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This paper describes the open loop configuration of the simulation and measurement of a controller hardware and a voice coil actuator for vibration control of a 11 kW motor on steel frame foundation. The paper discusses the phase response regarding damping behavior of the actuator force and identifies approaches for improvements. Further, the paper offers a comparison of measurements as a result of the run up of the motor in open loop and closed loop operation with rubber elements and with steel springs. It is shown that all vibration modes with vertical movement at the motor feet can be reduced. Finally, the paper discusses the change in the system’s natural frequencies due to the replacement of the rubber elements by steel springs.
In the paper, a generalized mathematical formulation for active vibration control of rotating machines with voltage-driven electrodynamic actuators between machine feet and steel frame foundation is derived. This generalized mathematical formulation is based on a state space description in the Laplace domain, where the state space vector is lead back, for considering the actuator forces. The aim of the paper is that this generalized mathematical formulation can be used now for arbitrarily models of rotating machines—1D-, 2D-, and 3D-models— with voltage-driven electrodynamic actuators between machine feet and steel frame foundation, and where the vertical vibration acceleration at each machine foot is lead back to a separate controller. Of course, this mathematical formulation can also be adopt easily to other boundary conditions. As an example, the generalized mathematical formulation is used here for a 1D-model of a rotating machine, to calculate the poles and the frequency response functions.
Purpose:
In the paper, a theoretical analysis—based on a 2D multibody model—is presented regarding active vibration control of a rotating machine with voltage-driven electrodynamic actuators between machine feet and steel frame foundation under multiple base excitations.
Methods:
Mathematical formulations are derived in the time domain and then transferred into the Laplace domain, where a state space formulation is used to describe the controlled vibration system. With this mathematical formulations, it is possible to analyze separately the two different kinds of actuator forces—the actuator forces, caused by the motion-induced voltage and the actuator forces caused by the control system—and their influence on the vibration behavior. Afterward, the
mathematical formulations are transferred into the Fourier domain, for considering harmonic excitations of the base. Also a numerical example is presented, where different cases regarding machine mounting and operation conditions are investigated and compared to each other.
Results:
It could be clearly demonstrated that with the presented control system, most of the resonance peaks in the frequency responses could be strongly damped.
Conclusions:
With the presented mathematical formulations, the controlled vibration system can be well described, considering separately the two different kinds of electrodynamic actuator forces and their influence.
In the paper, a state space model for vibration control with arbitrary controller structures for soft mounted induction motors with sleeve bearings fixed on active motor foot mounts is shown. Besides the mathematical description of the forced vibrations caused by dynamic rotor eccentricity, a procedure is presented to derive the threshold of vibration stability. The challenge of the paper is the use of arbitrary controller structures with different feedback strategies – feedback of the motor feet displacements, velocities or accelerations – in combination with a special vibration system. This specialty is, that the stiffness and damping matrices depend on the rotor angular frequency Ω, which corresponds to the excitation angular frequency, when analyzing the forced vibration, and depend additionally on the natural angular frequency 𝜔 stab of the critical mode, when analyzing the threshold of stability. After the mathematical description is shown, a numerical example of a 2-pole induction motor (power rating 2.4 MW) is presented, in which the threshold of stability is analyzed as well as the forced vibrations due to dynamic rotor eccentricity by investigating the bearing housing vibrations, the foundation vibrations and the actuator forces.
A theoretical analysis regarding active vibration control of rotating machines with current-controlled electrodynamic actuators between machine feet and steel frame foundation and with velocity feedback of the machine feet vibrations is presented. First, a generalized mathematical formulation is derived based on a state-space description which can be used for different kinds of models (1D, 2D, and 3D models). It is shown that under special boundary conditions, the control parameters can be directly implemented into the stiffness and damping matrices of the system. Based on the generalized mathematical formulation, an example of a rotating machine—described by a 2D model—with journal bearings, flexible rotor, current-controlled electrodynamic actuators, steel frame foundation, and velocity feedback of the machine feet vibrations is presented where the effectiveness of the described active vibration control system is demonstrated.
The paper presents a simplified 3D-model for active vibration control of rotating machines with active machine foot mounts on soft foundations, considering static and moment unbalance. After the model is mathematical described in the time domain, it is transferred into the Fourier domain, where the frequencies response functions regarding bearing housing vibrations, foundation vibrations and actuator forces are derived. Afterwards, the mathematical coherences are described in the Laplace domain and a worst case procedure is presented to analyze the vibration stability. For special controller structures in combination with certain feedback strategies, a calculation method is shown, where the controller parameters can be directly implemented into the stiffness matrix, damping matrix and mass matrix. Additionally a numerical example is presented, where the vibration stability and the frequency response functions are analyzed.
The paper presents a theoretical analysis of different vibration control strategies of soft mounted induction motors with sleeve bearings, using active motor foot mounts. After the vibration model is presented, different controllers in combination with different feedback strategies are mathematically investigated. The focus is here on the forced vibrations, caused by dynamic rotor eccentricity—rotor mass eccentricity, magnetic eccentricity and bent rotor deflection. After the mathematically coherences are described, a numerical example is shown, where the forced vibrations caused by bent rotor deflection are investigated, for different control strategies, where the mass matrix, the stiffness matrix and the damping matrix are influenced by different control parameters. The aim of the paper is to show the mathematically coherences and the possibility to influence the vibration behaviour, by different control strategies to optimize the vibration behaviour of soft mounted 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 an active vibration control system (AVCS). On the one hand the paper presents detailed 3D finite element models for vibration analysis and compares the vibration simulation results to vibration measurement results and on the other hand, the paper presents a comparison of different settings of the test bench-motor mounted directly on the steel frame foundation and motor mounted on the developed AVCS. Further, the comparison of experimental modal analyses with open and close control loop operation are shown to demonstrate the efficiency of the AVCS. Finally, the paper gives an outlook about the scaling of the AVCS for motors in the megawatt range.
In the paper, the vibration control of induction motors with sleeve bearings—mounted on soft steel frame foundations—using active motor foot mounts is analyzed. The presented model is based on a multibody model, considering electromagnetic influence, stiffness, and rotating damping of the rotor, stiffness and damping of the bearing housings with end shields, of the oil film in the sleeve bearings, and of the foundation. Additionally, the stiffness and damping of the motor foot mounts—which are positioned between the motor feet and the 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, including the control system. Based on a numerical example, it can be shown that the vibration behavior of soft mounted induction motors can be clearly improved and that critical speeds in the speed range can be avoided, using active motor foot mounts.