Rolling Model Research Articles

An Efficient Multi-Scale Modeling Method that Reveals Coupled Effects Between Surface Roughness and Roll-Stack Deformation in Cold Sheet Rolling

Abstract In thin-gauge cold rolling of metal sheet, the surface roughness of work rolls (WRs) is known to affect the rolled sheet surface morphology, the required rolling load, and the roll wear. While modeling of rough surfaces using statistical asperity theory has been widely applied to problems involving semi-infinite solids, the application of asperity distributions and their elastic-plastic behavior has not been considered in roll-stack models for cold sheet rolling. In this work, a simplified-mixed finite element method (SM-FEM) is combined with statistical elastic-plastic asperity theory to study contact interference and coupling effects between a rough work roll (WR) surface and the roll-stack mechanics in cold sheet rolling. By mixing equivalent rough surface contact foundations, Hertz foundations, and Timoshenko beam stiffness, an approach is created to efficiently model interactions between the micro-scale asperities and the macro-scale roll-stack deformation. Nonlinearities from elastic-plastic material behavior of the asperities and the sheet, as well as changing contact conditions along the roll length, are also accommodated. Performance of the multi-scale SM-FEM approach is made by comparison with a continuum finite element virtual material model. 3D studies for a 4-high mill reveal new multi-scale coupling behaviors, including nonuniform roughness transfer, and perturbations to the sheet thickness “crown” and contact force profiles. The described multi-scale SM-FEM approach is general and applies to rough surface contact problems involving plates and shear-deformable beams having multiple contact interfaces and arbitrary surface profiles.

Predictive analysis of quarterly electricity consumption via a novel seasonal fractional nonhomogeneous discrete grey model: A case of Hubei in China

Accurate electricity consumption forecasting plays a crucial role in electric power systems and is a challenging task due to its complicated mechanism induced by multiple influential factors. To address this problem, this paper develops a novel nonhomogeneous discrete grey model that considers seasonality by introducing a seasonal index into the fractional accumulation generation operator, which is abbreviated as SFNDGM. In addition, the introduction of a one-step ahead rolling mechanism can further improve its prediction performance. To enhance the efficacy, the particle swarm optimization (PSO) algorithm is employed to determine the fractional accumulation order. Subsequently, to demonstrate the effectiveness and superiority of the rolling SFNDGM model, this model is applied to simulate and predict Hubei’s quarterly electricity consumption from 2010Q4 to 2019Q3. The numerical results show that the proposed rolling model has a better performance than the other benchmark models. Therefore, the optimal model is utilized to predict Hubei’s quarterly electricity consumption by 2021, inferring that electricity consumption will continue to increase in the coming years. Based on the attained forecasts, several suggestions are put forward to promote the sustainable development of Hubei’s electricity consumption.

Modeling and exploiting the strip tension influence on surface imprinting during temper rolling of cold-rolled steel

To produce cold-rolled steel strips with specific mechanical properties and surface roughness typically temper rolling is adopted. In most cases, a uniform roughness pattern on the strip surface is mandatory. Due to the wear of the textured work rolls, their surface roughness (Ra) continuously reduces during the process, which should be accounted for process control. However, conventional temper rolling systems fail to guarantee a uniform surface roughness. In this work, the influence of strip tension on the imprinting of surface roughness during temper rolling is analyzed based on a multi-scale FE modeling concept to explore new ways for surface roughness control. This is done in simulation where, a macroscopic rolling model incorporating strip tension is coupled to a mesoscopic imprinting model and both models are validated using copper rolling trials. The influence of different thickness reductions, strip tensions and incoming strip's surface roughness on imprinting is modeled and compared. The numerical results reveal that a higher strip tension decreases the roughness transfer, which presents potential to control the roughness transfer ratio without changing other process parameters like the prescribed thickness reduction in the future.

Multiparameter Real-World System Identification Using Iterative Residual Tuning

AbstractIn this work, we consider the problem of nonlinear system identification using data to learn multiple and often coupled parameters that allow a simulator to more accurately model a physical system or mechanism and close the so-called reality gap for more accurate robot control. Our approach uses iterative residual tuning (IRT), a recently developed derivative-free system identification technique that utilizes neural networks and visual observation to estimate parameter differences between a proposed model and a target model. We develop several modifications to the basic IRT approach and apply it to the system identification of a five-parameter model of a marble rolling in a robot-controlled labyrinth game mechanism. We validate our technique both in simulation—where we outperform two baselines—and on a real system, where we achieve marble tracking error of 4% after just five optimization iterations.

Research into the Effect of Speed Mismatch during Continuous Rolling on the Process Parameters

The paper analyzes the influence of tension (dam) on the technological parameters of the rolling process (spreading, force and rolling torque). For the analysis, a model of continuous rolling in three adjacent stands was developed, using the Deform 3D software. The adequacy of the model was confirmed by comparing the experimental data from the small-section wire mill 150 and the simulation results. The error in determining the forming was 0.4%, and in determining the power parameters was 11%. Further, a computational experiment was planned, to identify the effect of mismatched of rolling speeds on technological parameters. According to the results of calculations, graphs of changes in technological parameters were constructed. It is established that, even small deviations of rolling speed from the matched mode lead to significant changes in technological parameters.

Forecasting and Modelling the Uncertainty of Low Voltage Network Demand and the Effect of Renewable Energy Sources

More and more households are using renewable energy sources, and this will continue as the world moves towards a clean energy future and new patterns in demands for electricity. This creates significant novel challenges for Distribution Network Operators (DNOs) such as volatile net demand behavior and predicting Low Voltage (LV) demand. There is a lack of understanding of modern LV networks’ demand and renewable energy sources behavior. This article starts with an investigation into the unique characteristics of householder demand behavior in Jordan, connected to Photovoltaics (PV) systems. Previous studies have focused mostly on forecasting LV level demand without considering renewable energy sources, disaggregation demand and the weather conditions at the LV level. In this study, we provide detailed LV demand analysis and a variety of forecasting methods in terms of a probabilistic, new optimization learning algorithm called the Golden Ratio Optimization Method (GROM) for an Artificial Neural Network (ANN) model for rolling and point forecasting. Short-term forecasting models have been designed and developed to generate future scenarios for different disaggregation demand levels from households, small cities, net demands and PV system output. The results show that the volatile behavior of LV networks connected to the PV system creates substantial forecasting challenges. The mean absolute percentage error (MAPE) for the ANN-GROM model improved by 41.2% for household demand forecast compared to the traditional ANN model.

Nonlinear Dynamic Modeling and Vibration Analysis of Faulty Rolling Bearing Based on Collision Impact

Abstract This study proposes a new nonlinear dynamic model of rolling bearing faults based on a collision impact system. The dynamic model accounts for the collision impact system consisting of the rolling elements and localized faults according to the nonlinear Hertzian contact. First, considering the impact of the rolling element and fault structure, the collision impact system between rolling element and localized fault is established, and the vibration responses of the collision impact system can be obtained. Second, the overall rolling bearing is treated as a mass-spring model, and the contact between the rolling element and raceway is treated as a nonlinear spring that conforms to the Hertzian contact deformation theory. Third, according to the Lagrange equation, overall potential energy, overall kinetic energy, elastic potential energy, and kinetic energy of the collision impact system are used to describe the vibration characteristics. Considering the impact of collision impact systems, a nonlinear dynamic model of rolling bearing faults is established. The simulated acceleration results based on the nonlinear dynamic model are compared to experimental results. The comparison indicates that the numerical model can be used to predict the vibration characteristics of rolling bearings faults effectively.

Shear-driven rolling of DNA-adhesive microspheres

Many biologically important cell binding processes, such as the rolling of leukocytes in the vasculature, are multivalent, being mediated by large numbers of weak binding ligands. Quantitative agreement between experiments and models of rolling has been elusive and often limited by the poor understanding of the binding and unbinding kinetics of the ligands involved. Here, we present a cell-free experimental model for such rolling, consisting of polymer microspheres whose adhesion to a glass surface is mediated by ligands with well-understood force-dependent binding free energy—short complementary DNA strands. We observe robust rolling activity for certain values of the shear rate and the grafted DNA strands’ binding free energy and force sensitivity. The simulation framework developed to model leukocyte rolling, adhesive dynamics, quantitatively captures the mean rolling velocity and lateral diffusivity of the experimental particles using known values of the experimental parameters. Moreover, our model captures the velocity variations seen within the trajectories of single particles. Particle-to-particle variations can be attributed to small, plausible differences in particle characteristics. Overall, our findings confirm that state-of-the-art adhesive dynamics simulations are able to capture the complex physics of particle rolling, boding well for their extension to modeling more complex systems of rolling cells.

The importance of equation η = μn 2 in dimensional analysis and scaled vehicle experiments in vehicle dynamics

Dimensional analysis has been very helpful in experimentation of very large or small-scale engineering systems. A good example would be experimentation on the aircrafts and ships, which was made cost-effective and simple by dimensional analysis. The history of dimensional analysis mentioned in the introduction section of the present document includes many of such applications. Automotive industry, however, never felt the need as the price or the size of land vehicles did not make experimentation so far-fetched; therefore, there are many crash tests which every new vehicle has to go through before mass production This changed with the imminent introduction of autonomous vehicles, which brought all the risks involved in experimenting with them. Many cost-effective experimental platforms are introduced, such as QCar https://www.quanser.com/products/qcar/ or laboratories, such as Scaled Autonomous Vehicles Indoor (SAVI) https://cast.tamu.edu/research/technology-demonstrator-platforms/scaled-autonomous-vehicles-indoor-tdp/. The present study will enable the results taken from such platforms to be translated to real-sized vehicles, enabling researchers to study dynamics of various vehicles. Classical vehicle equations of motion including constant velocity, accelerating bicycle model and roll model have been made dimensionless. The case of steady-state responses is also calculated in a dimensionless form. Some practical numerical examples are also mentioned as a proof of theory.

Methods for online measurement and control of section deviations during hot rolling of wire rod and bars

In the joint project PIREF, the metal forming group of the University of Duisburg-Essen has collaborated with the University of Applied Sciences Ruhr-West Mülheim (Ruhr), the University of Siegen, EMG Automation GmbH and SMS group GmbH to develop sensors, for an online measurement of material velocity and cross section as well as control models for the rolling process of wire rod and bars. The University of Duisburg-Essen provided a metal forming process model for the rolling process to assess the influencing parameters on the rolled section precision. A technique was found to segregate height- from width- influencing parameters from a measured cross-sectional area and actual roll gap. With this measuring technology and with help of the process model, rules for control of the rolling process to achieve close tolerances were obtained. The modelling was accompanied by rolling trials on a laboratory rolling mill at the University of Duisburg-Essen, where a typical Round-OvalRound pass sequence was used for validation of the rolling model concerning lateral spread, inlet and outlet velocity as well as rolling force and torque calculation. The present paper shows how the material flow and the distribution of the velocity in the roll gap can be described. In subsequent rolling of bar and rod in a continuous rolling mill the dimensions can be influenced by application of longitudinal stresses and screwdown. The application of stress can be achieved by an inter-stand velocity mismatch. With the developed models the necessary velocity mismatch can be calculated.

Computational modelling of cold rolling of ferritic iron containing ε-Cu precipitates

The precipitation strengthening of ferritic iron using copper particles was studied using a molecular dynamics model. The developed model simulated the cold rolling of a ferrite sample containing copper precipitates at three different thickness reductions. The dislocation density and the amorphous structure in the ferrite sample increased as the thickness reduction increased. The copper particles experienced severe elongation, and their aspect ratios increased as the thickness reduction increased. It was found that the copper particles lose the fcc structure and transform to amorphous and bcc structures. As the thickness reduction increases, a fraction of the atoms changing to the bcc structure dissolved into the ferrite matrix. The remaining bcc structure atoms were at the interface between the copper particles and the ferrite matrix. Tensile testing of the deformed samples confirmed that the copper particles strengthened the ferrite for up to 30 % thickness reduction, while above 30 % resulted in lower strength due to copper particles’ dissolution.

Methodology of developing mathematical-ANN hybrid model based mill setup model for hot strip rolling

Hot strip mill, one of the most important units of an integrated steel plant, is operated by mill setup model. The conventional mill setup models calculate thermal, reduction and speed schedules of the material being rolled using mathematical models derived from fundamental principles of heat transfer and plastic deformation. However, such mill setup models often compute inaccurate schedules leading to quality issues and operational problems. This paper describes a novel technique of developing a hybrid model by integrating mathematical models with artificial neural network (ANN) model. The trained hybrid models use a multivariable optimization algorithm to calculate the thermal, reduction and speed schedules during hot strip rolling. More than six hundred coils were successfully rolled in an industrial hot strip mill using the mill setup model developed under the present work. It is found that the mill setup model developed using the hybrid models is more accurate and faster than the mill setup models that use conventional mathematical models.

Study on the Effect of Stiffness Matching of Anti-Roll Bar in Front and Rear of Vehicle on the Handling Stability

In order to study the effect of front and rear anti-roll bar’s stiffness on vehicle’s handling stability, the structure and force of the anti-roll bar are analysed, and the vehicle’s rolling model, simplified car motion model and multi-body dynamics model of a car are established. The influence of stiffness change of the anti-roll bar on understeer of the vehicle is studied by constant radius cornering simulation. In swept-sine steering input simulation, the influence of stiffness change of the anti-roll bar on the response indexes of swept-sine steering input simulation are studied, the rule of these indexes changing with stiffness of anti-roll bar is obtained. It is found at high frequencies, due to the damping effect of the system, the influence of stiffness change on yaw rate gain is opposite to that of low frequency. In step steer input simulation, the influence of stiffness change of anti-roll bar on lateral acceleration and transition time are studied. Finally, this paper matches the stiffness of front and rear anti-roll bars of the vehicle based on swept-sine steering input simulation. The results show that the handling stability of the vehicle becomes relatively better after the stiffness of the anti-roll bars is matched.

Multiscale Interface Stress Characterisation in Cold Rolling

This paper provides a comprehensive review on the multiscale characterisation of interface stresses in cold rolling considering both the random asperity deformation and lubrication. The characterisation of the microscopic interface friction was analysed with the effects of lubricant shearing, asperity sliding, lubricant additives and oil-in-water emulsion. Multiscale modelling of rolling under different lubrication regimes was discussed in detail. Some open problems for further studies were also summarised.

Vertical–Horizontal Coupling Vibration of Hot Rolling Mill Rolls under Multi-Piecewise Nonlinear Constraints

This study establishes a vertical–horizontal coupling vibration model of hot rolling mill rolls under multi-piecewise nonlinear constraints considering the piecewise nonlinear spring force and piecewise nonlinear friction force constraints of the hydraulic cylinder in the vertical direction of the rolls, the piecewise stiffness constraints in the horizontal direction, and the influence of the nonlinear dynamic rolling force in the rolling process. Using the average method to solve the amplitude–frequency response equation of the coupled vibration system and taking the actual parameters of a 1780 mm hot rolling mill (Chengde Steel Co., Ltd., Chengde, China) as an example, we study the amplitude–frequency characteristics of the mill rolls under different parameter settings. The results show that the amplitude and resonance region can be reduced by appropriately reducing the external disturbance force and the nonlinear spring force of the hydraulic cylinder, appropriately increasing the nonlinear friction force, and eliminating the gap between the bearing seat and the mill housing, to avoid the amplitude jump phenomenon due to piecewise variation. Furthermore, using the singularity theory to study the static bifurcation characteristics of the coupled vibration system, we establish a relationship between the vibration parameters and the topological bifurcation solution of the coupled system. The transition sets and their corresponding bifurcation topological structure in three cases are given, and the steady and unsteady process parameter regions of the rolls are obtained. The dynamic behavior of the coupled vibration system can be controlled by varying the bifurcation parameter. This study provides a theoretical basis for restraining the vibration of hot rolling mill rolls and optimizing the process parameters.

L2-Gain Based Adaptive Robust Heel/Roll Reduction Control Using Fin Stabilizer during Ship Turns

The rolling and heeling experienced by a ship during turning will be more severe under the interference of winds and waves, which will seriously affect the navigation safety of the ship. The fin stabilizer is currently the best active anti-rolling device, which is usually used to reduce the roll of the ship during straight-line sailing. The purpose of this work is to study the use of fin stabilizers to reduce the rolling and heeling during ship turning, considering the non-linearity and uncertainty during the rotation. The 4 degrees of freedom (4-DOF) nonlinear motion model of a multi-purpose naval vessel is established. The forces and moments produced by fin stabilizers, rudders, propellers, and waves are also considered. The nonlinear control model of rotation and roll is derived and established. Given the non-linearity and uncertainty in the ship turning process, an L2-gain based robust adaptive control is proposed to control the fin stabilizers to reduce the turning heel and roll motion. The proof of the stability and the detailed design process of the controller are also given. Simulations are carried out to verify the effectiveness of the proposed control strategy. For comparison purposes, the simulation results under a well-tuned PID controller are also given. The simulation results show that the developed control strategy can effectively reduce the heel and roll during ship turns, and it has good robustness against uncertainty and internal and external interference.

Computationally Efficient Models of High Pressure Rolling for Wire Arc Additively Manufactured Components

High pressure multi-layer rolling is an effective method to reduce residual stress and distortion in metallic components built by wire arc additive manufacturing (WAAM). However, the mechanisms of the reduction in residual stress and distortion during multi-layer rolling are not well understood. Conventional finite element models for rolling are highly inefficient, hindering the simulation of multi-layer rolling for large WAAM components. This study aims to identify the most suitable modelling technique for finite element analysis of large WAAM component rolling. Four efficient rolling models were developed, and their efficiency and accuracy were compared with reference to a conventional large-scale rolling model (i.e., control model) for a WAAM built wall. A short-length transient model with fewer elements than the control model was developed to reduce computational time. Accurate predictions of stress and strain and a reduction in computational time by 96.5% were achieved using the short-length model when an implicit method for numerical solution was employed, while similar efficiency but less accurate prediction was obtained when an explicit solution method was adopted. A Eulerian steady-state model was also developed, which was slightly less efficient (95.91% reduction in computational time) but was much less accurate due to unrealistic representation of rolling process. The applicability of a 2D rolling model was also examined and it was found that the 2D model is highly efficient (99.52% time reduction) but less predictive due to the 2D simplification. This study also shows that the rigid roller adopted in the models is beneficial for improving efficiency without sacrificing accuracy.

Reliability Life Estimation Considered fault Correlation of Aerial Bearing

The purpose of this paper is to study the reliability life calculation model of aerial rolling bearing considered the correlation of failure model. By mean of collecting relevant experiment data of vibration signal and temperature signal in the life test of the aerial rolling bearings, and analyse time domain and frequency domain, we can analyse the main failure modes and mechanism (e.g. wear, fatigue). The characteristic parameters that characterize the healthy state of aerial rolling bearings obviously are extracted further. Considering that the bearings expose multiple failure modes in the working process in most case, bearing fault diagnosis method is based on fuzzy theory. It is used to clarify the failure mechanism of different failure modes and the degradation rule of performance characteristic parameters. It’s very essential that establish the clear relationships between performance degradation and symptomatic set. According to the fault diagnosis results, each of failure modes is established the performance degradation model respectively. Considering the correlation between multiple different failure modes, Copula theory is introduced to analyse the correlation between multiple failure modes. Base on Copula theory, it’s obtained the life distribution model of aerial bearing based on multiple failure modes. Life distribution model are verified by subsequent experiments, which show that life distribution model of aerial rolling bearing in this paper, is feasible and necessary.

Establishment of Thermal Ductile Fracture Criterion for As‐Cast 42CrMo Steel and Its Application in Hot Ring Rolling Process

The casting‐rolling compound forming process of ring parts is an advanced plastic forming technology that has been developed due to the merits of high efficiency and energy and material saving. However, cracks often occur during the hot ring rolling process, especially at the edges of the ring parts, which severely affects the forming quality. To predict and try to avoid the occurrence of cracks in the casting‐rolling compound forming process of ring parts, the high‐temperature fracture behaviors of as‐cast 42CrMo steel were investigated by thermodynamic experiment method. The high‐temperature tensile tests were carried out using the Gleeble‐3500D thermomechanical simulator at various temperatures and strain rates. Stress‐strain curves and fracture morphology were examined, through which the sensitivity of stress to temperature and strain rate and the effect of dynamic recrystallization and cavity evolution on fracture were found. The law of critical fracture strains was analyzed, and the model of critical fracture strain as a function of temperature and strain rate was established. Based on Oyane criterion, the thermal ductile fracture criterion was established in conjunction with the model of critical fracture strain. By embedding this thermal damage model into the finite element (FE) model for hot ring rolling of an as‐cast 42CrMo ring, the damage prediction for this process was realized, and the thermal ductile fracture criterion was proved to be reliable. From the FE results for hot ring rolling, mechanism of damage and fracture in the hot ring rolling process was analyzed. The damage threshold Cf is small, and the damage ratio D is large at the top and bottom edges of the inner surface area of the ring, which have the greatest propensity to cracking in the course of hot ring rolling. This is of great significance in terms of improving the forming quality of ring parts in the casting‐rolling compound forming process.

Funding Liquidity and the Valuation of Mortgage-Backed Securities

We study the relationship between funding liquidity and the valuation of mortgage-backed securities. Most of the financing for mortgage-backed securities occurs through a trade known as a dollar roll, the simultaneous sale and purchase of forward contracts on mortgage-backed securities that is analogous to a repurchase agreement. We develop a four-factor no-arbitrage model for valuing mortgage-backed securities that allows for the valuation of dollar rolls. Unlike previous models of the dollar roll, we allow for the possibility of a prepayment risk premium. We develop a new model-implied measure of funding liquidity of MBS investors that is independent of prepayment risk premia and agency credit spreads. We find that our implied funding liquidity spread is strongly related to measures of intermediary balance sheet constraints and primary dealer positions in mortgage-backed securities.