Finite Difference Modeling of the Interstand Evolutions of Profile and Residual Stress during Hot Strip Rolling

Elastic recovery and viscoplastic stress relaxation occur in the interstand of hot rolling, impacting the evolutions of strip profile and residual stress, which are major concerns for obtaining high-quality flat products. A better understanding of the evolutionary mechanisms would help develop shape control strategies. Therefore, a quasi-3D steady-state elasto-viscoplastic rolling model is developed based on the finite difference method. Predictions of spread, profile, and residual stress are validated through comparisons with a two-stand finite element model. The new model is also complemented with a roll stack model and with a viscoplastic constitutive model calibrated by hot compression tests to simulate a seven-stand hot rolling industrial experiment with low carbon steel. Comparisons between the predicted and measured profiles show a satisfactory accuracy. The simulation costs approximately a minute of CPU time, enabling the new model to run massive parametric campaigns for process optimization. It is found that during the interstand elastic recovery, the transverse compressive stress releases and the strip velocity tends to be uniform, revealing residual stress after a significant change of stress pattern. The stress relaxation mainly occurs at the edge near the roll bite and therefore increases the edge drop of the profile; it also decreases the center crown by changing the distribution of the rolling pressure in the roll bite.

Non-intrusive measurement of strip thickness and roll-bite length in metal rolling

It is important to monitor the rolled strip thickness standard to minimize material waste and loss of profit due to strip flatness defects, and also to maintain the product’s size and dimensional homogeneity. Several online measurement techniques are available but none of this can give an in situ measurement within the roll bite. Due to this, a novice experimental method utilizing ultrasonic reflection sensor mounted on one roll was developed for in situ measurement of strip thickness and roll-bite length during cold rolling process. A pitch–catch method was used whereby a piezoelectric element generated an ultrasonic pulse and transmitted to the contact interface evaluated on a pilot mill. The reflected signal was captured by a second piezoelectric element and analysed to determine the condition at the strip–roll interface. This approach was implemented on a pilot mill and reflections from various locations in the roll bite during the rolling were recorded. Recorded signals were used to estimate the rolled strip thickness and roll-bite length after the rolling process.

Ultrasonic roll bite measurements in cold rolling: Contact length and strip thickness

In cold rolling of thin metal strip, contact conditions between the work rolls and the strip are of great importance: roll deformations and their effect on strip thickness variation may lead to strip flatness defects and thickness inhomogeneity. To control the process, online process measurements are usually carried out; such as the rolling load, forward slip and strip tensions at each stand. Shape defects of the strip are usually evaluated after the last stand of a rolling mill thanks to a flatness measuring roll. However, none of these measurements is made within the roll bite itself due to the harsh conditions taking place in that area. This paper presents a sensor capable of monitoring strip thickness variations as well as roll bite length in situ and in real time. The sensor emits ultrasonic pulses that reflect from the interface between the roll and the strip. Both the time-of-flight of the pulses and the reflection coefficient (the ratio of the amplitude of the reflected signal to that of the incident signal) are recorded. The sensor system was incorporated into a work roll and tested on a pilot rolling mill. Measurements were taken as steel strips were rolled under several lubrication conditions. Strip thickness variation and roll-bite length obtained from the experimental data agree well with numerical results computed with a cold rolling model in the mixed lubrication regime.

Development of Mixed Lubrication Cold Rolling Model

Within past 20 years, high surface qualities of cold strip were demanded by automotive industry and electrical engineering. Main purposes of cold rolling processed are to provide high quality surface and generate appropriate roughness for different customs. Emulsion is a common coolant used in cold rolling processes, Properties of base oil in emulsion, concentration, roughness of work roll, rolling speed and reduction are important parameters, which dominate the surface qualities of cold rolled strip. Hence, a powerful cold rolling model which can describe complicate tribological behavior in roll bite is required. In this article, a cold rolling model which integrates roll deformation and mixed lubrication in inlet zone and biting area was developed. The thickness of oil film, fraction of contact area and coefficient of friction in roll bite are calculated.

Two-Dimensional Roll Bite Model with Lubrication for Cold Strip Rolling

To help optimize cold rolling operations, mixed lubrication models have been developed and embedded in roll bite models. The resulting models combine micro-fluidics in a porous medium (the lubricant flow between the contacting rough surfaces), microplasticity (roughness flattening / scratching), macro-plasticity (strip reduction) and roll thermo-elasticity. They are therefore really complex and need a lot of physical data. Based on previous developments, a new, simpler version of our lubrication model has been coupled with a new roll bite model recently presented: slab method for the strip elastic-plastic deformation (Prandtl-Reuss equations), a complete influence functions set for the roll deformation with circumferential displacements, and an efficient, adaptive relaxation technique when iterating between roll and strip models. The lubrication model is elaborated on Wilson and Sheu’s mixed lubrication model. The paper describes the implementation and compares its results with our previous, more complex version; a reasonable agreement is found. Several test cases of increasing difficulty show the robustness of the model and of its implementation. As a conclusion, a brief perspective is provided on how this new type of roll bite model could be used in industry.

Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill

In this work, a four high cold rolling mill is modeled as a spring-mass-damper system considering horizontally and vertically applied time-dependent forces due to the interaction between the strip and the working rolls. The effect of vibration of the moving strip on the work roll vibration is also considered for developing the governing equation of motion of the system which is found to be that of a nonlinear parametrically excited system. The governing equation of motion is solved by using the method of multiple scales to find the instability regions and frequency-response curves of the system. The critical amplitude of horizontal load in roll bite is calculated and the frequency-response is studied in detail considering the effect of various process parameters, such as velocity, thickness of strip, time delay, amplitude, and frequency of horizontal load in roll bite. This work can find application in the design and development of high speed and chatter free rolling mills.

Computing Flatness Defects in Sheet Rolling by Arlequin and Asymptotic Numerical Methods

Rolling of thin sheets generally induces flatness defects due to thermo-elastic deformation of rolls. This leads to heterogeneous plastic deformations throughout the strip width and then to out of plane displacements to relax residual stresses. In this work we present a new numerical technique to model the buckling phenomena under residual stresses induced by rolling process. This technique consists in coupling two finite element models: the first one consists in a three dimensional model based on 8-node tri-linear hexahedron which is used to model the three dimensional behaviour of the sheet in the roll bite; we introduce in this model, residual stresses from a full simulation of rolling (a plane-strain elastoplastic finite element model) or from an analytical profile. The second model is based on a shell formulation well adapted to large displacements and rotations; it will be used to compute buckling of the strip out of the roll bite. We propose to couple these two models by using Arlequin method. The originality of the proposed algorithm is that in the context of Arlequin method, the coupling area varies during the rolling process. Furthermore we use the asymptotic numerical method (ANM) to perform the buckling computations taking into account geometrical nonlinearities in the shell model. This technique allows one to solve nonlinear problems using high order algorithms well adapted to problems in the presence of instabilities. The proposed algorithm is applied to some rolling cases where “edges-waves” and “center-waves” defects of the sheet are observed.