Experimental analysis method and experimental system for vibration characteristics of deep-sea mining pipeline

Abstract

The invention relates to the technical field of ocean mineral resource development, and discloses an experimental method and an experimental system for vibration characteristics of a mining pipe, and the experimental method comprises the steps: carrying out a deep sea vibration simulation experiment on the mining pipe, and obtaining experimental strain data; correcting the experimental strain data for the first time according to the difference between the experimental ocean current and the actual ocean current; and according to the boundary effect of the simulation experiment, carrying out second correction on the experiment strain data. Therefore, the experimental strain data is corrected by considering the difference between the experimental ocean current and the actual ocean current and the influence of the water tank boundary on the vibration in the simulation experiment, so that the experimental strain data is closer to the actual situation, and the accuracy of the simulation result is further improved. Meanwhile, the ocean current has great influence on the data, so that the accuracy of data correction can be further improved by correcting the experimental strain data based on the difference between the experimental ocean current and the actual ocean current.

Description

Technical Field

[0001] This application relates to the field of marine mineral resource development technology, for example to an experimental analysis method and experimental system for the vibration characteristics of deep-sea mining pipelines. Background Technology

[0002] Deep-sea mining pipes are the only channel connecting seabed relay stations and surface mining vessels, playing a crucial role in marine mineral extraction systems. The main factors causing vibration in deep-sea mining pipes are the linear response induced by the oscillations of the mining vessel and vortex-induced vibrations caused by ocean currents. In practical engineering, the vibration response of the mining pipe excited by the coupling effect of these two factors is a significant cause of pipeline fatigue damage.

[0003] To analyze the vibration characteristics of mining pipes in the deep sea, a vibration testing system is typically used to conduct model experiments on the mining pipes. The data obtained from the experiments are then analyzed to obtain the vibration response characteristics of the mining pipes. However, the experimental environment differs from the real marine environment, which leads to a certain deviation between the experimental data and the real data, and consequently, inaccurate analysis results.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments, but rather as a prelude to the detailed description that follows.

[0006] This disclosure provides an experimental analysis method and system for the vibration characteristics of deep-sea mining pipelines to improve the accuracy of simulation results.

[0007] In some embodiments, the experimental analysis method for the vibration characteristics of deep-sea mining pipelines includes: conducting a deep-sea vibration simulation experiment on the mining pipeline to obtain experimental strain data; performing a first correction on the experimental strain data based on the difference between the experimental ocean current and the actual ocean current; analyzing the experimental strain data to determine the type of difference between the experimental ocean current and the actual ocean current; performing a first correction on the experimental strain data based on the type of difference; performing a second correction on the experimental strain data based on the boundary effect of the simulation experiment; constructing a water tank numerical model containing boundaries, reproducing the wave-generating signal of the simulation experiment in the water tank numerical model, and calculating the bounded vibration strain of the mining pipeline. In the numerical model of the water tank, open sea conditions are simulated to calculate the unbounded vibration strain of the mining pipe under no-boundary disturbance. Based on the mining pipe and the boundary, the area where the mining pipe is located is determined. When the mining pipe is located in the near-field or mid-field zone, the bounded vibration strain is used as the basis for determining the mining area. and the aforementioned unbounded vibration strain The experimental strain data were then corrected a second time.

[0008] In some embodiments, the experimental system for the vibration characteristics of the deep-sea mining pipe includes: a support device; a standard sinusoidal heave-sway system, or a roll-pitch system; the standard sinusoidal heave-sway system includes: a support frame disposed on the support device; a motor disposed on the support frame; a Scottish yoke mechanism, the power input of which is drivenly connected to the motor, and the power output of which is connected to the top of the mining pipe model via a tension meter; the Scottish yoke mechanism is slidably connected to the support frame along a numerical direction; or, the Scottish yoke mechanism is slidably connected to the support frame along a horizontal direction; the roll-pitch system is connected to the bottom of the support device; or, if the Scottish yoke mechanism is disposed along a numerical direction, the roll-pitch system is connected to the power output of the Scottish yoke mechanism, and the mining pipe model is connected to the roll-pitch system. The experimental analysis method and system for vibration characteristics of deep-sea mining pipelines provided in this disclosure can achieve the following technical effects: First, experimental strain data was obtained through a deep-sea vibration simulation experiment of a mining pipe. Analysis of this data determined the type of difference between the experimental and actual ocean currents, leading to an initial correction of the strain data based on this difference. Next, considering the boundary effects of the simulation, the bounded vibration strain of the mining pipe under bounded constraints and the unbounded vibration strain under unbounded constraints were calculated using a flume numerical model. This data, combined with the location of the mining pipe, resulted in a second correction of the strain data. By considering the differences between the experimental and actual ocean currents and the influence of the flume boundary on vibration in the simulation, the strain data is corrected to more closely approximate actual conditions, thus improving the accuracy of the simulation results. Furthermore, since ocean currents have a significant impact on the data, correcting the strain data based on the differences between the experimental and actual currents further enhances the accuracy of the correction. Additionally, differentiated corrections based on the type of difference between the experimental and actual ocean currents and the location of the mining pipe can also further improve the accuracy of the correction.

[0009] The above general description and the description below are exemplary and illustrative only and are not intended to limit this application. Attached Figure Description

[0010] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations and drawings do not constitute a limitation on the embodiments. Elements having the same reference numerals in the drawings are shown as similar elements. The drawings are not to be scaled. And wherein: Figure 1 This is a schematic diagram of the experimental analysis method for the vibration characteristics of a deep-sea mining pipeline provided in the embodiments of this disclosure; Figure 2 This is a schematic diagram of a method for first correction of experimental strain data based on the difference type when the difference type is frequency structure and nonlinearity missing, provided by an embodiment of this disclosure; Figure 3 This is a schematic diagram of a method for first correction of experimental strain data based on the difference type when the difference type is energy level difference, provided by an embodiment of this disclosure; Figure 4 This is a schematic diagram of a method for second correction of experimental strain data based on bounded vibration strain and unbounded vibration strain when the mining pipe is located in the near field zone, provided by an embodiment of this disclosure; Figure 5 This is a schematic diagram of a method for second correction of experimental strain data based on bounded vibration strain and unbounded vibration strain when the mining pipe is located in the mid-field zone, as provided in this embodiment of the disclosure. Figure 6 This is a schematic diagram of the experimental analysis method for the vibration characteristics of a deep-sea mining pipeline according to the second embodiment of this disclosure; Figure 7 This is a schematic diagram of the Scottish yoke mechanism arranged in the vertical direction in the experimental system for vibration characteristics of deep-sea mining pipelines provided in this embodiment of the present disclosure. Figure 8 This is a schematic diagram of the Scottish yoke mechanism arranged in the horizontal direction in the experimental system for the vibration characteristics of a deep-sea mining pipeline provided in this embodiment of the present disclosure. Figure 9 This is a schematic diagram of the roll-pitch system in the experimental system for the vibration characteristics of a deep-sea mining pipeline provided in this embodiment of the present disclosure. Figure 10 This is a schematic diagram of the Scottish yoke mechanism arranged in the vertical direction provided in the embodiments of this disclosure; Figure 11 This is a schematic diagram of the transmission arm in the Scottish yoke mechanism provided in this embodiment; Figure 12 This is a schematic diagram of the Scottish yoke mechanism arranged in the horizontal direction provided in an embodiment of this disclosure.

[0011] Figure label: 10. Support device; 11. First support structure; 12. Second support structure; 13. Corner bracket; 14. Fixing plate; 20. Bracket; 21. First slide groove; 30. Motor; 31. Support frame; 40. Scottish yoke mechanism; 41. Slide rod; 411. Guide rail; 42. Connecting part; 421. Sliding groove; 43. Transmission arm; 431. Rotating support arm; 432. Second slide groove; 433. Sliding part; 434. Rotating part; 50. Tension gauge; 60. Mining pipe model; 61. Marker point; 71. First connecting rod; 72. First support arm; 73. Second support arm; 74. First stop block; 75. Second stop block; 80. Floating platform; 90. Second connecting rod; 91. Rod body; 92. Slider; 100. Fixed support; 110. Image acquisition module; 111. Non-invasive high-speed camera; 120. Data acquisition terminal. Detailed Implementation

[0012] To provide a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this disclosure. In the following technical description, for ease of explanation, several details are used to provide a full understanding of the disclosed embodiments. However, one or more embodiments may still be implemented without these details. In other cases, well-known structures and devices may be simplified in their depiction to simplify the drawings.

[0013] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0014] Unless otherwise stated, the term "multiple" means two or more.

[0015] In this embodiment of the disclosure, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0016] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0017] The term "correspondence" can refer to an association or binding relationship. The correspondence between A and B means that there is an association or binding relationship between A and B.

[0018] Combination Figure 1As shown, this disclosure provides a first experimental analysis method for the vibration characteristics of deep-sea mining pipelines, including: S101, Deep-sea vibration simulation experiment was conducted on the mining pipe to obtain experimental strain data; S102, Based on the difference between the experimental ocean current and the actual ocean current, the experimental strain data is corrected for the first time: the experimental strain data is analyzed to determine the type of difference between the experimental ocean current and the actual ocean current; the experimental strain data is corrected for the first time based on the type of difference. S103. Based on the boundary effects of the simulation experiment, the experimental strain data are corrected for the second time: a numerical model of the water tank containing the boundary is constructed, and the wave-generating signal of the simulation experiment is reproduced in the numerical model to calculate the bounded vibration strain of the mining pipe. In the numerical model, open sea conditions are simulated to calculate the unbounded vibration strain of the mining pipe under no-boundary disturbance. The location of the mining pipe is determined based on the mining pipe and its boundary. When the mining pipe is located in the near-field or mid-field zone, the bounded vibration strain is considered. and unbounded vibration strain The experimental strain data were corrected a second time.

[0019] An experimental system utilizing the vibration characteristics of deep-sea mining pipelines was used to simulate the vibrations experienced by the pipeline in the deep sea. The parameters of the mining pipeline and the simulation parameters for various operating conditions are shown in the following tables: Table 1 Parameters of Mining Pipe

[0020] Table 2. Experimental simulation parameters of vortex-induced vibration of mining pipes under ocean current.

[0021] Table 3. Vibration simulation parameters of mining pipes oscillating and heaving in still water.

[0022] Table 4. Simulation parameters of vibration of mining pipe under the coupling effect of longitudinal and helical motions and ocean currents.

[0023] Table 5. Simulation parameters of the mining pipe's lateral and longitudinal swaying vibration in still water.

[0024] Table 6. Vibration simulation parameters of mining pipes under the coupled action of roll / pitch and ocean currents.

[0025] After the experiment, experimental strain data of the mining pipe were obtained. However, there will inevitably be deviations between the experimental data and the actual data. Therefore, the experimental data was processed to make it closer to the actual data.

[0026] First, based on the differences between the experimental and actual ocean currents, the experimental strain data were corrected for the first time. Specifically, this included: adjusting the experimental strain data... Analysis was conducted to determine the types of differences between the experimental and actual ocean currents. These differences primarily included two types: differences in energy levels and missing frequency structure and nonlinearity. Appropriate correction schemes were matched based on the type of difference, and the experimental strain data underwent initial correction.

[0027] Then, based on the boundary effects of the simulation experiment, a second correction is made to the experimental strain data after the first correction. Specifically, this includes constructing a 1:1 numerical model of the water tank, including its boundaries, in finite element software. The wave-generating signal from the physical simulation experiment is then reproduced in the water tank numerical model, and the bounded vibration strain of the mining pipe under this environment is calculated. In the same water tank numerical model, open sea conditions were simulated using the same wave-generating signal, and the unbounded vibration strain of the mining pipe in this environment (without boundary interference) was calculated. Then, the field area where the mining pipe is located is determined based on the boundary between the mining pipe and the water tank. Optionally, the field area includes a near-field zone, a mid-field zone, and a negligible zone. The negligible zone indicates that the distance between the mining pipe and the water tank boundary is relatively large, and the error caused by the boundary to the experimental data is negligible. Therefore, when the mining pipe is located in the near-field zone or the mid-field zone, the bounded vibration strain is used as the basis for determining the field area. and unbounded vibration strain A suitable correction scheme is matched, and the experimental strain data that have been corrected once are corrected a second time.

[0028] The experimental analysis method for vibration characteristics of deep-sea mining pipelines provided in this disclosure first obtains experimental strain data through a deep-sea vibration simulation experiment of the mining pipeline. Analysis of the experimental strain data determines the type of difference between the actual and uncontrolled ocean currents, and then the experimental strain data is corrected based on this type of difference. Next, considering the boundary effects of the simulation experiment, the bounded vibration strain of the mining pipeline under bounded constraints and the unbounded vibration strain under unbounded constraints are calculated using a flume numerical model. Combined with the location of the mining pipeline, the experimental strain data is corrected a second time. This method, by considering the differences between the experimental and actual ocean currents and the influence of the flume boundary on vibration in the simulation experiment, makes the experimental strain data closer to the actual situation, thereby improving the accuracy of the simulation results. Furthermore, since ocean currents have a significant impact on the data, correcting the experimental strain data based on the differences between the experimental and actual ocean currents can further improve the accuracy of the data correction. In addition, differentiated correction of the experimental strain data based on the type of difference between the experimental and actual ocean currents and the location of the mining pipeline can also further improve the accuracy of the data correction.

[0029] Optionally, the experimental strain data can be analyzed to determine the types of differences between the experimental and actual ocean currents, including: Numerical simulation was used to calculate the target strain data generated by the mining pipe under the same sea conditions.

[0030] Based on the experimental strain data and the target strain data, calculate the root mean square of the target strain data and the root mean square of the experimental strain data, respectively.

[0031] When the root mean square of the experimental strain data is less than the preset order of magnitude of the root mean square of the target strain data, the difference type is determined to be an energy level difference.

[0032] When the higher-order harmonics in the experimental strain data are less than the preset value, the difference type is determined to be frequency structure and nonlinearity deficiency.

[0033] Through data simulation, the target strain data that the mining pipe should produce under the same sea conditions as the simulation experiment were calculated. This was used as a correction benchmark. Based on experimental strain data... Calculate the root mean square of experimental strain data Based on target strain data Calculate the root mean square of the target strain data .if Much smaller than If the root mean square of the experimental strain data is less than the preset order of magnitude of the root mean square of the target strain data, then the difference between the experimental ocean current and the actual ocean current is determined to be an energy level difference.

[0034] Analyzing the experimental strain data, if the spectrum is pure and the higher-order harmonics are less than the preset value, the difference between the experimental ocean current and the actual ocean current is determined to be frequency structure and nonlinearity deficiency. In this way, by analyzing the experimental strain data, the type of difference between the experimental ocean current and the actual ocean current can be determined so as to accurately match the correction scheme and improve the accuracy of the data.

[0035] Optionally, combined Figure 2 As shown, the experimental strain data are corrected for the first time according to the type of difference, including: S201, when the difference type is energy level difference, calculate the scaling factor based on the root mean square of the target strain data and the root mean square of the experimental strain data; S202, the product of the scaling factor and the experimental strain data is used as the first corrected data.

[0036] If the difference between the experimental and actual ocean currents is of energy level, it indicates that the overall root mean square strain value obtained from the simulation experiment is much lower than the theoretical expectation or the prototype observation value. Therefore, when correcting the data, the scaling factor is calculated according to formula (1) based on the root mean square of the target strain data and the root mean square of the experimental strain data. : (1) Based on scaling factor and experimental strain data Calculate the corrected data according to formula (2). : (2) Thus, the corrected Strictly equal to This ensures consistency with actual or theoretical expectations on the energy scale, effectively elevating experimental data to the energy levels required for practical engineering or theory. Simultaneously, it maintains the original characteristics of the vibration signal without altering its frequency components, phase relationships, or waveform characteristics; only the amplitude is uniformly scaled.

[0037] Optionally, combined Figure 3 As shown, the experimental strain data are corrected for the first time according to the type of difference, including: S301, when the difference type is frequency structure and nonlinearity missing, advanced and simplified numerical models are performed using the same wave parameters to obtain strain data from the advanced numerical model. And simplified numerical model strain data .

[0038] S302, based on advanced digital model strain data And simplified numerical model strain data Model training is performed to obtain advanced numerical model strain data. And simplified numerical model strain data The mapping relationship.

[0039] S303, based on advanced digital model strain data And simplified numerical model strain data The mapping relationship is used to determine the first corrected data corresponding to the experimental strain data.

[0040] If the difference between experimental and actual ocean currents is characterized by frequency structure and nonlinearity loss, it indicates that the strain power spectral density plot shows peaks only at a few simple frequencies, lacking higher-order harmonics and low-frequency slow-drift oscillation responses. Therefore, when correcting the data, first use the same wave parameters to perform advanced and simplified numerical models, obtaining the advanced numerical model strain data respectively. And simplified numerical model strain data Training a model to learn and The mapping relationship is used to apply this model to experimental strain data. Data output by the model This is the data after the first correction.

[0041] This effectively compensates for the limitations of laboratory ocean current simulations in reproducing complex frequency structures and nonlinear dynamic characteristics. Avoiding biases that may arise from simple scaling, it uses intelligent learning to precisely add key nonlinear response features present in the actual ocean environment, such as higher-order harmonics and low-frequency slow-drift oscillations, to the experimental data. This makes the amplitude of the corrected experimental strain data closer to reality.

[0042] Optionally, based on the shortest distance between the riser and the water tank boundary. With the wavelength of the wave Determine the site area where the mining pipe is located. If Then the mining pipe is determined to be in the near-field zone. If Then the mining pipe is determined to be in the midfield zone. If If so, then the mining pipe is determined to be in the negligible zone.

[0043] Optionally, combined Figure 4 As shown, based on bounded vibration strain and unbounded vibration strain The experimental strain data were corrected a second time, including: S401, when the mining pipe is located in the near-field zone, the bounded vibration strain and unbounded vibration strain Performing a Fourier transform yields the distribution of vibrational energy of bounded vibrational strain at different frequencies. Distribution of vibrational energy at different frequencies of unbounded vibrational strain .

[0044] S402, based on the distribution of vibration energy at different frequencies of bounded vibration strain. Distribution of vibrational energy at different frequencies of unbounded vibrational strain Calculate the frequency domain correction factor.

[0045] S403, the data after the first correction Perform a Fourier transform and multiply it by the frequency domain correction factor.

[0046] S404 performs an inverse Fourier transform on the result of the multiplication, and the result of the transform is used as the data after the second correction.

[0047] When the mining pipe is located in the near-field zone, the reflected waves and incident waves at the boundary of the water tank will produce complex interference phenomena. This interference has different effects on wave components of different frequencies, causing the experimentally measured vibration strain to be amplified at some frequencies and suppressed at others, distorting the true frequency response characteristics. Bounded and unbounded data originate from the same excitation, and their differences are entirely caused by boundary effects.

[0048] Therefore, in this case, the bounded vibration strain and unbounded vibration strain Performing a Fourier transform yields the distribution of vibrational energy of bounded vibrational strain at different frequencies. Distribution of vibrational energy at different frequencies of unbounded vibrational strain This allows for the identification of the main frequencies, locking intervals, and higher-order harmonic components of vortex-induced vibrations.

[0049] according to and The frequency domain correction factor is calculated according to formula (3). : (3) The data after the first correction Perform a Fourier transform and compare it with the frequency domain correction factor. Multiply. Perform an inverse Fourier transform on the result of the multiplication, and use the result as the data after the second correction. As shown in formula (4): (4) Thus, when the mining pipe is in the near-field region, the vibration waveform of the structure in the time domain is decomposed into sinusoidal components of different frequencies by performing Fourier transforms on the bounded vibration strain and unbounded vibration. Then, based on the ratio of the Fourier transform results, a frequency domain correction factor is obtained. This frequency domain correction factor is used to further correct the data after the first correction, thereby improving the accuracy of the experimental data.

[0050] Optionally, combined Figure 5 As shown, based on bounded vibration strain and unbounded vibration strain The experimental strain data were corrected a second time, including: S501, based on bounded vibration strain, when the mining pipe is located in the mid-field zone. and unbounded vibration strain Calculate the overall energy level scaling factor.

[0051] S502, compares the overall energy level scaling factor with the data after the first correction. The product of these two values ​​is used as the second revised data.

[0052] If the mining pipe is located in the mid-field zone, then based on bounded vibration strain and unbounded vibration strain The overall energy level scaling factor is calculated according to formula (5). : (5) in, The root mean square value represents the strain value of unbounded vibration. It represents the root mean square value of the bounded vibration strain.

[0053] Scaling factor of the overall energy level Compared with the data after the first correction The product of these two values ​​is used as the data after the second correction. As shown in formula (6): (6) This can reduce the errors caused by boundary effects in experimental and actual mining operations.

[0054] Combination Figure 6 As shown, this disclosure provides a second experimental analysis method for the vibration characteristics of deep-sea mining pipelines, including: S101, Deep-sea vibration simulation experiment was conducted on the mining pipe to obtain experimental strain data; S102, Based on the difference between the experimental ocean current and the actual ocean current, the experimental strain data is corrected for the first time: the experimental strain data is analyzed to determine the type of difference between the experimental ocean current and the actual ocean current; the experimental strain data is corrected for the first time based on the type of difference. S103. Based on the boundary effects of the simulation experiment, the experimental strain data are corrected for the second time: a numerical model of the water tank containing the boundary is constructed, and the wave-generating signal of the simulation experiment is reproduced in the numerical model to calculate the bounded vibration strain of the mining pipe. In the numerical model, open sea conditions are simulated to calculate the unbounded vibration strain of the mining pipe under no-boundary disturbance. The location of the mining pipe is determined based on the mining pipe and its boundary. When the mining pipe is located in the near-field or mid-field zone, the bounded vibration strain is considered. and unbounded vibration strain The experimental strain data were corrected a second time; S104, A third correction is performed on the experimental data based on waves, suspended sediment bubbles, and attached materials: Correction coefficients are determined for wave factors, suspended sediment and bubble factors, and attached material factors; these correction coefficients are then compared with the data after the second correction. The product of these is used as the data after the third correction;

[0055] The wave conditions in real ocean environments are complex, and breaking waves and extreme waves (distorted waves) are difficult to accurately reproduce in simulation experiments. However, wave breaking and distorted waves generate huge, nonlinear impact loads, greatly increasing the dynamic response of risers, resulting in high-intensity, transient effects. Suspended sediments in the ocean increase the apparent density and viscosity of the fluid, thus slightly increasing drag and added mass. Bubbles significantly reduce the local density of the fluid, thereby reducing added mass. The mixing effect of bubble-driven two-phase flow can generally reduce the overall hydrodynamic load. The ocean is also full of plankton and attached organisms, which increase the diameter of the mining pipe, directly increasing wave forces, and also increase pipe roughness, significantly increasing the drag coefficient. All these factors affect the accuracy of experimental data.

[0056] Therefore, the correction coefficient corresponding to the wave factor is determined. Correction coefficients for suspended sediment bubble factors Correction coefficients corresponding to the attachment factor Compare each correction factor with the data after the second correction. The product of these two numbers is used as the data after the third correction. As shown in formula (7): (7) in, , , Values ​​range from 1.0 to 1.1.

[0057] Thus, by adjusting the coefficient The peak strain and vibrational energy level caused by extreme wave time are corrected by a correction factor. The effect of changes in the physical properties of the fluid medium on the overall vibration energy level is corrected by a correction factor. The effect of increased overall load due to changes in the geometry and surface properties of the mining pipe is corrected, thus making the experimental strain data closer to the true value.

[0058] Optionally, determine the correction coefficients corresponding to the wave factors, including: Vibration simulations were performed using a high-order nonlinear numerical wave pool that incorporates wave breaking and distorted wave models.

[0059] Obtain the first vibration strain under normal irregular wave conditions and the second vibration strain including extreme wave conditions .

[0060] The first vibration strain corresponding root mean square With the second vibration strain corresponding root mean square The ratio of is used as the correction coefficient corresponding to the wave factor.

[0061] Determining the correction factor At that time, a high-order nonlinear numerical wave pool model incorporating wave breaking distortion was used to simulate the mining pipe under the condition of "only ordinary irregular wave". and the second vibration strain under the "including extreme wave" condition And calculate the first vibration strain respectively. Second vibration strain corresponding root mean square and The correction factor is calculated according to formula (8). : (8) In this way, by using high-order numerical simulation to quantify the amplification effect of extreme waves on the vibration energy of mining pipes, the results of ordinary wave experiments in the laboratory are extrapolated and corrected to a more realistic and conservative design condition that includes extreme events, thereby significantly improving the safety margin of the engineering design of mining pipe systems.

[0062] Optionally, determine the correction factor corresponding to the attachment factor, including: Establish a finite element model of the mining pipe.

[0063] Based on the finite element model, the third vibration strain of a smooth mining pipe under waves was calculated. The fourth vibration strain of the mining pipe under waves, with increased diameter and roughness. .

[0064] The third vibration strain corresponding root mean square With the fourth vibration strain corresponding root mean square The ratio of is used as the correction factor for the attachment factor.

[0065] Determining the correction factor At that time, a finite element model of the mining pipe was established using finite element software. The first step was to calculate the initial response of the smooth mining pipe under waves. Then calculate the second response of the mining pipe with increased diameter and roughness. Calculate the strain of the third vibration separately. and the fourth vibration strain corresponding root mean square and The correction factor is calculated according to formula (9). : (9) In this way, using finite element simulation to quantify the impact of marine biofouling on the vibration energy of mining pipes allows for the extrapolation and correction of experimental results from laboratory-smooth new pipes to service conditions with biofouling, thereby providing a more accurate and conservative data basis for the full life-cycle design and fatigue analysis of mining pipes.

[0066] Combination Figures 7 to 9 As shown, the experimental system for the vibration characteristics of the deep-sea mining pipeline includes: a support device 10, and also includes: a standard sinusoidal heave-sway system, or a roll-pitch system.

[0067] The standard sinusoidal heave-sway system includes: support frame 20, motor 30 and Scottish yoke mechanism 40.

[0068] See Figure 7 and Figure 10 When simulating the standard sinusoidal heave motion of the mining pipe model 60: The support 20 is detachably connected to the side of the support device 10 along the vertical direction. The motor 30 is connected to the support 20 via a support frame 31, and the power output shaft of the motor 30 is horizontal. The Scottish yoke mechanism 40 is slidably connected to the side of the support 20 along the vertical direction. See also... Figure 8 and Figure 12 When simulating the standard sinusoidal oscillation motion of the mining pipe model 60: the bracket 20 is detachably connected to the top of the support device 10 along the horizontal direction. The motor 30 is connected to the bracket 20 via the support frame 31, and the power output shaft of the motor 30 is in a vertical position. The Scottish yoke mechanism 40 is slidably connected to the top of the bracket 20 along the horizontal direction.

[0069] The Scottish yoke mechanism has a power input section and a power output section. The power input section is connected to the power output shaft of the motor 30, and the power output section is connected to the top of the mining pipe model 60 via a tension meter 50. When the Scottish yoke mechanism 40 is set vertically, it converts the rotational motion of the motor 30 into linear motion, thereby driving the mining pipe model 60 to reciprocate up and down, performing standard sinusoidal heave motion. When the Scottish yoke mechanism 40 is set horizontally, it converts the rotational motion of the motor 30 into linear motion, thereby driving the mining pipe model 60 to reciprocate left and right, performing standard sinusoidal oscillation motion. Alternatively, the standard sinusoidal heave-oscillation system can simulate the vortex-induced vibration of the mining pipe model 60 under the action of a simple sinusoidal oscillating flow.

[0070] The roll-to-roll system is connected to the bottom of the support device 10, and the mining pipe model 60 is connected to the roll-to-roll system, thus performing roll or pitch motion under the drive of the roll-to-roll system. Alternatively, when the Scottish yoke mechanism 40 is set in the vertical direction, the roll-to-roll system is connected to the power output of the Scottish yoke mechanism 40, and the mining pipe model 60 is connected to the roll-to-roll system. In this way, when the roll-to-roll system is started alone, it can drive the mining pipe model 60 to perform roll or pitch motion; when both the Scottish yoke mechanism 40 and the roll-to-roll system are started, they can achieve a synergistic effect of heave-roll, or a synergistic effect under the action of roll-single oscillating flow.

[0071] This disclosure provides an experimental system for analyzing the vibration of a mining pipe under the combined effects of ship oscillation and ocean currents. The system includes a support device 10 for providing mounting positions for other components. It also includes a standard sinusoidal heave-sway system or a roll-pitch system. The standard sinusoidal heave-sway system includes a bracket 20, a motor 30, and a Scottish yoke mechanism 40. The motor 30 serves as the power source, and the Scottish yoke mechanism 40 is installed in different directions, either vertically or horizontally, and can drive the mining pipe model 60 to perform standard sinusoidal sway or heave motion under the drive of the motor 30. The roll-pitch system is connected to the bottom of the support device 10, or to the power output of the vertically positioned Scottish yoke mechanism 40. Thus, this system can simulate the heave, sway, roll, and pitch oscillations of a mining pipe vessel, or simulate the vortex-induced vibration of a mining pipe under the action of a simple sinusoidal oscillating flow. Moreover, the Scottish yoke mechanism 40, as a mechanism that can accurately convert rotational motion into linear sinusoidal motion, has the advantages of relatively simple structure, high motion accuracy, and smooth output motion. Applying it to this experimental system can achieve efficient and accurate simulation of mining ship oscillations and reduce costs.

[0072] Optionally, the mining pipe model 60 is made of PMMA plexiglass tube with a free end (unconstrained) at the bottom to simulate the suspended state of an actual deep-sea mining pipe.

[0073] Optionally, see Figures 10 to 12 The Scottish yoke mechanism 40 includes: a slide bar 41, a connecting part 42, and a drive arm 43. See also... Figure 11 The bracket 20 has a first groove 21 along its own setting direction (vertical or horizontal). See also Figure 12 A guide rail 411 is provided on one side of the slide rod 41. The guide rail 411 is arranged along the length direction of the first slide groove 21 and is slidably embedded in the first slide groove 21. The side of the connecting part 42 is connected to the end of the slide rod 41. Optionally, there are two slide rods 41, and the ends of the two slide rods 41 are respectively connected to opposite sides of the connecting part 42. At least one slide rod 41 is slidably embedded in the first slide groove 21 via the guide rail 411. For example, when the Scottish yoke mechanism 40 is arranged in a vertical direction, the ends of the two slide rods 41 are respectively connected to the upper and lower sides of the connecting part 42 (relative to the upper and lower sides of the connecting part 42). Figure 9 In contrast, the upper slide bar 41 is slidably embedded in the first slide groove 21. When the Scottish yoke mechanism 40 is arranged in the horizontal direction, the ends of the two slide bars 41 are respectively connected to the left and right sides of the connecting part 42 (relative to the horizontal direction). Figure 12 In this regard, the slide bar 41 located on the right side is slidably embedded in the first slide groove 21. The length of the slide bar 41 can be selected according to actual needs.

[0074] See Figure 10 and Figure 12 The connecting part 42 is provided with a sliding groove 421, and the length direction of the sliding groove 421 is perpendicular to the sliding direction of the slide rod 41. The first side of the transmission arm 43 is connected to the power output shaft of the motor 30, and the second side of the transmission arm 43 is provided with a power output end. The first and second sides of the transmission arm 43 are opposite sides, with the first side facing the power output shaft of the motor 30. The connection position between the transmission arm 43 and the motor 30 is close to one end of the transmission arm 43, and the power output end of the transmission arm 43 is located close to the other end of the transmission arm 43. The power output end of the transmission arm 43 is rotatably embedded in the sliding groove 421, thus forming a grooved mechanical connection with the sliding groove 421.

[0075] After the motor 30 starts, it drives the transmission arm 43 to rotate via its own power output shaft, and the power output end of the transmission arm 43 also rotates accordingly. Due to the restriction of the sliding groove 421, the connecting part 42 reciprocates in a straight line, thereby driving the slide rod 41 to reciprocate in a straight line. Therefore, the slide rod 41 serves as the final power output end of the Scottish yoke mechanism 40. The mining pipe model 60 is in a vertically suspended state and is connected to a slide rod 41 via a tension meter 50. For example, see... Figure 10 When the Scottish yoke mechanism 40 is set vertically, the top of the mining pipe model 60 is connected to the bottom of the slide bar 41 located on the lower side via a tension gauge 50. (See also...) Figure 12 When the Scottish yoke mechanism 40 is set in the horizontal direction, the mining pipe model 60 is connected to the bottom surface of the slide bar 41 located on the right side via the tension meter 50.

[0076] Combination Figure 10 and Figure 11 As shown, optionally, the transmission arm 43 includes a rotating support arm 431 and a sliding knob assembly. The first side of the rotating support arm 431 faces the power output shaft of the motor 30 and is drively connected to it. The second side of the rotating support arm 431 is opposite to its first side, and a second groove 432 is provided on the second side along the length of the slide rod 41. The sliding knob assembly serves as the power output end of the transmission arm 43, with one side embedded in the second groove 432 and the other side rotatably embedded in the sliding slot opening 421. Thus, the rotating support arm 431 rotates under the drive of the motor 30, and transmits force to the connecting part 42 through the sliding knob assembly, thereby driving the connecting part 42 and the slide rod 41 to perform linear reciprocating motion.

[0077] See you again Figure 11 Optionally, the sliding knob assembly includes a sliding part 433 and a rotating part 434. The sliding part 433 is cubic and is embedded in the second slide groove 432, and can slide along the second slide groove 432. When the sliding part 433 slides to a preset position, it is fixed in the preset position by fasteners, such as pins, bolts, etc. The rotating part 434 is cylindrical and is connected to the sliding part 433 and is rotatably embedded in the sliding groove opening 421. By adjusting the position of the sliding part 433 in the second slide groove 432, the length of the lever arm can be changed, thereby adjusting the swing amplitude of the connecting part 42 to simulate different degrees of vibration.

[0078] Combination Figure 7 , Figure 10 and Figure 12 As shown, optionally, a fixed support 100 is installed at the top of the mining pipe model 60, and the fixed support 100 is connected to the tension gauge 50.

[0079] Optionally, the support device 10 includes a first support structure 11 and a second support structure 12. The bottom of the first support structure 11 is fixed to the top of the water tank by a fixing plate 14. See also Figure 8 A horizontally positioned Scottish yoke mechanism 40 is mounted on top of the first support structure 11. See also... Figure 7 The bottom of the second support structure 12 is detachably connected to the top of the first support structure 11, and a vertically arranged Scottish yoke mechanism 40 is installed on the side of the second support structure 12. When simulating standard sinusoidal longitudinal vibration, the Scottish yoke mechanism 40 is vertically arranged on the side of the second support structure 12. When simulating standard sinusoidal heave vibration, the second support structure 12 is removed, and the Scottish yoke mechanism 40 is horizontally arranged on the top of the first support structure 11. This allows for easy disassembly and reassembly as needed.

[0080] Optionally, the bottom of the second support structure 12 is connected to the top of the first support structure 11 via a corner bracket 13.

[0081] Optionally, the first support structure 11 and the second support structure 12 are frame structures formed by connecting multiple rods. This saves materials while meeting the support requirements.

[0082] Optionally, see again Figure 9 The roll-pitch system includes: a first connecting rod 71, a magnet guide arm, a floating platform 80, and a second connecting rod 90. The first end of the first connecting rod 71 ( Figure 9 The upper end (shown) is connected to the bottom of the support device 10, i.e., the bottom of the first support structure 11. Alternatively, the top end of the first connecting rod 71 is connected to the power output part of the Scottish yoke mechanism 40 arranged vertically. The magnet guide arm is connected to the side of the first connecting rod 71, and at the same time, the magnet guide arm provides different guiding directions. The floating platform 80 is a square plate-shaped platform. The floating platform 80 includes a top surface, a bottom surface, and four sides. The center position of the top surface of the floating platform 80 is connected to the second end (shown) of the first connecting rod 71 via a hinge. Figure 9 The bottom end (shown) is hinged to the top of the mining pipe model 60 via a tension meter 50. One side is hinged to the first end of the second connecting rod 90. The second end of the second connecting rod 90 is slidably connected to the magnetic guide arm, and an inductor coil is provided at the second end of the second connecting rod 90. When the inductor coil is energized, it generates magnetism, which in turn generates an electromagnetic force between the inductor coil and the magnetic guide arm. Changing the current in the inductor coil can change the direction of the electromagnetic force, thereby driving the second end of the second connecting rod 90 to perform linear reciprocating motion. At the same time, in conjunction with the guiding direction of the magnetic guide arm, the second end of the second connecting rod 90 can be made to reciprocate in different directions, thereby causing the mining pipe model 60 to perform lateral or longitudinal motion.

[0083] Optionally, the magnet guide arm includes a first arm 72 and a second arm 73 on which magnets are uniformly arranged. Both the first arm 72 and the second arm 73 are horizontally arranged. The first end of the first arm 72 is connected to the side of the first connecting rod 71, and the second end is a free end. The first end of the second arm 73 is also connected to the side of the first connecting rod 71, and the second end is a free end. Meanwhile, the first arm 72 and the second arm 73 are perpendicular to each other in the horizontal plane.

[0084] The second connecting rod 90 includes a rod body 91 and a slider 92. The first end of the rod body 91 is hinged to the side of the floating platform 80 via a hinge. An inductor coil is wound around the surface of the slider 92. The bottom of the slider 92 is hinged to the second end of the rod body 91 via a hinge. A through hole is also provided on the slider 92 along the horizontal direction. When the first arm 72 passes through the through hole, the inductor coil is energized, and the slider 92 reciprocates along the first arm 72, thereby causing the mining pipe model 60 to perform periodic rolling motion. When the second arm 73 passes through the through hole, the inductor coil is energized, and the slider 92 reciprocates along the second arm 73, thereby causing the mining pipe model 60 to perform periodic pitching motion. Thus, by sliding the slider 92 onto the first arm 72 or the second arm 73, and in conjunction with the hinge structure, the simulation of rolling and pitching vibrations is achieved.

[0085] Optionally, the magnet guide arm further includes a first stop 74 and a second stop 75. The first stop 74 is disposed at the second end of the first support arm 72, and the second stop 75 is disposed at the second end of the second support arm 73. This prevents the slider 92 from slipping off the first support arm 72 / second support arm 73.

[0086] See you again Figure 7 The experimental system for the vibration characteristics of deep-sea mining pipelines also includes an image acquisition module 110 and a data acquisition terminal 120. The outer wall of the mining pipe model 60 is uniformly marked with black marker points 61 along its axial direction for vibration trajectory identification. The image acquisition module 110 is located outside the water tank and is used to acquire images of the IL and CF surfaces of the mining pipe model 60 to collect vibration process data. Optionally, the image acquisition module 110 includes two non-invasive high-speed cameras 111, which acquire images of the IL and CF surfaces respectively. The data acquisition terminal 120 is communicatively connected to the tension meter 50 and the image acquisition module 110.

[0087] During the experiment, the image acquisition module 110 captures the motion trajectory of the marker point 61 on the mining pipe model 60 in real time and transmits the captured data to the data acquisition terminal 120. The data acquisition terminal 120 analyzes the position coordinates of each marker point 61 at different times and the tension detected by the tension meter to calculate the vibration displacement data of the marker point 61 in the IL and CF directions, thereby obtaining the vibration response characteristics of the entire mining pipe model 60.

[0088] The experimental system for the vibration characteristics of deep-sea mining pipelines also includes a control system. The control system is communicatively connected to motor 30, providing power and motion control for the entire system.

[0089] The experimental system for simulating the vibration characteristics of deep-sea mining pipelines provided in this embodiment can be used to achieve multi-condition simulation: Vibration simulation under the combined action of pitch and ocean current: The inductor coil is energized (at this time, the slider 92 is set on the second support arm 73), and the water pump in the water tank (not shown in the figure) generates current, so that the mining pipe model 60 is subjected to both pitch and ocean current, thereby simulating its vibration response under the combined action of pitch and vortex-induced vibration. This working condition can simulate the scenario where the vibration response of the mining pipe is large in actual engineering.

[0090] Vibration simulation under the combined action of heave and roll, or vibration simulation under the combined action of roll and simple sinusoidal oscillation: The control system controls the motor 30 to start and the inductor coil to be energized (at this time, the Scottish yoke mechanism 40 is set vertically on the side of the second support structure 12, the first connecting rod 71 is connected to the bottom end of the slide rod 41 located on the lower side, and the slider 92 is set on the first support arm 72), so that the mining pipe model 60 is simultaneously excited by heave motion and roll motion, thereby simulating its vibration response under the combined action of heave and roll, or simulating the vibration simulation under the combined action of roll and simple sinusoidal oscillation. This working condition can simulate the scenario where the vibration response of the mining pipe is large in actual engineering.

[0091] Vibration simulation under the combined action of sway and ocean current: The control system starts the motor 30 (at this time, the Scottish yoke mechanism 40 is set on the top of the first support structure 11 in the horizontal direction), and at the same time, the water pump in the water tank (not shown in the figure) generates current, so that the mining pipe model 60 is subjected to the combined action of sway and ocean current, thereby simulating its vibration response under the combined action of sway and vortex-induced vibration. This working condition can simulate the scenario where the vibration response of the mining pipe is large in actual engineering.

[0092] Vibration simulation under the combined action of heave-roll-vortex-induced vibration: Based on the above vibration simulation under the combined action of heave-roll, a water pump (not shown in the figure) in the water tank is used to generate current so that the mining pipe model 60 is simultaneously subjected to heave, roll and ocean current, thereby simulating its vibration response under the combined action of heave-roll-vortex-induced vibration. This working condition can simulate the scenario with the largest vibration response of mining pipe in actual engineering, and has important guiding significance for pipeline structure design and safety assessment of deep-sea mining engineering.

[0093] The foregoing description and accompanying drawings fully illustrate embodiments of the present disclosure to enable those skilled in the art to practice them. Other embodiments may include structural and other changes. The embodiments represent only possible variations. Individual components and functions are optional unless explicitly required, and the order of operation may vary. Parts and features of some embodiments may be included or substituted for parts and features of other embodiments. Embodiments of the present disclosure are not limited to the structures described above and shown in the accompanying drawings, and various modifications and changes may be made without departing from its scope. The scope of the present disclosure is limited only by the appended claims.

Claims

1. An experimental analysis method for the vibration characteristics of deep-sea mining pipelines, characterized in that, include: Deep-sea vibration simulation experiments were conducted on the mining pipe to obtain experimental strain data; Based on the difference between the experimental ocean current and the actual ocean current, the experimental strain data is corrected for the first time: the experimental strain data is analyzed to determine the type of difference between the experimental ocean current and the actual ocean current; the experimental strain data is then corrected for the first time based on the type of difference. Based on the boundary effect observed in the simulation experiment, the experimental strain data is corrected a second time: a numerical model of the water tank containing the boundary is constructed, and the wave-generating signal from the simulation experiment is reproduced in the numerical model of the water tank to calculate the bounded vibration strain of the mining pipe. ; The open sea conditions were simulated in the numerical model of the water tank, and the unbounded vibration strain of the mining pipe under no-boundary disturbance was calculated. Based on the mining pipe and the boundary, the area where the mining pipe is located is determined. When the mining pipe is located in the near-field or mid-field zone, the bounded vibration strain is used as the basis for determining the mining area. and the aforementioned unbounded vibration strain The experimental strain data were then corrected a second time.

2. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 1, characterized in that, The analysis of the experimental strain data to determine the types of differences between the experimental and actual ocean currents includes: Numerical simulation was used to calculate the target strain data generated by the mining pipe under the same sea conditions. Based on the experimental strain data and the target strain data, calculate the root mean square of the target strain data and the root mean square of the experimental strain data, respectively. If the root mean square of the experimental strain data is less than the root mean square of the target strain data by a preset order of magnitude, the difference type is determined to be an energy level difference. When the higher-order harmonics in the experimental strain data are less than the preset value, the difference type is determined to be frequency structure and nonlinearity deficiency.

3. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 1, characterized in that, The first correction of the experimental strain data based on the type of difference includes: When the difference type is energy level difference, the scaling factor is calculated based on the root mean square of the target strain data and the root mean square of the experimental strain data. The product of the scaling factor and the experimental strain data is used as the data after the first correction.

4. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 1, characterized in that, The first correction of the experimental strain data based on the type of difference includes: When the discrepancy type is frequency structure and nonlinearity absence, advanced and simplified numerical models are performed using the same wave parameters to obtain strain data from the advanced numerical model. And simplified numerical model strain data ; Based on the advanced numerical model strain data And simplified numerical model strain data Model training is performed to obtain the advanced numerical model strain data. and the simplified numerical model strain data The mapping relationship; Based on the advanced numerical model strain data and the simplified numerical model strain data The mapping relationship is used to determine the first corrected data corresponding to the experimental strain data.

5. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 1, characterized in that, The bounded vibration strain and the aforementioned unbounded vibration strain The experimental strain data were corrected a second time, including: When the mining pipe is located in the near-field zone, the bounded vibration strain and the aforementioned unbounded vibration strain Performing a Fourier transform yields the distribution of vibrational energy of bounded vibrational strain at different frequencies. Distribution of vibrational energy at different frequencies of unbounded vibrational strain ; Based on the distribution of vibration energy at different frequencies of the bounded vibration strain. The distribution of vibrational energy of the unbounded vibrational strain at different frequencies Calculate the frequency domain correction factor; Perform a Fourier transform on the data after the first correction and multiply it by the frequency domain correction factor; Perform an inverse Fourier transform on the result of the multiplication, and use the result as the data after the second correction.

6. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 1, characterized in that, The bounded vibration strain and the aforementioned unbounded vibration strain The experimental strain data were corrected a second time, including: When the mining pipe is located in the mid-field zone, based on the bounded vibration strain and the aforementioned unbounded vibration strain Calculate the overall energy level scaling factor; The product of the overall energy level scaling factor and the first corrected data is used as the second corrected data.

7. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to any one of claims 1 to 6, characterized in that, The method further includes: The experimental data were corrected a third time based on waves, suspended sediment bubbles, and attached materials: correction coefficients were determined for wave factors, suspended sediment and bubble factors, and attached material factors, respectively; the product of each correction coefficient and the data after the second correction was used as the data after the third correction.

8. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 7, characterized in that, Determine the correction coefficients corresponding to wave factors, including: Vibration simulation was performed using a high-order nonlinear numerical wave pool that included wave breaking and distorted wave models. Obtain the first vibration strain under normal irregular wave conditions and the second vibration strain including extreme wave conditions ; The first vibration strain corresponding root mean square With the second vibration strain corresponding root mean square The ratio of is used as the correction coefficient corresponding to the wave factor.

9. The experimental analysis method for vibration characteristics of deep-sea mining pipelines according to claim 7, characterized in that, Determine the correction factors corresponding to the attachment factors, including: Establish a finite element model of the mining pipe; Based on the aforementioned finite element model, the third vibration strain of the smooth mining pipe under waves was calculated. The fourth vibration strain of the mining pipe under waves, with increased diameter and roughness. ; The third vibration strain corresponding root mean square With the fourth vibration strain corresponding root mean square The ratio of is used as the correction factor for the attachment factor.

10. An experimental system for the vibration characteristics of a deep-sea mining pipeline, characterized in that, include: Support device; A standard sinusoidal heave-swell system, or a roll-pitch system; The standard sinusoidal heave-swell system includes: A bracket is provided on the supporting device; The motor is mounted on the bracket; A Scottish yoke mechanism, wherein the power input part of the Scottish yoke mechanism is connected to the motor drive, and the power output part of the Scottish yoke mechanism is connected to the top of the mining pipe model through a tension meter; the Scottish yoke mechanism is slidably connected to the support along the numerical direction; or, the Scottish yoke mechanism is slidably connected to the support along the horizontal direction. The roll-pitch system is connected to the bottom of the support device; or, if the Scottish yoke is set along the numerical direction, the roll-pitch system is connected to the power output of the Scottish yoke, and the mining pipe model is connected to the roll-pitch system.

Images