An integrated thermal model of hot rolling

During the heavy plate rolling process, different production steps, i.e., roll passes, descaling passes, and air cooling periods, influence the temperature evolution of the plate. All these relevant aspects are covered by a one-dimensional thermal model proposed in this paper. Experiments were conducted in a rolling mill under realistic rolling conditions to parametrise and validate the model. Using pyrometer measurements, a simple model adaption strategy is developed, which can cope with uncertainties in the initial temperature profile. The model provides accurate predictions of the temperature evolution of the plate during the whole rolling process from the plate’s exit of the furnace to the last pass. Thus, it can be used for scheduling the production process. Based on the model, an observer can be designed.     

Dynamics of a Rolling Disk in the Presence of Dry Friction

In this paper we are interested in the dynamics and numerical treatment of a rolling disk on a flat support. The objective of the paper is to develop a numerical model which is able to simulate the dynamics of a rolling disk taking into account various kinds a friction models (resistance against sliding, pivoting and rolling). A mechanical model of a rolling disk is presented in the framework of Non-smooth Dynamics and Convex Analysis. In an analytical study, approximations are derived for the energy decay of the system during the final stage of the motion for various kinds of frictional dissipation models. Finally, the numerical and analytical results are discussed and compared with experimental results available in literature.     

Optimization model of recrystallization hot rolling of titanium-vanadium steels

An optimization model was built based on the data of a pilot-scale (4.5 MN load, 225 KW power capacity) rolling mill to minimize the austenite grain sizes of Ti–V steels, which prevail at the instant of completion of the static recrystallization during hot rolling. A computer program developed for this optimization model was run for the rolling schedule, which is designed according to the complete recrystallization case. An energy optimization model developed previously was applied to different rolling schedules. The grain size optimization results demonstrate the effectiveness of these modelling approaches in terms of final grain size, final plate thickness, measured and computed roll force and torque values for both the design of the thermomechanical schedules which produce plate with fine-grained microstructures, high strength, and notch toughness and the temperature-reduction schedules of conventional controlled rolling.     

On upper bounds of sequential stochastic production planning problems

In this paper we consider a class of problems that determine production, inventory and work force levels for a firm in order to meet fluctuating demand requirements. A production planning problem arises because of the need to match, at the firm level, supply and demand efficiently. In practice, the two common approaches to counter demand uncertainties are (i) carrying a constant safety stock from period to period, and (ii) planning with a rolling horizon. Under the rolling horizon (or sequential) strategy the planning model is repeatedly solved, usually at the end of every time period, as new information becomes available and is used to update the model parameters. The costs associated with a rolling horizon strategy are hard to compute a priori because the solution of the model in any intermediate time period depends on the actual demands of the previous periods.In this paper we derive two a priori upper bounds on the costs for a class of production planning problems under the rolling horizon strategy. These upper bounds are derived by establishing correspondences between the rolling horizon problems and related deterministic programs. One of the upper bounds is obtained through Lagrangian relaxation of the service level constraint. We propose refinements to the non-Lagrangian bounds and present limited computational results. Extensions of the main results to the multiple item problems are also discussed. The results of this paper are intended to support production managers in estimating the production costs and value of demand information under a rolling horizon strategy.     

LP modelling of the finishing hot rolling programme for low carbon steel coils

In this paper a mathematical model was developed to optimize the finishing rolling of hot rolled coils by increasing the productivity of the rolling programme, to help achieve the required level of quality assurance and to facilitate production planning and control in the hot rolling mill. A brief account of the technological and planning aspects of the hot rolling processes and mills relevant to strip steel is given. Linear (mixed integer) programming is used to formulate the objective function and the various types of constraints of the model. The model takes into consideration, the general aspects pertinent to hot rolling of low carbon steel and the characteristics of the hot rolling mills as stipulated by the operational codes and guidelines of the relevant establishments. Owing to the flexibility offered by linear programming the model can incorporate any modifications and/or additional requirements, if any, in case of other types of steel and/or other types of mills. The full modelling of the problem required the incorporation of some zero/one variable constraints. Owing to the complexity involved and the need to keep the model as simple as possible, it was decided to exclude these constraints and deal with them externally. HYPER LINDO PC was used to solve the programme. Using available data, in the case under consideration the model showed astonishing results in achieving the objectives. Taking into account the effect on the overall productivity as well as quality improvement, the investigation showed that a net improvement in conforming output to the effect of around 43%, could have been obtained had the model been used in the case under consideration.     

Integration of timetable planning and rolling stock in rapid transit networks

The aim of this paper is to propose an integrated planning model to adequate the offered capacity and system frequencies to attend the increased passenger demand and traffic congestion around urban and suburban areas. The railway capacity is studied in line planning, however, these planned frequencies were obtained without accounting for rolling stock flows through the rapid transit network. In order to provide the problem more freedom to decide rolling stock flows and therefore better adjusting these flows to passenger demand, a new integrated model is proposed, where frequencies are readjusted. Then, the railway timetable and rolling stock assignment are also calculated, where shunting operations are taken into account. These operations may sometimes malfunction, causing localized incidents that could propagate throughout the entire network due to cascading effects. This type of operations will be penalized with the goal of selectively avoiding them and ameliorating their high malfunction probabilities. Swapping operations will also be ensured using homogeneous rolling stock material and ensuring parkings in strategic stations. We illustrate our model using computational experiments drawn from RENFE (the main Spanish operator of suburban passenger trains) in Madrid, Spain. The results show that through this integrated approach a greater robustness degree can be obtained.     

Thermal analysis of hot strip rolling using finite element and upper bound methods

Thermal analysis of hot rolling process has been studied in this work. A finite element method has been coupled with an upper bound solution assuming, triangular velocity field, to predict temperature field during hot strip rolling operation. To do so, an Upwind Petrov–Galerkin scheme together with isoparametric quadrilateral elements has been employed to solve the steady-state heat transfer equation. A comparison has been made between the published and the model predictions and a good agreement was observed showing the accuracy of the proposed model.     

Prediction of temperature distribution and phase transformation on the run-out table in the process of hot strip rolling

In this paper a mathematical model based on the finite element method and the Scheil additivity rule is presented for predicting the temperature distribution and phase transformation behavior on the run-out table during the hot strip rolling of a low carbon steel. The model considers the austenite to ferrite and pearlite transformations, the temperature-dependent material properties of the cooling austenite as well as the austenite work hardening effect on the kinetics of austenite transformation. To determine the validity of the model predictions, the time-temperature histories of a low carbon steel rod in different cooling media were measured and also hot rolling experiments were performed. Good agreement between the predictions and the experimental results indicates the reliability of the model.     

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.     

Nonlinear modeling and analysis of a rolling element bearing with a clearance

Rolling element bearings are the key components in many rotating machinery. For efficient performance of the machine it is necessary to accurately predict the effect of various parameters and operating conditions on the machine’s behavior. This paper deals with the development of a nonlinear model of the rotor-bearing system on rolling element bearings with clearance. Clearance is an important nonlinearity which can cause bifurcations and chaos as has been shown in this paper. In this paper a detailed model for clearance is developed. In this model the inner race center and the outer race center are not assumed to be collinear when relations for deflections in the rolling element are developed. The model is non-dimensionalized and then analyzed to reveal rich nonlinear phenomena. Further, for better performance of any machine it is necessary to identify and stay out of chaotic regimes of operation. Hence, Lyapunov exponents and Poincaré mappings are used to analyze the system and determine the regions of chaotic response.     

A coupled mathematical model for the rollgap and interstand regions in a hot strip mill

In this paper we consider the process of hot-rolling steel strip.The thickness is reduced by passing the strip through a sequenceof rollers with reductions varying from 40% at the first rollpair to about 10% at the last pair. Between the roll pairs,the strip deflection curve is controlled by a looper roll. Amathematical model of the coupled roll gap and interstand regionis required to assist in the initial setup so as to spread theloads and torques evenly through the roll stands. The modelis of potential value in monitoring the transient behaviourof the rolling process. A review of the various models for eachregion and a coupled complete rolling model is described.     

A mathematical model and algorithms for the aircraft hangar maintenance scheduling problem

An aircraft hangar maintenance scheduling problem is studied, motivated by the aircraft heavy maintenance conducted in a hangar operated by an independent maintenance service company. The aircraft hangar maintenance scheduling problem in such context consists of determining a maintenance schedule with minimum penalty costs in fulfilling maintenance requests, and a series of hangar parking plans aligned with the maintenance schedule through the planning period. A mixed-integer linear programming (MILP) mathematical model, integrating the interrelations between the maintenance schedule and aircraft parking layout plans, is presented at first. In the model, the variation of parking capacity of the maintenance hangar and the blocking of the aircraft rolling in and out path are considered. Secondly, the model is enhanced by narrowing down the domain of the time-related decision variables to the possible rolling in and out operations time of each maintenance request. Thirdly, to obtain good quality feasible solutions for large scale instances, a rolling horizon approach incorporating the enhanced mathematical model is presented. The results of computational experiments are reported, showing: (i) the effectiveness of the event-based discrete time MILP model and (ii) the scalability of the rolling horizon approach that is able to provide good feasible solutions for large size instances covering a long planning period.     

Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process

This paper introduces an artificial neural network (ANN) application to a hot strip mill to improve the model’s prediction ability for rolling force and rolling torque, as a function of various process parameters. To obtain a data basis for training and validation of the neural network, numerous three dimensional finite element simulations were carried out for different sets of process variables. Experimental data were compared with the finite element predictions to verify the model accuracy. The input variables are selected to be rolling speed, percentage of thickness reduction, initial temperature of the strip and friction coefficient in the contact area. A comprehensive analysis of the prediction errors of roll force and roll torque made by the ANN is presented. Model responses analysis is also conducted to enhance the understanding of the behavior of the NN model. The resulted ANN model is feasible for on-line control and rolling schedule optimization, and can be easily extended to cover different aluminum grades and strip sizes in a straight-forward way by generating the corresponding training data from a FE model.     

A rolling stock circulation model for combining and splitting of passenger trains

This paper addresses the railway rolling stock circulation problem. Given the departure and arrival times as well as the expected numbers of passengers, we have to assign the rolling stock to the timetable services. We consider several objective criteria that are related to operational costs, service quality and reliability of the railway system.Our model is an extension of an existing rolling stock model for routing train units along a number of connected train lines. The extended model can also handle underway combining and splitting of trains.We illustrate our model by computational experiments based on instances of NS Reizigers, the main Dutch operator of passenger trains.     

Dynamic modelling and simulation of a hot strip finishing mill

Hot rolling is an essential industrial process in the production of sheet steel, a widely used product in manufacturing and construction. A finishing mill performs a set of operations in a hot strip rolling mill, and is a complex unit including many processes and control loops. Its modelling is a challenging task due to the variety of phenomena that occur within the mill, and variable transport delays. Model validation is also challenging due to a scarcity of measurements. On the other hand, a dynamic model that adequately reflects the numerous interactions between the mill units can be very useful for tasks such as high performance control design or vibration analysis. In this study, a one-dimensional model has been developed and validated against real plant data. The end use of the model is intended to be looper control analysis, but the model is kept sufficiently general so that it can be used or easily extended for other applications.     

Rolling of a non-homogeneous ball over a sphere without slipping and twisting

Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, J. Koiller and K. Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.      

The sea-wave elevation and multistability in a non-autonomous nonlinear Itô’s stochastic differential equation for the rolling angle of a ship

Prediction of the rolling behavior of ships in irregular sea remains one of the most difficult problems in ship engineering. The present work facilitates solution of this problem by derivation of a model which is meaningful from the subject-specific point of view and can efficiently be analyzed with the path-integration method. The model is a single Itô’s stochastic differential equation for the rolling angle of a ship located at a fixed spatial point. The equation appears to be of the third order and nonlinear. It takes into account the elevation of stochastic traveling sea waves. The stochasticity of the elevation is allowed for by stationary stochastic velocity of the waves. The works also notes the picture for the multistability of the derived model. Improvement of capabilities of the methods for multistable nonlinear systems is included in directions for future research.     

A rolling horizon approach for disruption management of railway rolling stock

This paper deals with real-time disruption management of rolling stock in passenger railway transportation. We describe a generic framework for dealing with disruptions of railway rolling stock schedules. The framework is presented as an online combinatorial decision problem, where the uncertainty of a disruption is modeled by a sequence of information updates. To decompose the problem and to reduce the computation time, we propose a rolling horizon approach: rolling stock decisions are only considered if they are within a certain time horizon from the time of rescheduling. The schedules are then revised as time progresses and new information becomes available. We extend an existing model for rolling stock scheduling to the specific requirements of the real-time situation, and we apply it in the rolling horizon framework. We perform computational tests on instances constructed from real-life cases of Netherlands Railways (NS), the main operator of passenger trains in the Netherlands. We explore the consequences of different settings of the approach for the trade-off between solution quality and computation time.     

Adhesive resistance in the rolling of elastic bodies

A model of the rolling of a rough cylinder on an elastic half-space when there is adhesive attraction between the surfaces, due to molecular interaction, is constructed. The contact characteristics and moment of the adhesive resistance to rolling are calculated.     

Determination of minimum required damping in stochastic following seas modeled by using Gaussian white noise

The aim of this study is to present an analytical method to determine the minimum required damping moment for a stable ship in stochastic following seas modeled by using Gaussian white noise. Stochastic differential equation is used as a mathematical model to represent rolling motion of a ship. First, the minimum required damping is obtained analytically by using Lyapunov function. Second, analytically obtained damping values are verified by integrating the nonlinear stochastic rolling motion equation by stochastic Euler method (Euler–Maruyama Schema) to deduce whether rolling motion is stable or not. It can be seen from the results of numerical computation that the ship is sufficiently stable for the minimum required damping value obtained by the use of Lyapunov function and the minimum required damping is highly dependent on natural frequency of roll, diffusion constant and maximum variation of initial metacentric height.