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.

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.

Detection and Quantitative Assessment of Damages in Beam Structures Using Frequency and Stiffness Changes

2013 ◽  
Vol 569-570 ◽  
pp. 1013-1020 ◽  
Author(s):  
Gilbert Rainer Gillich ◽  
Zeno Iosif Praisach
Keyword(s):  
Natural Frequency ◽  
Mode Shape ◽  
Quantitative Assessment ◽  
Vibration Modes ◽  
Stored Energy ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Mathematical Relation ◽  
3D Elements ◽  
Frequency Changes

This paper is concerned with vibration based non-destructive evaluation of structures, with a focus on quantitative assessment of damage. In previous works, a reliable method to locate open cracks in beams has been proposed and tested using both data from numerical simulations and laboratory experiments. It bases on the fact the natural frequency of a bending vibrations mode attend different changes, depending on the loss of stored energy for the slice on which the damage is located. As bigger the mode shape curvature value on that location, so bigger the loss of stored energy and consequently the natural frequency decrease in that mode. Analyzing the natural frequency changes for a larger series of vibration modes, it’s possible to precisely locate damages. The authors succeed to find a single mathematical relation describing the frequency changes for all bending vibration modes, involving one term defining damage’s location and one defining its depth. While the first term changes for different modes, being defined by the mode shape curvature, the second maintain its value for all modes, being affected just by damage depth. This finding permits decoupling the location issue with that of quantitative assessment of damage. Latest researches, presented in this paper, succeed by finding the relation between the second term of the relation and some mechanical characteristics of the beam, i.e. extending the proposed method by including evaluation of damage severity. The approach is illustrated on a cantilever beam, modeled with 3D elements.

scholarly journals Reduced Modelling for Turbine Rotor-Blade Coupled Bending Vibration Analysis

2011 ◽  
Vol 77 (775) ◽  
pp. 742-754 ◽  
Author(s):  
Akira OKABE ◽  
Takeshi KUDO ◽  
Koki SHIOHATA ◽  
Osami MATSUSHITA ◽  
Hiroyuki FUJIWARA ◽  
...  
Keyword(s):  
Vibration Analysis ◽  
Rotor Blade ◽  
Turbine Rotor ◽  
Bending Vibration ◽  
Turbine Rotor Blade

scholarly journals 535 Reduced Modeling for Turbine Rotor-Blade Coupled Bending Vibration Analysis

2011 ◽  
Vol 2011 (0) ◽  
pp. _535-1_-_535-11_
Author(s):  
Takeshi KUDO ◽  
Akira OKABE ◽  
Koki SHIOHATA ◽  
Osami MATSUSHITA ◽  
Hiroyuki FUJIWARA ◽  
...  
Keyword(s):  
Vibration Analysis ◽  
Rotor Blade ◽  
Turbine Rotor ◽  
Bending Vibration ◽  
Turbine Rotor Blade ◽  
Reduced Modeling

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.

scholarly journals Design and Performance Evaluation of a Single-Phase Driven Ultrasonic Motor Using Bending-Bending Vibrations

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 853
Author(s):  
Dongmei Xu ◽  
Wenzhong Yang ◽  
Xuhui Zhang ◽  
Simiao Yu
Keyword(s):  
Single Phase ◽  
Oblique Line ◽  
Ultrasonic Motor ◽  
Vibration Modes ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Output Performance ◽  
Resonance Frequencies ◽  
And Performance ◽  
Line Trajectory

An ultrasonic motor as a kind of smart material drive actuator has potential in robots, aerocraft, medical operations, etc. The size of the ultrasonic motor and complex circuit limits the further application of ultrasonic motors. In this paper, a single-phase driven ultrasonic motor using Bending-Bending vibrations is proposed, which has advantages in structure miniaturization and circuit simplification. Hybrid bending vibration modes were used, which were excited by only single-phase voltage. The working principle based on an oblique line trajectory is illustrated. The working bending vibration modes and resonance frequencies of the bending vibration modes were calculated by the finite element method to verify the feasibility of the proposed ultrasonic motor. Additionally, the output performance was evaluated by experiment. This paper provides a single-phase driven ultrasonic motor using Bending-Bending vibrations, which has advantages in structure miniaturization and circuit simplification.

Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

1999 ◽  
Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen
Keyword(s):  
Critical Speed ◽  
Floquet Theory ◽  
Rotor Dynamics ◽  
Steady State Response ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
State Response ◽  
Stability And Bifurcation ◽  
The Stability

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

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