3D Model for Active Vibration Control of Rotating Machines Mounted on Active Machine Foot Mounts Using Vibration Mode Co
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ORIGINAL PAPER
3D Model for Active Vibration Control of Rotating Machines Mounted on Active Machine Foot Mounts Using Vibration Mode Coupling by Asymmetry Ulrich Werner1 Received: 7 April 2020 / Revised: 14 September 2020 / Accepted: 22 September 2020 © The Author(s) 2020
Abstract 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. Keywords Active vibration control · Rotating machines · Actuators · 3D model · Vibration analysis
Introduction Large rotating machines are often directly mounted on elastic steel frame foundations, which sometimes lead to vibration problems, where e.g. critical speeds are lying in the operation speed range [1–5]. Implementing active vibration control [6–24] is an appropriate method to reduce vibrations, which is used in different technical applications. Here, the active vibration system consists of active machine foot mounts—actuators, which are positioned under the machine feet and only acting in vertical direction—and vibration sensors, which are mounted at each machine foot and detect * Ulrich Werner ulrich.werner@th‑nuernberg.de 1
Nuremberg Tech, Georg Simon Ohm University of Applied Sciences Nuremberg, Faculty EFI, 90489 Nuremberg, Germany
the vertical vibrations leading this information to separate controllers (Fig. 1). This concept was basically described and investigated in [25], but only for induction motors and it was only based on a plane 2D-model. In this paper, a general model for rotating machines mounted on actuators is derived, based on a 3D model. Additionally, the gyroscopic effect of the rotor is considered here in the paper. The 3D model is kept very simple here, because the main task is here not to derive a detailed mod
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