Roll Torque Research Articles

On instabilities of force and grain size predictions in the simulation of multi-pass hot rolling processes

In multi-pass rolling processes such as plate rolling, accurate predictions of roll force and torque over all roll passes are desired, so that the pre-calculated roll pass schedule can be put into practice without exceeding the limits of the roll stand. In this context, the grain size has two roles; the final grain size determines the product properties, and the evolution of grain size influences the force predictions. Since the grain size predicted after each roll pass enters the recrystallization kinetics and grain size evolution equations of the subsequent pass, a feed-back loop for the grain size calculation is created, which may become unstable so that the computed roll force and grain size become very sensitive to small variations in the input parameters. Although models for the evolution of grain size in multi-stage hot rolling have been applied in the industry for decades, their mathematical stability has not been given much attention, which poses difficulties for force and grain size predictions in cases subject to partial recrystallization. In this paper, the stability of a common semi-empirical model for static recrystallization and grain growth is investigated. The conditions under which instabilities occur are analyzed both for an industrial plate rolling pass schedule and for idealized load cycles. It is shown that complete recrystallization between roll passes leads to a stable grain size evolution, and that some states of partial recrystallization are unstable and hence problematic for force and grain size predictions. Instabilities in force and grain size predictions of an industrial pass schedules are analyzed by computing sensitivities using automatic differentiation of the model, showing that large amplification factors may occur if the states of partial recrystallization are treated by average strains and grain sizes. The instabilities are an inherent property of the closed-form equations for microstructure evolution for some states of partial recrystallization. However, the side effects of the instabilities can be reduced if the microstructure is not represented by average values of grain size and accumulated strain but by substructures generated by partial recrystallization. This way, the accuracy of roll force predictions can be considerably improved.

Flow Stress Evaluation in Hot Rolling of Steel

In this paper, an inverse analysis technique is used to obtain the flow curve of materials in a hot rolling finishing mill. This technique is based on minimization of the differences between the experimental and computed values. The flow curves and the friction coefficients at roll/work-piece interface are derived from two different models. Model I is based on simple slab method of analysis. Model II is based on a modified slab method in which the effect of shear stress in calculating the rolling force and torque is taken into account. It is shown that the developed inverse analysis technique is reliable and can simultaneously determine a more accurate flow stress for the material as well as a better estimation for the interface friction factors.

Rolling friction of adhesive microspheres

The rolling friction of adhesive microspheres is an important quantity as it determines the strength and stability of larger aggregates. Current models predict rolling forces that are 1 to 2 orders of magnitude smaller than observed experimentally. Starting from the well-known Johnson–Kendall–Roberts (JKR) contact description, we derive an analytical theory for the rolling friction based on the concept of adhesion hysteresis, e.g. a difference in apparent surface energies for opening/closing cracks. We show how adhesion hysteresis causes the pressure distribution within the contact to become asymmetrical, leading to an opposing torque. Analytical expressions are derived relating the size of the hysteresis, the rolling torque, and the rolling displacement, ξ. We confirm the existence of a critical rolling displacement for the onset of rolling, the size of which is set by the amount of adhesion hysteresis and the size of the contact area. We demonstrate how the developed theory is able to explain the large rolling forces and particle-size dependence observed experimentally. Good agreement with experimental results is achieved for adhesion hysteresis values of (Δγ/γ) ≃ 3 for polystyrene, and (Δγ/γ) ≃ 0.5 for silicates, at crack propagation rates of 0.1 µm s−1 and 1–10 µm s−1, respectively.

Finite-element analysis of a vertical twin-roll casting

Metallic strips can be produced by twin-roll casting, in which the melt is cooled, solidified, and rolled to a specific thickness. In the present study, the rigid-thermoviscoplastic finite-element method was applied to the analysis of complex phenomena including melt flow, heat transfer, solidification, and plastic deformation occurring in a vertical twin-roll casting of magnesium alloy AZ31. The melt was found to be confined in rotational motions of two symmetric vortexes developed at the roll entrance, and thus only the melt near the nozzle wall became solidified and rolled to a sheet. As the nozzle thickness increased, the vortex increased in size resulting in more bifurcation and instability, which are definitely adverse to material properties of the strip. The maximum cooling rate of 600 °C/s was found at the centerline as solidification took place at the roll exit. Other findings are also discussed including roll force, roll torque, and pressure distribution, which were greatly dependent upon the plastic deformation after solidification.

Analysis of Hot Tandem Rolling Force with Logarithmic Velocity Field and EA Yield Criterion

In order to analyze the hot tandem rolling force, a new logarithmic velocity field is proposed. Using the field and linear EA (equal area) yield criterion, the plastic deformation power for plate rolling is analyzed, and the friction power is obtained based on the co-line vector inner product method. Then analytical solution of plate rolling power functional is obtained. Finally, by minimizing the power functional, the rolling force and torque are received. Compared with those measured ones in hot tandem rolling on-line, the calculated rolling forces are in good agreement with the actual measured ones since the maximum error is less than 12%. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral angle, and stress state coefficient are discussed systematically.

Liftoff of a Motor-Driven, Flapping-Wing Microaerial Vehicle Capable of Resonance

This study presents the design of a novel minimalist liftoff-capable flapping-wing microaerial vehicle. Two wings are each directly driven by a geared pager motor by utilizing an elastic element for energy recovery, resulting in a maximum lift-to-weight ratio of 1.4 at 10 Hz for the 2.7 g system. Separate directly driven wings allow the system to both resonate and control individual wing flapping angle, reducing necessary power consumption, as well as allowing the production of roll and pitch body torques. With a series of varied prototypes, system performance is examined with change in wing offset from center of rotation and elastic element stiffness. Prototype liftoff is demonstrated with open loop driving a tethered prototype without guide wires. A dynamic model of the system is adapted and compared with the prototype experimental results for later use in prototype optimization.

Analysis of plate rolling by MY criterion and global weighted velocity field

A three-dimensional velocity field for plate rolling is proposed by global weighted method. Then, using the field and linear MY (mean yield) criterion, the power functional of internal deformation for plate rolling is analyzed. The collinear vector inner product is used in the friction power functional. Ultimately, analytical solution of total power functional is obtained. By minimizing the power functional, the rolling force and torque, as well as the stress effective factor are obtained. The calculated results by the solutions of rolling torque and force are compared with those of experimental ones. Good agreement is found and the maximum error percentage between them is less than 15.5%.

An investigation on the roll force and torque fluctuations during hot strip rolling process

Accurate prediction of the roll separating force and roll torque is critical to assuring the quality of the final product. Fluctuation of these parameters during the rolling process is even more important because of its effects on rolling setups, geometrical accuracy (especially flatness in strip rolling), and the uniformity of mechanical and microstructural properties of the rolled material. The main approach of the present study is a precision analysis of the roll force and roll torque and their instabilities during the rolling process. In doing so, a coupling multi-variable simulation model for hot strip rolling was built using non-linear thermo-viscoplastic finite element method. Fluctuations of roll force and torque about the steady-state operating point are derived and the effects of main process parameters such as rolling speed and strip reduction on these instabilities are investigated. To check the validity of the employed model, predicted results are compared with experimental data.

Slab Analysis of Large Cylindrical Shell Rolling

Considering the characteristics of large cylindrical shell rolling, such as double driving rolls, asymmetrical rolling and huge workpiece, a slab method was developed to establish the rolling force model. In this model, the non-uniform normal and shear stresses and the upper and lower surface temperatures of the workpiece were taken into account. Moreover, the flow stress model, considering the dynamic recovery and dynamic recrystallization behaviors of the material, was established. The rolling pressure distribution, the rolling force, the rolling torque and the neutral points could be calculated quickly and easily by the rolling force model. The predicted results were shown to be in good agreement with the measured values, which indicated that the model can satisfy the requirement of industrial application.

Estimation of Lateral Dynamics and Road Curvature for Two-Wheeled Vehicles: A HOSM Observer approach

In this work, two high order sliding mode observers under cascade form are proposed in order to estimate the important states and inputs affecting the lateral dynamics of two-wheeled vehicles. The first observer is based on a vision system and is used to estimate the lateral velocity of the vehicle. This velocity is considered as an additional measure for the second observer which is designed to estimate the tire forces, the roll angle and torque applied to the handle-bar.The main contribution of this work is the estimation of the tire forces even with the variation of the longitudinal velocity and without the prior knowledge of the pneumatic coefficients.

Simulation of Rolling Process of AZ31 Magnesium Alloy Sheet

To understand more about the rolling process of an AZ31 magnesium alloy sheet and the difference of simulation results between 2D and 3D, the rolling experiment of AZ31 was carried out and some useful data were obtained, and then the rolling processes were simulated by DEFORM2D and 3D respectively. The simulation results are in good agreement with the experimental results based on selecting the correct parameters of stress-strain relationship of AZ31, the friction factor with or without lubricant and the interfacial heat transfer coefficient. The influences of rolling reduction, workpiece temperature and roller temperature on the rolling load and torque are discussed and the difference of simulation results between 2D and 3D is illustrated.

Reducing production loss by prolonging service life of rolling mill shear pin with ultrasonic nanocrystal surface modification technology

Premature failure at the shear pin of stainless hot rolling mill caused by increasing productivity and fluctuation of roll torque raises significant downtime cost. To reduce downtime cost, UNSM (Ultrasonic Nanocrystal Surface Modification) treatment is applied to the neck groove of shear pin as the alternative to existing solutions. This treatment prevents premature failure, increases service life and reduces the number of replacements. Proper process variables of UNSM technology which give the strongest fatigue strength are determined by comparing with S-N curve of rotary bending test result. Surface roughness, hardness and compressive residual stress on three kinds of test specimens are analyzed together with SEM analysis of fracture surface. Real shear pins are produced by the property of highest fatigue strength and installed to the hot mill stand for validation. They come to pass as twice as the original operation cycle.

Accounting for shear deformation in fast models for plate rolling

For on-line prediction of roll force and torque, fast models have been available for a long time, which are mainly based on the slab method or other solution methods that allow for computing times in the range of seconds. Such fast models typically treat the rolling process as a plane strain problem and neglect shear deformation, which is always present in real processes. The shear deformation results in inhomogeneous strain profiles and thus might lead to inhomogeneity in microstructure over plate thickness. In this paper, a novel method is presented that allows for superposition of shear strain onto the strain state obtained from the slab method. The shear strains are interpolated from an extensive finite element (FE) parameter study of rolling processes that covers the entire parameter range of today’s plate rolling. For the regimes of very thick and thin plates different interpolation functions are introduced. It is shown that when the proposed shear strain model is combined with the slab method, similar results are obtained as with a full-scale FE calculation of the rolling problem but with a calculation time in the range of seconds.

Modelling hot rolling manufacturing process using soft computing techniques

Steel making industry is becoming more competitive due to the high demand. In order to protect the market share, automation of the manufacturing industrial process is vital and represents a challenge. Empirical mathematical modelling of the process was used to design mill equipment, ensure productivity and service quality. This modelling approach shows many problems associated to complexity and time consumption. Evolutionary computing techniques show significant modelling capabilities on handling complex non-linear systems modelling. In this research, symbolic regression modelling via genetic programming is used to develop relatively simple mathematical models for the hot rolling industrial non-linear process. Three models are proposed for the rolling force, torque and slab temperature. A set of simple mathematical functions which represents the dynamical relationship between the input and output of these models shall be presented. Moreover, the performance of the symbolic regression models is compared to the known empirical models for the hot rolling system. A comparison with experimental data collected from the Ere[gtilde]li Iron and Steel Factory in Turkey is conducted for the verification of the promising model performance. Genetic programming shows better performance results compared to other soft computing approaches, such as neural networks and fuzzy logic.

New multi-pass hot channel section rolling design by the finite element method

A new multi-pass hot shape rolling was designed based on a three-dimensional analysis of channel section beams in hot rolling by the finite element method. A complete production line in industry containing 13 passes in forming the section including break-down, intermediate, and finishing sequences is modeled. The output geometry and power consumption predicted by this simulation were verified against the practical data and the measured values of the production line of Zobahan Esfahan Company. Then, a sample caliber design process to achieve a specific cross section is prepared. The minimum possible number of passes consistent with the parameters affecting the spread is the main strategy of the new caliber design. Again this new caliber design is simulated using an explicit finite element code. The geometry and dimensions of the exit cross section, the separation force, roll torques, and the power consumption in each stage are calculated. Comparison of the new roll pass parameters and that of the conventional ones in industry is made to demonstrate the advantages of the new caliber design.

Optimization of shape rolling sequences by integrated artificial intelligent techniques

The present work introduces an expert system that automatically selects and designs rolling sequences for the production of square and round wires. The design strategy is aimed at reducing the overall number of passes assuming a series of process constraints, e.g., available roll cage power and torque, rolls groove filling behaviors, etc. The method is carried out into two steps: first a genetic algorithm is used to select the proper rolling sequence allowing to achieve a desired finished product; then, an optimization roll pass design tool is utilized for proper design of roll passes. Indeed, an artificial neural network (ANN) is utilized to predict the main geometrical characteristics of the rolled semi-finished product and technological requirements. The ANN was trained with a non-linear finite element (FE) model. The proposed methodology was applied to some industrial cases to show the validity of the proposed approach in terms of reduction of number of passes and search robustness.

Slab Analysis of Asymmetrical Rolling of Bonded Two-layer Sheets

In this paper, asymmetrical rolling of bonded two-layer clad sheets is studied using the slab method of analysis. It is assumed that the ingoing sheet is guided to horizontally enter the roll gap and that the work rolls may have different pressure distributions. Unlike the existing slab models, the slabs are not divided into two parts with different materials, and the whole slab is subjected to one stress field containing non-uniform normal and shear stresses acting on the vertical sides. By combining the sticking and coulomb friction models, a mixed friction model is proposed, and the work roll pressure distributions as well as the rolling force and torque are studied at different conditions. The predicted rolling force and torque of the proposed model are shown to be in a very good agreement with the analytical and experimental results of previous investigators.

Optimal design of a new 3D haptic gripper for telemanipulation, featuring magnetorheological fluid brakes

In this research work, a new configuration of a 3D haptic gripper for telemanipulation is proposed and optimally designed. The proposed haptic gripper, featuring three magnetorheological fluid brakes (MRBs), reflects the rolling torque, the grasping force and the approach force from the slave manipulator to the master operator. After describing the operational principle of the haptic gripper, an optimal design of the MRBs for the gripper is performed. The purpose of the optimization problem is to find the most compact MRB that can provide a required braking torque/force to the master operator while the off-state torque/force is kept as small as possible. In the optimal design, different types of MRBs and different MR fluids (MRFs) are considered. In order to obtain the optimal solution of the MRBs, an optimization approach based on finite element analysis (FEA) integrated with an optimization tool is used. The optimal solutions of the MRBs are then obtained and the optimized MRBs for the haptic gripper are identified. In addition, discussions on the optimal solutions and performance of the optimized MRBs are given.

Turning the Corner in Quadrupedal Arboreal Locomotion: Kinetics of Changing Direction While Running in the Siberian Chipmunk (Tamias sibiricus)

Arboreal animals frequently change directions during locomotion on tree branches, trunks, or twigs. Linear and rotational impulses required to change direction and rotate the body while running are largely unexplored. We trained Siberian chipmunks (Tamias sibiricus) to run on narrow cylindrical trackways. The first trackway was straight and the second had a 45° bend to the right. A force pole collected substrate reaction forces and torques, and linear and rotational impulses were calculated. When the chipmunks ran and jumped across the bend, they exerted strong impulses to the left, pushing the body to the right. Before the bend the substrate reaction yaw angular impulse rotated the animal to the new heading. After passing over the 45° bend in the trackway, opposing yaw angular impulses were exerted to stop the body's rotation. Rolling angular impulses were mostly similar between straight and turning trials. We conclude that mediolateral forces are more important than craniocaudal forces to change direction in locomotion. Yaw angular impulse is necessary to start and stop the rotation of the body around the center of mass. To avoid rolling during turns, the chipmunks relied on banking rather than exerting rolling torques.

유한요소해석과 반응표면법을 이용한 앵글바의 폭퍼짐 예측 및 공형설계에 관한 연구

In this paper, a method for prediction of spread is proposed to design proper roll profile taking into account spread in shape rolling of angle bar. The effect of the process variables on spread, such as draught ratio, bending angle and aspect ratio, is analyzed by FE-analysis and response surface method (RSM). Roll profiles for equal angle bar are designed with the spread predicted by the regression equation. Effectiveness of the designed roll profiles are verified by FE-analysis in which the flange length, strain distribution, mean strain and roll torque are compared with those by Geuze. Finally, the proposed method is applied to the design of roll profile for unequal angle bar. As a result, the final product can be obtained within the allowable tolerance of ±0.5 mm in length. Therefore, it is found that the prediction of spread can improve the efficiency of design roll profile in shape rolling of angle bar.