EP0709152B1 - Forming thin metallurgical products between two cylinders - Google Patents

Abstract

The appts. incorporates two cylinders (10, 11) installed in bearings (13, 14) on a frame (16). Each cylinder is provided with means (22) for measuring the position of its generatrix located diametrically opposite to the gap at three or more points in parallel planes (P1, P3, P5), and means (23) for measuring the position of its generatrix in the middle plane (P3) at an angle of 90 degrees relative to the gap. These measurements are used for continuous determination of the gap between the cylinders while the installation is in operation, with possible cylinder deformations taken into account.

Description

The present invention lies in the field of the manufacture of metal products, in general of flat and thin shape, such as steel strips or other metals, by shaping the product during passage between two cylinders of axes substantially which exert a compressive force on the product according to the preambles of claims 1 (method) and 7 (device) which are based on for example JP-A-61078537.

It applies more particularly to casting continuous of metals and alloys between two cylinders, at during which a strong heat exchange occurs between the cast metal and the cylinders energetically cooled which constitute two walls of the receiving mold molten metal, and also applies to other forming processes, for example rolling.

One of the major problems for obtaining a quality product is to know practically in permanently the air gap of the cylinders, to be able to act on thickness and convex regulations allowing to obtain a product of good geometric qualities, ie having a section of shape and dimension desired and constant over the length of the product.

By the expression "air gap of cylinders", we will designate thereafter not only the distance average separating the cylinders at the neck between these (narrowest passage, located in the plane common to the axes of the two cylinders), but also the form of passage to the collar, which is generally not exactly rectangular, either voluntarily, in the goal of obtaining a product with a slight bulge transverse, either due to the deformations of installation and cylinders.

• un écartement des cylindres par cédage de leur cage support, ou par recul des moyens de réglage en position de leurs paliers ( ces variations d'écartement n'étant d'ailleurs pas forcément identiques des deux côtés des cylindres, ce qui conduit à une dissymétrie de l'entrefer par rapport au plan médian perpendiculaire aux axes des cylindres),
• une flexion des arbres des cylindres,
• ou même une flexion propre de la paroi des cylindres.

These deformations result from the forces exerted by the product, which cause:

• a spacing of the cylinders by yielding their support cage, or by retraction of the adjustment means in position of their bearings (these spacing variations are not necessarily identical on both sides of the cylinders, which leads to an asymmetry the air gap with respect to the median plane perpendicular to the axes of the cylinders),
• bending of the cylinder shafts,
• or even a clean bending of the wall of the cylinders.

These deformations also result from exchanges thermal, which cause a thermal bomb effect general on the cylinders during their heating, and also cyclic local deformations during the cylinder rotation, due to contacting and successive separations of each zone of the cylinder with the product formed, in particular, in the case of casting between cylinders, the cast product which solidifies on cylinder contact.

To know as precisely as possible the shapes and dimensions of this air gap so it would necessary to measure the spacing at the neck between the cylinders, not just at a point across the width of the cylinders, but over this whole width, or at least several points along the two generatrices forming the collar.

As it is not possible to make these measurements in during casting operation, it is already known to use thickness and profile gauges allowing determine the shapes and dimensions of the product after its shaping. Besides the problem of the cost of these gauges, these can practically only be placed far away of the cervix, and the measurement performed therefore does not reflect the value of the air gap with a relatively large delay. In the event of a drift of this value, the correction cannot therefore be performed only late, which leads to irregularities in the longitudinal profile of the product made.

The invention aims to solve these problems, and particularly aims to allow a determination fast air gap, continuously during the operation product shaping, so that it can act almost instantly on the regulating members of the position of the cylinders, or on the control devices other parameters of the formatting operation, for maintain a constant air gap of shape and dimensions required, for example on the means of control of the "domed" of the cylinder.

• on mesure les variations, par rapport à cet état initial, de la position d'au moins trois points de la surface du cylindre, sur une génératrice située à 180° par rapport au col, c'est à dire diamétralement opposée au col, ces points étant situés respectivement au moins dans le dit plan médian et dans deux plans secondaires parallèles au plan médian et situés de part et d'autre du dit plan médian,
• on mesure, au moins dans le dit plan médian, la variation, par rapport à cet état initial, de la position d'un point situé sur une génératrice à 90° par rapport au col,
• on détermine par un modèle de calcul ou par des courbes expérimentales, les variations de la longueur du rayon du cylindre dans les dits plans, entre le col et l'une des situations à 90° ou 180°,
• à partir des dites mesures des variations de position des points du plan médian, respectivement situés à 90° et 180° par rapport au col, et de la dite variation de la longueur du rayon dans ce plan médian respectivement d'une part entre le col et la situation à 90° et d'autre part entre les situations à 90° et à 180°, on en déduit la valeur du cédage au centre et la valeur de la variation de la longueur du rayon au col par rapport à l'état initial,
• et on en déduit la valeur instantanée de l'entrefer au centre à partir de la dite valeur d'entrefer au centre à froid, de la valeur du cédage au centre et de la valeur de la variation de la longueur du rayon, ainsi que le profil de l'entrefer.

With these objectives in view, the invention relates to a process for continuously determining the air gap at the neck between two cylinders, of substantially parallel axes, of an installation for hot forming a thin metallic product. by passing said product between said cylinders, characterized in that, in an initial state, in the absence of the product and when cold, the value of the air gap in the center, that is to say at least in a median transverse plane of the installation and, during the shaping of the said product, and for each cylinder:

• the variations, with respect to this initial state, of the position of at least three points on the surface of the cylinder are measured, on a generator situated at 180 ° relative to the neck, that is to say diametrically opposite the neck, these points being situated respectively at least in the said median plane and in two secondary planes parallel to the median plane and situated on either side of the said median plane,
• we measure, at least in said median plane, the variation, compared to this initial state, of the position of a point located on a generator at 90 ° to the neck,
• the variations in the length of the radius of the cylinder in the said planes, between the neck and one of the situations at 90 ° or 180 °, are determined by a calculation model or by experimental curves,
• from said measurements of the variations in position of the points of the median plane, respectively situated at 90 ° and 180 ° relative to the neck, and from said variation of the length of the radius in this median plane respectively on the one hand between the neck and the situation at 90 ° and on the other hand between the situations at 90 ° and 180 °, we deduce the value of the yield in the center and the value of the variation of the length of the radius at the neck compared to the state initial,
• and the instantaneous value of the air gap in the center is deduced therefrom from the said value of the air gap in the cold center, the value of the yield in the center and the value of the variation of the length of the spoke, as well as the air gap profile.

So, thanks to the method according to the invention, it is possible so know precisely and quickly, and continuously during the manufacture of the product, the dimensions and practically exact shapes of the air gap, and therefore ensure that these remain within tolerances required, or, if there is a drift, correct it almost instantly by means of the various actuators which conventionally equip such an installation. We can so get a quality product and section constant over its entire length.

Preferably, we also measure the variations in the position of surface points located in the so-called secondary planes and at 90 ° to the collar. We can then precisely determine the asymmetry the air gap, i.e. the difference in spacing cylinders between their two edges, from the measure variations in position of points located respectively in the said secondary plans and in said situations at 90 ° and 180 °.

Preferably again, the profile is determined thermal of a generator distant from the neck, and finding in a situation where we measure variations position of at least three points of this generator, from a parameterized function defining the thermal deformation at a point of said generator depending on the axial position of this point and from of the said measurement of the variations of the position of the said at least three points, and we determine the profile thermal from the generator to the neck from said profile thermal generator away from the neck and said determination of variations in the length of the radius of the cylinder in the said planes, between the neck and the situation of the said generator distant from the neck.

The invention also relates to a device for shaping of thin metal products, such as bands, comprising two cylinders with substantially axis parallel defining between them a pass located in the common plane of their axes, support means provided bearings in which the ends turn axial of the shafts of said cylinders, and a chassis on which means for supporting at least one of the cylinders are guided and movable in translation in one direction bringing the cylinders closer or further apart.

According to the invention, this device is characterized in what it includes, for each cylinder, means of measuring the position of the generator diametrically opposite the neck, at three points respectively in a median plane perpendicular to the axes and in two secondary planes parallel to the median plane and located at proximity of the edges of the cylinders and the means of measurement, in said median plane, of the position of a generator located at 90 ° to the neck.

Preferably, to be able to measure precisely the asymmetry of the air gap, the device also includes means for measuring the position of the said generator located at 90 ° from the neck, in the said secondary plans.

According to an alternative embodiment, said means are position sensors attached to the said means for supporting the cylinders and the device additionally includes means for measuring variations spacing of said bearings.

According to another variant which makes it possible to overcome means for measuring the spacing of the bearings, the so-called means for measuring the position of the generator diametrically opposite the neck are sensors attached to the chassis.

• calculer les variations des positions mesurées des dites génératrices,
• déterminer, par un modèle de calcul prenant en compte les paramètres de coulée et/ou à partir de données expérimentales, les variations de la longueur du rayon du cylindre dans les dits plans, entre le col et l'une des situations à 90° ou 180°,
• calculer, à partir des dites variations de position et des dites variations de longueur du rayon, la valeur du cédage du cylindre au centre et la valeur de la variation de la longueur du rayon au col par rapport à l'état initial,
• et en déduire la valeur instantanée de l'entrefer au centre à partir de la valeur d'entrefer au centre à froid et de la valeur du cédage au centre et de la valeur de la variation de la longueur du rayon, ainsi que le profil de l'entrefer.

The device also includes calculation means connected to said measurement means for

• calculating the variations in the measured positions of said generators,
• determine, by a calculation model taking into account the casting parameters and / or from experimental data, the variations in the length of the radius of the cylinder in the said planes, between the neck and one of the situations at 90 ° or 180 °,
• calculating, from said position variations and from said radius length variations, the value of the yielding of the cylinder in the center and the value of the variation of the length of the radius at the neck relative to the initial state,
• and deduce the instantaneous value of the air gap in the center from the cold air gap value in the center and the value of the yield in the center and the value of the variation of the length of the spoke, as well as the profile of the air gap.

Other characteristics and advantages will appear in the description which will be made of a device for continuous casting between cylinders of thin strips in steel, according to the invention, and a method of continuous determination of the air gap between casting cylinders.

• la figure 1 est une représentation partielle simplifiée du dispositif de coulée,
• la figure 2 est une vue en demi-coupe axiale d'un cylindre équipant ce dispositif,
• la figure 3 est une vue de dessus simplifiée du dispositif de l'appareil de coulée .
• la figure 4 est une vue frontale du dispositif de la figure 3, en coupe selon le plan P₁ de la figure 3.

Reference is made to the appended drawings in which:

• FIG. 1 is a simplified partial representation of the casting device,
• FIG. 2 is a view in axial half-section of a cylinder fitted to this device,
• Figure 3 is a simplified top view of the device of the casting apparatus.
• FIG. 4 is a front view of the device of FIG. 3, in section along the plane P ₁ of FIG. 3.

The continuous casting device shown in figure 1 comprises, in known manner, two cylinders 10, 11, of parallel axes and located in a horizontal plane P, internally cooled and rotated by drive not shown. Such a cylinder is shown in simplified form in the drawing of the Figure 2 and includes a shaft 12, a body 31 linked to the shaft, and an outer ferrule 32, which constitutes the casting surface, held on the body by means known per se.

Conventionally, to obtain a band having a slight transverse curvature (necessary for treatments cold strip), the surface outer 34 of ferrule 32 should be slightly "in This is why the longitudinal profile (in the direction of the cylinder axis) of this surface, obtained by machining, is concave. This concavity is by elsewhere determined cold so that subsists, warm and at the neck, the desired "hollow" counts held that the initial concavity tends to be reduced by the effect of thermal bulging during the heating of the ferrule.

There is shown in Figure 2, so deliberately exaggerated, the shapes of the surface of the ferrule, cold, by dotted line 35, hot by reference 34, line 36 representing a generator theoretical straight line with respect to which the hollow, or the so-called concavity.

Returning to Figure 1, we see that the trees 12 are held in bearings 13F, 13M, 14F, 14M, or chocks, in which they revolve.

The bearings 13F, 14F of the cylinder 10 are linked by support means, for example a fixed cross member 15F relative to the chassis 16 of the device. 13M bearings, 14M of the other cylinder 11 are similarly connected by a cross member 15M guided on chassis 16, and movable on this, the position of the bearings 13M and 14M can be regulated by thrust cylinders 17, which provide also the reaction force opposing the effort spacing of the cylinders generated by the cast product.

The device also comprises means for measuring the position of the surface 34 of each cylinder. These measuring means comprise, for each cylinder, a set 20 of sensors 22 intended to measure the position of the surface 34 on a generatrix of this surface located in the horizontal plane P, diametrically opposite the neck, and at several points along this generator. In the drawing of FIG. 1, three sensors 22 have thus been represented, one being located in a vertical median plane P ₃ , and measuring the position of a point located substantially in the middle of said generator, the other two being located respectively in secondary vertical planes P ₁ and P ₅ , in the vicinity of the edges of the casting surface 34. To increase the accuracy of the measurements, additional sensors can be used, placed in intermediate positions.

The set 20 of sensors 22 is fixed relative to to chassis 16. These sensors are type sensors known in triangulation measurement applications, for example laser beam sensors, which can appreciate small variations in distance while being distant from the point whose position we want to determine. These sensors 22 are arranged so as to target the surface of cylinder 11 through a window 18 fitted for this purpose in the cross member 15M of said support cylinder. In this way, the measurement made by these sensors is a direct measurement of the position of the points targeted from the surface of cylinder 11 relative to the chassis 16, and therefore independent of the position of the bearings 13M, 14M.

Means for measuring the position of the surface 34 also include a set 21 of sensors 23, located below cylinder 11 in a vertical plane passing substantially through the axis of the cylinder, this assembly being fixed relative to the bearings 13M, 14M, and is therefore moving with these. The sensors 23 are by example of capacitive or inductive sensors, of measurement close together. The assembly 21 includes three sensors 23, located respectively in the same vertical planes as the sensors 22 of the assembly 20, which therefore make it possible to measure at three points the position of the generator the surface 34 located at 90 ° from the neck, downstream from the latter with respect to the direction of rotation of the cylinder.

Similarly, two sets 24, 25 of sensors are arranged near the second cylinder 10. It should be noted, however, that, given that the bearings 13F and 14F of this cylinder are fixed relative to the chassis 16, the sensors of the assembly 24 can then also be capacitive type sensors or inductive.

According to an alternative embodiment, shown in Figures 3 and 4, such sensors, susceptible only take measurements at short distance, can also be used in place of sensors 22, to measure the position of the points of the generator opposite the neck on cylinder 11. In this case, these sensors are fixed relative to the support means 15M of this cylinder, and additional sensors are provided for measuring the position of these support means relative to the chassis, for example sensors 26 arranged to measure gauge variations between the bearings of the two cylinders.

We will now describe, in relation to the Figures 3 and 4, the method of determining the air gap continuously during casting, using measurements performed by the aforementioned sensors.

• de la concavité initiale, à froid, des cylindres,
• de l'effet de bombé thermique et de la dilatation radiale des viroles, qui tendent à réduire cette concavité lors de l'échauffement des viroles,
• du cédage de l'ensemble des organes supportant les viroles, notamment la flexion des arbres des cylindres qui tend à augmenter la distance entre les cylindres au col.

Beforehand, it is recalled that the real air gap at the neck between the cylinders, during casting, depends on:

• of the initial concavity, cold, of the cylinders,
• the thermal doming effect and the radial expansion of the ferrules, which tend to reduce this concavity during the heating of the ferrules,
• the yielding of all the bodies supporting the ferrules, in particular the bending of the cylinder shafts which tends to increase the distance between the cylinders at the neck.

Given that the clamping forces are relatively small, and the large diameter ferrule by relative to its width, we can consider that the shell itself does not flex, or at least that this bending is negligible. However, the clean ceding of the ferrule can be taken into account in determining the air gap using a greater number of sensors for each set of sensors.

The ceding of the chassis 16 can also be considered negligible. However, using a arrangement of sensors such as that shown in Figures 3 and 4, we are completely free of this possible ceding since we measure the variations between the bearings of the cylinders, the ceding of the chassis then no longer having any influence on the measures.

• l'entrefer au centre, c'est-à-dire dans le plan médian de l'installation,
• la dissymétrie de l'entrefer,
• et le profil de la surface des viroles.

Furthermore, to know precisely the shapes and dimensions of the air gap at the neck during casting, it suffices to know at the neck:

• the air gap in the center, that is to say in the median plane of the installation,
• the asymmetry of the air gap,
• and the profile of the surface of the ferrules.

• l'épaisseur du produit coulé, en commandant des déplacements égaux des deux vérins de serrage 17,
• la dissymétrie transversale du produit, en commandant des déplacements différenciés de ces vérins,
• le profil du bombé, en agissant sur les échanges thermiques entre produit et virole, par exemple en faisant varier le refroidissement de la virole, ou la vitesse de rotation des cylindres.

Knowledge of these elements makes it possible to act in regulation on:

• the thickness of the cast product, by controlling equal displacements of the two clamping cylinders 17,
• the transverse asymmetry of the product, by controlling differentiated movements of these jacks,
• the profile of the crown, by acting on the heat exchanges between product and shell, for example by varying the cooling of the shell, or the speed of rotation of the cylinders.

eo : valeur de l'entrefer initial à froid entre les génératrices théoriques 36 des viroles,

e : valeur de l'entrefer réel,

b : valeur de la flèche à froid de la génératrice de la surface 34, résultant de l'usinage de cette surface.

Δx : valeur du cédage d'un cylindre,

e_d et e_g : valeurs de la variation de l'écartement entre paliers, de chaque côté des cylindres, mesurées par les capteurs 26,

ΔR : variation de la longueur du rayon du cylindre par rapport à sa longueur à froid (due à l'effet de bombé thermique et de la dilatation radiale),

δ : variation de la longueur du rayon pendant la rotation,

L : distance entre les deux paliers d'un cylindre,

l : distance axiale de chacun des plans verticaux contenant les capteurs, par rapport à un palier,

λ : largeur de la virole,

C : valeurs des variations de position de chaque point de la virole, mesurées par les capteurs 22, 23.

In the explanations which follow, to determine, from the measurements carried out by the various sensors, the value of the air gap in the center, the asymmetry, and the shape of the profile of the surfaces of the ferrules, the following notations will be used:

eo: value of the initial cold air gap between the theoretical generators 36 of the ferrules,

e: value of the real air gap,

b: value of the cold deflection of the generator of the surface 34, resulting from the machining of this surface.

Δx: value of the yield of a cylinder,

e _d and e _g : values of the variation in the spacing between bearings, on each side of the cylinders, measured by the sensors 26,

ΔR: variation of the length of the radius of the cylinder compared to its cold length (due to the effect of thermal bulging and of the radial expansion),

δ: variation of the length of the spoke during rotation,

L: distance between the two bearings of a cylinder,

l: axial distance of each of the vertical planes containing the sensors, relative to a bearing,

λ: width of the shell,

C: values of the position variations of each point of the shell, measured by the sensors 22, 23.

• les chiffres 1, 2, 3 accolés aux signes précédents indiquent la position angulaire où est considérée la valeur concernée : 1 indique la situation au col, 2 indique la situation à 90° par rapport au col, 3 indique la situation à 180° par rapport au col (diamétralement opposée au col),
• les chiffres indiqués en indice indiquent de manière similaire, la situation axiale : 3 correspondant à la situation dans le plan médian, 1 et 5 correspondant respectivement aux situations dans les plans secondaires, voisins des bords des viroles (on notera que les indices 2 et 4 correspondraient à des plans intermédiaires supplémentaires)..
• la lettre "F" indique que la valeur concerne le cylindre fixe 10, et la lettre "M" concerne le cylindre mobile 11.

Otherwise :

• the numbers 1, 2, 3 attached to the preceding signs indicate the angular position where the value concerned is considered: 1 indicates the situation at the pass, 2 indicates the situation at 90 ° with respect to the pass, 3 indicates the situation at 180 ° with respect to at the neck (diametrically opposite the neck),
• the figures indicated in subscript indicate in a similar way, the axial situation: 3 corresponding to the situation in the median plane, 1 and 5 corresponding respectively to the situations in the secondary planes, neighbors of the edges of the ferrules (it will be noted that the indices 2 and 4 would correspond to additional intermediate plans).
• the letter "F" indicates that the value relates to the fixed cylinder 10, and the letter "M" relates to the movable cylinder 11.

So, for example:

C2 ₃ M is the value, measured by the sensor 23, of the variation in position of the point on the surface 34 of the shell of the movable cylinder 11, a point located 90 ° from the neck and in the median plane.

δ23 ₁ is the variation in length of the radius, in the secondary plane P ₁ located in the vicinity of the edge of the ferrule, between the situation at 90 ° and the situation at 180 ° relative to the neck.

Finally, it is agreed to assign the symbol "F / M" to the sum of the values corresponding to the same measurement or variation for each cylinder (thus for example: C2 ₃ F / M = C2 ₃ F + C2 ₃ M) and d 'assign with the sign "+" all values corresponding to an increase in the air gap, and with the sign "-" those corresponding to a decrease in the air gap.

Note that the values of C relating to the 90 ° position (position "2") and used in formulas that follow are delayed by an equivalent time a quarter turn from the cylinder, so that the position variations taken into account in the same calculation relate to the same generator, although the measurements of these variations are carried out in different angular positions, in particular to get rid of a possible runout of the cylinders.

a) Pour la détermination de l'entrefer au centre e₃:

• Cédage de l'arbre d'un cylindre au centre (dans le plan médian) : Δx₃ = C3₃- (C2₃- δ23₃)
• Variation de rayon au col : ΔR₃ C2₃ + δ12₃

d'où l'entrefer réel au centre :

d'où : e3 = eo3 + b3F/M + C33F/M - 2.C23F/M + δ233F/M - δ123F/M La valeur de δ23₃-δ12₃ est faible et peut être déterminée par un modèle de calcul prenant en compte les paramètres de coulée, notamment vitesse et flux d'échange thermique, pour une virole donnée, ou des valeurs expérimentales. A noter aussi que cette valeur, d'après le modèle de calcul, ne varie pratiquement pas avec l'intensité du refroidissement de la virole.

b) : dissymétrie de l'entrefer : Les capteurs d'extrémité situés aux voisinage des bords et à 180° permettent de connaítre la dissymétrie : e1= eo1 - b1F/M + C31F/M- 2.C21F/M + δ231F/M - δ121F/M e5 = eo5 - b5F/M + C35F/M - 2.C25F/M + δ235F/M - δ125F/M    par définition, on pose : b₁ = b₅ (symétrie du profil en creux initial), d'où :

On peut admettre que les expressions A = (δ23₁F/M - δ23₅F/M) et B = (δ12₁F/M - δ12₅F/M) sont sensiblement nulles, car les conditions sont en principe identiques de chaque côté des cylindres et il s'agit de différences de valeurs sensiblement égales.D'autre part, eo₁ et eo₅ ont les valeurs suivantes : - eo1 = ed - (ed-eg).l1/L - eo5 = ed - (ed-eg).l5/L    d'où : (eo1-eo5) = [(ed-eg)/L].(l5-l1)    d'où la valeur de la dissymétrie : e1-e5 = [(ed-eg)/L].(l5-l1) + C31F/M - C35F/M - 2.(C21F/M - C25F/M)

c) : Profil On peut démontrer que le profil propre de bombé thermique de la surface 34 de chaque cylindre qui s'ajoute au profil à froid est de la forme : Y = K(Δ) . [2.e-β(λ/2) - e-β(x) - e-β(λ-x)]    β étant une constante, il y a lieu de calculer K qui est fonction du gradient de température à travers la paroi de la virole.

Given these notation conventions, the following equations can be written:

a) For the determination of the air gap at center e ₃ :

• Yield of the shaft of a cylinder in the center (in the median plane): Δx ₃ = C3 ₃ - (C2 ₃ - δ23 ₃ )
• Radius variation at the neck: ΔR ₃ C2 ₃ + δ12 ₃

hence the real air gap in the center:

from where : e 3 = eo 3 + b 3 F / M + C3 3 F / M - 2.C2 3 F / M + δ23 3 F / M - δ12 3 F / M The value of δ23 ₃ -δ12 ₃ is low and can be determined by a calculation model taking into account the casting parameters, in particular speed and heat exchange flux, for a given shell, or experimental values. Note also that this value, according to the calculation model, practically does not vary with the intensity of the cooling of the shell.

b): asymmetry of the air gap: The end sensors located in the vicinity of the edges and at 180 ° make it possible to know the asymmetry: e 1 = eo 1 - b 1 F / M + C3 1 F / M- 2.C2 1 F / M + δ23 1 F / M - δ12 1 F / M e 5 = eo 5 - b 5 F / M + C3 5 F / M - 2.C2 5 F / M + δ23 5 F / M - δ12 5 F / M by definition, we set: b ₁ = b ₅ (symmetry of the initial hollow profile), hence:

We can admit that the expressions A = (δ23 ₁ F / M - δ23 ₅ F / M) and B = (δ12 ₁ F / M - δ12 ₅ F / M) are substantially zero, because the conditions are in principle identical for each side of the cylinders and these are substantially equal value differences; on the other hand, eo ₁ and eo ₅ have the following values: - eo 1 = ed - (ed-eg) .l 1 / L - eo 5 = ed - (ed-eg) .l 5 / L from where : (eo 1 -eo 5 ) = [(ed-eg) / L]. (l 5 -l 1 ) hence the value of asymmetry: e 1 -e 5 = [(ed-eg) / L]. (l 5 -l 1 ) + C3 1 F / M - C3 5 F / M - 2. (C2 1 F / M - C2 5 F / M)

c): Profile It can be shown that the proper profile of the thermal convex surface 34 of each cylinder which is added to the cold profile is of the form: Y = K (Δ). [2 . e -β (λ / 2) - e -β (x) - e -β (λ-x) ] β being a constant, it is necessary to calculate K which is a function of the temperature gradient across the wall of the shell.

To take into account a possible lack of symmetry compared to the median plane, you must at least know a point of the curve on each side and therefore it takes minus three sensors. By averaging the values measured by the sensors close to the edges, we can determine the profile of the cylinder in relation to its axis.

In the case where there are three 180 ° sensors but one only 90 ° sensor, it will be necessary to take the value of the convex 180 °. If there are at least 3 sensors at 90 °, we can then take the value of the curved at 90 ° which, being more near the neck, will have a value closer to that of the neck, and therefore the profile at the neck will be determined more precisely.

To know the profile at the collar from the profile at 90 ° or 180 °, it is necessary to integrate the variations of radius between the neck and the position where the bulge is read:

So we have : ΔR i = C2 i - δ12 i hence, if the bulge is measured in the 90 ° situation of the neck: Y 1 = C2 3 - C2 1 + δ12 3 - δ12 1 Y 5 = C2 3 - C2 5 + δ12 3 - δ12 5

The values of δ12 ₃ and δ12 ₁ and δ12 ₅ , as said previously, can be determined using a model, either according to the casting parameters, or by the difference in the value of the convex between 180 and 90 °, or by experimental curves or values.

Knowing Y ₁ and Y ₅ , we can then determine the profile of each cylinder at the neck.

As will be understood, the device and the process according to the invention make it possible to determine with precision and continuously the real air gap between cylinders during casting, defining it by its value in the center, its possible asymmetry by relation to the median plane, and the shape of the generator of each cylinder at the neck.

The sensor (s) located at 90 ° to the neck are particularly used to determine the influence of variations in radius and profile of cylinders due to thermal bulge effects, since in this situation 90 °, the deformations due to the mechanical effects of efforts to separate the cylinders are negligible. he would therefore also be possible to carry out the measurements above the cylinders at 90 ° upstream of the collar. However, for reasons of space, it is easier to place the sensors below the cylinders. In addition, having regard to the curved measures thermal, such a position is favorable, because the bulging variations are less between the neck and the situation at 90 ° downstream, that between the pass and a situation at 90 ° upstream of the pass, since between these two last situations, the heating due to the entry into contact of molten metal with the ferrule is more brutal that the cooling which follows the separation of the strip casting from the cylinder surface.

The different measures indicated above actually allow you to determine variations in the air gap in service, compared to the cold air gap, effortlessly on the cylinders, these variations being caused both by the efforts exerted during casting only by the thermal deformations of the cylinders. It is therefore assumed that the shape of the profile of the cylinders cold is known. Practically, from the form of the hot generator desired to have the profile air gap compatible with the desired cross-section of the strip formed (this form being defined by a function mathematical), the equation for the curve of the cold profile used by the machine tool profile of the cylinders, this equation of the cold profile giving the depth of the profile at a point in function of the axial position of this point. Reciprocally, knowing the profile of the cold air gap by measuring of the value of the air gap in the center and by the said cold profile equation, and knowing the variations of position and form as mentioned above for each cylinder, it is possible to know the profile hot air gap with sufficient precision.

In the above, it was considered that the shape of the profile of a generator of the cylinder was a curve defined by a mathematical function, the measurements carried out by the sensors located in the three planes P ₁ , P ₃ , P ₅ making it possible to define the parameters of this curve and its position in the installation. It will be readily understood that, if there is a large number of sensors in planes parallel to P ₃ , in addition to the planes P ₁ and P ₅ , that is to say distributed along the width of the table of the cylinder of surface 34, it will then be possible to know directly by measurement the position of several points of the profile and, therefore, to know precisely the profile of the cylinders, and therefore the air gap, without it being necessary to know the shape of the initial profile.

It goes without saying that the invention does not apply only at continuous casting, but also, like already mentioned at the beginning, when rolling flat products, metallic or other.

Claims (13)

1. Method of continuously determining the gap at the neck between two rolls (10, 11), having substantially parallel axes, of an installation for the hot-shaping of a thin metal product by passing the said product between the said rolls, characterized in that the value of the gap at the centre (eo₃), that is to say in a transverse mid-plane (P3) of the installation, is measured in an initial state without the product and when cold and, during shaping of the said product, and for each roll:

   the variations (C3₁, C3₃, C3₅), with respect to this initial state, in the position of at least three points on the surface of the roll are measured along a generatrix lying at 180° to the neck, that is to say diametrically opposite the neck, these points lying respectively at least in the said mid-plane (P₃) and in two secondary planes (P₁, P₅) parallel to the mid-plane and lying on either side of the said mid-plane;

   the variation (C2₃), with respect to this initial state, in the position of a point lying on a generatrix at 90° to the neck is measured;

   the variations (δ12) in the length (R) of the radius of the roll in the said planes, between the neck and one of the 90° or 180° locations, is determined using a computer model or using experimental curves;

   computed therefrom, using the said measurements of the variations in position of the points in the mid-plane, these lying respectively at 90° and 180° with respect to the neck, and the said variation in the length of the radius in this mid-plane respectively, on the one hand, between the neck and the 90° location (δ12₃) and, on the other hand, between the 90° and 180° locations (δ13₃), are the value (Δx₃) of the roll spring at the centre and the value (ΔR₃) of the variation in the length of the radius at the neck with respect to the initial state;

   and computed therefrom, using the said value of the gap at the centre when cold and the value of the roll spring at the centre and the value of the variation in the length of the radius, is the instantaneous value (e₃) of the gap at the centre, as well as the profile of the gap.
2. Method according to Claim 1, characterized in that the variations in the position of the points on the surface which lie in the said secondary planes and at 90° to the neck are also measured.
3. Method according to either of Claims 1 and 2, characterized in that the thermal profile of a generatrix remote from the neck, and at a location (2) where the variations (C2₁, C2₃, C2₅) in position of at least three points of this generatrix are measured, is determined using a parametrized function defining the thermal deformation (Y) at a point on the said generatrix as a function of the axial position (1) of this point and using the said measurements of the variations in the position of the said at least three points, and the thermal profile of the generatrix at the neck is determined using the said thermal profile of the generatrix remote from the neck and the said determination of the variations (δ12) in the length of the radius of the roll in the said planes, between the neck and the location of the said generatrix remote from the neck.
4. Method according to either of Claims 2 and 3, characterized in that the dissymmetry (e₁ - e₅) of the gap is determined using the measurement of the variations (C3₁, C3₅, C2₁, C2₅) in position of the points lying respectively in the said secondary planes and in the said 90° and 180° locations.
5. Method according to any one of Claims 1 to 4, characterized in that the said variations (C3) in position of the points lying at 180° with respect to a reference fixed in space are measured.
6. Method according to any one of Claims 1 to 4, characterized in that the said variations (C3) in position of the points lying at 180° to respective means (15F, 15M) for supporting the rolls, including bearings in which the ends of the shafts of the rolls rotate, and the variations (e_d, e_g) in the separation of the said bearings at each of the said ends, are measured.
7. Device for shaping thin metal products, such as strips, which includes two rolls (10, 11), having substantially parallel axes, defining between them a neck lying in the common plane (P) of their axes, supporting means (15F, 15M) provided with bearings (13, 14) in which axial ends of the shafts (12) of the said rolls rotate, and a frame (16) on which the means for supporting at least one of the rolls are guided and can move translationally in a direction in which the rolls are moved closer together or further apart, characterized in that it includes, for each roll, means (22) for measuring the position of the generatrix diametrically opposite the neck, at least at three points located respectively in a mid-plane (P₃) perpendicular to the axes and in two secondary planes (P₁, P₅) parallel to the mid-plane and lying near the edges of the rolls and means (23) for measuring the position, in the said mid-plane, of a generatrix lying at 90° to the neck.
8. Device according to Claim 7, characterized in that it also includes means (23) for measuring the position, in the said secondary planes, of the said generatrix lying at 90° from the neck.
9. Device according to Claim 7 or 8, characterized in that the said measurement means are position sensors (22) attached to the said means for supporting the rolls and in that it furthermore includes means (26) for measuring the variations in the separation of the said bearings.
10. Device according to Claim 7, characterized in that the said means (22) for measuring the position of the generatrix diametrically opposite the neck are sensors attached to the frame.
11. Device according to one of Claims 7 to 10, characterized in that the said rolls (10, 11) are cooled casting rolls, intended to be brought into contact with the molten metal, of an installation for continuous casting between rolls.
12. Device according to Claim 7, characterized in that it includes computation means connected to the said measurement means (22, 23) for:

    computing the variations in the measured positions of the said generatrices;

    determining, by means of a computer model taking into account the casting parameters and/or using experimental data, the variations (δ12) in the length (R) of the radius of the roll in the said planes (P₁, P₃, P₅), between the neck and one of the 90° or 180° locations;

    computing, using the said position variations and the said variations in length of the radius, the value (Δx3) of the roll spring at the centre and the value (ΔR₃) of the variation in the length of the radius at the neck with respect to the initial state;

    and deducing therefrom the instantaneous value (e₃) of the gap at the centre, using the value of the gap at the centre when cold and the value of the roll spring at the centre and the value of the variation in the length of the radius, as well as the profile of the gap.
13. Device according to Claim 7, characterized in that the said measurement means comprise capacitive or inductive or laser-beam sensors.

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