Method for characterizing low-frequency mechanical vibration frequency of large-scale rotating mineral processing equipment

Abstract

A method for characterizing a low-frequency mechanical vibration frequency of large-scale rotating mineral processing equipment, relating to the interdisciplinary field of mineral processing and mechanical vibration engineering, capable of characterizing vibration frequencies of large-scale rotating mineral processing equipment. The method comprises: representing kinetic energy and potential energy of large-scale rotating mineral processing equipment as functions of generalized coordinates and their time derivatives, and constructing a Lagrange's equation; simplifying, modifying and optimizing the Lagrange's equation to obtain a motion equation of a drum of the large-scale rotating mineral processing equipment; performing theoretical derivation on the basis of a generalized coordinate system, so that measurement of mechanical vibration characteristics of the large-scale rotating mineral processing equipment can be implemented by means of measurement of displacement, velocity, and acceleration signals, and finally a mechanical vibration power spectrum amplitude and a mechanical vibration frequency are measured; deriving a rotating speed of the large-scale rotating mineral processing equipment on the basis of working characteristics and drum parameters of the large-scale rotating mineral processing equipment, and obtaining a critical rotating speed of the large-scale rotating mineral processing equipment; and on the basis of a physical relationship between the mechanical vibration frequency and the critical rotating speed of the large-scale rotating mineral processing equipment, obtaining an association between a primary mechanical vibration frequency and the critical rotating speed of the large-scale rotating mineral processing equipment.

Description

A method for characterizing low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment

[0001] This application claims priority to a Chinese patent application filed with the Patent Office of China on March 27, 2024, with application number 202410355014.9 and invention name “A method for characterizing low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment”, the entire contents of which are incorporated herein by reference. Technical Field

[0002] The present application relates to the interdisciplinary field of mineral processing and mechanical vibration engineering, and in particular to a method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment. Background Art

[0003] In recent years, the metal mining industry has made great progress in deep mining, green mining, and in-situ mining. As a new technology for the development of non-ferrous metal mines, the integrated underground mining, dressing and filling technology of metal mines is to arrange the mine waste rock lifting, waste rock transportation, ore crushing, ore dressing and processing, filling and auxiliary production facilities in the strata adjacent to the ore body, and carry out systematic, intensive and in-situ development of mineral resources, which can effectively take into account the economic and environmental balance of metal mineral resource development.

[0004] Low-frequency vibration typically refers to vibrations with frequencies ranging from a few hertz to tens of hertz. This type of vibration has a longer wavelength and can generate large stress waves in the rock. High-frequency vibration typically refers to vibrations with frequencies ranging from hundreds of hertz to a few thousand hertz, and has a shorter wavelength. Because the rock surrounding a cavern has high stiffness and strength, low-frequency vibration can generate large stress waves in the rock, potentially causing damage and deformation, increasing the risk of loosening, cracking, and collapse of the rock formations. In severe cases, it can even lead to the collapse of the cavern structure. Low-frequency vibration has a more significant impact on the rock surrounding a cavern than high-frequency vibration.

[0005] Based on this, how to develop a method to characterize low-frequency mechanical vibration frequency and provide accurate vibration frequency parameters for the stability research of underground mineral processing plant chambers is a technical problem that technicians in this field urgently need to solve. Summary of the Invention

[0006] In view of this, the purpose of this application is to overcome the shortcomings of the existing technology and provide a low-frequency mechanical vibration frequency characterization method for large-scale mineral processing rotating equipment, which can characterize the vibration frequency of large-scale mineral processing rotating equipment and provide accurate vibration frequency parameters for the stability study of underground mineral processing plant chambers.

[0007] This application provides the following technical solutions:

[0008] A method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment is provided, comprising:

[0009] Based on the principle of conservation of energy and the principle of least action, the kinetic energy and potential energy of large-scale mineral processing rotating equipment are represented as functions of the generalized coordinates of the Lagrangian equation of motion and their time derivatives, and the Lagrangian equation is constructed.

[0010] The Lagrange equations were simplified, modified and optimized to obtain the cylinder motion equations of large-scale mineral processing rotary equipment;

[0011] Based on the theoretical derivation of the cylinder motion equation, the mechanical vibration characteristics of the large-scale mineral processing rotating equipment are measured by obtaining the measured displacement, velocity and acceleration signals. The mechanical vibration characteristics include mechanical vibration frequency and vibration amplitude. In particular, based on the working characteristics of the large-scale mineral processing rotating equipment, the mechanical vibration frequency includes low-frequency vibration frequency.

[0012] Based on the working principle of large-scale mineral processing rotary equipment, the speed of large-scale mineral processing rotary equipment is deduced through the cylinder diameter of large-scale mineral processing rotary equipment to obtain the critical speed of large-scale mineral processing rotary equipment;

[0013] According to the physical relationship between the mechanical vibration frequency and the critical speed of the large-scale mineral processing rotating equipment, the correlation relationship between the low-frequency vibration frequency and the critical speed of the large-scale mineral processing rotating equipment is obtained.

[0014] Furthermore, the given parameters include motor power MP, cylinder diameter D, cylinder length L, cylinder mass M, cylinder processing capacity SAGC, cylinder nameplate processing capacity NC and cylinder rotation speed Ω.

[0015] Furthermore, the rotation speed of the cylinder of the large-scale mineral processing rotary equipment is represented by the angular velocity ω. Since there is energy loss in the grinding process of the large-scale mineral processing rotary equipment, the rotation speed of the cylinder is converted into the damping Z of the cylinder. In addition, the cylinder has the feeding and discharging functions during the grinding process. The generalized coordinates of the feeding and discharging of the cylinder are introduced, and the Lagrangian of the large-scale mineral processing rotary equipment is: V=V0-Zω 2 +U(q)

[0016] in, is the Lagrangian, T is the kinetic energy of the large-scale mineral processing rotating equipment, and V is the potential energy of the large-scale mineral processing rotating equipment;

[0017] The kinetic energy of large-scale mineral processing rotating equipment is:

[0018] Where J is the moment of inertia of the cylinder of large-scale mineral processing rotating equipment;

[0019] The potential energy of large-scale mineral processing rotating equipment is: V=V0-Zω 2 +U(q)

[0020] Among them, V0 is the basic potential energy of the large-scale mineral processing rotating equipment, Z is the rotational damping of the large-scale mineral processing rotating equipment, and U(q) is the potential energy of the remaining systems of the large-scale mineral processing rotating equipment.

[0021] Furthermore, the Lagrange equation is simplified, corrected and optimized to obtain the motion equation of the cylinder of the large-scale mineral processing rotary equipment, including:

[0022] Among them, Q i is the generalized force of the external force on the generalized coordinates of the large-scale mineral processing rotating equipment system, F ij is the external force, r j is the position vector;

[0023] Based on the normal working conditions of large-scale mineral processing rotary equipment and the conditions of uniform material, the position vector changes of the feeding and discharging of large-scale mineral processing rotary equipment are very small, that is:

[0024] Therefore, the motion equation of the cylinder can be simplified as:

[0025] Furthermore, under normal working conditions of large-scale mineral processing rotary equipment, assuming that the distribution state of the material inside the cylinder is uniform, that is, the density distribution of the material inside the cylinder is uniform, the distribution state of the material inside the cylinder will not change with the rotation of the cylinder, that is:

[0026] And the driving force F of the motor m is a constant, and is brought into the equation of motion of the cylinder, and the solution is: ω(t)=A·e rt

[0027] By shifting and simplifying the above formula, the expression for r is:

[0028] After corresponding analysis, we concluded that:

[0029] Further calculations give the general solution of ω(t):

[0030] Solve for the unknown constants C1 and C2, set the initial angular velocity of the cylinder to ω(0) = ω0, the angular displacement of the cylinder to θ(0) = θ0, and substitute the initial conditions into the general solution ω(t), considering Solving using the Newton-Leibniz formula, we finally get:

[0031] By solving the linear equations, we get:

[0032] Among them, the linear equations related to the unknown constants C1 and C2 can obtain the complete analytical solution of ω(t):

[0033] Furthermore, the mechanical vibration ω(t) i Considering the large-scale mineral processing rotating equipment as a black box entity with mass, damping and elastic parameter characteristics, the mechanical vibration in the rotating coordinate system of the large-scale mineral processing rotating equipment, which is the interaction between the external force, system damping and system rotational inertia, is converted into the mechanical vibration in the Cartesian coordinate system, then:

[0034] Among them, M is the mass matrix of the large-scale mineral processing rotating equipment system, C is the damping matrix of the large-scale mineral processing rotating equipment system, K is the elastic matrix of the large-scale mineral processing rotating equipment system, F is the external force matrix of the large-scale mineral processing rotating equipment system, x j 、 The displacement vector, velocity vector and acceleration vector of the mechanical vibration of the large-scale mineral processing rotating equipment system are obtained by measuring the displacement x of each component. j (t), speed and acceleration To determine, we have: x j (t) = A j sin(2πft+Φ j )

[0035] Among them, A represents the maximum amplitude of mechanical vibration, f represents the mechanical vibration frequency, and Φ represents the initial phase angle; the mechanical vibration characteristics of large-scale mineral processing rotating equipment are measured and extracted and converted into f and A values.

[0036] Furthermore, the critical angular velocity of the cylinder of large-scale mineral processing rotating equipment is derived based on the balance relationship between centrifugal force and gravity;

[0037] The balance between centrifugal force and gravity:

[0038] Among them, m mat For the cylinder material quality of large-scale mineral processing rotating equipment, lim is the critical angular velocity of the cylinder of the large-scale mineral processing rotary equipment, g is the acceleration of gravity, and D is the diameter of the cylinder of the large-scale mineral processing rotary equipment;

[0039] Large mineral processing rotary equipment cylinder speed ω lim for:

[0040] Large mineral processing rotary equipment cylinder speed Ω cs for:

[0041] The critical angular velocity ω of large-scale mineral processing rotating equipment lim Substitute Ω cs , the relationship between the critical speed of large-scale mineral processing rotating equipment and the cylinder diameter is obtained:

[0042] Taking into account that the actual operating speed is usually set between 70% and 80% of the critical speed, the operating speed of large-scale mineral processing rotating equipment is obtained:

[0043] The embodiments of the present application have the following advantages:

[0044] By adopting the low-frequency mechanical vibration frequency characterization method of large-scale mineral processing rotating equipment provided in this application, the measurement of the mechanical vibration characteristics of the mining equipment can be converted into the measurement of the displacement, velocity and acceleration of each component, and finally into the measurement of the maximum mechanical vibration amplitude A and the mechanical vibration frequency f. The maximum mechanical vibration amplitude A and the mechanical vibration frequency f are calculated by given parameters, and then the critical speed of the large-scale mineral processing rotating equipment is obtained, so as to obtain the relationship between the low-frequency vibration frequency and the critical speed of the large-scale mineral processing rotating equipment, thereby controlling the operating state of the large-scale mineral processing rotating equipment and providing accurate vibration frequency parameters for the stability research of the underground mineral processing plant chamber.

[0045] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings.

[0046] Figures in the specification

[0047] FIG1 shows a flow chart of a method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment;

[0048] FIG2 shows a flow chart of a method for characterizing short-term wave height distribution of large-scale mineral processing rotating equipment based on spectral width;

[0049] Figure 3 shows a schematic diagram of the mechanical vibration speed signal of a large-scale mineral processing rotating equipment;

[0050] FIG4 is a schematic diagram showing acceleration signals of the mechanical vibration frequency of the large-scale mineral processing rotating equipment in the X, Y, and Z directions provided in Example 1;

[0051] FIG5 is a schematic diagram showing an acceleration signal in the X direction of the mechanical vibration frequency of a large-scale mineral processing rotating equipment provided in Example 1;

[0052] FIG6 is a schematic diagram showing an acceleration signal in the Y direction of the mechanical vibration frequency of a large-scale mineral processing rotating equipment provided in Example 2;

[0053] FIG7 is a schematic diagram showing the acceleration signal in the Z direction of the mechanical vibration frequency of the large-scale mineral processing rotating equipment provided in the third embodiment. DETAILED DESCRIPTION

[0054] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application.

[0055] As shown in Figures 1 and 2, in order to solve the above technical problems, a method for characterizing low-frequency mechanical vibration of mineral processing rotating equipment includes the following steps:

[0056] S100. Based on the principle of conservation of energy and the principle of least action, the kinetic energy and potential energy of large-scale mineral processing rotating equipment are represented as functions of generalized coordinates and their time derivatives, and the Lagrangian equation is constructed.

[0057] S200. Simplify, modify and optimize the Lagrangian equation to obtain the cylinder motion equation of large-scale mineral processing rotating equipment.

[0058] S300. Based on the generalized coordinate system of the Lagrange equation and the cylinder motion equation, theoretical derivation is performed so that the measurement of the mechanical vibration characteristics of the large-scale mineral processing rotating equipment is obtained through the measured displacement, velocity and acceleration signals. The mechanical vibration characteristics include mechanical vibration frequency and vibration amplitude; wherein, based on the working characteristics of the large-scale mineral processing rotating equipment, the mechanical vibration frequency includes low-frequency vibration frequency.

[0059] S400. Based on the working principle of the large-scale mineral processing rotating equipment, the rotation speed of the large-scale mineral processing rotating equipment is deduced through the cylinder diameter of the large-scale mineral processing rotating equipment to obtain the critical rotation speed of the large-scale mineral processing rotating equipment.

[0060] S500. According to the physical relationship between the mechanical vibration frequency and the critical speed of the large-scale mineral processing rotating equipment, obtain the correlation relationship between the low-frequency vibration frequency and the critical speed of the large-scale mineral processing rotating equipment.

[0061] S600. Determine the maximum amplitude of the mechanical vibration and the mechanical vibration frequency through the measured mechanical vibration data, and perform comparative analysis based on the corresponding relationship between the maximum amplitude of the mechanical vibration power spectrum distribution and the mechanical vibration frequency to verify the derived mechanical vibration frequency characterization method.

[0062] In this embodiment, taking the semi-autogenous mill drum as an example, after the amplitude and vibration frequency expressions are derived, the rotation frequency of the semi-autogenous mill drum is measured, and the obtained frequency is cross-validated with the derived formula.

[0063] The Lagrange equation of motion is used to explore the influence of various factors on the vibration signals of large rotating machinery and equipment, and to determine the factors that lead to the complexity and diversity of the signals.

[0064] Specifically, the influencing factors include the damping Z of the large-scale mineral processing rotating equipment, the moment of inertia J of the large-scale mineral processing rotating equipment cylinder, the average density ρ of the large-scale mineral processing rotating equipment cylinder material, and the volume V of the large-scale mineral processing rotating equipment cylinder material. mat , cylinder diameter D of large-scale mineral processing rotating equipment, initial angular velocity ω0, and angular displacement θ0.

[0065] Specifically, the cylinder parameters include the damping Z of the large-scale mineral processing rotary equipment, the moment of inertia J of the large-scale mineral processing rotary equipment cylinder, the average density ρ of the large-scale mineral processing rotary equipment cylinder material, and the volume V of the large-scale mineral processing rotary equipment cylinder material. mat , the diameter D of the cylinder of the large-scale mineral processing rotary equipment, the initial angular velocity ω0, and the angular displacement θ0. This is equivalent to deriving the rotation speed of the large-scale mineral processing rotary equipment through the influencing factors of the large-scale mineral processing rotary equipment in S500 to obtain the critical rotation speed of the large-scale mineral processing rotary equipment.

[0066] The large-scale mineral processing rotating equipment system meets the requirements of a complete system. Based on the principle of conservation of energy and the principle of least action, the kinetic energy and potential energy of the system are expressed as functions of generalized coordinates and their time derivatives.

[0067] Specifically, construct its Lagrangian equation, which can be expressed as: in is the Lagrangian, q=(q1,q2,…,q N ) is a generalized coordinate, a function of time t, is the generalized velocity, represents the time derivative, represents partial differential.

[0068] Large-scale mineral processing rotating equipment is a system with multiple degrees of freedom. The rotation of the cylinder of large-scale mineral processing rotating equipment is the main movement of the system, which is expressed by angular velocity ω. Taking into account the energy loss in the grinding process, the rotation speed of the cylinder of large-scale mineral processing rotating equipment is corresponded to a damping. At the same time, considering the feeding and discharging effects in the grinding process, the generalized coordinates of feeding and discharging are introduced.

[0069] Specifically, the Lagrange equation of large-scale mineral processing rotating equipment is further listed as follows: in, is the Lagrangian, T is the kinetic energy of the large-scale mineral processing rotating equipment system, and V is the potential energy of the large-scale mineral processing rotating equipment system; J is the moment of inertia of the cylinder of large-scale mineral processing rotating equipment, V=V0-Zω 2+U(q), where V0 is the basic potential energy of the large-scale mineral processing rotating equipment system, Z is the damping of the large-scale mineral processing rotating equipment cylinder, and U(q) is the potential energy of the remaining systems of the large-scale mineral processing rotating equipment.

[0070] Specifically, according to the principle of least action, the motion equation of large-scale mineral processing rotating equipment is obtained, which is expressed as where Q i It is the generalized force of external force on the generalized coordinates of large-scale mineral processing rotating equipment system, which can be expressed as Among them, F ij is the external force, r j is the position vector.

[0071] Specifically, the motion equation of large-scale mineral processing rotating equipment can be expressed as: in, Expressed as the second and first order time derivatives of angular velocity, F m Expressed as motor driving force, F in Expressed as feed force; F out Expressed as the discharge force, r m Expressed as the cylinder position vector, r in Expressed as the feed position vector, r out Expressed as the discharge position vector.

[0072] Specifically, in order to simplify the complex nonlinear system motion solution problem of large-scale mineral processing rotating equipment, based on the assumption of normal working conditions and uniform materials of large-scale mineral processing rotating equipment, the position vector changes of feeding and discharging are very small, that is: The simplified equation of motion is obtained:

[0073] Under normal working conditions of large-scale mineral processing rotary equipment, it is assumed that the distribution state of the material inside the cylinder is uniform, that is, the density distribution of the material inside the cylinder is uniform, and the distribution state of the material inside the cylinder will not change with the rotation of the cylinder, that is, In addition, assuming that the driving force F of the motor m is a constant.

[0074] Specifically, substituting these assumptions into the simplified equation of motion, we can obtain:

[0075] Specifically, let the solution be ω(t) = A·e rt , substituting into the equation we get: Transpose and simplify to get: Solve for the expression of r:

[0076] Specifically, when When r1 and r2 are both real numbers, and r1>r2, the root of the equation is a real number. There are two different solutions, corresponding to the two vibration modes. Its physical meaning is the speed response of large-scale mineral processing rotating equipment under different vibration states. At this time, the vibration of the system is stable and can vibrate at a stable frequency. When large-scale mineral processing rotating equipment is working, when the speed changes slightly, the system may stabilize and vibrate at a specific frequency, which is determined by r1 and r2; when When r1 and r2 are both imaginary numbers, the vibration of the system is unstable. The system may not be able to vibrate stably at a specific frequency, but enter an unstable state. Therefore, the solution is: Where r1 and r2 are the two solutions of the above quadratic equation; C1 and C2 are unknown constants.

[0077] For large-scale mineral processing rotating equipment systems, according to their working characteristics and system parameters, the non-inertia moment of the material in the cylinder Among them, ρ is the average density of the material in the cylinder of the large-scale mineral processing rotary equipment, g is the acceleration of gravity, V mat is the volume of the material in the cylinder of the large-scale mineral processing rotary equipment, and D is the diameter of the cylinder of the large-scale mineral processing rotary equipment.

[0078] Specifically, we can get the expression of r:

[0079] Specifically, we can get the general solution of ω(t):

[0080] Solve for the unknown constants C1 and C2:

[0081] Specifically, assuming that the initial angular velocity is ω(0) = ω0 and the angular displacement is θ(0) = θ0, substituting the initial conditions into the general solution, we have: Taking into account The expansion is as follows:

[0082] Specifically, using the Newton-Leibniz formula to solve, we have:

[0083] From this we can get:

[0084] Specifically, by solving the linear equations, we can get:

[0085] The complete analytical solution of ω(t) can be obtained:

[0086] A further technical solution is to rewrite the mechanical vibration of large-scale mineral processing rotating equipment according to the mechanical vibration frequency range as follows: ω(t) i =ω(t) il +ω(t) im +ω(t) ih , where ω(t) il Represents mechanical vibration associated with low-frequency vibration (grinding noise, below 100 Hz), ω(t) im +ω(t) ih Indicates mechanical vibration associated with high-frequency vibration (above 100 Hz).

[0087] Specific, The first solution r1 corresponds to the balanced rotational vibration, which is usually characterized by a relatively slow motion state and a low vibration frequency. The angular velocity ω of large-scale mineral processing rotating equipment changes relatively little and changes slowly over time, belonging to the category of low-frequency mechanical vibration. The second solution r2 corresponds to the unbalanced rotational vibration, which is usually characterized by a relatively fast motion state change and a high vibration frequency, belonging to the category of medium- and high-frequency mechanical vibration. Then:

[0088] Considering that the cylinder of large-scale mineral processing rotary equipment is the most massive rotating working component, its moment of inertia and vibration energy are also the largest. Due to the connection between the cylinder and other components (such as supports and transmission devices), the vibration generated by the rotation of large-scale mineral processing rotary equipment can be transmitted to the entire equipment, becoming the main vibration component. In view of this, this application focuses on the low-frequency mechanical vibration of large-scale mineral processing rotary equipment.

[0089] Specifically, based on the generalized coordinate system of the Lagrangian motion equation of large-scale mineral processing rotating equipment, combined with the formula ω(t) i =ω(t) il +ω(t) im +ω(t) ih According to the principle of unified mechanical vibration frequency and unified degree of freedom, the large-scale mineral processing rotating equipment is regarded as a black box entity with mass, damping and elastic parameter characteristics. The mechanical vibration in the rotating coordinate system of the large-scale mineral processing rotating equipment, which is the interaction between the external force, system damping and system rotational inertia, is converted into the mechanical vibration in the Cartesian coordinate system. Then, we have: Where M is the mass matrix of the large-scale mineral processing rotating equipment system, C is the damping matrix of the large-scale mineral processing rotating equipment system, K is the elastic matrix of the large-scale mineral processing rotating equipment system, F is the external force matrix of the large-scale mineral processing rotating equipment system, x j 、 It is the mechanical vibration displacement vector, velocity vector and acceleration vector of the large-scale mineral processing rotating equipment system.

[0090] Specifically, the mechanical vibration characteristics of large-scale mineral processing rotating equipment can be determined by measuring the displacement, velocity and acceleration of each component, then: j (t) = A j sin(2πft+Φ j ), Where A represents the maximum amplitude of the mechanical vibration, f represents the mechanical vibration frequency, and Φ represents the initial phase angle.

[0091] Specifically, from the above analysis, it can be seen that the measurement and extraction of mechanical vibration characteristics of large-scale mineral processing rotating equipment are converted into the determination of f and A values.

[0092] Derivation of critical speed of large-scale mineral processing rotating equipment.

[0093] Specifically, based on the working principle of large-scale mineral processing rotary equipment, the critical speed is one of the most critical parameters of large-scale mineral processing rotary equipment. The critical speed refers to the ore and grinding balls in the mill cylinder being lifted up and rotating close to the inner wall of the cylinder when the cylinder rotates without sliding down. The balance relationship between centrifugal force and gravity can be expressed by the following formula: where m mat The material quality of the cylinder of large-scale mineral processing rotating equipment, ω lim is the critical angular velocity of the cylinder of large-scale mineral processing rotating equipment, g is the acceleration of gravity, and D is the diameter of the cylinder of large-scale mineral processing rotating equipment.

[0094] Specifically, the critical angular velocity of the cylinder of the large-scale mineral processing rotating equipment is obtained as follows:

[0095] Specifically, the critical angular velocity of large-scale mineral processing rotating equipment Substitution Obtain the relationship between the critical speed and cylinder diameter of large-scale mineral processing rotating equipment Considering that the actual working speed is usually set between 70% and 80% of the critical speed to ensure the high-speed operation of the mill and prevent equipment wear and safety problems caused by over-speed rotation, the reasonable speed (working speed) Ω of large-scale mineral processing rotating equipment is obtained. app :

[0096] Analyze the correlation between low-frequency vibration frequency and critical speed of large-scale mineral processing rotating equipment.

[0097] Specifically, based on the generalized coordinate system of the Lagrangian motion equation of large-scale mineral processing rotating equipment, combined with According to the principle of unified mechanical vibration frequency and unified simplification of machine freedom, large-scale mineral processing rotating equipment can be regarded as a black box entity with mass, damping and elastic parameter characteristics.

[0098] Specifically, under the normal working condition of the large-scale mineral processing rotary equipment, it is further assumed that the distribution state of the material inside the cylinder is uniform, that is, the density distribution of the material inside the cylinder is uniform, and the distribution state of the material inside the cylinder does not change with the rotation of the cylinder, that is:

[0099] Based on the above assumptions, the rotation speed of the cylinder is at the working speed, and the low-frequency vibration frequency of the large-scale mineral processing rotating equipment is linear with the critical speed, then:

[0100] Among them, f l is the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment, k and j are the slope and intercept of the linear model. This model assumes that the low-frequency vibration frequency is proportional to the critical speed, and the proportional constant k and offset j are determined by experimental data.

[0101] For example, in order to effectively carry out the mechanical vibration collection work of large-scale mineral processing rotating equipment, a stable and accurate measurement system is established, and research on the vibration signal feature extraction and reconstruction of large-scale mineral processing rotating equipment is carried out. A signal collection system centered on speed and acceleration sensors is used, and a semi-autogenous grinding mill in South Africa is selected as the object of mechanical vibration signal collection for vibration signal collection.

[0102] Continuous signal acquisition was performed while the equipment was operating in a stable state. To ensure signal integrity and accuracy, the acquisition frequency of the mechanical vibration signal was determined to be 1000 Hz, as shown in Figure 3. The corresponding coordinates in Figure 3 represent time, signal segmentation display, and mechanical vibration velocity signals, respectively. Figure 3 clearly shows that sampling at a frequency of 1000 Hz fully captures the main components of the mechanical vibration. The stability of the fundamental frequency is clearly visible, reflecting the overall rotational state. More importantly, the appearance of high-frequency components and impact waveforms is clearly related to the impact and collision of internal grinding media (such as steel balls or ore) with the mill cylinder. This impact characteristic is the core of the mill grinding process, and its intensity and frequency are likely related to the hardness, particle size, and mill fill rate of the material.

[0103] Although no distinct sideband frequencies are observed in the waveform in Figure 3, the presence of harmonics and sideband frequencies may indicate potential mechanical failures in rotating equipment. Specifically, certain patterns in the sideband frequencies may be early signs of wear or minor damage that may not be readily apparent but can be diagnosed through vibration analysis. Furthermore, the manifestation of nonlinear effects may be related to the dynamic response of the rotating equipment and changes in material loading. When material is ground and crushed, the load on the rotating equipment changes, potentially altering the dynamic balance of the cylinder and causing harmonics or modulation in the vibration waveform.

[0104] A cDAQ-9171 eight-channel data acquisition card is used for signal amplification, conversion and storage. The resulting mechanical vibration signal is converted into a power spectrum through Fourier transform, as shown in Figures 4, 5, 6 and 7. In Figures 4 to 7, the corresponding coordinates represent time, frequency and power spectrum, respectively. The figures show that the power spectrum values ​​are high at 0.5, 1 and 4 times the frequency, which is consistent with the constructed frequency characterization method, proving that the method of this application is correct.

[0105] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person skilled in the art may make various modifications and improvements without departing from the scope of the present application, and such modifications and improvements are all within the scope of protection of the present application.

Claims

1. A method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment, characterized in that: include: Based on the principle of conservation of energy and the principle of least action, the kinetic energy and potential energy of large-scale mineral processing rotating equipment are represented as functions of generalized coordinates and their time derivatives, and the Lagrange equation is constructed. The Lagrange equations were simplified, modified and optimized to obtain the cylinder motion equations of large-scale mineral processing rotary equipment; Based on the theoretical derivation of the cylinder motion equation, the mechanical vibration characteristics of the large-scale mineral processing rotating equipment are measured by obtaining the measured displacement, velocity and acceleration signals. The mechanical vibration characteristics include mechanical vibration frequency and vibration amplitude. In particular, based on the working characteristics of the large-scale mineral processing rotating equipment, the mechanical vibration frequency includes low-frequency vibration frequency. Based on the working principle of large-scale mineral processing rotary equipment, the speed of large-scale mineral processing rotary equipment is deduced through the cylinder diameter of large-scale mineral processing rotary equipment to obtain the critical speed of large-scale mineral processing rotary equipment; According to the physical relationship between the mechanical vibration frequency and the critical speed of the large-scale mineral processing rotating equipment, the correlation relationship between the low-frequency vibration frequency and the critical speed of the large-scale mineral processing rotating equipment is obtained.

2. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 1 is characterized in that: The Lagrange equation is: in, is the Lagrangian, q=(q1,q2,…,q N ) is a generalized coordinate, a function of time t, is the generalized velocity.

3. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 2 is characterized in that: The rotation speed of the cylinder of large-scale mineral processing rotary equipment is represented by angular velocity ω. Since there is energy loss in the grinding process of large-scale mineral processing rotary equipment, the rotation speed of the cylinder is converted into the damping Z of the cylinder. In addition, the cylinder has feeding and discharging functions during the grinding process. The generalized coordinates of the feeding and discharging of the cylinder are introduced, and the Lagrangian of the large-scale mineral processing rotary equipment is: V=V0-Zω 2 +U(q) in, is the Lagrangian, T is the kinetic energy of the large-scale mineral processing rotating equipment, and V is the potential energy of the large-scale mineral processing rotating equipment; The kinetic energy of large-scale mineral processing rotating equipment is: Where J is the moment of inertia of the cylinder of large-scale mineral processing rotating equipment; The potential energy of large-scale mineral processing rotating equipment is: V=V0-Zω 2 +U(q) Among them, V0 is the basic potential energy of the large-scale mineral processing rotating equipment, Z is the rotational damping of the large-scale mineral processing rotating equipment, and U(q) is the potential energy of the remaining systems of the large-scale mineral processing rotating equipment.

4. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 3 is characterized in that: The Lagrange equation is simplified, corrected and optimized to obtain the motion equation of the cylinder of large-scale mineral processing rotary equipment, including: Among them, Q i is the generalized force of the external force on the generalized coordinates of the large-scale mineral processing rotating equipment system, F ij is the external force, r j is the position vector; Based on the normal working conditions of large-scale mineral processing rotary equipment and the conditions of uniform material, the position vector changes of the feeding and discharging of large-scale mineral processing rotary equipment are very small, that is: Therefore, the motion equation of the cylinder can be simplified as:

5. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 4 is characterized in that: Under normal working conditions of large-scale mineral processing rotary equipment, it is assumed that the distribution state of the material inside the cylinder is uniform, that is, the density distribution of the material inside the cylinder is uniform, and the distribution state of the material inside the cylinder will not change with the rotation of the cylinder, that is: And the driving force F of the motor m is a constant and is substituted into the equation of motion of the cylinder, and the solution is: ω(t)=A·e rt By shifting and simplifying the above formula, the expression for r is: After corresponding analysis, we concluded that: Further calculations give the general solution of ω(t): Solve for the unknown constants C1 and C2, set the initial angular velocity of the cylinder to ω(0) = ω0, the angular displacement of the cylinder to θ(0) = θ0, and substitute the initial conditions into the general solution ω(t), considering Solving using the Newton-Leibniz formula, we finally get: By solving the linear equations, we get: Among them, the linear equations related to the unknown constants C1 and C2 can obtain the complete analytical solution of ω(t):

6. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 5 is characterized in that: According to the mechanical vibration frequency range, the mechanical vibration of large-scale mineral processing rotating equipment is rewritten as: ω(t) i =ω(t) il +ω(t) im +ω(t) ih Where ω(t) il Indicates low-frequency vibration, which refers to mechanical vibration less than 100 Hz, ω(t) im +ω(t) ih Indicates medium and high frequency vibration, which means mechanical vibration above 100Hz; Mode: The equilibrium rotational vibration corresponding to the first solution r1 of the two solutions is usually characterized by a relatively slow motion state and a low vibration frequency. The change in the angular velocity ω of large-scale mineral processing rotating equipment is relatively small and changes relatively slowly over time, which belongs to the category of low-frequency mechanical vibration. The unbalanced rotational vibration corresponding to the second solution r2 is usually characterized by rapid changes in motion state and high vibration frequency, belonging to the category of medium and high frequency mechanical vibration. Then:

7. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 6 is characterized in that: The mechanical vibration ω(t) i Considering the large-scale mineral processing rotating equipment as a black box entity with mass, damping and elastic parameter characteristics, the mechanical vibration in the rotating coordinate system of the large-scale mineral processing rotating equipment, which is the interaction between the external force, system damping and system rotational inertia, is converted into the mechanical vibration in the Cartesian coordinate system, then: Among them, M is the mass matrix of the large-scale mineral processing rotating equipment system, C is the damping matrix of the large-scale mineral processing rotating equipment system, K is the elastic matrix of the large-scale mineral processing rotating equipment system, F is the external force matrix of the large-scale mineral processing rotating equipment system, x j 、 The displacement vector, velocity vector and acceleration vector of the mechanical vibration of the large-scale mineral processing rotating equipment system are obtained by measuring the displacement x of each component. j (t), speed and acceleration To confirm, we have: x j (t)=A j sin(2πft+Φ j ) Among them, A represents the maximum amplitude of mechanical vibration, f represents the mechanical vibration frequency, and Φ represents the initial phase angle; the mechanical vibration characteristics of large-scale mineral processing rotating equipment are measured and extracted and converted into f and A values.

8. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 1 is characterized in that: The critical angular velocity of the cylinder of large-scale mineral processing rotating equipment is derived based on the balance relationship between centrifugal force and gravity; The balance between centrifugal force and gravity: Among them, m mat The material quality of the cylinder of large-scale mineral processing rotating equipment, ω lim is the critical angular velocity of the cylinder of the large-scale mineral processing rotary equipment, g is the acceleration of gravity, and D is the diameter of the cylinder of the large-scale mineral processing rotary equipment; Rotational speed of the barrel of large-scale mineral processing rotary equipment lim for: Large mineral processing rotary equipment cylinder speed Ω cs for: The critical angular velocity ω of large-scale mineral processing rotating equipment lim Substitute Ω cs , the relationship between the critical speed of large-scale mineral processing rotating equipment and the cylinder diameter is obtained: Taking into account that the actual operating speed is set between 70% and 80% of the critical speed, the operating speed of large-scale mineral processing rotating equipment is obtained:

9. The method for characterizing the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment according to claim 8, characterized in that: The distribution state of the material inside the cylinder is uniform, that is, the density distribution of the material inside the cylinder is uniform, and the distribution state of the material inside the cylinder will not change with the rotation of the cylinder, that is: Among them, the rotation speed of the cylinder is at the working speed, and the low-frequency vibration frequency of the large-scale mineral processing rotating equipment is linear with the critical speed, then: Among them, f l is the low-frequency mechanical vibration frequency of large-scale mineral processing rotating equipment, k and j are the slope and intercept of the linear model. The low-frequency vibration frequency of this model is proportional to the critical speed. The proportional constant k and offset j are determined by experimental data.

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