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17 pages, 1777 KiB  
Article
Reduced-Order Model Based on Neural Network of Roll Bending
by Dmytro Svyetlichnyy
Appl. Sci. 2025, 15(15), 8418; https://doi.org/10.3390/app15158418 - 29 Jul 2025
Viewed by 108
Abstract
Effective real-time control systems require fast and accurate models. The roll bending models presented in this paper are proposed for a real-time control system for the design of the rolling schedule. The roll bending, with other factors, defines the shape of the roll [...] Read more.
Effective real-time control systems require fast and accurate models. The roll bending models presented in this paper are proposed for a real-time control system for the design of the rolling schedule. The roll bending, with other factors, defines the shape of the roll surface, its convexity, and finally the shape of the final product of the flat rolling, its convexity, and its flatness. This paper presents accurate finite element (FE) models for a four-high mill. The models serve to obtain accurate solutions to the problem of roll bending, taking into account the rolling force, width of the rolling sheet (strip), initial shape of the roll surface, and the anti-bending force. The results of the FE simulation are used to train three models developed on the basis of the neural network (NN) for the solution of one direct and two inverse tasks. The pre-trained NN model gives accurate results and is faster than the FE model (FEM). The calculation time on a personal computer for one case of 3D FEM is 1 to 2 min, for 2D FEM it is 1 s, and for NN it is less than 1 ms. The results can be immediately used by other models of the real-time control system. A novelty of the research presented in the paper is the creation of complex applications of the FE method and an NN as a reduced-order model (ROM) for prediction of roll bending and calculation of sheet (strip) convexity, rolling, and anti-bending forces to obtain the required convexity. Full article
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33 pages, 4531 KiB  
Article
Development of the Theory of Additional Impact on the Deformation Zone from the Side of Rolling Rolls
by Valeriy Chigirinsky, Irina Volokitina, Abdrakhman Naizabekov, Sergey Lezhnev and Sergey Kuzmin
Symmetry 2025, 17(8), 1188; https://doi.org/10.3390/sym17081188 - 25 Jul 2025
Viewed by 154
Abstract
The model explicitly incorporates boundary conditions that account for the complex interplay between sections experiencing varying degrees of reduction. This interaction significantly influences the overall deformation behavior and force loading. The control effect is associated with boundary conditions determined by the unevenness of [...] Read more.
The model explicitly incorporates boundary conditions that account for the complex interplay between sections experiencing varying degrees of reduction. This interaction significantly influences the overall deformation behavior and force loading. The control effect is associated with boundary conditions determined by the unevenness of the compression, which have certain quantitative and qualitative characteristics. These include additional loading, which is less than the main load, which implements the process of plastic deformation, and the ratio of control loads from the entrance and exit of the deformation site. According to this criterion, it follows from experimental data that the controlling effect on the plastic deformation site occurs with a ratio of additional and main loading in the range of 0.2–0.8. The next criterion is the coefficient of support, which determines the area of asymmetry of the force load and is in the range of 2.00–4.155. Furthermore, the criterion of the regulating force ratio at the boundaries of the deformation center forming a longitudinal plastic shear is within the limits of 2.2–2.5 forces and 1.3–1.4 moments of these forces. In this state, stresses and deformations of the plastic medium are able to realize the effects of plastic shaping. The force effect reduces with an increase in the unevenness of the deformation. This is due to a change in height of the longitudinal interaction of the disparate sections of the strip. There is an appearance of a new quality of loading—longitudinal plastic shear along the deformation site. The unbalanced additional force action at the entrance of the deformation source is balanced by the force source of deformation, determined by the appearance of a functional shift in the model of the stress state of the metal. The developed theory, using the generalized method of an argument of functions of a complex variable, allows us to characterize the functional shift in the deformation site using invariant Cauchy–Riemann relations and Laplace differential equations. Furthermore, the model allows for the investigation of material properties such as the yield strength and strain hardening, influencing the size and characteristics of the identified limit state zone. Future research will focus on extending the model to incorporate more complex material behaviors, including viscoelastic effects, and to account for dynamic loading conditions, more accurately reflecting real-world milling processes. The detailed understanding gained from this model offers significant potential for optimizing mill roll designs and processes for enhanced efficiency and reduced energy consumption. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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18 pages, 4036 KiB  
Article
Development of Oil-Free Lubricants for Cold Rolling of Low-Carbon Steel
by Leon Jacobs, Delphine Rèche, Andreas Bán, Valentina Colla, Orlando Toscanelli, Martin Raulf, Martin Schlupp, Bas Smeulders, Mike Cook and Wim Filemon
Processes 2025, 13(4), 1234; https://doi.org/10.3390/pr13041234 - 18 Apr 2025
Viewed by 559
Abstract
Oil-in-water emulsions (O/W emulsions) are generally used to lubricate the cold rolling process of low-carbon steel. In addition to the obvious advantages of efficient lubrication and cooling of the process, there are also some disadvantages, mainly related to emulsion bath maintenance, subsequent production [...] Read more.
Oil-in-water emulsions (O/W emulsions) are generally used to lubricate the cold rolling process of low-carbon steel. In addition to the obvious advantages of efficient lubrication and cooling of the process, there are also some disadvantages, mainly related to emulsion bath maintenance, subsequent production steps and waste disposal. In some application areas, Oil-Free Lubricants (OFL’s) have been shown to be at least equally effective in decreasing friction and wear as conventional oil-based lubricants, while resulting in benefits related to waste disposal. In 2023, a project named “Transfer of aqueous oil free lubricants into steel cold rolling practice” (acronym ‘RollOilFreeII’) began, with it receiving funding from the Research Fund for Coal and Steel (RFCS). This project aims at an industrial application of Oil-Free Lubricants in the steel cold rolling process. The project builds on the work of the ‘RollOilFree’ project (also carried out in the RFCS-framework). This article briefly recapitulates the findings in the RollOilFree project and describes the objectives, benefits, activities and first results of the RollOilFreeII project. Notably, a pilot mill trial at high speed has been carried out, showing a good performance of the investigated OFLs. Back-calculated friction values were equal to, or even slightly lower than, reference O/W emulsions. The strip cleanliness with OFLs is much better than it is with the reference O/W emulsions. Only for a very thin product, as is the case in tinplate rolling, does the direct application of a conventional O/W dispersion (a high-particle-sized O/W emulsion) give a better performance than the investigated OFLs. Further development of OFLs should focus on this aspect. Full article
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15 pages, 3236 KiB  
Article
Optimization and Finite Element Simulation of Wear Prediction Model for Hot Rolling Rolls
by Xiaodong Zhang, Zizheng Li, Boda Zhang, Jiayin Wang, Sahal Ahmed Elmi and Zhenhua Bai
Metals 2025, 15(4), 456; https://doi.org/10.3390/met15040456 - 18 Apr 2025
Cited by 2 | Viewed by 628
Abstract
Roll wear significantly affects production efficiency and product quality in hot-rolled strip steel manufacturing by reducing roll lifespan and impeding the control of strip shape. This study addresses these challenges through a comprehensive analysis of the roll wear mechanism and the integration of [...] Read more.
Roll wear significantly affects production efficiency and product quality in hot-rolled strip steel manufacturing by reducing roll lifespan and impeding the control of strip shape. This study addresses these challenges through a comprehensive analysis of the roll wear mechanism and the integration of an elastic deformation model. We propose an optimized wear prediction model for work and backup rolls in a hot continuous rolling finishing mill, dynamically accounting for variations in strip specifications and cumulative wear effects. A three-dimensional elastic–plastic thermo-mechanical coupled finite element model was established using MARC 2020 software, with experimental calibration of wear coefficients under specific production conditions. The developed dynamic simulation software achieved high-precision wear prediction, validated by field measurements. The optimized model reduced prediction deviations for work and backup rolls to 0.012 and 0.004, respectively, improving accuracy by 5.3% and 3.25% for uniform and mixed strip specifications. This research provides a robust theoretical framework and practical tool for precision roll wear management in industrial hot rolling processes. Full article
(This article belongs to the Special Issue Advances in Metal Rolling Processes)
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15 pages, 5541 KiB  
Article
Real-Time Measurement Technology of Bearing Housing Clearance in a Rolling Mill
by Jiankang Xing, Yan Peng, Xiangyang Zhao and Xinxiang Hou
Sensors 2025, 25(6), 1887; https://doi.org/10.3390/s25061887 - 18 Mar 2025
Viewed by 494
Abstract
The assembly clearance between the bearing housing and rolling mill stand affects the roll change and rolling stability. In order to improve the accuracy and real-time measurement of the bearing housing clearance of the rolling mill, four kinds of measuring methods were designed, [...] Read more.
The assembly clearance between the bearing housing and rolling mill stand affects the roll change and rolling stability. In order to improve the accuracy and real-time measurement of the bearing housing clearance of the rolling mill, four kinds of measuring methods were designed, namely the laser ranging method, external force measuring method, internal force measuring method, and eddy current ranging method, and the characteristics of the four measuring methods were introduced, respectively. The real-time measuring experiment of bearing housing clearance was carried out in a 100 mm two-high mill in laboratory and a 1580 mm four-high hot tandem mill in the Qian’an Iron and Steel Company. The results show that clearance measurement technology is helpful to improve the accuracy of real-time measurements and can provide guidance for the clearance control work. Finally, based on the real-time measurement technology of bearing housing clearance, the control strategy of bearing housing clearance was developed. This technology is of great significance to realize the fine management of rolling mill clearance and to improve the intelligence level of rolling mill systems. Full article
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21 pages, 1908 KiB  
Article
Rolling Mill Looper-Tension Control for Suppression of Strip Thickness Deviation by Adaptive PI Controller with Uncertain Forward/Backward Slip
by Yu-Chan Huang and Chao-Chung Peng
Machines 2025, 13(3), 238; https://doi.org/10.3390/machines13030238 - 16 Mar 2025
Viewed by 748
Abstract
The looper-tension control is a crucial aspect of a hot strip finishing mill. It involves a highly nonlinear system with strong states coupling and uncertainty, and the performance directly impacts the thickness deviation, which is the most critical product index. From the system [...] Read more.
The looper-tension control is a crucial aspect of a hot strip finishing mill. It involves a highly nonlinear system with strong states coupling and uncertainty, and the performance directly impacts the thickness deviation, which is the most critical product index. From the system dynamics, it is known that tension is highly sensitive to the strip velocity variation, which is typically unmeasurable. Instead, it needs to be calculated through work roll speed and strip slip which contains uncertainties, negatively affecting tension control performance. First, a feedback linearization-based proportional–integral (PI) controller design approach is proposed for the hot rolling looper-tension system. Second, to reduce the impact of speed uncertainties and enhance thickness response, an adaptive PI controller is introduced. Validation was conducted by numerical simulations; the result indicates that an adaptive PI controller reduces the magnitude of thickness variation and shortens the duration of its impact, verifying the consistency between theoretical derivation. The proposed control method effectively addresses the impact of uncertainties encountered in real-world applications. Additionally, it simplifies control parameter adjustment in practical use, reduces testing time, and improves product quality. Full article
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25 pages, 9118 KiB  
Article
Intelligent Analysis and Optimization of Lubrication Status Factor Based on Dynamically Loaded Roll Gap in Cold Strip Rolling
by Shuren Jin, Xu Li, Pengfei Wang, Feng Luan, Fangsheng Chen, Dianhua Zhang and Haidong Zhang
Lubricants 2025, 13(2), 54; https://doi.org/10.3390/lubricants13020054 - 28 Jan 2025
Viewed by 1051
Abstract
Lubrication is a critical process in cold strip rolling, and the accurate characterization of lubrication characteristics is an essential factor affecting the strip quality. The roll bending and tilting roll in the flatness actuators change the loaded roll gap profile and affect the [...] Read more.
Lubrication is a critical process in cold strip rolling, and the accurate characterization of lubrication characteristics is an essential factor affecting the strip quality. The roll bending and tilting roll in the flatness actuators change the loaded roll gap profile and affect the lubrication characteristics by flatness dynamic correction, thus the mismatch between the actual and setting values of the lubrication status factor. Firstly, the flatness deviation correction model of roll bending and tilting roll based on the key information of the rolling process is established according to the high-order flatness target. Secondly, the characterization of the instantaneous oil film thickness in the work zone based on the loaded roll gap profile is derived from Reynolds’ equation. Finally, the explicit characterization method of the lubrication status factor in the rolling force model of the final stand is established with the work roll bending, tilting roll, and instantaneous oil film thickness of the work zone as variables, relying on the UCM five-stand, six-roll tandem cold rolling mill. The statistical evaluation and application results show that the mentioned optimization method can improve the setting accuracy of the rolling force by about 60% and the after-rolling gauge accuracy by about 50%. Full article
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16 pages, 10297 KiB  
Article
Effect of Electric Pulse Treatment on the Interfacial Properties of Copper/304 Stainless Steel Composite Thin Strips Fabricated by Roll Bonding
by Zefeng Wang, Xiaomiao Niu, Ming Wang, Yu Yang, Dongping He and Wangzhe Du
Metals 2025, 15(2), 112; https://doi.org/10.3390/met15020112 - 24 Jan 2025
Viewed by 934
Abstract
Annealing is a commonly used post-processing method for composite thin strips but suffers from drawbacks such as long processing time, high energy consumption, and susceptibility to oxidation. Replacing annealing with electric pulse treatment (EPT) can address these issues. In this study, a specially [...] Read more.
Annealing is a commonly used post-processing method for composite thin strips but suffers from drawbacks such as long processing time, high energy consumption, and susceptibility to oxidation. Replacing annealing with electric pulse treatment (EPT) can address these issues. In this study, a specially designed fixture was used to investigate the effects of pulsed current on the bonding strength of T2 copper (Cu)/304 stainless steel (SS) composite thin strips. The initial strip, with a 50% reduction rate, was prepared using a two-high mill, resulting in a Cu/SS composite strip with a thickness of 0.245 mm. Pulsed current treatment was applied with peak temperatures ranging from 350 °C to 600 °C. The results showed that EPT significantly improved the bonding strength. A pulsed current of 55 A resulted in the highest average peel strength of 10.66 ± 0.93 N/mm, with a maximum Fe content on the Cu side of 7.39 ± 0.84%, while a pulsed current of 65 A resulted in the highest Cu content on the SS side, reaching 57.54 ± 2.06%. This study demonstrates that EPT effectively controls the deformation behavior and interface state of composite strips, producing Cu/SS composite thin strips with high bonding strength. Full article
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15 pages, 6148 KiB  
Article
Microfluidic Monodispersed Microbubble Generation for Production of Cavitation Nuclei
by Renjie Ning, Blake Acree, Mengren Wu and Yuan Gao
Micromachines 2024, 15(12), 1531; https://doi.org/10.3390/mi15121531 - 23 Dec 2024
Cited by 2 | Viewed by 1526
Abstract
Microbubbles, acting as cavitation nuclei, undergo cycles of expansion, contraction, and collapse. This collapse generates shockwaves, alters local shear forces, and increases local temperature. Cavitation causes severe changes in pressure and temperature, resulting in surface erosion. Shockwaves strip material from surfaces, forming pits [...] Read more.
Microbubbles, acting as cavitation nuclei, undergo cycles of expansion, contraction, and collapse. This collapse generates shockwaves, alters local shear forces, and increases local temperature. Cavitation causes severe changes in pressure and temperature, resulting in surface erosion. Shockwaves strip material from surfaces, forming pits and cracks. Prolonged cavitation reduces the mechanical strength and fatigue life of materials, potentially leading to failure. Controlling bubble size and generating monodispersed bubbles is crucial for accurately modeling cavitation phenomena. In this work, we generate monodispersed microbubbles with controllable size using a novel and low-cost microfluidic method. We created an innovative T-junction structure that controls the two-phase flow for tiny, monodispersed bubble generation. Monodisperse microbubbles with diameters below one-fifth of the channel width (W = 100 µm) are produced due to the controlled pressure gradient. This microstructure, fabricated by a CNC milling technique, produces 20 μm bubbles without requiring high-resolution equipment and cleanroom environments. Bubble size is controlled with gas and liquid pressure ratio and microgeometry. This microbubble generation method provides a controllable and reproducible way for cavitation research. Full article
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24 pages, 40658 KiB  
Article
Application of Back-to-Back Hybrid Filter to a Hot Strip Mill with Cycloconverters
by Rafael Cabral Knaip Krause and Hélio Marcos André Antunes
Energies 2024, 17(23), 6019; https://doi.org/10.3390/en17236019 - 29 Nov 2024
Viewed by 741
Abstract
In steel mills that employ the hot strip mill process, cycloconverters with nominal power ratings in the megawatt range are commonly used to drive synchronous motors. However, these cycloconverters draw highly distorted currents from the power grid, causing significant voltage distortion at the [...] Read more.
In steel mills that employ the hot strip mill process, cycloconverters with nominal power ratings in the megawatt range are commonly used to drive synchronous motors. However, these cycloconverters draw highly distorted currents from the power grid, causing significant voltage distortion at the point of common coupling (PCC) and leading to numerous power quality (PQ) issues. Multi-stage passive filters are widely used to mitigate harmonics in this context. However, this approach can lead to harmonic resonance, exacerbating distortion and overloading the passive filtering system. This study presents a novel integration of a back-to-back hybrid filter, designed specifically for hot strip mills with cycloconverters at a steel mill located in the Metropolitan Area of Vitória, ES, Brazil. The proposed method combines active and passive filtering, where the active filter works in tandem with existing passive elements to compensate for harmonic components while damping resonances across a broad frequency range. Simulations are conducted to evaluate the hybrid filter’s efficacy in harmonic compensation and resonance damping, particularly during load expansion scenarios for the hot strip mill. Results indicate that the back-to-back hybrid filter significantly improves PQ by reducing harmonic overloads on pre-existing passive filter branches, thereby enhancing the reliability of the entire power system. This improvement is achieved with active filters of relatively low-rated capacity compared to the hot strip mill load, making it a cost-effective and scalable solution. Full article
(This article belongs to the Section K: State-of-the-Art Energy Related Technologies)
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14 pages, 14695 KiB  
Article
Identification and Regulation of Cold Rolling Interface State Based on a Novel Modified Forward Slip Model
by Yanli Xin, Zhiying Gao, Yong Zang and Xiaoyong Wang
Lubricants 2024, 12(12), 404; https://doi.org/10.3390/lubricants12120404 - 21 Nov 2024
Viewed by 992
Abstract
With the development of rolled steel strips towards higher strength and thinner thickness, negative forward slip has been frequently observed during the process of cold rolling, and this phenomenon closely related to interface is believed to seriously influence rolling stability. However, the existing [...] Read more.
With the development of rolled steel strips towards higher strength and thinner thickness, negative forward slip has been frequently observed during the process of cold rolling, and this phenomenon closely related to interface is believed to seriously influence rolling stability. However, the existing classic forward slip models are limited to calculating positive forward slip values and cannot reflect negative forward slip effects. Therefore, in this paper, based on BLAND-FORD forward slip theory, a novel modified forward slip model capable of predicting negative forward slip is established and verified, in which the corresponding flattened curve is characterized and a compensation coefficient related to actual tension and coil number is supplemented. Then, a dimensionless sensitivity factor is defined to compare and analyze the influences of various parameters on forward slip through the modified model, in order to pick a more effective and reasonable regulation approach. Finally, an idea of keeping stable forward slip through dynamic tension regulation is suggested and applied in the actual rolling process, and it is drawn that this strategy can be used to avoid fluctuations of process parameters and suppress mill chatter. As a result, the presented modified forward slip model can identify both positive and negative forward slips and is helpful in regulating the interface state and improving the stability of the rolling process. Full article
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10 pages, 2457 KiB  
Article
Research on the Prediction of Roll Wear in a Strip Mill
by Jianhua Wei and Aimin Zhao
Metals 2024, 14(10), 1180; https://doi.org/10.3390/met14101180 - 17 Oct 2024
Cited by 1 | Viewed by 1400
Abstract
In the process of hot rolling silicon steel, roll wear directly affect its shape. Accurate prediction of roll wear is an important condition for rolling qualified silicon steel strips. The traditional roll wear prediction model is established by the slicing method. The wear [...] Read more.
In the process of hot rolling silicon steel, roll wear directly affect its shape. Accurate prediction of roll wear is an important condition for rolling qualified silicon steel strips. The traditional roll wear prediction model is established by the slicing method. The wear of F5–F7 work rolls used for finishing rolling silicon steel on a 2250 mm production line in a steel mill was predicted by this model. It was found that there was deviation between the predicted results and the actual wear, and the prediction accuracy of the model was insufficient. Therefore, the wear of the surfaces of the rolls used for rolling silicon steel on this production line was studied. Based on the analysis of the work roll wear’s form and the rolling parameters that affect the roll wear, the traditional roll wear prediction model was optimized by the genetic algorithm. Finally, the optimized model was verified, and the prediction accuracy of the wear prediction model improved. The accurate prediction results provide a basis for the formulation of a shape control strategy when rolling silicon steel on this production line. Full article
(This article belongs to the Special Issue Advances in Metal Rolling Processes)
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19 pages, 8427 KiB  
Article
Theoretical Study of Asymmetric Bending Force on Metal Deformation in Cold Rolling
by Zhuwen Yan, Shuaizhen Pan, Yingxin Tang and Wenjun Cao
Metals 2024, 14(10), 1168; https://doi.org/10.3390/met14101168 - 13 Oct 2024
Cited by 2 | Viewed by 1391
Abstract
A three-dimensional elastic–plastic finite element model of a six-roll cold rolling mill has been developed using the finite element software ABAQUS. The actual parameters of the rolling mill have been incorporated into the finite element model, with the working conditions applied as boundary [...] Read more.
A three-dimensional elastic–plastic finite element model of a six-roll cold rolling mill has been developed using the finite element software ABAQUS. The actual parameters of the rolling mill have been incorporated into the finite element model, with the working conditions applied as boundary constraints and load conditions. Subsequently, a non-symmetrical bending force is introduced to the finite element model. Through simulation calculations, this study analyzes the patterns of change in the transverse pressure of the rolling mill and roller pressure during non-symmetrical bending, as well as the variations in strip thickness, crown, edge drop, and flatness. Additionally, the regulating function of the bending force is examined. Each adjustment of 5 t in the asymmetric bending force results in an increase of approximately 0.01 mm in the thickness of the positive bending side of the strip while causing a decrease of about 0.01 mm in the thickness of the negative bending side. Therefore, the application of asymmetric bending forces proves to be effective in controlling the shape of lateral wave defects on the edges of steel strips. Full article
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18 pages, 5389 KiB  
Article
Research on Dynamic Modelling, Characteristics and Vibration Reduction Application of Hot Rolling Mills Considering the Rolling Process
by Zhiwen Lu, Duolong Zhou, Danfeng Yu and Han Xiao
Machines 2024, 12(9), 629; https://doi.org/10.3390/machines12090629 - 6 Sep 2024
Cited by 1 | Viewed by 1016
Abstract
The impact of rolling mill vibration extends beyond product quality to equipment health, making vibration control crucial. This study addresses the issue of frequent abnormal vibration in hot strip finishing mills by employing a combination of theory, simulation, and experimentation to analyze the [...] Read more.
The impact of rolling mill vibration extends beyond product quality to equipment health, making vibration control crucial. This study addresses the issue of frequent abnormal vibration in hot strip finishing mills by employing a combination of theory, simulation, and experimentation to analyze the dynamic behavior of the mill and apply findings to on-site vibration suppression. Initially, a torsional-vertical-horizontal coupled dynamic model for the rolling mill has been developed, taking into account the rolling process. The accuracy of this model is established through both finite element simulations and actual experiments. Subsequently, the vibration characteristics of the rolling mill system are investigated under typical process parameters utilizing the established dynamic model. The results reveal that the vibration amplitude notably escalates with the increase of rolling reduction rate and rolling speed, and the difference in front and rear tension has little impact on the mill’s vibration. Furthermore, an increase in the temperature of the rolled piece reduces the overall vibration amplitude, and harder material results in greater overall mill vibration. Lastly, abnormal vibration in the F2 finishing mill at a hot rolling plant is effectively mitigated by reducing rolling reduction rate, which further validates the correctness of the findings. Full article
(This article belongs to the Section Machine Design and Theory)
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22 pages, 9939 KiB  
Article
A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process
by Xuezhi Wang, Kelin Chen, Yanli Lin and Zhubin He
Materials 2024, 17(15), 3739; https://doi.org/10.3390/ma17153739 - 28 Jul 2024
Cited by 1 | Viewed by 1038
Abstract
A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by [...] Read more.
A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. Full article
(This article belongs to the Special Issue Nonconventional Technology in Materials Processing-3rd Edition)
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