METHOD AND SYSTEM TO CHARACTERIZE ECCENTRICITY MODES INDUCED IN A MANUFACTURING PROCESS OF A SEAMLESS PIPE

Abstract

A method of characterizing at least one rotational and at least one linear eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe. The method comprises the steps of measuring a wall thickness profile along and around a length of the seamless pipe using a ultrasound-based measurement tool; applying a Fourier transform to the wall thickness profile to obtain a frequency spectrum; identifying one or more amplitude peaks in the frequency spectrum; associating each amplitude peak to a corresponding one of the at least one rotational eccentricity modes; filtering the one or more amplitude peaks out of the frequency spectrum; applying an inverse Fourier transform to the frequency spectrum to obtain a filtered wall thickness profile; and modeling the filtered wall thickness profile into a radial profile of the seamless pipe representative of the at least one linear eccentricity modes.

Claims

1. A method of characterizing at least one rotational and at least one linear eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe, the method comprises the steps of: a) measuring a wall thickness profile along a length and around a radius of the seamless pipe using an ultrasound-based measurement tool; b) applying a Fourier transform to the wall thickness profile to obtain a frequency spectrum; c) identifying one or more amplitude peaks in the frequency spectrum; d) associating each amplitude peak to a corresponding one of the at least one rotational eccentricity modes; e) filtering the one or more amplitude peaks out of the frequency spectrum; f) applying an inverse Fourier transform to the frequency spectrum to obtain a filtered wall thickness profile; and g) modeling the filtered wall thickness profile into a radial profile of the seamless pipe representative of the at least one linear eccentricity modes.

2. The method of claim 1, wherein the ultrasound-based measurement tool comprises a hollow passageway and one or more laser ultrasonic-based measuring probe projecting therein.

3. The method of claim 2, wherein the measuring a wall thickness profile along a length and around a radius of the seamless pipe comprises, concurrently: translating the seamless pipe through the hollow passageway; rotating the one or more measuring probes around the seamless pipe or rotating the seamless pipe; and probes around the seamless pipe or rotating the seamless pipe.

4. The method of claim 1, wherein the at least one rotational eccentricity modes comprises an eccentricity mode stemming from a rotation of a piercing mandrel during a piercing step of the manufacturing process of the seamless pipe.

5. The method of claim 4, comprising associating the eccentricity mode stemming from a rotation of a piercing mandrel with one or more amplitude peaks of the frequency spectrum at higher frequencies.

6. The method of claim 1, wherein the at least one rotational eccentricity modes comprises an eccentricity mode stemming from a rotation of a rotary hearth heating furnace during a heating step of the manufacturing process of the seamless pipe.

7. The method of claim 6, comprising associating the eccentricity mode stemming from a rotation of a rotary hearth heating furnace with one or more amplitude peaks of the frequency spectrum at lower frequencies.

8. The method of claim 1, further comprising characterizing the rotational eccentricity modes associated with amplitude peaks in the frequency spectrum.

9. The method of claim 8, wherein characterizing the rotational eccentricity modes comprises: applying a low-pass filter on the frequency spectrum selected to isolate said amplitude peaks, thereby obtaining a low frequency filtered frequency spectrum; applying an inverse Fourier transform to the low frequency filtered frequency spectrum, thereby obtaining a low frequency filtered wall thickness profile; and analyzing sub-profiles of the low frequency filtered wall thickness profile associated with the rotational eccentricity modes.

10. The method of claim 1, wherein filtering the one or more amplitude peaks out of the frequency spectrum comprises applying a high-pass filter to the frequency spectrum.

11. The method according to claim 1, wherein modeling the filtered wall thickness profile includes comprises mapping an internal diameter position of the seamless pipe with respect to the outer diameter position.

12. The method of claim 1, further comprising comparing radial profile of the seamless pipe representative of the at least one linear eccentricity modes to an expected radial profile of the seamless pipe.

13. A system for characterizing at least one rotational and at least one linear eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe, the system comprising: an ultrasound-based measurement tool to measure a wall thickness profile along and around a length of the seamless pipe; and a processor and a non-transitory computer-readable medium having stored thereon processor-executable instructions for: receiving the wall thickness profile from the ultrasound-based measurement tool; applying a Fourier transform to the wall thickness profile to obtain a frequency spectrum; identifying one or more amplitude peaks in the frequency spectrum; associating each amplitude peak to a corresponding one of the at least one rotational eccentricity modes; filtering the one or more amplitude peaks out of the frequency spectrum; applying an inverse Fourier transform to the frequency spectrum to obtain a filtered wall thickness profile; and modeling the filtered wall thickness profile into a radial profile of the seamless pipe representative of the at least one linear eccentricity modes.

14. The system of claim 13, wherein the ultrasound-based measurement tool comprises a hollow passageway and one or more measuring probe projecting therein.

15. The system of claim 14, wherein the one or more measuring probes are laser ultrasonic-based.

16. The system of claim 14, wherein the ultrasound-based measuring tool further comprises a rotational displacement system having the one or more measuring probes mounted thereon such that the one or more measuring probes can perform at least a complete revolution around the hollow passageway.

17. The system of claim 13, wherein the at least one rotational eccentricity modes comprises an eccentricity mode stemming from a rotation of a piercing mandrel during a piercing step of the manufacturing process of the seamless pipe.

18. The system of claim 14, wherein the at least one rotational eccentricity modes comprises an eccentricity mode stemming from a rotation of a rotary hearth heating furnace during a heating step of the manufacturing process of the seamless pipe.

19. The system of claim 13, wherein the non-transitory computer-readable medium further stores thereon processor-executable instructions for characterizing the rotational eccentricity modes associated with amplitude peaks in the frequency spectrum.

20. The system of claim 13, wherein the non-transitory computer-readable medium further stores thereon processor-executable instructions for comparing radial profile of the seamless pipe representative of the at least one linear eccentricity modes to an expected radial profile of the seamless pipe.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0042] FIG. 1 is a perspective view of a seamless pipe, in accordance with an embodiment.

[0043] FIG. 2 is a schematic flowchart illustrating the different steps of manufacturing the seamless pipe, in accordance with an embodiment.

[0044] FIG. 3 is a flowchart of a method for characterising eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe, in accordance with an embodiment.

[0045] FIG. 4 is a side elevation view of an ultrasound-based measurement tool to measure a wall thickness profile of a seamless pipe, comprising one measuring probe, in accordance with an embodiment.

[0046] FIG. 5 is a side elevation view of an ultrasound-based measurement tool, comprising two measuring probes, in accordance with an embodiment.

[0047] FIG. 6 is a side elevation view of an ultrasound-based measurement tool, comprising three measuring probes, in accordance with an embodiment.

[0048] FIG. 7 is a graph showing a measured wall thickness profile as a function of a longitudinal position of the seamless pipe, in an embodiment.

[0049] FIG. 8 is a graph showing a Fourier transform of FIG. 7, resulting in an amplitude as a function of a frequency, in an embodiment.

[0050] FIG. 9 is a is a graph showing a filtered wall thickness profile as a function of the longitudinal position of the seamless pipe, in an embodiment.

[0051] FIG. 10 is a radial profile model of the of the seamless pipe, in an embodiment.

[0052] FIG. 11 is a is a graph showing a wall thickness profile as a function of a longitudinal position of the seamless pipe, in an embodiment.

[0053] FIG. 12 is a radial profile model of the of the seamless pipe, in an embodiment.

[0054] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION

[0055] In the present description, similar features in the drawings have been given similar reference numerals. To avoid cluttering certain figures, some elements may not be indicated if they were already identified in a preceding figure. It should also be understood that the elements of the drawings are not necessarily depicted to scale, since emphasis is placed on clearly illustrating the elements and structures of the present embodiments. Positional descriptors indicating the location and/or orientation of one element with respect to another element are used herein for ease and clarity of description. Unless otherwise indicated, these positional descriptors should be taken in the context of the figures and should not be considered limiting. It is appreciated that such spatially relative terms are intended to encompass different orientations in the use or operation of the present embodiments, in addition to the orientations exemplified in the figures. Furthermore, when a first element is referred to as being on, above, below, over, or under a second element, the first element can be either directly or indirectly on, above, below, over, or under the second element, respectively, such that one or multiple intervening elements may be disposed between the first element and the second element.

[0056] The terms a, an, and one are defined herein to mean at least one, that is, these terms do not exclude a plural number of elements, unless stated otherwise.

[0057] The term or is defined herein to mean and/or, unless stated otherwise.

[0058] The expressions at least one of A, B, and C and one or more of A, B, and C, and variants thereof, are understood to include A alone, B alone, and C alone, as well as any combination of A, B, and C.

[0059] Terms such as substantially, generally, and about, which modify a value, condition, or characteristic of a feature of an exemplary embodiment, should be understood to mean that the value, condition, or characteristic is defined within tolerances that are acceptable for the proper operation of this exemplary embodiment for its intended application or that fall within an acceptable range of experimental error. In particular, the term about generally refers to a range of numbers that one skilled in the art would consider equivalent to the stated value (e.g., having the same or an equivalent function or result). In some instances, the term about means a variation of +10% of the stated value. It is noted that all numeric values used herein are assumed to be modified by the term about, unless stated otherwise. The term between as used herein to refer to a range of numbers or values defined by endpoints is intended to include both endpoints, unless stated otherwise.

[0060] The term concurrently refers herein to two or more processes that occur during coincident or overlapping time periods. The term concurrently does not necessarily imply complete synchronicity and encompasses various scenarios including time-coincident or simultaneous occurrence of two processes; occurrence of a first process that both begins and ends during the duration of a second process; and occurrence of a first process that begins during the duration of a second process, but ends after the completion of the second process.

[0061] In accordance with some aspects, there is provided a method of characterizing at least one rotational and at least one linear eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe.

[0062] Seamless pipes, also known as seamless tubes, may be understood as pipes or tubes that do not have any welding seam. In the context of the present description, the seamless pipe may for example be a solid metal tube made of any suitable metal, including but not limited to steel, stainless steel, carbon steel, copper, titanium, and nickel-alloy. Referring to FIG. 1, the seamless pipe 10 has a hollow cross-section surrounded by a wall 12, the wall of the seamless pipe extending between an inner surface 14 and an external surface 16. The wall 12 has a wall thickness t defined as the distance between the inner surface 14 and outer surface 16 along a radius r direction. Typical seamless pipes have a wall thickness in the centimeter range, for example from about 0.3 cm to about 10 cm, and in particular embodiment from about 0.5 cm to about 2 cm. The seamless pipe has an outside diameter OD along its external surface 16 which can range, typically, between about 5 cm and about 100 cm, and in particular embodiment from about 10 cm to about 40 cm. The length L of the seamless pipe may for example range from about 5 m to about 50 m, and in particular embodiment of about 30 m. The seamless pipe 10 may be destined for use in conveying fluid, such as oil, natural gas, gas, water and some solid materials.

[0063] The manufacturing process of seamless pipes generally follows the so-called Mannesmann process, as known in the art. While the Mannesmann process will be described below, it is understood that this description is provided by way of example only and that the characterizing methods and systems described herein may be used in conjunction with other hot forming processes to manufacture seamless pipes without departing from the scope of protection.

[0064] An overview of the Mannesmann process for manufacturing seamless pipes is shown in FIGS. 2A to 2E, which is based on an extract from www.theprocesspiping.com/introduction-to-seamless-pipe-manufacturingl, the entire contents of which is incorporated herein by reference. The process begins by providing a solid cylindrical hunk of metal, typically called a billet 5. The billet 5 is transformed into a seamless pipe according to the following series of steps: [0065] 1. FIG. 2A: Heating step. The step of heating typically involves uniformly heating the billet 5 in a rotary hearth heating furnace 210 to a temperature sufficient to allow the metal to become malleable. The temperature of the rotary hearth furnace can be for example range from about is 1290? F. (700? C.) to 2300? F. (1260? C.), and in a particular embodiment can be of about 2190? F (1200? C.). Once the billet 5 has reached the required level of malleability, the billet is discharged from the rotary hearth furnace 210. [0066] 2. FIG. 2B: Piercing step. Next, in the step of piercing, a small hole is first punched at one end of the billet 5, the small hole being used as a starting point and as a guide for rotary piercing. The billet 5 is then pierced by a piercing mandrel 220 to form a hollow pipe. The piercing mandrel can include a piercing bar (or bit) 224 on which a piercing plug 222 is mounted at its distal end. The piercing mandrel 220 rotates about a central axis x of the billet 5 while being translated along this central axis x, until the billet 5 takes the form of the hollow seamless pipe 10. The rotary piercing can be a very fast and dynamic step, with a rotation speed of the piercing mandrel from about 100 rpm to about 400 rpm. In some implementations, the seamless pipe 10 is circulated between at two or more barrel-shaped rolls 226 simultaneously to the piercing step. [0067] 3. FIG. 2C: Elongating step. A step of elongating the seamless pipe 10 is then performed, preferably by longitudinally translating the seamless pipe 10 in a mandrel mill 230 or by rotational stages similar to the piercing stage. The mandrel mill longitudinal elongation process comprises a plurality of rolling stands 232, each rolling stand 232 typically including a pair of rolls 234 positioned on either side of the seamless pipe 10, diametrically opposed to each other. In a non-limitative embodiment, the mandrel mill 230 includes at least two rolling stands 232, spaced apart from each other and rotated 90? from each other. In other embodiments, the mandrel mill may include four or eight rolling stands. While the seamless pipe 10 is translated in the mandrel mill 230, at least one preheated mandrel bar 236 is inserted in the hollow seamless pipe 10. The step of elongating therefore includes rolling the seamless pipe 10 through the mandrel mill 230 with the mandrel bar 236 inside to reach the final desired outside diameter OD of the seamless pipe 10 while controlling its wall thickness t. [0068] 4. FIG. 2E: Sizing step. Optionally, a step of sizing can also be performed after the elongating step, by longitudinally translating the seamless pipe (which may further optionally be re-heated in an oven 240 after the elongating step, if needed, as show in FIG. 2D) in a stretch mill 250. In a non-limitative embodiment, the stretch mill 250 may for example include a plurality of rolling stands 252, each of the rolling stands 252 comprises three rolls 254 evenly distributed along the perimeter of the seamless pipe, configured and positioned to create a round shape, and adapted to the requested gauge (OD) of the seamless pipe. After this last step, the seamless pipe is considered to meet the length L, outside diameter OD and wall thickness t as specified by the customer order.

[0069] The seamless pipe manufacturing process as described above, or equivalents thereof, can induce eccentricities in the wall thickness of the seamless pipe 10, that is, deviations from the expected uniform thickness. Different eccentricity modes can affect the seamless pipe profile differently, resulting in a wall thickness that is not equal along the length and/or the radius of the seamless pipe. The eccentricities induced are typically of two types: rotational eccentricity modes and linear eccentricity modes.

[0070] Rotational eccentricity modes are mainly induced by the steps of the process where a rotation is involved, such as piercing or rotational elongation steps. For example, during the piercing step of FIG. 2B, if the piercing plug 222 is defective or if the piercing plug 222 is slightly out of alignment with the piercing bar 224, the defect will be propagated helicoidally along the inner surface and/or outer surface of the seamless pipe, resulting in a rotational eccentricity mode of the wall thickness.

[0071] By contrast, linear eccentricity modes are typically induced by the steps of the process where a linear translation is involved, such as the elongating and sizing steps. For example, during the elongating step of FIG. 2C, if one of the rolling stands 232 exerts a higher pressure or rotation speed than another rolling stand 232 on the seamless pipe 10, the defect will be propagated longitudinally along the outer surface and/or inner surface of the seamless pipe, resulting in a linear eccentricity mode of the wall thickness.

[0072] Referring to FIG. 3, in accordance with one aspect, a method 100 for characterising at least one rotational and at least one linear eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe is shown, according to a non-limitative embodiment.

[0073] The method 100 includes a first step of measuring 110 a wall thickness t profile along the length L and around the radius r of the seamless pipe, using an ultrasound-based measurement tool.

[0074] The ultrasound-based tool may be embodied by any device or system which uses the propagation of ultrasound waves in a structure as a means of measuring its thickness. Referring to FIG. 4, there is shown a non-contact ultrasound-based measurement tool 20 according to one implementation. The ultrasound-based measurement tool 20 as illustrated includes a hollow passageway 25 and a measuring probe 22 projecting therein. In some implementations, the measuring probe is based on laser ultrasonic technology. In typical implementations, a generation laser (not shown) generates a short laser light pulse which impinges on the wall of the seamless pipe and is absorbed over a small volume on the surface thereof. The absorbed optical energy triggers a high-frequency sound pulse within the material of the wall of the seamless pipe, called the ultrasonic probing pulse. Simultaneously, a second laser emits a detection laser bean which is aimed at a different location on the wall of the seamless pipe where the ultrasonic probing pulse is excepted to travel. The reflections of the detection laser beam from this area are collected for analysis. The surface motion caused by ultrasound is encoded in the backscattered light.

[0075] Using an optical interferometric process, the surface motion is extracted from the collected light, and waveform analysis methods are then used directly on the extracted waveforms to obtain dimensional measurements. The measuring probe can be, without being limitative, the one disclosed in U.S. Pat. No. 6,078,397, the entire contents of which is incorporated herein by reference.

[0076] Still referring to FIG. 4, in one embodiment the seamless pipe 10 is translated in a longitudinal translation (i.e., without rotating on itself) through the passageway along its entire length L, without contact. Therefore, the wall thickness measurement is performed at each longitudinal position along the seamless pipe. It is understood that the ultrasound-based measurement tool 20 can be stationary and can be provided at the end of the manufacturing process and therefore the seamless pipe is supported by the manufacturing machines, such as there is no contact between the seamless pipe and the ultrasound-based measurement tool.

[0077] In one variant, the measuring probe 22 is mounted on a rotational displacement system 27, such that the probe 22 can perform at least a complete revolution around the hollow passageway 25, allowing a full circumference of the seamless pipe to be scanned (360?). In a non-limitative embodiment, the probe 22 performs only one complete revolution during the measurement step. Therefore, the wall thickness measurement is performed at least once at each radial position around the seamless pipe. It will be readily understood that in other variants, the same result may be accomplished by rotating the seamless pipe along its longitudinal axis while keeping the measuring probe in a fixed position.

[0078] Referring to FIGS. 5 and 6, in some implementations the ultrasound-based measurement tool 20 may include a plurality of measuring probes distributed around the circumference of the hollow passageway. In the illustrated example of FIG. 5 two measuring probes 22a and 22b are provided, projecting at radially opposed positions within the hollow passageway 25. In the example of FIG. 6 the ultrasound-based measurement tool includes three measuring probes 22a, 22b and 22c equidistantly positioned along the circumference of the hollow passageway 25. It will be readily understood that different numbers and configurations of measuring probes may be envisioned without departing from the scope of protection. Using more than one measuring probe 22 increase the precision of the measurement, in a same ratio as the number of probes. For example, the ultrasound-based measurement tool including one probe will have a precision p, while the ultrasound-based measurement tool including two probes will have a precision of p/2 and the ultrasound-based measurement tool including three probes will have a precision of p/3.

[0079] In the configuration where the ultrasound-based measurement tool 20 includes more than one probe 22, the plurality of probes 22 are preferably evenly distributed around the rotational displacement system 27 and are triggered simultaneously when measuring the thickness around the seamless pipe 10.

[0080] In another embodiment, an alternative measurement tool and method can be used to generate the wall thickness profile, such as and without being limitative radiometric gauges with high spatial resolution at the surface of the pipe.

[0081] The result of this first step is the wall thickness profile 30, as shown in FIG. 7. The wall thickness profile 30 generated shows a wall thickness (ordinate axis) at each longitudinal position along the seamless pipe (position on the abscissa axis). It is understood that a third parameter could be also considered in the wall thickness profile 30 (not shown), which is a radial or polar position of the probe around the central axis x, i.e., the (y, z) coordinates of the probe for each measurement point. As shown in FIG. 7, the wall thickness profile 30 can combine many harmonics of repetitive variations along the seamless pipe coming from different steps of the manufacturing. However, the repetitive aspect of the rotational eccentricities can hide the lower intensity of the linear eccentricities.

[0082] Referring back to FIG. 3, the method 100 further involves applying 120 a Fourier transform to the wall thickness profile to obtain a frequency spectrum (FIG. 8). As known in the art, the Fourier transform involves performing a translation of the wall thickness profile 30, corresponding to wall thickness vs position, into a frequency spectrum 40, corresponding to amplitude vs frequency.

[0083] The method next involves identifying 130 one or more amplitude peaks in the frequency spectrum 40. In reference to FIG. 8, several amplitude peaks 42, 44 can be identified. An amplitude peak 42, 44 is characterized by an amplitude at a certain frequency or in a certain frequency window that substantially exceeds the average of other amplitudes at other frequency.

[0084] The method next involves associating 140 each amplitude peak to a corresponding one of the at least one rotational eccentricity modes. As will be readily understood by one skilled in the art, because the rotational eccentricities are repeated in a periodic cycle, they are easily identifiable by a high amplitude at a specific frequency (amplitude peak). In an embodiment, each of the amplitude peak at a certain frequency can be associated to a specific rotational eccentricity. Such association can be calibrated directly in the manufacture where the method will be applied, depending on a specific manufacturing tool and process. Due to the high rotary speed of the piercing mandrel, and therefore the high repetition of potential rotational eccentricities, the piercing step is commonly associated with a low frequency and high amplitude of amplitude peaks. The heating step can also induce rotational eccentricities in the low frequency.

[0085] In some embodiments, the method may include an optional step of characterizing 142 the rotational eccentricity modes associated with amplitude peaks in the frequency spectrum. This may involve filtering 144 the at least one rotational eccentricity modes to characterize them. For example, a bandpass numeric filter can be applied on the frequency spectrum 40. The bandpass numeric filter passes frequencies within a certain range and rejects frequencies outside that range. For example, in the embodiment shown in FIG. 8, the bandpass filter is a low-pass filter applied on a frequency range between 0 Hz and 0.85 Hz, to isolate and keep the 2 amplitude peaks 42, 44 and to eliminate or reject the higher frequency. Once isolated, an inverse Fourier transform can be applied 146 to convert the filtered frequency spectrum into a low frequency filtered wall thickness profile 50, as shown in FIG. 9.

[0086] Referring now to FIG. 9, the low frequency filtered wall thickness profile 50 can be represented by a plurality of sub-profiles 52, 54, each one of the plurality of sub-profiles 52, 54 being associated to a specific rotational eccentricity as identified as amplitude peaks 42, 44 in the frequency spectrum 40. The sub-profiles may be analyzed 148 to obtain information on the individual rotational eccentricity modes. In the embodiment shown, the first sub-profile 52 corresponds to the first amplitude peak 42 and is a first rotational eccentricity induced by the manufacturing step of heating. The second sub-profile 54 corresponds to the second amplitude peak 44 and is a second rotational eccentricity induced by the manufacturing step of piercing.

[0087] By analyzing the low deviation of the first sub-profile 52, it can be concluded that the billet is substantially even heated in the rotary hearth heating furnace.

[0088] The analysis of the second sub-profile 54 can result in a verification and potential re-alignment of the piercing mandrel, considering the fast oscillating and higher deviation of the second sub-profile 54.

[0089] In an embodiment, the analysis of the sub-profiles 52, 54 can be performed by an operator of the manufacturing tool, by visually reviewing and interpreting the sub-profiles 52, 54. In an alternative embodiment, the analysis can be performed by a computer or processor, receiving as an input data the sub-profiles 52, 54, and generating as an output data the manufacturing steps inducing the rotational eccentricities.

[0090] Referring back to FIG. 3, the method 100 includes filtering 150 the one or more amplitude peaks out of the frequency spectrum. As explained above, the rotational eccentricity can have high amplitude at a specific frequency, and may hide the linear eccentricities, which have a lower amplitude. Therefore, the step of filtering the one or more amplitude peaks, corresponding to rotational eccentricities, results in eliminating them from the frequency spectrum to keep only the amplitude related to linear eccentricities. The filtering can be obtained by applying a high-pass numeric filter on the frequency spectrum 40. The high-pass frequency filter passes signals with a frequency higher than a certain cut-off frequency and rejects signals with frequencies lower than the cut-off frequency. For example, in the embodiment shown in FIG. 8, the high-pass filter can be applied with a cut-off frequency of about 0.8 Hz.

[0091] The method 100 further includes applying 160 an inverse Fourier transform to the high-pass filtered frequency spectrum to obtain a filtered wall thickness profile. Therefore, the filtered wall thickness profile can only represent the linear eccentricity modes.

[0092] Finally, the method 100 includes modeling 170 the filtered wall thickness profile into a radial profile of the seamless pipe representative of the at least one linear eccentricity modes. Modeling the filtered wall thickness profile includes mapping an internal diameter position of the seamless pipe with respect to the outer diameter position, using an approximation that the internal diameter and the external diameter can be considered perfectly round in first approximation. The modeling step result in a cross-section representation of the wall thickness of the seamless pipe in a radial position, such as the radial profile models 60, 60 of FIGS. 10 and 12. The radial profile model 60, 60 is a graphical representation of the solely linear eccentricity modes detected in the wall thickness of the seamless pipe.

[0093] In an embodiment, the method can further comprise a step of characterising the linear eccentricity modes induced by the manufacturing process, by comparing the radial profile model 60, 60 of the seamless pipe to an expected radial profile of the seamless pipe.

[0094] Referring to FIG. 10, an example of the radial profile model 60 obtained from the wall thickness profile 30 of FIG. 7 is shown. The radial profile model 60 corresponds to impact of linear eccentricity modes induced by the manufacturing step of elongating with a mandrel mill comprising two rolling stands (four rolls).

[0095] By analyzing the low deviation of the radial profile model 60 compared to an expected nominal profile, for example a perfect circle, it can be concluded that the four rolls apply a consistent pressure, and that there is a little overfilling (over thickness) at the corners meaning that the average pressure on the four rolls could be a little less to increase the roundness.

[0096] Referring to FIG. 12, the radial profile model 60 corresponding the wall thickness profile 30 of FIG. 11 is shown, corresponding to a different seamless pipe than the one of FIG. 10. In this embodiment, the analysis of the radial profile model 60 compared to an expected nominal profile 64 shows that the radial profile model 60 substantially deviates from the nominal profile 64, and even exceeds the acceptable tolerance of the nominal profile 66 in some points of deviation 68, 69. Therefore, it can be concluded that at least two of the four rolls apply an excessive pressure on the seamless pipe, resulting in an almost rectangular shape of the radial profile model 62. Corrective action may be taken by the operator of the manufacture toll to prevent such linear eccentricity modes by adjusting the rolls to reduce the slight bump in deformation between the radial profile model 60 and the expected nominal profile 64.

[0097] In an embodiment, the analysis of the radial profile model 60 can be performed by an operator of the manufacturing tool, by visually reviewing and interpreting the radial profile model 60. In an alternative embodiment, the analysis can be performed by a computer or processor, receiving as an input data the radial profile model 60, and generating as an output data the manufacturing steps inducing the linear eccentricities.

[0098] In some embodiment, as seen in FIGS. 4 to 6, a system 74 for characterizing at least one rotational and at least one linear eccentricity modes of a wall thickness of a seamless pipe induced during a manufacturing process of the seamless pipe can be provided. The system 74 can include an ultrasound-based measurement tool 20 as described in reference to FIGS. 4 to 6, and a processor 70 and a non-transitory computer-readable medium 72. The non-transitory computer-readable medium 72 can have stored thereon processor-executable instructions executing the method as described in reference to FIG. 3, namely: [0099] receiving the wall thickness profile from the ultrasound-based measurement tool; [0100] applying a Fourier transform to the wall thickness profile to obtain a frequency spectrum; [0101] identifying one or more amplitude peaks in the frequency spectrum; [0102] associating each amplitude peak to a corresponding one of the at least one rotational eccentricity modes; [0103] filtering the one or more amplitude peaks out of the frequency spectrum; [0104] applying an inverse Fourier transform to the frequency spectrum to obtain a filtered wall thickness profile; [0105] modeling the filtered wall thickness profile into a radial profile of the seamless pipe representative of the at least one linear eccentricity modes.

[0106] Several alternative embodiments and examples have been described and illustrated herein. The embodiments of the invention described above are intended to be exemplary only. A person of ordinary skill in the art would appreciate the features of the individual embodiments, and the possible combinations and variations of the components. A person of ordinary skill in the art would further appreciate that any of the embodiments could be provided in any combination with the other embodiments disclosed herein. It is understood that the invention may be embodied in other specific forms without departing from the central characteristics thereof. The present examples and embodiments, therefore, are to be considered in all respects as illustrative and not restrictive, and the invention is not to be limited to the details given herein. Accordingly, while the specific embodiments have been illustrated and described, numerous modifications come to mind. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.