Rock breaking vibration analysis method and device for high-power reamer shaft system

Abstract

A large-power reamer shaft system rock breaking vibration analysis method and device, through considering the coriolis force effect on the rotor dynamics modal analysis of the large-power reamer shaft system finite element model, the natural frequency, vibration mode and critical speed of the large-power reamer shaft system are obtained, and the risk of rotation resonance of the large-power reamer shaft system is determined; the reamer load time history under the rock breaking working condition is obtained, the modal superposition method is used for random vibration spectrum analysis of the large-power reamer shaft system finite element model, the displacement response power spectrum density (PSD) of each monitoring node is calculated, and the vibration energy distribution along the shaft is obtained; resonance is determined based on the input and output of random vibration spectrum analysis, and the dominant direction and resonance frequency band are identified when resonance occurs; the present application can accurately characterize the vibration characteristics of the large-power reamer shaft system under random rock breaking excitation, efficiently identify the resonance risk, realize vibration reduction optimization, and significantly improve the operation stability and hard rock operation adaptability of the large-power reamer shaft system.

Description

Technical Field

[0001] This invention relates to a technology in the field of dynamic control of dredging equipment, specifically a method and device for analyzing rock-breaking vibration of a cutter shaft system for cutter shafts with a rated cutter power greater than or equal to 2000kW or where there is a need for rock excavation. Background Technology

[0002] Cutter suction dredgers are core equipment for waterway dredging, port construction, and reclamation projects. The high-power cutter shaft system, as the core component for power transmission and hard rock cutting, is characterized by a large length-to-diameter ratio, long support span, harsh underwater conditions, and strong load randomness. During hard rock cutting operations, the shaft system is subjected to non-stationary, intermittent, and strong impact loads, easily leading to severe vibrations, bearing damage, seal failure, shaft fatigue cracks, and a significant decrease in operating efficiency. Existing technologies mainly employ deterministic finite element methods or steady-state harmonic response analysis. However, in actual rock breaking processes, multiple factors such as uneven rock strength distribution, random variations in cutter tooth thickness, and underwater cavitation effects result in significant randomness in the cutting load. Deterministic analysis methods cannot accurately describe the statistical characteristics of the system response under such random excitation, and are even less able to determine whether probabilistic resonance occurs. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, this invention proposes a method and apparatus for analyzing rock-breaking vibrations in high-power cutter shaft systems. Through a complete technical chain—model building → modal analysis → random vibration spectrum analysis → resonance discrimination → vibration reduction assessment—it can accurately characterize the vibration characteristics of high-power cutter shaft systems under random rock-breaking excitation, efficiently identify resonance risks, achieve vibration reduction optimization, and significantly improve the operational stability and hard rock operation adaptability of high-power cutter shaft systems.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a method for analyzing rock-breaking vibrations in a high-power cutterhead shaft system, comprising:

[0006] Step 1: After equating the high-power cutter shaft system to a multi-degree-of-freedom rotor system and constructing the corresponding dynamic equations, establish a random vibration power spectral density mapping relationship based on the dynamic equations based on modal transformation and Wiener-Khinchin theorem.

[0007] Step 2: Establish a three-dimensional model of the high-power cutter shaft system, mesh it, and apply bearing support and gearbox end constraint boundaries to obtain the finite element model of the high-power cutter shaft system, and set up monitoring nodes and local cylindrical coordinate system;

[0008] Step 3: Considering the Coriolis effect, perform rotor dynamic modal analysis on the finite element model of the high-power auger shaft system to obtain the natural frequency, mode shape and critical speed of the high-power auger shaft system, and determine the risk of self-rotation resonance of the high-power auger shaft system.

[0009] Step 4: Obtain the time history of the cutter load under rock breaking conditions, and use the modal superposition method to perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system. Calculate the displacement response power spectral density (PSD) of each monitoring node and obtain the vibration energy distribution diagram along the shaft.

[0010] Step 5: Based on the input and output of random vibration spectrum analysis, determine the resonance and identify the dominant direction and resonant frequency band at the resonance point; when the high-power cutter shaft system resonates with the rock breaking excitation during rock breaking, adjust the bearing support stiffness based on the principle of avoiding the resonant frequency, and recalculate and quantify the vibration reduction effect.

[0011] This invention relates to a high-power cutter shaft system rock-breaking vibration analysis device for implementing the above-mentioned method, comprising: a dynamic modeling module, a finite element modeling module, a modal analysis module, a random vibration analysis module, a resonance determination module, and a vibration reduction optimization module, wherein: the dynamic modeling module equates the high-power cutter shaft system to a multi-degree-of-freedom rotor system, constructs dynamic equations, and establishes a random vibration power spectral density mapping relationship; the finite element modeling module establishes a finite element model of the high-power cutter shaft system and sets up monitoring nodes and a local cylindrical coordinate system; the modal analysis module considers the Coriolis effect to perform rotor dynamic modal analysis on the finite element model of the high-power cutter shaft system, obtains the natural frequency, mode shape, and critical speed of the high-power cutter shaft system, and determines the risk of rotational resonance; The random vibration analysis module acquires the cutter load time history under rock-breaking conditions, and uses the modal superposition method to perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system. It calculates the displacement response power spectral density (PSD) of each monitoring node and obtains the vibration energy distribution map along the shaft. The resonance determination module performs resonance determination based on the input and output of the random vibration spectrum analysis, identifies the dominant direction of resonance, and records the resonance frequency band. The vibration reduction optimization module, based on the principle of avoiding resonance frequencies, adjusts the size of the high-power cutter shaft system, bearing support position, bearing support stiffness, etc., to make the natural frequency of the high-power cutter shaft system far away from the main peak frequency range of the external excitation load. It then performs rotor dynamic modal analysis and random vibration spectrum analysis again, and quantitatively verifies the vibration reduction effect.

[0012] Technical effect

[0013] This invention constructs the dynamic equations of a multi-degree-of-freedom rotor system, establishes a random vibration power spectral density mapping relationship, and combines high-precision finite element modeling, rotor dynamic modal analysis, random vibration spectrum analysis, and vibration reduction optimization to achieve accurate characterization of the rock-breaking vibration characteristics of a high-power cutter shaft system, efficient identification of resonance risk, and quantifiable verification of vibration reduction effect, significantly improving the accuracy of vibration analysis and the reliability of engineering applications. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention;

[0015] Figure 2 This is the flowchart for step 1;

[0016] Figure 3 This is a schematic diagram of the finite element model of the high-power auger shaft system and the local cylindrical coordinate system established along the shaft in the embodiment;

[0017] Figure 4 The diagram shows the Campbell diagram of the high-power auger shaft system in the embodiment.

[0018] Figure 5 The diagram shows the typical mode shapes of the high-power auger shaft system in the embodiment.

[0019] Figure 6 This is a schematic diagram of the cutter vertical load time history curve under a certain rock-breaking condition in the embodiment;

[0020] Figure 7 This is a PSD curve of the load acceleration in each direction under a certain rock-breaking condition in the embodiment;

[0021] Figure 8 This is a vibration energy distribution diagram obtained through random vibration spectrum analysis in the example;

[0022] Figure 9 This is a PSD curve of the lateral displacement response after vibration reduction in the embodiment.

[0023] Figure 10 This is a comparison of the peak PSD values ​​of the lateral displacement response before and after vibration reduction in the embodiment.

[0024] Figure 11 This is a schematic diagram of the resonance determination process in the embodiment;

[0025] Figure 12 This is a schematic diagram of the high-power cutter shaft system rock-breaking vibration analysis device in the embodiment. Detailed Implementation

[0026] like Figure 1 As shown in this embodiment, a method for analyzing the rock-breaking vibration of a high-power cutter shaft system is applicable to the vibration analysis, resonance identification, and vibration reduction optimization of the cutter shaft system in hard rock cutting conditions of large cutter suction dredgers. Specifically, it includes:

[0027] Step 1: Equip the high-power cutter shaft system as a multi-degree-of-freedom linear rotor system, construct the dynamic equations, and establish the power spectral density mapping relationship between the random external excitation and the overall response of the high-power cutter shaft system.

[0028] The high-power auger shaft system includes: multi-section shaft, flange, and bearing support. Under conditions of small deformation, linear support, and weak damping, it satisfies Hooke's law and the principle of linear superposition. It can be discretized into a finite number of independent translational and rotational components according to the support and cross-section, and therefore can be equivalent to a multi-degree-of-freedom linear rotor system.

[0029] The aforementioned dynamic equations are used to describe the mechanical response relationship between the displacement, velocity, acceleration and inertia, damping and stiffness of the system under external load. When the inertia, damping, stiffness of the system and the external load are known, the displacement, velocity and acceleration response of the system can be obtained by solving the dynamic equations.

[0030] The aforementioned random external excitation refers to the external load on the high-power cutter shaft system during rock breaking operations. Due to the uneven rock mass characteristics, intermittent rock breaking, changes in the state of the cutter teeth, and underwater cavitation effects during the rock breaking and cutting process, the rock breaking and cutting load has a high degree of randomness.

[0031] The establishment of the power spectral density mapping relationship between random external excitation and the overall response of the high-power cutter shaft system refers to: based on the theory of random vibration, transforming the rock-breaking vibration problem of the high-power cutter shaft system into the frequency domain for solution, and using the input power spectral density (PSD) to determine the probability distribution of the response of the high-power cutter shaft system under random load.

[0032] like Figure 2 As shown, step 1 specifically includes:

[0033] 1.1 The high-power auger shaft system is equivalent to a multi-degree-of-freedom linear rotor system, and the dynamic equations are constructed. ,in: , , These are the mass, damping, and stiffness matrices of the high-power cutter shaft system, respectively. , , These are the displacement vector, velocity vector, and acceleration vector, respectively. The external random excitation vector that the system receives; It is a time variable.

[0034] 1.2 Based on modal analysis, the displacement vector in the dynamic equation is decoupled into several single-degree-of-freedom modal equations, specifically: ,in: Undamped mode matrix, This represents the displacement vector in modal coordinates, i.e., the generalized coordinates after modal transformation. When the proportional damping and modes are orthogonal, the dynamic equations are decoupled into a series of modal coordinates. The single-degree-of-freedom modal equations are as follows: ,in: Let r be the generalized coordinates of the r-th modal. For the r-th mode generalized velocity, For the r-th mode generalized acceleration; , , , These are the natural frequency, damping ratio, modal mass, and modal generalized excitation force of the r-th mode, respectively. , Let r be the undamped mode shape vector. is the transpose of the r-th order undamped mode shape vector.

[0035] 1.3 The frequency response functions of the high-power auger shaft system are obtained by Fourier transform, specifically including:

[0036] ① Perform a Fourier transform on the single-degree-of-freedom modal equations to obtain the equations in the frequency domain. ,in: The imaginary unit, It is the angular frequency. Let r be the frequency domain complex amplitude of the generalized coordinates of the r-th mode. The frequency domain complex amplitude of the generalized excitation force of the r-th mode;

[0037] ②The relationship between the response and the excitation in the r-th frequency domain The frequency response function of the r-th mode of the high-power auger shaft system was obtained. .

[0038] 1.4. Based on the Wiener-Khinchin theorem, a conversion relationship between the autocorrelation function and power spectral density of random external excitation is established. The power spectral density function of each modal response is obtained by mapping the square of the frequency response function of each order to the power spectral density function of the excitation force of each order. Specifically, the power spectral density function of the response of the r-th order mode is... ,in: Let be the self-power spectral density function of the excitation force of the r-th modal, and be the external excitation power spectral density. , External excitation vector The autocorrelation matrix, The time-shifted excitation vector is the time-shifted vector. For delay parameters, For the transpose of the time-shifted excitation vector, The instantaneous load coupling matrix, The integral is half the duration; Let be the power spectral density matrix of the external excitation, i.e., the external excitation PSD.

[0039] 1.5 Based on the modal superposition method, the total response power spectral density matrix of the high-power cutter shaft system in physical coordinates is obtained. ,in: To solve for the Nth order mode.

[0040] Step 2: Establish a three-dimensional model of the high-power auger shaft system and mesh it. Apply bearing support and gearbox end constraints to obtain a finite element model. This finite element model is a three-dimensional model of the high-power auger shaft system after meshing, which includes the gearbox output shaft, several intermediate shafts, one auger shaft, auger head, and several connecting flanges. It is subject to bearing support constraints and gearbox end constraints, and monitoring nodes and a local cylindrical coordinate system are set up.

[0041] The aforementioned cutter head can replace the complex cutter head model using equivalent inertia.

[0042] The aforementioned application of bearing support constraints refers to: applying bearing spring constraints to the three-dimensional model of the high-power auger shaft system based on the characteristics and positions of each bearing, that is, simplifying each bearing support into a linear spring-damped support, in order to simulate the constraint of the bearing support on the high-power auger shaft system.

[0043] The aforementioned application of gearbox end constraint means that only the degree of freedom of rotation about the axis at the gearbox position is released.

[0044] like Figure 3 As shown, the deployment of monitoring nodes and local cylindrical coordinate system refers to: deploying 20 monitoring nodes along the axis, and establishing a local cylindrical coordinate system at each node location for torsional vibration rotational displacement extraction.

[0045] Step 3: Using the rotor dynamics method and considering the rotational Coriolis effect, perform rotor dynamics modal analysis on the finite element model of the high-power auger shaft system, calculate the natural frequency and mode shape of the high-power auger shaft system, draw the Campbell diagram, obtain the first-order critical speed of the shaft system, and determine the risk of self-rotation resonance of the high-power auger shaft system based on the working speed range of the high-power auger shaft system.

[0046] like Figure 4 As shown, the Campbell diagram is used to describe the relationship between the natural frequency of the rotor system and the rotational speed, to determine the critical speed, and to determine whether there is a risk of resonance in the operating speed range.

[0047] The aforementioned risk assessment of self-rotation resonance specifically involves: determining whether the operating speed of the high-power auger shaft system under normal operating conditions is lower than the critical speed to eliminate the risk of self-rotation resonance. When the operating speed range is lower than 75% of the first-order critical speed, it can be determined that the high-power auger shaft system will not resonate due to its own rotation. When the critical speed falls within the operating speed range, it is determined that the high-power auger shaft system may resonate due to its own rotation.

[0048] like Figure 4As shown, according to the Campbell diagram obtained by rotor dynamic modal analysis of the finite element model of the high-power auger shaft system in this embodiment, its first critical speed is 189 rpm, and its daily operating speed range is 0~40 rpm. The operating speed range is less than 75% of the first critical speed. Therefore, without considering assembly errors, it is determined that the high-power auger shaft system will not resonate due to its own rotation.

[0049] like Figure 5 As shown in Table 1, the natural frequencies and mode shapes of the high-power auger shaft system provided in this embodiment are as follows. As can be seen from the mode shape diagram, the first six natural frequencies of the high-power auger shaft system provided in this embodiment are 3.15~6.62Hz, mainly in the transverse bending mode shape; the seventh mode is torsional vibration with a frequency of 11.38Hz; and the twelfth mode is longitudinal vibration with a frequency of 27.10Hz.

[0050] Table 1 shows the first 12 natural frequencies and array configurations of the high-power cutter shaft system in the embodiment. .

[0051] Step 4: Obtain the time history data of the cutter load under rock breaking conditions, obtain the acceleration power spectral density (PSD) by Fourier transforming the time-domain load, and perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system using the modal superposition method. Calculate the displacement response power spectral density (PSD) of each monitoring node and obtain the vibration energy distribution diagram along the shaft.

[0052] The cutter load time history under rock breaking conditions refers to the time-domain load on the cutter during rock excavation operations over a period of time.

[0053] The aforementioned acceleration PSD is an input for performing random vibration spectrum analysis on the finite element model of the high-power cutter shaft system.

[0054] The input for the random vibration spectrum analysis can be acceleration PSD, displacement PSD, or velocity PSD.

[0055] The displacement response PSD is the output of random vibration spectrum analysis performed on the finite element model of the high-power cutter shaft system.

[0056] The vibration energy distribution diagram along the axis is a three-dimensional diagram that can intuitively represent the distribution of vibration energy along the axis.

[0057] Step 4 specifically includes:

[0058] 4.1 The time-domain load on the high-power cutter shaft system is decomposed along the four directions of X, Y, Z and torsion around the shaft to describe the rock-breaking vibration characteristics of the high-power cutter shaft system in each direction; for example... Figure 6The figure shown is a schematic diagram of the cutter vertical load time history curve under a certain rock breaking condition provided in an embodiment of the present invention.

[0059] 4.2. Obtain the acceleration power spectral density (PSD) by Fourier transforming the time-domain load; for example... Figure 7 The figure shown is the acceleration power spectral density (PSD) diagram of the loads in each direction under a rock-breaking condition after Fourier transform, provided in this embodiment.

[0060] 4.3. Based on the acceleration PSD curves of each load, identify the main peak frequency band and peak frequency of each load; such as... Figure 7 As shown, the main frequency of the loads in this embodiment is concentrated in the range of 2 to 4 Hz, which highly coincides with the first four natural frequencies of the high-power cutter shaft system, with a peak frequency of about 3 Hz.

[0061] 4.4. Based on random vibration theory, using the acceleration PSD of the various loads as input loads applied to the cutter head, the modal superposition method is used to perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system. The PSD of the displacement response at each monitoring node along the shaft is obtained, and the vibration energy distribution along the shaft is compiled into a three-dimensional diagram that visually represents the vibration energy distribution along the shaft, such as... Figure 8 As shown in the figure, the three axes are the node number, frequency, and displacement response PSD, respectively.

[0062] Step 5: Based on the input and output of random vibration spectrum analysis, determine the resonance, identify the dominant direction of resonance, and record the resonance frequency band.

[0063] In this embodiment, the input for the random vibration spectrum analysis is an acceleration PSD, such as... Figure 7 As shown.

[0064] In this embodiment, the output of the random vibration spectrum analysis is a vibration energy distribution diagram along the axis obtained by processing the displacement response PSDs of 20 monitoring nodes at different locations, as shown below. Figure 8 As shown.

[0065] like Figure 11As shown, the resonance determination refers to determining whether the high-power cutter shaft system resonates with the load subjected to rock excavation operations. Specifically: when the input external excitation PSD is a broadband spectrum, but the output response PSD shows obvious sharp narrow band peaks, it is determined that the high-power cutter shaft system resonates with the rock-breaking excitation during rock breaking; when the input external excitation PSD is a narrow band spectrum, and its narrow band center frequency and bandwidth are basically consistent with the narrow band center frequency and bandwidth of the output response PSD, and the amplitude is not significantly amplified (close to 1 time), it is more likely a characteristic of the excitation itself and should not be determined as the high-power cutter shaft system resonating with the rock-breaking excitation during rock breaking; when the narrow band peak of the output response PSD has an obvious frequency shift or bandwidth narrowing relative to the input external excitation PSD, or the amplitude is sharply amplified (reaching several times or even tens of times), it is determined that the high-power cutter shaft system resonates with the rock-breaking excitation during rock breaking.

[0066] The identification of the dominant direction of resonance refers to the following: when resonance occurs in only one direction and not in other directions, the direction in which resonance occurs is determined to be the dominant direction of resonance. Then, the resonance frequency band is determined and recorded based on the PSD response of the dominant direction of resonance.

[0067] When the high-power cutter shaft system resonates with the rock-breaking excitation during rock breaking, this embodiment adjusts the bearing support stiffness based on the principle of avoiding the resonance frequency, and re-performs rotor dynamic modal analysis and random vibration spectrum analysis to quantitatively verify the vibration reduction effect.

[0068] In the field of vibration reduction optimization of high-power cutter shaft systems, in addition to adjusting the bearing support stiffness, other methods such as adjusting the size of the high-power cutter shaft system and adjusting the bearing support position can also be selected. The purpose is still to keep the natural frequency of the high-power cutter shaft system away from the main peak frequency range of the external excitation load, so as to avoid resonance.

[0069] like Figure 9 The figure shows the PSD curve of the lateral displacement response of the high-power cutter shaft system after re-performing random vibration spectrum analysis by adjusting the bearing support stiffness of the high-power cutter shaft system to reduce vibration.

[0070] like Figure 10 As shown, the change in the peak value of the displacement response PSD before and after vibration reduction is represented by... Figure 10 It can be quantified that the PSD peak value in this embodiment is reduced by more than 80%, therefore the vibration reduction measure is deemed effective.

[0071] like Figure 12 As shown, the cutter shaft system rock-breaking vibration analysis device for implementing the above method in this embodiment includes: a dynamic modeling module, a finite element modeling module, a modal analysis module, a random vibration analysis module, a resonance determination module, and a vibration reduction optimization module.

[0072] Compared with existing technologies, this invention considers actual ship support constraints during finite element model construction, making its setting method more closely resemble the actual ship conditions. The modal analysis module encompasses rotor dynamics modal analysis, calculating the natural frequencies and mode shapes of the shaft system under actual rotation. The random vibration analysis module, based on the results of rotor dynamics analysis, introduces random vibration spectrum analysis, yielding more detailed and intuitive results. The resonance determination module uses the displacement response power spectral density along different nodes of the shaft system in each direction to determine the distribution of vibration energy along the shaft, thus determining whether resonance occurs during rock-breaking excavation. The vibration reduction optimization module can re-optimize the shaft system, bearing positions, or bearing support stiffness based on the vibration energy distribution of the shaft system under rock-breaking operations. By changing the mass stiffness matrix of the shaft system to be optimized, the optimized shaft system's modes and the distribution of vibration energy along the shaft system are obtained again, and the vibration reduction effect before and after optimization is quantified through comparative calculations. Furthermore, existing methods rely heavily on empirical or simplified single-axis modal analysis, resulting in significant errors.

[0073] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method and apparatus for analyzing rock-breaking vibrations of a high-power cutterhead shaft system, characterized in that, include: Step 1: After equating the high-power cutter shaft system to a multi-degree-of-freedom rotor system and constructing the corresponding dynamic equations, establish a random vibration power spectral density mapping relationship based on the dynamic equations based on modal transformation and Wiener-Khinchin theorem. Step 2: Establish a three-dimensional model of the high-power cutter shaft system, mesh it, and apply bearing support and gearbox end constraint boundaries to obtain the finite element model of the high-power cutter shaft system, and set up monitoring nodes and local cylindrical coordinate system; Step 3: Considering the Coriolis effect, perform rotor dynamic modal analysis on the finite element model of the high-power auger shaft system to obtain the natural frequency, mode shape and critical speed of the high-power auger shaft system, and determine the risk of self-rotation resonance of the high-power auger shaft system. Step 4: Obtain the time history of the cutter load under rock breaking conditions, and use the modal superposition method to perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system. Calculate the displacement response power spectral density (PSD) of each monitoring node and obtain the vibration energy distribution diagram along the shaft. Step 5: Based on the input and output of random vibration spectrum analysis, determine resonance and identify the dominant direction and resonance frequency band at resonance. The high-power cutter shaft system resonates with the rock-breaking excitation during rock breaking. Based on the principle of avoiding the resonant frequency, the bearing support stiffness is adjusted, and the vibration reduction effect is recalculated and quantified for verification.

2. The method and apparatus for analyzing rock-breaking vibration of a high-power cutterhead shaft system according to claim 1, characterized in that, Step 1 specifically includes: 1.1 The high-power auger shaft system is equivalent to a multi-degree-of-freedom linear rotor system, and the dynamic equations are constructed. ,in: , , These are the mass, damping, and stiffness matrices of the high-power cutter shaft system, respectively. , , These are the displacement vector, velocity vector, and acceleration vector, respectively. The external random stimulus vector acting on the system; It is a time variable; 1.2 Based on modal analysis, the displacement vector in the dynamic equation is decoupled into several single-degree-of-freedom modal equations, specifically: ,in: Undamped mode matrix, The displacement vector in modal coordinates, i.e., the generalized coordinates after modal transformation, is decoupled into a series of modal coordinates when the proportional damping and modes are orthogonal. The single-degree-of-freedom modal equations are as follows: ,in: Let r be the generalized coordinates of the r-th modal. For the r-th mode generalized velocity, For the r-th mode generalized acceleration; , , , These are the natural frequency, damping ratio, modal mass, and modal generalized excitation force of the r-th mode, respectively. , Let r be the undamped mode shape vector. is the transpose of the r-th order undamped mode shape vector; 1.3 The frequency response functions of the high-power auger shaft system are obtained by Fourier transform, specifically including: ① Perform a Fourier transform on the single-degree-of-freedom modal equations to obtain the equations in the frequency domain. ,in: The imaginary unit, It is the angular frequency. Let r be the frequency domain complex amplitude of the generalized coordinates of the r-th mode. The frequency domain complex amplitude of the generalized excitation force of the r-th mode; ②The relationship between the response and the excitation in the r-th frequency domain The frequency response function of the r-th mode of the high-power auger shaft system was obtained. ; 1.

4. Based on the Wiener-Khinchin theorem, a conversion relationship between the autocorrelation function and power spectral density of random external excitation is established. The power spectral density function of each modal response is obtained by mapping the square of the frequency response function of each order mode to the power spectral density function of the excitation force of each order mode. Specifically, the power spectral density function of the response of the r-th order mode is... ,in: Let be the self-power spectral density function of the excitation force of the r-th modal, and be the external excitation power spectral density. , External excitation vector The autocorrelation matrix, The time-shifted excitation vector is the time-shifted vector. For delay parameters, For the transpose of the time-shifted excitation vector, The instantaneous load coupling matrix, The integral is half the duration; Let be the power spectral density matrix of the external excitation, i.e., the external excitation PSD; 1.5 Based on the modal superposition method, the total response power spectral density matrix of the high-power cutter shaft system in physical coordinates is obtained. ,in: To solve for the Nth order mode.

3. The method and apparatus for analyzing rock-breaking vibration of a high-power cutterhead shaft system according to claim 1, characterized in that, Step 2 specifically involves: establishing a three-dimensional model of the high-power auger shaft system and meshing it, applying bearing support and gearbox end constraints to obtain a finite element model. This finite element model is a three-dimensional model of the high-power auger shaft system after meshing, including a gearbox output shaft, several intermediate shafts, an auger shaft, an auger head, and several connecting flanges. It is subject to bearing support constraints and gearbox end constraints, and monitoring nodes and a local cylindrical coordinate system are set up. The aforementioned application of bearing support constraints refers to: applying bearing spring constraints to the three-dimensional model of the high-power auger shaft system based on the characteristics and positions of each bearing, that is, simplifying each bearing support into a linear spring-damped support to simulate the constraint of the bearing support on the high-power auger shaft system; The aforementioned application of gearbox end constraint means that only the degree of freedom of rotation about the axis at the gearbox position is released.

4. The method and apparatus for analyzing rock-breaking vibration of a high-power cutterhead shaft system according to claim 1, characterized in that, The aforementioned risk assessment of self-rotation resonance is as follows: it is determined whether the operating speed of the high-power cutter shaft system under normal operating conditions is lower than the critical speed to eliminate the risk of self-rotation resonance. When the operating speed range is lower than 75% of the first-order critical speed, it is determined that the high-power cutter shaft system will not resonate due to its own rotation. When the critical speed falls within the operating speed range, it is determined that the high-power cutter shaft system may resonate due to its own rotation.

5. The method and apparatus for analyzing rock-breaking vibration of a high-power cutterhead shaft system according to claim 1, characterized in that, Step 4 specifically includes: 4.1 The time-domain load on the high-power cutter shaft system is decomposed along the four directions of X, Y, Z and torsion around the shaft to describe the rock-breaking vibration characteristics of the high-power cutter shaft system in each direction. 4.

2. Obtain the acceleration power spectral density (PSD) by Fourier transforming the time-domain load; 4.

3. Based on the acceleration PSD curves of each load, identify the main peak frequency band and peak frequency of each load. 4.4 Based on the theory of random vibration, the acceleration PSD of the load in each direction is used as the input load and applied to the cutter head. The modal superposition method is used to perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system. The displacement response PSD of each monitoring node along the shaft is obtained by solving the problem. The vibration energy distribution diagram along the shaft is obtained by organizing the data. That is, the displacement response PSD of each monitoring node along the shaft is read and drawn into a three-dimensional diagram that can intuitively represent the distribution of vibration energy along the shaft.

6. The method and apparatus for analyzing rock-breaking vibration of a high-power cutterhead shaft system according to claim 1, characterized in that, The resonance determination refers to determining whether the high-power cutter shaft system resonates with the load experienced during rock excavation. Specifically: when the input external excitation PSD is a broadband spectrum, but the output response PSD shows a distinct sharp narrow band peak, it is determined that the high-power cutter shaft system resonates with the rock-breaking excitation during rock breaking; when the input external excitation PSD is a narrow band spectrum, and its narrow band center frequency and bandwidth are basically consistent with the narrow band center frequency and bandwidth of the output response PSD, and the amplitude is not significantly amplified, i.e., close to 1 time, it is more likely a characteristic of the excitation itself and should not be determined as the high-power cutter shaft system resonating with the rock-breaking excitation during rock breaking; when the narrow band peak of the output response PSD has a significant frequency shift or narrower bandwidth relative to the input external excitation PSD, or the amplitude is amplified sharply, i.e., several times or even tens of times, it is determined that the high-power cutter shaft system resonates with the rock-breaking excitation during rock breaking.

7. The method and apparatus for analyzing rock-breaking vibration of a high-power cutterhead shaft system according to claim 1, characterized in that, The identification of the dominant direction of resonance refers to the following: when resonance occurs in only one direction and not in other directions, the direction in which resonance occurs is determined to be the dominant direction of resonance. Then, the resonance frequency band is determined and recorded based on the PSD response of the dominant direction of resonance.

8. A high-power cutter shaft system rock-breaking vibration analysis device for implementing the method of any one of claims 1-7, characterized in that, include: The system comprises four modules: dynamic modeling, finite element modeling, modal analysis, random vibration analysis, resonance determination, and vibration reduction optimization. Specifically: the dynamic modeling module equates the high-power cutter shaft system to a multi-degree-of-freedom rotor system, constructs dynamic equations, and establishes a random vibration power spectral density mapping relationship; the finite element modeling module establishes a finite element model of the high-power cutter shaft system and sets up monitoring nodes and a local cylindrical coordinate system; the modal analysis module considers the Coriolis effect and performs rotor dynamic modal analysis on the finite element model of the high-power cutter shaft system, obtaining the natural frequencies, mode shapes, and critical speeds of the high-power cutter shaft system, and determining the risk of rotational resonance; the random vibration analysis module obtains the vibration characteristics under rock-breaking conditions. For the cutter load time history, the modal superposition method was used to perform random vibration spectrum analysis on the finite element model of the high-power cutter shaft system, calculate the displacement response power spectral density (PSD) of each monitoring node, and obtain the vibration energy distribution map along the shaft. The resonance determination module performed resonance determination based on the input and output of the random vibration spectrum analysis, identified the dominant direction of resonance, and recorded the resonance frequency band. The vibration reduction optimization module, based on the principle of avoiding resonance frequencies, adjusted the size of the high-power cutter shaft system, bearing support position, bearing support stiffness, etc., to make the natural frequency of the high-power cutter shaft system far away from the main peak frequency range of the external excitation load, and re-performed rotor dynamic modal analysis and random vibration spectrum analysis, and quantitatively verified the vibration reduction effect.

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