Reduced Modeling for Turbine Rotor-Blade Coupled Bending Vibration Analysis

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Akira Okabe ◽  
Takeshi Kudo ◽  
Koki Shiohata ◽  
Osami Matsushita ◽  
Hiroyuki Fujiwara ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Rotor Blade ◽  
High Efficiency ◽  
Sliding Mode ◽  
Coupled System ◽  
Bending Vibration ◽  
Mass System ◽  
Joint Power ◽  
Nodal Diameter ◽  
Blade System

In a traditional turbine-generator set, rotor shaft designers and blade designers have their own models and design process which neglects the coupled effect. Since longer blade systems have recently been employed (Saito et al. 1998, “Development of a 3000 rpm 43-in. last stage blade with high efficiency and reliability,” International Joint Power Generation Conference, pp. 89–96.) for advanced turbine sets to get higher output and efficiency, additional consideration is required concerning rotor bending vibrations coupled with a one-nodal (k = 1) blade system. Rotor-blade coupled bending conditions generally include two types so that the parallel and tilting modes of the shaft vibrations are respectively coupled with in-plane and out-of-plane modes of blade vibrations with a one-nodal diameter (k = 1). This paper proposes a method to calculate the natural frequency of a shaft blade coupled system. According to this modeling technique, a certain blade mode is reduced to a single mass system, which is connected to the displacement and angle motions of the shaft. The former motion is modeled by the m-k system to be equivalent to the blade on the rotating coordinate. The latter motion is commonly modeled in discrete form using the beam FEM on an inertia coordinate. Eigenvalues of the hybrid system covering both coordinates provide the natural frequency of the coupled system. In order to solve the eigenfrequencies of the coupled system, a tracking solver method based on sliding mode control concept is used. An eight-blade system attached to a cantilever bar is used for an example to calculate a coupled vibration with a one-nodal diameter between the blade and shaft.

Reduced Modelling for Turbine Rotor-Blade Coupled Bending Vibration Analysis

2011 ◽  
Author(s):  
Akira Okabe ◽  
Takeshi Kudo ◽  
Koki Shiohata ◽  
Osami Matsushita ◽  
Hiroyuki Fujiwara ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Rotor Blade ◽  
Sliding Mode ◽  
Coupled System ◽  
Turbine Rotor ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Mass System ◽  
Nodal Diameter ◽  
Blade System

In a traditional turbine-generator set, rotor shaft designers and blade designers have their own models and design process which neglects the coupled effect. Since longer blade systems have recently been employed[1] for advanced turbine sets to get higher output and efficiency, additional consideration is required concerning rotor bending vibrations coupled with a one-nodal (k = 1) blade system. Rotor-blade coupled bending conditions generally include two types so that the parallel and tilting modes of the shaft vibrations are respectively coupled with in-plane and out-of-plane modes of blade vibrations with a one-nodal diameter (k = 1). This paper proposes a method to calculate the natural frequency of a shaft blade coupled system. According to this modeling technique, a certain blade mode is reduced to a single mass system, which is connected to the displacement and angle motions of the shaft. The former motion is modeled by the m-k system to be equivalent to the blade on the rotating coordinate. The latter motion is commonly modeled in discrete form using the beam FEM on an inertia coordinate. Eigenvalues of the hybrid system covering both coordinates provide the natural frequency of the coupled system. In order to solve the eigenfrequencies of the coupled system, a tracking solver method based on sliding mode control concept is used. An eight-blade system attached to a cantilever bar is used for an example to calculate a coupled vibration with a one-nodal diameter between the blade and shaft.

Experimental Study of Torsional-Bending Coupled Vibration of a Rotor System With a Bladed Disk

2013 ◽  
Author(s):  
Takeshi Kudo ◽  
Koki Shiohata ◽  
Osami Matsushita ◽  
Hiroyuki Fujiwara ◽  
Akira Okabe ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Torsional Vibration ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Active Magnetic Bearing ◽  
Coupled Vibration ◽  
Bending Vibration ◽  
Nodal Diameter ◽  
Rotor Systems ◽  
Bladed Disk

An experimental investigation was conducted to confirm the bending-torsion coupled vibration of a rotor system with a bladed disk. For a rotor with relatively long blades such as in the latest low-pressure steam turbines, coupled vibration with shaft torsional vibration represents the bladed disk natural frequency of a nodal diameter (k) of zero (umbrella mode). Today this well-known behavior is reflected in the design of steam turbine rotor systems to prevent the blade vibration resonance due to torque excitation caused by the electric power grid, a standard for which is proposed by ISO 22266-1. The bending-torsion coupled resonance of rotor systems occurs, however, under specific conditions due to rotor unbalance. When the rotor’s rotational speed (Ω) is equal to the sum/difference of the bending natural frequency (ωb) and torsional natural frequency (ωθ), namely, Ω = ωθ ± ωb, there is coupled resonance, which was experimentally observed with a rotor with a relatively simplified shape. In this study, the test apparatus for a flexible rotor system equipped with a shrouded bladed disk driven by an electric motor was constructed to confirm the vibration characteristics, by envisioning the bending-torsion coupled resonance as applied to actual rotor systems of turbo machinery. A radial active magnetic bearing (AMB) was employed to support the rotor by controlling bearing stiffness and damping, and applying lateral directional excitation of forward and backward whirl to the rotor. A servomotor was also equipped at the end of the rotor system to excite the torsional vibration. The resonance of a bladed disk with nodal diameter (k) of zero, which was coupled with the rotor’s torsional vibration, was observed under the above condition (Ω = ωθ − ωb) through AMB excitation of the rotor’s bending natural frequency. Conversely, the torsional excitation caused by the servomotor was confirmed as causing the coupled resonance of rotor bending vibration.

An improved dynamic load-strength interference model for the reliability analysis of aero-engine rotor blade system

2020 ◽  
pp. 095441002097289
Author(s):  
Bingfeng Zhao ◽  
Liyang Xie ◽  
Yu Zhang ◽  
Jungang Ren ◽  
Xin Bai ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Dynamic Load ◽  
Rotor Blade ◽  
Engineering Application ◽  
Weight Ratio ◽  
System Component ◽  
Aero Engine ◽  
Blade System ◽  
Improved Model ◽  
Engine Rotor

As the power source of an aircraft, aero-engine tends to meet many rigorous requirements for high thrust-weight ratio and reliability with the continuous improvement of aero-engine performance. In this paper, based on the order statistics and stochastic process theory, an improved dynamic load-strength interference (LSI) model was proposed for the reliability analysis of aero-engine rotor blade system, with strength degradation and catastrophic failure involved. In presented model, the “unconventional active” characteristic of rotor blade system, changeable functioning relationships and system-component configurations, was fully considered, which is necessary for both theoretical analysis and engineering application. In addition, to reduce the computation cost, a simplified form of the improved LSI model was also built for convenience of engineering application. To verify the effectiveness of the improved model, reliability of turbojet 7 engine rotor blade system was calculated by the improved LSI model based on the results of static finite element analysis. Compared with the traditional LSI model, the result showed that there were significant differences between the calculation results of the two models, in which the improved model was more appropriate to the practical condition.

Synergetic control of permanent magnet synchronous motor based on load torque observer

2018 ◽  
Vol 233 (8) ◽  
pp. 980-993 ◽  
Author(s):  
Tao Wang ◽  
Jikun Li ◽  
Yuwen Liu
Keyword(s):  
Control Theory ◽  
Permanent Magnet ◽  
High Efficiency ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Moment Of Inertia ◽  
Load Torque ◽  
Synergetic Control ◽  
The Moment

The control of permanent magnet synchronous motor has become an important research, and many control methods have been developed because of its high efficiency and energy-saving characteristics. This article proposes a new motor control approach based on synergetic approach in control theory (SACT) and sliding-mode control (SMC). Since the load torque of the motor will change, the moment of inertia will increase in the experiment. The load torque is estimated by the sliding-mode observer. The moment of inertia is calculated by the least squares method by adding a forgetting factor. The practical application of synergetic control theory broadens the train of thought to meet the demand of high-performance motor drive further. The simulation and experimental results show that this control scheme in this article can improve the transient response and system robustness of dynamic systems.

Speed Dependency of Coupled Rotor-Blade Torsional Natural Frequencies

2013 ◽  
Author(s):  
Ulrich Ehehalt ◽  
Balazs Becs ◽  
Xiaoping Zhou ◽  
Stefan Güllenstern
Keyword(s):  
Natural Frequency ◽  
Rotor Blade ◽  
Natural Frequencies ◽  
Low Pressure ◽  
Campbell Diagram ◽  
Calculation Results ◽  
Measured Speed ◽  
High Level ◽  
Blade Model ◽  
Proper Analysis

The natural frequencies of blades depend on the rotational speed of the rotor train as the stiffness changes with centrifugal loading. In the case of low pressure turbines with shrunk-on-disc design the coupled rotor-blade torsional natural frequencies can also show this property. For proper analysis of the speed dependency, a complete rotor-blade model which takes the elasticity of the blades into account is required. In this paper the torsional natural frequencies calculated with a complete rotor-blade model are compared with those calculated with a model in which blade elasticity is not included. The analysis clearly demonstrates that calculations without blade elasticity lead to different natural frequencies. By modeling the complete rotor and taking blade elasticity into account, it is demonstrated that the torsional natural frequencies of a complete rotor-blade model can also become speed dependent. As a consequence, a distinction between the natural frequencies at nominal speed and natural frequency at critical speeds becomes necessary. In the following, measured torsional natural frequencies at different rotating speeds of an individual low pressure rotor are presented. A comparison of the measured speed dependency of the torsional natural frequency with calculation results thereby taking the blade elasticity into account is conducted. The analysis shows that the measured speed dependency can be predicted with a high level of accuracy and can become important for modes which are dominated by the blades of the last stages. As a consequence of this analysis, a clear distinction between natural frequency at nominal and at critical speed has to be made for certain rotor and blade designs. It is shown that the use of the Campbell diagram is highly beneficial for designing rotor trains with large blades with regard to their torsional vibration behavior.

Modeling of a Wind Turbine Rotor Blade System

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Dayuan Ju ◽  
Qiao Sun
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Simulation Software ◽  
Wind Flow ◽  
Coupling Effects ◽  
Horizontal Axis Wind Turbine ◽  
Blade Vibration ◽  
Proposed Model ◽  
Blade System ◽  
Coupling Terms

In wind turbine blade modeling, the coupling between rotor rotational motion and blade vibration has not been thoroughly investigated. The inclusion of the coupling terms in the wind turbine dynamics equations helps us understand the phenomenon of rotor oscillation due to blade vibration and possibly diagnose faults. In this study, a dynamics model of a rotor-blade system for a horizontal axis wind turbine (HAWT), which describes the coupling terms between the blade elastic movement and rotor gross rotation, is developed. The model is developed by using Lagrange's approach and the finite-element method has been adopted to discretize the blade. This model captures two-way interactions between aerodynamic wind flow and structural response. On the aerodynamic side, both steady and unsteady wind flow conditions are considered. On the structural side, blades are considered to deflect in both flap and edge directions while the rotor is treated as a rigid body. The proposed model is cross-validated against a model developed in the simulation software fatigue, aerodynamics, structure, and turbulence (fast). The coupling effects are excluded during the comparison since fast does not include these terms. Once verified, we added coupling terms to our model to investigate the effects of blade vibration on rotor movement, which has direct influence on the generator behavior. It is illustrated that the inclusion of coupling effects can increase the sensitivity of blade fault detection methods. The proposed model can be used to investigate the effects of different terms as well as analyze fluid–structure interaction.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

2013 ◽  
Author(s):  
Hiroyuki Fujiwara ◽  
Tadashi Tsuji ◽  
Osami Matsushita
Keyword(s):  
Numerical Simulations ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Rotational Speed ◽  
Coupling Effect ◽  
The Other ◽  
Resonance Phenomenon ◽  
Horizontal Direction ◽  
Bending Vibration ◽  
Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

Design and HIL Validation of an Effective Super-Twisting Controller for Stick-Slip Suppression in Drill-String Systems

2021 ◽  
Author(s):  
Abdelbasset Krama ◽  
Mohamed Gharib ◽  
Shady S. Refaat ◽  
Alan Palazzolo
Keyword(s):  
Power Plants ◽  
High Efficiency ◽  
Sliding Mode ◽  
Drill String ◽  
Experimental Investigations ◽  
Small Scale ◽  
Oil Well ◽  
Stick Slip ◽  
Rock Interaction ◽  
The Real

Abstract This paper presents a novel controller for drill string systems based on a super-twisting sliding mode theory. The aim is to eliminate the stick-slip vibration and maintain a constant drill string velocity at the desired reference value. The proposed controller inherently attenuates the torsional vibration while ensuring the stability and high efficiency of the drill string. A discontinuous lumped-parameter torsional model of vertical drill strings based on four components (rotary table, drill pipes, drill collars and drill bit) is considered. The Karnopp friction model is adopted to simulate the nonlinear bit-rock interaction phenomena. In order to provide a more accurate evaluation, the proposed drill string controller is implemented with the induction motor, a variable frequency drive and a gearbox to closely mirror the real environment of oil well drill strings. The increasing demand for prototyping and testing high-power plants in realistic and safe environments has led to the advancement of new types of experimental investigations without hurting the real system or building a small-scale prototype for testing. The dynamic performance of the proposed controller has been investigated with MATLAB software as well as in a novel hardware in-the-loop (HIL) testing platform. A power plant is modeled and implemented in the real-time simulator OPAL-RT 5600, whereas the controllers are implemented in the dSPACE 1103 control board. The results obtained through simulation and HIL testing demonstrate the feasibility and high performance of the proposed controller.

A High-Efficiency Cascade Multilevel Class-D Amplifier

2012 ◽  
Vol 482-484 ◽  
pp. 559-564
Author(s):  
Guo Hua Xu ◽  
Ying Zhang ◽  
Ming Dong ◽  
Lu Wei Xu
Keyword(s):  
Sliding Mode Control ◽  
Power Amplifier ◽  
High Efficiency ◽  
Sliding Mode ◽  
Mathematic Model ◽  
Total System ◽  
Mode Control ◽  
Class D Amplifier ◽  
Class D ◽  
The Individual

A switch-mode power amplifier based on a cascaded multicell multilevel circuit topology is introduced in the paper. Due to the Carrier-Based phase-shifted modulation of the individual switching cells, the output voltage ripple of the total system is considerably small. Compared with traditional class- AB amplifiers that are very poor at efficiency, the proposed amplifier has the efficiency of 90% at the smaller distortion level. A multilevel class-D amplifier’s mathematic model is analyzed. The paper lays emphasis on the design of the sliding mode control and deducts the parameters, and then develops a 2kW cascade multilevel class-D power amplifier adopting sliding mode control. The research results show that this kind of amplifier increases the system bandwidth, which provides the system with fast following performance and stability, high efficiency, and low THD value of output signals.

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