1. Introduction
Web-core sandwich panels are lightweight structures with high specific strength and high specific stiffness. The structure is utilized in a variety of fields, such as aviation, aerospace, the marine shipbuilding industry, etc. [
1,
2,
3,
4]. The structure consists of two face panels and a periodic core made from webs (
Figure 1). Welding is considered as an effective process to join the face panel to the core panel through a T-joint. Considering the structural characteristics of the sandwich panels, it is sometimes impractical to weld such T-joints using conventional fillet welds, which is implemented from the core panel side. Instead, the welding must be implemented from the face panel side (backside of the fillet T-joint) to join the face panel to the core panels [
5,
6]. Many researchers have conducted in-depth studies of the influence of welding from the face panel side on the sandwich structure. The fundamental mechanical properties of hull steel CCS-B sandwich plate laser-welded joint and base metals were presented in [
7]. Li et al. [
8] built a mathematical model of the laser welding of steel with a T-joint to investigate the formation process of keyhole-induced porosity. Romanoff et al. [
9] proposed a novel approach to the structural analysis of patch-loaded laser-welded web-core sandwich panels which are sensitive to the response of the T-joint. Authors in [
4,
10] built a prediction model of weld formation for the laser-welded T-joint from the face panel side. Yong [
11] studied the effect of the laser process on the dissimilar-metals welding of AZ31B magnesium alloy and 304 stainless steel in the sandwich structure. In contrast to conventional joint welding, this special welding mode for the T-joint from the face panel side of the sandwich structure presents new challenges. To guarantee the welding quality, it is necessary to implement weld position detection—especially when the welding heat source is not aligned to the core panel due to assembly errors or thermal deformation.
As far as welded T-joints from the face panel side are concerned, weld position detection is pivotal for weld formation and joint performance. When the deviation of panel position becomes out of range, it leads to poor formation and unqualified joints. High-accuracy positioning of the welding may create good-quality welds with high precision and repeatability. Thus, it is necessary to detect the position of the core panel under the face panel when welding the T-joint from the face panel side. However, the face panels shield the core panels during the welding of the T-joint, which leads to “blind welding”. Some conventional weld position detection methods are not applicable in this special welding mode for T-joints. Accordingly, some researchers have conducted explorations of special detection technologies for T-joint welding from the face panel side. A special detection method for friction-stir-welded T-joints based on axial force has been reported in some works [
12,
13], where the deviation state from the center of the weld seam can be judged by detecting the feedback of the specimen’s axial force to the stir head. A method for detecting the welding deviation state by observing an image of the plasma vapor while the molten pool overflows the specimen during the welding process was proposed in [
14]. Another detection method based on backscattered X-rays has also been reported, and a preliminary study was carried out on a nickel-based alloy specimen with thickness 0.8 mm [
15,
16]. So far, the detection method based on axial force is only targeted at the weld position detection of friction-stir-welded T-joints, and is not available in other welding processes. Deviation detection based on plume images may fail in conditions where the molten pool remains inside the specimen and there are molten droplets or downward plumes, and it is difficult for large sandwich structures to capture the upward and downward plume images simultaneously during the welding process. Few investigations have been reported in the literature on weld position detection for T-joints in web-core sandwich structures using X-ray-based methods, where safety issues in the X-ray environment and the applicability to variable conditions (e.g., the dynamic detection performance under high welding speeds) are considered as the major problems that restrict the further development and application of the X-ray method. Accordingly, this work made efforts to reduce the radiation dose and improve the applicability of the X-ray method under variable conditions. Moreover, lighter materials (e.g., aluminum) and thicker panels which were not involved in the existing research have gained in popularity for sandwich structures in various fields, especially aviation and shipbuilding. Therefore, aluminum web-core sandwich panels were chosen to study the weld position detection of T-joints from the face panel side, aiming to provide a technical basis for the manufacturing of such sandwich structures. First, this paper analyzes the characteristics of the backscattered X-ray intensity signal and investigates an appropriate processing algorithm to extract the characteristic value of the acquired X-ray intensity signals representing the center of the T-joint. Then, this paper analyzes the relationship between the detected backscattered X-ray intensity signal and the parameters of the detection system and specimen, and develops an analytical model to calculate and optimize the detection parameters required for detecting the joint position of a given specimen. Finally, several experiments were carried out on an AA6061 aluminum alloy specimen with a thickness of 3 mm; the influence of signal processing algorithms and sampling frequency on the detection results were investigated in terms of detection accuracy and dynamic performance.
2. Detection Method and Characteristics of X-ray Intensity Signal
Weld position detection based on backscattered X-rays utilizes a collimated X-ray beam to scan the specimen along the cross section of a weld, as shown in
Figure 2. The intensity of the backscattered X-ray is acquired at different scanning positions, and then processed utilizing curve fitting to obtain the reference point which represents the center position of the T-joint (i.e., the center position of the core panel).
The key to detecting the T-joint position based on backscattered X-rays lies in locating the core panel under the face panel. While the well-collimated pencil-beam of the X-ray is irradiated at and penetrated through the face panel, the cumulative intensity of backscattering X-rays increases with the increase of the penetrated specimen volume. When the X-ray beam irradiates at the center of the core panel, the irradiated volume reaches the maximum and the backscattered X-ray intensity at this time is also a maximum value. Meanwhile, to reduce the attenuation length of X-ray and facilitate the adjustment of the relative position between X-ray source, detector, and specimen during the detection process, the X-ray source is utilized perpendicular to the face panel of specimen.
X-ray intensity is expressed by the counted value of photons in unit time [
17]. The counted value is a random variable, which obeys a Poisson distribution [
18]. Assuming that the average number of X-ray photons measured by the detector per unit time is
, the probability that the number of X-rays actually detected by the detector per unit time falls within the interval
is 68.3%. The degree of scatter of the measured values is expressed by the relative standard deviation, and the standard deviation of the measured values can be estimated as follows:
The relative standard deviation of the measured values can also be obtained by:
As can be seen from the above analysis, the actual measured value has a large fluctuation, which can be regarded as the interference of noise on the accurate signal. The blue curve in
Figure 3 is the detected X-ray intensity signals acquired for the same non-weld location at different times. From
Figure 3, it can be seen that the actual intensity values acquired for the same position were not the same even when the whole set of detection parameters remained constant. Therefore, it was necessary to process the original signal through an appropriate denoising algorithm to more accurately extract the characteristic value of the X-ray intensity signals representing the center position of the core panels.
On the other hand, the acquired X-ray intensity signal is the counted value of X-ray photons measured by the detector in a single sampling period, so the selection of the sampling frequency also has an influence on the X-ray intensity signal.
Figure 4 shows the acquired backscattered X-ray intensity signals at a non-weld position with two different sampling frequencies at a certain X-ray source intensity. As shown in
Figure 4, when the sampling frequency increased, the acquired X-ray intensity signal decreased, and the relative standard deviation of the signal increased according to Equation (2). While the sampling interval (sampling accuracy) remained constant, the higher sampling frequency led to a shorter time to finish one scan of the weld cross section. Thus, the higher sampling frequency was able to support the faster welding speed. Under the premise of ensuring the sampling accuracy, a relatively lower sampling frequency can be appropriately selected to reduce the dispersion degree of the acquired X-ray intensity signals.
5. Detection Process Parameter Optimization
As described in
Section 2, a well-collimated pencil-beam of X-rays was directed toward the specimen in the detection, and the X-rays backscattered from the specimen were collected by detector. In the above detection process, photon energy and X-ray intensity were gradually attenuated. The whole attenuation path of X-rays mainly includes the following sections: (1) the intensity attenuation of X-rays during the incident process; (2) the attenuation of intensity and energy of X-rays due to backscattering effect; (3) the intensity attenuation of the backscattered X-rays during their arrival from the backscattering position to the detector. In the attenuation path, the forms of interaction between X-ray and matter include: photoelectric effect, Compton scattering effect, pair production, Rayleigh scattering effect, Bremsstrahlung, ionization, and multiple scattering [
26]. All or some of above interaction forms may take effect to cause the attenuation of X-ray energy and intensity along the attenuation path. All interactions work together during the first and third attenuation sections above. For the second attenuation section, the predominant form of interaction would be Compton scattering when relatively low-energy X-rays (10 keV–1 MeV) are used [
16,
27]. Therefore, a single Compton scattering model is suitable to approximate the physical process of X-ray and matter interaction during the above second attenuation section.
According to the above analysis, an analytical model is put forward for calculating the intensity of backscattered X-rays acquired by the detector (Equation (11)). The influences of the three attenuation sections are included in the model, and the influences of other detection parameters (e.g., detector size and detection efficiency) on the acquired X-ray intensity are also considered. As shown in
Figure 11, assuming that a single-energy X-ray beam with energy
E0 is irradiated on a section of the specimen, the X-ray intensity detected by the detector in unit time is:
where
N is the backscattered X-ray intensity detected by the detector per unit time;
N0 is the intensity of the collimated incident X-ray beam (the number of X-ray photons passing through the unit area perpendicular to the direction of X-ray transmission in unit time);
ne is the average electron density in volume element irradiated by the incident X-ray beam;
is the differential cross section for Compton scattering (describes the probability that an incident X-ray photon with energy
E0 is scattered into the unit solid angle of the direction scattering angle
after interacting with an extra nuclear electron in the atom);
is the linear attenuation coefficient for the incident X-ray beam;
l0 is the attenuation length which the incident X-ray beam passes through the specimen;
is the linear attenuation coefficient for the backscattered X-ray beam;
l1 is the attenuation length which the backscattered X-ray pass through in the specimen;
is the solid angle to the volume element irradiated by the incident X-ray beam;
is the volume element irradiated by the incident X-ray beam; and
is the detection efficiency of the detector.
In Equation (11):
where
d is the attenuation length which the incident X-ray beam passes through in the face panel,
dr is the attenuation length which the incident X-ray beam passes through in the core panel.
In Equation (11):
where
ls is the attenuation length which the backscattered X-ray pass through in the face panel,
ds is the attenuation length which the backscattered X-ray pass through in the core panel.
In Equation (11):
where
Na is the Avogadro constant,
Z is the atomic number of the specimen material,
is the mass density of the specimen material, and
A is the atomic mass number of the specimen material.
In Equation (11):
where
r0 is the classical electron radius, taking the value 2.818 × 10
−15 m.
In Equation (15):
where
is the energy of the incident X-ray,
is the rest mass energy of an electron, taking the value 0.511 MeV.
Equations (11)–(16) describe the relationship between the X-ray intensity acquired by the detector and the parameters of the detection system and specimen, such as the parameters of the X-ray source (i.e., energy, intensity), the relative position parameters between source, specimen, and detector (i.e., scattering angle, source–specimen distance, specimen–detector distance), and the material and structure parameters of the specimen (i.e., material density, material atomic number, thickness).
On the other hand, it is necessary to identify the difference in the X-ray intensities from positions with and without a core panel, and this difference needs to significantly exceed the noise fluctuation of the X-ray intensity signal at the position with a core panel.
Suppose the X-ray intensity detected from positions with and without core panels are
Ns and
Nb. So, the noise fluctuation
σ of the X-ray intensity signal at the position with a core panel is
σ ≈ (Ns)1/2, and the difference in X-ray intensity from positions with and without core panel is ∆
N = Ns − Nb. Therefore, the condition for detecting weld should be ∆
N = K × σ, where
K represents the signal-to-noise ratio of detection. Considering that the radiation dose is proportional to the power of the X-ray source (
E0 × N0) in the detection process, in order to reduce radiation and improve the practicability of the detection method, the following optimal constraints under minimum radiation requirements can be obtained by taking
K as 2:
According to Equations (11)–(17), a range of detection system parameters were predetermined for a given specimen. The equations were utilized to obtain the appropriate parameters of the X-ray source in the detection system to reduce the radiation dose. To obtain the appropriate parameters of the X-ray source, the parameters of the specimen and the current detection system (listed in
Table 2 and
Table 3, respectively) were substituted into Equations (11)–(17). The backscattered X-ray intensities from positions with/without core panel (i.e.,
Ns and
Nb) were calculated under different X-ray photon energies and X-ray beam intensities.
X-ray photon energy is a measurement of the penetrating power of the X-ray. According to the attenuation process described above, the poor penetrating power would render the failure of backscattered X-rays from the core panel incapable of reaching the detector, regardless of X-ray beam intensity, resulting in the failure of weld position detection. Accordingly, X-ray photon energy has a predominating effect on both the detection and radiation dose.
Figure 12 shows the detected X-ray intensities (
Ns and
Nb) from positions with/without core panel under different photon energies while the X-ray beam intensity was constant. As shown in the figure, the X-ray photon energy should be at least 60–70 keV to achieve the required signal-to-noise ratio (SNR) under minimum radiation requirements.
On the other hand, the proposed detection method is essentially intended to identify the difference ∆N in the X-ray intensities from positions with/without core panel Ns/Nb, and ∆N needs to significantly exceed the noise fluctuation σ of the X-ray intensity signal at the position with the core panel. The difference ∆N is caused by the different amount of the X-rays which backscattered into the detector with or without the core panel. The intensity of these X-rays is not only determined by the core panel’s irradiated volume whose backscattered X-rays could reach the detector, but also the X-ray beam intensity which could reach the irradiated volume.
The X-ray photon energy E0 determines the depth of irradiated volume in the core panel, while the beam diameter determines the intersection of the irradiated volume. Considering that the X-ray intensity which reaches the core panel was less than the intensity reaching the face panel due to the attenuation of specimen, and that the beam diameter ideally remains constant, the depth of irradiated volume in the core panel would make a greater increment effect than the reduction effect of lesser X-ray intensity reaching the irradiated volume on the detected intensity difference ∆N to achieve the SNR required for weld position detection.
As shown in
Figure 13, with the X-ray beam intensity increased, the detected X-ray intensities (
Ns and
Nb) increased. The measurement noise
σ and the difference of detected X-ray intensity with/without core panel ∆
N also increased. However, due to the constant depth of irradiated volume determined by the X-ray photon energy, the reduction effect of less X-ray intensity reaching the irradiated volume gradually approached the increment effect of the depth of irradiated volume in the core panel on the detected intensity difference ∆
N with increasing X-ray beam intensity. In contrast, the increment of noise
σ kept increasing with the increment of X-ray beam intensity. This would cause a variable gradient of SNR of detection and influence the detection accuracy.
Considering the margin of detection parameters, the main detection parameters were determined as shown in
Table 4.