Claims:We claim:
1. A method (100) for determining temperature and cooling rates of a hot rolled steel coil comprising the steps of:
? receiving parameters (10) of the coil as input;
? processing the received parameters (20) comprising the steps of:
? calculating thermal conductivity (21),
? using the calculated thermal conductivity to calculate coil temperature evolution (22),
? post processing to locate the cold and hot point of the coil and calculating its temperature and cooling rate, and
? storing the location of cold and hot point of the coil, its cooling rate and temperature,(30)
2. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein the received parameter (10) comprises thickness of sheet and width of the coil.
3. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein the received parameter (10) comprises difference between inner and outer radius of the coil.
4. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein the received parameter (10) comprises micro-hardness of surface.
5. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein the received parameter (10) comprises oxide scale thickness.
6. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein the received parameter (10) comprises coiling temperature.
7. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein calculating the coil temperature evolution (22) considers contact of first wrap with the initially cold mandrel.
8. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein calculating the coil temperature evolution (22) considers conduction along wraps of the coil.
9. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 1, wherein calculating the coil temperature evolution (22) considers cooling by radiation and convection on all free surfaces of the coil.
10. The method (100) for determining temperature and cooling rates of a hot rolled steel coil as claimed in claim 7, wherein with the contact with mandrel is considered for 120 second.
, Description:FIELD OF THE INVENTION
[001] The present disclosure, in general, relates to hot rolled steel coils and, more particularly, to a method for determine temperature and cooling rates of a hot rolled steel coil.
BACKGROUND OF THE INVENTION
[002] Background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
[003] Thin Slab Caster and Rolling (TSCR) and Hot Strip Mill (HSM) employ hot rolling facilities used for production of thicker sections. Hot rolling is the process used to achieve higher reduction rates. During hot rolling material is deformed at high temperatures almost above recrystallization temperatures. These mills generally consist of a downcoiler, which is underneath floor level at the end of run-out-table. The down-coiler is 3-roller type with variable mandrel i.e., its diameter can be pre-expanded and collapsed. Material properties are effected by each stage starting from steelmaking to coiling. Coiling is a very important stage of rolling especially during rolling of micro-alloyed grades.
[004] Hot rolled strips can obtain lengths between 500–2100 meter, width of 800-2150 millimeter. In general coiling is done at temperatures around 500 -780 °C. The rolled strip reaches the downcoiler at high velocity and get winded up into coil. The coiled material is taken from downcoiler to coil yard through a conveyor. Through all this journey the coil cools down to steady state conditions at room temperature. This cooling process sometime takes more than four days also. Material properties are greatly influenced by relevant microstructure mechanisms such as precipitation, dislocation recovery and solid solution strengthening are result of solid state diffusion, which are functions of temperature.
[005] These mechanisms are greatly driven by the temporal distribution of temperature, initial cooling rates. So there is a requirement to know at what temperature coil is staying and for what duration. This information is important while designing chemistry and process parameters of any new product.
OBJECTIVES OF THE INVENTION
[006] A object of the invention is to provide a method for determining temperature of hottest and coldest spot in a coil.
[007] Another object of the invention is to provide a method for determining cooling rates of hottest and coldest spot in a coil.
[008] Another object of the invention is to provide a method is to identify location of hot spot having the maximum temperature in a coil.
[009] Yet another object of the invention is to provide a method is to identify location of cold spot having the minimum temperature in a coil.
[016] These and other objects and advantages of the present invention will be apparent to those skilled in the art after a consideration of the following detailed description taken in conjunction with the accompanying drawings in which a preferred form of the present invention is illustrated.

SUMMARY OF THE INVENTION
[017] The present invention provides for a method for determining temperature and cooling rates of a hot rolled steel coil.
[018] In accordance with an embodiment of an invention, the method for calculating temperature and cooling rates of a hot rolled steel coil comprising the steps of: receiving parameters of the coil as input, processing and displaying the cold and hot point of the coil and cooling rate.
[019] In accordance with said embodiment, processing the received parameters comprising calculating thermal conductivity, using the calculated thermal conductivity to calculate coil temperature evolution, post processing to locate the cold and hot point of the coil and cooling rate, and storing location of the cold and hot point of the coil of the coil and cooling rate. The processing is performed using any processor known in the art. Further, storing the cold and hot point of the coil and cooling rate in a storing unit as may be known in the art.
[020] In accordance with said embodiment, the received parameters comprise of thickness of sheet and width of the coil, difference between inner and outer radius of the coil, micro-hardness of surface, oxide scale thickness and coiling temperature.
[021] In accordance with said embodiment, calculating the coil temperature evolution considers contact of first wrap with the initially cold mandrel for 120 seconds, conduction along wraps of the coil, cooling by radiation and convection on all free surfaces of the coil.
[022] Various objects, features, aspects, and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components.
[023] It is to be understood that the aspects and embodiments of the disclosure described above may be used in any combination with each other. Several of the aspects and embodiments may be combined to form a further embodiment of the disclosure.
[024] The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
[025] The illustrated embodiments of the subject matter will be best understood by reference to the drawings, wherein like parts are designated by like numerals throughout. The following description is intended only by way of example, and simply illustrates certain selected embodiments of devices, systems, and processes that are consistent with the subject matter as claimed herein, wherein:
Figure 1: illustrates workflow of an exemplary method for determining temperature and cooling rates of a hot rolled steel coil, in accordance with the invention; and
Figure 2: illustrates a) Schematic representation of interface in between steel layers of hot rolled coil and (b) corresponding thermal resistance, in accordance with the invention.
[026] The figures depict embodiments of the disclosure for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles of the disclosure described herein.
DETAILED DESCRIPTION OF THE INVENTION
[024] While the embodiments of the disclosure are subject to various modifications and alternative forms, specific embodiment thereof have been shown by way of example in the figures and will be described below. It should be understood, however, that it is not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alterative falling within the scope of the disclosure.
[025] As used in the description herein and throughout the claims that follow, the meaning of "a," "an," and "the" includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of "in" includes "in" and "on" unless the context clearly dictates otherwise.
[026] The terms "comprises", "comprising", or any other variations thereof used in the disclosure, are intended to cover a non-exclusive inclusion, such that a device, system, assembly that comprises a list of components does not include only those components but may include other components not expressly listed or inherent to the system, or assembly, or device. In other words, one or more elements in a system or device proceeded by "comprises... a" does not, without more constraints, preclude the existence of other elements or additional elements in the system, apparatus or device.
[027] Hereinafter A method (100) for determining temperature and cooling rates of a hot rolled steel coil is explained in more detail.
[028] Referring to figure 1, which illustrates workflow of a method (100) for determining temperature and cooling rates of a hot rolled steel coil in accordance with an embodiment of the invention. The method (100) comprises the steps of:
receiving parameters (10) of the coil as input;
processing the received parameters (20) comprising the steps of:
calculating thermal conductivity (21),
using the calculated thermal conductivity to calculate coil temperature evolution (22),
post processing to locate the cold and hot point of the coil and calculating its temperature and cooling rate, and
storing the location of cold and hot point of the coil its cooling rate and temperature, (30)
.
[029] The method (100) determines cooling rate and temperature as function of time within the coil. This data is generated from the time point when coil is made. Each coil has different properties and dimensions. Receiving parameters (10) include
thickness of sheet, width of coil
difference between inner and outer radius of coil
micro-hardness of surface
oxide scale thickness, and
coiling temperature.
[030] Further, a processing unit as known in the art is utilized to process these parameters (20) and store the processed information in a storing unit as may be known in the art, and the results are displayed to a user (30). The processing (20) is discussed in more detail below.
[031] Coil cooling is an interesting phenomenon where both thermal and mechanical interactions take place simultaneously. Coil is formed by wrapping a steel strip around a mandrel. Thus, a section which cuts the coil radially is a stack of steel layers, we can assume it as an axisymmetric model and its successive wraps of coil as wall of a thick cylinder. Indeed, each steel layer is followed by a thin oxide layer and voids in between oxide scale. Thus, it is important to consider the effect of oxide scale, voids while modelling. We can assume thermal conductivity of its wall to be equivalent effect of steel layers, scale and voids (Fig 1). Thermal resistance of a unit
layer can be compiled by adding resistance due to individual layers.
R=R_steel+R_oxide+R_gap
[032] Heat resistance offered by steel and oxide layer can be calculated from following equation:
? R?_s=t_s/k_s R_o=t_o/k_o
where R, t and k represents thermal resistance, thickness and thermal conductivity of respective layers and subscript o, s and g is for oxide layer, steel layer and average gap between adjacent steel strips.
1/R_gap =1/R_(gap,cv) +1/R_(gap,ca) +1/R_(gap,rd)
[033] Thermal resistance offered by gap is overall effect of conduction through the asperities in contact, radiation in voids formed in between oxide layers also conduction through air. Thus, resistance due to gap can be given as:
where, R(gap,cv) is thermal resistance by voids, R(gap,ca) is resistance through asperities in contact and R(gap,rd) represents radiation in the voids formed in between adjacent steel strips.
[034] As pressure in between layers increase contact points deform causing increase in contact area. So, heat transfer through contact points changes with normal pressure applied. Equation 1 show that contact area due to interaction is not only proportional to load and interface pressure for plastic deformation is replaced by actual contact area,

A=P/(H+P)
[035] Where, P is the normal pressure experienced by the surface (MPa) and H is microhardness of material in MPa. Equation [2] thermal contact resistance between two identical surfaces is

R_(gap,ca)=s_p/(1.13k_s m) (1/A)^0.94
s_p is standard deviation of profile height for asperities, k_sis thermal conductivity of steel in W/moC and m is effective mean absolute surface slope (rad).
Now, thermal resistance by air is given as follows
R_(gap,cv)=t_a/((1-A?)k?_a )
where k_aand t_a are thermal conductivity of air and mean thickness of voids. The mean thickness of air is measured as a function of normal pressure, P (in MPa)
t_a=42.7 ×?10?^(-6) e^(-0.05P)
The thermal resistance of radiation in voids can be expressed as Eqn, 9
R_rd=1/(4(1-A)esT^3 )
where e, s and T are emissivity of coil surface, Stefan Boltzmann constant
(5.67E-8 W/m2K4) and absolute temperature of coil.
The above equations (1) to (9) are used by the inventors to find equivalent thermal conductivity (21) as given below.
k_eq= t/{t_s/k_s + (2t_o)/k_o + [(1.13k_s mA^0.94)/s_p + ((1-A?)k?_a)/(42.7 ×?10?^(-6) e^(-0.05P) )+ 4(1-A)esT^3 ]} 1
[036] Thermal conductivity can be calculated for various temperatures and varying normal pressure. All this methodology is incorporated in Thermal-conductivity.py script file (Fig 2). Data obtained from this step is fed into Coil-cooling simulation. This FE model allows computing the temperature evolution at any position in a coil half section starting from the beginning of the coiling and until the coil complete cooling down to ambient temperature. Simulation of only half section is done to reduce computing time, considering the assumption of a symmetrical cooling in the coil width. The simulation of the coil temperature evolution (22) considers:
the contact of the first wrap with the initially cold mandrel,
conduction along wraps of coil, and
cooling by radiation and convection on all free surfaces of the coil
[037] For this thermo-mechanical simulation, the contact with the mandrel is considered for a few seconds nearly 120 sec. After removal, the internal surface of the coil becomes a free surface, also submitted to radiation and convection and the simulation is performed until the coil reaches ambient temperature. This is a coupled thermal stress simulation done in implicit formulation using Abaqus. USDFLD subroutine is used for giving effect of radial compressive stress on thermal conductivity.
[038 ] Once this simulation is done post-process.py script will be invoked. This script will make sure to locate coldest and hottest point in the axi-symmetric plane of coil. After locating nodal number, its temperature values is extracted for different time frames. Then cooling rate at a particular time frame is estimated from following equation:

?Cooling rate?_i=(?Temperature?_i-?Temperature?_(i-1))/(?Time?_i-?Time?_(i-1) )
here i and i-1 are the time frame numbers.
[039] Post-Process.py script (23) will finally compile this data to a .dat file at a user defined location. This file will contain temporal distribution of cooling rate, temperature at hottest and coldest spot of coil. Also, it will have location of these spots. Further, the information will be displayed to a user (30).
[040] Each of the appended claims defines a separate invention, which for infringement purposes is recognized as including equivalents to the various elements or limitations specified in the claims. Depending on the context, all references below to the "invention" may in some cases refer to certain specific embodiments only. In other cases, it will be recognized that references to the "invention" will refer to subject matter recited in one or more, but not necessarily all, of the claims.
[041] Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all groups used in the appended claims.
[042] With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity.
[043] It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as "open" terms (e.g., the term "including" should be interpreted as "including but not limited to," the term "having" should be interpreted as "having at least," the term "includes" should be interpreted as "includes but is not limited to," etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles, ‘a', or "an" limits any particular claim containing such introduced claim recitation to inventions containing only one such recitation, even when the same claim includes the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an" (e.g., "a" and/or "an" should typically be interpreted to mean "at least one" or "one or more"); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of "two recitations," without other modifiers, typically means at least two recitations, or two or more recitations).
[044] The above description does not provide specific details of manufacture or design of the various components. Those of skill in the art are familiar with such details, and unless departures from those techniques are set out, techniques, known, related art or later developed designs and materials should be employed. Those in the art are capable of choosing suitable manufacturing and design details.
[045] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. It will be appreciated that several of the above-disclosed and other features and functions, or alternatives thereof, may be combined into other systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may subsequently be made by those skilled in the art without departing from the scope of the present disclosure as encompassed by the following claims.
[046] The claims, as originally presented and as they may be amended, encompass variations, alternatives, modifications, improvements, equivalents, and substantial equivalents of the embodiments and teachings disclosed herein, including those that are presently unforeseen or unappreciated, and that, for example, may arise from applicants/patentees and others.
[047] While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.