GB2085577A

GB2085577A - A method and apparatus for measuring tube wall thickness

Info

Publication number: GB2085577A
Application number: GB8032882A
Authority: GB
Original assignee: Fuji Electric Co Ltd; Kawasaki Steel Corp
Current assignee: JFE Steel Corp; Fuji Electric Co Ltd
Priority date: 1980-10-10
Filing date: 1980-10-10
Publication date: 1982-04-28
Also published as: SE8105766L; GB2085577B

Abstract

Sources 1A, 1B, 1C direct at least three beams 3A, 3B, 3C of radiation of known intensity through the tube 20 so as to intersect at measuring points A, B, C within the tube wall. Detectors 4A, 4B, 4C receive the emergent beams and measure their intensities. The attenuation of the beams is used to determine the tube wall thickness x1, x2, x3 at the measuring points A, B, C. The determination may make use of the method of least squares and may be effected by means of a computer. Measuring points common to a beam path may be spaced axially of the tube. An additional measuring point may be on only one beam path which passes through another measuring point at which beam paths intersect. <IMAGE>

Description

SPECIFICATION A method and apparatus for measuring tube wall thickness This invention relates to a method and apparatus for gauging the wall thickness of a tubular object by simultaneously measuring the thickness at several points on the periphery of the tubular object, in a non-contacting manner.

Generally, in manufacturing tubing such as seamless steel tubes, it is necessary to gauge accurately wall thicknesses or inner and outer diameters, both in the case of a cold manufacturing process, where the tubing is at ambient temperature, and in the case of a hot manufacturing process, where the tubing has a temperature of about 1 0000C. The requirements for such a method of measurement are that it takes place without contacting the tubing, that it be capable of being conducted under high temperature conditions of about 10000C, that the measurement have an accuracy of about + 50 um to + 200 ym for a wall thickness of about 5-40 mm, and that it be performed rapidly.Rapid operation is necessary in order to detect frequent variations of the wall thickness which occur along the periphery and length of the tubing.

One method which has been proposed is illustrated in Figs. 1 and 2. As seen in Fig. 1, the wall thickness of tubing 20 is measured along the parallel lines A, B, C and D, the line B contacting the outer periphery of the tubing at a point a. Thus, the measured dimension L of wall thickness varies as shown in Fig. 2. Taken along the line A, which does not cross the tubing periphery, the dimension L is zero.

Along the line B, which just contacts the outer periphery of the tubing 20, the dimension L is also zero.

Along the line C, which just contacts the inner periphery of the tubing 20, the dimension L reaches its maximum. Along the line D, where the dimension L is given by the sum of the widths of both left and right wall portions traversed by the line D, the dimension L is far smaller than the value taken along the line C. If the measurement takes place continuously with the position (of the line) shifting in the direction of the arrow, Y, the value of L follows the curve as shown in Fig. 2.

The wall thickness of the tubing 20 is therefore given by a distance h in the direction of arrow Y between a point B of a rise in that curve and a point C where the value of L reaches its maximum (Fig.

2). A measuring instrument (not shown) comprising a radiation source and radiation detector is used to obtain this curve. The source and detector are placed on the line A, on respective sides of the tubing, separated from each other by a distance greater than the diameter of the tubing 20. This measuring instrument is moved in the direction of the arrow Y, from a position on the line A through the positions of the lines B, C and D and so on, while its output indicates the varying value of L. The distance of movement in the Y direction, between the point where its output just begins to rise and the point where it reaches the maximum, is the wall thickness.

The method just described can achieve the measurement without touching the measured object.

However, it does not afford a high degree of accuracy in measurement, since an error in defining the position of the radiation beam causes an error in the measured value of wall thickness. It has another drawback in that rapid measurement is not readily achievable. Since a gamma-ray source is used for the radiation when measuring the thickness of a steel pipe wall a lengthy measurement operation is required as the source is massive and cannot be moved quickly for radiation beam scanning.

According to a first aspect of this invention there is provided a method of measuring the thickness of the wall of a circular cross-section tube, said method comprising the steps of selecting at least three distinct measuring points in said tube wall and distributed about the longitudinal axis of said tube, transmitting a plurality of radiation beams of known intensity in a plurality of different directions so that each beam passes through two of said measuring points, said directions being selected such that at least two of said radiation beams pass through each of said measuring points, detecting the intensities of said radiation beams, after having passed through said measuring points, to derive detected values to enable determination of said tube wall thickness from said known intensity values and said detected values of beam intensity.

According to a second aspect of this invention there is provided an apparatus for measuring the thickness of the wall of a circular cross-section tube said apparatus comprising at least three radiation beam sources, each for generating a beam of known intensity and arranged so that each beam has a different respective radiation path, said sources being positioned at different selected locations about a position to be occupied by a tube to be measured, and said sources being oriented such that each of said beam paths from said sources intersects at least two other beam paths at different points which are to be in said tube wall, beam intensity detection means for each of said sources positioned in the respective radiation path at a position to be beyond said tube, for producing a detected value of beam intensity to enable determination of said tube wall thickness from said known intensity values and said detected values of beam intensity.

Embodiments of this invention will now be described, by way of example, with reference to the accompanying drawings in which: Fig. 1 is a schematic cross-sectional view of a tube with lines indicating radiation beam scanning in a prior art arrangement: Fig. 2 is a diagram showing the measured dimension L (in ordinate) at various measuring positions of the radiation beam (in abscissa) for the arrangement illustrated in Fig. 1; Fig. 3 is a schematic diagram of a measuring arrangement forming a first embodiment of the invention, for measuring a tube shown in cross-section; Fig. 3A is a schematic diagram of a portion of the arrangement shown in Fig. 1 for the general case where a radiation beam passes through the tube wall;; Figs. 4, 5 and 6 are schematic diagrams of measuring arrangements forming respective second, third and fourth embodiments of the invention; Fig. 7 is a schematic diagram of a measuring arrangement in a fifth embodiment of the invention and illustrating the application of the method of least squares; Fig. 8 is a schematic diagram of a measuring arrangement in a sixth embodiment of the invention; and Fig. 9 is a schematic diagram of a measuring arrangement forming a seventh embodiment of the invention, where the tube is shown in perspective.

Referring to Fig. 3, the arrangement shown gauges wall thicknessesx1,x2, and x3 at respective measuring points A, B, and C, which divide the tube wall perimeter in cross-section into three equal parts.

The device has three measuring systems corresponding to the points A, B, and C. Each measuring system comprises a radiation source 1 A, 1 B, 1 C, a source assembly 2A, 2B, 2C which directs a radiation beam 3A, 3B, 3C in a fixed direction, and a detector 4A, 4B, 4C to measure the intensity of the radiation beam transmitted through the wall of the tube 20. Here, the letters, A, B, and C annexed to the reference numerals represent the component of the three respective systems. Those letters will be omitted hereinafter for simplicity except where specifically required.References |1, |2, and 13 are used below to denote the output signals of the respective detectors 4A, 4B and 4C when the radiation beams reach them through the tube wall, while 110, 120 and 130 denote the output signals of the respective detectors in the absence of the tube body (i.e., where the radiation beams reach them directly). Disposition of the measuring systems is such as is shown in Fig. 3, where each radiation beam passes through two measuring points and two beams pass through each measuring point.

From a fundamental formula in radiation transmission thickness measurement, the following equations hold, to give the relation between the detector output signals and the measured thickness xt, X2, X3 |1 = lio exp {- k (xl +:x2)l -------- (1) 12 = 120 exp {- k (x2 + X3)} -------- (2) 13-130 exp t-yk (x3 ±x1)i -------- (3) where denotes an absorption coefficient of the radiation in the tube material, and k denotes a value of an actual transit path length S of radiation beam through the tube wall through a measuring point (cf.

Fig. 3A) divided by wall thickness x at that point.

If the radiation beam extends in a radial direction with respect to the tube, i.e., if the angle 0-in Fig.

3 is zero, the value of k is 1. Provided that the number of measuring points the beam thickness and direction of radiation are adequately chosen with regard to the shape of the tube, the value.of k can be chosen to have minimal influence in spite of random fluctuations of the tube wall thickness.

A solution of the simultaneous equations (1 ) to (3) can be given by

The wall thicknessesx1,x2, andx3 can therefore be determined from the values of the detector output signals |10, |1, |20, i2, 130, and 13 and the constants y and k.

Though the embodiment described above illustrates the case where there are three measuring points, the technique can be adapted for any number n measuring points. Therefore designating x1, x2,..., xn as wall thicknesses at the respective measuring points, the following relationships (simultaneous equations) hold, being obtained by logarithmic transformation of equations corresponding to the above equations (1) to (3).

Using matrices, the simultaneous equations (7) can be written as:

1 1 0 -: -: -: -: -: 0 x1 b1 0 1 1 0 -: -: -: -: 0 x2 b2 0 0 1 1 0 -: -: -: 0 x3 b3 0 0 0 1 1 0 -: -: 0 # # x4 # = # b4 # (7a) -: -: -: -: -: -: -: -: -: -: --: 0 0 -: -: -: -: 0 1 1 xn-1 bn-1 1 0 -: -: -: -: 0 0 1 xn bn In the above, the number n is to be odd.

In the embodiment shown in Fig. 4 n = 9. There, the simultaneous equations determining wall thicknesses x1,x2,..., x9 are, from what is stated above represented by

1 1 0 0 0 0 0 0 0 x1 b1 0 1 1 0 0 0 0 0 0 # # x2 # #b2 0 0 1 1 0 0 0 0 0 x3 b3 0' 0' 0' 1 1 0' 0 0 0 X4 b4 0' 0' 0' 0' 1 1 0 0 0 x5 = b5 (8) 0 0 0 0 0 @ 1 0 0 x6 b6 0 0 0 0 0 0 1 1 0 x7 b7 0 0 0 0 0 0 0 1 1 # # x5 # # b5 1 0 0 0 0 0 0 0 1 x9 b9 Referring to Fig. 5, there is shown another embodiment where n = 9.The arrangement shown has the same number of measuring points as the arrangement shown in Fig. 4, but the relative position of the points through which each radiation beam passes are different, That is, combinations of the points in Fig. 4 are x1 with x2, x3 with x4, x4 with x5, and so on; however, in Fig. 5, the combinations are x1 with x4, x2 with x5, x3 with x6, x4 with x7, and so on.In the embodiment of Fig. 5, simultaneous equations yielding the wall thicknesses are represented by

1 0 0 1 0 0 0 0 0 x1 b1 0 1 0 0 1 0 0 0 0 x2 b2 0 0 1 0 0 1 0 0 0 # x3 # # b3 # 0 0 0 1 0 0 1 0 0 x4 b4 0 0 0 0 1 0 0 1 0 x5 = b5 (9) 0' 0 0' 0 0' 1 0 0- 1 x6 b6 1 0 0 0 0 0 1 0 0 x7 b7 0 1 0 0 0 0 0 1 0 x8 b8 0' 0 1 0 0 0 0' 0' 1 X9 b9 The above representation (9) can be rewritten as follows:-

1 1 0 x1 b1 # 0 1 1 # # x4 # = # b4 # 1 0 1 x7 b7 1 1 0 x2 b2 # 0 1 1 # # x5 # = # b5 # (10) 1 0 1 x8 b8 1 1 0 x3 b3 # 0 1 1 # # x6 # = # b6 # 1 0 1 x9 b9 The representation (10) indicates that the embodiment shown in Fig. 5 is identical to performing the calculations for the embodiment shown in Fig. 3 three times.

In Fig. 6 there is shown yet another embodiment where n = 9. Here, the combinations of the polnts through which the radlation beam passes are x1 with x6, x2 with x7, x3 with x8, x4 with x9, and so on.

In the embodiment shown in Fig. 6, the simultaneous equations for the wall thicknesses are represented by:

1 0 0 0 0 1 0 0 0 ] [x1] [b1 0 1 0 0 0- 0' 1 0 O X2 b2 0 0 1 0 0 0 0 1 0 x3 b3 0 0 0 1 0 0 0 0 1 x4 b4 1 0 0 0 1 0 0 O- O x5 = b5 (11) 0- 1 0' 0- 0' 1 0 0 0 X6 b6 0 0 1 0 0 0 1 0 0 x7 b7 0 0 0 1 0 0 0 1 0 x8 b8 0 0 0 0 1 0 0 0 1 x9 b9 As found for the embodiments shown in Figs. 4 to 6, several different simultaneous equations may be applied to measure the wall thicknesses at the points through which pass the beams. By obtaining the values of the thicknesses using beams passing through different combinations of points, an average of the measured values of the thickness at each measuring point can then be taken. This yields a better expected value of the wall thickness at each measuring point.

The expected value is given as follows, for example, for the thickness of the measuring point of x1, where three different combination modes of measurement are used to produce the three measured values x11, xg2, and x13, x1e- (1/3) (x11 + x,2 + xl3) -------- (12) where x1e denotes the expected value. This is the averaging method.

In general, statistical errors in radiation thickness measurement decrease as the wall thickness decreases. Therefor, in some cases, it is better to determine the expected value from a weighted average of the measured values. That is:

where p1, p2 and p3 are weighting factors.

Further, if a large number of sets of the systems of radiation source and detector can be used, the method of least squares can be applied to treat the measured values.

In Fig. 7 there is shown an embodiment having nine measuring points, where the method of least squares is employed for processing the data. If nine is the number of measuring systems whose beams are represented by solid lines each of which passes through two of the measuring points, the simultaneous equations for the thicknesses x, to xg are represented by Equation (8) above.If two more measuring systems are added as indicated by the illustration of their beams in broken line, the simultaneous equations to give the thicknesses are represented by Equation (14) below.

1 1 0 0 0 0 0 0 0 ] [x1 ] [b1 0 1 1 0 0 0 0 0' O X2 b2 0 0 1 1 0 0 0 0 O X3 b3 0 0 0 1 1 0 0 0 0 x4 b4 0 0 0 0 1 1 0 0 O x5 = b5 (14) 0 0 0 0- 0 1 1 0 O x6 b6 0 0 0 0 0 0 1 1 0 x7 b7 0 0 0 0 0 0 0 1 1 # x5 # # b5 1 0 0 0 0 0 0 0 1 x9 b9 1 0 0 1 0 0 0 0 0 b10 0 0 1 0 0 0 0 0 1 b11

From Equation (14), nine simultaneous equations referred to as Gauss' normal equation are obtained, and their solutions give the thicknesses calculated by the method of least squares. For completeness Gauss' normal equations, shown below, are represented by:

where [α α], [α ss], [α γ], ..., [α #], and [α b] are representation in Gauss notation, to denote the values defined by Equation (15") (shown below) where the form of Equation (15') is used in place of Equation (14).

The use of the method of least squares is not limited only to the above example of Equations (14) and (15), but is also applicable to other cases as for Equations (8), (9) and (1 1). Using A1, A2, and A3 to represent respective matrices of coefficients in the left hand-sides of Equations (8), (9) and (11), using iB B2, and B3to represent respective singie-column matrices of elements b in the right hand-sides of the equations, and using X to represent the single-column matrix of elements x, the following representation holds::

SA; X- = - B,1 From Equation (16), Gauss' normal equations can be introduced similarly as for Equation (15), and their solutions give the thicknesses calculated by the method of least squares. It is also possible to use the same measuring system for twice or more times the number of measurement operations to calculate the results by the method of least squares.

If the method of least squares is applied to the embodiment shown in Fig. 7 there may be a similarity in accuracy among the measured values by the nine measuring systems shown in solid lines in Fig. 7, while the two measuring systems shown in broken lines may produce measured values having different accuracies, since the radiation incidence angles with respect to the tube wall or the radiation beam path length in the tube wall are different It is preferable, therefore, to weight the measured values and thus equalize their accuracies, before attempting a calculation by the method of least squares.

A weighting coefficient p should be a value proportional to the inverse of the square of the standard deviation, in accordance to the general technique of the method of least squares. Thus, the coefficientp given by

where , denotes the standard deviation in the measured values of the measuring systems shown in solid lines of Fig. 7, and a2 denotes the corresponding standard deviation for the systems shown by broken lines.

The standard deviations depend on certain factors such as the detected radiation beam intensity (i.e., the representation of the radiation beam path length across the tube wall) and the construction of the detection circuit. Before the measurement by the method of least squares, a test is conducted, to obtain the standard deviations from which the value of coefficientp is calculated, using Equation (17).

Applying the weighting coefficient p to Equation (14), Equation (18) is obtained as below, introducing the method of least squares with the measured values equalized in accuracy.

[ 1 1 0 0 0 0 0 0 0 ] [ x1 ] [ b1 0 1 1 0 0 0 0 0 O x2 b2 0 0 1 1 0 0 0 0 O X3 b3 0 0 0 1 1 0 0 0 0 x3 b3 0 0 0 1 1 0 0 0 0 X4 b4 0 0 0 0 1 1 0 0 0 x5 = b5 (18) 0 0' 0' 0' 0 1 1 0' O X6 b6 0 0 0 0 0 0 1 1 0 x7 b7 0 0 0' 0' 0 0' 0 1 1 x8 b@ 1 0 0 0 0 0 0 0 1 [ x9 ] b9 P O' O' P O' 0 0- 0 0 pblo 0 0 P 0 0 0 0 0 P ] [ph11 The above weighted method of least squares can be applied not only to the example as shown in Equation (18), but also to any measurement having redundancy in the measuring systems. Equation (18) illustrates only one example.

The number of measuring points on the tube wall perimeter may have any value (provided it is three or more) and the number of measuring systems used should be n or more. It is not always necessary that the measuring points divide the tube wall perimeter into equal parts. Any arrangement of the points is permissible, provided that every measuring point is passed through by at least two radiation beams in different incidence directions. Then the n or more measuring systems produce that number n or more measure values, from which a set of simultaneous equations is obtained. Their solutions in turn give the wall thicknesses at the measuring points. Also, by using more than n measuring systems to produce more than n of the measured values there, it is possible to apply the method of least squares for obtaining the thicknesses.

Further, the invention includes embodiments where n is an even number not smaller than four. Fig.

8 shows one of such embodiments, where n = 8. By choosing an adequate odd number m not smaller than 3 of the measuring points from the number n of the points (in Fig. 8, m = 5), a set of simultaneous equations can be obtained, to give the wall thicknesses at those m points from the measured values of those points. Then, the wall thickness at any remaining measuring point can be given, by reference to a radiation beam which passes through that remaining measuring point and one of those m measuring points where the wall thickness has already been gauged. As in the previous embodiment, the method of least squares can be utilized for the processing of the measured intensities.

The method of least squares can be applied to the method described above as follows. In Fig. 8, x1, x2,. . ., x8 denote the wall thicknesses at respective measuring points. Suppose that five of those points are chosen, and the wall thicknesses x1, X3, X4, X6 and X7 are measured first. The simultaneous equations shown below can be obtained in a manner similar to that described above.

Here, the third equation has 1/ instead of 1/k because k = 1 for two of the measuring positions on the diameter of the tube wall circle, as previously explained.

From the above simultaneous equations, the solutions can be obtained as follows:

where

Thus the thicknesses remaining unknown are X5,X8 and x2. Radiation beams are then passed through X5 in combination with x1, x8 with x4,and with x6, respectively. The equation shown below can thus be obtained

The value of x1 is known, therefore, the value of X5 can be determined. Similarly,

and-x4 and X6 are known. Thusxs and x2 can be found.

It is not essential that all of the measuring points be in one sectional plane perpendicular to the axis of the tube. Those points may be distributed in different planes such as shown in Fig. 9. In Fig. 9, measuring points A and B are in one plane perpendicular to the tube axis, but the other point C is in another such plane.

The embodiments described above present an improved method of tube wall thickness measurement in a non-contact manner using radiation transmission, with high accuracy, using no moving parts, and capable of rapid measurement.

By selecting adequate kinds of radiation and energy intensities, the invention can be applied to various tubular products of glass, plastics, rubber, paper fibre and metals, and also, of course, to various hollow products having orderly sectional shapes other than tubes. It is also possible for the invention to use infrared, visible or ultraviolet light, x-ray, or various particle rays as the radiation. Further, if a computer is employed for processing the measured data, the invention can favourably realise a fairly rapid or perhaps real-time measurement.

Claims

1. A method of measuring the thickness of the wall of a circular cross-section tube, said method comprising the steps of selecting at least three distinct measuring points in said tube wall and distributed about the longitudinal axis of said tube, transmitting a plurality or radiation beams of known intensity in a plurality of different directions so that each beam passes through two of said measuring points, said directions being selected such that at least two of said radiation beams pass through each of said measuring points, detecting the intensities of said radiation beams, after having passed through said measuring points, to derive detected values to enable determination of said tube wall thickness from said known intensity values and said detected values of beam intensity.

2. A method according to claim 1 wherein said detected values are processed to determine the tube wall thickness.

3. A method as set forth in claim 2 wherien said detected values are processed in accordance with the method of least squares to determine the wall thickness.

4. A method as set forth in any one of the preceding claims wherein at least two of said measuring points common to each of at least two beams are axially spaced from each other.

5. A method as set forth in any one of the preceding claims wherein one or more additional measuring points are used and are each passed through by only one radiaiton beam which also passes through one of said measuring points at which radiation beams intersect.

6. A method according to any one of the preceding claims wherein the measuring points are equispaced about the tube longitudinal axis.

7. A method of measuring the thickness of the wall of a circular cross-section tube, said method being substantially as described herein with reference to any one of Figs, 3 to 9 of the accompanying drawings.

8. An apparatus for measuring the thickness of the wall of a circular cross-section tube, said apparatus comprising at least three radiation beam sources, each for generating a beam of known intensity and arranged so that each beam has a different respective radiation path, said sources being positioned at different selected locations about a position to be occupied by a tube to be measured, and said sources being oriented such that each of said beam paths from said sources intersects at least two other beam paths at different points which are to be in said tube wall, beam intensity detecting means for each of said sources positioned in the respective radiation path at a position to be beyond said tube, for producing a detected value of beam intensity to enable determination of said tube wall thickness from said known intensity values and said detected values of beam intensity.

9. An apparatus according to claim 8 and including means for processing said detected values to determine said tube wall thickness.

10. An apparatus as set forth in claim 9 wherein said processing means is arranged to treat said detected values in accordance with the method of least squares.

1 An apparatus according to claim 8 or claim 9 wherein said processing means is a computer arranged to receive said detected values directly from the detecting means.

t2. An apparatus as set forth in any one of claims 8 to 11 wherein at least two of said selected locations are axially spaced from each other so that the associated beam paths have axial components.

13. An apparatus as set forth in any one of claims 8 to 12 and further comprising one or more additional radiation beam sources, the or each of which is oriented such that its beam path passes through a measuring point at which beam paths intersect and passes through an additional measuring point lying only on said beam path of the additional source.

14. An apparatus according to any one of claims 8 to 13 wherein the beam sources are equispaced about the longitudinal axis of the tube position.

15. An apparatus for measuring the thickness of the wall of a circular cross-section tube, said apparatus being substantially as described herein with reference to any one of Figs. 3 to 9 of the accompanying drawings.