Experimental Analysis of Dynamic Stiffness Coefficient of the New Mn-Cu Alloy Annular Parts

Based on excitation-resonance mass testing principle, a proper experiment testing system is designed for annular parts. The dynamics characters of the axis sleeve, which is made of a new Mn-Cu alloy and used as a vibration reductor in high acceleration rotary testing machine for fusee, is investigated. The relationship between stiffness coefficient and utilizing frequency is obtained, and the simplified dynamics model of crystal is established From the viewpoint of crystal microstructure of the Mn-Cu alloy, the experiment result is analyzed by the viscoelastic theory, and the characters of stress and strain in the condition of high frequency are discussed. The results indicate that the Mn-Cu alloy annular parts are fit to be used on the high accleration rotary testing machine for fusee.

Analysis on Stiffness and Damping Performance of Active Magnetic Bearing System

The relations of the stiffness and damping performance to the structure parameters of an active magnetic bearing (AMB) system and the frequency specificity of the control loop are analyzed. The effects of the control current phase on the stability, the stiffness and the damping properties of the system are presented.Meanwhile,a new concept of complex damping coefficient,the practical meanings of some system properties, and the calculation methods are discussed and described.

Improved Stiffness Modeling for An Exechon‑Like Parallel Kinematic Machine(PKM)and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.

Effects of fundamental structure parameters on dynamic responses of submerged floating tunnel under hydrodynamic loads

This paper investigates the effects of structure parameters on dynamic responses of submerged floating tunnel （SFT） under hydrodynamic loads. The structure parameters includes buoyancy-weight ratio （BWR）, stiffness coefficients of the cable systems, tunnel net buoyancy and tunnel length. First, the importance of structural damp in relation to the dynamic responses of SPT is demonstrated and the mechanism of structural damp effect is discussed. Thereafter, the fundamental structure parameters are investigated through the analysis of SFT dynamic responses under hydrodynamic loads. The results indicate that the BWR of SFT is a key structure parameter. When BWR is 1.2, there is a remarkable trend change in the vertical dynamic response of SFT under hydrodynamic loads. The results also indicate that the ratio of the tunnel net buoyancy to the cable stiffness coefficient is not a characteristic factor affecting the dynamic responses of SFT under hydrodynamic loads.

Mechanical Characteristics of Radial Magnetic Bearing

This paper is based on the example of a radial magnetic bearing possessed of eight-pole, and derives the calculation formulas of static and dynamic mechanical characteristics of the bearing, in which the shape and curvature of surface, eccentricity and tilt of the journal are taken into account. Variations of the static and dynamic characteristics of the radial magnetic bearing versus static tilt parameters of journal are discussed. The outcomes show that the static tilt of the journal has influence on the mechanical characteristics of radial magnetic bearing, and change the static load capacity between two radial magnetic bearings and exert coupling effect between them. To study the dynamics of a practical rotor-magnetic bearing system, at least six stiffness coefficients in each radial magnetic bearing must be considered in ideal case, and twelve stiffness coefficients must be considered in general case of tilting journal. Such a find can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh’s quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Generalized stiffness and effective mass coefficients for power-law Euler-Bernoulli beams

We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials.We provide the generalized stiffness and effective mass coefficients for the power-law Euler-Bernoulli beams under standard geometric and load conditions.In particular,our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law.Since there are no known solutions to the dynamic power-law beam equations,solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.

Effect of the Wall Thickness of the Vessel on FFRCT of Carotid Artery Stenosis

Fractional flow reserve(FFR)computed from computed tomography angiography(CTA),i.e.,FFRCT has been used in the clinic as a noninvasive parameter for functional assessment of coronary artery stenosis.It has also been suggested to be used in the assessment of carotid artery stenosis.The wall thickness of the vessel is an important parameter when establishing a fluid-structure coupling model of carotid stenosis.This work studies the effect of the vessel wall thickness on hemodynamic parameters such as FFRCT in carotid stenosis.Models of carotid stenosis are established based on CTA image data using computer-aided design software.It is assumed that the vessel wall is a linear elastic and isotropic material,and the blood an incompressible Newtonian fluid.Under the pulsating flow condition,ANSYS Transient Structural and CFX are used to simulate the blood flow of fluid-structure coupling in the carotid stenosis model in order to obtain hemodynamic parameters and the corresponding FFRCT.The results show that when the elastic modulus of the vessel wall is fixed,FFRCT will decrease with the increase of the wall thickness.Similarly,FFRCT will decrease with the increase of the elastic modulus when the wall thickness is fixed.The difference in hemodynamic parameters such as FFRCT,however,is relatively small if the stiffness of the two models are close.The results demonstrate that the effect of the vessel wall thickness,especially for a model with small elastic modulus,should be taken into account in using FFRCT for functional assessment of carotid stenosis.Moreover,under the linear elasticity and isotropic material assumptions,the stiffness coefficient may replace the elastic modulus and wall thickness as a parameter reflecting material property of the vessel wall in the carotid stenosis model.

CALCULATION OF ELASTIC DAMPING CHARACTERISTICS OF ROTOR SUPPORT MADE OF METAL RUBBER MATERIAL UNDER VARIABLE LOADS

A metal rubber（MR） dry friction damper was designed based on the load supported by the rotor. An experimental apparatus for obtaining hysteresis loops of support under the precession load was designed. The elastic-damping characteristics of the ring-shaped MR damper used as a rotor support under variable loads were presented by studying the hysteresis loops of the damper. The vibration rigidity and the energy dissipation coefficient were calculated from the hysteresis loops, based on the description of the deformation process of the MR element with simple structure in a dimensionless coordinating system. The calculation results showed that the energy dissipation coefficient in the inner of MR element and on the boundary between the damper and the frame of the rotor support were approximately equal. The comparison of the hysteresis loops for a precession load and a one-axial load indicated a large difference when the coefficient of the energy dissipation and the stiffness of the MR damper were concerned.

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.

Spectral properties and identification of aerostatic bearings

Modified rotor kit Bently Nevada was used for dynamic characteristics measurements of new developed aerostatic bearings.Mathematical model of these bearings is considered as linear.Model was identified with the help of harmonic force excitation independently from the speed of journal rotation.The stiffness and damping matrices were identified for different air inlet pressures.The calculated spectral properties allow to determine the stability boundary for suitable variation of model parameters.

Energetic Nature of Rigidity

The work is to present the energetic nature of the rigidity. It starts with the definition by introducing the notion of sensual magnitudes with the pyramidal structure of all surrounding magnitudes known by a human being. Next the selection of the subject is provided in view of a smooth categorization of magnitudes describing the reality. The adequate description of the considered mechanical phenomenon is presented by formulating general stiffness characteristics. There are several characteristics analyzed, both functional and parametric. An essential, quite a new one is the characteristic of stiffness energy measure which is the stiffness potential. The proper and gained stiffness potentials situated on stable and unstable potential fields have been analyzed. An example of using of this theory to practice is given. It has been referred to a cylindrical grinder case. The presented theory allowed describing the entire stiffness characteristics, including its initial very essential course which has been usually, though inequitably, extrapolated by a straight line segment coming out of zero point with zero coordinates.

Investigation into improving the efficiency and accuracy of CFD/DEM simulations

The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and accuracy of this model are investigated. Parameter studies are performed; in these studies, the stiffness coefficient, the fluid time step and the processor number are varied under conditions with different numbers of particles and different particle diameters. The obtained results are compared with measurements to derive the optimum parameters for CFD/DEM simulations. The results suggest that the application of higher stiffness coefficients slightly improves the simulation accuracy. However, the average computing time increases exponentially. At larger fluid time steps, the results show that the average computation time is independent of the applied fluid time step whereas the simulation accuracy decreases greatly with increasing the fluid time step. The use of smaller time steps leads to negligible improvements in the simulation accuracy but results in an exponential rise in the average computing time. The parallelization accelerates the DEM simulations if the critical number for the domain decomposition is not reached. Above this number, the performance is no longer proportional to the number of processors. The critical number for the domain decomposition depends on the number of particles. An increase in solid contents results in a shift of the critical decomposition number to higher numbers of CPUs.