Analysis of the Effects of Parallel and Angular Misalignment in Hyperstatic Rotors Equipped With Oil-Film Bearings

2011 ◽  
Author(s):  
P. Pennacchi ◽  
A. Vania ◽  
S. Chatterton
Keyword(s):  
Reynolds Equation ◽  
Nonlinear Effects ◽  
Element Model ◽  
System Response ◽  
Angular Misalignment ◽  
Oil Film ◽  
Rotating Machine ◽  
Parallel Misalignment ◽  
Spectral Components ◽  
The Time Domain

Misalignment is one of the most common sources of trouble of rotating machinery having couplings between the shafts. Ideal alignment is a chimera and the coupling flanges of the shafts are never ideally aligned, presenting angular and/or parallel misalignment (defined also as radial misalignment or offset). In particular, during the shaft rotation, if coupling misalignment between the shafts of a statically aligned line is excessive, a periodical change, of the load on the bearings in hyperstatic shaft-lines, occurs. If the rotating machine is equipped with oil-film bearings, the change of the loads on the bearings causes also the variation of their oil-film dynamic characteristics, i.e. damping and stiffness, and the complete system cannot be considered as linear. In the paper, this phenomenon is modelled accurately and analyzed by considering the simulated response of a misaligned rotor train in the time domain. A finite element model is used for the hyperstatic rotor, while bearing characteristics are calculated by integrating Reynolds equation (considering the actual type and dimensions of the bearings) as a function of the instantaneous load acting on the bearings, caused by the coupling misalignment. Nonlinear effects are highlighted and the spectral components of system response are analyzed, in order to give pertinent diagnostic information.

scholarly journals Analisis Ketidaksesumbuan Poros (Misalignment) pada Rotordinamik Berdasarkan Sinyal Suara

2021 ◽  
Vol 12 (2) ◽  
pp. 487-495
Author(s):  
Dedi Suryadi ◽  
◽  
M Reza Febriyanto ◽  
Fitrilina Fitrilina
Keyword(s):  
Rotor Dynamics ◽  
Sound Signal ◽  
Peak Amplitude ◽  
Test Results ◽  
Motor Shaft ◽  
Angular Misalignment ◽  
Parallel Misalignment ◽  
Spectrum Characteristic ◽  
The Time Domain ◽  
Sound Spectrum

This research aims to identify misalignment of the rotor dynamics based on sound spectrum characteristic. In this study, rotor dynamics consist of motor, shaft, coupling and bearings. Three types of misalignment were considered, namely parallel, angular, and combination misalignment. In order to obtain the best signal, microphones were used as sensors to capture sound signal placed on coupling and each bearing. The signal obtained was in time series. The sound signal in the time domain is then filtered to remove noise signals, which are then transferred to be signals in the frequency domain using Fast Fourier Transform (FFT). From the test results, it is found that in the case of parallel misalignment, the sound frequency spectrum is obtained with a peak amplitude at 2x rpm. The case of angular misalignment obtained a sound spectrum with a peak amplitude value and is dominant at 1x rpm than 2x rpm. Meanwhile, in the case of a combination of parallel and angular misalignment, a peak amplitude sound spectrum appears at 1x rpm and 2x rpm with relatively close spacing between the peaks of the sound spectrum. The result shows that sound signal can be used for identification of misalignment of the rotor dynamics.

scholarly journals Response Characteristics of Looseness-Rubbing Coupling Fault in Rotor-Sliding Bearing System

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Liu ◽  
Zengyuan Xue ◽  
Lei Jia ◽  
Tuo Shi ◽  
Hui Ma
Keyword(s):  
Finite Element ◽  
Simulation Analysis ◽  
Element Model ◽  
Rotor System ◽  
Sliding Bearing ◽  
Oil Film ◽  
Response Characteristics ◽  
The Time Domain ◽  
Coupling Fault ◽  
Bearing System

For the diagnosis of looseness-rubbing coupling fault of rotor-sliding bearing system caused by bolt looseness fault, the mechanical model and finite element model of dual-disc rotor system with looseness-rubbing coupling fault are established based on the nonlinear finite element method, nonlinear oil film force, looseness stiffness model, and Hertz contact theory. With the augmented Lagrange method, contact constraint conditions are dealt with to ensure that the rotary disk and casing contact with each other meeting boundary penetrating depth within the prescribed tolerance range. And then the dynamics characteristics of the health rotor system supported by sliding bearing are studied. Combined with experimental study and simulation analysis, it is found that the looseness-rubbing coupling fault is often characterized by rubbing fault, the lower part of the time-domain fluctuated shape is denser, while the upper part is relatively loose, and multiple nested half ellipse is shown in orbit diagram. Because of the loosing stiffness and rubbing force, the phenomenon of unstable oil film is depressed. The appearance of the first- and second-order oil film oscillation phenomenon is delayed. It could be used as a theoretical basis for diagnosing looseness-rubbing coupling fault of rotor-sliding bearing system.

One Explanation for 2N Response due to Misalignment in Rotors Connected by Flexible Couplings

2012 ◽  
Author(s):  
Raul D. Avendano ◽  
Dara W. Childs
Keyword(s):  
System Response ◽  
Unit Load ◽  
Running Speed ◽  
Angular Misalignment ◽  
Related Factors ◽  
Static Tests ◽  
Side Load ◽  
Fixed Direction ◽  
Parallel Misalignment ◽  
Reaction Component

Misalignment in turbomachinery is commonly thought to produce two-times-running-speed (2N) response. The source of 2N vibration response was investigated, starting with the development of finite-element models for three flexible disc-pack couplings (4-bolt, 6-bolt, and 8-bolt couplings). Parallel and angular misalignments were analyzed. The resultant lateral stiffness terms had 1N, 2N, and 3N harmonic components versus the shaft rotation angle. The 4-bolt coupling had large 1N stiffness components under angular and parallel misalignment. The 6-bolt coupling had only a 1N reaction component under angular misalignment, while parallel misalignment showed a strong 2N reaction component, larger than either the 1N or 3N components. Under angular misalignment, the 8-bolt model produced large 1N reaction components. Under parallel misalignment, it produced 1N, 2N, and 3N components that were similar in magnitude. All the couplings behaved linearly in the range studied. Some experts attribute observed 2N response to nonlinear bearing forces produced by bearings at high unit loads. Static tests for a 5-pad tilting-pad journal bearing with unit loads up to 34.5bars produced small 2N motion components that did not grow with increasing unit load. A Jeffcott-rotor model with shaft stiffness orthotropy and a fixed-direction side load predicts that 2N response depends on three related factors: (1) the degree of orthotropy (the 1N stiffness variation magnitude), (2) the magnitude of the side load, and (3) the relative ratio of running speed to rotor 1st natural frequency, (ω/ωn). The 2N response magnitude is largest when ω is close to ωn/2. The side load is required to create 2N response due to shaft stiffness orthotropy. Misaligned couplings create precisely the same (very old) physical model as a two-pole turbogenerator rotor with a gravity side load (gravity critical speed). The response of a 2-rotor/coupling system with parallel and angular misalignment was simulated using a time-transient code. When the frequency ratio was 0.5, the system response with the 4-bolt and 6-bolt coupling had a synchronous 1N component as well as a significant 2N component. Parallel misalignment at a coupling produces stiffness orthotropy and a fixed-direction side load. For ranges of running speed near ωn/2, these two elements can combine to produce 2N response.

One Explanation for Two-Times Running Speed Response Due to Misalignment in Rotors Connected by Flexible Couplings

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Raul D. Avendano ◽  
Dara W. Childs
Keyword(s):  
System Response ◽  
Unit Load ◽  
Running Speed ◽  
Angular Misalignment ◽  
Related Factors ◽  
Static Tests ◽  
Side Load ◽  
Fixed Direction ◽  
Parallel Misalignment ◽  
Reaction Component

Misalignment in turbomachinery is commonly thought to produce two-times running-speed (2N) response. The source of 2N vibration response was investigated, starting with the development of finite-element models for three flexible disk-pack couplings (four-bolt, six-bolt, and eight-bolt couplings). Parallel and angular misalignments were analyzed. The resultant lateral stiffness terms had 1N, 2N, and 3N harmonic components versus the shaft rotation angle. The four-bolt coupling had large 1N stiffness components under angular and parallel misalignment. The six-bolt coupling had only a 1N reaction component under angular misalignment, while parallel misalignment showed a strong 2N reaction component, larger than either the 1N or 3N components. Under angular misalignment, the eight-bolt model produced large 1N reaction components. Under parallel misalignment, it produced 1N, 2N, and 3N components that were similar in magnitude. All the couplings behaved linearly in the range studied. Some experts attribute observed 2N response to nonlinear bearing forces produced by bearings at high unit loads. Static tests for a five-pad tilting-pad journal bearing with unit loads up to 34.5 bars produced small 2N motion components that did not grow with increasing unit load. A Jeffcott-rotor model with shaft stiffness orthotropy and a fixed-direction side load predicts that 2N response depends on three related factors: (1) the degree of orthotropy (the 1N stiffness variation magnitude), (2) the magnitude of the side load, and (3) the relative ratio of running speed to rotor first natural frequency, (ω/ωn). The 2N response magnitude is largest when ω is close to ωn/2. The side load is required to create 2N response due to shaft stiffness orthotropy. Misaligned couplings create precisely the same (very old) physical model as a two-pole turbogenerator rotor with a gravity side load (gravity critical speed). The response of a two-rotor/coupling system with parallel and angular misalignment was simulated using a time-transient code. When the frequency ratio was 0.5, the system response with the four-bolt and six-bolt coupling had a synchronous 1N component as well as a significant 2N component. Parallel misalignment at a coupling produces stiffness orthotropy and a fixed-direction side load. For ranges of running speed near ωn/2, these two elements can combine to produce 2N response.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

scholarly journals Research on the Time-Domain Dielectric Response of Multiple Impulse Voltage Aging Oil-Film Dielectrics

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1948
Author(s):  
Chenmeng Zhang ◽  
Kailin Zhao ◽  
Shijun Xie ◽  
Can Hu ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Time Domain ◽  
Dielectric Response ◽  
Early Stage ◽  
Debye Model ◽  
Polarization Current ◽  
Depolarization Current ◽  
Oil Film ◽  
Impulse Voltage ◽  
The Time Domain ◽  
Film Dielectric

Power capacitors suffer multiple impulse voltages during their lifetime. With the multiple impulse voltage aging, the internal insulation, oil-film dielectric may deteriorate and even fail in the early stage, which is called accumulative effect. Hence, the time-domain dielectric response of oil-film dielectric with multiple impulse voltage aging is studied in this paper. At first, the procedure of the preparation of the tested samples were introduced. Secondly, an aging platform, impulse voltage generator was built to test the accumulative effect of capacitor under multiple impulse voltage. Then, a device was used to test the time-domain dielectric response (polarization depolarization current, PDC) of oil-film dielectric in different aging states. And finally, according to the PDC data, extended Debye model and characteristic parameters were obtained by matrix pencil algorithm identification. The results indicated that with the increase of impulse voltage times, the time-domain dielectric response of oil-film dielectric changed accordingly. The polarization current curve moved up gradually, the insulation resistance decreased when subjected to the repeated impulses. In frequency domain, the frequency spectrum of tan δ changed along with the impulse accumulation aging, especially at low frequency. At last, combined with the aging mechanism of oil-film dielectric under multiple impulse voltage, the test results were discussed.

Controllability Ellipsoid to Evaluate the Performance of Mobile Manipulators for Manufacturing Tasks

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Stephen L. Canfield ◽  
Reabetswe M. Nkhumise
Keyword(s):  
Time Domain ◽  
Controller Design ◽  
Control Design ◽  
Quantitative Measure ◽  
Space Representation ◽  
System Response ◽  
Geometric Representation ◽  
Mobile Manipulators ◽  
Control Parameters ◽  
The Time Domain

This paper develops an approach to evaluate a state-space controller design for mobile manipulators using a geometric representation of the system response in tool space. The method evaluates the robot system dynamics with a control scheme and the resulting response is called the controllability ellipsoid (CE), a tool space representation of the system’s motion response given a unit input. The CE can be compared with a corresponding geometric representation of the required motion task (called the motion polyhedron) and evaluated using a quantitative measure of the degree to which the task is satisfied. The traditional control design approach views the system response in the time domain. Alternatively, the proposed CE views the system response in the domain of the input variables. In order to complete the task, the CE must fully contain the motion polyhedron. The optimal robot arrangement would minimize the total area of the CE while fully containing the motion polyhedron. This is comparable to minimizing the power requirements of robot design when applying a uniform scale to all inputs. It will be shown that changing the control parameters changes the eccentricity and orientation of the CE, implying a preferred set of control parameters to minimize the design motor power. When viewed in the time domain, the control parameters can be selected to achieve desired stability and time response. When coupled with existing control design methods, the CE approach can yield robot designs that are stable, responsive, and minimize the input power requirements.

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

A Theoretical Analysis of Floating Bush Journal Bearing With Axial Oil Film Rupture Being Considered

2002 ◽  
Vol 124 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Kiyoshi Hatakenaka ◽  
Masato Tanaka ◽  
Kenji Suzuki
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Speed Ratio ◽  
Shaft Speed ◽  
Film Rupture ◽  
State Behavior ◽  
Oil Film ◽  
Rotordynamic Coefficients ◽  
The Stability ◽  
Very High

A new modified Reynolds equation is derived with centrifugal force acting on the hydrodynamic oil film being considered. This equation, together with a cavitation model, is used to obtain the steady-state equilibrium and calculate the rotordynamic coefficients of lightly loaded floating bush journal bearings operating at very high shaft speeds. The bush-to-shaft speed ratio and the linear cross-coupling spring coefficients of the inner oil film is found to decrease with the increase in shaft speed as the axial oil film rupture develops in the inner oil film. The present model can give reasonable explanation to the steady-state behavior and the stability behavior of the bearing observed in actual machines.

scholarly journals Experimental Nonlinear Modeling of a Rotating Machine with an Oil Film Bearing

2002 ◽  
Vol 10 (2) ◽  
Author(s):  
Chiou-Fong Chung ◽  
Pi-Cheng Tung ◽  
Chiang-Nan Chang
Keyword(s):  
Nonlinear Modeling ◽  
Oil Film ◽  
Rotating Machine
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