Study on the characteristics of the torque vibration and the detection of the gap

2.1. Experimental bobbin tool FSW system

The bobbin tool FSW machine has three axes (Fig. 1), which are denoted $X$ (perpendicular to the tool axis and in the direction of welding), $Y$ (perpendicular to the direction of welding) and $Z$ (parallel to the tool axis and in the plunge direction). The spindle is driven by a variable frequency asynchronous motor with a maximum continuous power of 7.5 kW and a maximum speed of 3000 rpm. It is equipped with torque sensor capable of sensing torque up to 200 N∙m. Through the hollow channel, the torque sensor line is connected with a sample circuit which has via analog-to-digital channel (5 v range and 12 bit) on a board based on microprocessors. After the treatment with the microprocessor, the torque signals are sent to the wireless transmission module. A piezoelectric acceleration sensor located on the edge of workpiece (Fig. 1(c)). The weak vibration signals are processed by using the amplifier and a series of anti-aliasing filter circuit. These signals are converted to digital signal by A/D converter which can be processed by computer, so as to finish the collection of vibration signal. During the welding process, torque sensor, sample circuit and wireless module have synchronous rotary speed. Through the wireless receiving module, the torque signal is fed into a computer, where signals are stored and displayed. A sample frequency of 500 Hz was utilized in all experimental studies.

FSW tools were made using HM1 tool steel. The diameter of the upper shoulder and lower shoulder were 24 mm and 23 mm, respectively. The distance between two shoulders was 5.85 mm. The pin diameter is 10 mm, its surface has two screw with opposite rotating direction. The material in these experiments is 6061 aluminum ally (Al-0.6Si-1.0Mg) with a T4 heat treatment. The plates were machined with a consistent dimension of 230×160×6 mm to obtain comparable results. Travel speed ($v$) and rotary speed ($N$) varied respectively from 10 to 170 mm/min and from 350 to 700 rpm in all experimental studies. But in each experiment, $\omega$ was constant.

Fig. 1Experimental device and its structure

a) Bobbin tool FSW machine

b) Torque detection device

c) Vibration sensor

2.2. Experimental procedures

As shown in Fig. 2(a), two gaps along the y direction were arranged in the welding path, the distance ($L$) between two gaps is 80 mm, the maximum gap width is 0.8 mm, the length along the $y$ direction is 24 mm, the vibration sensor is in the midpoint of plate side. The welding process can be divided into several segments with different travel speed as the following: 10, 20, 30, 50, 70, 90, 110, 130, 150 and 170 mm/min. The speed segment durations are 35 s, 15 s, 3 s, 3 s, 3 s, 3 s, 3 s, 3 s, 3 s and 3 s. The dashed line is the boundary between the different travel speeds as seen in Fig. 2(b). In order to generate more energy to preheat the metal and produce enough plastic metal, the reason for the lower traverse speed and longer duration when start welding. This approach also prevents pin be broken easily.

Initial experiments were conducted to derive a qualitative understanding of bobbin tool friction stir welding processes with and without gaps. There are two scenarios in this research, the one scenario is referred to “zero width gap”. In this scenario, tool friction stirs a solid piece of material. The other scenario is referred to “Non-zero width gap”. Also, there are two constant known gaps in the welding path, and the gap width is 0.4 mm, 0.6 mm, respectively.

Fig. 3 shows the unfiltered torque curve in two scenarios, the unfiltered torque data are very noisy due to electrical noise in the circuits and noise due to the BTFSW process itself.

Fig. 2Bobbin tool FSW scenarios

a) Schematic diagram of gap position

b) Travel speed variation curve

Fig. 3Torque history for bobbin tool FSW operations with N= 350 rpm and v varies from 0 to 170 mm/min

a) Non-gap

b) Gap width is 0.4 mm, 0.6 mm

When the welding tool passes through the vibration sensor, the vibration signal is strongest during the whole welding process, as shown in Fig. 4(a). As the tool is away from the vibration sensor, the vibration signal is gradually weakened. Different from the vibration signal, however, the torque signal presents a relatively stable periodic characteristics, as shown in Fig. 4(b). If we want to find the vibration characteristics of the welding process, we need a moving vibration sensor. This adds to the difficulty of installation and inspection costs. Further, vibration signals and torque signals have the same vibration frequency. It became apparent that we could get the stable vibration characteristics by torque signal.

Due to the torque signal contains oscillatory signal and noise, fast Fourier Transformation (FFT) and WT method were applied to the detection process. After FFT, the relationship between the specific frequency and amplitude of the torque signal was shown in Fig. 4(c). The torque signal contained a main periodic signal (about 10.78 Hz). After WT, pigment concentration represents the signal strength of the specific frequency (Fig. 4(d)). Obviously, the low-frequency signal exits in the whole welding process, but the main periodic signal (around 10.78 Hz) exists only in the middle of the process (40 s-140 s), that is not significant at the primary and ending stage.

2.3. Analysis of the low frequency torque

Based on the analysis above, the raw torque data were filtered with a one-order Butterworth digital filter with cutoff frequency of 3 Hz. The cutoff frequency of 3 Hz provides sufficient bandwidth to detect the torque signal as the tool traverses the gap. The filtering substantially removed the inherent noise (Fig. 5).

Fig. 4Spectrum analysis of torque signal (350 rpm)

a) Local vibration signal

b) Local torque signal

c) Fast Fourier transformation

d) Time-frequency diagram

Fig. 5Low frequency torque for bobbin tool FSW operations with N= 350 rpm and v varies from 0 to 170 mm/min

a) Non-gap

b) Gap width is 0.4 mm, 0.6 mm

Visibly, the torque value is very small in the primary welding stage (less than 50 s). The welding speed increase 20 mm/min per 3 s, Subsequently, torque also increases at the same time. When the traverse speed increased to 170 mm/min, it remains the same during the rest of the process; with the welding process continues, low frequency torque decreased slowly. Once the welding tool closer to the plate edge (about 140 s), the torque decreased rapidly when the tool gradually withdraws from the workpiece.

The deviation is apparent as the tool transverse the gap with $N=$350 rpm and $v=$170 mm/min (Fig. 6). The decreasing trend of the torque is visible. The smaller gap widths, the torque deviation will be less. Furthermore, noise still exists in the filtered torque data, and several local peaks appeared before or after pin contacts the gap.

2.4. Analysis of the periodic torque

A six-order Butterworth band pass digital filter was designed via trial and error, it provides sufficient noise reduction while not substantially delaying the torque signal, its transfer function is:

where $z$ is the discrete forward shift operator. When bobbin tool FSW operations with $N=$350 rpm and travel speed varies from 0 to 170 mm/min, the main periodic signal is shown in Fig. 7. The amplitude of periodic signal is small at the primary and the end stage of welding process; this is primarily due to a lack of friction. In addition, the amplitude of main periodic oscillating signal will increase before or after pin contacts the gap, but many several local peaks also appeared in this case, this raises the gap detecting difficulty (Fig. 8).

Fig. 6Torque history for bobbin tool FSW when the pin traverses across the gap

a) Gap width is 0.4 mm

b) Gap width is 0.6 mm

Fig. 7Periodic torque history for bobbin tool FSW

a) Non-gap

b) Two gaps

Fig. 8Enlarged local periodic torque history

a) Gap width 0.4 mm

b) Gap width 0.6 mm

Obviously, the presence of gap inevitably brings about a mutation for torque signal; this is an essential feature of welding process, but too many local extremes appear before or after pin contacts the gap. Thus, it is necessary to find an effective algorithm to detect the presence of the gap.

2.5. Gap detecting algorithms

In this study, the TF algorithm based on the gauss function is applied. The wavelet analysis can describe the local mutation signal; the local extreme point of a WT module corresponds to the mutation point of origin signal if this wavelet function can be considered as a derivative of a smooth function. Accordingly, zero crossing point of a WT module corresponds to the mutation point when this wavelet function can be considered as the second derivative of a smooth function. So the extreme or zero crossing point of WT module can be applied to detect a mutation, this method can fully describe the local feature of torque signal. According to the feature of the Fourier transform, the convolution of the torque derivative and filter is equal to the convolution of torque and filter derivative, the relationship is as the following:

where $h\left(t\right)$ is the convolution of $T\left(t\right)$ and $\theta \left(t\right)$, $T\left(t\right)$ is the torque signal, $\theta \left(t\right)$ is filter, $\otimes$ is convolution operator. $\theta \left(t\right)$ is Gaussian function, it is continuous and has second derivative, and then the following formulas can be defined:

where $s$ is scale factor. Obviously, ${\psi }^{\left(1\right)}\left(t\right)$, ${\psi }^{\left(2\right)}\left(t\right)$ meet the admissible condition of wavelets. Then the WT using ${\psi }^{\left(1\right)}\left(t\right)$ and ${\psi }^{\left(2\right)}\left(t\right)$ are defined as the following:

Therefore, $\left(T\mathrm{*}\theta \right)\left(t\right)$ is the result of smoothing and eliminating noise by $\theta \left(t\right)$, and its first order derivative and second derivative are ${\psi }^{\left(1\right)}\left(t\right)$ and ${\psi }^{\left(2\right)}\left(t\right)$, respectively. The smoothing effect of $\theta \left(t\right)$ has a slight impact on mutation in torque data when the scale factor ($s$) is small, but the impact cannot be ignored when s is larger. In order to select the appropriate scale factor ($s$), a set of experiments was conducted with four different scale factor ($s$) (0.9, 1.0, 1.3, 1.5), $N=$ 400 rpm, and $V=$ 170 mm/min, as seen in Fig. 9. For each scale factor ($s$), the algorithm can detect the mutation point, the mutation point is the local maximum value of ${\psi }^{\left(1\right)}\left(t\right)$ and zero of ${\psi }^{\left(2\right)}\left(t\right)$.

Under $s=$1 and 1.3, the WTs of the low frequency torque signal is shown in Fig. 10. When $s=$1.0, the algorithm can detect multiple mutation point ($t=$75.5 s, 79.8 s, 86 s), and when $s=$ 1.3, only one mutation point is detected ($t=$79.8 s). If $s<$1.0, the algorithm is so sensitive that more mutation point will be detected. Nevertheless, if $s\ge$ 1.5, the detecting algorithm is lack of sensitivity, the small mutation is neglected during the period of the pin goes through the gap. Hence, $s=$ 1.3 is used for the gap detecting algorithm developed in this study.

As shown in Fig. 10, when scale factor was lager ($s=$1.3), the emergence of clear mutation point was delayed in this case (delay time is close to 5.14 s). Compared with the wavelet transforms of the low frequency torque (leading time is close to 1.8 s), the upper envelope of the main periodic signal is not suitable for detecting the gap by the wavelet transforms algorithm. Then the low frequency torque signal will be the focus of following study.

Fig. 9The WTs of the low frequency torque signal for operations with N= 400 rpm, V= 170 mm/min, and 0.35 mm gap

a) Torque and WT with $s=$ 1

b) Torque and WT with $s=$ 1.3