Rotational Moment Of Inertia Research Articles

Dynamic behavior of pin-free beam with torsional spring and hub at pinned end

This paper described the free vibration of a Euler-Bernoulli beam and discovered the first five dimensionless natural frequencies and mode shapes of motion for the pin-free beam model with a helical spring and rotating mass on the pinned side of the beam. The effect of changing the dimensionless torsional stiffness ratios was investigated, as was the effect of changing the dimensionless rotational inertia torque ratios Concerning the vibration properties of the beam. The mathematical equations that regulate the pin-free beam model were constructed using the exact analytical solution, establishing the Admissible Function and the natural frequency equation for the basic pin-free beam system. The approximate Rayleigh-Ritz approach was then used to determine the first five dimensionless natural frequencies, as well as the movement pattern for the pin-free beam model with a helical spring and a rotating mass on the side of the hinge. The results demonstrated that modifying the beam's natural frequencies is dependent on the ratios of the additional torsional spring parameters as well as the ratios rotational moment of inertia. The threshold system frequencies increase when the spring parameters are the major factor, and decrease when the inertia moment parameters are the main factor. Both play a role in influencing natural frequency to varied degrees. Unifying the final distribution of parameters might lead to optimizing the impact of parameters on the natural frequencies of the system.

Collective-subspace requantization for sub-barrier fusion reactions: Inertial functions for collective motions

The adiabatic self-consistent collective coordinate (ASCC) method is used to determine the optimum reaction path and to calculate the potential and the inertial functions of the reaction model. The properties of the inertial functions are investigated with the ASCC method, in comparison with those of the cranking formulae. In addition, the properties of the pair rotation are investigated in the BCS pair model. The moments of inertia for rotation in both the real and the gauge spaces may decrease as the deformation develops.

Effect of damping and rotor moment of inertia on stability of self-synchronization for two unbalanced rotors

The self-synchronization of rotors in a nonlinear system has both academic and practical importance because of its applicability as a source of excitation for vibratory machines. Although the characteristics of such self-synchronization can be clarified by analyzing the periodic solutions of the equations of motion, only self-synchronization corresponding to the stable periodic solution is realized in actual systems. The stability of the solution is thus one of the most important characteristics of self-synchronization. In this paper, to stabilize periodic solutions suitable for application to vibratory machines, the effects of the damping of the rigid body and the moment of inertia of the rotors on stability are examined using a system that consists of two unbalanced rotors installed in a rigid body. High-precision analysis conducted using the shooting method shows that it is possible to stabilize the instabilities caused by period-doubling and Hopf bifurcations while keeping other characteristics, such as the synchronous frequency and the rigid body amplitude, mostly unchanged. The findings of this study can serve as a guide to extending the range of stable periodic solutions and are thus expected to be useful in the design of systems that utilize the self-synchronization of rotors.

Design of optimal-robust control of step motors with partially unknown parameters and disturbances

The paper describes the design of a novel control law for step motor under participially unknown parameters and bounded external disturbances. The unknown parameters and disturbances are related to the motor torque, the rotor moment of inertia, the viscous friction, the resistance and the load torque. The design of a novel control law is based on feedback linearization and linear robust control. The gain of a linear control law is calculated by solving the linear matrix inequality and some optimization problems. The simulations illustrate the efficiency of the proposed scheme in comparison with classical PID-controller and adaptive control law.

A rectified unidirectional rotary PTO for two-body wave energy converters

This work presents a new mechanism for a mechanical power take-off (PTO) system that can be used in a variety of wave energy converters (WECs). This mechanism uses two ball screws to convert the relative linear motion of the WEC bodies into unidirectional rotary motion. The resulting rotary motion finally causes a generator to rotate and generate electricity. Due to the oscillatory nature of the wave, the relative velocity of the WEC bodies will have a sinusoidal motion; therefore, the angular velocity of the ball screw becomes zero at two moments during one period of movement. The designed mechanism prevents the generator shaft from changing its direction of rotation at these moments. This mechanism also decouples the generator shaft from the ball screw when the angular velocity of the generator shaft exceeds the angular velocity of the ball screw due to its rotational moment of inertia. As the relative velocity of the bodies increases, the generator shaft is re-coupled to the ball screw and, in consequence, rotates at the angular velocity of the ball screw. This article examines the effect of using the present mechanism on increasing the electrical output power of the WEC at different wave frequencies.

Topology Optimization for the Manufacturable and Structurally Safe Synchronous Reluctance Motors With Multiple Iron Webs and Bridges

The goal of this article is to develop a new topology optimization framework that can secure the manufacturability of the synchronous reluctance motors (SynRMs) with multiple iron webs and bridges while satisfying the required electromagnetic and mechanical performances. In the SynRM, multiple iron webs and bridges are crucial to achieve a higher torque and a structural safety. A minimum thickness of the web and bridge should also be guaranteed to achieve manufacturability. To acquire the optimal SynRM that can satisfy the above characteristics, a two-stage topology optimization framework is proposed with an individual filtering-and-penalization scheme. This proposed scheme can individually control the number and thickness of multiple iron webs and bridges in the rotor to obtain the manufacturable and structurally safe SynRMs. For the abovementioned purpose, topology optimization is formulated to minimize a torque ripple while satisfying the desired average torque, structural compliance, and a rotational moment of inertia. Average torque and structural compliance are evaluated by performing the electromagnetic and structural finite element analyses, respectively, at each iteration of topology optimization. Here, design-dependent loads are considered in the radial and circumferential directions to reflect a high-speed rotation. Through investigating the optimized SynRM designs with various filter radii, the relationship among the torque, structural pattern, and stress distribution is examined. Finally, the experimental results with the manufactured prototypes validate the feasibility and potential of the proposed design method.

Dynamic Parameter Estimation for a Washing Machine

In this study, an analytical concept is explored in the simulation environment, and an unbalanced load detection technique is examined to determine its applicability. To continue the development process, a mathematical model for a horizontal washer is developed to comprehend the characteristics of an unbalanced load with respect to various sizes of balanced loads. The mathematical model is then divided into a regressor vector and an estimator vector. Finally, estimates of the unbalanced load, the unbalance location, and the rotational moment of inertia are compared to their references in the simulation environment.

Enhanced moments of inertia for rotation in neutron-rich nuclei

Ground-state moments of inertia (MoI) are investigated for approximately 1700 even–even nuclei from the proton drip line to the neutron drip up to Z=120 and N=184. The cranked Hartree–Fock–Bogoliubov equation is solved in the coordinate space using the Skyrme and pairing energy density functionals. This model well describes the available experimental data of the first excited Iπ=2+ state energy of more than 300 nuclides possessing appreciable deformation. The MoI is found to greatly increase near the drip line, whereas the deformation is found to be not as strong as estimated by the empirical relation when the pairing functional including the isovector-density dependence is adopted. The currently used pairing functionals produce large uncertainties in the prediction of E(21+) values near the neutron drip line.

Seismic Wave Propagation Through Layered Reduced Micropolar Medium

AbstractThe ground motions recorded in the near‐field regions of earthquakes reveal that, along with translational motions the rotational motions can severely damage structures. To capture these ground rotations more realistically, the present study makes a novel attempt to model the Earth medium as a horizontally layered reduced micropolar half‐space. Layers in this medium are characterized by five material constants: Lame's constant (), Eringen's shear modulus (), density (), rotational moment of inertia (), and an additional material constant (). Cylindrical coordinate system is used to analytically derive the Green's functions and obtain the response of the layered Earth medium subjected to a point earthquake force. The analytically obtained surface translations and rotations involve integrations over the wavenumber and frequency parameters and hence, are evaluated numerically. These solutions converge to corresponding classical elastic medium when the micropolar medium parameters obey the relations and , where is the maximum frequency considered in the simulation. Thereafter, ground motions are simulated for several combinations of earthquake magnitudes and epicenter distances by modeling the Earth medium as an eight layered reduced micropolar half‐space. Further, ground motions for the 2012 Wutai earthquake were simulated using the proposed model and compared with the response of classical elastic medium. The comparisons indicate that the surface rotations are significantly higher in the case of reduced micropolar medium. The proposed formulation can be extended to simulate ground motions for finite‐fault seismic sources.

Attitude stability control of micro-nano satellite orbit maneuver based on bias momentum

In this paper, an attitude stability control strategy based on cold air micro propulsion microsatellite orbital maneuver is designed. Firstly, the influence of environmental disturbance moment, uncertainty of rotational moment of inertia and thrust eccentricity moment on the attitude stability of the micro-nano-satellite is considered, and the attitude dynamics model of the micro-nano-satellite based on biased momentum wheel and magnetic moment device is established. Then, the disturbance moments such as environmental disturbance moments, rotational inertia uncertainty and thrust eccentricity moments are analyzed. In order to suppress the influence of various internal and external disturbance factors on the stability of the micro-nano-satellite during the deorbiting process, a robust adaptive sliding mode variable structure controller is designed. The designed robust adaptive sliding mode controller is able to compensate for various disturbances adaptively. The robust adaptive sliding-mode variable structure controller is designed with a reasonable distribution of torque considering the characteristics of bias momentum wheel control and magnetic control. Finally, numerical simulations are performed, and the simulation results show that the system has good robustness.

Modeling of rocking frames under seismic loading

AbstractA novel modeling approach for the seismic response assessment of rocking frames is presented. Rocking frames are systems with columns that are allowed to fully, or partially, uplift. Despite the apparent lack of a mechanism to resist lateral forces, they have a remarkable capacity against earthquake loading. Rocking frames are found in old structures, for example, ancient monuments, but it is also a promising design concept for modern structures such as bridges or buildings. The proposed modeling can be implemented in a general‐purpose structural analysis software, avoiding the difficulties that come with the need of formulating and solving specifically tailored differential equations, or the use of detailed computational models. Different configurations of a rocking portal frame problem are examined. The model is based on rigid, or flexible, beam elements that describe the members of the frame. Negative‐stiffness rotational springs are smartly positioned at the rocking interfaces in order to simulate the rocking restoring moment, while the mass and the rotational moment of inertia are considered either lumped or distributed. Both the cases of rigid and flexible piers/columns are discussed, while it is shown that frames with restrained columns can be considered in a straightforward manner. A simple alternative based on an equivalent oscillator that follows the generalized rocking equation of motion is also investigated. The efficiency and the accuracy of the proposed modeling is demonstrated with the aid of carefully chosen case studies.

Retardational Effect and Hopf Bifurcations in a New Attitude System of Quad-Rotor Unmanned Aerial Vehicle

The effect of retardation along second vector of angular velocity on a new attitude system of quad-rotor unmanned aerial vehicle (QUAV) is examined in this paper. Catastrophic and hovering conditions of rotor dynamics are verified through bifurcation analysis. It is analyzed that disturbed rotor dynamics during yaw maneuvering lead towards the existence of oscillations and hamper the efficiency of attitude system. We have categorically signified the situation where remote controller of attitude system cannot prevent flipping and consequently, shortens the life of QUAV. This type of situation arises in a strong wind friction zone where positive drag force of rotor dynamics is impeded by the magnitude of rotational moment of inertia. Moreover, subcritical and zero-Hopf bifurcations aroused due to retardational effect in attitude system are analyzed with the aid of normal form and averaging theory. Numerical simulations are also provided for validation of analytical results.

A new displacement model for nonlinear vibration analysis of fluid-conveying anisotropic laminated tubular beams resting on elastic foundation

A new displacement model for nonlinear vibration analysis of fluid-conveying anisotropic laminated tubular beams resting on a Pasternak-type foundation is presented. Based on Hamilton's principle, the motion equations and boundary conditions are obtained by using a new high-order shear deformation tubular beam model with a von Kármán-type of kinematic nonlinearity, in which warping, shear deformation and rotational moment of inertia of cross-section and contributions of the relationship of exact curvature are considered. A numerical solution using the differential quadrature method (DQM) with an iterative algorithm is employed to determine the nonlinear frequencies and amplitude-frequency responses of fluid-conveying anisotropic laminated tubes with different boundary conditions. A detailed parametric study is conducted to analyze influence of different type of boundary conditions, and geometrical and physical properties. Numerical results demonstrate that the geometrical and physical properties, elastic foundation, boundary conditions, initial geometry imperfection, critical flow velocity and frequency-response of the fluid-conveying tubes have significant effect on dynamic behavior of anisotropic laminated composite tubes.

Multi-Objective Optimization of the Halbach Array Permanent Magnet Spherical Motor Based on Support Vector Machine

The fundamental harmonic amplitude and waveform distortion rate of the air-gap flux density directly affect the performance of a permanent magnet spherical motor (PMSM). Therefore, in the paper, the axial air-gap magnetic field including the end leakage of the Halbach array PMSM is analyzed and optimized. In order to reduce the calculation time of the objective function, the air gap magnetic field model adopts a non-linear regression model based on support vector machine (SVM). At the same time, the improved grid search (GS) algorithm is used to optimize the parameters of SVM model, which improves the efficiency and accuracy of parameter optimization. Considering the influence of moment of inertia on the dynamic response of the motor, the moment of inertia of the PMSM is calculated. This paper takes the air gap magnetic density fundamental wave amplitude, waveform distortion rate and rotor moment of inertia as the optimization objectives. The particle swarm optimization (PSO) algorithm is used to optimize the motor structure with multiple objectives. The optimal structure design of the PMSM is selected from all of non-dominated solutions by the technique for order preference by similarity to an ideal solution (TOPSIS). The performance of the motor before and after the optimization is analyzed by the method of finite element (FEM) and experimental verification. The results verify the effectiveness and efficiency of the optimization method for the optimal structure designing of the complex PMSM.

Potential energy models of excited compound nucleus

Potential energy is important ingredient in static and dynamical investigations of a nuclear fission process. The calculation of surface, nuclear, Coulomb, rotational, curvature, congruence, and Wigner energy functionals is presented for large variety of nuclear shapes generated by a {c,h,α} parametrization. Using these functionals one can calculate the potential energy in several macroscopic models of the liquid-drop type. A numerical code which calculates all these quantities is made available. Program summaryProgram Title: FRM_epotCPC Library link to program files:http://dx.doi.org/10.17632/h7r43t7dnh.1Licensing provisions: CC BY NC 3.0Programming language: C++Nature of problem: The shape dependence of the surface, nuclear, Coulomb, rotational, curvature, congruence, and Wigner energy functionals together with the moments of inertia for rotation, center-of-mass distance between nascent fragments are calculated for deformed shapes of the fissioning compound nucleus. These functionals allow to calculate the potential energy in several macroscopic models of the liquid-drop type for a large variety of nuclear shapes.Solution method: The shape of the fissioning nucleus is described by the {c,h,α} parametrization. This parametrization determines the axially symmetric shapes in cylindrical coordinates. The potential energy functionals are calculated using numerical integration procedure as a function of the three shape parameters. Using these functionals one can generate potential energy of the nucleus in four different versions of the liquid-drop model. All subroutines, which define the nuclear shape are separated from the code, which calculates the potential energy functionals. Thus, the program could be easily adopted for any other shape parametrization in case if it is given in cylindrical coordinates.

A refined beam theory for bending and vibration of functionally graded tube-beams

This paper presents a novel approach for analyzing transverse bending and vibration of functionally graded circular cylindrical tubes with radial nonhomogeneity. Different from the Euler-Bernoulli and Timoshenko theories of beams, a refined beam theory or third-order shear deformation beam theory for radially graded tubes is proposed, where warping, shear deformation and rotational moment of inertia of cross-section are all considered. The shear correction coefficient is not needed. Coupled governing equations for the deflection and rotation about the neutral axis of cross-section are derived from equilibrium equations, and then converted to a single fourth-order partial differential governing equation. The deflection and stress distribution for cantilever and simply-supported tubes are derived explicitly. The frequency equations for free flexural vibration of radially graded hollow cylinders with clamped-clamped, pinned-pinned, and clamped-free ends are obtained and the natural frequencies are calculated for different power-law gradients and various length/thicknesses ratios. The effects of radial gradient on the stress distribution and the natural frequencies are analyzed in detail.

Technical Review: Indirect Tire Pressure Monitoring Systems and Tire Vibrations

ABSTRACT Indirect tire pressure monitoring systems (ITPMSs) have been an active area of research for the past 2 decades. Researchers worldwide have strived to develop estimation techniques for the detection of the change in tire pressure by using the vibration information present in the speed signal. Different groups have used a torsional vibration model for the tire, owing to its torsional stiffness and rotational moment of inertia. The standard antilock braking system (ABS) speed sensor signal is analyzed for these vibrations. Different estimation algorithms try to detect the change in this vibration frequency, which indicates the change in the torsional stiffness of the tire as a result of variation in the pressure. Tire vibrations have been studied in great detail for the past 5 decades, and there are various models of tire vibrations available in the literature. These models range from physics-based analytical models to finite element models (FEMs). Analytical models take benefit from the mathematics developed for rotating elastic thin shells and plates, whereas FEMs use simulation tools to develop vibration models of the tire. A detailed literature survey of ITPMSs and tire vibration models reveals that there is no correlation between the vibrations detected in the speed signal and the vibrations predicted in the tire vibration models. Researchers have developed tire vibration models that do not take into consideration the effects of vibrations on the speed signal; although, to the best of our knowledge, signal processing and estimation experts who have developed methods for ITPMSs have not validated the true source of observed vibrations in the speed signal and could not present a viable theoretical explanation. In this review, a comprehensive study of the ITPMS techniques and tire vibration models is presented, with an aim to find a correlation between them. The review begins with a brief introduction to the topic followed by state of the art, then a detailed review of ITPMSs and the methods for their realizations in the automotive industry. Finally, tire vibration models are presented in detail, and possible links between vibration models and ITPMS vibrations are sorted.

Effects of substructure mass participation on natural period of multi-column base isolated bridges

The mass of substructure is a main component of isolated bridges that affects the natural period and consequently forces and displacements of isolated bridges. The substructure mass consists of four components including pier mass, cap beam mass, pier rotational moments of inertia, and cap beam rotational moments of inertia. This paper investigates the effects of these components on the period of first longitudinal and transverse modes of multi-column continuous-span isolated bridges. For this purpose, 3-DOFs and 2-DOFs analytical models of a multi-column isolated bridge are developed and the natural periods of the models are validated in two horizontal directions. Moreover, the bridges design codes like AASHTO, ignore completely the substructure mass in the simplified method and present a SDOF analytical model for isolated bridges. The AASHTO SDOF model is not appropriate for all isolated bridges, because the increase in the stiffness ratio of the isolator to the substructure, increases the errors in calculating the fundamental period of the model. To overcome this limitation, a modified SDOF model is presented in this paper. In the proposed model, the substructure mass participation (SMP) is added to the superstructure. The value of SMP depends on the geometry of bridges and stiffness of the substructure and isolators. The analysis results show that using this model instead of the AASHTO model, decreases the errors significantly. Therefore, this model is recommended as a simple and accurate approach.

Связь вращательного момента инерции молекулы с хроматографическим временем удерживания в ряду алканов. Новые индексы удерживания.

Earlier it was shown that cause of physicochemical properties oscillation and splitting into even and odd groups in the organic compounds homologous series is the rotational motion energy, determined by the molecule structure. In turn, the organic compound structure can be numerically described or expressed in terms of rotational motion inertia moment. It was logical to assume the correlation between the retention time and rotational motion inertia moment. In order to establish the connection of molecule rotational inertia moment with the chromatographic retention time, a mixture of normal structure alkanes (C6-C17) was experimentally analyzed and corresponding graphs were constructed confirming the assumptions made. A new chromatographic index IJ was proposed, which has advantages over the Kovats index (IK).

Thouless-Valatin rotational moment of inertia from linear response theory

Spontaneous breaking of continuous symmetries of a nuclear many-body system results in appearance of zero-energy restoration modes. Such modes introduce a non-physical contributions to the physical excitations called spurious Nambu-Goldstone modes. Since they represent a special case of collective motion, they are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total angular momentum operator. We examine the role and effects of the pairing correlations on the rotational characteristics of heavy deformed nuclei in order to extend our understanding of superfluidity in general. We use the finite amplitude method of the quasiparticle random phase approximation on top of the Skyrme energy density functional framework with the Hartree-Fock-Bogoliubov theory. We have successfully extended this formalism and established a practical method for extracting the Thouless-Valatin rotational moment of inertia from the strength function calculated in the symmetry restoration regime. Our results reveal the relation between the pairing correlations and the moment of inertia of axially deformed nuclei of rare-earth and actinide regions of the nuclear chart. We have also demonstrated the feasibility of the method for obtaining the moment of inertia for collective Hamiltonian models. We conclude that from the numerical and theoretical perspective, the finite amplitude method can be widely used to effectively study rotational properties of deformed nuclei within modern density functional approaches.