Vision-Based Measurement for Catenary Transverse Vibrations in the Winding Mine Hoist

Ma, Xiqiang; Yang, Fang; Yin, Xinke; Xue, Yujun

doi:https://doi.org/10.1155/2022/1323284

Shock and Vibration

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 1323284 | https://doi.org/10.1155/2022/1323284

Vision-Based Measurement for Catenary Transverse Vibrations in the Winding Mine Hoist

Xiqiang Ma,^1,2Fang Yang,^1,2Xinke Yin,^1,2and Yujun Xue^1,2

Academic Editor: Jinxin Liu

Received25 Oct 2021

Accepted19 Jan 2022

Published11 Feb 2022

Abstract

The characteristics of rope vibration of the winding mine hoist are one of the main evaluation indices for evaluating the characteristics of the engineering mechanics and the safety coefficient of the hoist system. For this purpose, research was conducted on the vision-based measurement method for catenary transverse vibration. Firstly, a high-speed camera was utilized to capture grayscale images of the catenary transverse vibration. Secondly, the region of interest (ROI) was selected, and the ROI was binarized based on the wavelet edge extraction algorithm. Thirdly, in the ROI, the centroid position of the rope was obtained by calculating the matrix, which was described by the binary, and later, the transverse vibration signal of the catenary was obtained. Finally, the empirical mode decomposition (EMD) method was used to remove the periodic excitation caused by the displacement of the catenary winding. The experimental results show that the proposed method quickly and accurately comprehends the noncontact measurement of the catenary transverse vibration, and this method could also provide the technical support necessary for the measurement and evaluation of the safety parameters of the hoisting system.

1. Introduction

The smooth winding of the wire rope on the drum is one of the conditions required for the safe and stable operation of the winding mine hoist. As the groove of the wire rope of the drum consists of crossover zones, when the wire rope winds on the drum, it causes the transverse vibration of the wire rope. If the transverse vibration displacement of the wire rope is too large, it could lead to error in coiling or could even cause the rope to come out of the head sheave groove, or the rope could even come in contact with stationary objects [1]. The excessive transverse vibration displacement of the wire rope will cause rope jumping fault and then will lead to the tension change of the ropes. Thus, the excessive transverse vibration of the rope affects the enwinding process of the mine hoist [2]. Therefore, the transverse vibration of the catenary of the winding mine hoisting systems is taken as the main evaluation index for the orderly arrangement and the engineering safety of the multilayer winding wire rope. Given the abovementioned reasons, meaningful research on the transverse vibration monitoring technology of the catenary ensures the safe operation of the winding mine hoist.

In recent years, the corresponding theoretical research concerning the wire rope vibration of the mine hoist has been conducted extensively. Mukhopadhyay et al. analyzed the internal stress of the steel wire rope of the hoisting system and concluded that the stress of the wire rope increased sharply with an increase in the hoisting height [3]. Based on the Hamilton principle, Kaczmarczyk and Ostachowicz established and solved the transverse and longitudinal vibration and the equation of coupled vibration of the double rope winding hoisting system of the ultradeep wells in South Africa. Also, the dynamic response law of the wire rope under different excitation speeds is mainly discussed [4, 5]. Peng et al. established the vibration equation of the hoisting system based on the Hamilton principle, deduced the excitation function of different forms of rope grooves, verified the vibration equation using the Galerkin method, and analyzed the transverse vibration response of different forms of rope groove excitation along with the running state curve of a Blair-type rope hoisting test platform as the motion parameter input [6]. Based on the Hamilton principle, Zhang et al. established a dynamic model of variable length double rope hoisting system and studied the variation characteristics of wire rope tension difference under the transitional excitation between circles [7]. Zhu and Ni, and Zhuand and Chen established a mathematical model for the transverse vibration characteristics of the arbitrarily variable length axial moving rope, deduced the vibration equation and the energy expression of the axial moving rope based on the Hamilton principle, and used numerical simulation to minimize the transverse vibration amplitude of the axial moving rope [8, 9]. Sandilo and Horssen established a mathematical model for the lateral vibration of the variable cable length system and controlled the influence of the length change and running speed as well as tension on the lateral vibration of the cable system [10]. Guo et al. designed a tension and displacement monitoring method for the transverse vibration of the simulation model by using time-frequency technology through the ADAMS/cable simulation model [11, 12]. These studies theoretically explain the causes of wire rope vibration and also show that wire rope vibration is an important factor affecting the safe operation of the hoist [13, 14].

In order to detect the vibration information of wire rope in real time, scholars have carried out a lot of research works [15–19]. Cunha et al. measured the transverse vibration displacement of a cable-stayed bridge with the help of a laser Doppler vibrometer, which can be measured at multiple points. The results show that the accuracy of the measurement of the device meets the requirements for the research on the vibration law of the cable-stayed bridge [20]. Kim used the multitemplate matching algorithm to process the high-speed moving target image, which was marked on the rope. Although the moving image turned out to be blurry, it effectively obtained the displacement of vibration of the rope and then calculated the vibration mode of the rope [21]. Ji and Chang proposed a vibration test method based on computer vision technology without a target mark. In this method, a single ordinary camera was used for the video acquisition of the cable vibration, and an optical flow analysis method was used to solve the problem of structural vibration direction in the image formed due to a small field of vision. The vibration time history of the cable was effectively captured, and its vibration characteristics were measured accurately [22]. Yao et al. used a high-speed camera to shoot the running process of the hoisting wire rope situated directly below the rope string. He used a mean-shift tracking algorithm to process the obtained video sequence of the rope string vibration offline and obtained the displacement parameters of the transverse vibration of the wire rope through the size proportion relationship of the object [23]. Cai et al. proposed a method based online scanning image technology to detect the transverse vibration of the lifting wire rope at the boundary of the friction wheel so as to identify the natural frequency of the transverse vibration of the rope and the tension characteristics of the lifting wire rope during the constant speed operation of the lifting system [24]. Kimand and Kim proposed a digital image processing method to measure the tension of bridge hanger cables. In this method, the dynamic response of the hanger cable is remotely measured by acquiring digital images through a vision-based system [25]. Therefore, digital image processing technology is a convenient and efficient cable vibration measurement method [26–33].

The current research mainly focuses on the friction hoist and does not involve the detection of transverse spatial vibration displacement of the wire rope in the winding hoisting system. Taking the transverse spatial vibration of the wire rope of the winding hoist as the research object, this paper uses the high-speed camera to capture the working process of the wire rope under the lifting condition and designs an image processing algorithm to extract the transverse vibration information of the wire rope. On this basis, a wavelet edge extraction algorithm with an adaptive threshold setting is used to improve the accuracy of detection of the catenary outline. Thus, a binary matrix describing the catenary outline is obtained. We use this binary matrix to calculate the centroid position of the catenary outline, and the empirical mode decomposition (EMD) method is employed to eliminate the disturbance of displacement caused by the winding of the wire rope. Finally, to verify the correctness of the measurement method, experimental research was carried out on the test platform of the multirope winding hoisting system.

2. Visual Measurement Principle

A type of winding mine hoisting system is shown in Figure 1. The main structure of the winding hoisting system consists of wire ropes, headgear sheaves, drums, and a conveyance. The catenary passes from the drum over the sheave, and the vertical rope is constrained to the conveyance. Grooves are installed on the surface of the drum.

The parallel grooves, as shown in Figure 1, consist of two symmetrical helical crossovers. In Figure 1, R_d denotes the drum radius, and d is the diameter of the wire rope. When the winding drum is working, the crossover zone offsets the wire rope by half of its diameter until the wire rope reaches the drum flange. In this process, when the wire rope passes through a crossover zone or a layer change, additional displacements occur relative to the nominal transport motion.

To facilitate the vibration measurement of the catenary rope, the direction of transverse vibration needs to be defined. During the winding process of the drum, the catenary generates two directions for the transverse vibration. As shown in Figure 1, the U-direction is taken along the radial direction of the main shaft of the winding drum, named as the radial transverse vibration; the W-direction is taken along the axial direction of the main shaft, named as the axial transverse vibration.

In the experimental site, the background environment of the catenary is found to be more complicated; thus, a white background board is used to reduce the effect of background noise from the wire rope image. In the collected grayscale image, the black wire rope and the white background provides a sharp contrast. To measure the transverse vibration displacement of the catenary, a high-speed camera (iX Camera iSPEED 220) is used to collect the transverse vibration images of the catenary. The collected images sync with the computer through the Camera-Link bus. The layout of the catenary transverse vibration image acquisition is shown in Figure 2. A white background plate was set in the measurement direction of the catenary to reduce the interference of the background noise of the image. The location of the measuring point is located at a distance of 2.5 meters away from the winding drum. The size of the vibration image is set to 896 × 200 (px) (max. 1600 × 1600 pixels), and the frame rate is 256 (fps) (max. 600fps for 1600 × 1600 pixels).

3. Vibration Image Processing Method

The vibration displacement of the catenary can be calculated by using the following method as shown in Figure 3.

Point O is the starting point at the 0th time, and it is on the static reference line. Point P is the measurement point at tth point of time; it is present on the dynamic reference line. In each tth frame, the vibration displacement of the catenary is the displacement relative to the balance position in the 0th frame. The transverse vibration displacement L(t) at point P can be expressed aswhere q is the scale factor (i.e., the ratio of the actual displacement of the measured point to the pixel displacement), n is the frame number of each picture, and f_s is the sampling frequency.

Using the calculation method mentioned above, each frame can be processed accordingly. Thus, by calculating a series of image sequences in this method, the time-domain value of the transverse vibration of the catenary is obtained.

The vibration displacement images of the catenary obtained by the high-speed camera are grayscale. To obtain the vibration displacement value of the catenary rope, the image processing software used for processing the vibration image of the catenary is developed using C++ Builder. There are four steps in the image processing method, as shown in Figure 4.

3.1. The Setting of the ROI

As the large size of an image hinders the efficiency of image processing, the ROI region is established. The image that is not required to be processed is ignored to improve the efficiency of the image processing. From the point of view of the microelement, in the region of the ROI, the axial contour of the catenary (with a small axial distance) can be approximately regarded as two parallel straight-line segments. The centroid position of the catenary in the ROI does not change with the transverse vibration of the catenary in the direction of the axis.

The row number range of pixels in the ROI area is determined according to the actual situation, but the principle of row number selection of pixels in the ROI area is to ensure that the centroid position of the suspension rope in the ROI area does not change. However, in the axial direction of the image, the set value of the row number of pixels in the ROI image would be maximum, to increase the number of sampling pixels and to reduce the calculation error. By the selection of row pixel number of indifferent ROI areas, the experimental results show that 10 rows of pixels are the best.

3.2. Edge Extraction of the Catenary

To improve the accuracy of detection, the contour edge of the wire rope in the ROI area is detected adaptively. Through the wavelet edge extraction algorithm based on the adaptive threshold, the image edge is scanned by the β × β window, and the threshold is obtained by the wavelet transform coefficient of the window. The selection criteria of the adaptive threshold K of the algorithm is defined in the equation:where K₀ is the initial value, e₀ is the window influence coefficient, and P_i,j is the wavelet coefficients corresponding to the current window. In the experiments, K₀ is taken as 5, and e₀ is taken as 1, respectively.

In actual use, the effect of the image edge detection is affected by the size of the window. A significantly small window leads to the increase in false detection rate and the false edge; on the other hand, an overly large window leads to difficulty in the image edge extraction and the loss of edge information. Therefore, the window size is set to be the same as the area size of the ROI, that is, the image edge is accurately extracted within ten lines of pixels.

3.3. Building the Binary Matrix

After the edge detection, the ROI area can be binarized. The binarized matrix Q of a × b is defined aswhere a is the height of the ROI region (in pixels), b is the width of the ROI region (in pixels), and c_(i,j) is the element in the matrix Q. According to the contour of the catenary obtained by edge detection, the matrix Q is transformed into a binary matrix composed of 0 and 1.

3.4. Calculation of the Centroid Position of the Catenary

By using the matrix centroid, we can obtain the coordinates of the centroid position of the ROI area in the direction of the width of the X-axis (U-direction):where i is the row mark of the matrix Q, j is the column mark of matrix Q, and is the pixel coordinate value of the catenary centroid position in the direction of the width of the X-axis.

The coordinate value L of the actual position of the center of gravity in the ROI region can be obtained from equations (1) and (4):

The actual transverse vibration displacement S_t in the wire rope centroid of the ROI area can be obtained from equations (1) and (5):where L₀ is the coordinate value of the initial time position.

The sampling period T (1/fps) is the time interval between the two adjacent frames of the high-speed camera. The time-domain waveform of the U-direction transverse vibration of the catenary can be obtained by simultaneous equations (1) and (6), respectively. Similarly, according to formulas (1) to (6), the time-domain waveform of the W-direction transverse vibration of the steel wire rope can be obtained.

4. Experimental Validation

4.1. Experimental Objective

An experiment was carried out in the multirope winding hoist test rig built at the State Key Laboratory of Heavy Mining Equipment. The detailed parameters and experimental conditions of each component of the multirope winding hoist test rig are shown in Table 1.

The lifting height of this hoisting system test rig is approximately 39 meters. To simulate the multilayer winding process, the wire rope is wound on the drum for three layers. The wire rope wound can only be about 1.5 circles (including about 11.5 circles of friction rings) on the first layer, 13 circles on the second layer, and about 1 circle on the third layer, respectively. The speed of the hoisting system is 1.0 m/s or 1.8 m/s, and the trapezoidal speed operation diagram shown in Figure 5 is used for the hoisting system.

4.2. Experimental Result

The position information of the steel wire rope in each frame of the image is extracted through the image processing algorithm. The time-domain waveform of the actual vibration displacement of the wire rope in the U-direction and W-direction is shown in Figures 6 and 7, respectively. The transverse vibration curve of the catenary with a lifting speed of 1.0 m/s is shown in Figure 6, and Figure 7 shows the vibration curve of the catenary with 1.8 m/s. At different lifting speeds, the catenary transverse vibration shows a similar trend.

(a)

(b)

(a)

(b)

As shown in Figures 6 and 7, when the catenary is wound on the first layer, the vibration displacement in the U-direction is close to 0 because the winding radius does not change, and the excitation of the interlayer transition device remains 0. It is the transition area between the grooves that excites the W-direction vibration of the catenary. The first layer consists of 1.5 circles; thus, there are two transition areas between the circles in each rope groove. This makes the catenary transverse vibration response consist of two pairs of peaks and troughs when it is wound on the first layer. When the catenary is wound on the second layer, it needs to be wound 13 times along the axis of the drum, and hence, there are 26 pairs of vibration peaks and troughs. The distance between the first circle centreline of the groove and the 13th centreline of the groove is 132 mm, which is consistent with the vibration displacement of the wire rope of 130 mm, during the end of winding the second layer of the wire rope as shown in Figures 6(b) and 7(b). In conclusion, the results of the vibration displacement of the steel wire rope obtained by the image processing of visual inspection are accurate and reliable.

5. Data Analysis

Due to the displacement of the catenary in the winding process along the axial direction of the drum, the catenary vibration curves in Figures 7 and 8 show an obvious upward or downward trend. For further analysis, the displacement caused by the rope winding needs to be removed from the transverse vibration data. Thus, the empirical mode decision (EMD) method is used to remove the interference of the rope displacement.

(a)

(b)

This method is based on the local characteristic time scale of the signal, which decomposes the signal into the sum of several intrinsic modal functions (IMFs). The decomposed individual IMF components highlight the local characteristics of the data, which can be analyzed more accurately and effectively by the characteristic information of the original data [33]. After the periodic excitation generated by the displacement of the rope winding is removed by the EMD empirical mode composition, the actual catenary vibration displacement in the U-direction and W-direction is obtained, as shown in Figures 8 and 9. The frequency-domain waveform of the catenary vibration after removing the interference displacement is obtained by using the FFT, as shown in Figures 10 and 11.

(a)

(b)

(a)

(b)

(a)

(b)

Through the comparison and analysis of the U-direction and W-direction time-domain waveform of the catenary, it can be found that during the beginning of the winding process, the response curve of the catenary transverse vibration is relatively sparse. Correspondingly, at the beginning of the winding process, the frequency of the catenary transverse vibration is found to be relatively low. This is seen because the winding speed of the hoisting system increases from zero at the initial stage. When the speed does not reach a maximum, the excitation frequency of the parallel groove increases with the increase in speed, but it is smaller than that of the uniform speed stage. When the winding enters a relatively stable stage, the transverse vibration displacement of the catenary increases significantly, especially the vibration displacement in the U-direction. As the winding process enters a relatively stable stage, the acceleration of the hoisting system changes abruptly. Also, periodic changes in the excitation of the parallel groove increase the catenary transverse vibration. From Figures 7 to 10, we can see the relationship between the vibration in the U and W directions and the excitation of parallel grooves more closely. The different winding speed also reflects the same change trend. It also shows that the measurement method has a good consistency.

6. Conclusion

In this paper, the vision method is used to obtain the transverse vibration displacement signal by studying the image processing algorithm of the catenary. After experimental validation, the following conclusions can be drawn:(1)The image processing method of the transverse vibration displacement signal of the catenary improves the accuracy in detection of the wire rope vibration, and the time-domain curve of the catenary transverse vibration are obtained intuitively and conveniently.(2)Through experimental validation, the measurement method of the transverse vibration of the catenary provides a practical and effective method for the vibration monitoring of the wire rope in the hoisting system.(3)This method could be used to ensure the safe operation of the hoist and provides a test method for the detection of the motion state of the wire rope of the hoisting system.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

Acknowledgments

This study was supported by the National Basic Research Program of China (no. 973 Program 2014CB049401), Scientific and Technological Key Project in Henan Province (no. 202102210263), Scientific and Technological Key Project in Henan Province (no. 202102210078), and Key Scientific Research Projects of Colleges and Universities in Henan Province (19A460017).

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Copyright © 2022 Xiqiang Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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