Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed

We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.     

Magnetic recording characteristics of a flexible disk with a non-magnetic underlayer

We have examined a flexible disk for high recording density (35 kFCI, 542 tpi), and with a maximum transfer rate of 4.5 MBPS. By setting the magnetic layer thickness at less than 0.4 μm, the media coercivity at more than 120 kA/m, and applying it to a non-magnetic underlayer, we have realized useful flexible disk media wear resistance of 2×10⁷ passes.     

The coupled transverse vibrations of a spinning membrane disk with a central hub

The results of an investigation of the effect of hub coupling on the transverse free vibrations of a spinning membrane disk are presented. The equations of motion are formulated by an energy method and Rayleigh-Ritz procedure. It is found by using assumed modal distributions consisting of the normal modes for the spinning membrane with a rigidly clamped hub that the problem partitions into sub-problems associated with (i) symmetric vibrations involving only the generalized coordinates from the symmetric input modes, (ii) unsymmetric vibrations involving only the input modes with one nodal diameter, and (iii) unsymmetric vibrations involving input modes with more than one nodal diameter. The degree of hub coupling is found to depend primarily on the ratio of the mass of the membrane to the mass of the disk and on the ratio of the radius of the hub to the radius of the disk.     

大口径薄片激光器失调输出特性

对大口径的薄片激光器的失调输出特性进行了理论和实验研究,V-型腔由平面输出耦合镜和凹面反射镜及孔径光阑组成。基于矩阵光学和失调衍射积分方程得到了激光器的功率失调曲线。实验测量了在200 Hz泵浦频率下加入不同孔径光阑后谐振腔失调对输出功率的影响和谐振腔失调对光束质量的影响,以及在300 Hz泵浦频率下输出功率分别与平面输出耦合镜和凹面反射镜失调的关系。实验结果表明:失调输出功率和失调角度成二次函数关系,失调容限和腔镜口径成正比,光束质量因子随失调角度的增大而变小。     

The transverse vibration of spinning aeolotropic disk

The paper represents a general treatment of the problem of transverse vibration of a thin high speed rotating aeolotropic elastic circular disk of uniform thickness.     

Dynamic stability of rotating flexible disk perturbed by the reciprocating angular movement of suspension-slider system

To simulate the dynamic process of a magnetic head reading/writing data in a hard disk drive, a rotating flexible thin disk perturbed by the reciprocating angular movement of a suspension-slider system is modelled, where the suspension-slider system is considered as a mass-damping-spring loading system. A system dynamic model is formulated as a parametrically excited system, and its dynamic stability is studied by Hill’s method involving harmonic balance. The reciprocating angular movement of the suspension-slider system causes system parametric instability at some angular movement frequencies. The large-amplitude angular movement is especially dangerous, and angular movement frequency must be reduced when the slider works at large radii of the disk. The parametric instability can be avoided or suppressed by operating at: low-frequency and small-amplitude reciprocating angular movement, small mass, large natural frequency and damping of the suspension-slider system, and low-speed rotation of the disk.     

Determination of the energy levels of total and internal rotation of arbitrary polyatomic molecules with a single internal rotation axis

An algorithm is developed for calculating the eigenvalues of the Hamiltonian operator in the case of asymmetric-asymmetric molecules with a common axis of internal rotation, taking into account the total and internal rotation of these molecules. The algorithm is based on the Ritz variational method. A program is written for reducing a symmetric band matrix to tridiagonal form with subsequent diagonalization of the resulting matrix.State Textile Academy, Ivanovo. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–88, October, 1995.     

Beam alignment with the axis of a rotation stage for laser fabrication of microcircular structures

An optical technique to align laser beam with the axis of a rotating stage is proposed for laser fabrication of circular microstructures. The laser beam is first aligned parallel to the rotation axis and subsequently adjusted to coincide with the axis. An optical arrangement consisting of two quadrant photodiodes for the x- and y-directions and a specially designed beam splitter is utilized for the alignment. Mathematical modeling of the alignment system is carried out to estimate alignment errors caused by misalignment of mirror surfaces in the beam path. It is shown that parallelness of the laser beam to the rotation axis is a key factor to reduce alignment errors. The proposed method was applied to a microstereolithography system and proved that the laser beam can be aligned within a distance of about 25 μm from the rotation axis.     

Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z = 500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ? in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ? in far-field. At receiving plane z = 500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.     

ECT of ethanol and hexane mixtures in the spinning disk system

The paper presents the research results of electrostatic charging tendency (ECT) of ethanol and hexane mixtures, a liquid of a simple chemical structure and high purity (pro analysis). The research work was carried out in a spinning disk system, where the factors influencing the value of the electrification current registered were the composition of the mixture and the rotational speed of the disk. The research results showed that the biggest ECT changes occur in the range of up to 10% of ethanol content in hexane and the electrification current characteristic has a visible maximum for the mixture, the contents of which constitute 95% of hexane volume and 5% of ethanol by volume. In the next stage of the research work physicochemical and electric parameters were measured in order to determine the connection between the properties of the mixtures under study and the amount of the electrification current generated.     

A spinning shell around a Kerr black hole in a slow rotation approximation

This paper explores a thin shell of ideal fluid surrounding a Kerr black hole assuming a slow rotation and retaining only first order terms of expansion in angular momentum. It is shown that a physically feasible shell rotates rigidly in this approximation and that the interior black hole mass is constrained by other parameters of the system. Furthermore, it is shown that the local inertial frames are “dragged” by the shell as the shell radius approaches the gravitational radius, which is similar to results of studies considering a flat interior.     

高斯光束通过含失调窄缝光阑的失调光学系统的传输特性

 利用硬边窄缝光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了高斯光束经含失调窄缝光阑的失调光学系统传输的近似解析式。模拟结果表明输出光束场分布与光束参量、光阑尺寸、ABCD矩阵元、光阑失调量和光学系统失调量有关。针对给定的光学系统和高斯光束定量分析了各失调量对输出光束场分布的影响,结果表明:光阑横向位移、光学系统横向位移和角位移均引起垂直于z轴截面内明显的光强非轴对称分布。当光阑半宽度为1 mm时,光阑的衍射作用使腰斑半径为0.5 mm的高斯光束产生-1.586π～1.465π范围的相对相移,且光阑横向位移、光学系统横向位移和角位移均引起焦平面前后相对相移的迅速变化。随光阑宽度变小,各失调量对输出光束特性的影响越明显。     

Determination of aerodynamic characteristics of turbine vanes with vertical rotation axis

Presented below are the results of tests of turbine vanes with vertical rotation axis aimed at determination of their aerodynamic characteristics. Three types of vanes with the profiles in the form of semicylinder, semiellipse, and semiellipse with stabilizing plane have been tested. The last type of vane has been tested with stationary and rotary stabilizing planes.     

Vibrational response of a moving suspension-slider loading system exciting a rotating flexible disk

To investigate the vibrational response of the magnetic read/write head in hard disk drives this paper models a rotating flexible disk excited by a moving suspension-slider system which is considered to be a mass-dashpot-spring loading system, with the initial unstressed transverse runout integrated into the rotating disk dynamic model. The slider motion on the disk surface is driven by the suspension rotating at a constant speed. By subtracting the steady-state deflection component from the instantaneous deflection response of the rotating disk system, the relative vibration transverse deflection of the slider caused by the motion of the suspension-slider loading system is obtained. The effects of the slider initial and final positions, speed of movement, the disk rotational speed, and the disk mode of the initial transverse runout on the maximum amplitude of the relative vibration deflection are analyzed.     

Determination of the losses in a ruby laser with a misaligned resonator

A technique for the determination of the losses in a ruby laser with a misaligned resonator is presented. It is shown that a probabilistic formula for the power generation correctly describes the relation between the generated power and the angle between the resonator mirrors if the experimentally determined loss figures are inserted into this formula.