Vertical Vibration of Moving Strip in Rolling Process Based on Beam Theory

The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.

Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated viscoelastic soil layer

Based on elasticity and the theory of saturated porous media, and regarding the pile and the soil as a single phase elastic and a saturated viscoelastic media, respectively, the dynamical behavior of vertical vibration of an end-bearing pile in a saturated viscoelastic soil layer is investigated in the frequency domain using the Helmholtz decomposition and variable separation method. The axisymmetrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer are obtained, and the analytical expression of the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures using a numerical method. Effects of the saturated soil parameters, modulus ratio of the pile to soil, slenderness ratio of pile and pile＇s Poisson ratio, etc. on the stiffness factor and damping are examined. It is shown that, due to the effect of the transversal deformation of the pile and the radial force of the saturated viscoelastic soil acting on the pile, the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly different from those derived from the classical Euler-Bernoulli rod model, especially at some specific excitation frequencies. Therefore, there are limitations on applicability of the Euler-Bernoulli rod model in analyzing verticai vibration of the pile. More accurate analysis should be based on a three-dimensional model.

PERFORMANCE OF ULTRA-LOW FREQUENCY PASSIVE VERTICAL VIBRATION ISOLATION SYSTEM WITH REVERSE PENDULUM

A novel long period passive vertical vibration isolatorconstructed by mounting reverse pendu- lums on two pairs of torsionsprings is presented. By theoretical analysis and numericalcalculation, it is shown that the isolator can achieve much longerresonant period due to gravitational positive feedback and is smallerin size than the current torsion spring isolators with the samegeometric parameters.

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the halfspace is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Predhohn integral equations of the second kind and solved by numerical procedures. In the numerical extortples, the dynamic colnpliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

VERTICAL VIBRATION ANALYSIS OF AXISYMMETRIC SATURATED SOIL

Based on Biot＇s dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of satu rated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.

Application of dynamic vibration absorber for vertical vibration control of corrugated rolling mill

A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling process.Considering the nonlinear damping and nonlinear stiffness between the corrugated interface,a three-degree-of-freedom nonlinear vertical vibration mathematical model of corrugated rolling mill based on dynamic vibration absorber control is established.The multi-scale method is used to solve the amplitude–frequency characteristic curve equation of the installed dynamic vibration absorber(DVA)system.The effects of stiffness coefficient and damping coefficient on the amplitude–frequency characteristic curve are analyzed.The expressions of the dynamic developed factor of the corrugated roll are derived,and the influence laws of mass ratio,frequency ratio and damping ratio on the dynamic amplification factor are analyzed.The optimal parameters of the DVA are obtained by adaptive genetic algorithm.The control effect of the DVA on the nonlinear vertical vibration is studied by numerical simulation.The feasibility of the designed dynamic absorber is verified through experiments.The results show that the designed dynamic absorber can effectively suppress the vertical vibration of the corrugated roller.

Structural relaxation and avalanche dynamics of particle piles under vertical vibration

Granular matter can exhibit solid or liquid behavior,which contains complex physical mechanisms.In this work,we experimentally investigated the structural relaxation and avalanche dynamics of particle piles under vertical vibration.The influence of vibration parameters on the avalanche process was studied.The morphological features of avalanches were recorded and classified using high-speed camera.The effects of vibration parameters and particle properties on the relaxation mode are obtained.It is found that the evolution of particle pile height with time can be described by an exponential decay function.The relaxation rate and avalanche characteristics of four types of particles with different sizes are discussed.At the same acceleration level,for two larger particles,a smaller amplitude(A=0.025 mm)leads to a faster relaxation rate,while for two smaller particles,a large amplitude(A=0.500 mm)leads to a faster relaxation rate.The analogy powder surface tension is introduced to address the cohesion and flowability evolution of particles under vibration.

Research and application on three-dimensional seismic and vibration isolation for building

This paper presents the study of a three-dimensional(3D) isolation system.Firstly,the authors investigated the effects of an innovative 3D isolator,which was composed of a connecting plate,a rubber pad for vibration isolation in the vertical direction and a horizontal rubber bearing for seismic isolation in both horizontal directions.Secondly,the authors designed such a vibration isolation system and installed it underneath two specific residential buildings which were built directly over an existing subway communication hub platform in Beijing.These buildings required good performance vibration and seismic isolation system to reduce the impact from the running of nearby subway trains.Finally,in situ tests were conducted for both the isolated and the non-isolated buildings for the purpose of comparison.The test results showed that the maximum acceleration response level of the isolated superstructure is reduced by 10% as compared to that of the platform.The maximum attenuation of vibration reaches up to 25 dB.The 3D system explored in this paper is very effective in control and suppression of building vibration induced by earthquakes or running of trains.

Experimental study and analysis on the rising motion of grains in a vertically-vibrated pipe

Previous experimental investigations have shown that when a narrow pipe is inserted into a granular bed and is vibrated vertically but the granular bed is kept still, the grains in the bed can enter the pipe and rise against gravity along the pipe and finally stabilized at a certain height. The growth velocity and final stable height of the grain column inside the pipe can be controlled by varying the vibration conditions. In this paper, we discuss those experimental findings. We establish a mathematic relation between the grain column height（h） and time（t）, and by using the relation we discuss the change of the growth velocity（ dh/ dt） and acceleration（ d^2h/ dt^2） with t and h, respectively. We also analyze the mechanism of the rising motion of the grains during vibration. Furthermore, we derive a theoretical expression for describing the final stable height（h st）, which shows that the main factors influencing the height are vibration strength（Γ）, bulk density of grains,inner diameter of the pipe, and vibration frequency, and that h st increases nonlinearly in the presence of air and linearly in a vacuum environment with increasing Γ.

Non-Linear Vibration and Stability of Moving Strip With Time-Dependent Tension in Rolling Process

The strip with a time-dependent tension moves, namely a harmonically varying tension about a constant initial tension. The nonlinear vibration model of moving strip between two mills with time-dependent tension was established. Approximate solutions were obtained using the method of multiple scales. Depending on the variation of the tension, three distinct cases arise： frequency away from zero or two times the natural frequency; frequency close to zero; frequency close to two times the natural frequency. For frequency close to zero and away from zero and two times the natural frequency, the system is always stable. For frequency close to two times the natural frequency, the stability is analyzed respectively when the trivial solution exists and the nontrivial solution exists. Numerical simulation was made on some 1660 mm tandem rolling mill, and the stable regions and unstable regions for parametric resonance are determined with different cases. The rolling speed and the thickness of strip have strong influences on the stability of principle parametric resonances. But the distance between two mills has little influence on the stability of principle parametric resonances.

Vibration characteristics of multi-parametric excitations and multi-frequency external excitations of rolling mill under entry thickness fuctuation of strip

A dynamic rolling force model with multi-parametric excitations and multi-frequency external excitations caused by entry thickness fuctuation of strip was established.Based on the dynamic rolling force,a nonlinear vertical vibration model with multi-parametric excitations and multi-frequency external excitations was established.The method of multiple scales was used to solve the amplitude-frequency characteristic equation of primary resonance of the nonlinear vibration system of a rolling mill.The transition set and the topology structure of systematic global bifurcation were obtained by using the singularity theory.Finally,primary resonance characteristics of the system under entry thickness fuctuation of strip were analyzed by using actual parameters of the rolling mill.The global bifurcation curves with the change of amplitude and frequency of entry thickness fuctuation of strip were obtained by using numerical simulation,and many dynamic behaviors were found such as single-cycle motion,multi-cycle motion and chaotic motion,which can provide a theoretical reference for further restraining the vibration of a rolling mill.

A new vibration mechanism of balancing machine for satellite-borne spinning rotors

The centrifugal force and overturning moment generated by satellite-borne rotating payload have a significant impact on the stability of on-orbit satellite attitude, which must be controlled to the qualified range. For the satellite-borne rotors＇ low working revs and large centroidal deviation and height, and that the horizontal vibration produced by centrifugal force is not of the same magnitude as the torsional vibration by overturning moment, the balancing machine＇s measurement accuracy is low. Analysis shows that the mixture of horizontal vibration and torsional vibration of the vibrational mechanism contribute mainly to the machine＇s performance, as well as the instability of vibration center position. A vibrational mechanism was put forward, in which the horizontal and torsional vibration get separated effectively by way of fixing the vibration center. From experimental results, the separation between the weak centrifugal force signal and the strong moment signal was realized, errors caused by unstable vibration center are avoided, and the balancing machine based on this vibration structure is able to meet the requirements of dynamic balancing for the satellite＇s rotating payloads in terms of accuracy and stability.