Thermal conductivity measurements on xonotlite-type calcium silicate by the transient hot-strip method

The experimental results of the thermal conductivities of xonotlite-type calcium silicate insulation materials were presented at different temperatures and pressures. Two appropriative surroundings, i.e. an elevated temperature surrounding from ambient temperature to 1450 K and a vacuum surrounding from atmosphere pressure to 10-3 Pa, were designed for the transient hot-strip （THS） method. The thermal conductivities of xonotlite-type calcium silicate with four densities from ambient temperature to 1000 K and 0.045 Pa to atmospheric pressure were measured. The results show that the thermal conductivity of xonotlite-type calcium silicate decreases apparently with the fall of density, and decreases apparently with the drop of pressure, and reaches the least value at about 100 Pa. The thermal conductivity of xonotlite-type calcium silicate increases almost linearly with T0, and increases more abundantly with low density than with high density. The thermal conductivity measurement uncertainty is estimated to be approximately 3% at ambient temperature, and 6% at 800 K.

DYNAMIC RESPONSE OF PLATES DUE TO MOVING VEHICLES USING FINITE STRIP METHOD

Dynamic response of beam-like structures to moving vehicles has been extensively studied. However, the study on dynamic response of plates to moving vehicles has so far received but scant attention. A plate-vehicle strip for simulating the interaction between a rectangular plate and moving vehicles was described. For the portion of strips that are in direct contact with the moving vehicles, the plate-vehicle strips were employed. Conventional plate finite strips were used to model the portion of strips that are not directly under the action of moving vehicles. In the analysis, each moving vehicle is idealized as a one-foot dynamic system with tire unsprung mass and sprund mass interconnected by a spring and a dashpot. The numerical results obtained from the proposed method agree well with available results.

Thermal conductivity characterization of ultra-thin silicon film using the ultra-fast transient hot strip method

Thermal conductivity is an important material parameter of silicon when studying the performance and reliability of devices or for guiding circuit design when considering heat dissipation, especially when the self-heating effect becomes prominent in ultra-scaled MOSFETs.The cross-plane thermal conductivity of a thin silicon film is lacking due to the difficulty in sensing high thermal conductivity in the vertical direction.In this paper, a feasible method that utilizes an ultra-fast electrical pulse within 20 μs combined with the hot strip technique is adopted.To the best of our knowledge, this is the first work that shows how to extract the cross-plane thermal conductivity of sub-50 nm(30 nm, 17 nm, and 10 nm)silicon films on buried oxide.The ratio of the extracted cross-plane thermal conductivity of the silicon films over the bulk value is only about 6.9%, 4.3%, and 3.8% at 300 K, respectively.As the thickness of the films is smaller than the phonon mean free path, the classical heat transport theory fails to predict the heat dissipation in nanoscale transistors.Thus, in this study, a ballistic model, derived from the heat transport equation based on extended-irreversible-hydrodynamics(EIT), is used for further investigation, and the simulation results exhibit good consistence with the experimental data.The extracted effective thermal data could provide a good reference for precise device simulations and thermoelectric applications.

A New Model for Simulation of Cold Roll-Forming of Tubes by Using Spline Finite Strip Method

A new model,called object model,for the simulation of cold roll-forming of tubes is presented.The model inherits the advantages of old models and is the embodiment of forming process that the strip is rolled step by step from feed rollers to last rolling pass.The elastic-plastic large deformation spline finite strip method based on updated Lagrangian method has been developed by improving the stiffness and transition matrix.Combined theory formulas and new analytical model,the forming process of a tube has been simulated successfully as an example.The analytical results are submitted and indicate that the proposed simulation method and new model are applicable.

Influence of Participating Radiation on Measuring Thermal Conductivity of Translucent Thermal Insulation Materials with Hot Strip Method

The hot strip method,as one typical transient method,is widely used to measure the effective thermal conductivity of thermal insulation materials at various temperatures.Since the test theory is based on solving the energy equation via heat conduction,the test result will be questionable when measuring thermal insulation materials,such as silica aerogel and photovoltaic glazing,in which the participating thermal radiation is a dominant heat transfer mode at high temperature.In this study,numerical investigation is employed to reveal the measurement reliability of hot strip method when applied to translucent thermal insulation materials.By reproducing the dynamic conduction-radiation coupled heat transfer process within the translucent materials numerically,the effective thermal conductivity of translucent materials with varying extinction coefficients are obtained at various temperatures.Comparisons are made for the effective thermal conductivity of translucent materials determined by the hot strip method,one-dimensional steady state method,transient plane source method and Rosseland model.Large discrepancies are found among the effective thermal conductivity determined by different methods for translucent materials with low extinction coefficient.The thermal conductivity obtained from the hot strip method is overestimated at elevated temperature when compared with that from one-dimensional steady state method.In order to measure the effective thermal conductivity of translucent materials accurately,the effect of thermal radiation should be considered for different transient methods.

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method,the stream surface strip element method,for simulating the three-dimensional deformation of plate and strip rolling process was proposed.The rolling deformation zone was divided into a number of stream surface(curved surface)strip elements along metal flow traces,and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation.The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve,of which the lateral distributions were expressed as the third-power spline function,and the altitudinal distributions were fitted in the quadratic curve.From the flow theory of plastic mechanics,the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed.Compared with the streamline strip element method proposed by the first author of this paper,the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction,and realizes the precise three-dimensional analysis and computation.The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.

Study on increasing calculation precision and convergence speed of streamline strip element method

The calculation precision and convergence speed of streamline strip element method are increased by (using) the method whose initial value of the exit lateral displacement is determined with strip element variation method, and the accurate tension lateral distribution model is adopted based on the original third power spline function streamline strip element method. The basic theory of the strip element method is developed. The calculated results by the improved streamline strip element method and the original streamline strip element method are compared with the measured results, showing that the calculated results of the improved method are in good agreement with the measured results.

Strip Layer Method for Analysis of the Three-Dimensional Stresses and Spread of Large Cylindrical Shell Rolling

As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a typical rotary forming technology, and the upper and lower rolls have different radii and speeds. To quickly predict the three-dimensional stresses and eliminate fishtail defect, an improved strip layer method is developed, in which the asymmetry of the upper and lower rolls, non-uniform deformation and stress, as well as the asymmetrical spread on the end surface are considered. The deformation zone is divided into a certain number of layers and strips along the thickness and width, respectively. The transverse displacement model is constructed by polynomial function, in order to increase the computation speed greatly. From the metal plastic mechanics principle, the three-dimensional stress models are established. The genetic algorithm is used for optimization calculation in an industrial experiment example. The results show that the rolling pressure, the normal stresses, the upper and lower friction stress distributions are not similar with those of a general plate rolling. There are two relative maximum values in rolling pressure distribution. The upper and lower longitudinal friction stresses change direction nearby the upper and lower neutral points, respectively. The fishtail profile of spread on the end surface is predicted satisfactorily. The reduction could be helpful to eliminate fishtail defect. The large cylindrical shell rolling example illustrates the calculation results acquired rapidly are good agreements with the finite element simulation and experimental values of previous study. A highly effective and reliable three-dimensional simulation method is proposed for large cylindrical shell rolling and other asymmetrical rolling.

A New Approach Based on Iterative Method for the Characterization of a Micro-Strip Line with Thick Copper Conductor

In this work, we applied two electromagnetic models for the characterization of a planar structure including a flat, thick copper conductor. Indeed the first model is consisted by modeling two metal ribbons without bulkiness, placed one above the other at a distance of h2 equal to the thickness of the thick conductor. This approach has been implemented and tested by the iterative method. The results of simulations have been compared with those calculated by the Ansoft HFSS software, and they are in good concordance, validating the method of analysis used. The second model is based on the calculation of the effective permittivity of the medium containing the thick conductor. This medium consists of a metallic region of complex relative permittivity , the rest of this medium is filled with air er2 = 1. The effective permittivity eeff calculated from these two relative permittivity er2 and . Comparing the simulation results of this new formulation of the iterative method with those calculated by the software Ansoft HFSS shows that they are in good matching which validates the second model.

An Optimization Model for the Strip-packing Problem and Its Augmented Lagrangian Method

This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.

Transverse Distributions of Front and Back Tension Stresses in Cold Strip Rolling

In this paper,such a new lateral displacement function is proposed that the lateral flow velocity is con- tinuous at the entry and the exit of deformation zone.A new kind of finite strip method—the third power B-spline finite strip method—is put forward to simulate strip rolling process.Front and back tension stresses are formulated.The computed results of the transverse distributions of the front and back tension stresses are close to the experimental results.The paper lays a foundation for further analysing the three-dimensional stresses and deformations of strip rolling.

Comparison of methods for vibration analysis of electrostatic precipitators

The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.

Complete Mill Simulation of the Rolling Process of 1660 mm Hot Strip Continuous Mills

The three-dimensional plastic deformations of strip are analyzed using the stream surface strip element method, the elastic deformations of rolls are analyzed using the influence coefficient method, the analyzing and computing model of shape and crown of 4-high mill was established by combining them, and the rolling process of 1660 mm hot strip continuous mills was simulated. The simulated results tally well with the experimental results. The modei and the method for simulation of shape analysis and control of hot strip mills were provided.

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.

DYNAMIC BEHAVIOR OF TWO PARALLEL SYMMETRIC PERMEABLE CRACKS IN A PIEZOELECTRIC STRIP

The dynamic behavior of two parallel symmetric cracks in a piezoelectricstrip under harmonic anti-plane shear waves is studied using the Schmidt method for permeable cracksuface conditions. The cracks are parallel to the edge of the strip. By means of the Fouriertransform, the problem can be solved with the help of two pairs of dual integral equations. Theseequations are solved using the schmidt method. The results show that the stress and the electricdisplacement intensity factors depend on the geometry of the cracks, the frequency of incidentwaves, the distance between cracks and the thickness of the strip. It is also found that theelectric displacement intensity factors for the permeable crack surface conditions are much smallerthan those for the impermeable crack surface conditions.

Re-reddening on Strip Surface After Water Cooling

After water cooling, there is a big temperature difference between the center and the surface of strip, which leads to the heat transfer from the center to the surface, and the surface temperature can rise in a short time. The finite element method was used to simulate the phenomena of re-reddening on the surface of strip and to analyze the temperature field of hot roiled strip during laminar cooling, and the periodical variation curve of the cooling rate was obtained during water cooling and subsequent re-reddening. The results show that the critical line of the cooling rate is at 1/3 of the half-thickness from the strip surface. The regression model of the relation of rereddening temperature, time, and distance from the surface was obtained in the re-reddening region. Re-reddening regularity on the surface of strip under the condition of different thickness and cooling rate was also studied.

Bearing capacity analysis using the method of characteristics

Using the method of characteristics,the bearing capacity for a strip footing is analyzed.The method of characteristics leads to an exact true limit load when the calculations of the three terms in the bearing capacity formula are consistent with one collapse mechanism and the soil satisfies the associated flow rule.At the same time,the method of characteristics avoids the assumption of arbitrary slip surfaces,and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses.The exact solution without superposition approximation can still be expressed by Terzaghi＇s equation of bearing capacity,in which the bearing capacity factor N γλ is dependent on the dimensionless parameter λ and the friction angle φ.The influence of groundwater on the bearing capacity of the shallow strip footing is considered,which indicates that when the groundwater effect is taken into account,the error induced by the superposition approximation can be reduced as compared with dry soil condition.The results are presented in the form of charts which give the modified value（Nwγλc /Nγλc） of bearing capacity factor.Finally,an approximated analytical expression,which provides results in close agreement with those obtained by numerical analysis in this paper,has been suggested for practical application purposes.

Stress concentration factor expression for tension strip with eccentric elliptical hole

Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empiricai method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli＇s photo-elastic experiment and Isida＇s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.

Three-Di mensional Model for Strip Hot Rolling

A three-dimensional model for strip hot rolling was developed, in which the plastic deformation of strip, the thermal crown of rolls, roll deflection and flattening were calculated by rigid-plastic finite element method, finite difference method, influential function method and elastic finite element method respectively. The roll wear was taken into consideration. The model can provide detailed information such as rolling pressure distribution, contact pressure distribution between backup rolls and work rolls, deflection and flattening of work rolls, lateral distribution of strip thickness, and lateral distribution of front and back tensions. The finish rolling on a 1 450 mm hot strip mill was simulated.

Analysis of the thermal profile of work rolls in the hot strip rolling process

A 2-dimension axisymmetric model was developed by the finite-differencemethod, which can be used to predict the transient temperature field and thermal profile of workrolls in the hot strip rolling process. To demonstrate the accuracy and reliability of the solutiondeveloped, the calculation results were compared with the production data of a 1700 mm hot striprolling mill and good agreement was found between them. The effect of strip width and roll shiftingon the thermal expansion of the work rolls was studied. It is found that the strip width has markedeffect on the efficient thermal crown. Initially, when the rolling strip changes from narrow towide, a bigger efficient thermal crown can be quickly achieved; afterwards, when the rolling stripchanges from wide to narrow, not only the influence of uneven wear can be reduced but also theexcessive efficient thermal crown can be avoided. It is also found that the work roll shifting has adeterminate but not obvious effect on the reduction of the efficient thermal crown, and will makethe strip shape unstable without being used properly.