Pipe eccentricity measurement using laser triangulation

doi:10.1016/j.imavis.2006.04.021

Image and Vision Computing

Volume 25, Issue 7, 1 July 2007, Pages 1194-1203

https://doi.org/10.1016/j.imavis.2006.04.021 Get rights and content

Abstract

A pipe eccentricity measurement system based on laser triangulation is presented. The custom measurement head implements the Scheimpflug condition to ensure maximum working depth and integrates an FPGA to perform real time image processing at a rate of 200 frames per second. The eccentricity of the pipe is estimated by approximating the position of the upper tangent point of the pipe and used as a measure of its straightness. The correlation coefficients for the parameters r, x₀ and y₀ estimating from a least square approximation of a circle via the algebraic distance are theoretically derived, demonstrated using Monte-Carlo simulation and experimentally verified. It is shown that perturbation of the measurement, leads to less uncertainty in the estimated position of the tangent point than for the centre point. Harmonic filtering based on Elliptical Fourier Descriptors is used to filter the measurement data.

Laboratory measurements show that the repeatability is in the order of 1 μm. The accuracy of industrial measurements exhibits a systematic bias of −4 μm and has a standard deviation of 2.6 μm. Selected measurements from the production plant are presented to show that the deviation of the cross-section of the pipe from a perfect circle can be determined from the measured radius of curvature.

Introduction

The motivation for this work arises from the need of automatic inspection of the straightness of steel pipes within the production process. There are two main reasons why straightness is an essential quality feature: first, the critical load, which a pipe can withstand before buckling, is dependent on the straightness of the pipe; second, to ensure the quality of the threads at the end of the pipes for screwed pipe connections, the straightness of the pipe is crucial.

Presently a mechanical tactile sensor is used to measure the eccentricity. However this system is error-prone due to particles on the surface, such as scale, and has high maintenance costs due to abrasion.

Solutions based on machine vision, which are contactless and therefore not susceptible to abrasion, are barely discussed in literature. Lu et al. [1] present an experimental solution based on light sectioning. Several triangulation sensors are placed along the longitudinal axis of the pipe and measure the 3D center position of the section profile by applying an ellipse fitting routine on the data. The deviation of these positions from a straight line is used as a measure for the straightness of the pipe. This solution does not take into account a-priori knowledge of how the pipes are produced and which errors may result from the production process.

The solution presented here is also based on laser triangulation. However, in contrast to Ref. [1] only two light sectioning measurement heads are required, independent of the length of the pipe. Furthermore, due to the full calibration of the laser plane and the resulting metric data, a simpler and faster circle fitting procedure can be used. However, a prerequisite for the simpler measurement setup is, that the pipe rotates around its longitudinal axis during measurement. The measurement system is integrated in an existing production plant and in the company-wide quality control system.

Section snippets

Measurement principle

The pipes being measured are rolled seamless-pipes. Three rolls, with a relative pitch of 120°, are used to determine the final dimension of the pipe (cf. Fig. 1). After the final pass in the rolling stand, the tubes are straightened using a roller-straightening-machine. In this process step the material of the tube is extended beyond its elastic limit, this does not change the dimension of the pipe, but leads to a reliable straightening. The problem is that the first and last meter of the

Plane-of-light measurement head

The principle optical arrangement of the plane-of-light measurement head is shown in Fig. 4. A laser, with cylindrical optics, projects a line onto the surface of the material. The laser optics is selected such that the Raleigh region [3] lies in the planned measurement range; this results in the maximum measurement resolution. The Raleigh region of the laser, is that region in which the laser line is optimally focused and has the minimum width.

The plane of light illuminates the surface of the

Fitting circular arcs

Much work has been published on fitting circles, and it is considered to be a standard procedure. However, in the context of metrology it is necessary to consider the nature of the data which are available and the procedure used to fit the circle: the uncertainty of the coefficients determined by the fit is dependent on both.

A linear least squares algebraic-distance fitting of a circle has been selected; since 200 fits must be performed per second, a recursive nonlinear fitting would have been

Processing the sequence of measurements

The measurement procedure described in Section 2.1 is performed 200 times per second during rotation of the pipe; it is ensured that the pipe is measured over a minimum of one complete revolution. This delivers a sequence of measurements with high density around the circumference of the pipe (see Fig. 12).

The data acquired in this manner is not strictly periodic; since, in general, it does not envelope an integer number of revolutions. The next step is to automatically identify the exact number

Laboratory verification of the system

A test target was manufactured to enable the verification of the system under laboratory conditions. The target consists of four eccentric discs, see Fig. 16, of different sizes covering the complete range of radii, which must be measured in the application. The discs are rotated at constant angular velocity during measurements. The true eccentricity of the rotating discs has been determined using a tactile measurement machine (Zeiss Prismo 7 HTG) by an accredited measurement laboratory.

Industrial measurement results

The measurement results from six different pipes measured in the production plant are shown in Fig. 18, Fig. 19, Fig. 20, Fig. 21, Fig. 22, Fig. 23. The original production pipe numbers are used to identify the plots; this ensures the traceability to the original production data.

Some improvement in the performance of the measurement system could be achieved by performing a least mean square approximation of the position of the upper tangent position by a sine wave and using the amplitude of the

Conclusion

A pipe eccentricity measurement system based on light sectioning has been developed for industrial inspection of rolled seamless pipes. An algebraic least square fitting of a circle to the cross-sectional data are performed, whereby the upper-tangent point is used to estimate the eccentricity of the pipe and the radius of the circle is used as an estimate of the radius of curvature. It is shown that perturbation of the measurement, leads to less uncertainty in the estimated position of the

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Pipe eccentricity measurement using laser triangulation

Abstract

Introduction

Section snippets

Measurement principle

Plane-of-light measurement head

Fitting circular arcs

Processing the sequence of measurements

Laboratory verification of the system

Industrial measurement results

Conclusion

On-line measurement of the straightness of seamless steel pipes using machine vision technique

Sensors and Actuators A

Laser

The scheimpflug’s patent

Photo Techniques

Computation of homographies