Numerical investigation on damping coefficient of the integral squeeze film damper

The elimination of rotor vibration is usually achieved by applying additional damping to the system.Squeeze film dampers are widely used in various aerospace and turbine equipments.The research is carried out on flow characteristics in the integral squeeze film dampers(ISFDs).The dynamic response to the operation condition is investigated through the computational fluid dynamics(CFD) model of ISFD.Due to the large pressure loss at the oil inlet,the oil film force only changes slightly with the increase of oil supply pressure,and the damping increases slightly.The vibration amplitude only affects the film force,but has no effect on the damping.The oil film force and damping show an upward tendency with the decrease of thickness of the end seal clearance.

Measurement of stiffness and damping coefficient of rubber tractor tires using dynamic cleat test based on point contact model

The ride vibration of a tractor is affected mostly by the stiffness and damping coefficient of the seat suspension,cabin suspension,cabin rubber mounts,and rubber tires.However,in the case of rubber tractor tires,the stiffnesses and damping coefficients have not been researched adequately thus far,and it is not simple to measure these characteristics.In this study,a method for measuring and analyzing the stiffnesses and damping coefficients of rubber tractor tires,which were the input parameters for the tractor ride vibration simulation,was proposed.The cleat test,proposed in this study,did not require separate and complicated test equipment,unlike the conventional methods.The test was conducted simply by measuring acceleration under the driving conditions of the vehicle without detaching tires from the vehicle body or setting up additional test equipment.Based on the ground-vertical acceleration data obtained,the stiffness was calculated using the logarithmic decrement method,and the damping coefficient was calculated using least squares exponential curve fitting.The result of the cleat test indicated that the front tires had stiffnesses of 486.08-570.69 kN/m and damping coefficients of 4.02-4.52 kN·s/m;the rear tires had stiffnesses of 409.42-483.79 kN/m and damping coefficients of 2.21-2.67 kN·s/m.During the test,40 mm height cleats were installed on the track and the speed of the tractor was set to 7 and 10 km/h,which were the most common speeds during the operation.This study is meaningful in that it has presented a new method that improves the practicality of results,reduces cost,and simplifies the test process for measuring the stiffnesses and damping coefficients of rubber tractor tires.

Linear and quadratic damping coefficients of a single module of a very large floating structure over variable bathymetry:Physical and numerical free-decay experiments

The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure.However,the linear damping is frequently underestimated,especially for the natural frequency.To investigate the sloping seafloor effects on the damping terms of a single module of a semi-submersible Very Large Floating Structure(VLFS),this paper revisits the conventional formulation and further proposes the direct integration method for obtaining the linear and quadratic damping coefficients from free-decay tests.Numerical free-decay simulations of the single module over variable bathymetry are carried out by the CFD numerical tank.Corresponding model tests are also implemented to verify and validate against the numerical solutions.The effects of the sloping seafloor,as well as the water depth,on the hydrodynamic coefficients are investigated based on the validated CFD modeling.Both numerical and experimental results indicate that the acquisition of the linear and quadratic damping coefficients is sensitive to the data-processing and identification approaches.For the case studied in present paper,the identification errors introduced by the conventional method are 1.5%while they are 0.5%using the direct integration method.The quadratic damping coefficient for heave mode decreases about 10.4%when the sloping angle increases from 0 to 6 deg.

Study on Hydrodynamic Coefficients of Double Submerged Inclined Plates

Added mass and damping coefficients are very important in hydrodynamic analysis of naval structures. In this paper,a double submerged inclined plates with ‘/\’ configuration is firstly considered. By use of the boundary element method(BEM) based on Green function with the wave term, the radiation problem of this special type structure is investigated. The added mass and damping coefficients due to different plate lengths and inclined angles are obtained. The results show that: the added mass and damping coefficients for sway are the largest. Heave is the most sensitive mode to inclined angles. The wave frequencies of the maximal added mass and damping coefficients for sway and roll are the same.

Macroscopic damping model for structural dynamics with random polycrystalline configurations

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro-nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom （SDOF） along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro-nano scales is set up.

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.

Numerical Modeling on Hydrodynamic Performance of A Bottom-Hinged Flap Wave Energy Converter

The hydrodynamic performance of a bottom-hinged flap wave energy converter （WEC） is investigated through a frequency domain numerical model. The numerical model is verified through a two-dimensional analytic solution, as well as the qualitative analysis on the dynamic response of avibrating system. The concept of ＂optimum density＂ of the bottom-hinged flap is proposed, and its analytic expression is derived as well. The frequency interval in which the optimum density exists is also obtained. The analytic expression of the optimum linear damping coefficient is obtained by a bottom-hinged WEC. Some basic dynamic properties involving natural period, excitation moment, pitch amplitude, and optimum damping coefficient are analyzed and discussed in detail. In addition, this paper highlights the analysis of effects on the conversion performance of the device exerted by some important parameters. The results indicate that ＂the optimum linear damping period of 5.0 s＂ is the most ideal option in the short wave sea states with the wave period below 6.0 s. Shallow water depth, large flap thickness and low flap density are advised in the practical design of the device in short wave sea states in order to maximize power capture. In the sea state with water depth of 5.0 m and wave period of 5.0 s, the results of parametric optimization suggest a flap with the width of 8.0 m, thickness of 1.6 m, and with the density as little as possible when the optimum power take-off （PTO） damping coefficient is adopted.

Wind-Induced Vibration Control for Substation Frame on Viscous Damper

In order to study the wind-induced vibration control effect of the viscous damper on the large-scale substation frame,this paper takes the large-scale 1000 kV substation frame of western Inner Mongolia as an example.The time-history sample of pulsating wind load is simulated by harmonic superposition method based on Matlab software.6 kinds of viscous damper arrangement schemes have been designed,and SAP2000 finite element software is used for fine modeling and input wind speed time history load for nonlinear time history analysis.The displacement and acceleration of a typical node are the indicators of wind vibration control.The wind-induced vibration control effects of different schemes under different damping parameters have compared,and the damping parameters are analyzed for the optimal layout scheme.The results show that a viscous damper has installed in the lower layers of the substation;a viscous damper is placed between the ground column and the lattice beam.It is an integrated optimal solution.The wind-induced vibration control effect of the optimal scheme is sensitive to the viscous damper parameters,and the control effect does not increase linearly with the increase of the damping index and the damping coefficient.Corresponding to different damping indexes,the damping coefficient has a better range of values.

WATER SURFACE WAVE RADIATION GENERATED BY MULTIPLE CYLINDERS OSCILLATING WITH IDENTICAL FREQUENCY

The water surface wave radiation problem caused by multiple cylinders oscillating with identical frequency was solved in frequency domain by the boundary element method using simple Green's function in the inner water region combined with the eigenfunction expansions in the outer water region. The numerical method is suitable to the situation of constant depth of outer regions and complicated boundary conditions of inner region, while the oscillating modes, motion amplitudes and phases of the cylinders may be different from one another. The second order potential and hydrodynamic forces acting on each cylinder were evaluated completely by perturbation method. Compared with the case of single oscillating cylinder, hydrodynamic interference phenomena, such as wave resonance and negative added mass, of the radiation problem due to the oscillatory motions of multiple cylinders are identified which is of engineering importance to the design of moorings and other facilities involving multiple structures.

Research on VSG Frequency Characteristics and Energy Storage Device Capacity and Charge-Discharge Characteristics Based on Feedforward Branch

Renewable energy is connected to the grid through the inverter,which in turn reduces the inertia and stability of the power grid itself.The traditional grid-connected inverter does not have the function of voltage regulation and frequency regulation and can therefore no longer adapt to the new development.The virtual synchronous generator(VSG)has the function of voltage regulation and frequency regulation,which has more prominent advantages than traditional inverters.Based on the principle of VSG,the relationship between the frequency characteristics and the energy storage capacity of the feedforward branch-based virtual synchronous machine(FVSG)is derived when the input power and grid frequency change.Reveal the relationship between the virtual inertia coefficient,damping coefficient,and frequency characteristics of VSG and energy storage capacity.An energy storage configuration method that meets the requirements of frequency variation characteristics is proposed.A mathematical model is established,and the Matlab/Simulink simulation software is used for modeling.The simulation results verify the relationship between the inertia coefficient,damping coefficient,and energy storage demand of the FVSG.

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.

The Functional Role of the Hollow Region of the Butterfly Pyrameis atalanta (L.) Scale

Questions concerning the functional role of the hollow region of the butterfly Pyrameis atalanta （L.） scale are experimentally investigated. Attention was initially directed to this problem by observation of the complex microstrucmre of the butterfly scale as well as other studies indicating higher lift on butterfly wings covered with scale. The aerodynamic forces were measured for two oscillating scale models. Results indicated that the air cavity of an oscillating model of the Pyrameis atalanta （L.） scale increased the lift by a factor of 1.15 and reduced the damping coefficients by a factor of 1.38. The modification of the aerodynamic effects on the model of butterfly scale was due to an increase of the virtual air mass, which influenced the body. The hollow region of the scale increased the virtual air mass by a factor of 1.2. The virtual mass of the butterfly scale with the hollow region was represented as the sum of air mass of two imaginary geometrical figures： a circular cylinder around the scale and a right-angled parallelepiped within the hollow region. The interaction mechanism of the butterfly Pyrameis atalanta （L.） scale with a flow was described. This novel interaction mechanism explained most geometrical features of the airpermeable butterfly scale （inverted V-profile of the ridges, nozzle of the tip edge, hollow region, and openings of the upper lamina） and their arrangement.

Wave radiation by a horizontal circular cylinder submerged in deep water with ice-cover

Using the multipoles method,we formulate the problems of water wave radiation(both heave and surge)by a submerged circular cylinder in water with an ice-cover,the ice-cover being modelled as an elastic plate of very small thickness.This leads to an infinite system of linear equations which are solved numerically by standard techniques.The added-mass and damping coefficients for a heaving and surge problems are obtained and depicted graphically against the wave number for various values of flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities.When the flexural rigidity and surface density of ice-cover are taken to be zero,the ice-cover tends to free-surface then the curves for added-mass and damping coefficients exactly coincide with the curves for the case of water with free surface.Also it is observed that the added-mass and damping coefficients for the two modes of motion are here also the same.

A fast transient response low dropout regulator with current control methodology

A transient performance optimized CCL-LDO regulator is proposed.In the CCL-LDO,the control method of the charge pump phase-locked loop is adopted.A current control loop has the feedback signal and reference current to be compared,and then a loop filter generates the gate voltage of the power MOSFET by integrating the error current.The CCL-LDO has the optimized damping coefficient and natural resonant frequency, while its output voltage can be sub-l-V and is not restricted by the reference voltage.With a 1μF decoupling capacitor,the experimental results based on a 0.13μm CMOS process show that the output voltage is 1.0 V;when the workload changes from 100μA to 100 mA transiently,the stable dropout is 4.25 mV,the settling time is 8.2μs and the undershoot is 5.11 mV;when the workload changes from 100 mA to 100μA transiently,the stable dropout is 4.25 mV,the settling time is 23.3μs and the overshoot is 6.21 mV.The PSRR value is more than -95 dB.Most of the attributes of the CCL-LDO are improved rapidly with a FOM value of 0.0097.