets whole mistuned bladed disk. Transient vibration characteristics of bladed disk are crucial during startup. Therefore, in this paper, transient vibration characteristics of the multi-packets whole bladed disk are studied. A developed mathematical model is used to calculate the transient vibration response of the multi-packets whole bladed disk. The number of bladed packets on the transient vibration localization of the multi-packets mistuned whole bladed disk is discussed. The results indicate that the bladed packets are able to reduce the transient vibration localization. The results suggest that the bladed packet is an alternative approach to reduce the vibration localization of bladed disk caused by mistuning. Moreover, the different number of bladed packets will produce various behaviors of transient vibration localization of multi-packets whole mistuned bladed disk system.

Beam-Vibration Analysis With the Electric-Analog Computer

1950 ◽  
Vol 17 (1) ◽  
pp. 13-26
Author(s):  
G. D. McCann ◽  
R. H. MacNeal
Keyword(s):  
Steady State ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Analog Computer ◽  
Accurate Solution ◽  
Rotary Inertia ◽  
Beam Vibration ◽  
Lumped Constant ◽  
Electric Analog

Abstract The authors have developed a true dynamic analogy which has been used with the Cal Tech electric-analog computer for the rapid and accurate solution of both steady-state and transient beam problems. This analogy has been found well suited to the study of beams having several coupled degrees of freedom, including torsion, simple bending, and bending in a plane. Damping and effects such as rotary inertia may be handled readily. The analogy may also be used in the study of systems involving combined beams and “lumped-constant” elements.

Vibration Behavior and Serviceability of Arched Prestressed Concrete Truss Due to Human Activity

2018 ◽  
Vol 18 (12) ◽  
pp. 1850146 ◽  
Author(s):  
Jiang Li ◽  
Jiepeng Liu ◽  
Liang Cao ◽  
Y. Frank Chen
Keyword(s):  
Steady State ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Current Trend ◽  
Threshold Values ◽  
Transient Vibration ◽  
Vibration Behavior ◽  
Detailed Evaluation ◽  
Floor Systems ◽  
Floor Vibration

The current trend toward longer spans and lighter floor systems, combined with reduced damping and new activities, have resulted in an increasing complaints on floor vibration from building owners and occupants. Heel-drop, jumping, and walking impacts, which may lead to discomfort problems in daily life, were imposed on a large-span arched prestressed concrete truss (APT) girder system studied. The natural frequencies, peak acceleration, average root-mean-square acceleration (ARMS), maximum transient vibration value (MTVV), and perception factor for the girder were obtained and checked against the existing codes and standards. The purpose of this paper is to provide researchers and engineers with a detailed evaluation on the vibration behavior of the APT girder under different human activities, with a comprehensive review on the relevant criteria and some suggestions. Lastly, the following threshold peak accelerations are suggested: 650[Formula: see text]mm/s2 for transient heel-drop impact, 1450[Formula: see text]mm/s2 for transient jumping impact, and 250[Formula: see text]mm/s2 for steady-state walking. In addition, the threshold values of 90[Formula: see text]mm/s2 and 50[Formula: see text]mm/s2 are suggested for MTVV and ARMS, respectively, under steady-state walking.

Effects of Suspension Design on the Attitudes of a Car during Braking and Acceleration

1973 ◽  
Vol 187 (1) ◽  
pp. 787-794
Author(s):  
J. R. Ellis
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
Coupled Systems ◽  
Two Degrees Of Freedom ◽  
Simulation Techniques ◽  
Non Linear ◽  
Non Linear Systems ◽  
Effort Distribution

Two degrees of freedom models of a car are employed to demonstrate the effects of the suspension derivative ∂ x/∂ z on the pitch and bounce attitudes during braking or accelerating. The work equation is employed to show that brake effort distribution between the axles has a significant effect on the attitudes when anti-dive suspension characteristics are utilized. The steady-state positions in both pitch and bounce are developed for linear systems of typical suspensions that may be either standard or coupled systems. Non-linear systems are considered using simulation techniques. A description of some simulation circuits is contained in an appendix.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

Piezothermoelasticity and Control of Piezoelectric Laminates Exposed to a Steady-State Temperature Field

1993 ◽  
Author(s):  
H. S. Tzou ◽  
R. Ye
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Degrees Of Freedom ◽  
Sensors And Actuators ◽  
System Equation ◽  
Thermal Fields ◽  
Steady State Temperature ◽  
And Control ◽  
Internal Degrees Of Freedom

Abstract Piezothermoelastic effects of distributed piezoelectric sensors and actuators are investigated. Vibration control of piezoelectric laminates subjected to a steady-state temperature field is studied. A new 3-D piezothermoelastic finite element with three internal degrees of freedom is formulated using a variational formulation. A system equation for the piezoelectric continuum exposed to combined elastic, electric, and thermal fields is formulated. Distributed sensing and control equations are derived. All these effects are studied in a case study.

Transient Vibration and Feedback Control of an Inductrack Maglev System

2020 ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang ◽  
Hao Gao
Keyword(s):  
Steady State ◽  
Feedback Control ◽  
Dynamic System ◽  
Permanent Magnets ◽  
Preliminary Investigation ◽  
Lookup Table ◽  
Lumped Mass ◽  
Transient Vibration ◽  
Transient Model ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation envisioned in 1990s, the Inductrack system with permanent magnets (PMs) aligned in Halbach arrays has been intensively studied and applied in many projects. Due to the nonlinear, time-varying electro-magneto-mechanical coupling in such a system, the dynamic behaviors are complicated with transient responses, which in most cases can hardly be predicted with fidelity by a steady-state Inductrack model. Presented in this paper is a benchmark 2-DOF transient Inductrack model, which is derived from the first laws of nature, without any assumed steady-state quantities. It is shown that the dynamic response of the Inductrack dynamic system is governed by a set of nonlinear integro-differential equations. As demonstrated in numerical simulations with the transient model, unstable vibrations in the levitation direction occur when the traveling speed of the vehicle exceeds a threshold. To resolve this instability issue, feedback control is implemented in the Inductrack system. In the development, an assembly of Halbach arrays and active coils that are wound on the PMs is proposed to achieve a controllable source magnetic field. In this preliminary investigation, the proposed control system design process takes two main steps. First, a PID controller is set and tuned based on a simple lumped-mass dynamic system. Second, the nonlinear force-current correlation is obtained from a lookup table that is pre-calculated by steady-state truncation of the full transient Inductrack model. With the implemented feedback control algorithms, numerical examples display that the motion of the vehicle in levitation direction can be effectively stabilized at different traveling speeds. Although only a 2-DOF transient model is used here, the modeling technique and the controller design approach developed in this work are potentially applicable to more complicated models of Inductrack Maglev systems.

Higher Order Finite Elements for the Accurate Prediction of Temperature Gradients in Heat Conduction Problems

2014 ◽  
Author(s):  
Donovan A. Aguirre-Rivas ◽  
Karim H. Muci-Küchler
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Degrees Of Freedom ◽  
Neumann Boundary ◽  
Transient Heat Conduction ◽  
Field Variable ◽  
Higher Order ◽  
Temperature Gradients ◽  
Functional Representation ◽  
Higher Order Finite Elements

When the Finite Element Method (FEM) is used to solve heat conduction problems in solids, the domain is typically discretized using elements that only include the nodal values of the temperature as Degrees of Freedom (DOFs). If the values of the spatial temperature gradients are needed, they are typically computed by differentiating the functional representation for the temperature inside the elements. Unfortunately, this differentiation process usually leads to less accurate results for the temperature gradients as compared to the temperature values. For elliptic problems, like steady state heat conduction, with Neumann Boundary Conditions (BCs), recent research related to Adini’s element suggests that higher order elements that include spatial derivatives of the primary field variable as nodal DOFs are promising for obtaining accurate values for those quantities as well as providing a higher order of convergence than conventional elements. In this paper, steady state and transient heat conduction problems which involve Dirichlet BCs or both Dirichlet and Neumann BCs are studied and a new auxiliary BC is proposed to increase the accuracy of the FE solution when Dirichlet BCs are present. Examples are used to illustrate that Adini’s elements converge faster and are more computationally economical than the conventional Lagrange linear elements and Serendipity quadratic elements when auxiliary BCs are used.

Experimental Investigations of Single and Multi-Fault in Rotor System

2014 ◽  
Vol 541-542 ◽  
pp. 628-634
Author(s):  
S.P. Mogal ◽  
D.I. Lalwani
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Real Life ◽  
Rotor System ◽  
Vibration Response ◽  
Experimental Investigations ◽  
Multiple Faults ◽  
Single Fault ◽  
Vibration Behavior ◽  
Combined Action

Many researchers dealt with single fault but in real life situations, combined action of two or more single faults are usually present. Multi-faults (two and three combinations) were studied by few researchers. Researchers have mostly studied the vibration behavior of a rotor with misalignment, unbalance and rub separately. This paper presents one such case, where multiple faults are considered together in a rotor system, i.e. misalignment, unbalance and rub. The objective of this paper is to experimentally investigate the vibration response of combined of three faults misalignment, unbalance and rub using Fast Fourier Transform (FFT). FFT spectrum of combination of three faults misalignment, unbalance and rub show 1 X and 2 X are predominant and many sub harmonics are generated.1X peak represent unbalance, 2X peak represents misalignment and sub harmonics shows rub fault.

The Galloping Response of a Two-Degree-of-Freedom System

1974 ◽  
Vol 41 (4) ◽  
pp. 1113-1118 ◽  
Author(s):  
R. D. Blevins ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Natural Frequencies ◽  
Analytic Solutions ◽  
Degree Of Freedom ◽  
Approximate Analysis ◽  
Stability Criteria ◽  
Integer Multiple ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.

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