Lateral vibration control of a shafting-hull coupled system with electromagnetic bearings

Abstract

In order to suppress lateral vibration transmission and reduce acoustic radiation of a shafting-hull coupled system, a new approach using electromagnetic bearings in the shafting system is proposed. The dynamic characteristics of the electromagnetic bearings, especially the equivalent stiffness and damping as well as the applicable scope of linearization of the electromagnetic bearings, are analysed at first. With the equivalent parameters, a dynamic model of the shaftinghull coupled system is established subsequently by using the frequency response synthesis method to derive frequency response functions associated with the lateral vibrations. Finally, the influence of the control parameters of the electromagnetic bearings on vibration transmission in the shafting-hull system is studied. Analysis results indicate that lateral vibration responses are suppressed significantly when electromagnetic bearings are introduced into the shafting-hull system, and as a result, sound radiation of the system is reduced, which demonstrates that the proposed approach is effective in controlling vibration transmission in the shafting system.

The Boundary Element Method in Acoustics: A Survey

“…Modal analysis via the finite element method returns a standard and sparse eigenvalue problem (88), modal analysis by the boundary element method yields a non-linear eigenvalue problem (69) and hence the hybrid coupled FEM-BEM system is also non-linear. There are several reported implementations of coupled fluid-structure modal analysis using the boundary element method [19,[255][256][257]265,284,287,[289][290][291][292][293][294][295][296][297][298][299][300][301]. The coupled matrices are generally much larger than for the boundary element method alone and this can be resolved by determining the response in the dry structural modal basis and coupling that with the boundary element model [299,301].…”

Influence of electromagnetic bearings on lateral vibrations and sound radiation of a shaft-hull system

“…where Q = {Q 1y , Q 1z , Q 2y , Q 2z , Q 3x , Q 3y , Q 3z } T is the interfacial force vector, F = {F x , F y , F z } T is the disturbance force vector, H Q is a 7-by-7 matrix, H F is a 7-by-3 matrix and the elements of these matrices are the FRFs between Point 0 and Points 1-6; more details of H Q and H F can be referred to Qin et al 15 For example, when F is given as {0, 1, 0} T , that is, the unit vertical force at Point 0, the matrix Q can be calculated by equation (4). And then by substituting matrix F and matrix Q into equations (1) and (2), the displacements can be obtained.…”

“…where Q = { Q 1 y , Q 1 z , Q 2 y , Q 2 z , Q 3 x , Q 3 y , Q 3 z } T is the interfacial force vector, F = { F x , F y , F z } T is the disturbance force vector, H Q is a 7-by-7 matrix, H F is a 7-by-3 matrix and the elements of these matrices are the FRFs between Point 0 and Points 1–6; more details of H Q and H F can be referred to Qin et al 15…”

“…Among these bearings, the rear bearing and the front bearing are commonly water-lubricated rubber bearings which will cause friction noise due to poor lubrication. Qin et al 15 studied the influence of the EMBs only by changing the equivalent stiffness and damping at the bearings. But in this article, the dynamic magnetic forces of the EMBs are considered as the active control forces acting on the shaft and counteracting on the hull structure and possible performance on vibration transmission suppression and reduction of sound radiation is investigated.…”

Investigation on vibration transmission control of a shafting system with active orthogonal support

“…Hu et al (2012) proposed an active control method to attenuate the longitudinal vibration of shafting systems, and the experimental results indicate that the control method can effectively suppress periodic disturbances. Qin et al (2019) proposed a new approach that uses electromagnetic bearings to suppress lateral vibration transmission and reduce acoustic radiation. Zheng et al (2019) investigated an adaptive control method with dynamic interpolation for the active longitudinal vibration control of propulsion shafting systems.…”