Description:TECHNICAL FIELD

Present disclosure relates in general to a field of manufacturing technology which includes surface treatment for hot rolled strips. Particularly, but not exclusively, the present disclosure relates to an aspect of determining a catenary depth of a strip in a pickling tank. Further, embodiments of the disclosure, discloses a method employing a computational solution for quantifying, measuring, and controlling the catenary depth during continuous surface treatment of the strip in the pickling tank.

BACKGROUND OF THE DISCLOSURE

Steel is an alloy of iron, carbon, and other elements such as Phosphorous (P), Sulphur (S), Nitrogen (N), Manganese (Mn), Silicon (Si), Chromium (Cr), etc. Because of its high tensile strength and low cost, steel may be considered as most viable choice for major components manufacturing in a wide variety of applications. Some of the applications of the steel may include buildings, ships, tools, automobiles, machines, bridges, and numerous other applications.

Steel may be generally manufactured as steel slabs by processes such as casting including but not limiting to continuous casting, and then the steel is formed into various shapes depending on the application. One such common form of steel is a steel sheet which is obtained by converting the steel slab into steel sheet by series of metal forming processes to find its use in the sheet metal industry. During drawing of the steel sheet from steel slabs, processes such as hot rolling and cold rolling are carried out.

Conventionally, hot rolling may be performed in a Hot Strip Mill (HSM) which is an integral part of an integrated steel plant. The primary objective of HSM is to make strips from slabs and acquire intended properties in the strips. Typically, HSM has two sections- Roughing Mill and Finishing Mill. Roughing Mill is essentially a single strand reversing mill whose function is to reduce the thickness of the slabs as well as break the cast structure. After roughing, strips go into the finishing mill. The job of a finishing mill is to reduce the thickness of the strips and incorporate requisite properties into the strips. The strips may be used for producing various products like cutting saws, automotive components (Circlips, Washers, Springs, and Recliner, Driven and disc plate), gardening tools, surgical blade, springs, measuring devices, wire rods, tire bead wires, deep drawn high strength wires, wires for suspension bridges, and others.

Generally, the hot rolled strip or sheet is subjected to a pickling process. The pickling process is performed for removing of scales and other surface defects on the strip. Post this process, the strip is subsequently subjected to rinsing. Further, pickling refers to a treatment that is used to remove impurities such as rust and scale from the surface of the strip. During hot working processes, an oxide layer (referred to as “scale”, due to the scaly nature of its appearance) develops on the surface of the metal. Before subjecting the steel sheet or strip to cold rolling processes, hot rolled steel goes through a pickling line to remove the scales from the surface and make it easier to work. To restore the best corrosion resistant performance, the damaged metal layer must be removed, exposing a fully alloyed steel strip surface. The oxide layer and the impurities on the surface of the strip is removed by dipping the strip into a pickle liquor. The pickle liquor may be hydrochloric or sulfuric acid. For steels that have a higher carbon content, a two-step pickling process is required, with additional acids used. The pickling process chemically removes oxides and scales that are from both the top and bottom surfaces of the strip.

The pickling process involves pulling of the strip by motor driven bridle rollers or by a tension bridle in a catenary fashion under a controlled speed through a series of several troughs or tanks. The strip may be pulled through three to eight pickling tanks, combined measure adding up to seventy to a hundred meters in length and each pickling tank may be rectangular or isosceles/ trapezoidal in shape. The hot rolled strips are conveyed continuously in the pickling tank by having it pass through deflector rollers and helper rollers which act to motivate the strip. A substantial tension is created in the initial section of the strip by placing a drag on the pay-off reel which create catenary profile on the strip inside the pickling tank. Here the substantial tension created by the tension reel develops the velocity difference between encoder reel and pay of reel. If the tension applied to the strip is relatively too high, the velocity differences along the prescribed addressed section is negligible which results in catenary lifting process and the said strip passes over the liquid surface, leading to poor pickling. Conversely, if the tension applied is too small, the velocity difference along the prescribed addressed section is relatively higher which results in catenary bottom sliding in which the strip comes into sliding contact with the side wall surface of the pickling tank. The catenary bottom sliding may cause scratches on the surface of the strip.

US patent 3704993 discloses a regenerative system that provides adequate tension and speed to process the steel strip throughout the pickling process line. The regenerative system makes proper connection via servo control among, pay of reel system, bridle roll system and tension reel system to maintain a precise speed of strip in continuous pickling line. However, the patent does not fulfil the precise condition of catenary under pickling and catenary bottom or side sliding for various dimensions of steel strip which are processed in continuous pickling line. This condition should never be untended because it may deteriorate the final product quality. Also, the’993 patent lacks reflecting of the magnitude of the catenary depth of processed strip inside the pickling tank.

Further, Japanese Patent Application N0. JP2008007981A, discloses a catenary sensor to measure the catenary depth of steel strip inside the pickling tank. Additional bridal roll is also fitted between primary and secondary bridal roll. This arrangement adjusts the rotational speed of the bridle roll upstream of the pickling tank so that the catenary curve of the steel strip in the pickling tank is within the allowable range. However, the labour and cost required to maintain the sensor is excessive. These sensors are best suited for rectangular or square shaped pickling tank where it is easy to predict the catenary lifting and catenary bottom sliding condition, but it cannot predict the catenary side of the sliding condition in isosceles trapezoid shaped pickling tank.

The present disclosure is directed to overcome one or more limitations stated above or any other limitations associated with the conventional arts.

SUMMARY OF THE DISCLOSURE

One or more shortcomings of the prior art are overcome by a method and a product as claimed and additional advantages are provided through the method as described in the present disclosure.

Additional features and advantages are realized through the techniques of the present disclosure. Other embodiments and aspects of the disclosure are described in detail herein and are considered a part of the claimed disclosure.

In one non limiting embodiment of the disclosure, a method for determining a catenary depth of a strip in a pickling tank is disclosed. The method includes steps of receiving operating parameters corresponding to speed of a flattener roller and speed of an encoder roller traversing the strip through the pickling tank, and time taken for the strip to traverse along length of the pickling tank by a control unit. The control unit further determines a sag length of the strip based on a derivative of vertical depth of the strip within the pickling tank estimated from the parameters received by the control unit. The next step involves calculating total sag length based on the determined sag length and a sag length due to weight of the strip by the control unit. The control unit determines a sag angle between the strip and an imaginary top surface of the pickling tank based on cosine inverse of a first angel estimated by the calculated total sag depth of the strip. The control unit further determines a maximum sag depth of the strip based on the determined sag angle. The final step involves the aspect of determining the catenary depth of the strip based on the determined maximum sag depth of the strip and a maximum depth of the pickling tank by the control unit.

In an embodiment, the control unit computes the derivative of vertical depth by estimating algebraic sum of exponential to the power of length accumulated due to differential speed of flattener roller with displacement of the strip and inverse exponential to the power of length accumulated due to differential speed of flattener roller with displacement of the strip.

In an embodiment, the sag length due to weight of the strip is pre-determined based on parameters of the strip including modulus of elasticity of the strip, thickness of the strip, width of the strip, span length of the strip, and load due to self-weight of the strip.

In an embodiment, the sag length due to weight of the strip is determined by a fist subset of parameters and a second subset of parameters wherein, the first subset of parameters is the multiple of load due to self-weight of the strip and horizontal distance from the encoder roller to a central point of the tank divided by the multiple of 24, modulus of elasticity of the strip and moment of area of the strip.

In an embodiment, the second subset of parameters are computed by the algebraic difference and the algebraic sum between thrice of span length of the strip, multiple of twice the span length of the strip and from a horizontal distance of the encoder roller to the central point of the tank and by considering three times the horizontal distance from the encoder roller to the central point of the tank, respectively.
In an embodiment, total sag length of the strip is determined based on an empirical expression as an algebraic sum of the determined sag length of the strip and the sag length due to weight of the strip.

In an embodiment, the sag angle is determined by a trigonometric equation based on plurality of the parameters including span length of the strip and total sag length of the strip.

In an embodiment, the first angle for estimating the sag angle is determined by dividing span length of the strip with the twice of total sag length of the strip.

In an embodiment, the sag angle is determined by the algebraic difference between half of p and cosine inverse of a first angel.

In an embodiment, the maximum sag depth is determined by computing the multiple of a third subset of parameters and a fourth subset of parameters wherein, the third subset of parameters is half of horizontal distance from the encoder roller to the central point of the tank.

In an embodiment, the fourth subset set of parameter is computed by an inverse tangent function of tangent of half the sag angle.

In an embodiment, the catenary depth of the strip is determined based on an empirical expression as an algebraic difference of the maximum depth of the pickling tank and the determined maximum sag depth of the strip.

In an embodiment, the operational speed of the flattener roller is greater than the speed of the encoder roller for imparting a catenary shape to the strip traversing through the pickling tank.

In an embodiment, the catenary depth of a strip is determined in the pickling tank which is of a trapezoidal shape.

In an embodiment, the speed of the flattener roller and the speed of the encoder roller is varied by the control unit based on the determined catenary depth of the strip in the pickling tank.

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.

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 ACCOMPANYING FIGURES

The novel features and characteristics of the disclosure are set forth in the appended description. The disclosure itself, however, as well as a preferred mode of use, further objectives, and advantages thereof, will best be understood by reference to the following detailed description of an illustrative embodiment when read in conjunction with the accompanying figures. One or more embodiments are now described, by way of example only, with reference to the accompanying figures wherein like reference numerals represent like elements and in which:

Fig. 1 is a schematic drawing of continuous pickling line, according to an exemplary embodiment of the present disclosure.

Figure 2 schematic drawing of catenary formation in continuous pickling line, according to an exemplary embodiment of the present disclosure.

Figure 3 shows a perspective view of a top region of the pickling tank, according to an exemplary embodiment of the present disclosure.

Fig. 4 is a side view of the pickling tank with co-ordinates of strip catenary in pickling tank, according to an exemplary embodiment of the present disclosure.

Fig. 5 is a flowchart illustrating the method for determining a catenary depth of a strip in a pickling tank, according to an exemplary embodiment of the present disclosure.

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 methods illustrated herein may be employed without departing from the principles of the disclosure described herein.

DETAILED DESCRIPTION

The foregoing has broadly outlined the features and technical advantages of the present disclosure in order that the detailed description of the disclosure that follows may be better understood. Additional features and advantages of the disclosure will be described hereinafter which form the subject of the description of the disclosure. It should also be realized by those skilled in the art that such equivalent methods do not depart from the scope of the disclosure. The novel features which are believed to be characteristic of the disclosure, as to method of operation, together with further objects and advantages will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure.

In the present document, the word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or implementation of the present subject matter described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.

While the disclosure is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and will be described in detail below. It should be understood, however that it is not intended to limit the disclosure to the form disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the spirit and the scope of the disclosure.

The terms “comprises”, “comprising”, or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a method that comprises a list of acts does not include only those acts but may include other acts not expressly listed or inherent to such method. In other words, one or more acts in a method proceeded by “comprises… a” does not, without more constraints, preclude the existence of other acts or additional acts in the method.

Embodiments of the present disclosure disclose a method for determining a catenary depth of a strip in a pickling tank. The strip is made to pass though the pickling tank for surface treatment of a hot rolled strip. In some scenarios, if the tension applied to the strip is relatively too high, the velocity differences is negligible which results in catenary lifting process and the strip passes over the liquid surface, causing poor pickling. Conversely, if the tension applied is too small, the velocity difference is relatively higher which results in catenary bottom sliding in which the strip comes into sliding contact with the side wall surface of the pickling tank. The catenary bottom sliding may cause scratches on the surface of the strip. Conventional methods of monitoring the catenary depth of the strip involve sensors and are labour intensive practices. Moreover, these conventional methods are also only applicable for rectangular shaped pickling tanks.

According to various embodiment of the disclosure, a method for determining a catenary depth of a strip in a pickling tank is disclosed. The method includes steps of receiving operating parameters corresponding to speed of a flattener roller and speed of an encoder roller traversing the strip through the pickling tank, and time taken for the strip to traverse along length of the pickling tank by a control unit. The control unit further determines a sag length of the strip based on a derivative of vertical depth of the strip within the pickling tank estimated from the parameters received by the control unit. The next step involves calculating total sag length based on the determined sag length and the sag length due to weight of the strip by the control unit. The control unit determines a sag angle between the strip and an imaginary top surface of the pickling tank based on cosine inverse of a first angle estimated by the calculated total sag depth of the strip. The control unit further determines a maximum sag depth of the strip based on the determined sag angle. The final step involves the aspect of determining the catenary depth of the strip based on the determined maximum sag depth of the strip and a maximum depth of the pickling tank by the control unit.

Henceforth, the present disclosure is explained with the help of figures of a method of manufacturing high-strength steel sheet. However, such exemplary embodiments should not be construed as limitations of the present disclosure since the method may be used on other types of steels where such need arises. A person skilled in the art may envisage various such embodiments without deviating from scope of the present disclosure.

Fig. 1 is a schematic drawing of continuous pickling line (100) and Fig. 2 is schematic drawing of catenary formation of a strip (103) in the continuous pickling line (100). The continuous pickling line (100) may include a plurality of pickling tanks (108) for the surface treatment of the strip (103). Each of the plurality of pickling tanks (108) may be filled with a suitable pickle fluid and the pickle fluid in an embodiment may be a suitable acid. The surface of the strip (103) may be treated by means of an acid bath including but not limited to hydrochloric acid.

With reference to Fig. 1, the continuous pickling line (100) may include a plurality of un-coilers or pay of reels. The continuous pickling line herein includes a primary pay of reel (101) and a secondary pay off reel (102). The hot rolled strip (103) that is initially received from a hot strip mill, may be unwrapped for processing by a processor (104). The primary pay of reel (101) and the secondary pay off reel (102) are used to guide the strip (103) to the processor (104) and may also break the oxide scale present over the strip (103). The processor (104) receives the strip (103) and may be directed though a breaker roll [not shown] housed in the processor. The breaker roll may minimize the tendency of the strip (103) to break. The strip (103) is further guided to a welder assembly (105). The strip (103) in the welder assembly (105) may be reshaped or cut suitably and may be welded to impart square shape to throughout the length of the strip (103). The assembly (105) may cut and weld the edges of the strip (103) to impart the square shape to the strip (103). The continuous pickling line (100) also includes a primary guide roll (106) and a secondary guide roll (111). The primary guide roll (106) and the secondary guide roll (111) may guide the strip through the plurality of pickling tanks (108) and a rinsing assembly (109). The primary guide roll (106) and the secondary guide roll (111) convey the strip (103) throughout the entry and exit of the processing line. The primary guide roll (106) initially conveys the strip (103) from the welder assembly (105) into the plurality of pickling tank (108) through a flattener roller (107). The continuous pickling line (100) including the flattener roller (107) receives the strip (103) form the primary guide roll (106) and imparts a pre-determined speed to the strip (103) while guiding the strip (103) into the plurality of pickling tank (108). The flattener roller (107) provides a flattener reference ratio which facilitates and enables the entry speed of strip (103) inside the pickling tank (108). The flattener roller (107) may be any known mechanism or method in the art for imparting speed to the stirp (103), as the strip (103) traverses through the pickling tank (108).

The pickling tank (108) may include pickle fluid and the strip (103) may be guided through the pickle fluid inside the pickling tank (108). As the strip (103) traverses through the pickling tank (108) and the pickling fluid, a chemical reaction take place with the pickle fluid where, black oxide scales from the surface of the strip (103) is generated during hot rolling process which are suitably removed. The strip (103) from the pickling tank (108) may further be guided through the rinsing assembly (109) where, the residual acid on the surface of the strip (103) from the plurality of pickling tank (108) is removed. The rinsing assembly (109) may also include a provision for drying the strip (103). Excess water on the strip (103) may be removed or dried to prevent the formation of rust. The strip from the rinsing assembly (109) may further be guided through an oiler (110). The oiler (110) may add a thin layer of oil on the surface of the strip (103). The thin layer of oil may be added for preventing the formation of rust on the surface of the strip (103). The strip (103) from the rinsing assembly (109) may be received by the secondary guide roll (111) and the strip (103) may be coupled to an edge cutter (112). The edge cutter (112) may remove the edges of the strip (103) to ensure there are no edge defects to the strip (103). Defects such as cracks or minor edge damages may be sheared suitably to guarantee a continuous and uniform strip (103) width. The strip (103) is coupled to an encoder roller (113) which also imparts speed to the strip (103) traversing throughout the continuous pickling line (100) similar to the flattener roller (107). The encoder roller (113) may be an assembly of an encoder and the edge cutter where, the encoder imparts speed to the strip (103) and the edge cutter trims the edges of the strip (103). The encoder roller (113) may maintain the desired tension by means of a tension reel (114). The tension reel (114) may maintain the desired tension throughout the continuous pickling line (100) and a binding reel (115) may be used to coil the pickled strip (103) suitably.

The flattener rollers (107) and the encoder rollers (113) are configured to impart a drooping structure or a catenary shaped structure to the strip (103). The flattener roller (107) and the encoder roller (113) may be operated at differential speeds. Initial threading process of the strip (103) is set by maintaining the speed or tension on the flattener roller (107) and the encoder roller (113) in equilibrium. The speed of the flattener roller (107) and the encoder roller (113) is initially maintained at very low magnitude. The speed for threading lies between 40 meter per minute to 60 meter per minute. Further, once the threading is completed, the speed of the flattener roller (107) is considerably increased (107) by 1.001 to 1.5 times with respect to fixed line speed of the encoder roller (113). The speed of the flattener roller (107) and the encoder roller (113) may be fixed based on various parameters of the strip (102) including width, thickness, and grade of the strip (103). The speed of the secondary guide roll (111) is directed through the tension reel (114) by the application of encoder roller (113). Whereas speed of the primary guide roll (106) is directed through the encoder roller (113). Hence, the difference in speed is created along the flattener roller (107) and the encoder roller (113) which leads to a differential speed. Due to the differential speed, the flattener roller (107) seeks to pass the more length of the strip (103) to the encoder roller (113), but the encoder roller (113) does not receive the whole length of the strip (103) because of lesser speed. Therefore, drooping characteristic is predominant between the flattener roller (107) and the encoder roller (113). Consequently, the catenary shape is imparted to the strip (103) traversing through the plurality of pickling tank (108). The catenary shape that is imparted to the strip (103), causes the strip (103) to accumulate inside the plurality of pickling tank (108).

In an embodiment, plurality of pickling tanks (108) may be used for removing the surface impurities of the strip (103). More particularly three to eight pickling tanks (108) which combinedly measuring 70 to a 100 meter in length may be used. Each individual pickling tank (108) consists of primary bridal roll (203) and secondary bridal roll (204) at entry and exit, respectively.

With reference to the Fig. 2 catenary formation in the continuous pickling line (100) with the plurality of pickling tank (108) is shown. The strip (103) may be traversed though multiple pickling tanks (210, 211,212, 213 and 214). Each pickling tank (210, 211,212, 213 and 214) may be trapezoidal in shape as seen from the Fig. 3. The plurality of pickling tank (108) may include two side walls (404 and 405) that are parallel to each other and these two side walls (404 and 405) may be interconnected with a front wall (301) and a rear wall (302) that are oriented in a non-parallel orientation to define a trapezoidal shape to the plurality of pickling tank (108). The front wall (401) and the rear wall (402) may be defined at a pre-determined angle (306) with respect to the side walls (404 and 405). The angle (306) may vary between 1° to 89° degree for a trapezoidal shaped pickling tank (108) and may be 90° rectangular shaped pickling tank (108).

Further, each pickling tank (210, 211,212, 213 and 214) may include a primary bridal roll (203) and a secondary bridal roll (204). The primary bridal roll (203) plays a pivotal role to entry of the strip (103) at higher speed and the secondary bridal roller (204) plays pivotal role to deliver the strip (103) to the next pickling tank (211,212, 213 and 214). The secondary bridal roller (204) may operate at lower speeds and the secondary bridal roller (204) may be coupled to the encoder roller (113). Whereas the primary bridal roll (203) may be coupled to the flattener roller (107). The differential speed between the primary bridal roller (203) and the secondary bridal roller (204) imparts the catenary shape to the strip (103) inside each pickling tank (210, 211,212, 213 and 214). The method of determining the catenary depth (C) of the strip (103) inside each pickling tank (108) is explained in detail below.

Fig. 4 is a side view of the pickling tank (108) with co-ordinates of the strip (103) catenary in the pickling tank (108) and Fig. 5 is a flowchart illustrating the method for determining the catenary depth (C) of the strip (103) in the pickling tank (108). The first step [301] involves, receiving the operating parameters corresponding to speed of the flattener roller (107) and speed of the encoder roller (113) by a control unit associated with the pickling line. The time taken for the strip (103) to traverse along the length of the pickling tank (108) may also be estimated and the same may be received by the control unit. The sag length (S) of the strip (103) is initially determined by means of a derivative of vertical depth (y) of the strip (103). The vertical depth (y) is estimated as an algebraic sum of exponential to the power of length accumulated due to differential speed of flattener roller (107) with displacement of the strip (103) and inverse exponential to the power of length accumulated due to differential speed of flattener roller (107) with displacement of the strip (103). The corresponding equation for estimating vertical depth is given in the below equation no. 1. Further, the next step 302 involves determining a sag length (S) of the strip (103) based on a derivative of vertical depth (y) of the strip (103) within the pickling tank (108). The sag length (S) may be estimated from the parameters received by the control unit.

The corresponding equations for determining the vertical depth (y) and the sag length (S) are given below.

The general form for a flattened catenary is the sum of two exponential functions, based on the hyperbolic function {y}=coshx:
y= a(e^bx+e^(-bx) )/2-1 ….. equation (1)

Value of b will be calculated from the extra length accumulated due to differential speed between the flattener roller (107) and the encoder roller (113). Value of b is also calculated from the time taken for the strip (103) to pass span length of 17m.
Value of a should be calculated from approximate method which will be equivalent to span length. Here in above equation, “y as yb” represents the vertical depth and “ x” represents the displacement along the mid of span length.
From the above equation, the value of ‘S’ which is position along the catenary curve is calculated where, the half of span curve length corrosponds to the deepest point of catenary curve.
The strip (103) is of almost a catenary shape inside the pickling line (100), but not quite similar because of the weight of the strip (103) suspended from the rollers. Herein, an assumption is made that strip (103) is a flattened catenary. For convenience, the origin is placed at the lowest point of the pickling tank (108).
The required curve (after initial analysis and some guess) passing through (-x/2, y), (0, 0) and (x/2, y) is given by:
y= (x*(e^bx+e^(-bx) ))/2-1 …..equation (3)
The derivative of function will be (equation 3):
?y/?x= (x/2)/(b/2) ×((e^bx+ e^(-bx))/2) …..equation (4)
Using the length of a curve formula from the equation 2, with start point and end point “x”, the sag length (S) is determined.
The control unit may further estimate a sag length (Y1) due to weight of the strip (103). The sag length (Y1) due to weight of the strip (103) may be estimated based on pre-determined parameters of the strip (103) including modulus of elasticity of the strip (103), thickness of the strip (103), width of the strip (103), span length of the strip (103), and load due to self-weight of the strip (103). The sag length (Y1) due to weight of the strip (103) is determined by a fist subset of parameters and a second subset of parameters. The first subset of parameters is the multiple of load due to self-weight of the strip (103) and horizontal distance from the encoder roller to a central point of the pickling tank (108) divided by the multiple of 24, modulus of elasticity of the strip (103) and moment of area of the strip (103) as described below in the equation no. 6. Further, the second subset of parameters are computed by the algebraic difference and the algebraic sum between thrice of span length of the strip (103), multiple of twice the span length of the strip (103) and from a horizontal distance of the encoder roller to the central point of the tank (108) and by considering three times the horizontal distance from the encoder roller to the central point of the tank (108) respectively. The first and second subset of parameters are detailed in the below equation no. 6.
The condition of strip (103) as a uniformly distributed load beam on rollers is illustrated below. Hence to evaluate the deflection (maximum deflection is delta), following formula is adopted which depends on the load factor (w), modulus of elasticity (E), span length (L), and second moment of area (I).
Y1= wx/24EI (l^3-2*l*x^2+x^3 ) …..equation (6)
Max deflection = 5 wL4/384EI, which will be derived from above equation (Y1)
E = modulus of elasticity of steel sheet.
I = second moment of area, m4
I= (th)×((?wd?^3 ))/12 …..equation (7) where, I = second moment of area, th = thickness of steel sheet, and wd = width of steel sheet.
l = L=span length under consideration, in m
x = horizontal distance from reaction point, in m
w = uniformly distributed load. (self-weight in N/m)
The above equation shows the downwards deflection of the strip (103) due to its own weight at any section in terms of “x” with respect to span length.
The next step 303 involves calculating the total sag length (SL) of the strip (103). The total sag length (SL) of the strip (103) is determined based on an empirical expression as an algebraic sum of the determined sag length (S) of the strip (103) and the sag length (Y1) due to weight of the strip (103). The total sag length (SL) will be evaluated as S_l=S+Y1 …..equation (8)
Further, the next step 304 involves determining a sag angle (Ø) of the strip (103). The sag angle (Ø) is determined by a trigonometric equation based on plurality of the parameters including span length of the strip (103) and total sag length (SL) of the strip (103).
The maximum sag depth can be calculated from the below Cesaro equation.
+ Ø=2*?tan?^(-1) (tan h?( ?x/2a)) …..equation (9)
In the above equation Ø is angle of sag and, “a” is the maximum sag depth.
The angle of sag Ø can be calculated from trigonometry, as from the equation 8. The equation below has been derived from co-ordinate system trigonometry algorithm. The approximated angle of sag the sag angle (Ø) is determined by the algebraic difference between half of p and cosine inverse of a first angel (f) as detailed in the below equation 10.
Ø= p/2- ?Cos?^(-1) f …..equation (10)
“f” in the above equation 10 is a first angle (f) and is determined for estimating the sag angle (Ø). The first angle (f) is determined by dividing span length (L) of the strip (103) with the twice of total sag length (SL) of the strip (103) as described in the below equation.
f= L/S_l ,
Where, Ø is angle of sag, L is span length, Sl is sag length (hypotenuse value). After obtaining the value of Ø from the equation 10, the maximum sag depth can be calculated by re-arranging the equation 9 as below:

The maximum sag depth is determined at step 305 by computing the multiple of a third subset of parameters and a fourth subset of parameters. The third subset of parameters is half of horizontal distance from the secondary bridal roller to the central point of the tank (108). The fourth subset set of parameter is computed by an inverse tangent function of tangent of half the sag angle (Ø).
From the above expression the value of “a” which is maximum sag depth as shown in Fig. 4 is estimated. The catenary depth (C) of the strip will be calculated at step 106 as per design evaluation of tank (108). The catenary depth (C) of the strip (103) is determined based on an empirical expression as an algebraic difference of the maximum depth (Yb) of the pickling tank (108) and the determined maximum sag depth (a) of the strip (103). The equation for determining the catenary depth (C) of the strip (103) is detailed below.
C= Y_b-a …..equation (12)
Here, Y_b is maximum depth of tank (108).
Based on the determined catenary depth (C) of the strip (103), the control unit may vary the speed of the flattener roller (107) and the speed of the encoder roller (113). The catenary depth (C) of the strip (103) inside the said pickling tank (108) may be compared with an initially measured allowable height of the pickling tank (108). If the catenary depth (C) lies below to the allowable height, the control unit interprets that the strip (103) is too close or colliding with the bottom surface of the tank (108). Consequently, computational method provides new differential speed to the flattener roller (107) and the encoder roller (113) which enables the catenary depth (C) of the strip (103). The speed may be determined to operate the flattener roller (107) and the encoder roller (113) such that the allowable height so that the strip (103) is sufficient to prevent catenary lift and catenary bottom/side sliding condition inside the pickling tank (108) in normal operating practice of the continuous pickling line (100).
Further, the data with regards to the strip (103) specification like width, thickness and grade may already be stored in a memory unit associated with the control unit. Once all the input which are required for catenary depth prediction (C) is received from database, the computational method calculate the catenary depth (C) for the strip (103) and the same may be depicted to the user by a suitable user interface. With reference to the below Table 1, the user interface may generate an alarm is the determined catenary depth (C) of the strip (103) is lesser than the allowable depth of the tank (108). The control unit may set off alarm to signals indicative of bad or risk condition of catenary depth (C) for faulty operating practices to operator. The control unit may suggest the optimal operating practices as well. If the operating conditions are good i.e., the determined catenary depth (C) of the strip (103) is greater than the allowable depth of the tank (108), the control unit will not set of an alarm and the operational conditions may be tabulated for further reference.
Width Thickness Flattener roller Encoder roller Catenary depth Allowable depth Condition/alarm
mm mm rpm rpm m m
1220 2.4 136.5 130 0.221 0.174 good
1220 2.4 137.15 130 0.197 0.174 good
1220 2.4 137.8 130 0.172 0.174 bad
1250 2.5 131.25 125 0.221 0.178 good
1250 2.5 131.87 125 0.192 0.178 good
1250 2.5 132.7 125 0.171 0.178 bad
1540 2.4 103 100 0.298 0.22 good
1540 2.4 103.5 100 0.266 0.22 good
1540 2.4 104 100 0.218 0.22 bad

In an embodiment, the above-mentioned method of determining catenary depth (C) of the strip (103) is completely computational without any additional use labour or sensors. Consequently, the method of determining catenary depth (C) of the strip (103) is cost-effective. In an embodiment, the method of determining catenary depth (C) of the strip (103) inside the pickling tank (108) of the present disclosure is applicable for trapezoidal shaped tanks (108) and rectangular shaped tanks (108). Since the method of determining catenary depth (C) of the strip (103) inside the pickling tank (108) is computational and relies only on the specification of the strip (103), the catenary depth (C) of the strip (103) may be determined for tanks (108) of any given shape.
Equivalents:

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.

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). Furthermore, in those instances where a convention analogous to "at least one of A, B, and C, etc." is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., "a system having at least one of A, B, and C" would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to "at least one of A, B, or C, etc." is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., "a system having at least one of A, B, or C" would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase "A or B" will be understood to include the possibilities of "A" or "B" or "A and B."

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.

Referral Numerals

Referral Numerals Description
100 Continuous pickling line
101, 102 Pay off reels
103 Strip
104 Processor
105 Welder assembly
106 Primary guide roll
107 Flattener roller
108, 210, 211, 212, 213, 214, 215 Pickling tank
109 Rinsing assembly
110 Oiler
111 Secondary guide roll
112 Edge cutter
113 Encoder roller
114 Tension reel
115 Binding reel
203 Primary bridal roll
204 Secondary bridal roll
C Catenary depth
Ø Angel of sag
f First angle
Yb Maximum depth of tank
S Sag length
Y1 Sag length due to self-weight of the strip
SL Total sag length

Claims:
A method for determining a catenary depth (C) of a strip (103) in a pickling tank (108), the method comprising:
receiving by a control unit, operating parameters corresponding to speed of a flattener roller (107) and speed of an encoder roller (113) traversing the strip (103) through the pickling tank (108), and time taken for the strip (103) to traverse along length of the pickling tank (108);
determining, by the control unit, a sag length (S) of the strip (103) based on a derivative of vertical depth (y) of the strip (103) within the pickling tank (108) estimated from the parameters received by the control unit;
calculating, by the control unit, total sag length (SL) based on the determined sag length (S) and a sag length (Y1) due to weight of the strip (103);
determining, by the control unit, a sag angle (Ø) between the strip (103) and an imaginary top surface of the pickling tank (108) based on cosine inverse of a first angel (f) estimated by the calculated total sag depth (SL) of the strip (103);
determining, by the control unit, a maximum sag depth (a) of the strip (103) based on the determined sag angle (Ø);
determining, by the control unit, the catenary depth (C) of the strip (103) based on the determined maximum sag depth (a) of the strip (103) and a maximum depth (Yb) of the pickling tank (108).

The method as claimed in claim 1 comprises, computing by the control unit the derivative of vertical depth (y) by estimating algebraic sum of exponential to the power of length accumulated due to differential speed of flattener roller (107) with displacement of the strip (103) and inverse exponential to the power of length accumulated due to differential speed of flattener roller (107) with displacement of the strip (103).

The method as claimed in claim 1 wherein, the sag length (Y1) due to weight of the strip (103) is pre-determined based on parameters of the strip (103) including modulus of elasticity of the strip (103), thickness of the strip (103), width of the strip (103), span length of the strip (103), and load due to self-weight of the strip (103).

The method as claimed in claim 1, wherein the sag length (Y1) due to weight of the strip (103) is determined by a fist subset of parameters and a second subset of parameters wherein, the first subset of parameters is the multiple of load due to self-weight of the strip (103) and horizontal distance from the encoder roller (113) to a central point of the tank (108) divided by the multiple of 24, modulus of elasticity of the strip (103) and moment of area of the strip (103).

The method as claimed in claim 4 wherein, the second subset of parameters are computed by the algebraic difference and the algebraic sum between thrice of span length of the strip (103), multiple of twice the span length of the strip (103) and from a horizontal distance of the encoder roller (113) to the central point of the tank (108) and by considering three times the horizontal distance from the encoder roller (113) to the central point of the tank (108) respectively.

The method as claimed in claim 1 wherein, total sag length (SL) of the strip (103) is determined based on an empirical expression as an algebraic sum of the determined sag length (S) of the strip (103) and the sag length (Y1) due to weight of the strip (103).

The method as claimed in claim 1 wherein, the sag angle (Ø) is determined by a trigonometric equation based on plurality of the parameters including span length of the strip (103) and total sag length (SL) of the strip (103).

The method as claimed in claim 1, wherein the first angle (f) for estimating the sag angle (Ø) is determined by dividing span length (L) of the strip (103) with the twice of total sag length (SL) of the strip (103).

The method as claimed in claim 1 wherein, the sag angle (Ø) is determined by the algebraic difference between half of p and cosine inverse of a first angel (f).

The method as claimed in claim 1 comprises, determining the maximum sag depth by computing the multiple of a third subset of parameters and a fourth subset of parameters wherein, the third subset of parameters is half of horizontal distance from the encoder roller (113) to the central point of the tank (108).

The method as claimed in claim 10 wherein, the fourth subset set of parameter is computed by an inverse tangent function of tangent of half the sag angle ((Ø).

The method as claimed in claim 1 wherein, the catenary depth (C) of the strip (103) is determined based on an empirical expression as an algebraic difference of the maximum depth (Yb) of the pickling tank (108) and the determined maximum sag depth (a) of the strip (103).

The method as claimed in claim 1 wherein, the operational speed of the flattener roller (107) is greater than the speed of the encoder roller (113) for imparting a catenary shape to the strip (103) traversing through the pickling tank (108).

The method as claimed in claim 1 wherein, the catenary depth (C) of a strip (103) is determined in the pickling tank (108) which is of a trapezoidal shape.

The method as claimed in claim 1 comprises, varying by the control unit, the speed of the flattener roller (107) and the speed of the encoder roller (113) based on the determined catenary depth (C) of the strip (103) in the pickling tank (108).