Takahiro Kondou

Modeling of eddy current damper composed of spherical magnet and conducting shell

If a conducting plate moves through a nonuniform magnetic field, eddy currents are induced in the conducting plate. The eddy currents produce a magnetic force of drag, known as Flemings left-hand rule. This rule means that a magnetic field perpendicular to the direction of movement generates a magnetic damping force. We have fabricated the eddy current damper composed of the spherical magnet and the conducting shell. The spherical magnet produces the axisymmetric magnetic field, and the shape of the conducting shell appears to combine a semispherical shell conductor and a cylinder conductor. When the eddy current damper works, the conducting shell is fixed in space, and the spherical magnet moves under the conducting shell. In this case, since there are magnetic flux densities perpendicular to the direction of movement, eddy currents flow inside the conducting shell, and then a magnetic force is produced. The reaction force of this magnetic force acts on the spherical magnet. In our study, eddy current dampers composed of a magnet and a conducting plate have been modeled using infinitesimal loop coils. As a result, magnetic damping forces are obtained. Our modeling has three merits as follows: the equation of a magnetic damping force is simple in the equation, we can use the static magnetic field obtained using FEM, the Biot-Savart law or experiments and the equation automatically satisfies boundary conditions using infinitesimal loop coils. In this study, we explain simply the principle of this method, and model an eddy current damper composed of a spherical magnet and a conducting shell. The analytical results of the modeling agree well with the experimental results.Copyright

Magnetic Damper Consisting of a Combined Hollow Cylinder Magnet and Conducting Disks

It is recognized that unstable vibration occurs at a rotating speed above the major critical speed by a rotating-conducting-disk type magnetic damper, but not by a rotating-circular-magnet type magnetic damper. In addition, magnetic dampers generally have relatively poor damping performance. In the present work, two new rotating-circular-magnet type magnetic dampers, (which consist of a combined hollow cylinder magnet with alternating directional magnetic poles), are introduced and their design method is presented. Applying the modeling method that the authors have been studying, a prototype magnetic damper with a combined magnet is fabricated and the damping ratios from the analytical results agree well with those from the experimental results. Rotating tests are performed and it is confirmed that unstable vibration does not occur at a rotating speed of more than twice the major critical speed. Based on these findings, an optimally designed magnetic damper with a combined magnet is developed and a damping ratio of 0.25 (damping coefficient of 215 Ns/m) is achieved.

Pattern Construction Generated in a Winder System of Textile Machine.

Elastic yarns in the winder system of a textile machine are deformed into a certain convex polygon in the process of winding at an operating speed of the bobbin holder rotating viscoelastically in contact with the drive roll. The polygonal deformation increases and develops into a serious vibration of the machine. This paper presents a model and a theoretical analysis to investigate the mechanism of this vibration phenomenon which is regarded as instability due to the time lag. The bobbin holder and the drive roll are both modelled by the one-mass one-shaft system. From the numerical computations using parameters obtained experimentally, the analytical results showed a good agreement with the phenomenon generated in the actual machines.

Calculations of lateral-torsional coupled vibration in AC motor-driven geared rotor system with mode synthesis approach

The calculation model by applying mode synthesis method for lateral (bending)-torsional coupled vibration of two-shaft geared motor-driven rotor system is proposed in this study. Mode synthesis method, which enables to greatly reduce degrees of freedom without increasing calculation errors, is essential for such time and memory consuming vibration calculation. This calculation model deals with stiffness and non-proportional damping for bearings or seals for lateral directions as inner elements comprising inner systems, whereas stiffness of gear tooth contact for its normal direction is handled as a boundary element as provision for further extension to more complicated tooth contact model. The reduced calculations of eigenvalues, frequency response analysis and transient excitation analysis for coupled lateral-torsional vibration were performed. The results show that reduced model properly inherits selected vibration modes from original DOF model.

A high-performance method of vibration analysis for large-scale nonlinear systems (application to flexural vibration of straight-line beam structure with nonlinear supports)

A rational method of dimensional reduction is developed in order to analyze accurately a nonlinear vibration generated in a large-scale structure with locally strong nonlinearity. In the proposed method, the state variables of linear nodes are transformed into the modal coordinates by using the real constrained modes that is obtained by fixing the nonlinear nodes, and a small number of modal coordinates that have a significant effect on the computational accuracy of the solution are selected and utilized in the analysis by combining them with the state variables of nonlinear nodes that are expressed in the physical coordinates. The remaining modes that have little effect on the computational accuracy are appropriately approximated and are eliminated from the system. From the reduced model constructed by these procedures, the steady state periodic solution and the stability, the transient solution and the quasi-periodic solution can be computed with a very high degree of computational accuracy and at a high computational speed. The effectiveness of the proposed method is verified by the computational results obtained for a straight-line beam structure with nonlinear supports.

Application of Transfer Influence Coefficient Method to Inverse Iteration Method.

The inverse iteration method is one of the most effective methods of eigenvalue analysis and is suited for both vibration and structural analyses. It can compute eigenvalues in the order of increasing absolute value, the convergence of iterative computation can be accelerated by applying the technique of origin shift. However, the inverse iteration method must be able to solve a large-sized simultaneous linear algebraic equation in every iterative process. In order to improve the computation accuracy and the computation speed of the inverse iteration method, we introduce the concept of the transfer influence coefficient method into the iterative process. The transfer influence coefficient method is advantageous in that it can solve simultaneous linear algebraic equations, and the memory size required in the computation is extremely decreased. The present method is applied to both the undamped and the damped systems.

直列形非線形構造物の強制振動解析 : 第2報, 断片線形系の取扱いと数値計算結果

A numerical computational method is suggested for the nonlinear analysis of a piecewise linear system including a system with clearances which is often found in practical mechanical structures. When this method is combined with the analytical method for the nonlinear system based on the concept of harmonic balance, the piecewise linear system is analyzed with high accuracy. The validity of the incremental transfer influence coefficient method formulated in the previous report for the structure connected in series is verified by the numerical computational results for some examples, as compared with those of the incremental harmonic balance method and the incremental transfer matrix method. As a result, it was confirmed that the incremental transfer influence coefficient method was the most effective among the three methods as the degrees of freedom of the structure treated become large and the accuracy of an approximate solution becomes high.

Nonlinear harmonic and parametric resonances of a roller chain stretched horizontally.

Chain has a heavy weight and a high tension stiffness, which are distinctive feature different from that of string. This paper describes the nonlinear harmonic and parametric resonances of a roller chain stretched horizontally, which is regarded as a system with many degree of freedom, when the elongation of the chain during vibration is taken into account. The resonance treated in this report is one of the resonances excited by combined forcing and parametric excitations in which the ratio of the frequency of the forced lateral displacement acting at the left end to that of the tension fluctuation is 1:2. The vibrationn characteristics are computed for three kinds of chain and are compared with the ones obtained from the experiments. In particular the effect of the chain weight upon the resulting vibrations is considered. A fine agreement between experimental and analytical results was confirmed.