Description: A METHOD OF PREDICTING SHAPE OF BENDING DISTORTION OF A LONG WELDED STRUCTURE

FIELD OF THE INVENTION
The present subject matter described herein relates to welding. More specifically, the present invention relates to a method that predicts shape of bending distortion of a long welded structure comprising a plurality of welds located either above or below the longitudinal CG axis of a model welded structure.
BACKGROUND OF THE INVENTION
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.
Welding is one of the major fabrication process used in a variety of industries like power, petrochemical, railways, transportation etc. It involves the joining of two similar (or) dissimilar materials by application of localised heat along the faying surfaces (or) interface regions, with or without the application of pressure, so as to produce a sound joint with a strong metallurgical bond. The localised application of heat causes the weld metal and the adjoining base metal regions which are heated intensely to undergo a plastic deformation and this leads to the occurrence of warpage or distortion in welded components. The negative effects of weld distortion include fit-up problems in assembly due to dimensional change, loss of strength, loss of aesthetics etc. Hence, welding industries always strive to control the distortion to the least possible extent so that these negative effects can be averted.
The control of distortion, in many cases, can be achieved only when the behaviour and magnitude of distortion of the welded structure are known beforehand. So, it will be necessary to make a reasonable estimate of how much the component will distort after welding. In the case of long welded structures, the weld undergoes a shrinkage on account of thermal contraction tendency of the weld material, which is a common feature in all welded structures. While the weld metal shrinks, the rest of the material, which was not exposed to the intense heat developed by the welding arc, resists the free shrinkage of the weld metal. To overcome the resistance offered by the rest of the material, a reaction force develops in the weld axis which is called as the ‘Shrinkage Force’ (SF). The ‘Shrinkage Force’ will always be developed along the weld line. If there happens to be an eccentricity, ‘e’ between the weld axis and the CG axis of the structure, then the SF creates a moment about the CG axis, which bends the welded structure resulting in the formation of a curvature as schematically shown in Figure 1.
Further, when weld metal (102) is deposited on one of the long edges (top edge, in this case) of a rectangular plate (101) as shown in Figure 1, the rectangular plate (101) undergoes a bending distortion (104), as shown therein, on account of the shrinkage force developed in the weld. The equation for determining the distortion (shown as ‘D’ in Figure 1) at the mid-span of the edge welded plate is given as:
D= (C.L^2)/8………… Equation (1)
Where,
C – Curvature developed in the weld segment on account of its shrinkage (mm-1)
L – Length of the weld segment (mm)
It is known that for a given plate geometry, its material grade and the welding parameters, the curvature attained by the weld segment after full cooling, is a constant. Then, the equation (1) represents a parabola. Thus, it is understood that the weld segment, upon shrinkage, attains a curved shape in the form of parabolic arc. In order to find out the distorted shape of the welded structure, it is just enough to find out the value of curvature ‘C’ mentioned in equation (1). Once ‘C’ value is known, the distorted shape of the weld can be easily plotted. Thus, the whole job of determining the shape of bending distortion just narrows to finding out the curvature of the weld segment.
There are some analytical formulas for prediction of curvature, but these do not provide correct estimates since the temperature bound variation of the various material properties are not factored in such formulas. Hence, in order to accurately determine the curvature and thus the shape of bending distortion of welded structure, Finite Element Modelling (FEM) technique is used.
For implementing the FEM, the welded structure needs to be modelled and meshed. Then, the boundary conditions representing a real time welding scenario has to be incorporated i.e. the heat flow of the moving welding arc has to be simulated and the necessary clamping conditions have to be imposed on the welded structure.
Nowadays, FEM is implemented through software and hence the above mentioned steps are easily done. The various governing equations regarding the heat transfer from the arc, heat loss from the job, the generation of thermal strain, elastic and inelastic strains are solved in a transient manner in the software. Finally, the distorted shape of the welded structure upon full cooling of the weld can be obtained from the output of the software.
Since the FEM does matrix based computations for solving the governing equations concerning the dynamic heat flow that occurs during welding, the time taken for obtaining the distortion results for a single run of a weld will typically will be anywhere between a few hours to few days depending on the number of elements and number of nodes present in the meshed model. Particularly, if the welded structure is of a very high length or of very high cross sectional dimensions, then the FE model of such a structure will consist of huge number of elements and nodes. This will lead to very high computational time. The problem will be worsened when there is a need to experiment with multiple combinations of boundary conditions and weld sequences. Each and every run of FE simulation will consume enormous amount of time, making the whole exercise highly tedious. While there is an advantage of accuracy of distortion results obtained from FEM, there is a shortfall in terms of the time required for simulation.
Patent CN104573314A describes a method of forecasting welding deformation of multi-layer welding. The unknown parameters of an equation connecting the welding linear energy with the inherent strain, are determined experimentally, initially. Then, inherent strain of every weld pass is calculated and finally distortion of the welded structure is computed using FEM by inputting value of inherent strain obtained from calculations.
Patent US7649623B2 specifies a method for optical measurement and examination of a welded assembly for any distortion after welding. This invention uses a series of cameras and a stationary reference object with very low thermal coefficient of expansion. The welded assembly’s image is captured along with that of the reference object, at multiple instances, during the cycle of welding. For each of these images sets, the correction factor to be applied on the welded assembly’s image is arrived at by examining the size of the reference image. This helps in calibration and determination of accurate position of the welded assembly and is also helpful in determining the distortions, if any of the welded assembly.
It is seen from the prior art that methodologies like experimentation combined with FEM, use of cameras or laser scanners for measurement of distortion, etc. are being used for measurement of distortion and none of the discussed prior arts cited above have disclosed a combined method using both FEM and mathematical modelling for distortion prediction in long welded structures.
Thus, to take advantage of the FEM in accurately determining weld distortion and at the same time to reduce the computational time of prediction of distortion by FEM of long welded structures, the present invention provides a hybrid method, wherein a first stage of computation is made using FEM technique and then the next stage of predicting of bending distortion.
OBJECTS OF THE DISCLOSURE
It is therefore the object of the present disclosure to overcome the aforementioned and other drawbacks in prior arts.
It is a primary object of the present disclosure to provide a method which utilizes for accurate prediction of the distorted shape and magnitude of distortion in long welded structures.
It is another object of the present disclosure to method that is faster than a conventional FEM approach.
These and other objects and advantages of the present subject matter will be apparent to a person skilled in the art after consideration of the following detailed description taken into consideration with accompanying drawings in which preferred embodiments of the present subject matter are illustrated.
SUMMARY OF THE INVENTION
One or more drawbacks of conventional systems and process are overcome, and additional advantages are provided through the apparatus/composition and a method as claimed in the present disclosure. Additional features and advantages are realized through the technicalities of the present disclosure. Other embodiments and aspects of the disclosure are described in detail herein and are considered to be part of the claimed disclosure.
Solution to one or more drawbacks of existing technology and additional advantages are provided through the present disclosure. Additional features and advantages are realized through the technicalities of the present disclosure. Other embodiments and aspects of the disclosure are described in detail herein and are considered to be a part of the claimed disclosure.
The present disclosure offers a solution in the form of a method of predicting shape of bending distortion of a long welded structure comprising a plurality of welds located either above or below the longitudinal CG axis, the method comprising of applying necessary boundary conditions on model welded structures, obtaining curvature values ‘Ci’ and ‘Cr’ formed in a distorted shape of the model welded structure using a Finite Element Modelling (FEM) technique and determining distorted shape of the model welded structure using the curvature values ‘Ci’ and ‘Cr’ and applying equation of a parabolic arc corresponding to welded segments and equations of straight lines that correspond to non-welded segments.
In an aspect of the invention, the shape of the bending distortion is determined by plotting the parabola in a X-Y coordinate space defined between the limits x = -L/2 to x = +L/2.
In an aspect of the invention, the shape of the bending distortion is determined by plotting the parabola in a X-Y coordinate space defined between the limits x = -L/2 to x = +L/2.
In an aspect of the invention, the shape of the bending distortion is determined by plotting the parabola in a X-Y coordinate space wherein X veries from ‘-L1/2’ to ‘+L1/2’.
In an aspect of the invention, the shape of the bending distortion is determined by plotting the parabola in a X-Y coordinate space wherein X varies from ‘-L/2’ to ‘+L/2’.
In an aspect of the invention, the shape of the bending distortion is determined by plotting the parabola in a X-Y coordinate space wherein X varies from ‘0’ to ‘+L1/2’.
In an aspect of the invention, a coefficient of a second degree term present in the equation of the parabolic arc is determined to be half the magnitude of the curvature of that parabolic arc.
In a further aspect of the invention, a coefficient of the first degree term present in the equation of the parabolic arc is found by equating the first derivative of the equation of the parabolic arc to the slope of any adjacent parabolic arc or a straight line.
In an aspect of the invention, a constant term present in the equation of the parabolic arc is determined lastly by utilizing the above two equations and anyone coordinate points defined by the adjacent parabolic arc or the straight line.
In an aspect of the invention, a coefficient of first degree term and constant of the straight lines representing non-welded portions of the welded structure are found out by enforcing the condition that such straight lines are tangential to the neighboring parabolic arc representing a weld segment.
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.
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.
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 DRAWINGS
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:-
It is to be noted, however, that the appended drawings illustrate only typical embodiments of the present subject matter and are therefore not to be considered for limiting of its scope, for the present disclosure may admit to other equally effective embodiments. The detailed description is described with reference to the accompanying figures. In the figures, a reference number identifies the figure in which the reference number first appears. The same numbers are used throughout the figures to reference like features and components. Some embodiments of system or methods or structure in accordance with embodiments of the present subject matter are now described, by way of example, and with reference to the accompanying figures, in which:
Fig. 1a illustrates a formation of distortion and curvature in a rectangular plate deposited with a full length on its top edge according to the present invention;
Fig. 1b illustrates a formation of distortion and curvature in a rectangular plate deposited with a full length on its bottom edge in accordance with the present invention;
Fig. 1c illustrates a formation of distortion and curvature in a rectangular plate deposited with a weld for a partial length on its top edge in accordance with with the present invention;
Fig. 1d illustrates a formation of distortion and a resultant curvature in a rectangular plate deposited with full length welds on both the top and bottom edges in accordance with with the present invention;
Fig. 1e illustrates a formation of distortion and curvatures in a rectangular plate deposited with unequal length of welds on its top and bottom edges in accordance with with the present invention;
Fig. 2 illustrates a determination of curvature caused by single weld and double weld for plate model of small length to be used for Finite Element Modelling in accordance with the present invention;
Fig. 3 illustrates a method of predicting shape of bending distortion in accordance with the present invention.
A person skilled in the art will easily 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.
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.
DETAIL DESCRIPTION OF INVENTION WITH REFERENCE TO THE ACCOMPANYING DRAWINGS OF THE PREFERRED EMBODIMENTS:
While the embodiments of the disclosure are subject to various modifications and alternative forms, a specific embodiment thereof has 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 alternatives falling within the scope of the disclosure.
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 such 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 or device.
The present invention is related to a method of determining shape and magnitude of bending distortion of long welded structures. This method results in faster and accurate prediction of shape of bending distortion in long welded structures.
Referring to Fig. 2 and Fig. 3, Since the curvature of the weld is independent of the length of the weld, initially the model welded structure (201, 202) of the same cross section as that of the rectangular plate (101) but with a length much shorter than the original rectangular plate (101) is modelled and meshed using the FEM.
In the first step (301), the necessary boundary conditions such as energy input of welding (in Joule/mm), the size of the arc (in all three dimensions), the travel speed of the welding arc (mm/second), trajectory of the welding arc, clamping conditions (i.e. fixation of nodes that are assumed as non-moving due to action of clamps) etc. are incorporated in the model welded structure (201, 202) using the FEM. In first condition, the model welded structure (201) has weld either on top edge or at bottom edge (as shown in Fig. 1a-1c). In second condition, the model welded structure (202) has welds placed on both the top edge and bottom edge, (as shown in Fig. 1d or Fig. 1e).
In the second step (302), the curvature (205, 206) formed in the distorted shape (203, 204) of the model welded structure (201, 202) is determined using the FEM. For, the first condition for the model welded structure (201), the value ‘Ci’ is obtained. By plotting the displacements of all nodes present in the model welded structure (201), a polynomial equation of second degree is fitted to the curve formed by the locus of all such nodal displacements. This represents a parabola. Then, the curvature (Ci) of the parabolic shape at the mid-span of the model welded structure (201) is calculated from the polynomial equation so fitted. This is done by setting the curvature value (Ci) equal to twice the value of the coefficient of the second degree term of the polynomial equation so fitted. Now, irrespective of length of the weld, this curvature approximately stays constant.
The procedure followed for the model welded structure (201) above is repeated for the model welded structure (202) as well and the value ‘Cr’ is obtained.
After solving the model welded structure (202), the distorted shape (204) and resultant curvature (206) is obtained from the FEM. The term ‘resultant curvature’ is used to indicate that the curvature is the result of two welds, one on each sides of the longitudinal CG axis of the plate. The value of the resultant curvature (206) is called ‘Cr’.
As done previously for Ci, the displacement of nodes on the first weld line are plotted and the curvature attained in the model welded structure (202) is found out by doubling the coefficient of the second degree term of the polynomial equation fitted to the polynomial curve obtained as the locus of all such nodal displacements. This is called as the resultant curvature (Cr).
In the third step (303), the distorted shape (203, 204) of the model welded structure (201, 202) is determined using the ‘Ci’ and ‘Cr’ values so obtained. Some worked out examples are enumerated as ‘Case-1’ to Case-5’ and described in detail hereinafter.
Prior to proceeding to the examples, the following rules are kept in mind while forming and solving the equations of the parabolic arcs representing the welded segments and the straight lines representing the non-welded portions of a welded plates shown as examples in Figures 1a, 1b, 1c, 1d, 2 and 3.
The equation fitted to any parabolic arc (representing the distorted shape of welded segment) comprises of three terms namely, a second degree term, a first degree term and a constant term. If in case, the parabola passes through origin and has its vertex at the origin, then the first degree term and second degree term will become zero.
The coefficient of second degree term of the equation representing any given parabolic arc (representing the distorted shape of welded segment) is always equal to half the magnitude of the curvature of the parabolic arc
The coefficient of first degree term of the equation representing any given parabolic arc (representing the distorted shape of welded segment) is found out by equating the first derivative of the said equation to the slope of any neighbouring parabolic arc or straight line
The constant term of the equation representing any given parabolic arc (representing the distorted shape of welded segment) is found out by solving simultanesously the equation of the parabola and the neighboring parabolic arc or straight line by using the common point of intersection. While solving the two equations, the values of first degree term and second degree terms as found above are also utilized.
The coefficient of the first degree term and constant term of any straight line segment representing the non-welded portion of the welded plate are found out by utilizing the condition that such straight lines are tangential to a neighbouring parabolic arc representing the distorted shape of welded segment.
The solved examples are presented hereinafter, explaining how the above rules are put into use for determination of distorted shape of the welded plates presented in Figures 1a, 1b, 1c, 1d and 1e.
Ref. to Figure 1a. In the first case, the weld metal (102) is deposited for full length on the top edge above of the CG axis (103) of the rectangular plate (101). The rectangular plate (101) undergoes a bending distortion (105) on completion of welding leading to formation of curvature, Ci in the plate. The bending distortion (105) of the top edge of the rectangular plate (101) where the weld was deposited, can be defined as a parabola with the general equation:
y=C_i/2.x^2………… Equation (1)
The above equation is developed assuming that the weld has nearly the same curvature along its length and that the origin is fixed exactly at the vertex of the parabola. If the value of curvature (Ci) is known, then the bending distortion (105) of the top edge of rectangular plate (101) can be found out simply by plotting the parabola in a X-Y coordinate space defined between the limits x = -L/2 to x = +L/2 where ‘L’ represents the length of the weld segment.
Ref. to Figure 1b. In the second case, if the weld metal (105) is placed on the bottom side of the CG axis (103) of the same rectangular plate (101), then the plate again undergoes a bending distortion (106), but in the reverse direction, with the curvature being same in magnitude but opposite in sign to the case. In such a condition, the bending distortion (106) of the bottom edge of the plate where the weld was deposited, can be defined as a parabola with the general equation :
y=-C_i/2.x^2………… Equation (2)
As stated earlier, the above equation is developed assuming that the weld has nearly the same curvature along its length and that the origin is fixed exactly at the vertex of the parabola. The minus sign indicates that the case represented by Figure 1b is exactly the mirror image (about X-axis) of the case represented in Figure 1a. In other words, for both the cases shown in Figures 1a and 1b, the bending distortion (105, 106) is identical, but the one shown in Figure 1a has a positive curvature whereas the one shown in Figure 1b has a negative curvature. The bending distortion (105, 106) is plotted for all values of x ranging from x = -L/2 to x = +L/2 where ‘L’ represents the length of the weld segment.
Ref. to Figure 1c. In the third case, the weld segment (107) is laid only for a partial length, on the top edge of the rectangular plate (101). In such a condition, the distorted shape of the weld segment (107) is given by equation (1), mentioned earlier. The vertex of the parabola is fixed at the origin and the parabola is formed within the length where the weld is laid in the top edge. Thus, this defines and fixes the parabola in the X-Y coordinate space.
The non-welded segments namely (109) and (110) act as tangents to the parabolic shape attained by the weld segment (107) on its either ends. Let the point of tangency of straight line (109) with parabola (108) be defined as (X1, Y1), shown as bending distortion (111). If the welded length is defined as L1, then we have
X1 = L1/2
Since (X1, Y1) lies in the parabola which is defined by equation (1), ‘Y1’ can be determined as
Y1=C_i/2.〖(X1)〗^2………… Equation (3)
M1, the slope of the parabola at (X1, Y1), is obtained by differentiating equation (1) and substituting the coordinate point.
M1=Ci.X1………… Equation (4)
The equation of tangent line (9) is given by
y=M1.x+K1 ………… Equation (5)
Since (X1, Y1) lies in the line defined above
K1=M1.X1-Y1 ………… Equation (6)
Thus, now equation (5) is completely defined now. Allowing X to vary from L1/2 to L, the total length of the top edge of the plate, the distorted shape of the non-welded line (109) can be plotted.
Using the same procedure followed for tangent line (109), the equation of tangent line (110) is defined as
y=M2.x+K2 ………… Equation (7)
Where,
M2=Ci.X2………… Equation (8)
K2=M2.X2-Y2 ………… Equation (9)
Now,
Using equation (7) and allowing X to vary from ‘-L/2’ to ‘-L1/2’, the straight line (110) representing the non-welded portion of the top edge of the rectangular plate (101) is plotted.
Using equation (1) and allowing X to vary from ‘-L1/2’ to ‘+L1/2’, the parabolic arc representing the bending distortion (111) of the weld segment of the top edge of the rectangular plate (101) is plotted.
Using equation (5) and allowing X to vary from ‘+L1/2’ to ‘+L/2’, the straight line (110) representing the non-welded portion of the top edge of the rectangular plate (101) is plotted.
Thus, the distorted shape of top edge of the rectangular plate (101) is plotted, once ‘Ci’ value is known.
Ref. to Figure 1d. In the fourth case, the top edge of the rectangular plate (101) is welded completely and then the bottom edge of the rectangular plate (101) is again welded completely. Under such conditions, the curvature ‘Ci’ developed in the weld segment upon completion of top edge weld, is reduced to a smaller value ‘Cr’ on completion of the weld on the whole length of the bottom edge of the rectangular plate (101). Thus, the final distorted shape is a parabola possessing a curvature of magnitude ‘Cr’. Using this fact, the equation of the parabolic shape representing the bending distortion (112) of the top edge of the rectangular plate (101) is given as:
y=C_r/2.x^2………… Equation (10)
By allowing X to vary from ‘-L/2’ to ‘+L/2’ in the above equation, the distorted shape (112) of the top edge of the rectangular plate (101) is plotted.
Ref. to Figure 1e. In the fifth case, a weld segment (113) of length ‘L1’ is placed on the top of the plate firstly. Then, yet another weld segment (114) of length ‘L2’ is deposited on the bottom edge of the rectangular plate (101). Let the whole length of the top edge of the rectangular plate (101) be equal to ‘L’. Then, the bending distortion (115) of top edge of the rectangular plate (101) is composed of:
a straight line AB representing a non-welded portion (from x = ‘-L/2’ to x = ‘-L2/2’)
a parabolic arc BC of curvature ‘-Ci’ since this portion is deflected by the action of weld segment L2 in excess of L1. (from x = ‘-L2/2’ to x = ‘-L1/2’)
a parabolic arc CD with a curvature ‘-Cr’ since both the top and bottom weld segments interact, resulting in a resultant curvature smaller than the curvature ‘Ci’, caused by a single weld segment. (from x = ‘-L1/2’ to x = ‘+L1/2’)
a parabolic arc DE of curvature ‘-Ci’ since this portion is deflected by the action of weld segment L2 in excess of L1. (from x = ‘+L1/2’ to x = ‘+L2/2’)
a straight line EF representing a non-welded portion (from x = ‘+L2/2’ to x = ‘+L/2’)
Further, it is clear that the bending distortion (115) of the top edge of the rectangular plate (101) is symmetrical about the positive ‘Y’ axis. Hence, it will be sufficient to plot the distorted shape in the positive half of the X axis, which can then the mirrored about the ‘Y’ axis. Accordingly, the following equations are derived.
Equation of parabolic arc CD is given by equation (10). In order to model the bending distortion (115) for positive values of X, the X values are allowed to vary from ‘0’ to ‘+L1/2’.
Then the equation of parabolic curve DE is to be determined. This curve can be expressed by the general equation
y= A_1 x^2+B_1 x+C_1 …………. Equation (11)
The parabolic curve DE has a curvature of magnitude ‘-Ci’ which is nearly a constant along its length. So,
A_1=-C_i/2 …………. Equation (12)
Let the coordinates of point ‘D’, the intersection point of curves CD and DE, be (X3, Y3)
Remembering that slope of the curves CD and DE are equal at point D and X3 = L1/2, we have
B_1=(Ci-Cr).(L_1/2) …………. Equation (13)
Since (X3, Y3) is a point that lies in the parabolic curve DE, we have
C_1=1/8.(3Cr-Ci).〖L_1〗^2 …………. Equation (14)
Since the equation (11) is completely known now, the parabolic curve DE is plotted by allowing x coordinate to vary from ‘+L1/2’ to ‘+L2/2’.
Let the point E be referred by the coordinate points (X4, Y4). Since E lies in parabolic curve DE, the value of Y4 is obtained as
Y4= A_1 〖(L_2/2)〗^2+B_1 (L_2/2)+C_1 …………. Equation (15)
Now, the equation of the straight line EF is given by
y=M3.x+K3 ………… Equation (16)
Where,
M3=2A_1 X4+B_1………… Equation (18)
K3=Y4-M3.X4 …………. Equation (19)
Now, the equation (16) is fully known. Using this equation, the bending distortion (115) of the non-welded segment is plotted by allowing X to vary from ‘L2/2’ to ‘L/2’.
All the above case-specific examples were shown to prove that once ‘Ci’ and ‘Cr’ are known from the second step comprising an FEM analysis on a short FE model, then the overall distorted shape of the rectangular plate (101) is determined by claculating the distortion by solving the equations of parabolas and straight lines that respectively denote the welded portions and non-welded portions of the rectangular plate (101).
TECHNICAL ADVANTAGES
With the help of the solution as proposed herein in the context of the present disclosure, the curvature is determined using FEM, wherein only a small length of the welded structure is modelled. This means quicker and accurate estimate of curvature values.
The FEM is performed just once initially for determining the weld curvature. Subsequently, the distorted shapes corresponding to any weld sequence can be easily evaluated by merely solving few equations. Hence, this will be of great use to shop floor engineers to quickly evaluate the effect of various weld sequences on the final distortion magnitude and to arrive at a best weld sequence with least distortion.
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 disclosures 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. Also, 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 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 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.”
It will be further appreciated that functions or structures of a plurality of components or steps may be combined into a single component or step, or the functions or structures of one-step or component may be split among plural steps or components. The present disclosure contemplates all of these combinations. Unless stated otherwise, dimensions and geometries of the various structures depicted herein are not intended to be restrictive of the disclosure, and other dimensions or geometries are possible. Also, while a feature of the present disclosure may have been described in the context of only one of the illustrated embodiments, such feature may be combined with one or more other features of other embodiments, for any given application. It will also be appreciated from the above that the fabrication of the unique structures herein and the operation thereof also constitute methods in accordance with the present disclosure. The present disclosure also encompasses intermediate and end products resulting from the practice of the methods herein. The use of “comprising” or “including” also contemplates embodiments that “consist essentially of” or “consist of” the recited feature.
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.
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.
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 particulars 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 analogues 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”.
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.
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.
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.
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.
, C , Claims:WE CLAIM
1. A method (300) of predicting shape of bending distortion (105, 106, 111, 112, 115) of a long welded structure (101) comprising a plurality of welds located either above or below the longitudinal CG axis (103), the method (300) comprising steps of:
applying (301) necessary boundary conditions on model welded structures (201, 202);
obtaining (302) curvature values ‘Ci’ and ‘Cr’ formed in a distorted shape (203, 204) of the model welded structure (201, 202) using a Finite Element Modelling (FEM) technique; and
determining (303) distorted shape (203, 204) of the model welded structure (201, 202) using the curvature values ‘Ci’ and ‘Cr’ and applying equation of a parabolic arc corresponding to welded segments and equations of straight lines that correspond to non-welded segments.
2. The method (300) as claimed in claim 1, wherein the shape of the bending distortion (105) is determined by plotting the parabola in a X-Y coordinate space defined between the limits x = -L/2 to x = +L/2.
3. The method (300) as claimed in claim 1, wherein the shape of the bending distortion (106) is determined by plotting the parabola in a X-Y coordinate space defined between the limits x = -L/2 to x = +L/2.
4. The method (300) as claimed in claim 1, wherein the shape of the bending distortion (111) is determined by plotting the parabola in a X-Y coordinate space wherein X varies from ‘-L1/2’ to ‘+L1/2’.
5. The method (300) as claimed in claim 1, wherein the shape of the bending distortion (112) is determined by plotting the parabola in a X-Y coordinate space wherein X varies from ‘-L/2’ to ‘+L/2’.
6. The method (300) as claimed in claim 1, wherein the shape of the bending distortion (115) is determined by plotting the parabola in a X-Y coordinate space wherein X varies from ‘0’ to ‘+L1/2’.
7. The method (300) as claimed in claim 1, wherein a coefficient of a second degree term present in the equation of the parabolic arc is determined to be half the magnitude of the curvature of that parabolic arc.
8. The method (300) as claimed in claim 1-7, wherein a coefficient of the first degree term present in the equation of the parabolic arc is found by equating the first derivative of the equation of the parabolic arc to the slope of adjacent parabolic arc or a straight line.
9. The method (300) as claimed in claim 1-8, wherein a constant term present in the equation of the parabolic arc is determined lastly by utilizing the above two equations and the common point of intersection between the said parabolic arc and an adjacent parabolic arc or straight line
10. The method (300) as claimed in claim 1-9, wherein a coefficient of first degree term and constant of the straight lines representing non-welded portions of the welded structure are found out by enforcing the condition that such straight lines are tangential to the neighboring parabolic arc representing a weld segment.