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Vertical rolling is an important technique used to control the width of continuous casting slabs in the hot-rolling field. Accurate prediction of vertical rolling force is a core point maintaining rolling-mill equipment. Owing to the limitation of the algorithm in use, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling-force model to improve prediction accuracy. An innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion is presented in this paper. First, the maximal width of a dog-bone region is determined by the slip-line method, and the dog-bone shape is described using a sine-function model. Second, the velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the total power of the vertical rolling process. Finally, the analytical solution of the rolling force and the dog-bone-shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. Moreover, the effectiveness of the proposed mechanical model is verified by measured data in the strip hot-rolling field and other models’ results. Results show that the prediction accuracy of the vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness, and friction factor on dog-bone shape size and vertical rolling force are discussed.

The Marangoni effect induced by organic vapor has drawn considerable attention in integrated circuit manufacturing for eliminating watermark defects encountered in the wafer drying process. Accordingly, a vertical rotational Marangoni (VRM) dryer based on the combination of the Marangoni effect and centrifugal force is proposed and developed. In particular, the hydrodynamic behavior of the VRM dryer is investigated to reveal the mechanism of ultraclean drying. A three-dimensional model of the VRM dryer is proposed, and the flow field of the water film and distribution of organic species are adequately analyzed. The results show that the rotational velocity and wettability significantly affect the coverage uniformity of the water film, and the exposure region at the three-contact line leads to the watermark. Furthermore, the coupling behavior of the Marangoni effect and centrifugal force is revealed. A higher rotational velocity leads to worse integrity of the water film covering, and thus, fainter Marangoni effect. Polishing and cleaning experiments are conducted to verify the effectiveness of theoretical analysis. The results indicate that the optimized rotational velocity for the hydrophilic surface is higher than that of the hydrophobic surface. The mechanism analysis of wafer drying based on the VRM drying technology provides effective guidance for ultraclean surface manufacturing during the cleaning process.

The wafer backside grinding process has been a crucial technology to realize multi-layer stacking and chip performance improvement in the three dimension integrated circuits (3D IC) manufacturing. The total thickness variation (TTV) control is the bottleneck in the advanced process. However, the quantitative analysis theory model and adjustment strategy for TTV control are not currently available. This paper developed a comprehensive simulation model based on the optimized grinding tool configuration, and several typical TTV shapes were obtained. The relationship between the TTV feature components and the spindle posture was established. The linear superposition effect of TTV feature components and a new formation mechanism of TTV shape were revealed. It illustrated that the couple variation between the two TTV feature components could not be eliminated completely. To achieve the desired wafer thickness uniformity through a concise spindle posture adjustment operation, an effective strategy for TTV control was proposed. The experiments on TTV optimization were carried out, through which the developed model and TTV control strategy were verified to play a significant role in wafer thickness uniformity improvement. This work revealed a new insight into the fine control method to the TTV optimization, and provided a guidance for high-end grinding tool and advanced thinning process development.

Accurate calculation of the heat source in the roll gap during the cold rolling process is the basis for a well-designed coolant system, which is particularly important for reducing roll wear and improving the flatness quality of strip steel. Although many established numerical models have high precision in calculating the work roll temperature, complex modeling processes and large calculation times result in the inability to predict work roll temperature quickly for the application of automatic control systems. Therefore, the authors develop a new analytical heat source model to calculate the axial temperature distribution of the work roll in the cold rolling process. First, according to the deformation characteristics of strip cold rolling, the deformation zone is divided into a plastic zone and two elastic zones, and the length of each deformation zone is calculated considering the effect of tension. Then friction heat generated in the elastic zone is calculated. Second, new exponential velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the deformation heat and friction heat generated in the plastic zone. Finally, the work roll temperature prediction model is established by contemplating the heat source of the roll gap, emulsion heat transfer, air cooling, and contact heat transfer with the intermediate roll. By repeatedly optimizing the weighted coefficient d of intermediate principal shear stress on the yield criterion, the maximum error between the calculated results and the actual measured cold roll temperature data is reduced to 3.1%. Then, the effects of the reduction ratio, rolling speed, and resistance to deformation on the deformation heat and friction heat are discussed. And the variation of temperature field of the work roll with time is analyzed quantitatively.

Cleaning processes draw considerable attention in integrated circuit manufacturing because of the rapid development of technology nodes. Bare silicon wafer cleaning after chemical mechanical polishing (CMP) is one of the most difficult processes used to meet the extremely strict industrial requirements. Herein, the silicon wafer cleaning mechanism is studied in detail. The effects of megasonic and brush cleaning on nanoparticle removal are both analysed through experiments and simulations. The experimental results show that chemical concentration, megasonic vibration power, and brush clamp gap all significantly affect the cleaning performance, and that excessive megasonic power reduces the cleaning performance because more defects are introduced. A model of megasonic nozzle trajectory is also proposed, and optimized parameters, especially the relative velocity between the wafer rotation and nozzle movement, are critical to removing nanoparticles effectively. Furthermore, analysis of combining megasonic and brush cleaning shows that including megasonic cleaning improves the wafer cleaning performance by several orders of magnitude. Based on the optimized cleaning conditions, an ultraclean wafer surface is achieved after CMP.

Marangoni drying is widely employed in integrated circuit manufacturing to remove water from the wafer surface. The organic vapor blown at the meniscus induces a strong Marangoni effect, which stri...

As an important optical component in laser system, silicon mirror surface is required to have micron-level flatness and subnanometer-level roughness. The research concentrates on how to improve roughness as far as possible while maintaining flatness of silicon mirror surface during chemical mechanical polishing (CMP) process. A polishing edge effect model is established to explain the reason of flatness deterioration, and a roughness theoretical model is set up to get the limit of perfect surface roughness. Based on the models above, a polishing device is designed to maintain the surface flatness, and the optimized polishing process parameters are obtained by orthogonal tests to get a near-perfect surface roughness. Finally the maintenance of flatness and the improvement of roughness can be achieved at the same time in one step of CMP process. This work can be a guide for silicon mirror manufacture to improve optical reflection performance significantly.

Marangoni drying induced by organic vapor is an important process in integrated circuit manufacturing to obtain an ultra-clean surface, but its application is limited by the utilization of flammable vapor. Thermal Marangoni drying induced by a temperature gradient is a safe and environmentally friendly technology. However, the regulation of thermal Marangoni-driven flow is complicated, and current understanding of the thermal Marangoni drying mechanism is inadequate. In this work, we present a coupled model of thermal Marangoni drying that combines the two-phase flow, heat transfer, and water vapor transfer in air. The evolution of entrained water film thickness, dynamics of Marangoni-driven flow, and evaporative cooling are numerically simulated. The results show that the achieved minimum residual thickness of the entrained water film is thinned more than tenfold compared with that of the wafer withdrawn without the thermal Marangoni effect. The temperature rise and Marangoni stress grow dramatically in the film and meniscus at the initial time, and then they remain as almost invariant after achieving the dynamic equilibrium between the heating and evaporative cooling. The convective water vapor transfer in air and the reduction of entrained water film thickness improve the evaporative flux, which in turn suppresses the increase in the thermal Marangoni effect until the dynamic equilibrium is attained. Furthermore, the higher heat source, lower wafer thermal conductivity and smaller wafer thickness can enhance drying performance. The investigation of drying dynamics will contribute to a comprehensive understanding of the thermal Marangoni drying process and provide guidance to its industrial applications.

Marangoni drying is a highly concerned technology in the integrated circuit (IC) manufacturing, which removes the deionization (DI) water on the wafer surface in the wet cleaning process after chemical mechanical polishing (CMP). When the wafer is withdrawn from a DI water bath, Marangoni effect is induced by the organic vapor blown at the meniscus. It contributes to the backflow and stripping of the entrained water on the wafer and then achieves an ultraclean surface. Herein, the Marangoni drying performance is experimentally investigate using a self-developed drying device. Firstly, the visible water film on the wafer surface before and after Marangoni drying is observed. It indicates that Marangoni effect dramatically increases the critical withdrawal velocity where the visible water is formed. Further, the fluorescent particles are added in DI water, and the drying performance is characterized by counting the deposited particles using a fluorescent microscope. Such a method indirectly reflects the drying performance. The experimental results show that withdrawal velocity, organic vapor flux and blown angle exert significant impacts on the drying performance.

Vertical rolling is an important technique to control the width of continuous casting slab in hot rolling field. Accurate prediction of vertical rolling force is a core point to maintain rolling mill equipment. Due to the limitation of the algorithm, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling force model to improve the prediction accuracy. This paper presents an innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion. Firstly, the maximal width of dog bone region is determined by the slip-line method and described the dog bone shape via sine function model. Furthermore, proposed velocity and corresponding strain rate fields satisfy kinematically admissible condition is used to calculate the total power. Finally, the analytical solution of the rolling force and dog bone shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. And the effectiveness of the proposed mechanical model is verified by measured data in strip hot rolling field and other models’ results. The results shows that the prediction accuracy of vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness and friction factor on dog-bone shape size and vertical rolling force are discussed.

This study presents a new mathematical model for edge rolling force and dog-bone shape using the combination of slip-line and exponent velocity field. The slip-line field of the dog-bone area is drawn out based on the deformation characteristics of edge rolling and the maximal depth of dog-bone zone is determined. Then a new exponent velocity field and corresponding strain rate field which satisfy kinematically admissible condition are proposed to analyze the edge rolling force based on upper bound approach. The upper bound solutions of dog-bone shape and rolling force are obtained by minimizing the total power which contains the internal plastic power, frictional and shear powers. The effects of reduction rate, initial thickness and roll radius on dog-bone shape size and edge rolling force are discussed. The results obtained by the combined solution in this paper are compared with measured data in strip hot rolling field and finite element method (FEM) simulation results, and a good agreement is found.

A three-dimensional mathematical model for edge rolling using sine function dog-bone shape and the dual-stream function (DSF) method is established to research the plastic deformation of the slab at the vertical roll gap. A kinematically admissible velocity field is derived through DSF based on sine function model and the slab total power functional is obtained according to the upper bound theorem. The upper bound solutions of dog-bone shape and rolling force are solved numerically via minimizing the total power function by using the Matlab Optimization Toolbox. Satisfactory results are given while compared with experimental data in reference and FEM simulation, with good convergence, in various rolling conditions such as engineering strain, initial thickness and roll radius.

With the rapid development of high-energy laser system, thick silicon mirror, as an important optical component to reflect laser, is required to have a surface with micron-level flatness, which poses significant challenges to silicon mirror manufacture process. Fine rotation grinding (FRG) is a typical efficient method for silicon mirror manufacture. A geometric model is developed in this paper to research silicon mirror surface figure control mechanism in FRG process. The model demonstrates the relationship between the grinding spindle obliquity and the mirror surface figure. From an application perspective, the relationship between the spindle obliquity and the spindle dial gauge indication is further presented. Based on this model, a MATLAB program is designed to give a series of simulation results for researching spindle adjustment regularity and getting the most ideal spindle obliquity. Besides, several grinding experiments are carried out. The simulation and experiment results are in good agreement, and a silicon mirror surface with the flatness of less than 2 μm is achieved. The proposed grinding geometric model can provide an actual guide for grinding spindle adjustment to control the surface figure of silicon mirror.

This paper analyzed the evolution of microstructure, composition, and impact toughness across the fusion line of high-strength bainitic steel weldments with different heat inputs. The main purpose was to develop a convenient method to evaluate the HAZ toughness quickly. The compositions of HAZ were insensitive to higher contents of alloy elements (e.g., Ni, Mo) in the weld metal because their diffusion distance is very short into the HAZ. The weld metal contained predominantly acicular ferrite at any a heat input, whereas the main microstructures in the HAZ changed from lath martensite/bainite to upper bainite with the increasing heat input. The evolution of HAZ toughness in relation to microstructural changes can be revealed clearly combined with the impact load curve and fracture morphology, although the results of impact tests do not show an obvious change with heat input because the position of Charpy V notch contains the weld metal, HAZ as well as a part of base metal. As a result, based on the bead-on-plate welding tests, the welding parameter affecting the HAZ toughness can be evaluated rapidly.

Accurate determination of a chemical mechanical planarization (CMP) process reaching the end point is an important problem in the CMP process. In present work, the variation of the motor power signal of the polishing platen in the CMP process has been investigated, and the moving average method with 121-points moving window was used to smooth the original signal curve. Experiment results showed that the processed signal could facilitate the extraction of end-point feature for the in-situ end-point detection (EPD) system and it was relatively steady before and after the layer transition stage, which made it more reliable to detect the end point in situ. Comparing with other EPD methods, the system was less complicated, and it was easier to code for algorithm development. Finally, further analysis was performed and series of experiments provided a planarized via-revealed surface with low via dishing.

The rolling force model was the core factor for the control system of the cold rolled sheet, the prediction accuracy affect the final flatness and the strip thickness directly. A novel approach for the rolling force prediction of cold rolled sheet was first proposed based on the plastic mechanics, in which the cylindrical velocity field was used to analyze the metal flow in the deformation region by the upper bound analysis in this paper. The analysis solution of rolling torque, rolling force and stress state coefficient are obtained by minimizing the total power which contain the internal plastic power, frictional power, shear power and tense power. Moreover, the effects of frictional factor, reduction ratio and the tense on the location of neutral point and stress state coefficient are discussed, respectively, and the validity of the proposed model was verified by comparing with the traditional models. The calculation process was programed and applied in the control system of one 1450 mm cold tandem mill successfully, the prediction results was in good agreement with the actual measured ones, and deviation proportion in the range of ±10.0% reached 97.3%, it can meet the requirements of the control system in cold rolling process.

In this study, a specially designed carrier with a one-zone pneumatic loading system that uses a thick copper disk as the workpiece was developed. Comparative studies of the fluid pressure and workpiece orientation between the disk and wafer carriers during chemical mechanical polishing were conducted. The results reveal that the copper disk leans down toward the leading edge and produces a negative-dominated (approximately 70%) fluid pressure, which differs from the multi-zone carrier but agrees with other studies in which the fluid pressure is measured from the disk side. Different balancing statuses and wedged gaps are formed in these two structures.

A parabolic velocity field is proposed to get the minimum required rolling force in hot rolling process, the equal area yield criterion is used to calculate the plastic deformation power, the collinear vector inner product method is used to get friction power, the analytical equation of strip rolling power functional is obtained, and the required rolling force was calculated by minimizing the power functional. Meanwhile, the location of neutral point, shape factor, and stress state coefficient are discussed. The accuracy of the proposed theoretical model is examined through comparing with the experimental measured ones and online measured ones, it shows good agreement, the relative error of rolling force is less than 9.1%, and the proposed model is considered to be effective in hot tandem rolling process.

In this paper, three-dimensional velocity field is proposed by means of stream function method with bisecting yield criterion in chamfer edge rolling of ultra-heavy plate. Parabolic dog-bone shape function is derived so as to obtain velocity field with fixed angle of chamfer edge by stream function method, dog-bone shape coefficient η can be derived from volume invariant condition, and then the plastic deformation power, shear power as well as friction power are obtained respectively with the bisecting yield criterion. Summing up the power contributions, total power functional is presented, from which minimum value can be obtained by searching method, and vertical rolling force and torque are also finally obtained. The predictions of roll force and torque are compared with different angles of chamfer edge as well as different plate thicknesses. The results are shown to be in a very good agreement with the analytical and experimental results.

There is an increasing requirement for improved accuracy of the rolling models which are widely used in rolling plant in order to produce high-quality products, because this accuracy is important for rolling schedule setup and automatic control. A three-dimensional mathematical model for cold rolling using tangential velocity field and energy method is firstly proposed to investigate the deformation of the strip at the roll gap based on elastic and plastic mechanics. The field and geometrical approximation yield criterion are used to integrate the internal plastic deformation power. The friction power is analyzed using the co-line vector inner product method. Finally, the analytical expressions of roll separating force and roll torque are obtained quickly considering the effect of roll flattening on the roll separating force. The predicted roll separating forces are consistent with other researchers’ models, especially for on-line measured roll separating forces in a tandem cold rolling plant. The accurate predicted results provide valuable guidelines for optimization of rolling process.

The microstructures of high strength bainitic steel weldments were characterized, and their hydrogen permeability was investigated by the electrochemical permeation technique. The effective diffusion coefficient in the welded joint increases with heat input, while the hydrogen concentration at the sub-surface decreases with increasing heat input, mainly due to coarsening grain and inclusion sizes. Compared with as-welded specimens, the tempered membranes have lower effective diffusion coefficient and higher density of hydrogen traps due to newly formed carbides acting as hydrogen trapping sites that are derived from the decomposition of martensite-austenite constituents. These were further confirmed by the partial permeation technique.

This work described the manufacture of hot rolled X100 pipeline steels at the laboratory based on thermomechanically controlled processing (TMCP) and high-temperature processing (HTP) concepts. Continuous cooling phase transformation was assessed by dilatometric tests for both steels. Microstructures were characterized using optical and electron microscopes to elaborate the evolution of mechanical properties with process parameters. The main microstructures for both steels were changed from granular bainite to lath bainite/martensite or acicular ferrite with increasing cooling rate. However, the TMCP steel always had lower transformation critical temperatures than the HTP steel. After hot rolling, the TMCP steel with predominantly acicular ferrite showed more excellent mechanical properties than the HTP steel with mainly granular bainite. In this sense, the combined addition of Mo and low Nb is superior to high Nb content for the alloy design of X100 pipeline steel. The optimum performance of TMCP steel can be obtained using the following process parameters: 820 °C finish rolling temperature, 460 °C final accelerated cooling temperature, and 25 °C/s cooling rate. The statistical analysis of precipitates showed that their type, morphology, and size distribution were similar for both steels, implying that the effect of high Nb content seems not to be exploited completely in as-rolled HTP steel.

The thickness of the plate in temperature gradient rolling is first divided into 2 m elements, and m is an undetermined parameter which can be limited. Based on these thickness elements with different temperatures, the rolling force of this advanced process is first analyzed with slab method. Also the predictions of thickness ratio with different temperatures and reductions of each thickness elements are proposed in this paper. The results measured after rolling experiments are used to compare with these calculated by this model in order to verify its accuracy. In the experiment, a multi-metals riveting plate in the same temperature is designed to simulate a single metal one in gradient temperatures based on the thickness elements. Since the model is based on an analytical method which is strongly supported by the rolling theories, it can be applied in real gradient temperature rolling for ultra-heavy plate.

An analytical model, in which unequal radii are replaced with an equivalent radius, is creatively proposed to predict the rolling force and roll torque in general case of snake rolling. With the model, the effects of roll radius ratio, roll speed ratio, offset distance between rolls, reduction and friction coefficient on rolling forces in hot snake rolling of aluminum alloy are obtained. Also, the thicknesses of slab are investigated in different zones, which firstly propose the changes of thickness during snake rolling. Owing to the good agreement with the results measured in experiments and calculated by finite element method and other traditional models, those calculated by the proposed model are verified. The proposed model can be used to predict more accurate theoretical results for snake rolling force and torque.

Edge rolling plays a vital role in width control of strip rolling, where plastic deformation concentrates in the edge of the slab. Then, the center of the slab remains its initial shape. The local deformation is different from overall one which obtained in horizontal rolling. In this paper, dog-bone shape is creatively described by a continuous symmetric parabola used to describe, and based on the complex mathematical function, a kinematically admissible continuous velocity field for edge rolling is established. Finally, the upper deformation power function is yielded. Based on minimum of the power, the results in edge rolling force and torque are obtained. Some vertical rolling forces for copper and aluminum experiments are calculated by the function, and then, also the results are verified by the traditional models. Anyway, the maximum error is less than 18 %. This is a crossover study on both mathematical curve and mechanical analysis which can be seen as a combination of the theory and engineering.

When the thicknesses of the outer layers are different in sandwich rolling, based on the different kinds of arrangements with the hard and soft materials the thickness ratio of two outer layers is changed differently during the rolling process. After the first analysis of the different outer thicknesses sandwich rolling, the rules for final thickness ratio of the two outer layers are proposed. In soft–hard–soft sheets (s–h–s) the thickness ratio of outer layers is remained in the final bonded sandwich sheet however in hard–soft–hard sheets (h–s–h) the thickness ratio is alleviated by sandwich rolling itself. A model based on slab method is proposed to analyze this phenomenon and 4 groups of experiments with Al and Cu as well as steel are conducted. The results calculated by the model well agree with those measured in the experiments. Then the accuracy and worthy of the model are verified.

The automatic width control of the strip that is used in vertical rolling is a key issue in the hot strip rolling process. It is the first time that the internal deformation power and the friction power are obtained by using angular bisector yield criterion and Pavlov projection principle in the vertical rolling. At the same time, the shear power is determined by use of the integral mean value theorem. Then the vertical rolling force and shape parameters are obtained by minimizing the total power functional. The relative error of rolling forces is less than 8.29 % compared with those measured on-line in a hot strip rolling plant. Moreover, the formula forms of the three powers mentioned above are greatly simplified and improved.

Multi-pass submerged arc welding was performed on the HSLA steels using multi-microalloyed electrodes in the present work, and three different heat input processes were employed to investigate the microstructure evolution and corresponding mechanical properties of weldments. The emphasis was placed on studying the influence of microstructure aspects on impact toughness of weld metal and HAZ with different heat inputs to reveal fracture micromechanism and to optimize the welding system. According to the experimental results, the acceptable welding parameters were ascertained for the studied steel to obtain a good balance of high strength and toughness welded joint. The optimal range of size distribution of non-metallic inclusion formed in the weld metal was determined and the essential causes of deteriorated HAZ toughness were revealed. Keywords: HSLA steel, Submerged arc welding, Impact toughness, Acicular ferrite

Wafer drying induced by Marangoni effect is crucial to achieving an ultraclean surface in integrated circuit manufacturing. According to the previous opinions, the entrained water film on wafer surface was stripped by Marangoni effect, and thus the watermark defect induced by evaporation was inhibited. However, the influence of particle removal induced by Marangoni effect on the ultraclean surface preparation is lack of adequate understanding. The present work implements an experimental and numerical investigation of wafer cleaning behavior engendered by Marangoni effect during the wafer withdrawn process. The impacts of critical process parameters and substrate properties on the particle removal efficiency are systematically studied. The results show that Marangoni effect has better cleaning performance on the glass substrate compared with that of silicon and copper. The numerical simulation indicates that the Marangoni effect is more dramatic on glass substrate owing to the better wettability. Furthermore, the stress analysis reveals the adsorption force of fluorescent particle on the copper surface is stronger than that of silicon and glass. Therefore, particle cleaning on the copper surface is much more difficult. The investigation of cleaning performance driven by the Marangoni effect will contribute to a comprehensive understanding of the mechanism of ultraclean surface preparation.

In this paper, sandwich rolling with symmetrical thickness and materials is intensively studied. The inner metal is out of touch with both upper and lower rolls in the sandwich sheets, and all the forces are delivered from upper and lower sheets. This special character makes the relative slip distance and elongation distance appear. Then, the defected length is formed during the sandwich rolling. It verifies that the point where both inner and outer metals have the same velocity is also the point where the two metals are both deformed. Slab method is first applied in predicting the defected length of the sandwich sheets. Sandwich rolling experiments with aluminum and copper are conducted. The results obtained in this paper are also compared with those measured in experiments and calculated by stream function model recorded in references. So the model can be used in the real work conditions. It is helpful to find the best shearing position in the head of the sandwich sheets. The cost of materials is reduced based on the present model. When sheets are rolled in continual rolling passes, the defected length can be more important and serious. Specifically, if the sheets are wide, expensive and multilayer, the shearing position can be more significant to the industrial application.

Friction coefficients in spread formulas were studied under low width-to-thickness ratio. The effects of all the factors on friction were considered as different roughness of surfaces. After lead rolling experiments in 5 different roughness grades, friction coefficients were obtained. With changing width-to-thickness ratio, reduction rate and ratio of diameter of roller to thickness, all the nominal friction coefficients which can be used in these formulas were calculated. Then, a fitting expression was proposed, comparing with the results measured in 232 times tests, the errors of the nominal friction coefficients calculated by the expression are mostly less than 12%. After a certain times self-learning, the errors are no more than 2%. With the varying nominal friction coefficients, the spread will be predicted more accurately. When the nominal friction coefficient is used to predict the spread under the real working condition, the results calculated are also in agreement with the measured ones, and the errors are less than 2%. This credible reference and solution about how to set the friction coefficient in spread formulas would also be used in practical industrial production.

A new sine velocity field is proposed to analyze total power in the roll gap for rolling in hot strip finishing mill. The field and linear geometric midline yield criteria are used to calculate the plastic deformation power, and the collinear vector inner product method is used to get friction power. Then analytical equation of strip rolling power functional is obtained. Finally, the roll force and torque can be calculated by minimizing the power functional. In the model, average deformation resistance is determined by the thermo-mechanical coupled analysis. The prediction accuracy of the proposed model is examined through comparing with the on-line measured results in a hot strip finishing mill. It shows that the predicted roll forces are in good agreement with the measured ones, and the maximum error is less than 12 %. Moreover, the effects of various rolling conditions, such as thickness reduction, friction factor, and shape factor, on roll force, location of neutral angle, and stress-state coefficient are discussed systematically.

Vertical rolling is a vital method for width control in rolling, which has its own deformation characteristic. During the processing, plastic deformation does not go further into center of slab, only in edge where the deformation will be occurred. In this paper, an anti-symmetric parabola is creatively used to describe dog-bone shape and innovatively applied to establish a knematically admissible continuous velocity field for vertical rolling. Based on this field, an analytical form of total deformation power is obtained which is a function of reduction geometric parameters, and friction factor m, as well as parameter of A which is to be determined. With minimization of total power results in rolling forces and torque calculated by this new method is obtained. Copper and aluminum experiments conducted by S.-E.Lundberg are used to verified the results calculated by formula in present paper and compared with those by Lundberg and Duckjoongs’ models. The error is no more than 13%, (average error 7%).

As an ultra-clean wafer drying technique, Marangoni drying has been widely applied in the integrated circuits manufacturing process. When the wafer is vertically withdrawn from a deionization water bath, Marangoni stress along the meniscus, which is induced by the organic vapour, strips off the water film entrained on the wafer surface, and the wafer drying is thereby realized. In this work, a numerical model is presented that is comprised of the film, meniscus, and bulk regions for Marangoni drying. The model combines the transfer of organic vapour from air to water and the withdrawal of the wafer from the bath. The evolution of the entrained water film thickness, the tangential velocity, and the stress at the air–water interface are quantitatively investigated. The results reveal that the thickness of the entrained water film is reduced by more than one order of magnitude compared with the wafer withdrawn process without the Marangoni effect. In addition, owing to the receding of the contact line, it is found that the capillary pressure gradient dramatically increases, which contributes to the sudden increase in the tangential velocity in the dynamic meniscus. Moreover, the tangential velocity decreases in the static meniscus adjacent to the dynamic meniscus, which results from the redistribution of the interfacial concentration of the organic species driven by the Marangoni flow.