EP0988903A1 - Method of rolling a metal product - Google Patents

Abstract

The process involves rolling a metal product in at least one rolling cage (1) associated with a calculation unit (4) comprising a calculator and a mathematical model for regulating the rolling force applied by the tightening apparatus (17). The installation used to implement the process comprises: (a) a rolling cage having two spaced columns (11); (b) at least two superposed working rolls (12, 12') between the columns of the cage; (c) device for control of feed of the product (2) for rolling in a rolling nip (22) delimited by two arcs of contact (20, 20') of the product (2) with the two rolls, between an inlet and an outlet section of the rolling nip (22); tightening apparatus (17) for applying pressure on the rolls and the cage to regulate the gap between the working rolls (12, 12') corresponding to a desired reduction in thickness and to maintain the gap during the rolling pass by applying between the working rolls (12, 12') a rolling force that depends on the mechanical and physical characteristics of the cage and the product and the conditions of passage of the metal in the rolling nip, and determines a yielding effect for different elements of the cage tending to augment the gap; and (d) devices (31, 32) controlled by a calculation unit (4) comprising a calculator (40) associated with a mathematical model, to regulate the tightening apparatus. Before each pass the calculation unit (4) associated with the mathematical model (40) determines a predictable value of the contraction stress of the metal corresponding to the deformation to be realized in the considered pass by taking into account during rolling the microcrystalline structure of the metal constituting the rolling product (2). The rolling force to be applied in order to obtain the desired thickness reduction is calculated before each pass as a function of the predictable value of the contraction stress and its development during rolling.

Description

The subject of the invention is a method of rolling a metallic product and applies more particularly to hot rolling of flat products such as slabs or strips from a roughing or casting rolling mill keep on going.

Hot rolling is usually done by successive rolling passes in an installation comprising one or more rolling stands. Each cage can be used as a reversible rolling mill performing a number of reduction passes, alternately back and forth, until you get the desired thickness. But we can also perform a single rolling pass in each cage. The installation then operates in a tandem rolling mill, the rolled product being taken simultaneously in all cages and its thickness successively reduced in each cage.

The invention applies especially to rolling with hot steels and their alloys but is also usable, under certain conditions, for the rolling of non-ferrous metals such as aluminum and its alloys.

Generally, a rolling mill includes a cage rigid support having two columns spaced between which are placed at least two working cylinders superimposed which define a product passage air gap to laminate. In a classic arrangement called quarto, the working cylinders are each supported on a cylinder larger diameter support. In a montage said sexto, intermediate cylinders are interposed between working cylinders and support cylinders.

At least the support cylinders are provided, at their ends, of trunnions turning in chocks sliding mounted in fitted windows respectively on the two columns of the cage, parallel to a clamping plane, generally vertical, passing substantially through the axes of the working cylinders.

The rolling mill is associated with means for controlling the scrolling of the product between the cylinders, at a certain forward speed. In the case of a reversible rolling mill, which alternately rolls in two opposite directions, advancement control means are constituted, usually two roller tables, respectively, one roller table placed upstream of the cage, in the direction of scroll, to order product engagement and a other roller table placed downstream to receive the product after rolling.

In hot rolling, the product is heated, before rolling, up to a temperature of around 1200 ° C in the case of steel, so as to facilitate the deformation of the metal and its flow between the cylinders. Generally speaking, in fact, in a process of rolling, the product has a thickness greater than the spacing of the cylinders and, when it comes into contact with them, it is driven by friction then pinched between the two cylinders, with metal flow and thickness reduction, up to a thickness substantially equal to the spacing between the generators opposite the two working cylinders. We can thus define a rolling area defined by the contact arcs between each cylinder and the product.

Laminating is therefore carried out from a part raw such as a slab or strip having a thickness variable which can range from a few millimeters to several hundreds of millimeters and a pass is made on each pass thickness reduction which can vary, for example, by 50 mm to a few tens of millimeters.

During rolling, the rolls tend to deviate from each other and must therefore be maintained by an opposite rolling force which in a quarto rolling mill is applied to the chocks of the support cylinders.

These clamping means therefore serve, on the one hand to prior adjustment of the spacing between the cylinders and, on the other hand, to the maintenance of it during the pass of rolling. They generally consist of screws or hydraulic cylinders mounted on the cage and supported respectively on the two chocks of a cylinder of support, the other being blocked in height. However, other arrangements are possible. For example, we can use support cylinders with an envelope rotatably mounted around a fixed shaft and supported by this via a series of cylinders. These then constitute clamping means exerting the force of rolling which is thus distributed over the entire length of the air gap.

In any case, under the effect of the force of rolling, there is inevitably some yielding of the different organs of the cage, which increases slightly the spacing of the cylinders set when empty and therefore has the effect to reduce the planned crushing. To achieve precision the desired thickness reduction, it is therefore necessary to estimate the value of the surrender, so as to compensate it also exactly as possible.

The rolling force to be applied to maintain of a given spacing between the cylinders depends on the deformation conditions of the product in the grip of passage between the cylinders.

Conversely, the maximum thickness reduction possible is a function of the rolling force that we can apply, taking into account the capacities of the rolling mill.

The reduction in thickness that can be achieved with each pass is therefore limited and this is why the rolling of a raw product is normally carried out in several successive passes, each determining an elementary thickness reduction compatible with the capacity. of the rolling mill. The total thickness reduction from a gross thickness e _o to a final thickness e _n can be obtained in n passes according to a process of progressive thickness reduction, called rolling scheme, which depends on the capacity of the rolling mill and the adjustment means available, the mechanical and physical characteristics of the stand and of the product, as well as the tolerances to be observed in terms of thickness and flatness.

Depending on the capacities of the installation which disposes, we can define a simple rolling scheme in which is carried out, at each pass, the same reduction of medium thickness. The number of passes to perform depends then, simply, from the total thickness reduction to achieve.

However, it may be necessary to increase the number of passes required since the reduction in thickness chosen average must be determined so as to be compatible, for all passes, with product and cage characteristics. Now, for improve productivity, there is obviously an interest in reduce, as much as possible, the number of passes to carry out.

But it was also observed that the final quality of the product, and in particular its flatness, was linked to conditions under which rolling is carried out and that not all thickness reduction schemes are equivalent when you want to get a quality product determined.

For example, even if we can define a certain temperature of the product at the start of rolling, this varies from one pass to the next. Indeed, the product cools during the waiting time between two successive passes but the deformation of the metal leads, conversely, to a heating of the product during the pass and we can be leads to cooling the product between two passes to avoid too much cumulative heating.

However, the conditions of deformation of the product, which determine the rolling force to apply, depend obviously the nature of the metal and its temperature.

We therefore have an interest in obtaining a product with determined qualities, to follow an optimal pattern which depends not only the mechanical capacity of the installation but also of the desired final quality for the product.

In recent years, we have sought to achieve automation of the rolling process of a flat product to obtain the expected thickness with good flatness and using a minimum number of passes without overload the rolling stand (s).

In such a system, it is necessary to control, at each pass, the adjustment of the clamping means to apply a force of lamination allowing thickness reduction maximum compatible with the capacity of the rolling mill. This rolling force is estimated based on the different rolling parameters on which the conditions depend metal flow in the right-of-way, in particular the reduction thickness to be performed, the speed of travel and the temperature of the product as it enters the rolling mill.

According to the practice known hitherto in the most advanced installations, from global parameters like, for example, the constraint flow of a metal according to its nuance and its temperature, reference tables of the rolling conditions previously observed for steel known, so as to deduce the conditions to be respected when the same steel is found again in the production program of an installation.

For that, it is necessary to make an estimate of the force predictable rolling in each case. However, this can only be appreciated globally from observations made during previous rolling operations. A such an estimate is not precise enough to settle the rolling conditions during each pass so that effectively obtain the optimal thickness reduction and, in particular, ensure compensation for ceding.

The invention remedies this drawback and has for object, thanks to advances in modeling, a new process for determining more precisely the rolling force to be applied to comply with a rolling. In addition, the invention makes it possible to act automatically and in real time on the settings of the rolling mill to modify these on each pass measurements made in the previous pass, so that continuously adapt the rolling scheme by optimizing the settings on each pass.

• une cage de maintien ayant deux colonnes écartées,
• au moins deux cylindres de travail superposés entre les colonnes de la cage,
• des moyens de commande de l'avancement du produit avec laminage de celui-ci dans une emprise de laminage délimitée par deux arcs de contact du produit avec les deux cylindres, entre une section d'entrée et une section de sortie de l'emprise,
• des moyens de serrage prenant appui, respectivement, sur les cylindres et sur la cage, pour le réglage d'un écartement entre les cylindres de travail correspondant à une réduction d'épaisseur à réaliser et pour le maintien dudit écartement pendant la passe de laminage, par application, entre les cylindres de travail, d'une force de laminage qui dépend des caractéristiques mécaniques et physiques de la cage et du produit et des conditions d'écoulement du métal dans l'emprise de laminage, et détermine un effet de cédage des différents organes de la cage tendant à augmenter ledit écartement e,
• des moyens de réglage desdits moyens de serrage, commandés par un calculateur associé à un modèle mathématique.

The invention therefore generally relates to a method of rolling a metal product in an installation comprising:

• a support cage having two spaced apart columns,
• at least two working cylinders superimposed between the columns of the cage,
• means for controlling the progress of the product with rolling thereof in a rolling area delimited by two arcs of contact of the product with the two cylinders, between an inlet section and an outlet section of the area,
• clamping means bearing, respectively, on the rolls and on the stand, for adjusting a spacing between the working rolls corresponding to a reduction in thickness to be produced and for maintaining said spacing during the rolling pass, by applying, between the working rolls, a rolling force which depends on the mechanical and physical characteristics of the cage and the product and on the flow conditions of the metal in the rolling area, and determines a yielding effect of the different members of the cage tending to increase said spacing e,
• means for adjusting said clamping means, controlled by a computer associated with a mathematical model.

In accordance with the invention, the computer associated with the mathematical model determines, before each pass x, a predictable value of the flow stress of the metal corresponding to the deformation to be carried out in the pass x considered, taking into account the evolution, during rolling, the microcrystalline structure of the metal constituting the product to be laminated, and the rolling force F _x to be applied to obtain the desired thickness reduction is calculated before each pass x as a function of the value thus provided for the stress flow and its evolution during rolling.

In a particularly advantageous manner, the rolling force F _x to be applied for a rolling pass is calculated by taking account of the foreseeable variation, along the grip, of the flow stress of the metal during said pass x.

For this purpose, the rolling area is divided into a series of p adjacent elementary slices M _i , M ₂ , ... M _i , ... M _p , each corresponding to an elementary length of advance of the product between the cylinders, with an elementary deformation ε _i of the product in each slice M _i between an inlet section of thickness e _i-1 and an outlet section of thickness e _i , that, from the indications given by the mathematical model , the computer determines, for each slice M _i , a predictable value σ _i of the metal flow stress, corresponding to said elementary deformation ε _i and deduces therefrom the elementary rolling force dF _i to be applied in the slice considered Mi for carry out said elementary deformation ε _i and that, by integration of the elementary forces dF _i in the successive sections M ₁ , M ₂ , ... M _i , ... M _p , the computer determines the overall rolling force to be applied to achieve the desired thickness reduction, and controls, as a function of the overall force thus calculated, the adjustment of the clamping means for maintaining the spacing of the cylinders making it possible to obtain the desired thickness reduction e _x-1 -e _x , taking into account the flow conditions of the metal along the right-of-way and the yielding effect resulting from said overall force.

It should be noted, however, that the invention also makes it possible to determine the rolling force F _x to be applied during a pass x by taking into account the foreseeable value of the metal flow stress resulting from the evolution of the microcrystalline state of the metal during the previous passes.

Generally, the rolling is carried out according to a rolling scheme allowing an overall thickness reduction e _o -e _n to be carried out in n successive passes, each rolling pass x effecting a thickness reduction e _x-1 -e _x .

According to another characteristic of the invention, the calculator determines, by iteration, the rolling scheme to be observed by calculating in advance, for each pass x, the maximum thickness reduction leading to a force of predictable rolling Fx compatible with the capacity of the rolling mill, depending on a set of parameters rolling including product thickness and temperature and its forward speed before entering said pass x, so as to take into account the foreseeable evolution of the microstructure of the metal from one pass to the next.

In particular, the computer can be associated with permanent measurement means, during the pass, effective values of a set of parameters of rolling including the rolling force applied to each instant, the speed of advancement of the product and the temperature thereof respectively at the inlet and at the exit from the rolling mill. So, at each pass x, the calculator can compare these actual measured values with the values said parameters taken into account initially for said pass x in determining the rolling pattern, so as to resume the calculation of it and introduce, in where necessary, correction factors to parameters taken into account, in order to adapt the rolling scheme in the following passes.

In a preferred embodiment of the invention, to take account of the evolution of the microcrystalline structure of the metal during rolling, establish at least one modeling equation valid for a family of metals with microcrystalline behavior similar, from hot deformation tests carried out on test pieces of at least one standard metal of this family, said equations depending on a set of parameters related to the composition of the standard metal, we implant the initial equations thus established in the model mathematical and, for the rolling of a product of a metal of the same family as the standard metal, we wedge the model on the metal to be laminated by modifying the parameters said theoretical equations as a function of results deformation tests carried out on a metal having a composition at least close to that of the metal to be laminated.

Particularly advantageously, to define the modeling equations, we determine a quantity intermediate linked to the rate of deformation of the metal and varying substantially linearly depending on the flow constraint in at least one domain of deformation and, based on deformation tests carried out for a series of temperatures and strain rates maintained constant, one establishes a diagram of work hardening on which the variations of said intermediate quantity can be represented approximately, in said deformation domain, by a family of lines to which corresponds at least one differential equation linear, linking deformation to stress flow and can be integrated by the computer.

From such a work hardening diagram, one can establish at least two differential equations connecting the deformation to the flow stress, respectively a first linear equation giving by integration analytic, an expression of the strain as a function of flow constraint and a second equation likely to be digitally integrated to determine the predictable flow stress corresponding to a deformation to be achieved.

In another embodiment, the equations of modeling having been established initially for a standard metal and implanted in the mathematical model, these equations can be calibrated on the metal to be laminated, first performing at least one rolling pass, at least at least one product consisting of the metal to be laminated, in at least a rolling stand, adjusted in a conventional manner and measuring, during each pass, on the one hand the force of rolling actually exercised and, on the other hand, the parameters used by the computer to determine, at using the initial modeling equations, the strength of lamination to exercise theoretically. By a method of numerical regression, we can determine the modifications to bring to the parameters of said initial equations of so as to obtain modeling equations specific to metal to be laminated.

• on établit un premier diagramme d'écrouissage comportant une série de courbes représentatives, pour chaque température T, de la variation du taux d'écrouissage =dσ/dε en fonction de la contrainte d'écoulement σ,
• on transforme les données numériques relatives à chaque courbe pour établir un second diagramme d'écrouissage normalisé comportant une série de courbes représentatives de la variation, en fonction de la contrainte d'écoulement normalisée σ*=σ/µ_(T), d'une grandeur intermédiaire 2*σ* égale au double du produit de ladite contrainte découlement normalisée, par le taux d'écrouissage normalisé * = /µ_(T), µ_(T) étant le module de cisaillement élastique à la température considérée,
• lesdites courbes ayant chacune au moins une partie sensiblement rectiligne située dans au moins un domaine II, III du diagramme, et lesdites parties rectilignes étant sensiblement parallèles dans chaque domaine,
• on modélise chaque partie sensiblement rectiligne selon une première équation du type : kσ*+k'= 2*σ* = b2dρ/dε    en utilisant comme variable intermédiaire la densité de dislocation ρ telle que σ = µb √ ρ,
• et l'on effectue une intégration analytique de la première équation de façon à établir, au moins pour chacun des domaines II, III, une seconde équation de modélisation ε = -2/kb2 [Xsln(1-x/xs)+x] + λ en posant x = b √ ρ = σ/µ = σ* et x_s = - k'/k, λ étant une constante d'intégration,
• les paramètres k et k' étant déterminés, pour chacun des deux domaines II, III, à partir de la partie rectiligne d'une courbe du second diagramme d'écrouissage correspondant sensiblement à la température du métal et à la vitesse de déformation prévisibles à l'entrée de la cage.

The invention also covers a particularly advantageous method for exploiting the test results so as to establish the modeling equations. In such a method, from the results of deformation tests each carried out at a constant temperature and speed of deformation:

• a first work hardening diagram is established comprising a series of curves representative, for each temperature T, of the variation in the work hardening rate  = dσ / dε as a function of the flow stress σ,
• one transforms the numerical data relating to each curve to establish a second standard work hardening diagram comprising a series of curves representative of the variation, according to the normalized stress of flow σ * = σ / µ _(T) , of a intermediate quantity 2 * σ * equal to twice the product of said normalized flow stress, by the normalized work hardening rate  * =  / µ _(T) , µ _(T) being the elastic shear modulus at the considered temperature,
• said curves each having at least one substantially rectilinear part situated in at least one domain II, III of the diagram, and said rectilinear parts being substantially parallel in each domain,
• each substantially rectilinear part is modeled according to a first equation of the type: kσ * + k '= 2 * σ * = b 2 dρ / dε using as an intermediate variable the dislocation density ρ such that σ = µb √ ρ,
• and an analytical integration of the first equation is carried out so as to establish, at least for each of the domains II, III, a second modeling equation ε = -2 / kb 2 [X s ln (1-x / x s ) + x] + λ by setting x = b √ ρ = σ / µ = σ * and x _s = - k '/ k, λ being an integration constant,
• the parameters k and k 'being determined, for each of the two domains II, III, from the rectilinear part of a curve of the second work hardening diagram corresponding substantially to the temperature of the metal and to the rate of deformation predictable at l entrance to the cage.

In each area II, III of the diagram of hardening, the coefficients k and k 'of the first modeling equation can be determined by the calculator following a numerical regression method, from temperature and representative parameters the crystalline state of the metal at the entrance to the cage.

To take into account the evolution of the flow stress along the rolling right-of-way, it is divided into a series of successive sections M ₁ , M ₂ , ... M _i , ... M _p , each corresponding to an elementary deformation ε _i , and the computer determines before each pass, as a function of the rolling parameters measured at the entry of the stand, the predictable flow stress σ _i in each of said slices M _i by digital integration inverse of the second modeling equation as a function of the elementary deformation ε _i to be produced in the section considered M _i and deduces therefrom the elementary rolling force dF _i to be applied in said section M _i , the overall rolling force being calculated by integration said elementary forces along the right-of-way.

The invention also covers many other advantageous features which are the subject of the subclaims.

It should be noted that, because it allows to calculate precisely, and at any time of rolling, the value predictable flow constraint, the process according to the invention can be integrated at several levels into the rolling process.

In particular, the rolling parameters being measured during each rolling pass, the computer can check whether the overall rolling force calculated in as a function of the thickness reduction provided for in the diagram lamination is compatible with the capacities of the installation and if said expected thickness reduction uses, so said capacities and modify, if necessary, the rolling scheme for the following passes.

But the invention will be better understood by the following description of a particular embodiment, given by way of example and illustrated by the accompanying drawings.

Figure 1 shows schematically a cage of rolling associated with tightening control means according to the invention.

Figure 2 schematically illustrates the process of rolling of the product between two working rolls.

Figure 3 is a diagram showing the evolution of the flow stress of the rolled metal as a function of the deformation in the grip.

Figure 4 is a diagram showing the evolution of the rate of work hardening of the metal in the grip in function of the flow stress.

Figure 5 is a work hardening diagram illustrating a new representation of the evolution of flow conditions in the right of way.

Figure 6 illustrates the use of the diagram of hardening for the establishment of the equations of modelization.

Figure 1 shows schematically a cage rolling 1 consisting, as usual, of two spread columns 11 connected by crosspieces not represented and between which are placed several superimposed cylinders. In the example shown, the cage is quarto type and therefore includes two working cylinders 12, 12 'defining an air gap 10 of the passage of the product 2 to laminate and resting on the side opposite the product, respectively on two additional support cylinders 13, 13 ' large diameter. Each cylinder is rotatably mounted at its ends, on two pins carried by bearings mounted in chocks, respectively working 14, 14 ' and support 15, 15 '. These are threaded in windows provided on the two columns 11 of the cage and provided with guide faces along their sides from which slide the chocks of the cylinders, parallel to a clamping plane P in which are placed substantially the axes of the cylinders.

The cage 1 is also associated with means product progress, for example, two roller tables 16, 16 'placed on either side of the cage in the case a reversible rolling mill. The rollers of the table rollers 16 placed upstream are rotated by in order to control the progress of product 2 which commits between the working cylinders 12 or 12 'and is driven by friction in the air gap 10. After reduction of its thickness, product 2 is received by the roller table downstream 16 '.

Of course, the difference between the width of the air gap and the initial thickness of the product must be limited to avoid a refusal of engagement given the diameter of the cylinders 12, 12 'and of the thrust force exerted by the roller table 16.

The rolling of product 2 tends to spread the working cylinders which rest on the cylinders of support 13, 13 '. To maintain the spacing, the cage is therefore provided with clamping means, for example jacks hydraulic or mechanical 17, mounted on each column 11 and bearing on the chocks 15 of the support cylinder upper 13, lower support chocks 15 ' can be simply supported by shims 18.

Preferably, the clamping means are jacks hydraulics 17 conventionally supplied by a circuit globally identified by reference 3, associated with a servovalve 31 controlled by a regulator 32. The regulator 32 is associated with position sensors 33 and position sensors pressure 34. In this way, the clamping means 17 can be controlled in position and pressure, so that determine, on the one hand the spacing e of the generators supporting working cylinders 12, 12 'determining the thickness of the air gap 10 and, on the other hand, the maintenance the spacing chosen during rolling, by application, between the cylinders, a clamping force called the force of rolling, which can be measured by the sensor 34.

In known manner, the spacing of the cylinders can also be regulated by separate cylinders, the cylinders clamping 17 then essentially serving to apply the rolling force to maintain the gap.

Furthermore, the cage 1 is also provided with other sensors for measuring the various rolling parameters, by example of pyrometers 35, 35 'for temperature measurement of product 2, respectively before entering the cage and after leaving it, as well as means 36 of measurement of the speed of rotation of one of the cylinders work, to determine the speed of advancement of the produced in the right-of-way between the cylinders.

The signals from all the sensors and corresponding to the measurements carried out are displayed in inputs of a measurement unit 4 which includes a calculation capable of developing a control signal from the regulator 32 for controlling the clamping means of so as to adjust and maintain the desired spacing between the working cylinders 12, 12 '.

According to the invention, the calculation unit 4 comprises a calculator 40 associated with a programmed mathematical model of in order to calculate very precisely the rolling force to apply, from modeling equations representative of the behavior of the metal and, in particular, of its flow conditions in the right of way between the cylinders.

FIG. 2 schematically illustrates the process of reducing the thickness of the metal product 2 between the two cylinders 12, 12 '. In general, the product 2 comprises an upstream part 21, of thickness e _x-1 , a central part 22 corresponding to the passage area between the cylinders which is limited by two contact arcs 20, 20 ', and a downstream part 23 having a thickness e _x which, in practice, is slightly greater than the spacing e ' _x of the working rolls 12, 12'.

The roller table 16 whose rollers are driven in rotation, determines the progress of the product to a speed V1 of engagement in the rolling mill. The end front of product 2 then comes into contact with the two cylinders 12, 12 '. The friction between the cylinder wall and the product determines its engagement in the grip between the cylinders, with thickness reduction and flow of metal. This results in a slight widening of the product but, essentially, an elongation of it, the amount of metal being retained. Therefore, the downstream part 23 of the product advances at a higher speed V2 to V1. The two cylinders 12, 12 'are rotated at a certain angular speed and, conventionally, we distinguishes a neutral point 24 of the product for which the tangential forward speed V3 is equal to the speed peripheral cylinders 12, 12 '. Along the two arches of contact 20, 20 'between the product and the cylinders, the tangential speed of advancement of the product therefore increases gradually from V1 to V2. It is lower than V3 in upstream of the neutral section 24 and higher than V3 downstream.

The value of friction at the interface between the product and the cylinders therefore varies throughout the arc of contact 20, the relative speed itself being variable and canceling out at the neutral section 24.

We know that the rolling force per unit of width can be calculated by the Sims relation: F = Q f .KL in which Q _f is a friction factor, L the length of the contact arc 20 and K a factor representative of the mean value of the flow stress σ of the metal during deformation.

The friction factor Q _f, which is a function of the ratio of the length L of the contact arc 20 to the average thickness h of the product, can be estimated with fairly good accuracy.

So we have Q f = f (L / h)

These quantities can be calculated in a known manner from the radius of the working rolls, from the thickness of product at the entrance of the cage and the spacing of cylinders at the exit of the right-of-way.

As indicated, due to a certain degree of elasticity of the metal, the outlet thickness e _x is slightly greater than the actual thickness e ' _x of the air gap between the cylinders, the difference being able to be determined in a known manner.

The K factor depends on the temperature, the composition of the product and its structure but we observed that it was also necessary to involve phenomena complexes such as the evolution of the microstructure metallic during deformation.

As indicated above, even in installations perfected, so far we have limited ourselves to putting in memory of the global parameters, determining the conditions deformation of the product depending on the nuance of steel, so as to establish a reference table of rolling conditions for a known steel. We could then use the same parameters when the same steels found in the installation production book rolling. However, for that, it was necessary to estimate the mean value of the flow stress σ for in deduce the factor K, so as to calculate the force of rolling by applying the Sims relation.

In addition, in the case of steels which have not been previously rolled, we could only proceed by approximation.

The object of the invention, on the contrary, is a new process in which the overall rolling force to be applied can be more accurately determined by giving them ways to take into account the evolution of the microstructure crystal of the metal during rolling to estimate the value of the flow stress σ of the metal at a time determined of the rolling.

For this, the depositor has conducted studies metallurgical very advanced with a large number laboratory experiments that have led to a new representation of the representative parameters of the intimate evolution of the microstructure of steel, allowing a modeling of this evolution according to overall rolling objectives (thickness reduction, flatness, temperature), this representation leading to modeling equations programmed in the model mathematical and likely to be integrated by the computer 40 associated with the central 4 for controlling rolling mill actuators.

We were thus able to develop an adjustment process clamping means integrating modeling as well developed to apply the force between the cylinders exactly needed.

In addition, such a method also makes it possible to adapt the rolling scheme under the conditions observed at each pass and thus follow an optimal rolling pattern.

The method according to the invention makes it possible to take account changes in the metal flow conditions, a part during successive passes and on the other hand, the along the right-of-way, in the same pass.

To this end, the rolling area is divided into a series of p adjacent elementary slices M ₁ , M ₂ , ... M _i , ... M _p . As shown diagrammatically in FIG. 2, each elementary section M _i corresponds to an elementary length of advance l _i of the product between the cylinders, with an elementary deformation ε _i which is defined, in known manner, from the reduction of thickness e _i-1 -e _i to be carried out in the section considered, e _i-1 being the thickness of the entry section of the section and e _i the exit thickness.

According to the temperature T of the metal, the deformation ε corresponding to the thickness reduction requested at the level considered of the grip and the speed of deformation ε ˙ = dε / dt, various metallurgical phenomena can occur during the advancement of the product in the right of way.

These phenomena, which have been described in various recent studies, can be summarized as follows:

First of all, we note that the metal hardens which translates into an increase in its dislocation density ρ. This quantity, which can be measured on a sample metallic using an electron microscope in transmission, represents the cumulative length, per unit of volume of metal, linear crystal defects called dislocations.

We know that the dislocation density, which is commonly evaluated in meters per cubic meter, is linked to the flow stress σ by the Taylor relation: σ = µb √ ρ where b is a constant and µ is the elastic shear modulus of the metal. We know that this module depends on the temperature T of the metal and is given by the formula µ (T) = E (T) / 2 (1 + ν) in which E (T) is the elastic modulus called Young's modulus and ν the Poisson's ratio.

Then we observe that, very quickly, while work hardening continues, there is also a so-called restoration phenomenon, which tends to decrease the dislocation density ρ by mutual annihilation of neighboring dislocations.

In addition, for most steels, it can produce, beyond a certain deformation, a phenomenon called dynamic recrystallization, which tends to decrease the dislocation density ρ.

So we had the idea that taking into account these phenomena, we could analyze the behavior of metal at during a deformation so as to deduce an estimate fairly precise predictable value of the constraint of flow, which is the first factor on which the rolling force and which is constantly changing from one pass to the next and even during a pass, along the right-of-way passage of the product between the cylinders.

It is precisely this evolution which had not taken into account so far, the rolling force being calculated from an average value of the flow stress appreciated overall for the whole of the right-of-way.

The invention makes it possible, on the contrary, to take account of the variation of the flow stress linked to the evolution of the microstructure during rolling and therefore provides the means to estimate much more specifies that previously the rolling force to be applied for obtain and maintain the desired thickness reduction at each pass.

For this, we studied in depth the behavior of steel when drawing curves from which we were able to establish modeling equations likely to be implemented in a mathematical model associated with a calculator control of the rolling mill so that it can calculate the rolling force to be applied for each pass in function of a set of estimated or measured parameters.

The steps of the method according to the invention are illustrated in Figures 3 to 6.

The evolution of the flow stress σ comes out of the diagram of figure 3 which indicates, for different temperatures T1, T2, ..., variations in the current value in the grip of the flow stress σ, indicated in ordinate, according to the cumulated deformation ε indicated on the abscissa assuming, which is close to reality, that the deformation ε and the temperature T vary at velocities, respectively ε ˙ = dε / dt and T ˙ = dT / dt substantially constants along the right of way.

The curves in Figure 3 were established from laboratory experiments, for example tests of homogeneous hot compression performed at temperatures T1, T2 ... on test pieces of the same metal.

It has been observed that, to account for behavior of metal, it was interesting to use, as a variable intermediate, the rate of work hardening  = dσ / dε which, for a given deformation and temperature, corresponds to the slope of one of the curves in Figure 3.

To interpret the physical phenomena managing the metal deformation, so we will draw a first diagram of work hardening representing the evolution of the rate of work hardening  as a function of the flow stress σ.

However, we prefer to use the standardized quantities  * =  / µ (T) and σ * = σ / µ (T) µ _(T) being the elastic modulus as defined above.

Figure 4 gives an example of this first diagram work hardening, each curve representing the variation of normalized rate of work hardening  * according to the stress of normalized flow σ *, for a temperature T and a constant strain rate ε ˙.

It can be seen that the shape of the curves thus obtained changes when the rate of deformation and the temperature vary.

For the implementation of the invention, we then had the idea of transforming the digital data that allowed to obtain the curves of figure 4, by a change of variable likely to lead to usable curves for simple modeling in a computer.

It appeared, in fact, that it is particularly advantageous, to use as an intermediate variable the product 2 * .σ * of twice the rate of work hardening normalized by the normalized flow stress.

We thus obtain a second work hardening diagram, represented in figure 5, which indicates the variation of the size 2 * .σ *, indicated on the ordinate, depending on the normalized flow stress σ * indicated on the abscissa.

As before, we place ourselves at temperature and constant strain rate, the transformation being performed for each curve.

By way of example, on the second work hardening diagram of FIG. 5, one indicated at the top right the strain rate ε auxquelles and the temperature T to which correspond the curves of the diagram. There are thus different groups of experimental curves. For example, on the diagram, we have drawn differently, four curves 51, 52, 53, 54 corresponding, respectively, to temperatures of 885 ° C, 935 ° C, 985 ° C, 1035 ° C, for the same strain rate ε ˙ = 3.6 s ^-1 and five curves 50 ', 51', 52 ', 53', 54 ', 55', corresponding respectively to temperatures of 835 ° C, 885 ° C, 935 ° C , 985 ° C, 1035 ° C, for a deformation speed ε ˙ = 0.36 s ^-1 ten times less.

We note that, particularly advantageous in this new field of representation (2 * .σ *, σ *), each curve has at least two parts practically rectilinear, these rectilinear parts being, in each area, substantially parallel to each other.

As shown in Figure 6, we can thus distinguish, in the second hardening-strain diagram, two domains II and III which cover the most large part of the useful range of deformation and in which the magnitude 2 * .σ * varies significantly linear as a function of the flow stress normalized σ *. The nonlinear domain IV corresponds to the appearance and development of recrystallization dynamic.

Of course, each type of steel corresponds to a specific diagram and in each diagram each curve and therefore each line corresponds to a temperature and at a determined rate of deformation but interpolations are possible.

To model these curves, it is advantageous to take the density of dislocation ρ defined above.

Indeed, the differentiation of equation (3) called Taylor gives: dσ / dρ = µ.b / 2 √ ρ from which we can draw:  * = dσ / µdε = b / 2 √ ρ.dρ / dε As σ * = σ / µ = b √ ρ, we have: 2 * σ * = b 2 dρ / dε

Given that in each of the two areas II and III of figure 6, the quantity 2 * σ * varies so substantially linear as a function of σ *, the straight lines of the figure 6 can roughly be substituted for curves of figure 5.

These curves being substantially parallel, we can write the equation of the lines in the following linear form: 2 * .σ * = b 2 dρ / dε = kσ * + k ' which constitutes a first equation for modeling the behavior of the metal, in which the constants k and k 'can be taken from the diagram in FIG. 6, k being the slope of the line representative of the curve considered and k' a constant.

The two families of lines corresponding to the steel considered, which have different slopes, respectively k _II and k _III for each of the two domains II and III where the behavior is linear, are therefore represented by equations which can be programmed in the mathematical model associated with the computer 40. The latter can then, by known mathematical methods, carry out an analytical integration of equation (9) which leads, for each domain II, III to an expression of the deformation ε of the form: ε = -2 / kb 2 (x s l not (1-x / x s ) + x) + λ by asking : x = b √ ρ. = σ / µ = σ * and x s = -k '/ k, λ being a constant of integration.

The initial value of the flow stress in domain II and the continuity at the junction points between two corresponding straight lines in domains II and III makes it possible to determine the values of the integration constants λ _II and λ _III corresponding respectively to domains II and III.

It should be noted that, for simplicity, the law of evolution has been made to depend on a minimum set of four parameters k _II , k _III , x _s2 , x _s3 (11).

However, these parameters could be more many, so as to take into account the relationships between them.

Each work hardening diagram, established from test results, corresponds to a steel of composition determined.

By way of example, the diagrams in FIGS. 3 to 6 have been drawn up experimentally for a steel having the following composition, in percentages by weight:
C: 0.08; Mn: 1.1; If: 0.25; Fe: the rest.

We see in Figure 6 that, for example in the domain II, for each strain rate ε ˙, we can establish the equations of a family of parallel lines 61, 62, 63, 34 corresponding to various temperatures of deformation, 885 °, 935 °, 985 ° and 1035 °.

The same is true - in area III and for other rates of deformation.

In the description of the process which follows, it is assumed that, knowing the composition of the steel to be rolled, we have could, from preliminary tests, determine the equations modeling corresponding to the behavior of this steel for certain strain rates and at various temperatures. These modeling equations are therefore implanted in the mathematical model associated with calculator 40 which can thus, for a product consisting of the same metal, define the applicable modeling equation at a considered time of rolling, taking into account the speed deformation and temperature of the product at this time.

The parameters (11) on which the law of evolution depends of the model can be identified from tests, by example of homogeneous hot compression performed in laboratory, each at deformation speed and constant temperatures, so as to determine the curves representative stress-strain studies of behavior of steel under these conditions.

As indicated above, the parameters k _II , k _III , which are the slopes of the lines being used for the modelization of the law of hardening, respectively in domains II and III depend only on the composition of the steel and its grain size, ie the crystalline state which the metal has reached after the various successive rolling passes.

The parameters x _s2 , x _s3 depend, moreover, on the strain rate ε ˙ and on the temperature T.

After determining the parameters (12), the equations (10) and (11) representative of the metal to be laminated and implanted in the mathematical model will allow the computer (40) to adjust the clamping means in proceed as follows:

• la force de laminage appliquée entre les cylindres qui est donnée par une mesure de pression dans les vérins de serrage 17 ou bien par une cellule de mesure de force associée aux cales 34 ;
• l'entrefer exact des cylindres de travail donné par le capteur de mesure de position 33 associé aux dispositifs de serrage ;
• la température du produit à l'entrée et à la sortie du laminoir, donnée par les capteurs 35, 35' ;
• la vitesse réelle de laminage donnée par un capteur de mesure 36 installé sur l'arbre moteur de la cage et indiquant la vitesse angulaire des cylindres de travail.

As indicated, the rolling mill is equipped with sensors which make it possible, during each rolling pass, to measure the following quantities in real time:

• the rolling force applied between the rolls which is given by a pressure measurement in the clamping cylinders 17 or by a force measuring cell associated with the shims 34;
• the exact working air gap given by the position measuring sensor 33 associated with the clamping devices;
• the temperature of the product entering and leaving the rolling mill, given by the sensors 35, 35 ';
• the actual rolling speed given by a measurement sensor 36 installed on the drive shaft of the stand and indicating the angular speed of the working rolls.

In addition, the rate of deformation of the metal can be determined at each point of the right-of-way, depending on the reduction in thickness to be carried out and the speed of rolling.

In practice, as shown in FIG. 2, the computer 40 will divide the right-of-way 20 into a series of sections M ₁ , M ₂ ..., M _i ..., M _p . For each slice M _i , it determines the thickness reduction to be carried out ε _i = e _i-1 -e _i and the rolling speed at the considered location of the right-of-way, and can deduce therefrom the strain rate ε ˙ _i .

Knowing the product temperature at the entry of the cage and the deformation conditions, the mathematical model can estimate the product temperature and the rate of deformation in the section M _i considered to deduce the right of the diagram of FIG. 6 and , the modeling equations (9, 10) applicable in this section, by making the interpolations necessary to take into account the temperature and the speed of deformation when these do not correspond to those of the tests.

By inverse numerical integration of the second modeling equation (10), for example using the finite difference method, the computer can determine, for each slice M _i , the predictable value σ _i of the flow stress corresponding to the deformation elementary ε _i to be produced and then draw from it the estimated value of elementary rolling force dF _i to be applied in said slice M _i .

Knowing thus the elementary rolling force in each of the sections of the right-of-way, the computer can then, by integration, determine the overall rolling force F _x to be applied to the whole of the right-of-way by the clamping means 27 during the pass x.

Furthermore, all the physical and mechanical characteristics of the various members of the cage as well as the conditions of elastic deformation of the latter have been programmed in the computer. The latter can therefore, from the overall rolling force F _x thus calculated, determine the predictable yielding effect during this pass and control the adjustment of the clamping means 17 so as to compensate for this yielding.

Likewise, the calculator takes into account mechanical and physical characteristics of the product, in particular of its elasticity, to determine the slight increase in the thickness of the product that is produced, known manner, at the exit of the rolling mill.

Taking all these factors into account, the computer can therefore very precisely determine the air gap e ' _x which will have to be adjusted and maintained between the working rolls 12, 12' to obtain the desired thickness reduction e _x-1 -e _x and controlling, during the pass considered, the adjustment of the clamping means, so as to apply between the rolls the rolling force actually necessary to maintain this air gap.

As indicated, the work hardening diagrams for establishing the modeling equations, are established from test results.

When we know in advance the composition of the metal to be laminated, testing is possible required on test pieces of this metal. The equations established for a metal can, moreover, be put memory to be used when comes back in produces a previously rolled metal.

However, when you have to laminate a new metal, it is often not possible to establish, in the way which has just been indicated, modeling equations whose parameters have values specific to metal the mine.

To avoid testing every time we have to laminate a new metal, so we developed methods for using established equations previously and already present in the mathematical model.

These methods are based on the fact that, for metals of the same type, the general shape of the curves of the work hardening diagram, which illustrates the behavior of metal during deformation, remains similar and that the equations of lines corresponding to these curves and established for one metal can be adapted to another metal by simply correcting the parameters (12).

In practice, we will therefore carry out tests on a metal-type representative of a family of metals having a analogous behavior, to diagram work hardening such as that of Figures 5 and 6, in order draw the modeling equations (10) and (11) representative of this metal, which are implanted in the mathematical model.

Then, when you have to roll a metal from the same family but of different composition, just wedge the model on this new metal and it is preferable keep it as fast as possible.

In a first method according to the invention, we performs tests on a selection of steels beforehand representative of a chemical composition domain for which one wishes to calibrate the model with, for each of them, different values of initial grain size, which determine the starting state of the microstructure of the metal. In addition, tests are carried out for different values temperature and strain rate so that cover an area of demand corresponding to efforts developed during the different passes of rolling and for which the model is established.

From the results of the tests thus carried out on test pieces, the work hardening diagrams are established correspondents which are similar to those of FIGS. 4 and 5. The modeling equations specific to each of the steels can then be calibrated by determining, by known numerical regression techniques, the game (12) of four parameters of the hardening law applicable to the steel considered.

These mathematical methods of numerical regression are applied, in the field studied, to empirical laws involving the chemical composition and the grain size as well as the temperature and the rate of deformation for the parameters x _s2 , x _s3 .

The calculated values of these parameters, from domain III modeling can be changed to take into account, in area IV, the appearance of dynamic recrystallization.

We thus calibrated the model on a domain of composition covered by the various steels for which tests could be carried out.

When the steel to be rolled has a composition different while staying in the field on which is rigged the model it is possible, using, for example, Choquet's phenomenological model of determining the initial grain size and infer from it, by methods known, the corrections to be made to the coefficients of the work hardening law to adapt it to the steel to be rolled.

It should be noted that these operations are carried out by the calculator and that the model can therefore be calibrated very quickly when a new steel arrives in production, from when it falls within the composition domain covered by the tests carried out beforehand.

When the steel to be rolled has substantially the same composition as one of these steels, it suffices, for each pass, determine the right of the model corresponding to rolling conditions,

We will see, however, later how these tests can also be replaced by rolling passes set manually.

Equations (9) and (10) of the mathematical model being thus wedged on the metal to be laminated, the calculator will now able to adjust the clamping means by proceeding as follows :

Such a calibration method is valid in the most cases because we generally know in advance the production program and we were therefore able to necessary tests.

However, the way the model takes into account the evolution of the metal structure also allows implement a simpler calibration method, by particular for laminating products made of steel leaving the field of chemical composition for which the model had been programmed.

In this other method, tests on test pieces are simply replaced by the first passes of rolling carried out on the product to be rolled with a setting manual.

Indeed, a rolling installation being always planned for a certain type of product, the model math associated with the computer could be programmed, as indicated above, from tests carried out on a typical metal.

At the start, we make the first passes of rolling by manually adjusting the rolling mill and measuring, in real time simply compares the rolling parameters applied.

By the numerical regression methods recalled higher and using the Choquet model, we can determine the parameters of the equations applicable to thus laminated product.

The programmed equations are thus calibrated on the new metal depending on the behavior of it in rolling course, from the indications given by the passes manually adjusted.

The process which has just been described therefore makes it possible to determine with great precision, before each pass of rolling, the air gap to maintain and the rolling force to apply by the clamping means, taking into account, not only of the nature of the product and its dimensions but also of the state of the metal following the previous pass, as well as the foreseeable variation of the stress flow along the right-of-way, during the pass. However, the invention also has other advantages.

Indeed, the differential equations (10) and (11) established as indicated above, allow, in because of their linear nature, to link in the two sense the deformation ε to the flow stress σ because they can be integrated in a sense, analytically, to express the deformation according to the stress, and the other way, digitally, to connect the strain stress.

It follows that the method, object of the invention, can be integrated on several levels in the process of rolling.

In particular, we have seen that, the real parameters of rolling and, in particular, the force applied between the cylinders, exact air gap, product temperature at the input and output and the rolling speed are continuously measured by the sensors installed on the rolling mill.

From these indications and using the equations programmed in the mathematical model, the computer can therefore recalculate the force to be applied between the cylinders under actual rolling conditions observed to compare it with the force measured during the same rolling pass. This comparison allows a adaptation of the game (12) of the parameters of the law of evolution defined by modeling equations and recalculate with these readjusted coefficients, the adjustment of the rolling mill for the next pass, and so on, for each pass of the rolling scheme initially planned by the strategy.

If there are too large differences, the measurements carried out then make it possible to modify the values retained during laboratory tests for recalculate the entire thickness reduction strategy of the product and establish a new rolling scheme.

Therefore, for each reduction of the thickness, the model can take into account the measurements performed during rolling to introduce factors of correction to the values of the parameters of the law evolution predetermined by laboratory data. Of more, if significant differences are found, the method according to the invention allows the calculation of the rolling diagram in order to modify it for the passes of reduction remaining to be executed, this readjustment operation and of verification being carried out during each pass of rolling until the final thickness is obtained.

The method according to the invention is therefore applicable successively at the start of rolling then, at each step, by determining both the precision of the tolerances of the manufactured product as well as the optimization of the use of the industrial production tool.

Indeed, the process can be integrated into the strategy for calculating the rolling scheme using a method iterative optimization taking into account the data general of the installation and those of the product.

In such a method, before rolling, the computer 40 receives general data relating to product entering the rolling mill, the chemical composition of steel, gross product thickness, temperature at the entrance to the rolling mill, the final thickness targeted, etc. that the predictable flow stress and the force of lamination to be applied to achieve thickness reduction data can be accurately calculated it's possible, at each pass, to check if the reduction of thickness provided for by the rolling scheme leads to a excessive rolling force, requiring a decrease in this reduction in thickness or, on the contrary, if we can achieve greater thickness reduction leading to an acceptable rolling force.

Therefore, taking into account the power available on the rolling stand (s), forces possible and target final thickness targets, the calculator associated with the mathematical model can adapt the rolling scheme so as to use the capabilities of installation in optimal conditions, the model can effectively take into account, on each pass, the state of the product leaving the previous pass.

Of course, the invention is not limited to details of the embodiments which have just been described, the process being adaptable to the circumstances in remaining within the protection framework defined by the claims. In particular, it is only for example that the figure shows a quarto rolling mill, the process being applicable in the same way to a duo, a sexto or any other type of hot rolling mill. Likewise, the invention has been described for a rolling stand, but is applicable in the same way to all cages, reversible or not, a hot rolling installation, these cages can be insulated to constitute the rougher of a train to strips, hot or work in tandem, for example to constitute the finisher of the band train, or form a unit operating in continuous tandem.

In addition, for simplicity, we have established equations modeling dependent on only four parameters, but that these could be more numerous.

Besides, the idea of the invention being to estimate the metal flow stress using the knowledge acquired on the behavior of metals, such that the Taylor and Sims relationships or the Choquet model, we could obviously take advantage of the evolution of these knowledge to improve or modify the process by taking into account, in another way, the evolution of metal structure during deformation.

Likewise, other calculation methods could be imagined to solve numerically the equations of the law of evolution. In particular, we could use, for the adjustment model, a method direct calculation of the flow stress without taking as an intermediate variable the density of dislocation. Other methods of experimentation, other than hot compression, but to determine the stress as a function of strain could also be used.

The reference signs inserted after the technical characteristics mentioned in the claims are intended only to facilitate the understanding of them and in no way limit them the scope.

Claims (19)

Method of rolling a metal product by successive passes in an installation comprising: a holding cage (1) having two spaced apart columns (11), at least two superimposed working rolls (12, 12 ') between the columns of the cage, means (16) for controlling the progress of the product (2) with rolling of the latter in a rolling grip (22) delimited by two arcs of contact (20, 20 ') of the product (2) with the two cylinders (12, 12 '), between an inlet section and an outlet section of the right-of-way (22), clamping means (17) bearing, respectively, on the cylinders and on the cage (1), for adjusting a spacing (10) between the working cylinders (12, 12 ') corresponding to a reduction in thickness to be produced and for maintaining said spacing during the rolling pass, by application, between the working rolls (12, 12 ′), of a rolling force which depends on the mechanical and physical characteristics of the stand (1) and of the product (2) and of the flow conditions of the metal in the rolling area, and determines a yielding effect of the various members of the cage tending to increase said spacing, means (31, 32), controlled by a calculating unit (4) comprising a calculator (40) associated with a mathematical model, for adjusting the clamping means, characterized by the fact that, before each pass (x), the calculation unit (4) associated with the mathematical model (40) determines a predictable value of the metal flow stress corresponding to the deformation to be carried out in the pass ( x) considered, taking into account the evolution, during rolling, of the microcrystalline structure of the metal constituting the product (2) to be laminated, and that the rolling force (F _x ) to be applied to obtain the reduction of desired thickness (e _x-1 -e _x ) is calculated before each pass (x) as a function of the value thus predicted of the flow stress and of the development thereof during rolling. Laminating process according to claim 1, characterized in that the rolling force (F _x ) to be applied for a rolling pass (x) is calculated taking into account the foreseeable variation along the right-of-way (22) , of the metal flow stress during said pass (x). Laminating method according to claim 2, characterized in that, in order to take account of the variation in the flow stress, the laminating area is divided into a series of p adjacent elementary slices (M _i , M ₂ ,. ..M _i , ... M _p ), each corresponding to an elementary length of advancement of the product between the cylinders, with an elementary deformation (ε _i ) of the product in each section (M _i ) between an inlet section of thickness (e _i-1 ) and an output section of thickness (e _i ), which, from the indications given by the mathematical model, the computer (4, 40) determines, for each slice (M _i ) , a predictable value (σ _i ) of the metal flow stress, corresponding to said elementary deformation (ε _i ) and deduces from it the elementary rolling force (dF _i ) to be applied in the section considered (M _i ) to achieve said elementary deformation (ε _i ) and that, by integration of the f elementary orces (dF _i ) in the successive sections (M ₁ , M ₂ , ... M _i , ... M _p ), the computer determines the overall rolling force to be applied to achieve the desired thickness reduction, and control, as a function of the overall force thus calculated, the adjustment of the clamping means (17) for maintaining the spacing (e ' _x ) of the cylinders (12, 12') allowing the reduction in thickness ( e _x-1 -e _x ) desired, taking into account the conditions of flow of the metal along the right-of-way and the yielding effect resulting from said overall force. Method according to one of claims 1, 2, 3, characterized in that the rolling force (F _x ) to be applied during a pass (x) is determined taking into account the foreseeable value of the stress d flow of the metal resulting from the evolution of the microcrystalline state of the metal during the previous passes. Laminating method according to one of claims 1 to 4, in which the lamination is carried out according to a lamination scheme making it possible to achieve, in n successive passes, an overall thickness reduction (e _o -e _n ), each pass (x) rolling making a reduction in thickness (e _x-1 -e _x ),
characterized by the fact that the calculating unit (4, 40) calculator determines, by iteration, the rolling scheme to be observed by calculating in advance, for each pass (x), the maximum thickness reduction leading to a foreseeable rolling force Fx compatible with the capacity of the rolling mill (1), as a function of a set of rolling parameters comprising the thickness and temperature of the product (2) and its speed of advance before entering said pass (x), so as to take into account the foreseeable evolution of the microstructure of the metal from one pass to the next and along the right-of-way, during the pass (x) considered. Laminating process according to claim 5, characterized by the fact that the calculation unit (4) is associated with means (34, 35, 36) of permanent measurement, during the pass, effective values of a set rolling parameters including the rolling force applied at all times, the forward speed of the product (2) and the temperature thereof respectively at the entrance and exit of the rolling mill (1) and that, at each pass (x), the calculation unit (4) compares these values values measured at the values of said parameters taken into account initially counts for said pass (x) in the determination of the rolling pattern, so as to resume calculation thereof and introduce, if necessary, correction factors to the parameters taken into account, so to adapt the rolling scheme in the following passes. Laminating method according to one of claims 3 to 6, characterized in that the predictable value (σ _i ) of the flow stress in each section (M _i ) of the rolling area (22) is determined by the calculation unit (4, 40) as a function of the position in the right-of-way (22) of the section considered, taking into account the temperature of the metal measured before the product (2) enters the rolling stand ( 1), the speed of deformation in said slice (M _i ), and the evolution of the crystalline state of the product during rolling, in the preceding passes and along the grip during the pass considered (x). Laminating method according to one of previous claims, characterized in that, to take into account the evolution of the structure microcrystalline of the metal during rolling, it is established at least one modeling equation valid for a family of metals with microcrystalline behavior similar, from hot deformation tests carried out on test pieces of at least one standard metal of this family, said equations depending on a set of parameters related to the composition of the standard metal, we implant the initial equations thus established in the model mathematical and, for the rolling of a product of a metal of the same family as the standard metal, we wedge the model on the metal to be laminated by modifying the parameters said theoretical equations as a function of results deformation tests carried out on a metal having a composition at least close to that of the metal to be laminated. Laminating process according to claim 8, characterized by the fact that to define the equations of modeling, an intermediate quantity linked to the rate of deformation of the metal and varying so substantially linear as a function of the constraint flow in at least one deformation domain (II) and, from deformation tests carried out for a series temperatures and strain rates maintained constants, one establishes a work hardening diagram on which the variations of said intermediate quantity can be represented approximately, in said area of deformation (II), by at least one family of straight lines (61, 62 ...) to which at least one equation corresponds differential of linear form, linking the deformation to the flow constraint and can be integrated by the computer (40). Laminating process according to claim 9, characterized in that, from the diagram work hardening, one establishes at least two equations differentials linking deformation to stress of flow, respectively a first form equation linear giving by analytical integration, an expression deformation as a function of flow stress and a second equation capable of being integrated numerically to determine the flow stress predictable corresponding to a deformation to be carried out. Laminating method according to one of Claims 8 to 10, characterized in that the modeling equations are established from results of hot deformation tests carried out at various temperatures and at various strain rates held constant for each test, over a series of specimens of at least one metal having a composition at less close to that of the product to be laminated. Laminating method according to claim 11, characterized by the fact that the modeling equations are established from homogeneous compression tests at hot carried out on test pieces. Laminating method according to one of Claims 11 and 12, characterized in that the modeling equations are established from several series of hot deformation tests carried out on several series of metallic test pieces having, in each series, a specific composition, the compositions different series being chosen so as to cover a selection of metals representative of a field of composition on which the model is set, with values different initial grain sizes, and testing being performed, for each series, at different temperatures and strain rates representative of a area of stress on which the model is calibrated, taking into account foreseeable rolling conditions. Laminating method according to one of Claims 8 to 10, characterized in that the modeling equations are initially established for a metal-type and implanted in the mathematical model and that, to calibrate said equations on the metal to be laminated, we first performs at least one rolling pass of at least at least one product consisting of the metal to be laminated, in at least a rolling stand (1) conventionally adjusted by measuring, during each pass, on the one hand the force of rolling actually exercised and, on the other hand, the parameters rolls used by the calculation unit (4, 40) calculator to determine, using the equations of initial modeling, the rolling force to be exerted theoretically and, by a numerical regression method, the modifications to be made to the parameters are determined said initial equations to obtain equations of specific modeling of the metal to be laminated. Laminating method according to one of Claims 8 to 14, characterized in that, from deformation test results each carried out at constant temperature and strain rate, we determines at least one deformation domain (II, III) for which we can establish a first modeling equation of linear form giving the expression of the variations of a intermediate function of the flow stress linked to the rate of deformation and from which determines, by analytical integration, a second equation modeling giving, in said field (II, III), a expression of the strain as a function of the stress of flow and, by reverse digital integration of said second equation, the calculator determines, as a function of the deformation to be carried out and for each pass, taking into account rolling parameters at the entrance of the cage, the value predictable of the metal flow stress and deducts the rolling force to be applied to achieve said deformation. Laminating process according to claim 15, characterized in that, on the basis of the results of deformation tests each carried out at a constant temperature and speed of deformation, a first work hardening diagram is established comprising a series of curves representative, for each temperature T, of the variation in the work hardening rate  = dσ / dε as a function of the flow stress σ, one transforms the numerical data relating to each curve to establish a second standard work hardening diagram comprising a series of curves representative of the variation, according to the normalized stress of flow σ * = σ / µ (T), of a intermediate quantity 2 * σ * equal to twice the product of said normalized flow stress, by the normalized work hardening rate  * =  / µ _(T) , µ (T) being the elastic shear modulus at temperature considered, said curves each having at least one substantially rectilinear part located in at least one domain (II, III) of the diagram, and said rectilinear parts being substantially parallel in each domain, each substantially rectilinear part is modeled according to a first equation of the type: kσ * + k '= 2 * σ * = b 2 dρ / dε using as an intermediate variable the dislocation density ρ such that σ = µb √ ρ, and an analytical integration of the first equation is carried out so as to establish, at least for each of the domains (II, III), a second modeling equation ε = -2 / kb 2 [X s ln (1-x / x s ) + x] + λ by setting x = b √ ρ = σ / µ = σ * and x _s = - k '/ k, λ being an integration constant, the parameters k and k 'being determined, for each of the two domains (II, III), from the rectilinear part of a curve of the second work hardening diagram corresponding substantially to the temperature of the metal and to the speed of foreseeable deformation at the entrance of the cage. Laminating method according to claim 16, characterized in that, in each of the areas II, III of the work hardening diagram, the coefficients k and k 'of the first modeling equation are determined by the calculator following a numerical regression method, from temperature and representative parameters the crystalline state of the metal at the entrance to the cage. Laminating method according to one of claims 15 to 17, characterized in that, the rolling area being divided into a series of successive slices M ₁ , M ₂ , ... M _i ... M _p each corresponding at an elementary deformation (ε _i ), the computer determines before each pass, as a function of the rolling parameters measured at the entrance to the stand, the predictable flow stress (σ _i ) in each slice (M _i ) of l 'grip by inverse digital integration of the second modeling equation as a function of the elementary deformation (ε _i ) to be produced in the section considered (M _i ) and deduces therefrom the elementary rolling force dF _i to be applied in said section M _i , the overall rolling force being calculated by integrating said elementary forces along the right-of-way. Laminating method according to one of previous claims, characterized in that, at during each rolling pass, the parameters of rolling are measured continuously so as to check whether the overall rolling force calculated as a function of the thickness reduction foreseen by the rolling scheme is compatible with the capacities of the installation and if said planned thickness reduction optimally uses said capacities, the computer modifying, in the event of need, the rolling scheme for the following passes.

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