Method for determining a temperature of a steel beam after water-cooling, associated electronic system

Abstract

A method for determining a temperature of a steel beam (2) after the beam has been water-cooled in a cooling machine, the method comprising: - acquiring cooling configuration data specifying which faces of the beam are impinged by water jets, and what are the corresponding water flow values, - for the different faces (W1, W2, F1 – F6) of the beam, determining, from the cooling configuration data, what cooling regime undergoes the face of the beam considered, the cooling regime being selected among, at least: direct water-cooling; powered cooling when the face has no water projected thereon, by any of the jets, but, for an other of said faces which adjoins laterally the face considered, said other face has water projected thereon; air-cooling; - computing cooling powers for the different faces of the beam, depending on the corresponding cooling regimes, and, when appropriate, depending on the associated water flow value.

Description

Method for determining a temperature of a steel beam after water-cooling, associated electronic system

[0001] The technical field is that of producing steel beams, for instance steel beams for buildings, bridges and other structures. It concerns more particularly the control of heat treatments applied to such beams during a production process, and the determination of a temperature reached during such a heat treatment.Te c h n i c a I b a c k g r o u n d

[0002] For obtaining high performance steel beams (typically big beams called “jumbo” intended for instance for building skyscrapers), it is known, after the hot-rolling operations, to cool down the steel beam quickly using water jets, but in a well-controlled manner. Figure 1 schematically represents the evolution, with time t, of the temperature T at the surface of a steel beam, during such a water-cooling process. First (phase Ph1 in figure 1), the beam is cooled in air. Then it is water cooled quickly in a cooling machine (phase Ph2), and the temperature T drops significantly. And then, the beam ends its cooling in air (phase Ph3). During the water cooling, it is mainly the superficial part of the beam that is cooled down. And so, during the subsequent phase Ph3, the heat that remained in the bulk of the beam is gradually released and the surface temperature T thus temporarily increases after the beam has traversed the cooling machine (it becomes moderately high again) before finally decreasing (see figure 1).

[0003] This re-increase of the surface temperature, usually called « self-tempering », is useful from a metallurgic point of view if well controlled. In particular, it is useful to control the cooling of the beam in order to obtain a “self-tempering” temperature TST (which is the maximum over time t reached by the temperature T of the surface of the beam, after the beam has exited the cooling machine) that is close to a desired, target self-tempering temperature (well suited to optimize the final mechanical properties of the beam).

[0004] Controlling the self-tempering temperature obtained during such a cooling process is challenging due to the thermal inertia in this process (this temperature is reached once the fast cooling process itself is finished) and due to the rather complex thermal evolution for the beam. In this context, it would thus be very useful to be able to predict accurately a value of the selftempering temperature TST, or more generally to predict the thermal evolution of the beam during the cooling process. This would be useful too for a post-characterization of a beam, after its cooling (in order to estimate mechanical properties of the beam that has been produced, for instance).Summary

[0005] The instant technology concerns, inter alia, a method for determining a temperature TsT Of a steel beam after the beam has been water-cooled in a cooling machine, the method comprising: acquiring cooling configuration data specifying which faces of the beam are impinged by waterjets, and what are the corresponding water flow values, for the different faces of the beam, determining, from the cooling configuration data, what cooling regime undergoes the face of the beam considered, the cooling regime being selected among, at least: direct water-cooling; powered cooling when the face has no water projected thereon, by any of the jets, but, for an other of said faces which adjoins laterally the face considered, said other face has water projected thereon; air-cooling; computing cooling powers for the different faces of the beam, depending on the corresponding cooling regimes, and, when appropriate, depending on the associated water flow value.

[0006] The instant technology concerns, in particular, a method for determining a temperature TsT Of a steel beam according to claim 1.

[0007] This method may comprise one or several additional features, defined in claims 2 to 12, considered alone or in combination.

[0008] The instant technology also concerns an electronic monitoring device according to claim 13, and a beam processing installation according to claim 14. The beam processing installation may further comprise a temperature sensor for measuring the input temperature, an additional temperature sensor for measuring the intermediate temperature, and an actuator or a low-level controller for controlling the speed with which the beam moves. The instant technology also concerns a computer program whose execution on a computer (possibly connected to relevant sensors, actuators or controller), makes the computer to execute the method for controlling presented above. The instant technology also concerns a non-transitory computer-readable medium storing such a computer programD eta i I e d d es c ri pt i o n

[0009] The instant technology will now be described in more detail and illustrated by examples without introducing limitations, with reference to the appended figures.

[0010] Figure 1 schematically represents the evolution overt time t of a surface temperature of a steel beam, during a quench and self-tempering thermal treatment of the beam.

[0011] Figure 2 schematically represents a beam processing installation for applying a quench and self-tempering thermal treatment to a beam.

[0012] Figure 3 is a schematical perspective view of a part of an H-shape beam, to be processed in the beam processing installation of figure 2.

[0013] Figure 4 schematically represents a cross section the beam of figure 3.

[0014] Figures 5, 6 and 7 schematically represents a T-beam, a U-beam and an L-beam, respectively.

[0015] Figure 8 schematically represents flange and web water jets cooling the beam, in a cooling machine of the beam processing installation of figure 2.

[0016] Figure 9 schematically represents cooling sections and subsections of a cooling machine of the beam processing installation of figure 2.

[0017] Figure 10 schematically represents a discretization of the beam of figure 3, into multiple longitudinal samples.

[0018] Figure 11 schematically represents the evolution with temperature of a coefficient involved in the computation of a water cooling power.

[0019] Figures 12 to 16 schematically represent a computed temperature difference, resulting from a cooling of the beam in the cooling machine, against a corresponding measured temperature difference, for multiple tests achieved for different beams.

[0020] Figure 17 schematically represents, as a block diagram, steps of a method for controlling the beam processing installation of figure 2.

[0021] Figure 18 schematically represents, as a block diagram, steps of a method for determining self-tempering temperatures reached by a beam during its processing, based on the process parameters that were actually employed during the cooling of the beam.Beam processing installation

[0022] Figure 2 schematically represents a beam processing installation 1 which comprises a hot rolling mill to shape a beam 2, a cooling machine 30 for water-cooling the beam once output by the rolling mill, and an electronic system 10 configured, inter-alia, for determining one or more cooling setpoints for the beam water-cooling. Here, the rolling mill comprises a roughing mill (not represented in figure 2), then an intermediate mill (also called main mill) which is a tandem mill 4, here, and then a finishing mill 3. The beam 2 is hot when processed in the rolling mill: its temperature is typically higher than 800°C, or even higher than 900 °C. In the beam processing installation 1 , the beam is moved parallel to its axis, along the installation axis x, from the intermediate mill to the finishing mill and then to the cooling machine. The cooling machine 30 is arranged downstream of the rolling mill, along the path x followed by the beam 2 in the beam processing installation. More particularly, the cooling machine is arranged downstream of the last rolling stand of the rolling mill, that is downstream of the finishing mill 3, here. There is no other rolling stand between the last stand of the rolling mill and the cooling machine 30.

[0023] The distance between a tandem mill output and the finishing mill input may, like here, be higher than the length of the beam 2 (in other words, the maximum length for the beamsprocessed in the installation is equal or smaller than this distance, here). The cooling machine 30 is located immediately downstream of the finishing mill.

[0024] The beam processing installation 1 is equipped also with: a first temperature sensor 6 arranged to measure a surface temperature of the beam 2 at an upstream position Oe located upstream of the cooling machine 30. Here, the upstream position Oe is located upstream of the intermediary mill (that is, upstream of the tandem mill 4); this measured temperature is called the input temperature; a second temperature sensor 8 arranged to measure another surface temperature of the beam 2, at an intermediary position Os located between the upstream position Oe and the cooling machine; here, the intermediary position Os is located between the intermediary mill (here, the tandem mill 4) and finishing mill 3, and- A third temperature sensor 9 arranged to measure another surface temperature of the beam 2 after the beam has traversed the cooling machine 30 (output temperature).

[0025] The temperature sensors may be pyrometers, or infrared cameras, for instance.

[0026] The beam 2 is a steel beam, or in other words a steel profile (or a steel section). Its length may be from 10 to 200 meters at this stage of the manufacturing process (it may be subsequently cut to shorter lengths). Generally, the beam 2 comprises one or two flanges and a web which extends transversely with respect to the flange(s). When it comprises two flanges, the web connects the two flanges to each other. The web is perpendicular or substantially perpendicular to the flange(s). The web and the flanges may each form a substantially flat (and elongated) plate. In the detailed example presented here, the beam 2 is an H-beam (its section has an H shape), as represented in figure 3. The two flanges 22 and 23 correspond to the two vertical bars of the H, while the web 21 corresponds to horizontal, transverse bar of the H.

[0027] For the beam 2, thermal exchanges, by radiation and due to the contact with air or water, occur at the beam’s surface, also designated as the beam outer surface (this surface is accessible for cooling the beam, using waterjets for instance). As represented in figure 4, the beam’s surface (surface of the beam that is exposed, accessible for cooling the beam), is mainly composed by (is.: a major part, or even 80% of this surface is composed by the following): a first web face W1 and a second web face W2 opposite each other (W1 being an upper web face and W2 a lower web face), and two or three (depending on the shape of the section of the beam) flange faces for each flange; here three flanges faces F1 , F2, F3 for the first flange 22 and three other flange faces F4, F5, F6 for the second flange 23 (F1 and F4 are outer flangefaces, both F2 and F5 are inner and upper flange faces and both F3 and F6 are inner and lower flange faces).

[0028] The web and flange faces F1 - F6, W1 , W2 are also designated as the beam faces, or simply as the faces in the following. Each of these faces is one of the main faces of the web, or of the flange considered (each web face is parallel to the web, and each flange face is parallel to the flange). In other words, these faces are not the small end faces of the beam (at the head and at the tail of the beam), nor the thin edge faces extending along the longitudinal edges of the flanges (such as the upper edge face that joins the flange faces F1 and F2). It is noted that one or more of the edge faces may still be water-cooled.

[0029] It is noted that, in other embodiments, the beam may have a different section shape. For instance, it may be an I-beam or a Z-beam (with two flanges and one web). It may also be a T-beam (figure 5) with one flange (corresponding to the horizontal bar of the T) and a web (corresponding to the vertical bar of the T). In this case, the outer surface of the beam, accessible for the cooling, comprises mainly three flange faces and two web faces. It may also be a U-beam (figure 6), that is forming a U-shape channel, with a web forming the bottom of the channel and two flanges extending upward from the web. In this case, the outer surface of the beam, accessible for the cooling, comprises mainly two (instead of three) flange faces for each flange, and the two web faces. The beam may also be an L-beam (that is, a steel angle), with one flange and one web (in this case, each of the two parts of the angle can be designated, indifferently, as the web, or as the flange).

[0030] The cooling machine may comprise one, two, or more successive cooling sections. Each cooling section is arranged to be traversed by the beam, and for emitting waterjets that strike some or all of the beam’s faces. Here the cooling machine comprises a first cooling section 31 and a second cooling 32, located one after the other along the installation axis x (figures 2 and 9). The different cooling sections may be formed by distinct devices, or may correspond to different, successive longitudinal portions of a same device.

[0031] The cooling machine is arranged so that the jets belonging to one of the cooling sections can be controlled independently from the jets of the other(s) cooling section(s).

[0032] At least one, here each cooling section is arranged for emitting (figure 8): flange jets FJ, for projecting water on one or more of the flange faces F1 , F2, F3, F4, F5, F6 (meaning that these jets strike flange faces), and- web jets WJ, for projecting water on one or both of the web faces W1 , W2.

[0033] In this document, when water is projected on a face by one of the jets, it means that this water is projected directly on this face by the jet considered, which strikes this face (with a jet impingement). In the following, the flange jets and the web jets may be indifferently (and possibly collectively) referred to as the jets.

[0034] The cooling machine is arranged so that the web jets WJ can be controlled independently from the flange jets FJ.

[0035] More generally, the cooling machine is arranged so that multiple groups of jets (or even all the jets) can controlled independently from each other (using electrically controllable valves). Here, in particular, the first and second cooling sections 31 and 32 each comprises two successive subsections (311 , 312 and 321 , 322 respectively - figure 9), the web jets of which being controllable independently those of the other subsection. For instance, for the part of the beam that is in the first cooling section 31 , for a first half of this part of the beam, the web may be water cooled while for a second half of this part of the beam, the web is not water cooled (no jet striking it).

[0036] The cooling machine arranged as above describe enables to use multiple different cooling configurations for cooling the beam.

[0037] For instance, the flanges 22, 23 may be water-cooled but not the web 21 , both in the first cooling section 31 and in the second cooling section 32. Or both the flanges and the web may be water-cooled, in both cooling sections. Or: in the first cooling section 31 , the flanges 22, 23 may be water-cooled but not the web 21 , while in the second cooling section both the flanges and the web are water-cooled.

[0038] In figure 9, the faces struck by jets are hatched while the faces in white have no jet striking them. So, in the cooling configuration represented in figure 9: the jets of the first cooling section 31 are off (both the flange jets and the web jets), the flange jets FJ of the second cooling section 32 are on, the web jets of the first subsection 321 of the second cooling section 32 are off, and the web jets of the second subsection 322 of the second cooling section 32 are on.

[0039] Being able to use multiple different cooling configurations is very useful. Indeed, some geometrical imperfections of the beam output by the rolling mill, such as squareness defects, flatness defects or evenness defects can be corrected using dedicated cooling configurations (for which not all the jets are on). Besides, the fact that the jets of the second cooling section 32 are controllable independently from those of the first cooling section 31 gives more flexibility, regarding the choice of the thermal route followed by the beam (e.g.: progressive cooling, or more abrupt cooling), and thus more flexibility in terms of final mechanical properties for the beam.

[0040] In the embodiment described here, the web faces W1 , W2 are horizontal while the flange faces F1 - F6 are vertical. W1 is the upper web face (it is upward facing) while W2 is the lower web face (downward facing).

[0041] The beam processing installation 1 comprises a low-level controller 13 for controlling actuators of the beam processing installation 1 , in particular for controlling valves of the cooling machine 30, and for controlling the finishing mill 3, whose rolling speed fixes the speed atwhich the beam traverses the colling machine 30. The low-level controller 13 is also connected to sensors of the beam processing installation 1 (in particular one or more speed sensors and presence sensors for detecting the presence of the beam at different positions along the processing path). It may implement control loops such as PID loops. It receives the cooling setpoints from the higher-level electronic system 10. In particular, it receives from the electronic system 10 a speed setpoint, instructions specifying which of the above-mentioned jets are to be on and which are to be off, and one or more water flow setpoints for the jets that are to be on. The low-level controller 13 is configured to implement close to the actuators control, yet less elaborate control strategies than the electronic system 10 (for instance in the form of a proportional, integral, and possibly derivative control loop). The low-level controller 13 may take the form of a programmable logic controller (PLC) or other industrial-like computer or programmable circuit. It is operatively connected to the electronic system 10 and to the above- mentioned actuators and sensors (for instance through a local data bus).

[0042] Here, the electronic system 10 comprises a server 11 and a terminal 12. The terminal may be a human-machine interface (such as a display screen, possibly with an entering device like a keyboard and / or a pointing device like a mouse pad and / or buttons). The terminal may also be a standalone computer. Alternatively, the electronic system 10 may take the form of a stand-alone computer (including a human-machine interface), rather than a server with a distinct, possibly remote human-machine interface. Anyhow, the electronic system 10 comprises at least a progressor and a memory and can be programmed so as to execute elaborate tasks like numerical simulations. The electronic system 10 is operatively connected (through a local network, of through the internet, for instance) to an industrial database 14, itself connected to remote services 15 or users, such as production analytics services or supply chain tracking services.

[0043] The electronic system 10 (more precisely the server 11 , here) is programmed to execute the method for controlling the beam cooling presented below.Method for controlling the beam cooling.

[0044] This method is based on a numerical simulation of the temporal evolution of the temperature field within the beam. Executing this simulation iteratively enables to determine the cooling setpoint(s), here the speed setpoint v0*, which is transmitted to the low-level controller 13 which then controls the actuator(s) of the installation 1 based on this setpoint(s). The cooling setpoint(s) is determined such that, for this setpoint, a predicted self-tempering temperature TST (predicted by the numerical simulation) matches a target self-tempering temperature T*STJ. By matching it is meant being equal to, within 20°C, or even within 10°C or 5°C. The numerical simulation is a finite differences computation. Regarding spatial variables (in addition to the temporal variable t), it may, like here, be a two-dimensional simulation, the two spatial dimensions corresponding to two coordinates along two transverse directions eachperpendicular to the beam’s axis. It takes into account the beam dimensions and chemical composition. It takes also into account at least one temperature of the beam 2 measured before the beam 2 enters the cooling machine 30, here the input temperature Tm (the intermediate temperature Tintj is also taken into account, here, for adjusting the cooling setpoint just before the beam enters the cooling machine 30).

[0045] In terms of discretization, here, the beam is divided into a number n of consecutive longitudinal portions Pj, with i from 1 to n (figure 5), also called samples. The portion Pi is the head portion of the beam (located at its heading end, that is at the end of the beam that comes out of the finishing mill first). Pnis the tail portion (in other words end portion) of the beam, n may be from 3 to 100, or even from 3 to 50, and each sample may be from 0.2 to 5 meters long or even from 1 to 5 meters long. For at least one longitudinal sample, in practice, a two- dimensional temperature field is computed, and its evolution over time t is computed, for a period encompassing at least the transit through the cooling machine 30 and a subsequent air-cooling. Here, this period spans at least: from the measurement of the input temperature, to a delivery of the beam at the end of the beam processing installation 1 .

[0046] The determination of the speed setpoint v0*, achieved by executing the above- mentioned numerical simulation several times, is carried out for one portion of the beam, noted Pj (j having a fixed value, from 1 to n, for instance j=4). Speed setpoints Vj*, adjusted portion by portion (using more simple calculation rules), are then derived from v0*, for the different portions Pj, i=1 , ... ,n of the beam.

[0047] One remarkable aspect of the numerical simulation of the temporal evolution of the temperature field within the beam is the method employed for determining the cooling powers for the heat exchanges occurring at the beam surface. This aspect is presented first, below.

[0048] Determining the cooling setpoint(s) by iterative numerical simulations (which require significant computation time), while it is to be used for real-time, on-line control, is achieved thanks to specific arrangements that are presented below in a second time, with reference to figure 17.Coo / infj po wers at the beam surface

[0049] The cooling powers corresponding to the heat exchanges at the beam surface are computed for the beam’s faces above mentioned (web faces W1 , W2, and flange faces F1 - F6), which, together, form most of the beam surface.

[0050] Determination of the applicable cooling regimes

[0051] Generally, the colling power for a portion of the beam that is within the cooling machine (and thus water-cooled) is different from the cooling power for portions of the beam that are outside the cooling machine (which are air-cooled). Besides, within the cooling machine, the cooling power may be different from one face of the beam to another, depending on which faces are water-cooled.

[0052] For each cooling section 31 , 32, and also, when applicable, for each cooling subsection 311 , 312, 321 , 322 (for the web faces, the presence the different subsections is taken into account, here, but not for the flange faces), it is determined, for each of the beam faces W1, W2, F1 - F6, what is the cooling regime undergone by the face considered, in the cooling section considered, given the cooling configuration employed in the cooling machine.

[0053] More particularly, in the instant method, the electronic system 10 executes the following steps: acquiring: o cooling configuration data specifying which of the jets are on and which of said jets are off, in the cooling machine 30, o water flow values for the jets that are on, each cooling section 31 , 32, and , when applicable, for each cooling section, and for each of said faces W1 , W2, F1 - F6 of the beam, determining, from the cooling configuration data, what cooling regime undergoes the face of the beam considered in the cooling section (or possibly in the cooling subsection) considered, the cooling regime being selected among, at least, or in other words a cooling regime, for the part of face considered, among:- a : direct water cooling,- b : powered cooling,- c : air cooling,- d : run-off water cooling,

[0054] For the portion of the beam Pj (for which the above-mentioned thermal numerical simulations are achieved), for the (simulated) temporal period during which Pj is in the cooling machine (completely, or partially), cooling powers for the different web and flange faces W1 , W2, F1 - F6 are computed, taking into account the cooling regimes (a, b, c or d) that have been determined for said faces, and taking into account one or more of the water flow values, when the cooling regime is a and when the cooling regime is b.

[0055] The cooling conditions corresponding to these different cooling regimes a, b, c and d, as well as ways to compute the corresponding cooling powers are presented in more detail below.

[0056] The cooling conditions to be applied in the cooling machine 30, that is the specification of which of the jets are to be on, and which ones are to be off, as well as the corresponding water flow values, may, like here, be determined by a dedicated module (eg: a dedicated subprogram or sub-routine, or a dedicated electronic module), depending on the metallurgical heat treatment aimed at and / or depending on flatness / squareness corrections to be applied to the beam. These cooling conditions, and the water flow values may also be entered manually by an operator (through the human-machine interface). Anyhow, for determining the applicablecooling regimes, these cooling conditions (in practice, the cooling conditions data) and corresponding water flow values, are inputs.

[0057] Air cooling

[0058] For the parts of those faces that are located outside the cooling machine 30, and that are not in a rolling stand (not in the course of being laminated by a working roll of the tandem or finishing roll 3, 4), the heat exchanges are mostly achieved by thermal radiation and due to the contact with air. For these parts of the beam faces, the cooling power per unit surface (for instance per square meter), noted Pc, is computed asPc ~ Pair T Pradiative (e — 1)

[0059] Pradiative 'scomputed for instance according to the following expression:with F the form-factor, s the emissivity of the beam surface, o the Stefan-Boltzmann constant, Tsurf the temperature at the surface of the beam, for the face of the beam considered, and Tajrthe temperature of air, in the beam processing installation.

[0060] Pairmay be computed according to the following expression:Pair = HTCair. (Tsurf- Tair) (eqn - 3)WithWhere C1 and C2 are two constants, where the exponent p is from 2 to 5, and where v is the speed of the beam 2 (speed with which the beam is moved, along the axis x of the beam processing installation 1). In eqn-4, the term vpreflects the influence of forced-convection cooling, while the term depending on Tsurf Ta irreflects free convection cooling.

[0061] This cooling regime (c: air cooling) applies also to the parts of the beam faces that are within the cooling machine 30 but that are not struck by any of the waterjets and for which the cooling regime is neither powered cooling nor run-off water cooling.

[0062] Direct water cooling

[0063] For each of the beam faces W1 , W2, F1 - F6, when the beam face considered is struck (directly) by some of the waterjets, in the cooling section or subsection considered, the cooling regime for that face is a: called direct water cooling. The corresponding cooling power per unit surface, noted Pa, depends on water flow rate Q projected on the beam face considered. More particularly, Pamay be computed as being equal to, or substantially equal to (which means, here, equal within 10%, or even within 5% or 2%) to:C. HTCref(Tsurf). Qa(eqn - 5) where:C is a multiplicative coefficient; C may have a fixed value, or it may be the sum of a mean value and of a corrective term that varies depending on a temperature Twater of the projected water,Q is the water flow projected on the part of the face of the beam considered, expressed as a volume per unit time and per unit surface (eg: liters per second and per square meter - alternatively, Q could be expressed as a mass of water per unit time and per unit surface, in kg / (m2.s), for instance), the exponent a is a constant from 0.5 to 4, or even from 0.5 to 2, and / - / TCref(Tsurf) is a function of the temperature TSUrf.

[0064] In practice, the function / 7TCref(TSurf) decreases with TSUrf, at least when TSUrf is above 200°C. / 77"Cref may be: divided by 2 or 2,5 when TSUrf varies from 200°C to 400°C, divided by 2 when TSUrf varies from 400°C to 600°C, and when TSUrf varies from 600°C to 800°C, and divided by 3 or 4 when TSUrf varies from 800°C to 1000°C. HTC<ef may more particularly vary according to the curve represented in figure 11 , where HTC<ef is represented in arbitrary units against TSUrf (expressed in °C).

[0065] It has been observed that the eqn-5 leads to a good agreement between predictions and measurements, for the thermal evolution of the beam (as illustrated by figures 15 and 16 presented further below).

[0066] Taking the decrease of HTC with TSUrf enables to reflect that cooling is more efficient, with a higher Heat transfer coefficient, when TSUrf is moderately high (in the 400-700°C range) instead of very high (above 800°C). taking this variation into account enables to avoid excessive cooling, and increases the temperature prediction (and control) accuracy.

[0067] powered cooling and run-off water cooling

[0068] For the parts of the beam faces W1 , W2, F1 - F6 that are located inside the cooling machine 30 and that are not struck by any of the waterjets, the cooling regime may be an air and thermal radiation cooling, just as outside the cooling machine (the corresponding cooling power per unit surface being then Pc). However, remarkably, two other possible cooling regimes are taken into account, for the parts of beam faces with no direct water cooling: the so-called powered cooling regime, and the run-off water regime.

[0069] The powered cooling regime concerns a beam face not struck by any of the jets, but that have another beam face that adjoins it laterally and that is struck by some of the jets, in the cooling section considered. As this ‘adjoining’ other face is struck by water jets, the face considered benefits non-directly from this water cooling, and cools down faster than for regular air cooling (or than in the presence of remaining run-off water). This cooling regime if for instance the one undergone by the part of the web face W1 that is in the cooling subsection 321 , in the cooling configuration represented in figure 9. By “laterally adjoining, it is meant that the two beam faces in question are adjacent (and with no other beam face between them), incontact with each other along the beam (in contact with each other along a contact line or contact seam that extends parallel to the beam axis, at the faces junction).

[0070] Here, for the powered cooling regime, the cooling power, per unit surface, Pb is computed as being equal, or substantially equal to: the cooling power Pafor the adjoining face in question (which undergoes direct water cooling) multiplied by a proportionality coefficient. This proportionality coefficient may in particular be all the smaller than the beam face undergoing powered cooling is wide. The cooling power Pb may then be computed as follow: woPb= — Pa(eqn - 6) w where w is the width of the face in question and w0is a constant width.

[0071] w is the extension of that face transversely, perpendicularly to the beam axis (perpendicularly to axis x, here). The constant w0has a value that is representative of a typical transverse dimension of the beam. It is for instance from 0.1 to 0.6 meter (when w is expressed in meter). For instance, for the beam 2 of figure 2, if part of the web face 1 undergoes powered cooling, then the width w used in eqn-6 is the width of the web, that is the distance between the two flange faces F2 and F5.

[0072] Eqn-6 reflects (inter alia) that when the web is wide, the adjoining flange faces, directly water cooled, are distant from the middle of the web which makes powered cooling less efficient for the central part of the web (which is reflected by the decrease of Pb with w).

[0073] Figures 12 and 13 show exemplary test results illustrating that taking into account this powered cooling regime, for the faces concerned, and determining the cooling power Pb as above described, leads to an accurate determination of the thermal evolution of the beam.

[0074] Figures 12 and 13 represents, for several beams cooled in the beam processing installation 1 : the quantity Tmt, i - T out (in °C) where Tout is the output temperature (at the sensor 9) as determined by numerical simulation of the thermal evolution of the beam, as function of the quantity Tmt - Tout (in °C), corresponding to the actual, measured temperatures.

[0075] The numerical simulation employed for determining Tout is the same as the one above described, but starting from the intermediate temperature Tmt, i (instead of starting from the initial temperature T ), and at an instant corresponding to the passage of the beam portion Pj at the position Os (instead of Os).

[0076] These test results gather data for different, varied web thicknesses, moving speeds, and web widths w (with values from 0.35 to 0.72 meter for w); the beams are all H-beams, like in figure 2. The cooling configuration of the cooling machine is one with flange jets on in cooling sections 31 and 32, and web jets on in the subsection 322 but off elsewhere. For the results presented in figure 12, the cooling power for the parts of the web face W1 undergoing poweredcooling is computed as being proportional to the cooling power Pafor the adjoining flange faces, which undergo direct water cooling, but with a constant proportionality coefficient which is independent of the web width. For the results presented in figure 13, the cooling power Pb for the parts of the web face W1 undergoing powered cooling is computed according to eqn-6 above. In figures 12 and 13, the straight-line “y=x” corresponds to a perfectly accurate numerical simulation.

[0077] As illustrated by figures 12 and 13, taking into account the powered regime above presented, with a cooling power proportional to the one for the adjoining, directly cooled faces, leads to accurate prediction. Figure 13 illustrates that having a proportionality coefficient in the form w0 / w further improves this accuracy (better accuracy, smaller dispersion).

[0078] The run-off water cooling regime concerns a beam face not struck by any of the jets, in the cooling section or subsection considered, but that has some (run-off, remaining) water on it due to water projected on the beam in an other of the cooling sections or subsections. It concerns more particularly a beam face which is horizontal and upward facing, not struck by any of the jets in the cooling section or subsection considered, but with jets projecting water on this face in another of the cooling sections or subsections (located upstream or downstream of the section considered), or with jets projecting water, in another of the cooling sections, on a beam face which adjoins the face considered and which extends upward from the face considered.

[0079] The run-off cooling regime is the one applicable in the first cooling section 31 , for the upper web face W1 of the beam, in the cooling configuration of figure 9, for instance.

[0080] If a beam face, not struck by any of the water jets, has run off water on it in the cooling section considered, but has another beam face that adjoins it laterally and that is struck by some of the jets in this cooling section, then the cooling power is computed using the expression for powered cooling, not for run-off water cooling.

[0081] For the run-off water cooling, the cooling power Pd, per unit surface, may be computed according to:Pd = HTCd. (Tsurf- Twater) (eqn - 7) where HTCd is a constant heat transfer coefficient.

[0082] HTCd is for instance from 700 W / (m2.°C) to 1500 W / (m2.°C) or even from 800 W / (m2.°C) to 1100 W / (m2.°C).

[0083] The cooling configuration of figure 9 is an example of a cooling configuration for which the four cooling regimes above mentioned, a, b, c and d, are present. More specifically, when the cooling configuration of figure 9 is employed, the cooling regimes for the different beam faces are the followings.

[0084] For the flange faces F1 - F6, in the first cooling section 31 , the cooling regime is regime c: air cooling.

[0085] For the flange faces F1 - F6, in the second cooling section 32, the cooling regime is a: direct water cooling.

[0086] For the upper web face W1 , and also for the lower web face W2, in the second subsection 322 of the second cooling section 32, the cooling regime is a: direct water cooling.

[0087] For the upper web face W1 , and also for the lower web face W2, in the first subsection 321 of the second cooling section 32, the cooling regime is b: powered cooling. Indeed, this part of the web face W1 , or W2, is not struck directly by any of the jets, in the subsection 321 , but it has other faces (namely the flange faces F2 and F5), that adjoin it laterally, and that are struck by waterjets in the subsection 321.

[0088] For the upper web face W1 , in the first cooling section 31 , the cooling regime is d: runoff water cooling, as above mentioned. While for the lower web face W2, in the first cooling section 31 , the cooling regime is c: air cooling.

[0089] The way to determine the applicable cooling regimes, and to compute the corresponding cooling powers, has been illustrated above in the case of an H-beam. This method can be applied as well to other beam shapes. For instance, for T-beam, if the flange faces undergo direct water cooling, but the web faces haven’t any jet striking them, it will be determined that the web faces undergo the powered cooling regime above described, with a cooling power equal to Pb.

[0090] Figures 14 to 16 show exemplary test results illustrating that the above method for determining cooling powers leads to an accurate determination of the thermal evolution of the beam. Figures 14 to 16, for several beams cooled in the beam processing installation 1 : the quantity Tmt, i - T out (in °C) where Tout is the output temperature (at the sensor 9) as determined by the numerical simulation of the thermal evolution of the beam, as function of the quantity Tmt - Tout (in °C), corresponding to the actual, measured temperatures.

[0091] These test results gather data for different, varied web thicknesses, moving speeds, and web widths w; the beams are all H-beams, like in figure 2. The cooling configuration of the cooling machine is one with flange jets on in cooling sections 31 and 32, and web jets on in the subsection 322 but off elsewhere.

[0092] For the results presented in figure 14, the only cooling regimes considered are direct cooling regime, air cooling and run-off water cooling (with an adjustment of numerical parameters of the cooling laws, achieved so as to optimize as much as possible the prediction accuracy). Figure 14 represents the quantity Tmu - Tout both for temperatures at a point of a flange face, and at a point of a web face.

[0093] For the results presented in figure 15 and 16, the powered cooling regime is taken into account, when applicable, in addition to the cooling regimes a, c and d. In figure 15, the quantityT jnt.i " T out represented is for temperatures at a point of a flange face, while in figure 16 it is for a point of a web face.

[0094] In figures 14 to 16, the straight-line “y=x” corresponds to a numerical simulation that would be perfectly accurate.Real-time contra / based on numerical simulations

[0095] An exemplary embodiment of the method for controlling the beam processing installation is represented, as a block diagram, in figure 17.

[0096] To have the time to execute multiple numerical simulations of the temporal evolution of the beam, in order to identify a suitable speed setpoint v0*, before the beam enters the cooling machine, these simulations are launched in advance, while the beam is significantly upstream of the cooling machine.

[0097] More specifically, the execution of these iterative simulations (iterations of step s4, in figure 17) is launched as soon as the input temperature Tm of the beam has been measured (Tm is measured in step s1 - see figure 17). The input temperature T is measured here on a heading part of the beam, this heading part corresponding for instance to a first fourth of the beam. The portion denoted Pj is the portion of the beam of the beam (in other words the longitudinal sample of the beam) on which Tm is measured. Here, in practice, Pj is the fourth longitudinal sample (j=4). Still, it is noted that the discretization of the beam into n longitudinal samples plays no significant role during the steps s1 to s5 described below, and more generally during the simulations made to determine values for the one or more cooling setpoints, here the speed setpoint v0*. Regarding the on-line control of the installation, this discretization plays a role when repeating steps s6, s7 and sc for the different, successive portions Pj of the beam (with i from 1 to n), to determine adjusted speed setpoints v* (adjusted respectively for these successive portions Pj). The input temperature T is measured when the heading part of beam passes at the input position 06, before the last rolling pass in the tandem mill 4, for instance just after the last-but-one pass in the tandem mill, here.

[0098] This in-advance triggering allows to determine the speed setpoint v0*, before the beam enters the cooling machine, and even before it enters the finishing mill 3. Yet, it may partially limit the accuracy of the prediction of the temporal evolution of the beam’s temperature, as the simulated time period is longer (and comprises rolling passes).

[0099] To overcome this partial limitation, the intermediate temperature Tmt,j of the portion Pj (or, possibly, of another portion Pj of the beam) is measured by the second temperature sensor 8 just upstream of the finishing mill 3, when this portion Pj passes at the intermediary position Os (step s6). The measured intermediary temperature T t,j (or, possibly T t ) is compared with the predicted intermediary temperature Tmt.caic computed by numerical simulation, and a corrected, adjusted the speed setpoint Vj* (orv*) is determined based on this comparison (step s7). Then, in step sc, the electronic system 10 sends the corrected speed setpoint Vj* to thelow-level controller 13, which controls then the speed of rotation of the rolls of the finishing mill 4 so that the speed at which the beam travels matches the corrected speed setpoint v*. This measurement-based correction of the speed setpoint allows for re-adjusting the temperature prediction, to somehow re-align the thermal simulation onto the actual thermal path followed by the beam.

[0100] In the method of figure 17, the determination of the cooling regimes, undergone by the different faces W1 , W2, F1 - F6 of the beam, is achieved in a step s2, based on the cooling configuration data, as above explained.

[0101] In step s1 , the input temperature Tm of the portion Pj is measured. Immediately after step s1 , a first execution of step s4 is achieved.

[0102] In step s4, the temporal evolution of the temperature field within the portion Pj is computed starting from an initial state for which a surface temperature (at a given position on the beam surface), for the portion Pj, equals Tm.

[0103] The temporal evolution of this temperature field is then computed, time step by step (using a finite differences method, here), until a moment corresponding to a final delivery of the beam, after its cooling. This temporal evolution is computed: based on given, fixed, values of the water flows in the cooling machines (values that are preset before the executions of step s4), and based on a candidate speed setpoint vc*, for the speed at which the beam traverse the cooling machine (in other words, for this simulation, it is supposed that v= vc*).

[0104] To compute the temporal evolution of the temperature field within the portion Pj, the powers (for instance in Watts per square meter), corresponding to the heat exchanges at the surface of the beam, are computed for the different phases of the beam processing. For a transfer from one position to another, in air, a cooling power corresponding to air cooling and radiation cooling is computed. When rolled in the tandem mill 3 or in the finishing mil 4, specific thermal models for that rolling operation are employed, for the heat exchanges. And when in the cooling machine 30, for each surface of the beam, the cooling power is computed depending on the cooling regime undergone by the face considered (colling regime that has been determined in step s2), and, when applicable, depending the water flow values for the relevant waterjets.

[0105] When computing the temporal evolution of the temperature field within the portion Pj, the fact that phase transformations (like austenite to ferrite, to bainite or to martensite transformations) may occur in the steel during its cooling is also taken into account, and the chemical composition of the steel of the beam is also taken into account (as it influences, among other things, the values of the phase transition temperatures).

[0106] Regarding the temperature TST, predicted by numerical simulation in step s4, in this embodiment, it is the maximum over time reached by the temperature of the surface of theportion Pj of the beam, after this portion of the beam has exited the cooling machine (as illustrated in figure 1).

[0107] Step s4 is executed repeatedly for different candidate speed setpoints, until the predicted TST temperature matches the target self-tempering temperature T*STJ for the portion Pj (which is tested in step s5). The target self-tempering temperature T*STJ for the portion Pj may, like here, be global (uniform) target self-tempering temperature T*ST for the beam.

[0108] Once a candidate speed point, for which TST matches T*STJ, has been found, the speed setpoint v0* is set to equal this candidate speed point and the repetitions of step s4 stop. The repetitions of step s4 also stop if the total number of executions of step s4 reaches a maximum number of repetitions allowed (equal to 10, here). In this case, the speed setpoint Vo* equals the candidate speed setpoint for which the difference between TST matches T*STJ was the smallest.

[0109] Here, the cooling configuration and the water flow values remain unchanged, during the different executions of step s4. In other words, in this embodiment, only the candidate speed setpoint is modified from one execution of step s4 to the other.

[0110] The step s2 above mentioned is executed before step s4 (and s2 is not iterated; it is executed just once).

[0111] The determination of the speed setpoint v0* (by repeatedly executing step s4), which is time consuming, is achieved just once, here, for one longitudinal sample of the beam only, namely for the portion Pj. Conversely, the adjustment of the speed point, based on the measured intermediate temperature, is achieved for all the successive portions Pj of the beam, with i=1 , ... ,n, thus determining n adjusted speed setpoints v*, each adapted specifically to the cooling of the associated beam portion Pj.

[0112] The set of steps s6, s7 and scis thus executed several times successively, for i from 1 to n. In step s6, the intermediate temperature Tint, i of the portion Pj is measured by the second temperature sensor 8, when this portion passes at the intermediary position Os.

[0113] In step s7, an adjusted speed setpoint v* is computed for the portion Pj, based on Vo*, Tmt, i and Tjnt,caic. Tint, caic is intermediary temperature as predicted by numerical simulation during the execution of step s4 for which the (candidate) speed setpoint equalled v0*.

[0114] In particular, if Tint.caic equals Tmtj, the speed setpoint may be left uncorrected (that is, v*= Vo*), while if Tint.caic departs from Tmtj, the adjusted speed setpoint v* differs from v0* all the more than Tint.caic differs from Tintj.

[0115] The correction applied may be such that L / v* - L / v0* is proportional to the difference T int.j " T int.calc, L being the length to be travelled to traverse the cooling machine. The proportionality coefficient for this correction is determined from the results of the executions of step s4, and depends on the respective influences of the transit time L / v, and of the intermediate temperature, onto the TST temperature obtained.Method for characterizing the beam produced.

[0116] The method for determining the cooling regimes for the different faces of the beam depending on the cooling configuration, and for computing the corresponding cooling powers, has been presented above in the context of a control method. The method for determining these cooling regimes can also be applied for determining a posteriori the self-tempering temperature TST reached by the different portions of the beam Pj, i=1..n , based on the cooling conditions that were actually employed during the beam processing.

[0117] Such a post-characterization is very useful, as final properties of the beam, in particular final mechanical properties depend on the self-tempering temperature actually obtained (and, more generally, depend on the thermal path followed during this quench and self-tempering thermal treatment).

[0118] Figure 18 represents steps of such a post-characterization method.

[0119] Values of the process parameters actually employed are acquired in step sacq. More particularly, in step sacq, the following quantities are acquired, for each portion Pj of the beam:- the intermediate temperature Tjnt measured for that portion (when it passes at position Os),- the speed vmat which this portion traverses the colling machine, measured by a speed sensor, and also, here,- transit times: between the intermediary position Os and the cooling machine 30, through the cooling machine 30, and between the cooling machine 30 and the third temperature sensor 9.

[0120] The cooling configuration data, and water flow values, are also acquired, in step sacq(these quantities being the same for all the different portions, here).

[0121] Then, for each portion Pj of the beam, a step Scomp is executed to determine, by numerical simulation, the self-tempering temperature TST for that portion. This numerical simulation is achieved as above explained for the control method (for step s4 of the control method), except that the simulation:- starts from the intermediary position Os, instead of the input position Os,- starts from a temperature that is the intermediate temperature Tjnt instead of the input temperature Tin,- is based on the actual, measured speed of the beam (not on a candidate speed setpoint).

[0122] In particular, the cooling powers in the cooling machines are computed as above described.

[0123] The self-tempering temperatures TSTJ for the different beam portions Pi, i=1 , ... ,n, thus computed by the electronic system 10, may be stored in the database 14, associated with an identifier of beam 2 (such as a serial number of the beam).

[0124] Besides, during the computation of the temporal evolution of temperature field within the portion Pi, the temporal evolution of the metallurgical phase(s) of the steel is alsocomputed, here (for instance, values of phase fractions, at different positions within the beam section, and its evolution with time). Final values of these phase fractions (more specifically, a 2D field of values of the phase fractions, for the beam portion considered), obtained after this thermal treatment, are thus obtained in step Scomp, and stored in the database 14.

[0125] The temperatures TST , and possibly the phase fractions values, may then be used for assessing the quality of the beam, that is assessing its adequation with targeted mechanical properties, during a subsequent quality check step.

Claims

CLAIMS1. A method for determining a temperature Ts-r of a steel beam (2) after the beam has been water-cooled in a cooling machine, the beam coming out of a rolling mill and traversing then the cooling machine (30), the beam comprising a web (21) and one or two flanges (22, 23), the surface of the beam, comprising mainly a first web face (W1) and a second web face (W2) opposite each other, and two or three flange faces (F1 , F2, F3, F4, F5, F6) for each flange, the cooling machine comprising one or more cooling sections (31 , 32), each arranged for emitting: o flange jets (FJ), for projecting water on one or more of the flange faces (F1 , F2, F3, F4, F5, F6), and o web jets (WJ), for projecting water on one or both of the web faces (W1 , W2), the method comprising: acquiring: o an input temperature (Tm, Trnt ), measured on a portion of the beam (Pi) before said portion of the beam enters the cooling machine, o cooling configuration data specifying which of said jets (FJ, WJ) are on and which of said jets (FJ, WJ) are off, o water flow values for the jets that are on, for each cooling section (31 , 32), and for each of said faces (W1, W2, F1 - F6) of the beam, determining, from the cooling configuration data, what cooling regime undergoes the face of the beam considered in the cooling section considered, the cooling regime being selected among, at least: a : direct water-cooling: the face has water projected thereon by one or more of said jets, in the cooling section considered, b : powered cooling: the face has no water projected thereon, by any of the jets of the cooling section consider, but, for an other of said faces which adjoins laterally the face considered, said other face has water projected thereon by one or more of said jets, in the cooling section considered, c : air-cooling, for said portion of the beam (Pi), computing cooling powers for the different web and flange faces (W1 , W2, F1 - F6) respectively, taking into account the cooling regimes that have been determined for said faces, and taking into account one or more of the water flow values when the cooling regime is a and when the cooling regime is b,determining the temperature TST based at least on the input temperature (Tm, Tmu) and on said cooling powers, the temperature TST being a temperature of said portion of the beam after the portion of the beam has traversed the cooling machine (30).

2. A Method according to claim 1 wherein, when the cooling regime is b, the cooling power, per unit surface, for the face of the beam considered, in the cooling section (31 , 32) considered, is computed as being equal or substantially equal to:- the cooling power, per unit surface, in said cooling section, for said other face of the beam which adjoins laterally the face considered,- multiplied by a proportionality coefficient.

3. A Method according to claim 2, wherein said proportionality coefficient is all the smaller than the face of the beam considered (W1 ; W2) is wide.

4. A method according to anyone of claims 1 to 3, wherein the cooling regime is selected among a, b, c and also:- d : run-off water cooling: the face considered has no water projected thereon in the cooling section (31) considered but has some run-off water on it due to water projected on the beam in an other (32) of the cooling sections.

5. A method according to the preceding claim wherein, for each of the faces of the beam, when: the face (W1) of the beam is horizontal and upward-facing, the jets of the cooling section (31) considered are off, and, in said other cooling section (32), some jets project water on the face (W1) considered, or on an other of said faces (F2, F5) which adjoins the face (W1) considered and which extends upward from the face considered, then, it is determined that the cooling regime for the face (W1) considered, in the cooling section (31) considered, is d.

6. A method according to the claim 4 or 5 wherein, when the cooling regime is d, then, the cooling power, per unit surface, is computed as being equal, or substantially equal to:a temperature difference TSUrf -Twater between a surface temperature TSUrf of the beam (for the face of the beam considered), and a temperatureTWater of the water projected, multiplied by a constant heat transfer coefficient HTCd.

7. A method according to anyone of the preceding claims wherein, when the cooling regime is a, the cooling power, per unit surface, is computed as being equal or substantially equal to C. / 7TCref(TSurf).Qawhere: TSUrf is a surface temperature of the beam (for the part of the face of the beam considered), C is a multiplicative coefficient, Q is the water flow per unit surface projected on the face of the beam in the cooling section considered, a is from 0.5 to 4 and / 7TCref(TSurf) is a function of TSUrf.

8. A method according to the preceding claim, wherein the function / 7TCref(TSurf) decreases with TSUrf, at least when TSUrf is above 200°C.

9. A method according to anyone of the preceding claims wherein the temperature TST that is determined is the maximum overtime reached by the temperature of the surface of said portion (Pi) of the beam, after said portion (Pi) has exited the cooling machine (30).

10. A method according to anyone of the preceding claims, further comprising:Comparing the temperature TST that has been determined with a target self-tempering temperature T*STJ,Determining one or more cooling setpoints (v0*), depending on the result of the comparison of the temperature TST with the target self-tempering temperature T*STJ,Controlling the beam processing installation (1) based on said one or more cooling setpoints (v0*), or based on one or more corrected cooling setpoints (v*) determined from the one or more cooling setpoints (v0*).

11. A method according to claim 10, wherein the one or more cooling setpoints comprise a speed setpoint (v0*) for a speed (v) at which the beam traverses the cooling machine.

12. A method according to anyone of claims 1 to 9, further comprising measuring a speed Vm.i at which the portion of the beam (Pi) traverses the colling machine, and wherein the temperature TST is determined based also on the speed vm.

13. An electronic system (10) comprising at least a processor and a memory, configured for executing the method according to anyone of the preceding claims.

14. A beam cooling installation (1) comprising: the electronic system (10) of the preceding claim, and the cooling machine (30) for water-cooling the beam (2).

15. A computer program comprising instructions whose execution on a computer makes the computer to execute the method according to anyone of claims 1 to 12.

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