Institut für leistungselektronische Systeme ELSYS
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- Active vibration control (11)
- Induction motors (11)
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- Active vibation control (7)
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- Induction motor (6)
- Electromagnetic field damping (5)
- Motor foot mounts (5)
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The paper presents a theoretical analysis of different feedback concepts for active vibration control of rotating machines with current-controlled electrodynamic actuators between the machine feet and the steel frame foundation. A generalized mathematical formulation—based on a detailed formulation and on simplified formulations—has been derived, which can be used for different vibration models with different degrees of discretization. In the simplified mathematical formulations, the control parameters are implemented directly in the stiffness and damping matrix of the vibration system or, under special conditions, even directly in the stiffness and damping coefficients of the actuators. For these limit conditions, the controlled system can be replaced by a substituted mechanical system, which allows rapid predictions and optimizations regarding active vibration control of rotating machines without too much effort. Based on the generalized mathematical formulations, a very simplified model of an induction motor is analyzed with typical excitations such as mechanical unbalance, electromagnetic forces in the air gap, and vibrations of the base. The paper shows how the vibration system is affected by different feedback concepts and demonstrates the effectiveness of these concepts.
Purpose: In this work, active vibration control of rotating machines mounted on active machine foot mounts is investigated.
Methods: Therefore, a simplified 3D model is derived and the mathematical coherences are described. Different mathematical solutions are presented for special boundary conditions and a method called “vibration mode coupling by asymmetry” is derived.
Results: It could be shown that a symmetrical system with a machine design, where the center of gravity lies symmetrically between the machine feet with a vertical distance, and where all actuators are identical, represents a system, where all vibration shapes but one can be influenced by the controllers, when the gyroscopic effect can be neglected. In this case, a special vibration shape occurs—where the machine is only rotating at its vertical axis—which cannot be influenced by the controllers. When the stiffness and/or damping in axial and/or horizontal direction of only one actuator will be changed—which will lead to an asymmetrical system—the vibration shape with pure rotation at the vertical axis will not exist anymore. Now, the vibration shapes will become more coupled and they all can be influenced by the controllers, which is here called “vibration mode coupling by asymmetry”.
Conclusions: With the here presented method of “vibration mode coupling by asymmetry”, all vibrations mode shapes can
now be active controlled.
In the paper a theoretical analysis is deduced regarding vibration control of large induction motors – power rating >=1 MW – with roller bearings, using actuators between motor feet and a soft steel frame foundation. Based on a multibody model, the mathematical coherences are shown, including the feedback control system. Afterwards a numerical example of a soft mounted, converter driven, 2-pole induction motor (1.6 MW) with ball bearings is presented, where the bearing housing vibrations and the foundation vibrations are analyzed with and without control system. It could be shown, that without vibration control system the operating speed range cannot be used completely because of resonances, caused by the soft foundation. Therefore, critical speed areas occur, where steady state operation is not possible. However, with the vibration control system, the whole operating speed range can be used. The aim of the paper is to show the capability of using a vibration control system with actuators between motor feet and a soft foundation, for avoiding off-limits areas for the operation speed of large induction motors.
This paper describes the vibration behaviour of a small (11 kW) two pole induction motor, which is mounted on an elastic steel frame foundation with a special actuator system. This paper presents natural frequencies as a result of experimental model analysis of the whole system – motor, actuator system and steel frame foundation – and compares them to the numerical modal analyses using a finite element model. Additionally, forced vibrations are measured using the actuators as a shaker to de rive the resonance frequencies of the system. The measured natural frequencies by modal analysis, the measured resonance frequencies and the simulated natural fre quencies are compared to each other. Additionally, the necessary electrical power of the electrodynamic actuators is analysed.
The paper shows an analytical vibration model for stability analysis of soft mounted induction motors with sleeve bearings, especially focusing on the influence of electromagnetic field damping on the limit of vibration stability. The model is a multibody model, considering the electromagnetic influence – including the electromagnetic field damping effect –, stiffness and internal material damping of the rotor structure, stiffness and damping of the bearing housings and end shields, stiffness and damping of the foundation elements and stiffness and damping of the oil film of the sleeve bearings. The aim of the paper is to unite all these influences in a model and to derive a procedure for calculating the limit of vibration stability, with considering the electromagnetic field damping effect. Additionally, a numerical example is presented, where the influence of electromagnetic field damping on the limit of vibration stability is shown, as well as the influence of the foundation elements and of the internal damping of the rotor. The procedure and conclusions can also be adopted into finite-element analysis.
The paper shows a method how to detect the first critical bending speed of induction rotors supported in roller bearings, by using the electromagnetic excitation due to static rotor eccentricity. The advantage of using this kind of excitation is that the so produced electromagnetic force acts with double electrical supply frequency (2f1). Therefore, it is possible to excite the first bending mode by variating the electrical supply frequency f1, while the rotor is operated below the first critical bending speed. With the information about natural frequency of the first bending mode of the rotor, it is now possible to calculate the real roller bearing stiffness in reverse.
The paper shows an analytical rotordynamic model for stability analysis of induction rotors, supported in sleeve bearings, especially considering the influence of electromagnetic field damping and internal material damping of the rotor. The model contains radial and tangential electromagnetic forces considering electromagnetic field damping, stiffness and internal material damping of the rotor structure, stiffness and damping of the support, and stiffness and damping of the oil film of the sleeve bearings. The aim is to unite all these influences in one analytical model and to derive a procedure for calculating the limit of rotor stability.
In the paper, the threshold of vibration stability of induction motors with flexible shafts and sleeve bearings, mounted on soft steel frame foundations with active motor foot mounts, is analyzed. The developed model is based on a multibody model, considering electromagnetic influence, stiffness and internal damping of the rotor, stiffness and damping of the bearing housings and end shields, stiffness and damping of the foundation and stiffness and damping of the oil film of the sleeve bearings. Additionally the stiffness and damping of the motor foot mounts – which are positioned between the motor feet the soft steel frame foundation – are considered, as well as the controlled forces which are applied in the vibration system by the motor foot mounts, using PD-controllers. The aim of the paper is to unite all these influences in a mathematical model and to derive a procedure for calculating the threshold of vibration stability. Based on a numerical example it can be shown, that the threshold of stability can be pushed to very high rotor speeds, using active motor foot mounts.
The paper shows the influence of dynamic magnetic eccentricity on the
sleeve bearing housing vibrations of induction motors, considering electromagnetic field damping. The analytical model contains electromagnetic forces in respect of electromagnetic field damping, stiffness and internal (rotating) damping of the rotor, dynamic magnetic eccentricity, stiffness and damping of the support, and stiffness and damping of the oil film of the sleeve bearings. Based on an analytical rotordynamic model, a practicable method is presented, showing how to consider electromagnetic field damping, when analyzing forced vibrations caused by dynamic magnetic eccentricity, which can also be adopted in a Finite-Element-Analysis.
The paper shows an analytical rotordynamic model for induction rotors, supported in sleeve bearings, especially focusing on the influence of electromagnetic field damping on the forced rotor vibrations. The analytical model contains electromagnetic forces in respect of electromagnetic field damping, stiffness and internal material damping of the rotor, typical dynamic eccentricities of an induction rotor – mass eccentricity, bent rotor deflection and magnetic eccentricity –, stiffness and damping of the support, and stiffness and damping of the oil film of the sleeve bearings. With this rotordynamic model a useful possibility is shown, how to consider electromagnetic field damping, when analyzing forced vibrations caused by dynamic eccentricities. The aim of the paper is to show a method – based on a simple rotor dynamic model – how to consider electromagnetic field damping, which can also be adopted in Finite-Element-Analysis.