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The non-contact magnetostrictive sensor (MsS) has been widely used in the guided wave testing of pipes, cables, and so on. However, it has a disadvantage of low excitation efficiency. A new method for enhancing the excitation efficiency of the non-contact MsS for pipe inspection using guided waves, by adjusting the axial length of the excitation magnetic field, is proposed. A special transmitter structure, in which two copper rings are added beside the transmitter coil, is used to adjust the axial length at the expense of weakening the excitation magnetic field. An equivalent vibration model is presented to analyze the influence of the axial length variation. The final result is investigated by experiments. Results show that the excitation efficiency of the non-contact MsS is enhanced in the whole inspection frequency range of the L(0,2) mode if the axial length is adjusted to a certain value. Moreover that certain axial length is the same for pipes of different sizes but made of the same material.

Magnetostrictive sensors (MsSs) have been widely used in many fields [

Two types of MsSs have been used in GWT, the contact sensor and non-contact sensor.

Hence, the non-contact magnetostrictive sensor (MsS) is suitable for testing of steel pipes or cables with coatings, which are usually costly or unable to be removed. Nevertheless, due to the low magnetostriction of the tested component itself, the non-contact MsS has a lower conversion efficiency and lower sensitivity compared with contact sensors. Notice that the sensitivity of the MsS is defined as a measure of the smallest defect signal which can be discernible on the inspection signal [

In the literature, many other ways to obtain higher excitation efficiency for the non-contact MsS used in GWT have been tried. For a given ferromagnetic object under inspection, the strength of the static magnetic field in the component, produced by the magnetizer, determines the energy conversion efficiency from the alternating magnetic field induced by the sensor coil to the elastic field transmitting in the tested component [

Compared with the above methods, an easier way to increase sensor excitation efficiency is to develop a new sensor coil structure. In recent years, a three part coil has been developed to generate the guided wave under a specific frequency [

In this paper, we present a method to enhance the excitation efficiency of the magnetostrictive transmitter for pipe inspections by optimizing the axial length of the excitation magnetic field. What's more, the enhancement can be realized under the frequency range of L(0,2) mode rather than a single frequency.

To achieve this objective, a special structure, adding two copper rings beside the transmitter coil, is used here to adjust the axial length. The structure is similar to the one used by Seco

For an alternating magnetic field produced by the transmitter coil in a pipe, there are some parameters could be used to describe the distribution of the field, including the strength, the depth, the axial length, and the shape of the distribution, as shown in

The strength stands for the maximum of the magnetic field strength of the field. The depth is the skin depth and the axial length is the axial range where the alternating magnetic field exists. The shape of the distribution is the geometrical shape of the magnetic field strength in the whole skin area when the above three parameters are determined. The alteration of transmitter structures may change these four parameters, and the four parameters influence the excitation efficiency. Usually the axial length of the excitation magnetic field is influenced by the material of the pipe and the structure of the transmitter coil. However, the conventional structure cannot meet the requirement of adjusting the axial length conveniently. A special structure is needed to adjust the axial length. A structure, in which two copper rings are added beside the transmitter coil, is used in this paper. The detailed comparison between the conventional structure and the special structure is presented as follows.

The conventional structure of the non-contact magnetostrictive transmitter is shown in

In the FEM model, only the alternating magnetic field is of concern. Thus the existence of the back irons and the permanent magnets are ignored. Two different widths have been chosen, 20 mm and 30 mm. The former one is defined as the coil A, and the latter the coil B. The turn numbers of both coils are 20 and the inner diameters are 40 mm. Both coils are wrapped by copper wires of 1 mm diameter. The outer diameter and the wall thickness of the pipe are 38 mm and 3 mm, respectively. The relative magnetic permeability is 200 and the electrical conductivity is 1 × 10^{7} S/m. The direction of the pipe axis is defined as _{z}_{z}

As we can see, firstly, the strength of alternating magnetic field produced by coil A is stronger than that of coil B. Secondly, it is hard to distinguish the difference between the axial lengths of the two alternating magnetic fields. Thirdly, the both axial alternating magnetic fields are quite different from each other in the shapes of the distribution. Compared with the axial alternating magnetic field produced by coil B, the field produced by coil A is stronger in the

To sum up, the strength, the shape and the axial length of the alternating magnetic field are all changed with the variation of coil width. Moreover, the change of the axial length is very small. Hence, the axial length is hard to adjust with the conventional structure. The relationship between the axial length and the sensor excitation efficiency cannot be obtained using the conventional structure. A special structure is needed to adjust the axial length and minimize other changes of the excitation magnetic field.

A special structure is used in this paper as shown in

The detailed alternating magnetic field produced by this transmitter is calculated through FEM. The above coil A is here used as the transmitter coil. The excitation current flowing through the coil is a two cycle sine burst at 120 kHz. The peak to peak value is 30 A. The skin depth of the copper rings is 0.2 mm and the thickness of the copper rings should be larger than the skin depth. Hence, a thickness of 0.5 mm is chosen here. The permanent magnets are placed on them. Therefore, the static magnetic field changes little compared with the conventional structure. The parameters of pipe are the same as mentioned above. _{z}

Because of the existence of the two copper rings, the axial lengths of the alternating magnetic fields are both close to

From the above analysis, the alternating magnetic field mainly just exists in the length between the two copper rings, where the static magnetic field produced by permanent magnets also exists. The main components of both fields are along the pipe axis. Based on the magnetostriction effect, an alternating magnetostrictive force is produced in the skin depth area and its direction is also mainly along the pipe axis, as shown in

An ultrasonic wave is then directly induced by the vibration. According to Snell's law, the wave undergoes the mode conversion, reflection and refraction at the inner and outer face of the pipe wall [

This action is similar to the action of ferromagnetic strip when using the contact transmitter as shown in

According to the above analysis, both the skin depth area and the ferromagnetic strip are locations where vibration occurs firstly and could be regarded as the vibration sources during the generation progress of guided waves. When the strength of the vibration source increases, the strength of guided waves would be stronger. For the ferromagnetic strip, its vibration strength is greatly impacted by its natural frequency and the excitation current frequency. The closer the excitation current frequency is to the natural frequency of the strip, the stronger is the vibration and the higher is the excitation efficiency of the contact transmitter.

Therefore, in a similar way, for the noncontact transmitter, the skin depth area, as the vibration source, can be taken into account individually without concerning other ranges of the pipe. In this way, the skin depth area could be simplified to a clamped–clamped pipe model. The length of this model is determined by the axial length of the alternating magnetic field. If the natural frequency of the equivalent model can be calculated, the relationship between the axial length and the natural frequency could be got. Then the relationship between the axial length and the excitation efficiency could be analyzed qualitatively, so the problem becomes how to calculate the natural frequency of the equivalent model.

According the classical vibration theory, for a pipe, the natural frequency is deduced from:
_{e}_{e}_{e}_{sk}

Considering the distribution of magnetostrictive force is not uniform in both the axial and radial direction, _{e}_{e}

Substituting Equations from _{n}

As analyzed above, the excitation efficiency shall be enhanced when the excitation current frequency is close to the natural frequency of the equivalent model. There is a range of excitation frequency under which the excitation efficiency is enhanced. The center of frequency range is the natural frequency. It is because that the actual excitation current is not a single frequency signal but a bandwidth limited signal with a center frequency. Therefore, if the above special structure is used in the transmitter, as the distance between two copper rings decreases, the natural frequency of the equivalent model increases and the above-mentioned frequency range should be moved to higher frequency domain.

What's more, from _{n}_{e}_{n}

The model present here is an equivalent model of the skin depth area. It is used to calculate the relationship between the axial length of the excitation magnetic field and the nature frequency. However, the nature frequency is only an intermediate parameter. The relationship between the nature frequency and the excitation efficiency can only be analyzed qualitatively.

Therefore, using the equivalent model, the objective of this research, which is the influence of the axial length on the excitation efficiency of the MsS can only be analyzed qualitatively as well. The final quantitative analysis to get the relationship between the axial length of the excitation magnetic field and the excitation efficiency of the MsS must be realized by experiments.

In order to identify the analysis, two pipes, whose materials are both steel 20, are used as the specimens. The Young's modulus is 2.06 × 10^{11} Pa and density is 7,850 kG/m^{3}. The outside diameter of the first pipe (pipe A) is 38 mm, wall thickness is 3 mm and length is 2.8 m. The outside diameter of the second pipe (pipe B) is 25 mm, wall thickness is 2.5 mm and length is 2.8 m. Pipe A is an intact pipe. An artificial defect has been made on pipe B, consisting of a through hole whose diameter is 5 mm, as shown in

The frequency dispersion curves of both pipes are shown in _{n}

The experimental set-up is illustrated in

The amplified sine pulse current is provided to the transmitter coil. The received voltage signal of the receiver coil is amplified by a pre-amplifier, then digitized and sampled by a 16-bits data acquisition card and finally interfaced to a computer.

The amplitude of received signal is in direct proportion to the strength of the alternating magnetic field if the magnetostriction is linear 12. Firstly we change the peak-to-peak amplitude of the excitation current (_{pp}_{pp}_{pp}_{pp}_{pp}_{pp}

To observe the actual effect of the alternating magnetic field axial length variations, experiments on pipe A were done under five different conditions using the conventional structure without the copper ring and the special structure with the two copper rings (_{pp}

The relationship between excitation frequency and the peak-to-peak amplitude of the first end reflected signals under different conditions (without copper rings, _{pp}_{pp}

It is obvious that the enhancements of excitation efficiencies are all different under the same excitation frequency. As analyzed above, all these differences are due to the variations of the axial length. For each _{L}_{L}_{L}_{n}_{n}_{e}_{e}

Furthermore, when

As discussed in Section 3.2, the relationship between the axial length and the excitation efficiency of the MsS should be the same for the pipes with the same material. To verify this point, experiments on pipe B have been done. The dispersion curve of pipe B is shown in

According to the results of the former experiments, the axial length

The comparison of defect signals obtained under 140 kHz and 170 kHz under two conditions (without copper rings and

To sum up, the proposed method of designing a suitable excitation magnetic field range can enhance the excitation efficiency of non-contact MsS used in GWT. The enhancement effect can be obtained under the inspection frequency range of L(0,2) mode. Moreover, the suitable excitation magnetic field range is the same for pipes of the same material but of different sizes.

This paper provide a method to enhance the excitation efficiency of the non-contact MsS used in GWT in the inspection frequency range of the L(0,2) mode. Unlike other methods of enhancing the excitation efficiency of the non-contact MsS, the method is based on adjusting the axial length of the excitation magnetic field at the expense of weakening the strength of the excitation magnetic field. A special structure is used to adjust the axial length. An equivalent model of the skin depth area is present based on the analysis of the generation progress. The relationship between the axial length of the excitation magnetic field and the natural frequency is calculated using the model. Then the influence of the axial length on the excitation efficiency of the MsS is discussed qualitatively. The excitation efficiency of the non-contact MsS should be enhanced in the frequency range around the nature frequency of the skin depth area. The final influence is analyzed by experiments.

The experimental results fit well with the qualitative analysis. The proposed method of designing a suitable excitation magnetic field range can enhance the excitation efficiency of non-contact MsS used in GWT. The enhancement effect can be obtained in the whole inspection frequency range of L(0,2) mode rather than a single frequency. The method proposed here does not increase the cost and complexity of the inspection system. Moreover, the suitable excitation magnetic field range is the same for the pipes of the same material but different sizes. It means that the optimal axial length obtained on one pipe can be used for the other pipes of the same material. The steps of the proposed method can be summarized as follows:

Obtain the Young's modulus

Calculate the dispersion curve of the pipe and choose the inspection frequency range of L(0,2) mode.

Set the natural frequency _{n}

Do the experiments according to the ranges of the length

Get the relationship between absolute length

Select the optimal absolute length

The method proposed in this paper is based however on a qualitative analysis using the equivalent model and the quantitative analysis based on the experiments. The quantitative relationship between the axial length of the excitation magnetic field and the excitation efficiency of the non-contact MsS used in GWT can only be obtained through experiments. A comprehensive finite element model or theoretical model [

This work is supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51205148 and the National Major Scientific Instrument Development Project under Grant No. 2012YQ09017502.

The authors declare no conflict of interest.

The principle of GWT using MsSs.

The structures of MsSs used in GWT. (

The parameters of the alternating magnetic field produced by a solenoid coil.

The conventional structure of the transmitter for the longitudinal guided wave testing.

The alternating magnetic field produced by the conventional structure.

The axial magnetic field strength (_{z}

The special structure of the transmitter for the longitudinal guided wave testing.

The alternating magnetic field produced by the special structure when

The alternating magnetic field produced by the special structure when

The guided wave generation progress (

The specimen (pipe B) with a through hole used for defect inspection.

The group velocity dispersion curve of both pipes. (

The relationship between _{n}

The experimental arrangement diagram.

The typical data of the experiments on the intact pipe (pipe A) obtained at 30 A _{pp}

(

The experiment results of pipe A. (_{pp}_{pp}

The typical signal obtained on pipe B when

The peak to peak amplitudes (_{pp}

The comparison of defect signals obtained under (

The compensation ratio of _{pp}_{L}_{n}

_{pp} |
_{L} |
_{n} |
|||||||
---|---|---|---|---|---|---|---|---|---|

20 | 6892 | 1.11 | - | 172 | - | ||||

25 | 7299 | 1.05 | 160 | 138 | 13.7% | ||||

30 | 7499 | 1.02 | 140 | 115 | 17.8% | ||||

40 | 7651 | 1 | 100 | 86 | 14% |