502 分散制御による多自由度振動系の共振点駆動 : クロスフィードバック制御の付加によるロバスト性の向上

A control method has been developed to always excite a multi-degree-of-freedom system efficiently at a resonance frequency. When an excitation point corresponds to a vibration detection point in the multi-degree-of-freedom system, a phase lag at a resonance frequency and a phase lead at an anti-resonance frequency alternately appear in the vibration characteristics, and the phase lag becomes 90° at all the resonance frequencies. Therefore, if a controller that has a phase lag of 90° and a constant gain in a wide frequency range is used, self-excited vibration is generated at all the resonance frequencies. The self-excited vibration controller can be expressed as the sum of the positive velocity feedback control with a high gain in a high frequency domain and the integral control of the displacement with a high gain in a low frequency domain. A local feedback controller for each actuator consists of a self-excited vibration controller, a saturation element that limits excitation force, and a negative velocity feedback controller that provides damping. A driving at a resonance point system using many actuators with local feedback control, that is, decentralized control, is excellent in its adaptability to the environment, in its extendibility, and in its fault tolerance. In addition, the self-excited vibration mode can be freely switched on by changing the frequency of the sine wave that causes the self-excited vibration.

For the forced excitation of a large structure such an airplane using one actuator, all of the natural vibration modes cannot be excited because the vibration does not propagate in the entire structure. Therefore, vibration test of a large structure uses a lot of actuators. When we drive a lot of actuators by multi-point excitation using centralized control, we have to adjust command signals, such as excitation frequencies, magnitude and phase of the excitation force, to every natural vibration mode. However, it takes a long time to measure natural vibrations in this way. Thus, we use a method for driving at resonance point by using the self-excited vibration generated by the local feedback control that an excitation point corresponds to a vibration detection point. However, the self-excited vibration cannot excite all of the natural vibration modes because some natural vibration modes have changed to the other one which is easily excited. Then, we use forced entrainment to excite all of the natural vibration modes by giving continuous exciting force to the actuator situated on the tip of the object in order to synchronize the self-excited vibration actuators. We carried out an experiment about excited point and excited force performing more appropriate, and as a result, we found an appropriate those. Therefore, we carried out an experiment about excited point and excited force performing more appropriate, and as a result, we found an appropriate those. By doing forced entrainment properly, all of the natural vibrations could be measured.

This paper describes measurement of natural vibration of acoustic space by multi-point excitation using decentralized control. A set of acoustic excitation system consists of a speaker, a microphone, and a local feedback controller. The acoustic excitation system handles the frequency range from 100Hz to 500Hz higher than a mechanical vibration system does. So the phase lag of an actuator, the dead time by propagation of sound, and the dead time by sampling of a controller influence the local feedback control. First, the various phase lag in the acoustic excitation system are identified. The speaker has the second vibration property derived from mechanical resonance, and the first delay property derived from induced voltage of coil. The propagation of sound from the speaker to the microphone causes the dead time. Sampling time of the controller also causes the dead time from the input signal to the output signal. Second, the way to compensate these phase lag in the acoustic excitation system is proposed. Resonance of the speaker makes the phase decrease 180 degree at the resonant frequency. To suppress a change in the phase in the frequency range from 100Hz to 500Hz, the resonant frequency moves to less than 100 Hz. The phase lead and the phase lag after the resonant frequency movement are compensated by the second order phase lag-lead element. The natural vibration of one-dimensional/two-dimensional acoustic space is self-excited by the acoustic excitation system with the phase compensation. By closing the feedback loop, the first mode natural vibration is excited. By adding sinusoidal signal from outside, all natural vibration in the frequency range from 100Hz to the 500Hz is self-excited (forced entrainment).

Step-type compound planetary gear sets are widely applied in vehicle systems. Comprehensive dynamic model of step-type compound planetary gear sets, which includes translational, rotational vibrations and static transmission errors, was established. Natural vibration characteristics of the system, such as natural frequencies and vibration modes, were analyzed. Belt shape distribution characteristics of its natural frequencies was researched. According to vibration characteristics of both central components and planets, natural vibration modes of the system are classified into three types: central components translational vibration and planets random vibration, central components rotational vibration and planets identical vibration, central components static and adjacent planets reverse vibration mode.

In this study, a 3D model of a two‐step sine movable tooth drive is developed in the UG software. The finite element model (FEM) analysis package, ANSYS, is used to calculate the natural frequencies and vibration modes of the drive system. The results show that the first twenty natural frequencies can be classified into five families, including the total system vibration mode, single‐element vibration mode, two‐element vibration mode, three‐element vibration mode, and four‐element vibration mode. The effects of the system parameters on the natural frequencies and the vibration modes are investigated. The track amplitude, the movable tooth radius, the radius of the movable tooth rotation, and the number of movable teeth affect the natural frequencies and vibration modes of the drive system.

A schematic description of a stand based on a digital speckle interferometer with a diffuse reference wave is given, which makes it possible to determine the natural frequencies and vibration modes of the blades in real-time. In the frequency range of 100 ... 3000 Hz, an experimental study of the vibration characteristics of a turbine rotor blade of a gas turbine engine was carried out, under free boundary conditions, which were achieved by placing the blade on soft silicone racks. Blade dimensions: height along the trailing edge - 288 mm, a chord in the middle section - 88.5 mm. 7 modes of vibrations have been identified. The technology of creating a solid-state geometric model of a rotor blade based on a faceted body obtained by 3D scanning with an accuracy of 0.01 mm is presented. The finite element method, using the Lagrange variation principle, is used to calculate the values of natural frequencies and vibration modes of a blade based on the developed geometric model. Concerning the frequency range 100 ... 3000 Hz, using the Ansys Workbench software package, a series of calculations of the resonant frequencies of the blade, by the finite element method, in the range of variation of the values of mechanical properties was carried out: Young's modulus E = 200 ... 230 GPa; Poisson's ratio μ = 0.26 ... 0.3. The density of the material: ρ = 7830 kg / m³, determined experimentally, by the method of hydrostatic weighing. The final element used in the calculation is (tetrahedron) SOLID 187; the minimum element size is 0.6 mm. The total number of elements is about 1.5 ∙ 10⁶. Based on the two-dimensional spline interpolation of the calculated data, the dependence of the standard deviation of the calculated and experimental values on the adopted mechanical properties of the material of the rotor blade is built. In the range of values E = 215 ... 217 GPa and μ = 0.295 ... 0.3, the minimum standard deviation of the calculated frequencies from their experimental values is 0.73%. Provided the value of the standard deviation of frequencies is 1%, the range of values of mechanical properties will be: E = 211 ... 220 GPa and μ = 0.26 ... 0.3. It is shown that narrowing the studied range of values of Young's modulus and Poisson's ratio does not significantly affect the results obtained.

Abstract. Research on the vibration characteristics of the mechanical systems is a necessary step for the stable and reliable operation of high-end equipment. The 6 degrees of freedom parallel mechanism is proposed for the supporting mechanism of the antenna. First, the dynamic equations of the moving platform and branch of the mechanism are established. The closed-form dynamics of the mechanism are derived based on the Newton–Euler method. In addition, the vibration equation of the parallel antenna is established based on the vibration theory, and the relationship between the natural frequency, displacement response, and vibration frequency is obtained. Afterward, the pitch and roll poses of a 1.8 m aperture antenna are developed based on a MATLAB software simulation. The actuation forces of parallel antenna under no-load and load conditions are simulated. Finally, the natural frequencies and vibration modes of the initial position and roll (20∘) are simulated based on the Adams software vibration analysis module. Furthermore, the relationship between the displacement response of the moving platform and the resonant frequency is studied based on the harmonic response analysis. The control strategy based on the dynamic model improves the control accuracy of parallel antenna. This research work provides a guarantee for the dynamic characteristics analysis and engineering application of parallel antenna.

Based on the principle of axial active magnetic bearing system with single degree of freedom, the difference between magnetic system vibration mode and the traditional bearing system vibration mode were described. Initial four order natural frequencies and vibration mode were calculated by the module of modal analysis of ANSYS11. Axial displacement and control current influence on natural frequencies and vibration mode were also analyzed. At last they were compared with the results of experimental modal analysis. Analysis shows that there was a certain difference between the results of finite element method and experimental model analysis, but the difference was small. It provided theoretical basis for flexible system design and dynamic design.

In this paper, a micro electromagnetic harmonic drive system is proposed. Considering Van der Waals force, dynamics equation of the flexible ring for the micro drive system is deduced and resolved. Using the equations, the effects of the molecule force on the natural frequencies and vibration modes of the drive system are investigated. Results show that considering molecule force, natural frequencies of the flexible ring are reduced and its vibration modes are changed. For lower order modes, smaller clearance between the flexible ring and stator, smaller thickness of the flexible ring and larger radius of the flexible ring, the effects of the molecule force on the natural frequencies and vibration modes are more obvious.

A method for determining the location and depth of a notch has been developed on the basis of the results of a finite-element analysis of natural vibration modes of a cantilever with a notch. A phenomenological relationship is obtained that relates the degree of cantilever damage to the characteristic features of its natural vibration modes. A new diagnostic sign of the degree of cantilever damage is proposed, which is the angle between the tangents on the plot of the natural form of the fourth vibration mode. An approximate equation is deduced that describes the dependence of the angle between the tangents at the “break” point of the shape of the fourth vibration mode on the depth of a notch in the cantilever.

The mode characteristics and the parameter sensitivity for a two-stage NGW spur planetary gear system are studied based on the principles of structure natural dynamical characteristics. Considering the influence of flexible structure including shaft, the planet carrier, and the ring-gear, the coupled lateral-torsional-axial vibration dynamical model of the planetary gear system is established under the generalized coordinate system using the shafting element method. With the model, the natural frequency and vibration mode are solved, and the results indicate that the flexibility of ring-gear has a greater effect on natural frequency. Several distinct types of vibration mode are summarized, such as planet torsional mode, sun-gear shaft axial mode, ring-gear axial mode and so on. However, the translational mode which is one of the modes in the coupled lateral-torsional lumped mass model is not found in this study. Within the scope of the time-varying, mesh stiffness mainly affects the planet torsional mode of corresponding stage. Furthermore, the variation of radial bearing stiffness will also do effect on axial vibration mode, and the variation of bearing stiffness not only affects the vibration modes of adjacent stage of planetary gear train, but also affects the nonadjacent stage. The results demonstrate the coupling characteristics of the system under the free vibration condition.

The paper reports an algorithm to analytically solve one of the problems in the mechanics of elastic bodies, which is associated with studying the natural vibrations of a composite two-stage plate whose concave part is smoothly aligned with the part of a constant thickness. We have defined patterns for stating the boundary and transitional conditions, which should be taken into account when considering the natural vibrations of a two-stage plate.The ratios have been obtained, which make it possible to study the distribution of deflections and determine the values of amplitudes of the curved vibrations of the plate. It was noted that the modes of vibrations are based on the symmetry and factorization methods that we had developed and refined earlier. Specifically, it has been found that the deflections can be explored through expressions that are derived through the sum of relevant solutions to two linear second-order differential equations with variable coefficients.Based on the proposed approach, a system consisting of eight homogeneous algebraic equations has been defined, which allowed us to build a frequency equation for the plate rigidly fixed along the inner contour and free along the outer contour. We have determined the values for the plate’s natural frequencies for the first three modes of natural vibrations. Moreover, in order to verify and expand a set of plates of different configurations, the plates with two types of concave in their variable part have been considered. The new approaches and the ratios based on them could be useful for the further advancement of methods for solving similar problems in mathematical physics on natural values. A practical implementation is the problems about the vibrations of plates with variable thickness and of different modes

To realize metal foil consolidation, a push–pull high-power ultrasonic consolidation resonance system is designed. Firstly, the structure of a high-power piezoelectric transducer was designed and calculated, the push–pull ultrasonic consolidation resonance system was designed according to requirements of ultrasonic consolidation. Secondly, the finite element modal analysis of the ultrasonic consolidation resonance system was carried out, the natural frequency and vibration mode were obtained. The dynamic simulation of the ultrasonic consolidation resonance system was carried out based on the four-terminal network method and MATLAB/Simulink, the displacement of piezoelectric transducer and the resonance system was obtained, the output displacement of piezoelectric transducer and the consolidation sonotrode end surface is 6 μm and 20 μm respectively. Thirdly, the dynamic model of the consolidation resonance system was established, according to the transfer function, the root locus method and frequency response method were used to analyze the characteristics of the system. Finally, the sweep frequency and impedance measurement of piezoelectric transducer were carried out, and the sweep frequency and fixed frequency measurement of the ultrasonic consolidation resonance system were also carried out. Experimental results show that the resonant frequency of piezoelectric transducer is 19,875 Hz, and the minimum impedance value is 261.43 $$\Omega$$ when the frequency is near 20 kHz. When applying 120 V and 160 V voltage signal, the resonant frequency is 20,039 Hz and 20,055 Hz, the maximum displacement of the sonotrode which is excited by double piezoelectric transducers is about 16 μm. The ultrasonic consolidation machine is fabricated, which can meet requirements of metal foil consolidation, such as high-power and amplitude.

ACOUSTIC INSULATION PROVIDED BY A SINGLE WALL SEPARATING TWO CONTIGUOUS TUNNELS VIA BEM

High reliability and performance are requested to main propulsion turbine for LNG carrier. In respect of reliability concerning vibration characteristics of turbine structure to avoid resonance with propeller excitation, this paper describes the results of the vibration analysis on the model of supporting structure of propulsion turbine by finite element method and excitation test on the actual machine on board. Calculated vibration characteristics such as natural frequency, vibration mode and acceleration response agree well with the measurement results of excitation test. -Reprinted from Journal of the M.E.S.J., Vol. 29, No. 2 –