EP4101553B1 - Cooling of a rolled stock upstream of a finishing train of a hot rolling plant - Google Patents

Description

The invention relates to a method for cooling a rolling stock in a cooling section arranged in front of a finishing train of a hot rolling mill, through which the rolling stock is transported along a cooling section path once at a predetermined transport speed or several times in alternating directions, each with a predetermined transport speed. The specified transport speed can vary over time. But it can also be constant over time. The cooling section has a cooling device with an effective area or several cooling devices arranged one behind the other along the cooling section path, each with an effective area, the effective areas of adjacent cooling devices directly adjoining one another and with each cooling device in the effective area of which a coolant flow of a coolant can be output onto a rolling stock surface of the rolling stock, which can be set between the value zero and a maximum value specific to the cooling device

Furthermore, the invention relates to a cooling section for cooling a rolling stock in front of a finishing train of a hot rolling plant, the cooling system having a cooling device or several cooling devices arranged one behind the other along a cooling section path through the cooling section, with which a coolant flow of coolant can be output, which is between can be set to the value zero and a maximum value specific to the cooling device and comprises a plurality of transport rollers which are set up to transport the rolling stock along the cooling section path through the cooling section.

In a hot rolling mill, a metallic rolling stock, for example a steel strip, is rolled to reduce its thickness. A hot rolling mill often has a so-called Preparing mill and a so-called finishing mill. In the roughing train, the rolling stock is rolled into a so-called roughing strip with a roughing strip thickness. The pre-strip is fed to the finishing train via a so-called intermediate roller table, in which the thickness of the rolling stock is further reduced from the pre-strip thickness to a final thickness.

The rolling stock is fed to the roughing train, for example, at a temperature in the range of 1100°C to 1200°C. For example, the rolling stock is heated to this temperature with a heating furnace before the roughing train, or the already heated rolling stock is delivered directly to the roughing train. In the intermediate rolling table, the rolling stock is not formed, that is, its thickness is not reduced by rolling, but the rolling stock is merely cooled, that is, the temperature of the pre-strip is reduced, for example to a temperature in the range between 700 ° C and 900 ° C.

The cooling of the rolling stock in the intermediate roller table serves to limit the inlet temperature of the rolling stock when it enters the finishing train. The inlet temperature is limited for metallurgical reasons, for example in order to suppress recrystallization in the rolling stock during the transport of the rolling stock through the finishing train, in particular in the production of so-called thermomechanically rolled products such as tubular steel or microalloyed steel, and/or in order to achieve a high surface quality , for example in the production of automobile outer skin or can sheet metal. Furthermore, it is often advantageous to achieve a desired inlet temperature for the finishing train as quickly as possible when transporting the rolling stock through the intermediate roller table.

On the other hand, excessive cooling of the rolling stock in the intermediate rolling table can lead to undercooling of surface areas of a surface of the rolling stock. Such undercooling can lead to phase transformations in areas of the rolling stock near the surface, which impair the product quality of the product produced in the rolling process and should therefore be avoided. In order to prevent such undercooling, it is required that a surface temperature of a surface of the rolling stock in the intermediate rolling table does not fall below a certain minimum value.

EP 2 873 469 A1 discloses an operating method for cooling a flat rolling stock in a cooling section with cooling devices arranged along the cooling section, from which a coolant can be dispensed onto the rolling stock when the rolling stock is transported through the cooling section. Cooling capacities are determined for the cooling devices by means of a simulation of the transport of rolling stock points through the cooling section and the cooling devices are controlled according to these cooling capacities when the rolling stock is transported through the cooling section.

From the DE 10 2019 216261 A1 A method mentioned at the beginning and a cooling section mentioned at the beginning are known for cooling a rolling stock.

The invention is based on the object of specifying a method and a cooling section for cooling a rolling stock in front of a finishing train of a hot rolling mill, with which the rolling stock is cooled without the surface temperature of a rolling stock surface of the rolling stock falling below a predetermined minimum value.

The object is achieved according to the invention by a method with the features of claim 1 and a cooling section with the features of claim 13.

Advantageous embodiments of the invention are the subject of the subclaims.

In the method according to the invention, a minimum value for a surface temperature of the surface of the rolling stock is taken during the transport of the rolling stock through the cooling section. In order to maintain the minimum value, each cooling device is assigned a setting value for the coolant flow for each cooling section pass through the cooling section and by means of each cooling device a coolant flow is output to the rolling stock surface for each cooling section pass, which is set to the setting value assigned to the respective cooling device for the cooling section pass.

• ein Vorgabewert für einen von der Kühleinrichtung auszugebenden Kühlmittelstrom spätestens unmittelbar vor Eintritt des Walzgutabschnittes in den Wirkbereich der Kühleinrichtung entgegengenommen oder bestimmt,
• ausgehend von einer Anfangsenthalpieverteilung und/oder Anfangstemperaturverteilung in dem Walzgutabschnitt beim Eintritt in den Wirkbereich der Kühleinrichtung anhand eines physikalischen Modells eine Enthalpieverteilung und/oder Temperaturverteilung in dem Walzgutabschnitt beim Austritt aus dem Wirkbereich der Kühleinrichtung berechnet und
• der Einstellwert derart bestimmt, dass er den von der Kühleinrichtung auf die Walzgutoberfläche auszugebenden Kühlmittelstrom unter den Nebenbedingungen quasi-maximiert, dass der Einstellwert den Vorgabewert nicht überschreitet und eine aus der Anfangsenthalpieverteilung und/oder Anfangstemperaturverteilung abgeleitete oder eine aus der berechneten Enthalpieverteilung und/oder berechneten Temperaturverteilung des Walzgutabschnitts abgeleitete Oberflächentemperatur der Walzgutoberfläche beim Austritt aus dem Wirkbereich der Kühleinrichtung den Minimalwert nicht unterschreitet.

To determine the setting values for a cooling section pass, the cooling section passes through the cooling section at least once for a rolling stock section of the rolling stock at the predetermined transport speed simulated. Each simulated cooling section run is successively for each cooling device

• a default value for a coolant flow to be output by the cooling device is received or determined at the latest immediately before the rolling stock section enters the effective range of the cooling device,
• starting from an initial enthalpy distribution and/or initial temperature distribution in the rolling stock section upon entry into the effective range of the cooling device, an enthalpy distribution and/or temperature distribution in the rolling stock section upon exiting the effective range of the cooling device is calculated using a physical model and
• the setting value is determined in such a way that it quasi-maximizes the coolant flow to be output from the cooling device to the rolling stock surface under the additional conditions that the setting value does not exceed the specified value and one derived from the initial enthalpy distribution and/or initial temperature distribution or one derived from the calculated enthalpy distribution and/or calculated one Temperature distribution of the rolling stock section derived surface temperature of the rolling stock surface when exiting the effective range of the cooling device does not fall below the minimum value.

When simulating a cooling section run, the enthalpy distribution calculated for the first effective range passed through and/or the calculated temperature distribution upon exiting the first effective range passed through is also used for each two effective areas passed through by the rolling stock section immediately one after the other during the cooling section pass Entry into the other effective area assigned. An original initial enthalpy distribution and/or original initial temperature distribution is assumed for the first cooling device through which the rolling stock section passes through the cooling section.

In the method according to the invention, each cooling section pass of the rolling stock is first simulated at least once for a rolling stock section of the rolling stock, with setting values for the coolant flows of all cooling devices being determined during the simulation. These setting values are then used to control the cooling devices when the rolling stock actually passes through the cooling section. The setting value for a cooling device is determined during a simulation of a cooling section run in such a way that the coolant flow determined by the setting value is quasi-maximal under the additional conditions, that the setting value does not exceed a specified value and a surface temperature of the rolling stock surface determined during the simulation when exiting the effective range the cooling device does not fall below a minimum value. The default value for the coolant flow of a cooling device is either determined during the simulation or, for example, received from a higher-level controller.

The quasi-maximal coolant flow here is understood to mean a coolant flow that is maximum under the stated additional conditions or that approximates the maximum coolant flow within the scope of a control engineering design. This takes into account that an exact maximization of the coolant flow is not necessary in practice, since a simulation is based on a mathematical model that only models the cooling section and therefore does not represent it exactly, so that there are small deviations of the simulation from the real cooling process in the cooling section anyway must be accepted. In addition, an exact maximization of the coolant flow can require an unreasonably high computational effort and stand in the way of carrying out the simulation as quickly as possible.

The quasi-maximization of the coolant flows advantageously enables optimized cooling of the rolling stock during transport through the cooling section. The default values for the setting values of the coolant flows can be used Target temperature at the end of the cooling section of the rolling stock can be specified, which is adapted to a desired inlet temperature of the rolling stock when entering the finishing train. The additional condition that the surface temperatures of the rolling stock surface determined during the simulation do not fall below the minimum value for the surface temperature when exiting the effective ranges of the cooling devices advantageously prevents the above-mentioned undercooling of the rolling stock surface, which reduces product quality, during the transport of the rolling stock through the cooling section. The minimum value is accordingly specified in such a way that such undercooling of the rolling stock surface is avoided.

In one embodiment of the method according to the invention, at least one cooling device, in particular each cooling device, for each simulated cooling section pass of a rolling stock section, the setting value according to w _i = f _i ( T _i ⁱⁿ (0)) w _i ^V as the product of f _i ( Ti ⁱⁿ (0 )) and w _i ^V assigned, where i is a value of a running index assigned to the cooling device, which numbers the effective areas of the cooling devices in the order in which they are passed through by a rolling stock section during the cooling section passage. Here, w _i ^V is the default value for the coolant flow to be output by the cooling device, T _i ⁱⁿ (0) is a surface temperature of the rolling stock surface derived from the initial enthalpy distribution and/or initial temperature distribution when it enters the effective range of the cooling device, T ^min is the minimum value for the surface temperature the rolling stock surface and ΔT _i ^res is a predeterminable reserve temperature difference. f _i ( T ) is a function that is zero for T ≤ T ^min , one for T ≥ T ^min +Δ T _i ^res and increases strictly monotonically in the interval [ T ^min , T ^min + Δ T _i ^res ].

In the aforementioned embodiment of the method according to the invention, the additional condition that the setting value does not exceed the default value is realized by the function _fi ( T ) not exceeding the value one. The additional condition that the surface temperature of the The rolling stock surface does not fall below the minimum value when it leaves the effective range of the cooling device, can be achieved by a suitable choice of the reserve temperature difference ΔT _i ^res . The quasi-maximization of the coolant flow is achieved by the monotonic increase of the function f _i (T) from zero to one.

In an alternative embodiment of the method according to the invention to the aforementioned embodiment, the setting value for at least one cooling device, in particular for each cooling device, is determined for each simulated cooling section pass by first determining the surface temperature of the rolling stock surface as it exits the effective range of the cooling device for the default value for the coolant flow of the cooling device is calculated. The setting value is set equal to the default value if the surface temperature calculated for the default value does not fall below the minimum value. Otherwise, the calculation of the surface temperature at the exit from the effective range for at least one coolant flow that is smaller than the default value is iterated to determine a setting value of the coolant flow for which the calculated surface temperature at the exit from the effective range matches the minimum value with sufficient accuracy . A sufficiently precise match is understood to mean, for example, a match up to an absolute or relative deviation, the amount of which does not exceed a predetermined tolerance value.

The aforementioned embodiment of the method according to the invention also realizes the above-mentioned additional conditions. This embodiment realizes an exact maximization of the coolant flow if the surface temperature actually corresponds to the minimum value after its iterated calculation. However, slightly exceeding the minimum value is acceptable for the reasons mentioned above and represents a quasi-maximization of the coolant flow.

In a further embodiment of the method according to the invention, the maximum value of the coolant flow specific for the respective cooling device is accepted as a default value for the coolant flow for each simulated cooling section run.

The aforementioned embodiment of the method according to the invention enables, in particular, the fastest possible cooling of the rolling stock when passing through a cooling section by setting each default value to the maximum value of the coolant flow specific to the respective cooling device.

In an alternative embodiment of the method according to the invention to the above-mentioned embodiment, a total amount of coolant is determined for a simulation of a cooling section passage of a rolling stock section, which is to be output at most in total to the surface part of the rolling stock surface belonging to the rolling stock section during the cooling section passage, and the default values for the coolant flows of the simulated cooling section run-through are determined depending on the total amount of coolant and the transport speed specified for the cooling section run-through. The term coolant quantity always means the integral over a coolant flow during the running time of the rolling stock section under consideration through the effective range of one or more cooling devices. It can also happen that a coolant flow acting on a section of rolling stock does not always have the same effect. Then the amount of coolant means an integral weighted according to the cooling effect of the coolant flow. The physical unit of the coolant flow is, for example, m ² /s corresponding to a specific coolant flow in m ³ /s per m of width of the cooling device. The physical unit of the amount of coolant is then m ² corresponding to an amount of coolant in m ³ per m width of the cooling device.

In the aforementioned embodiment of the method according to the invention, a cooling effect of the entire cooling section run and thus a target temperature of the rolling stock after the cooling section run can be specified by the total amount of coolant. The default values for the coolant flows of the simulated cooling section run are then determined depending on the total amount of coolant, so that the total amount of coolant is distributed to the cooling devices using the default values.

In a further development of the aforementioned embodiment of the method according to the invention, a target average temperature of the rolling stock is taken after a cooling section pass. During each simulation of a cooling section run of a rolling stock section, an average temperature of the rolling stock section is calculated at the end of the cooling section run and, if the calculated average temperature does not correspond sufficiently precisely to the target average temperature, for a subsequent simulation of a cooling section run of a rolling stock section, the total amount of coolant is changed by the calculated average temperature of the target average temperature to align. This advantageously makes it possible to change the total amount of coolant iteratively in order to achieve the target average temperature with sufficient accuracy at the end of a cooling section run. A sufficiently precise agreement between the calculated average temperature and the target average temperature is understood to mean, for example, an agreement up to an absolute or relative deviation, the amount of which does not exceed a predetermined tolerance value. In this further development, a target average temperature of the rolling stock is specified as the target temperature of the rolling stock after passing through the cooling section and the total amount of coolant is adjusted to the target average temperature.

Furthermore, it can be provided that in a simulation of a cooling section passage of a rolling stock section, each A residual amount of coolant is assigned to the cooling device. The total amount of coolant is assigned to the first cooling device of the cooling section passage as the remaining amount of coolant. Each additional cooling device is assigned as the residual coolant amount the residual coolant amount of the previous cooling device of the cooling section passage minus the amount of coolant that would be output by the previous cooling device in accordance with the setting value of the coolant flow determined for it on the surface part of the rolled material surface belonging to the rolling stock section. The default value of the coolant flow of a cooling device is then determined according to w _i ^V = w _i ^max min(1, W ^R / W _i ^max ) as the product of w _i ^max and min(1, W ^R / W _i ^max ), where w _i ^max is the maximum value of the coolant flow of the cooling device, W ^R is the residual amount of coolant assigned to the cooling device and W _i ^max is a maximum amount of coolant that can be dispensed with the cooling device onto the surface part of the rolling stock surface belonging to the rolling stock section during the cooling section pass. min(1, W ^R / W _i ^max ) denotes the minimum of the two values 1 and W ^R / W _i ^max . In this embodiment of the method according to the invention, the default values for the coolant flows of the cooling device are determined during the simulation of a cooling section run by assigning a residual coolant quantity to each cooling device and determining the default value for the cooling device depending on the residual coolant quantity.

Alternatively, it can be provided that, when simulating the cooling section passage of the rolling stock section, a setting value is determined for a cooling device that is smaller than a default value accepted for the cooling device, and if there is at least one subsequent cooling device that is reached later during the cooling section passage and for which a received default value is smaller than the maximum value of the coolant flow of this cooling device, the default value for at least one such subsequent cooling device is increased by to adapt the total amount of coolant to be dispensed during the cooling section pass to the surface part of the rolling stock surface belonging to the rolling stock section to the total amount of coolant determined for the cooling section pass. This embodiment of the method according to the invention is based on default values received at the beginning of a simulation. The default values are adjusted during the simulation if necessary if the setting value determined for a cooling device during the simulation falls below the associated default value. When adjusting the default values, default values for subsequent cooling devices are increased, as far as possible, in order to adapt the cooling effect of the cooling section passage to the cooling effect corresponding to the total amount of coolant.

In a further embodiment of the method according to the invention, in order to calculate the enthalpy distribution and/or temperature distribution in the rolling stock section when it exits the effective range of a cooling device during a simulation of a cooling section pass of the rolling stock section, a one-dimensional heat conduction equation is solved, which determines the enthalpy distribution and/or temperature distribution in the rolling stock section along a Rolling stock thickness direction describes. To solve the heat conduction equation, for example, boundary conditions are taken into account that parameterize cooling of the rolled stock section by thermal radiation, coolant dispensed onto the surface of the rolled stock, heat dissipated into the ambient air and heat dissipated to transport rollers transporting the rolled stock. The rolling stock thickness direction is a direction from a top surface to a bottom surface of the rolling stock or vice versa from the bottom surface to the top surface of the rolling stock.

The aforementioned embodiment of the method according to the invention takes into account that a heat flow in the longitudinal or transverse direction within the rolling stock compared to one Heat flow in the rolling stock thickness direction of the rolling stock is negligible. Therefore, to calculate the enthalpy distribution and/or temperature distribution in the rolling stock section with sufficient accuracy, a one-dimensional heat conduction equation can be used, which describes the enthalpy distribution and/or temperature distribution in the rolling stock section along the rolling stock thickness direction. This significantly reduces the computational effort and time compared to using a two- or three-dimensional heat conduction equation. The boundary conditions mentioned take into account the essential influences on the development of the enthalpy distribution and temperature distribution in the rolling stock.

In a further embodiment of the method according to the invention, the surface temperature of a surface part of the rolling stock surface belonging to the rolling stock section is measured at at least one measuring point, which is passed by a rolling stock section before a cooling section pass, and the original initial enthalpy distribution and / or original initial temperature distribution for a simulation of a cooling section pass of the rolling stock section are determined depending on the at least one measured surface temperature.

The method according to the invention can also be carried out for a top surface of the rolling stock or a bottom surface of the rolling stock or separately for the top surface of the rolling stock and the bottom surface of the rolling stock of the rolling stock.

A cooling section according to the invention comprises, in addition to the features of a cooling section mentioned at the outset, a control unit which is set up to operate the cooling section according to the method according to the invention according to one of the preceding claims.

In one embodiment of a cooling section according to the invention with several cooling devices, the cooling devices arranged along the cooling section path according to their maximum values of the coolant flows that can be output, so that the maximum values decrease monotonically towards the finishing train. This advantageously enables rapid cooling of the rolling stock at the beginning of the cooling section. Furthermore, the cooling devices in the rear part of the cooling section can be designed to be simpler and more cost-effective than the cooling devices in the front part of the cooling section, since in the rear part of the cooling section the surface temperature of the rolling stock surface has generally already reached the minimum value and therefore only requires a small cooling capacity there becomes.

• FIG 1 schematisch eine Warmwalzanlage,
• FIG 2 ein Ablaufdiagramm des erfindungsgemäßen Verfahrens,
• FIG 3 ein Ablaufdiagramm eines ersten Ausführungsbeispiels eines Verfahrensschrittes des erfindungsgemäßen Verfahrens,
• FIG 4 ein Ablaufdiagramm eines zweiten Ausführungsbeispiels eines Verfahrensschrittes des erfindungsgemäßen Verfahrens,
• FIG 5 ein Ablaufdiagramm eines dritten Ausführungsbeispiels eines Verfahrensschrittes des erfindungsgemäßen Verfahrens,
• FIG 6 ein Ablaufdiagramm eines vierten Ausführungsbeispiels eines Verfahrensschrittes des erfindungsgemäßen Verfahrens,
• FIG 7 Temperaturverläufe von Temperaturen in einem Walzgutabschnitt vor und während eines Kühlstreckendurchlaufs.

The characteristics, features and advantages of this invention described above, as well as the manner in which these are achieved, will be more clearly and clearly understood in connection with the following description of exemplary embodiments, which will be explained in more detail in connection with the drawings. Show:

• FIG 1 schematically a hot rolling mill,
• FIG 2 a flow chart of the method according to the invention,
• FIG 3 a flowchart of a first exemplary embodiment of a method step of the method according to the invention,
• FIG 4 a flowchart of a second exemplary embodiment of a method step of the method according to the invention,
• FIG 5 a flowchart of a third exemplary embodiment of a method step of the method according to the invention,
• FIG 6 a flowchart of a fourth exemplary embodiment of a method step of the method according to the invention,
• FIG 7 Temperature curves of temperatures in a rolling stock section before and during a cooling section run.

Corresponding parts are provided with the same reference numbers in the figures.

Figure 1 (FIG 1 ) schematically shows a hot rolling mill 1. The hot rolling mill 1 comprises a heating furnace 3, a roughing train 5, an intermediate roller table 7, a finishing train 9, an outlet cooling area 11 and a coiling area 13. The hot rolling mill 1 causes a rolling stock 15 to be rolled in the direction of the heating furnace 3 transported to the reel area 13.

The heating furnace 3 is arranged in front of the roughing train 5 and is set up to heat the rolling stock 15 to a certain temperature, for example in the range from 1100 ° C to 1200 ° C.

The roughing train 5 has at least one roughing mill stand 17. In the roughing train 5, the rolling stock 15 is rolled into a roughing strip with a roughing strip thickness which is, for example, in the range between 30 mm and 170 mm.

The rolling stock 15 is transported from the roughing train 5 to the finishing train 9 at a predetermined transport speed by the intermediate roller table 7. The intermediate roller table 7 has an exemplary embodiment Cooling section 19 according to the invention. The cooling section 19 comprises a plurality of cooling devices 21, 22, 23 arranged one behind the other along a cooling section path through the cooling section 19, a plurality of transport rollers 25 which are set up to transport the rolling stock 15 along the cooling section path through the cooling section, and a control unit 27 which is set up to operate the cooling section 19 according to an exemplary embodiment of the method according to the invention for cooling the rolling stock 15. Examples of embodiments of the method according to the invention are described below using the Figures 2 to 6 described. In Figure 1 A cooling section 19 with three cooling devices 21, 22, 23 is shown as an example. However, the cooling section 19 can also have a different number of cooling devices 21, 22, 23.

With each cooling device 21, 22, 23, a coolant flow of a coolant 35 can be output in an effective area 31, 32, 33 of the cooling device 21, 22, 23 onto a rolling stock surface 29 of the rolling stock 15, which is between the value zero and one for the cooling device 21, 22, 23 specific maximum value can be set. The coolant 35 is, for example, water. In Figure 1 the rolling stock surface 29 is a top surface of the rolling stock 15. In other exemplary embodiments, the rolling stock surface 29 can be a bottom surface of the rolling stock 15, with the cooling devices 21, 22, 23 then being arranged below the rolling stock 15. Furthermore, the cooling section 19 can have cooling devices 21, 22, 23 for both the top and bottom surfaces of the rolling stock 15. In the latter case, the method according to the invention is carried out separately for the top and bottom surfaces of the rolling stock 15.

Each cooling device 21, 22, 23 is designed, for example, as a cooling beam which extends along a width of the rolling stock 15 and has a plurality of nozzles with which coolant 35 can be dispensed onto the rolling stock surface 29 is. The effective areas 31, 32, 33 are assigned to the cooling devices 21, 22, 23 in such a way that the effective areas 31, 32, 33 of adjacent cooling devices 21, 22, 23 directly adjoin one another. For example, the cooling devices 21, 22, 23 are arranged along the cooling section path in accordance with their maximum values of the coolant flows that can be output, so that the maximum values decrease monotonically towards the finishing train 9.

In the intermediate roller table 7, a measuring device 37 is also arranged at a measuring point 39 in front of the cooling section 19, which is set up to record a surface temperature of the rolling stock surface 29. For example, the measuring device 37 has a pyrometer for this purpose.

The finishing train 9 includes several finishing train rolling stands 41 and finishing train cooling devices 43, which are each arranged between two finishing train rolling stands 41 and with which finishing train coolant 45 can be dispensed onto the rolling stock surface 29. In the finishing train 9, the thickness of the rolling stock 15 is reduced to a final thickness using the finishing train rolling stands 41.

In the outlet cooling area 11, outlet cooling devices 47, 49 are arranged, with which outlet coolant 51 can be dispensed onto the rolling stock surface 29. In the outlet cooling area 11, the rolling stock 15 is cooled behind the finishing train 9.

At least one rolled stock reel 53 is arranged in the reel area 13 and is set up to wind up the rolled stock 15.

Figure 2 (FIG 2 ) shows a flow chart of the method according to the invention with method steps 100, 200, 300 for cooling the rolling stock 15 in the cooling section 19.

In a first method step 100, the control unit 27 receives a minimum value T ^min for a surface temperature of the rolling stock surface 29 during the transport of the rolling stock 15 through the cooling section 19. The minimum value T ^min is specified, for example, by a higher-level controller (not shown) or by an operator of the hot rolling mill 1. The minimum value T ^min is a surface temperature of the rolling stock surface 29, which should not be fallen below during the transport of the rolling stock 15 through the cooling section 19.

In a second method step 200, for a cooling section pass of the rolling stock 15 through the cooling section 19, each cooling device 21, 22, 23 is assigned a setting value for the coolant flow to be output from the cooling device 21, 22, 23 to the rolling stock surface 29. Exemplary embodiments of the second method step 200 are described below based on Figures 3 to 6 described in more detail.

In a third method step 300, each cooling device 21, 22, 23 is used to output a coolant flow onto the rolling stock surface 29 during the cooling section run, which flow is set to the setting value assigned to the respective cooling device 21, 22, 23 for the cooling section run in the second method step 200.

The method steps 200 and 300 can also be carried out several times, so that the setting values of the cooling devices 21, 22, 23 are changed if necessary during the transport of the rolling stock 15 through the cooling section 19. This is in Figure 2 indicated by the arrow symbols shown in dashed lines.

For example, the rolling stock 15 is divided into several rolling stock sections, which pass through the effective areas 31, 32, 33 of the cooling devices 21, 22, 23 one after the other, and the method steps 200 and 300 are successively carried out for every section of rolled stock. In this case, in the second method step 200, a setting value for the coolant flow to be output from the cooling device 21, 22, 23 to the part of the rolling stock surface 29 belonging to the rolling stock section is determined for the cooling section passage of a rolling stock section through the cooling section 19 of each cooling device 21, 22, 23 assigned.

In the third method step 300, by means of each cooling device 21, 22, 23, a coolant flow is output to the part of the rolling stock surface 29 belonging to the rolling stock section during the cooling section passage, which is applied to that of the respective cooling device 21, 22, 23 for the cooling section passage of the rolling stock section in the second method step 200 assigned setting value is set. In this case, a delay time period is preferably taken into account for each cooling device 21, 22, 23, which elapses between the change in the setting value of the cooling device 21, 22, 23 and the change in the coolant flow actually output by the cooling device 21, 22, 23 to the changed setting value the setting value of the cooling device 21, 22, 23 is changed at a time which is the delay time before the time at which the rolled stock section enters the effective range 31, 32, 33 of the cooling device 21, 22, 23.

Figure 3 (FIG 3 ) shows a first exemplary embodiment of the second method step 200 with sub-steps 201 to 216 for determining the setting values of the cooling devices 21, 22, 23 for a cooling section passage of the rolling stock 15 through the cooling section 19. The cooling section passage is at least once for a rolling stock section of the rolling stock 15 with the transport speed specified for it is simulated. A running index i = 1, ..., n numbers the effective areas 31, 32, 33 of the cooling devices 21, 22, 23 in the order in which they are removed from a rolling stock section the cooling section pass through, where n denotes the number of cooling devices 21, 22, 23 (as already explained above, are in Figure 1 three cooling devices 21, 22, 23 are shown only as examples; the method is described below for a general number of cooling devices 21, 22, 23).

In a first sub-step 201, a target average temperature is determined T ^S of the rolled stock section after passing through the cooling section, that is, after passing through all effective areas 31, 32, 33. After the first sub-step 201, a second sub-step 202 is carried out.

In the second sub-step 202, a total amount of coolant W is received from coolant 35, which is to be dispensed at most in total during the cooling section passage onto the surface part of the rolled material surface 29 belonging to the rolled material section. After the second sub-step 202, a third sub-step 203 is carried out.

In the third sub-step 203, the total coolant amount W is assigned to a residual coolant amount W ^R as an initial value and the running index i is assigned the value 1 as an initial value. After the third sub-step 203, a fourth sub-step 204 is carried out for the running index value i = 1.

In the fourth sub-step 204, an initial temperature distribution T _i ⁱⁿ ( x ) is received or adopted in the rolling stock section along a rolling stock thickness direction upon entry into the effective region 31, 32, 33 with the respective current value of the running index i . The rolling stock thickness direction is perpendicular to a transport direction of transporting the rolling stock 15 through the cooling section 19 from the top surface to the bottom surface of the rolling stock 15. x denotes a variable along the rolling stock thickness direction, where x = 0 is a point on the top surface of the rolling stock 15 and x = d at the point x = 0 along the rolling stock thickness direction opposite point on the underside surface of the rolling stock 15.

For the running index value i = 1, an original initial temperature distribution is taken as the initial temperature distribution T ₁ ⁱⁿ ( x ), which is derived, for example, from a surface temperature of the rolling stock surface 29, which was detected by the measuring device 37, and/or from a heating temperature of the heating furnace 3. For example, the initial temperature distribution T ₁ ⁱⁿ ( x ) is modeled as a parabolic temperature distribution in the rolling stock thickness direction between an assumed core temperature in the middle between a top and a bottom surface of the rolling stock 15 and the surface temperature detected by the measuring device 37, the core temperature being, for example, from the heating temperature of the heating furnace 3 is derived.

For each running index value i > 1, the temperature distribution _T ⁱ -1 ^out ( x ) is adopted as the initial temperature distribution T _i in ( x ), which was determined in the previous execution of sub-step 207 for the effective range 31, 32, 33 with the running index value i - 1 became: $$\begin{array}{cc}i>1:& {T_i}^{\mathit{in}}\left(x\right)\end{array}={T_{i-1}}^{\mathit{out}}\left(x\right)$$

Alternatively or in addition to the initial temperature distribution T _i ⁱⁿ ( x ), an initial enthalpy distribution h _i ⁱⁿ ( x ) can be accepted or adopted in the sub-step 204 in an analogous manner for the current running index value i . After the fourth sub-step 204, a fifth sub-step 205 is carried out.

In the fifth sub-step 205, a default value w _i ^V for the coolant flow of the cooling device 21, 22, 23 is determined with the current value of the running index i . For this purpose, for example, a maximum amount of coolant W _i ^max is determined, which can be adjusted to the cooling device 21, 22, 23 The surface part of the rolling stock surface 29 belonging to the rolling stock section can be output during the cooling section pass. The maximum coolant quantity W _i ^max depends in particular on the maximum value w _i ^mαx of the coolant flow that can be dispensed and on the predetermined transport speed, which is specific for the cooling device 21, 22, 23. The default value w _i ^V is then defined as the product of the maximum value w _i ^mαx and the minimum min(1, W ^R / W _i ^max ) of the two values 1 and W ^R / W _i ^max : $${w_i}^v={w_{\mathrm{<figure-callout\; id="1"\; label="i\; Max\; min"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">i</figure-callout>}}}^{\mathit{Max}}\min \left(1,W^R/{W_i}^{\mathit{Max}}\right)$$

In other words, the default value w _i ^V corresponds to the maximum value w _i ^mαx of the outputable coolant flow specific to the cooling device 21, 22, 23 if the current value of the residual coolant quantity W ^R is greater than the maximum coolant quantity W _i ^mαx or equal to the maximum coolant quantity W _i is ^max . Otherwise, the default value w _i ^V is the quotient of the current value of the residual coolant quantity W ^R and an effective throughput time W _i ^max / w _i ^max of the rolled stock section through the effective range 31, 32, 33 with the current value of the running index i . After the fifth sub-step 205, a sixth sub-step 206 is carried out.

In the sixth sub-step 206, the setting value w _i of the coolant flow for the cooling device 21, 22, 23 is assigned the default value w _i ^V determined for this coolant flow in the previous execution of the fifth sub-step 205 with the current value of the running index i as the initial value. After the sixth sub-step 206, a seventh sub-step 207 is carried out.

In the seventh sub-step 207, a temperature distribution T _i ^out ( x ) in the rolling stock section along the rolling stock thickness direction as it exits the effective region 31, 32, 33 is calculated with the current value of the running index i . The temperature distribution T _i ^out ( x ) is calculated using a physical model that shows the temporal development of the temperature distribution in the rolled stock section described by a one-dimensional heat conduction equation. The heat conduction equation is solved for the boundary conditions mentioned below with the associated initial temperature distribution T _i ⁱⁿ ( x ) as the temperature distribution upon entry into the respective effective range 31, 32, 33.

Alternatively or in addition to the temperature distribution T _i ^out ( x ), in the seventh sub-step 207 an enthalpy distribution h _i ^out ( x ) can be calculated analogously in the rolling stock section as it exits the effective area 31, 32, 33 with the current value of the running index i , if in the previous execution of the fourth sub-step 204 an associated initial enthalpy distribution h _i ⁱⁿ ( x ) was received or adopted upon entry into this effective range 31, 32, 33.

A simple form of the heat conduction equation is $$\frac{\partial T\left(x,t\right)}{\partial t}=a\frac{{\partial }^{2}T\left(x,t\right)}{\partial x^2}$$

die Temperaturleitfähigkeit des Walzguts 15, wobei λ seine Wärmeleitfähigkeit,

seine Dichte und c seine Wärmekapazität bezeichnen.There is

the thermal conductivity of the rolling stock 15, where λ is its thermal conductivity,

denotes its density and c denotes its heat capacity.

verwendet und für die unterseitige Oberfläche wird $$j_{\mathrm{u}}\left(T_{\mathrm{u}}\right)={\epsilon }_{\mathrm{u}}\left(T_{\mathrm{u}}^4-T_{\mathrm{e}}^4\right)+f_{\mathrm{L}}\left(T_{\mathrm{u}},T_{\mathrm{e}},v\right)+f_{\mathrm{R}}\left(T_{\mathrm{u}},T_{\mathrm{e}},v\right)+f_{\mathrm{w}}\left(T_{\mathrm{u}},v,T_{\mathrm{w}},w_{\mathrm{ui}}\right)$$

verwendet. Dabei sind v die mittlere Transportgeschwindigkeit während des Durchlaufs durch den Wirkbereich, fortan einfach mit Transportgeschwindigkeit bezeichnet, ε _o ein Abstrahlkoeffizient von Wärmestrahlung der oberseitigen Oberfläche und ε _u ein Abstrahlkoeffizient von Wärmestrahlung der unterseitigen Oberfläche, der aufgrund der Reflektion von Wärmestrahlung an den Transportrollen 25 kleiner als ε _o ist. f_L (T _o,T _e,v) und f _L(T _u,T _e,v) sind Funktionen, die die Abkühlwirkung der Umgebungsluft in Abhängigkeit von der Oberflächentemperatur T _o des Walzguts 15 an der oberseitigen Oberfläche beziehungsweise von der Oberflächentemperatur T _u des Walzguts 15 an der unterseitigen Oberfläche, der Umgebungstemperatur T _e und der Transportgeschwindigkeit v beschreiben. f _R(T _u,T _e,v) ist eine Funktion, die die Kühlwirkung der Transportrollen 25 in Abhängigkeit von der Oberflächentemperatur T _u, der Umgebungstemperatur T _e und der Transportgeschwindigkeit v beschreibt. f_w (T _o,v,T_w ,w _oi) ist eine Funktion, die die Kühlwirkung einer oberseitigen Kühleinrichtung 21, 22, 23, das heißt einer die oberseitige Oberfläche des Walzguts 15 kühlenden Kühleinrichtung 21, 22, 23, mit dem Laufindexwert i in Abhängigkeit von der Oberflächentemperatur T _o, der Transportgeschwindigkeit v, der Kühlmitteltemperatur T_w und dem durch den Einstellwert w_oi gegebenen Kühlmittelstrom der Kühleinrichtung 21, 22, 23 beschreibt. f_w (T _u,v,T_w ,w _ui) ist entsprechend eine Funktion, die die Kühlwirkung einer unterseitigen Kühleinrichtung 21, 22, 23 mit dem Laufindexwert i in Abhängigkeit von der Oberflächentemperatur T _u, der Transportgeschwindigkeit v, der Kühlmitteltemperatur T _w und dem durch den Einstellwert w_ui gegebenen Kühlmittelstrom der Kühleinrichtung 21, 22, 23 beschreibt.The heat flow density j _o for the top surface ( x = 0) and the heat flow density j _u for the bottom surface ( x = d ) of the rolling stock 15 are required as boundary conditions for the heat conduction equation (3). For example, for the top surface $$j_{\mathrm{O}}\left(T_{\mathrm{O}}\right)={\epsilon }_{\mathrm{O}}\left(T_{\mathrm{O}}^4-{\mathrm{<figure-callout\; id="4"\; label="T\; e"\; filenames="imgf0007.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{e}}^{\mathrm{}}\right)+f_{\mathrm{L}}\left(T_{\mathrm{O}},T_{\mathrm{e}},v\right)+f_{\mathrm{w}}\left(T_{\mathrm{O}},v,T_{\mathrm{w}},w_{\mathrm{ooh}}\right)$$

used and for the underside surface $$j_{\mathrm{u}}\left(T_{\mathrm{u}}\right)={\epsilon }_{\mathrm{u}}\left(T_{\mathrm{<figure-callout\; id="4"\; label="u"\; filenames="imgf0007.png"\; state="\{\{state\}\}">u</figure-callout>}}^4-{\mathrm{<figure-callout\; id="4"\; label="T\; e"\; filenames="imgf0007.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{e}}^{\mathrm{}}\right)+f_{\mathrm{L}}\left(T_{\mathrm{u}},T_{\mathrm{e}},v\right)+f_{\mathrm{R}}\left(T_{\mathrm{u}},T_{\mathrm{e}},v\right)+f_{\mathrm{w}}\left(T_{\mathrm{u}},v,T_{\mathrm{w}},w_{\mathrm{ugh}}\right)$$

used. Here v is the average transport speed during the passage through the effective area, henceforth simply referred to as transport speed, ε _{o is} a radiation coefficient of thermal radiation from the top surface and ε _u is a radiation coefficient of thermal radiation from the bottom surface, which is smaller due to the reflection of thermal radiation on the transport rollers 25 as ε is _o . f _L ( T _o , T _e , v ) and f _L ( T _u , T _e , v ) are functions that determine the cooling effect of the ambient air depending on the surface temperature T _o of the rolling stock 15 on the top surface and on the surface temperature T _u of the rolling stock 15 on the underside surface, the ambient temperature T _e and the transport speed v . f _R ( T _u , T _e , v ) is a function that describes the cooling effect of the transport rollers 25 as a function of the surface temperature T _u , the ambient temperature T _e and the transport speed v. f _w ( T _o , v , T _w , w _oi ) is a function that represents the cooling effect of a top-side cooling device 21, 22, 23, that is to say a cooling device 21, 22, 23 cooling the top surface of the rolling stock 15, with the running index value i as a function of the surface temperature T _o , the transport speed v, the coolant temperature T _w and the coolant flow of the cooling device 21, 22, 23 given by the setting value w _oi . f _w ( T _u , v , T _w , w _ui ) is accordingly a function that determines the cooling effect of a cooling device 21, 22, 23 on the bottom with the running index value i as a function of the surface temperature T _u , the transport speed v, the coolant temperature T _w and the coolant flow of the cooling device 21, 22, 23 given by the setting value w _ui .

mit den einfacher zu beschreibenden Abhängigkeiten der Kühlwirkung f _T(T,v) von der Transportgeschwindigkeit v und der jeweiligen Oberflächentemperatur T = T_o oder T = T_u , der Abhängigkeit der Kühlwirkung g_T (T _w) von der Kühlmitteltemperatur T _w und der Abhängigkeit der Kühlwirkung h_w (w) vom Kühlmittelstrom w = w_oi oder w = w_ui einer oberseitigen oder unterseitigen Kühleinrichtung 21, 22, 23 mit dem Laufindexwert i. An Stellen des Kühlstreckenweges, an denen kein Kühlmittelstrom von einer oberseitigen Kühleinrichtung 21, 22, 23 auf das Walzgut 15 ausgegeben wird, gilt f_w(T₀ ,v,T_w ,w _oi) = 0. Entsprechend gilt f_w (T_u ,v,T_w ,w_ui ) = 0 an Stellen des Kühlstreckenweges, an denen kein Kühlmittelstrom von einer unterseitigen Kühleinrichtung 21, 22, 23 auf das Walzgut 15 ausgegeben wird.The function f _w is often separated to enable easier parameterization, for example according to $$f_{\mathrm{w}}\left(T,v,T_{\mathrm{w}},w\right)=f_{\mathrm{T}}\left(T,v\right)G_T\left(T_{\mathrm{w}}\right)H_w\left(w\right)$$

with the easier to describe dependencies of the cooling effect f _T ( T , v ) on the transport speed v and the respective surface temperature T = T _o or T = T _u , the dependence of the cooling effect g _T ( T _w ) on the coolant temperature T _w and the dependence of the cooling effect h _w ( w ) on the coolant flow w = w _oi or w = w _ui of a top side or underside cooling device 21, 22, 23 with the running index value i . At points on the cooling section path where no coolant flow is output from a top-side cooling device 21, 22, 23 onto the rolling stock 15 , f _w (T ₀ , v , T _w , w _oi ) = 0 applies. Correspondingly, f _w ( T _u , v , T _w , w _ui ) = 0 at points on the cooling section path where no coolant flow is output from a cooling device 21, 22, 23 on the bottom to the rolling stock 15.

When the method according to the invention is carried out for top-side and bottom-side cooling devices 21, 22, 23, it is carried out separately for the top-side cooling devices 21, 22, 23 and the bottom-side cooling devices 21, 22, 23. In Figure 3 applies to the top-side cooling devices 21, 22, 23 accordingly w _i = w _oi and to the bottom-side cooling devices 21, 22, 23 correspondingly w _i = w _ui etc., whereby the running range of the running index i for the top-side cooling devices 21, 22, 23 can distinguish from the running range of the running index i for the underside cooling devices 21, 22, 23.

An alternative form of the heat conduction equation is $$\frac{\partial }{\partial t}{\displaystyle \sum _{k=1}^m{p}_k{H}_k}-\frac{\partial }{\partial x}\left[\frac{\lambda \left(H,{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,\dots ,p_m\right)}{\rho }\frac{\partial T\left(H,{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,\dots ,p_m\right)}{\partial x}\right]=0$$

gilt. Weiterhin gibt es für jeden Phasenanteil bekannte Abhängigkeiten zwischen der Enthalpiedichte h_k des jeweiligen Phasenanteils und der zugehörigen Temperatur T_k , d. h. die Temperatur T_k = T_k (h_k ) ist eine streng monoton steigende Funktion des Enthalpiedichteanteils h_k . Dabei gilt T₁ (h₁ ) = T ₂(h₂ ) = ··· = T_m (h_m ) = T, da die Temperatur an einer Stelle x nur einen Wert haben kann, der für alle Phasenanteile gleich ist. Durch Lösen dieses Gleichungssystems lässt sich die Funktion T(h,p ₁ , ... , p_m ) berechnen. Entsprechend lässt sich die Wärmeleitfähigkeit λ als Funktion der Enthalpiedichte h und der Phasenanteile p ₁, ... , p_m ausdrücken. Die Größe ρ bezeichnet die für alle Phasenanteile gleich angenommene Dichte des Walzguts 15.In equation (5) , p _k , k = 1, ... , m are phase components of the rolled stock 15, for example an austenite component, a ferrite component, a cementite component and/or other components. The phase components are always non-negative and their sum is one. The quantity h is an enthalpy density, where $H={\displaystyle {\sum }_{k=1}^m{p}_k{H}_k}$

applies. Furthermore, for each phase component there are known dependencies between the enthalpy density h _k of the respective phase component and the associated temperature T _k , ie the temperature T _k = T _k ( h _k ) is a strictly monotonically increasing one Function of the enthalpy density component h _k . The following applies: T ₁ ( h ₁ ) = T ₂ ( h ₂ ) = ··· = T _m ( h _m ) = T , since the temperature at one point x can only have one value that is the same for all phase components. By solving this system of equations, the function T ( h,p ₁ , ... , p _m ) can be calculated. Accordingly, the thermal conductivity λ can be expressed as a function of the enthalpy density h and the phase proportions p ₁ , ... , p _m . The size ρ denotes the density of the rolling stock 15, which is assumed to be the same for all phase components.

ansetzen.The phase proportions can be calculated as required, in particular in conjunction with the solution to the heat conduction equation. For example, you can use a coupled differential equation system for the phase components $$\begin{array}{cc}\frac{\mathrm{d}{p}_k}{\mathrm{d}t}=f_{\mathrm{p}k}\left(T,{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,\dots ,p_m\right),& k=1,\dots ,m\end{array}$$

put on.

in dem Walzgutabschnitt beim Austritt aus dem Wirkbereich 31, 32, 33 mit dem jeweils aktuellen Wert des Laufindex i zu berechnen.Equation (3) or equations (5) and (6) are calculated with the boundary conditions according to equations (4a) and (4b) for an initial temperature distribution T _i ⁱⁿ ( x ) or an initial enthalpy distribution h _i ⁱⁿ ( x ) and initial phase proportions p _{1 i} , ... , p _mi solved to obtain a temperature distribution T _i ^out ( x ) or an enthalpy distribution h _i ^out ( x ) and phase components $p_{1i}^{\mathit{out}},\dots ,p_{\mathit{mi}}^{\mathit{out}}$

in the rolling stock section when leaving the effective area 31, 32, 33 with the current value of the running index i .

The functions f _L , f _w , f _R entering equations (4a) and (4b) are suitably parameterized in a manner known from the prior art, for example as so-called B-splines. In some cases closed representations can also be specified. In this regard, for example, the Publication W. Timm et al. (2002), Modeling of heat transfer in hot strip mill runout table cooling, Steel Research, 73: 97-104, https://doi.org/10.1002/srin.200200180 referred. In equation (6) the functions f _L , f _w , f _R are each set as the product of a heat flow constant Q̇ _i and dimensionless correction functions f _i , where the index i stands for the respective type of cooling (through air, coolant or transport rollers), see also, for example, equations (7) to (9) the aforementioned publication for cooling by air, the equations (11) to (14) for (various types of) cooling by coolant and equation (10) for cooling by transport rollers.

After the seventh sub-step 207, an eighth sub-step 208 is carried out.

In the eighth sub-step 208, it is checked whether the temperature T _i ^out (0) calculated in the seventh sub-step 207 on the rolling stock surface 29 when exiting the effective area 31, 32, 33 with the current value of the running index i exceeds the minimum value T ^min or is equal to the minimum value T ^min (in the case that the rolling stock surface 29 is the underside surface of the rolling stock 15, here T _i ^out (0) should be replaced by T _i ^out ( d ) or the choice of coordinate x should be adjusted so that x = 0 denotes the underside surface of the rolling stock 15). If this is not the case, a ninth sub-step 209 is carried out. Otherwise, a tenth sub-step 210 is carried out.

The ninth sub-step 209 is therefore always carried out when the calculated surface temperature of the rolling stock surface 29 when exiting the effective area 31, 32, 33 with the current value of the running index i falls below the minimum value T ^min , that is, when the current setting value w _i is too high for this value of the running index i . In the ninth sub-step 209, this setting value w _i is therefore assigned a new (smaller) value, for example using a Newton method in such a way that the surface temperature calculated for the new setting value w _i is approximated to the minimum value T ^min . The seventh sub-step 207 and the eighth sub-step 208 are then carried out again, i.e. the surface temperature at the exit from the effective range 31, 32, 33 with the current value of the running index i is calculated for the new setting value w _i . This is repeated until the calculated surface temperature agrees with the minimum value T ^min or slightly exceeds it, for example by a maximum of 10 ° C, preferably by a maximum of 5 ° C. The tenth sub-step 210 is then carried out.

berechnen. Nach dem zehnten Teilschritt 210 wird ein elfter Teilschritt 211 ausgeführt.In the tenth sub-step 210, the value of the residual coolant quantity W ^R is changed by subtracting from the previous value the coolant quantity W _{i corresponding} to the setting value w i, which is supplied by the cooling device 21, 22, 23 with the current value of the running index i to the surface part of the rolling stock surface 29 belonging to the rolling stock section would be output. The amount of coolant W _i can be determined, for example, according to $$W_i=\frac{w_i{W_i}^{\mathit{Max}}}{{w_i}^{\mathit{Max}}}$$

calculate. After the tenth sub-step 210, an eleventh sub-step 211 is carried out.

In the eleventh sub-step 211 it is checked whether the current value of the running index i has reached the final value n , that is, whether the simulated cooling section run has ended. If this is not the case, a twelfth sub-step 212 is carried out. Otherwise, a thirteenth sub-step 213 is carried out.

In the twelfth sub-step 212, the value of the running index i is incremented. The fourth sub-step 204 is then carried out for the new value of the running index i .

aus der bei der vorhergehenden Ausführung des siebten Teilschritts 207 berechneten Temperaturverteilung T_n ^out (x) berechnet. Gemäß Gleichung (8) ist die berechnete Durchschnittstemperatur nach dem simulierten Durchlaufen aller Wirkbereiche 31, 32, 33 eine über die Dicke des Walzguts 15 gemittelte Temperatur beim Austritt aus dem Wirkbereich mit dem Laufindexwert i = n, das heißt beim Austritt aus dem bei dem Kühlstreckendurchlauf zuletzt durchlaufenen Wirkbereich. Nach dem dreizehnten Teilschritt 213 wird ein vierzehnter Teilschritt 214 ausgeführt.In the thirteenth sub-step 213, an average temperature of the rolled stock section is determined after the simulated passage through the cooling section, that is, after the simulated passage through all effective areas 31, 32, 33. calculated. This average temperature is, for example, according to $${{\bar{T}}_n}^{\mathit{out}}=\frac{1}{d}{\displaystyle \underset{0}{\overset{d}{\int }}{T_n}^{\mathit{out}}\left(x\right)\mathrm{d}x}$$

from the temperature distribution T _n ^out ( x ) calculated in the previous execution of the seventh sub-step 207. According to equation (8), the calculated average temperature after the simulated passage through all effective areas 31, 32, 33 is a temperature averaged over the thickness of the rolling stock 15 at the exit from the effective area with the running index value i = n , that is, at the exit from the cooling section pass effective range last passed through. After the thirteenth sub-step 213, a fourteenth sub-step 214 is carried out.

In the fourteenth sub-step 214 it is checked whether the average temperature calculated in the previous execution of the thirteenth sub-step 213 T _n ^out with sufficient accuracy with the target average temperature T ^S of the rolled stock section after the cooling section passes. A sufficiently precise match is understood to mean, for example, a match up to an absolute or relative deviation, the amount of which does not exceed a predetermined tolerance value. Is the average temperature correct? T _n ^out not sufficiently accurate with the target average temperature T ^S , a fifteenth sub-step 215 is carried out after the fourteenth sub-step 214. Otherwise, after the fourteenth sub-step 214, a sixteenth sub-step 216 is carried out.

The fifteenth sub-step 215 is therefore carried out when the calculated average temperature T _n ^out is not sufficiently accurate to the target average temperature after the simulated cooling section run T ^S matches. If the calculated average temperature T _n ^out the target average temperature T ^S exceeds, this indicates that the total amount of coolant W used as the basis for the simulated cooling section run was too small. If the calculated average temperature T _n ^out the target average temperature T If the value falls below ^S , this indicates that the total amount of coolant W used as the basis for the simulated cooling section run was too large. Therefore, in the fifteenth sub-step 215, the value of the total amount of coolant W is changed, for example by an amount that is dependent on the deviation of the calculated average temperature T _n ^out of the target average temperature T ^S depends. This allows the calculated average temperature T _n ^out after the next simulated cooling section run of the target average temperature T ^S can be approximated. The adjustment of the total amount of coolant W can be improved in later simulated cooling section runs, for example using a Newton method.

erreicht oder überschreitet oder die Restkühlmittelmenge W^R nach Ausführen des Teilschrittes 210 für i = n nicht Null geworden ist, d. h. die anfängliche Gesamtkühlmittelmenge W zu groß war. Der Maximalwert W^max ist eine maximale Kühlmittelmenge, die von allen Kühleinrichtungen 21, 22, 23 zusammen bei dem Kühlstreckendurchlauf (mit der für ihn vorgegebenen Transportgeschwindigkeit) des Walzgutabschnitts auf den zu dem Walzgutabschnitt gehörenden Teil der Walzgutoberfläche 29 ausgebbar ist.After the fifteenth sub-step 215, the third sub-step 203 is carried out with the new value of the total amount of coolant W , that is to say a further simulation of the cooling section run of the rolling stock section is started with the changed value of the total amount of coolant W. The simulation of the cooling section cycle is repeated with a changed value of the total coolant quantity W until the calculated average temperature T _n ^out after a simulated cooling section run is sufficiently accurate to the target average temperature T ^S matches, or the value of the total coolant quantity W becomes zero or a maximum value $W^{\mathit{Max}}={\displaystyle {\sum }_{i=1}^n{W_i}^{\mathit{Max}}}$

reached or exceeded or the remaining amount of coolant W ^R did not become zero after carrying out sub-step 210 for i = n , ie the initial total amount of coolant W was too large. The maximum value W ^max is a maximum amount of coolant that can be transferred from all cooling devices 21, 22, 23 together during the cooling section passage (at the transport speed specified for it) of the rolling stock section Part of the rolling stock surface 29 belonging to the rolling stock section can be output.

If the calculated average temperature T _n ^out after a simulated cooling section run is sufficiently accurate to the target average temperature T ^S matches, the sixteenth sub-step 216 is carried out after the fourteenth sub-step 214 of this simulated cooling section run.

When the value of the total coolant amount W becomes zero, each setting value w _i , i = 1, ... , n is assigned the value zero, that is, ∀ i : w _i = 0 is set, and then the sixteenth sub-step 216 is carried out. If the value of the total amount of coolant W reaches or exceeds the maximum value W ^max , each setting value w _i is assigned the maximum value w _i ^mαx specific for the respective cooling device 21, 22, 23, that is, Vi: w _i = w _i ^mαx is set, and then the sixteenth sub-step 216 is carried out. The cases in which the total amount of coolant W becomes zero or reaches or exceeds the maximum value W ^max are in the Figures 3 and 4 not shown for clarity. These cases are exceptional cases, since in the case W = 0 no active cooling of the rolling stock 15 in the cooling section 19 is implied and in the case W = W ^max a maximum possible cooling of the rolling stock 15 in the cooling section 19 is implied, in which each cooling device 21, 22, 23 the maximum possible coolant flow specific to the cooling device 21, 22, 23 is output.

In the sixteenth sub-step 216, the second method step 200 is ended and the setting value w _{i of} the coolant flow last determined in method step 200 is saved for each cooling device 21, 22, 23. The coolant flow of the respective cooling device 21, 22, 23 is set to this setting value w _i in the third method step 300.

Figure 4 (FIG 4 ) shows a second exemplary embodiment of method step 200. This exemplary embodiment differs from that based on Figure 3 described first exemplary embodiment only in a modification of the sub-step 206 and the omission of the sub-steps 208 and 209. Therefore, only the changes compared to the one based on Figure 3 described first embodiment described and commented.

bestimmt. In Gleichung (9) ist w_i ^V der Vorgabewert, der bei der vorhergehenden Ausführung des Teilschrittes 205 für den Kühlmittelstrom der Kühleinrichtung 21, 22, 23 mit dem aktuellen Wert des Laufindex i bestimmt wurde. T_i ⁱⁿ (0) ist ein Wert der Oberflächentemperatur der Walzgutoberoberfläche 29 beim Eintritt in den Wirkbereich 31, 32, 33 dieser Kühleinrichtung 21, 22, 23, der aus der bei der vorhergehenden Ausführung des Teilschrittes 204 entgegengenommenen Temperaturverteilung T_i ⁱⁿ (x) abgeleitet wird. Im Fall, dass die Walzgutoberoberfläche 29 die unterseitige Oberfläche des Walzguts 15 ist, ist in Gleichung (9) und Figur 4 T_i ⁱⁿ (0) durch T_i ⁱⁿ (d) zu ersetzen oder die Wahl der Koordinate x so anzupassen, dass x = 0 die unterseitige Oberfläche des Walzguts 15 bezeichnet.In the sub-step 206, in this exemplary embodiment, during a simulated cooling section run of a rolled stock section, the setting value w _i of the coolant flow for the cooling device 21, 22, 23 is adjusted according to the current value of the running index i $$w_i=f_i\left({T_i}^{\mathit{in}}\left(0\right)\right){w_i}^v$$

certainly. In equation (9), w _i ^V is the default value that was determined in the previous execution of sub-step 205 for the coolant flow of the cooling device 21, 22, 23 with the current value of the running index i . T _i ⁱⁿ (0) is a value of the surface temperature of the surface of the rolling stock 29 when it enters the effective area 31, 32, 33 of this cooling device 21, 22, 23, which is derived from the temperature distribution T _i ⁱⁿ ( x ) taken in the previous execution of sub-step 204. is derived. In the case that the rolling stock surface 29 is the underside surface of the rolling stock 15, in equation (9) and Figure 4 To replace T _i ⁱⁿ ( 0 ) with T _i ⁱⁿ ( d ) or to adapt the choice of coordinate x so that x = 0 denotes the underside surface of the rolling stock 15.

T^min ist der im ersten Verfahrensschritt 100 entgegengenommene Minimalwert für eine Oberflächentemperatur der Walzgutoberfläche 29 während des Transports des Walzguts 15 durch die Kühlstrecke 19. ΔT_i ^res ist eine Reservetemperaturdifferenz, die derart vorgegeben wird, dass die Oberflächentemperatur der Walzgutoberfläche 29 beim Austritt aus dem Wirkbereich 31, 32, 33 der Kühleinrichtung 21, 22, 23 mit dem Laufindexwert i selbst dann den Minimalwert T^min nicht unterschreitet, wenn die Oberflächentemperatur der Walzgutoberfläche 29 beim Eintritt in diesen Wirkbereich 31, 32, 33 größer als T^min +ΔT_i ^res ist und der von der Kühleinrichtung 21, 22, 23 mit dem Laufindexwert i auf die Walzgutoberfläche 29 ausgegebene Kühlmittelstrom maximal ist, das heißt den für die Kühleinrichtung 21, 22, 23 spezifischen Maximalwert w_i ^mαx annimmt. ΔT_i ^res wird beispielsweise in einer separaten Simulation eines Kühlstreckendurchlaufs des Walzguts 15 oder anhand eines mathematischen Modells der Kühlstrecke 19 in Abhängigkeit von einer Heiztemperatur des Erwärmungsofens 3 und der Transportgeschwindigkeit des Walzguts 15 bestimmt. Die Reservetemperaturdifferenz ΔT_i ^res kann vom Wert des Laufindex i abhängen, das heißt für voneinander verschiedene Kühleinrichtungen 21, 22, 23 können voneinander verschiedene Reservetemperaturdifferenzen vorgegeben werden. f _i (T ) is a function that is zero for T ≤ T ^min , one for T ≥ T ^min +Δ T _i ^res and increases strictly monotonically in the interval [ T ^min , T ^min +Δ T _i ^res ]. For example, the function f ( T ) in the interval [ T ^min , T ^min +Δ T _i ^res ] is defined according to $$T^{\mathit{min}}\le T\le T^{\mathit{min}}+{{\mathit{\Delta T}}_i}^{\mathit{res}}:f_i\left(T\right)=\frac{T-T^{\mathit{min}}}{{{\mathit{\Delta T}}_i}^{\mathit{res}}}$$

T ^min is the minimum value received in the first method step 100 for a surface temperature of the rolling stock surface 29 during the transport of the rolling stock 15 through the cooling section 19. ΔT _i ^res is a reserve temperature difference that is specified in such a way that the surface temperature of the rolling stock surface 29 when leaving the effective range 31, 32, 33 of the cooling device 21, 22, 23 with the running index value i does not fall below the minimum value T ^min even if the surface temperature of the rolling stock surface 29 when entering this effective range 31, 32, 33 is greater than T ^min +Δ T _i ^res is and the coolant flow output from the cooling device 21, 22, 23 with the running index value i onto the rolling stock surface 29 is maximum, that is to say it assumes the maximum value w _i ^mαx specific for the cooling device 21, 22, 23. Δ T _i ^res is determined, for example, in a separate simulation of a cooling section pass of the rolling stock 15 or based on a mathematical model of the cooling section 19 as a function of a heating temperature of the heating furnace 3 and the transport speed of the rolling stock 15. The reserve temperature difference Δ T _i ^res can depend on the value of the running index i , that is to say that different reserve temperature differences can be specified for cooling devices 21, 22, 23 that are different from one another.

This in Figure 4 The second exemplary embodiment of method step 200 shown is simpler than that in Figure 3 shown first embodiment, because the sub-steps 208 and 209 and thus the potential iteration of the sub-steps 207 to 209 are omitted. In particular, the second exemplary embodiment of method step 200 generally requires less computing effort than the first exemplary embodiment and therefore generally also requires a shorter computing time or a lower computing capacity. In contrast, the first exemplary embodiment of the method step 200 generally enables the rolling stock 15 to cool more quickly than the second exemplary embodiment, since the iteration of the sub-steps 207 to 209 enables a more precise adjustment of the setting values for the coolant flows of the cooling devices 21, 22, 23 to the minimum value T ^min .

It has already been stated above that one embodiment of the method according to the invention provides for the method steps 200 and 300 to be carried out successively for rolled stock sections of the rolled stock 15, which pass through the effective areas 31, 32, 33 of the cooling devices 21, 22, 23 one after the other. In this embodiment of the method according to the invention, the method step 200 is carried out, for example, for each rolled stock section according to one of the Figures 3 or 4 described exemplary embodiments carried out. However, it is also possible as an alternative using the Figures 3 and 4 to modify the exemplary embodiments described for this embodiment of the method according to the invention.

Figure 5 (FIG 5 ) shows such a modification of the in Figure 3 shown embodiment. In this modification, a second running index j is used, which numbers the rolled stock sections. In the second sub-step 202, as in Figure 3 In the exemplary embodiment shown, an initial total amount of coolant W is received from coolant 35. In addition, in the second sub-step 202, the value 1 is assigned to the second running index j as an initial value. The sub-steps 203 to 214 are for the current value of the second running index j, that is, for the associated rolled stock section, like the sub-steps 203 to 214 of in Figure 3 shown embodiment executed.

In the case that the average temperature calculated in sub-step 213 T _n ^out with sufficient accuracy with the target average temperature T ^S of the rolled stock section after the cooling section pass corresponds, but now after the sub-step 214 in a sub-step 217 the value of the second running index j is incremented. In the case that the average temperature calculated in sub-step 213 T _n ^out not with sufficient accuracy with the Target average temperature T ^S of the rolled stock section after passing through the cooling section corresponds, as in Figure 3 In the exemplary embodiment shown, the value of the total amount of coolant W is changed in sub-step 215, and then the value of the second running index j is incremented in sub-step 217. It is accepted that rolled stock sections with small values of the second running index j have an average temperature after passing through the cooling section that does not yet match the target average temperature with sufficient accuracy T ^S matches.

After the sub-step 217, the sub-step 203 is carried out for the new value of the second running index j , that is to say a simulation of the cooling section passage of the subsequent rolling stock section is started with a possibly changed total coolant quantity W. At the in Figure 5 In the exemplary embodiment shown, a cooling section run is simulated exactly once for each rolling stock section and a total amount of coolant W , possibly adjusted in sub-step 215, is transferred to the simulation of the cooling section run of the subsequent rolling stock section. In this way, the second method step 200 carried out for a rolled stock section is linked to the second method step 200 carried out for the subsequent rolled stock section. After each execution of the second method step 200, the setting value w _i of the coolant flow determined in this execution of the method step 200 for the respective value of the second running index j is stored for each cooling device 21, 22, 23. The setting values _w i stored for a value of the second running index j are not overwritten by the setting values w _i determined for another value of the second running index j .

The repeated execution of the second method step 200 is ended when the second running index j reaches a final value. For example, after each execution of the second method step 200, it is checked whether the second Run index j has reached the final value, and substep 217 is only executed if this is not the case. Otherwise, the repeated execution of the second method step 200 is terminated. This is in Figure 5 not shown for clarity.

Furthermore, we would have to Figure 5 Strictly speaking, sizes that have an index i or n have an additional index j , insofar as these sizes can differ from one another for different values of the second running index j . For example, the setting value would have to be designated w _ij instead of w _i . This was also the case Figure 5 omitted for the sake of clarity.

The third method step 300 can also be carried out separately for each rolled stock section and can be carried out independently of the other rolled stock sections. The third method step 300 can already be carried out for a value k of the second running index, in which the coolant flow w i determined for this value k _is created by means of the cooling devices 21, 22, 23 during the cooling section passage of the rolling stock section with the value k of the second running index the rolled stock section is output while the second method step 200 is carried out for values j of the second running index with j > k . For this purpose, it is determined for each cooling device 21, 22, 23 in method step 300, depending on the transport speed or the transport speed progression over time, when the rolled stock section with the value k will be in the effective range 31, 32, 33 of the cooling device 21, 22, 23 . Taking into account the associated delay time, the cooling device 21, 22, 23 is then set such that it outputs the coolant flow w _i determined for this value k exactly when the rolled stock section with the value k is in the effective range 31, 32, 33 of the cooling device 21, 22, 23 is located.

Figure 6 (FIG 6 ) shows one to Figure 5 analogous modification of the in Figure 4 shown embodiment of the second method step 200.

The exemplary embodiments of the method according to the invention described above can also be carried out if the rolling stock is transported through the cooling section 19 several times. For example, the finishing train 9 can have a reversing stand through which the rolling stock 15 is guided several times in an alternating direction. Then the rolling stock 15 can also be transported several times in an alternating direction through the cooling section 19. In this case, method steps 200 and 300 are carried out for each cooling section run. For example, in this case, a second measuring point is provided behind the cooling section 19, that is between the intermediate roller table 7 and the finishing train 9, at which a surface temperature of a surface part of the rolling stock surface 29 belonging to a rolling stock section is recorded before the rolling stock section is removed from the second measuring point Cooling section 19 passes through. For a simulation of this cooling section pass of the rolling stock section, an original initial enthalpy distribution and/or original initial temperature distribution is determined as a function of the surface temperature of the surface part of the rolling stock surface 29 belonging to the rolling stock section, which is detected at the second measuring point.

Furthermore, the intermediate roller table 7 can have several cooling sections 19, or a cooling section 19 can have several partial cooling sections, for which the method according to the invention is carried out separately (each partial cooling section is then understood as a cooling section in the sense of the invention). If, for example, an intermediate measuring point is arranged in the intermediate roller table 7, at which a surface temperature of the rolling stock 15 is recorded, the method according to the invention can be used separately for a first partial cooling section or cooling section, which is arranged between the first measuring point 39 and the intermediate measuring point is, and for a second partial cooling section or cooling section, which is arranged between the intermediate measuring point and the finishing train 9. An original initial temperature distribution and/or an original initial enthalpy distribution for the second partial cooling section or cooling section is then determined as a function of the surface temperature of the rolling stock 15 detected at the intermediate measuring point. The procedure can be carried out accordingly if several intermediate measuring points are arranged in the intermediate roller table 7, at each of which a surface temperature of the rolling stock 15 is recorded.

Figure 7 (FIG 7 ) shows examples of temperature curves of temperatures T _K , T _S and resulting when using the method according to the invention T in a rolling stock section before and during a cooling section pass through a cooling section 19 as a function of the time t. T _K denotes a core temperature in the rolling stock section in the middle between a top and a bottom surface of the rolling stock 15. T _S denotes a surface temperature on the rolling stock surface 29 of the rolling stock 15. T denotes an average temperature of the rolled stock section, which is defined analogously to equation (8).

The rolled stock section enters the cooling section 19 approximately 3 s after a time zero point. Due to the cooling effect of cooling devices 21, 22, 23 at the beginning of the cooling section 19, the surface temperature T _S drops quickly from approximately 1070 ° C when the rolled stock section enters the cooling section 19 to the minimum value T ^min , which in this case is approximately 800 ° C and of the surface temperature T _S is reached about 5.5 s after the time zero point. In the further course of the cooling section passage of the rolling stock section, its surface temperature T _S is kept relatively constant at the minimum value T ^min according to the invention by cooling devices 21, 22, 23 of the cooling section 19 until the rolling stock section emerges from the cooling section 19 approximately 7.7 s after the time zero point. The surface temperature T _S then rises again due to the lack of cooling as heat comes from inside the Rolling stock section is guided to the rolling stock surface 29. The core temperature T _K of the rolled stock section remains relatively constant at approximately 1100°C during the cooling section passage. The average temperature T of the rolled stock section falls from approximately 1090°C to approximately 1020°C during the cooling section passage.

Although the invention has been illustrated and described in detail by preferred embodiments, the invention is not limited by the examples disclosed and other variations may be derived therefrom by those skilled in the art without departing from the scope of the invention as defined by the claims.

Reference symbol list

1

Hot rolling mill

3

Heating oven

5

Vorstrasse

7

Intermediate roller table

9

Finishing road

11

Discharge cooling area

13

Reel area

15

rolling stock

17

roughing mill stand

19

cooling section

21, 22, 23

Cooling device

25

Transport roller

27

Control unit

29

rolling stock surface

31, 32, 33

Effective range

35

coolant

37

Measuring device

39

Measuring point

41

Finishing mill mill

43

Finishing line cooling device

45

Finished line coolant

47, 49

Outlet cooling device

51

Discharge coolant

53

rolled stock reel

100, 200, 300

Procedural step

201 to 217

Partial step

t

Time

TK

Core temperature

T.S

Surface temperature

T

Average temperature

Claims (14)

1. Method for cooling a rolled product (15) in a cooling section (19) which is arranged upstream of a finishing train (9) of a hot rolling mill (1) and through which the rolled product (15) is transported along a cooling section path once at a predetermined transport speed or several times in alternating directions, each time at a predetermined transport speed, and which has a cooling device (21, 22, 23) with an active region (31, 32, 33) or a plurality of cooling devices (21, 22, 23) arranged one behind the other along the cooling section path, each with an active region (31, 32, 33), wherein the active regions (31, 32, 33) of adjacent cooling devices (21, 22, 23) are directly adjacent to one another and with each cooling device (21, 22, 23) in its active region (31, 32, 33) a coolant flow of a coolant (35) can be delivered onto a rolled product surface (29) of the rolled product (15), which can be set between the value zero and a maximum value specific to the cooling device (21, 22, 23),
   characterized in that

   - a minimum value for a surface temperature (T_s) of the rolled product surface (29) is accepted during the transport of the rolled product (15) through the cooling section (19),

   - in order to maintain the minimum value, a set value for the coolant flow is assigned to each cooling device (21, 22, 23) for each cooling section pass through the cooling section (19), and

   - a coolant flow is delivered onto the rolled product surface (29) by means of each cooling device (21, 22, 23) for each cooling section pass, which is set to the set value assigned to the relevant cooling device (21, 22, 23) for the cooling section pass,

   - wherein, in order to determine the set values for a cooling section pass, the cooling section pass is simulated at least once for a rolled product section of the rolled product (15) through the cooling section (19) at the predetermined transport speed, wherein, for each simulated cooling section pass, successively for each cooling device (21, 22, 23)

   -- a default value for a coolant flow to be delivered by the cooling device (21, 22, 23) is received or determined at the latest immediately before the rolled product section enters the active region (31, 32, 33) of the cooling device (21, 22, 23),

   -- based on an initial enthalpy distribution and/or initial temperature distribution in the rolled product section upon entry into the active region (31, 32, 33) of the cooling device (21, 22, 23), an enthalpy distribution and/or temperature distribution in the rolled product section upon exit from the active region (31, 32, 33) of the cooling device (21, 22, 23) is calculated using a physical model,

   -- the set value is determined in such a way that it quasi-maximizes the coolant flow to be delivered from the cooling device (21, 22, 23) onto the rolled product surface (29) under the secondary conditions, that the set value does not exceed the default value and a surface temperature of the rolled product surface (29) derived from the initial enthalpy distribution and/or initial temperature distribution or a surface temperature of the rolled product surface (29) derived from the calculated enthalpy distribution and/or calculated temperature distribution of the rolled product section does not fall below the minimum value upon exit from the active region (31, 32, 33) of the cooling device (21, 22, 23),

   -- wherein for each two active regions (31, 32, 33) passed through in immediate succession by the rolled product section during the cooling section pass, the enthalpy distribution and/or calculated temperature distribution calculated for the first active region (31, 32, 33) passed through upon exit from the first active region (31, 32, 33) passed through is assigned to the other active region (31, 32, 33) as the initial enthalpy distribution and/or initial temperature distribution upon entry into the other active region (31, 32, 33), and

   -- wherein an original initial enthalpy distribution and/or original initial temperature distribution is accepted for the first cooling device (21, 22, 23) through which the rolled product section passes during the cooling section pass.
2. Method according to Claim 1, wherein at least one cooling device (21, 22, 23) for each simulated cooling section pass of a rolled product section is assigned the set value according to w_i = f_i (T_i ⁱⁿ (0))w_i ^V , wherein w_i ^V is the default value for the coolant flow to be delivered by the cooling device (21, 22, 23), T_i ⁱⁿ (0) is a surface temperature of the rolled product surface (29), derived from the initial enthalpy distribution and/or initial temperature distribution, upon entry into the active region (31, 32, 33) of the cooling device (21, 22, 23), T^min is the minimum value for the surface temperature (T_S) of the rolled product surface (29), ΔT_i ^res is a predeterminable reserve temperature difference, and f_i(T) is a function that is zero for T ≤ T^min , is one for T ≥ T^min +ΔT_i ^res , and in the interval [T^min , T^min +ΔT_i ^res ] increases strictly monotonically.
3. Method according to Claim 1, wherein the set value for at least one cooling device (21, 22, 23) is determined for each simulated cooling section pass by first calculating the surface temperature of the rolled product surface (29) upon exit from the active region (31, 32, 33) of the cooling device (21, 22, 23) for the default value for the coolant flow of the cooling device (21, 22, 23) and setting the set value equal to the default value if the surface temperature calculated for the default value does not fall below the minimum value, and otherwise the calculation of the surface temperature upon exit from the active region (31, 32, 33) is iterated for at least one coolant flow that is smaller than the default value in order to determine a set value of the coolant flow for which the calculated surface temperature upon exit from the active region (31, 32, 33) matches the minimum value with sufficient accuracy.
4. Method according to one of the preceding claims, wherein for each cooling device (21, 22, 23) the maximum value of the coolant flow specific to the relevant cooling device (21, 22, 23) is accepted as the default value for the coolant flow for each simulated cooling section pass.
5. Method according to one of Claims 1 to 3, wherein a total coolant quantity of coolant (35) is determined for a simulation of a cooling section pass of a rolled product section, which coolant quantity is to be delivered at most in total onto the surface part of the rolled product surface (29) belonging to the rolled product section during the cooling section pass, and the default values for the coolant flows of the simulated cooling section pass are determined in dependence on the total coolant quantity and the transport speed specified for the cooling section pass.
6. Method according to Claim 5, wherein a target average temperature of the rolled product (15) is received after a cooling section pass, in each simulation of a cooling section pass of a rolled product section an average temperature of the rolled product section at the end of the cooling section pass is calculated and, if the calculated average temperature does not correspond sufficiently accurately to the target average temperature, the total coolant quantity is changed for a subsequent simulation of a cooling section pass of a rolled product section in order to bring the calculated average temperature into line with the target average temperature.
7. Method according to Claim 5 or 6, wherein a residual coolant quantity is assigned to each cooling device (21, 22, 23) during a simulation of a cooling section pass of a rolled product section, wherein the total coolant quantity is assigned to the first cooling device (21, 22, 23) of the cooling section pass as the residual coolant quantity and each further cooling device (21, 22, 23) is assigned, as residual coolant quantity, the residual coolant quantity of the preceding cooling device (21, 22, 23) of the cooling section pass minus the coolant quantity that would be delivered by the preceding cooling device (21, 22, 23) according to the coolant flow set value determined for it on the surface part of the rolled product surface (29) belonging to the rolled product section, and the default value of the coolant flow of a cooling device (21, 22, 23) is determined according to w_i ^V = w_i ^max min(1,W^R /W_i ^max ), wherein w_i ^max is the maximum value of the coolant flow of the cooling device (21, 22, 23), W^R is the residual coolant quantity assigned to the cooling device (21, 22, 23) and w_i ^max is a maximum coolant quantity that can be delivered with the cooling device (21, 22, 23) onto the surface part of the rolled product surface (29) belonging to the rolled product section during the cooling section pass.
8. Method according to Claim 5 or 6, wherein, if a set value is determined for a cooling device (21, 22, 23) during the simulation of the cooling section pass of the rolled product section which is smaller than a default value received for the cooling device (21, 22, 23), and if there is at least one subsequent cooling device (21, 22, 23) which is reached later during the cooling section pass and for which a default value received is smaller than the maximum value of the coolant flow of this cooling device (21, 22, 23), the default value for at least one such subsequent cooling device (21, 22, 23) is increased in order to adapt the total quantity of coolant to be delivered onto the surface part of the rolled product surface (29) belonging to the rolled product section during the cooling section pass to the total coolant quantity determined for the cooling section pass.
9. Method according to one of the preceding claims, wherein a one-dimensional heat conduction equation describing the enthalpy distribution and/or temperature distribution in the rolled product section along a rolled product thickness direction is solved to calculate the enthalpy distribution and/or temperature distribution in the rolled product section upon exit from the active region (31, 32, 33) of a cooling device (21, 22, 23) during a simulation of a cooling section pass of the rolled product section.
10. Method according to Claim 9, wherein, to solve the heat conduction equation, boundary conditions are taken into account which parameterize cooling of the rolled product section by thermal radiation, coolant delivered onto the rolled product surface (29), heat dissipated to the ambient air from the rolled product section and heat dissipated from the rolled product section to transport rollers transporting the rolled product (15) .
11. Method according to one of the preceding claims, wherein the surface temperature (T_S) of a surface part of the rolled product surface (29) belonging to the rolled product section is measured at at least one measurement point (39), which is passed by a rolled product section before a cooling section pass, and the original initial enthalpy distribution and/or original initial temperature distribution for a simulation of a cooling section pass of the rolled product section are determined in dependence on the at least one measured surface temperature (T_S) .
12. Method according to one of the preceding claims, which is carried out for a rolled product top surface (29) or a rolled product bottom surface (29) or separately for the rolled product top surface (29) and the rolled product bottom surface (29) of the rolled product (15).
13. Cooling section (19) for cooling a rolled product (15) upstream of a finishing train (9) of a hot rolling mill (1), the cooling section (19) comprising

    - a cooling device (21, 22, 23) or a plurality of cooling devices (21, 22, 23) arranged one behind the other along a cooling section path through the cooling section (19), with each of which a coolant flow of a coolant (35) can be delivered onto a rolled product surface (29) of the rolled product (15), which can be set between the value zero and a maximum value specific to the cooling device (21, 22, 23),

    - a plurality of transport rollers (25) which are designed to transport the rolled product (15) along the cooling section path through the cooling section (19),

    characterized in that the cooling section (19)

    - comprises a control unit (27) which is designed to operate the cooling section (19) in accordance with the method according to one of the preceding claims.
14. Cooling section (19) according to Claim 13 with a plurality of cooling devices (21, 22, 23) which are arranged along the cooling section path according to their maximum values of the deliverable coolant flows, so that the maximum values decrease monotonically towards the finishing train (9).

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