CN118153227B - Simulation analysis method for vibration response of gear box - Google Patents
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Abstract
The invention provides a simulation analysis method of vibration response of a gear box, which relates to the technical field of vibration analysis of the gear box, and the invention establishes a high-precision digital model of the gear box according to the digital twin technology, generates an optimal external force vector for work, generates a second-order differential equation of vibration of each functional part of the gear box according to a quality matrix, a damping matrix and a rigidity matrix of the gear box, adopts sensors arranged on actual gear box parts to acquire data, and generating a functional vibration vector index according to the generated external force vector by combining a second-order differential equation of vibration of each functional part of the gear box, decomposing and superposing the external force vector of each functional part by using the functional vibration vector index, generating a comprehensive vibration vector index by combining the decomposed optimal external force vector of work, and reflecting the difference between the current working state and the optimal working state of the gear box on the whole by using the comprehensive vibration vector index.
Description
Technical Field
The invention relates to the technical field of gearbox vibration analysis, in particular to a gearbox vibration response simulation analysis method.
Background
In modern engineering, a gear box is used as an important mechanical transmission component, the reliability and performance of the gear box directly affect the working efficiency and the safety of the whole mechanical system, vibration problems are one of key factors affecting the performance of the gear box, and can cause additional stress, noise and even mechanical faults, and the vibration problems also affect the service life of the gear box, so that vibration response analysis of the gear box in the running process is important to predicting the reliability of the gear box, reducing the maintenance cost and improving the running efficiency.
The main evaluation factor of the vibration of the gear box is the external force vector born by the gear box, the external force vector refers to the mathematical expression of external force acting on the whole or parts of the gear box, the mathematical expression has two attributes of magnitude and direction, the direct causal relationship exists between the vibration of the gear box and the external force vector, the vibration of the gear box is the direct result of the external force vector acting on the mechanical structure, the magnitude, direction and action point of the force directly influence the vibration characteristic of the gear box, and the gear box can be designed and optimized through the causal relationship, thereby reducing unnecessary vibration, improving the mechanical efficiency and prolonging the service life.
In the prior art, the dynamic characteristics in a complex working environment cannot be accurately reflected mainly depending on the test result of a gear box prototype, or complex interaction in actual operation is ignored depending on a simplified gear box mathematical model, so that the defects of the prior art are overcome: whether the gearbox model or the simplified mathematical model of the gearbox is an output dynamic response of the gearbox, the external force vector of the whole gearbox and each part of the gearbox cannot be analyzed, the vibration of the gearbox cannot be analyzed fundamentally, the inaccuracy of analysis is caused, faults cannot be predicted effectively, further maintenance or adjustment cannot be performed timely, and the downtime and maintenance cost are increased.
Disclosure of Invention
The invention aims to provide a simulation analysis method for vibration response of a gear box, which aims to solve the problems in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a simulation analysis method for vibration response of a gear box comprises the following specific steps:
according to a design drawing of the gear box, using CAD software to create the geometric shape of each component of the gear box, assembling the components according to the design drawing to form a three-dimensional model of the gear box, importing the three-dimensional model into a digital twin platform, inputting structural parameters of each structure of the three-dimensional model, and generating the digital twin model of the gear box, wherein the structural parameters comprise material properties and geometric dimensions;
Dividing a digital twin model of the gear box into a plurality of functional parts according to the structure and the function, generating a mass matrix, a damping matrix and a rigidity matrix of the gear box according to the material attribute and the geometric dimension of each part, and generating a second-order differential equation of vibration of each functional part of the gear box according to the mass matrix, the damping matrix and the rigidity matrix of the gear box;
Setting a sensor at each functional part of an actual gear box, collecting displacement vectors, speed vectors and acceleration vectors of each functional part of the gear box, generating external force vectors of each functional part according to a second-order differential equation of vibration of each functional part, decomposing the external force vectors of each functional part, generating components in three directions of x, y and z in a Cartesian coordinate system, and superposing the components to generate comprehensive external force components of the functional part along the three directions of x, y and z;
generating an optimal external force vector of the work of the gear box according to a digital twin model of the gear box, decomposing the optimal external force vector, and generating components in three directions of x, y and z in a Cartesian coordinate system;
according to the external force vectors of all functional parts of the gear box, carrying out data analysis by combining preset vibration thresholds of the external force vectors of all functional parts to generate a functional vibration vector index, carrying out comprehensive analysis on comprehensive external force components of the functional parts along the x, y and z directions and components of the optimal external force vectors along the x, y and z directions to generate a comprehensive vibration vector index;
And generating a vibration evaluation index by integrating the vibration vector index and the functional vibration vector index, comparing the vibration evaluation index with a preset abnormal evaluation index threshold, and sending or not sending an early warning signal according to a comparison result.
Further, the material properties of each structure of the three-dimensional model comprise material density, elastic modulus, rigidity data and weight, the geometric dimensions of each structure of the three-dimensional model comprise shape dimension and installation position data, and the functional parts divided according to the digital twin model of the gear box comprise an input shaft part, an output shaft part, a gear set part and a shell bracket part.
Further, the mass matrix M of the generated gearbox is:
Wherein m 1、m2、m3 and m 4 represent the weights of the input shaft portion, the output shaft portion, the gear set portion, and the housing bracket portion, respectively;
the damping matrix C of the gear box is generated as follows:
Wherein c 1、c2、c3 and c 4 are damping coefficients of the input shaft portion, the output shaft portion, the gear set portion and the housing bracket portion, respectively;
the stiffness matrix K of the gearbox is generated as:
Where k 1、k2、k3 and k 4 are the local stiffness of the input shaft portion, the output shaft portion, the gear set portion and the housing carrier portion, respectively.
Further, the second order differential equation of the generated input shaft partial vibration is:
wherein FSR represents an external force vector of the input shaft portion, AndAn acceleration vector, a velocity vector, and a displacement vector, respectively, representing the input shaft portion;
The second differential equation of the generated output shaft partial vibration is:
wherein FSR represents an external force vector of the output shaft portion, AndRespectively representing an acceleration vector, a velocity vector and a displacement vector of the output shaft portion;
the second differential equation for the generated gear set partial vibrations is:
wherein FCL represents an external force vector of the gear set portion, AndRespectively representing an acceleration vector, a velocity vector and a displacement vector of the gear set part;
the second differential equation of the generated housing bracket part vibration is:
wherein FWK represents an external force vector of the housing bracket portion, AndThe acceleration vector, the velocity vector and the displacement vector of the housing bracket portion are represented, respectively.
Further, when external force vectors of all the functional parts are generated, acceleration vectors, speed vectors and displacement vectors corresponding to the input shaft part, the output shaft part, the gear set part and the shell support part are respectively acquired through sensors, and the external force vectors corresponding to the input shaft part, the output shaft part, the gear set part and the shell support part can be generated by combining weight data, damping coefficients and local rigidity data of the input shaft part, the output shaft part, the gear set part and the shell support part in a quality matrix M, a damping matrix C and a rigidity matrix K of the gear box and inputting the weight data, the damping coefficients and the local rigidity data into a second-order differential equation corresponding to the vibration of the functional parts.
Further, according to the external force vector of each functional part of the gear box, a specific calculation formula according to which the functional vibration vector index is generated is as follows:
CNzd＝α*e(|FSR|-FSRy)+β*e(|FSC|-FSCy)+γ*e(|FCL|-FCLy)+δ*e(|FWK|-FWKy)
Wherein GN zd represents a functional vibration vector index, FSRy, FSCy, FCLy and FWKy represent external force vector vibration thresholds of the input shaft portion, the output shaft portion, the gear train portion, and the housing bracket portion, respectively, α, β, γ, and δ represent an input shaft weight, an output shaft weight, a gear train weight, and a housing bracket weight, respectively, and α > β > γ > δ >0, α+β+γ+δ=1.
Further, when the external force vector is decomposed along three directions of x, y and z, the x direction is the axial direction of an input shaft of the gear box, the y direction is in a plane formed by the axial lines of the input shaft and an output shaft of the gear box, the y direction is vertical to the x direction, and the z direction is vertical to a plane formed by the y direction and the x direction;
When generating comprehensive external force components of the functional part along three directions of x, y and z, decomposing four external force vectors of an input shaft part external force vector FSR, an output shaft part external force vector FSC, a gear group part external force vector FCL and a shell support part external force vector FWK along the three directions of x, y and z, superposing vectors in each direction, respectively generating an x-direction comprehensive external force component, a y-direction comprehensive external force component and a z-direction comprehensive external force component, and respectively calibrating the four external force vectors as follows: zw x、Zwy and Zw z.
Further, the optimal external force vector is marked as Zj, and after the optimal external force vector is decomposed along the x, y and z directions, the components in the three directions are respectively marked as follows: zj x、Zjy and Zj z;
the specific formula according to which the integrated vibration vector index is generated is as follows:
wherein ZH zd represents the integrated vibration vector index;
the logic on which the vibration evaluation index is generated by integrating the vibration vector index and the functional vibration vector index is as follows:
Where ZH pg represents a vibration evaluation index, GN zd represents a functional vibration vector index, ε 1 and ε 2 represent a functional weight coefficient and a comprehensive weight coefficient, respectively, and ε 1>ε2 >1.
Further, when the vibration evaluation index is greater than or equal to a preset abnormality evaluation index threshold, an early warning signal is sent out when the vibration of the gear box is abnormal, and when the vibration evaluation index is smaller than the preset abnormality evaluation index threshold, the vibration of the gear box is in a normal range, and no early warning signal is sent out.
Compared with the prior art, the invention has the beneficial effects that:
According to the invention, a high-precision digital model of the gear box is established by utilizing a digital twin technology, an optimal external force vector for work is generated, a second differential equation of vibration of each functional part of the gear box is generated according to a quality matrix, a damping matrix and a rigidity matrix of the gear box, data are acquired by adopting sensors arranged on actual gear box parts, the second differential equation of vibration of each functional part of the gear box is combined, a functional vibration vector index is generated by combining the generated external force vectors, the vibration condition of each functional part of the gear box can be reflected by the functional vibration vector index, the external force vectors of each functional part are decomposed and overlapped, the combined optimal external force vector for work after decomposition is combined, a comprehensive vibration vector index is generated, and the difference between the current gear box working state and the optimal working state is reflected on the whole by the comprehensive vibration vector index;
In the invention, because the data are collected through the sensors arranged on the actual gear box components and the external force vectors are generated for decomposition, a dynamic and real-time monitoring and analyzing means is provided, the vibration characteristics under the actual working condition can be reflected more accurately, because the acceleration effect of the whole scheme is based on the data collected in real time rather than theoretical calculation or preset assumption, the accuracy and timeliness of analysis are obviously improved, the invention is not single analysis, the external force vectors and the whole external force vectors of all parts of the gear box are combined, the working state of the gear box is analyzed by adopting the components, the whole and the final fusion mode, the evaluation of the vibration of the gear box is closer to the actual working condition, and powerful data support is provided for maintenance and optimization,
Drawings
FIG. 1 is a schematic flow chart of the overall method of the present invention;
fig. 2 is a schematic view of the three directions x, y and z of the present invention.
In the figure: an input shaft portion 10, an output shaft portion 20, a gear set portion 30, and a housing bracket portion 40.
Detailed Description
The present invention will be further described in detail with reference to specific embodiments in order to make the objects, technical solutions and advantages of the present invention more apparent.
It is to be noted that unless otherwise defined, technical or scientific terms used herein should be taken in a general sense as understood by one of ordinary skill in the art to which the present invention belongs. The terms "first," "second," and the like, as used herein, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that elements or items preceding the word are included in the element or item listed after the word and equivalents thereof, but does not exclude other elements or items. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "up", "down", "left", "right" and the like are used only to indicate a relative positional relationship, and when the absolute position of the object to be described is changed, the relative positional relationship may be changed accordingly.
Examples:
referring to fig. 1-2, the present invention provides a technical solution:
a simulation analysis method for vibration response of a gear box comprises the following specific steps:
Step 1: according to a design drawing of the gearbox, CAD software is used for creating the geometric shape of each component of the gearbox, the components are assembled according to the design drawing to form a three-dimensional model of the gearbox, the three-dimensional model is imported into a digital twin platform, structural parameters of each structure of the three-dimensional model are input, and the digital twin model of the gearbox is generated, wherein the structural parameters comprise material properties and geometric dimensions.
In this embodiment, the design drawing of the gearbox includes detailed dimensions and assembly relationships of all components of the gearbox, in CAD software, three-dimensional geometric shapes of each individual component are created according to dimensional details on the drawing, and after modeling of all individual components is completed, the components are assembled according to correct relative positions and directions according to the design drawing, so that a three-dimensional model of the gearbox can be obtained.
The digital twin platform adopts one of ANSYS, siemens NX, PTC Creo or Dassau LT SYSTEMS, a three-dimensional model created in CAD software is imported into the selected digital twin platform, and the correct material properties are distributed for each component to generate the digital twin model of the gear box.
Further, the material properties of each structure of the three-dimensional model include material density, elastic modulus, stiffness data, and weight, and the geometric dimensions of each structure of the three-dimensional model include shape dimensions and mounting position data.
Step 2: dividing a digital twin model of the gear box into a plurality of functional parts according to the structure and the function, generating a mass matrix, a damping matrix and a rigidity matrix of the gear box according to the material property and the geometric dimension of each part, and generating a second-order differential equation of vibration of each functional part of the gear box according to the mass matrix, the damping matrix and the rigidity matrix of the gear box.
In the present embodiment, the functional portions divided according to the digital twin model of the gear box include an input shaft portion 10, an output shaft portion 20, a gear train portion 30, and a housing bracket portion 40.
Further, the mass matrix M of the generated gearbox is:
Wherein m 1、m2、m3 and m 4 represent the weights of the input shaft portion 10, the output shaft portion 20, the gear set portion 30 and the housing bracket portion 40, respectively;
the damping matrix C of the gear box is generated as follows:
wherein c 1、c2、c3 and c 4 are damping coefficients of the input shaft portion 10, the output shaft portion 20, the gear set portion 30 and the housing bracket portion 40, respectively;
the stiffness matrix K of the gearbox is generated as:
where k 1、k2、k3 and k 4 are the local stiffness of the input shaft portion 10, the output shaft portion 20, the gear set portion 30 and the housing bracket portion 40, respectively.
In this embodiment, the mass matrix, the damping matrix and the stiffness matrix are parameters for dynamic characteristics of the gearbox, and the dimensions of the parameters are the same as the number of functional parts divided by the digital twin model of the gearbox, and the mass matrix, the damping matrix and the stiffness matrix in this embodiment all adopt diagonal arrays, wherein elements on diagonal lines represent mass, damping coefficient and local stiffness corresponding to each functional part.
The mass, damping coefficient and local stiffness data corresponding to each functional part are dependent on a digital twin model of the gearbox, and in the digital twin model of a gearbox, the specific method for obtaining the mass, damping coefficient and local stiffness data of the input shaft part 10, the output shaft part 20, the gear set part 30 and the housing bracket part 40 is as follows:
The method comprises the steps of obtaining the volume of each component from the geometric data and the material density of a digital twin model, applying the material density of each component to the corresponding volume, multiplying the volume by the density to obtain the mass, carrying out dynamic simulation through the digital twin model, obtaining the response and vibration attenuation of each functional part, and calculating the rigidity according to the geometric size and the material elastic modulus of the component by combining the response and vibration attenuation of each functional part with an empirical formula in industry standard or literature.
In the present embodiment, the input shaft portion 10 includes: an input shaft for transmitting power from the power source to the gearbox; an input shaft bearing for supporting the input shaft and allowing it to rotate while reducing friction; the output shaft portion 20 includes: an output shaft for transmitting power from the gearbox to the mechanical components of the final drive, an output shaft bearing for supporting the output shaft and allowing it to rotate while reducing friction; the gear train portion 30 includes: the gear, gear shaft supporting the gear and bearing supporting the gear shaft in the gear box; the housing bracket portion 40 includes: a housing surrounding all the internal components of the gearbox, and a bracket for supporting the bearings and shaft.
In the present embodiment, the second order differential equation of the generated vibration of the input shaft portion 10 is:
where FSR represents an external force vector of the input shaft portion 10, AndRespectively representing an acceleration vector, a velocity vector, and a displacement vector of the input shaft portion 10;
the second differential equation of the generated output shaft portion 20 vibration is:
where FSC represents the external force vector of the output shaft portion 20, AndAn acceleration vector, a velocity vector, and a displacement vector, respectively, representing the output shaft portion 20;
The resulting second differential equation for the vibration of the gearset portion 30 is:
Where FCL represents the external force vector of the gearset portion 30, AndRepresenting the acceleration, velocity and displacement vectors, respectively, of the gearset portion 30;
The second differential equation of the generated vibration of the housing bracket portion 40 is:
Where FWK represents the external force vector of the housing bracket portion 40, AndThe acceleration vector, the velocity vector, and the displacement vector of the housing bracket portion 40 are represented, respectively.
The present embodiment treats the input shaft portion 10, the output shaft portion 20, the gear set portion 30 and the housing bracket portion 40 as one mass point, simplifies the external force vector of each portion to a single scalar value, and the second order differential equation of vibration of each portion describes the dynamic behavior of each functional portion.
Step 3: the method comprises the steps of arranging sensors at each functional part of an actual gearbox, collecting displacement vectors, speed vectors and acceleration vectors of each functional part of the gearbox, generating external force vectors of each functional part according to a second-order differential equation of vibration of each functional part, decomposing the external force vectors of each functional part, generating components in the x, y and z directions in a Cartesian coordinate system, superposing the components, and generating comprehensive external force components of the functional part along the x, y and z directions.
When the displacement, speed and acceleration vectors of the input shaft, the output shaft, the gear set and the shell support of the gearbox are to be collected, displacement sensors are used for measuring the displacement of each functional part in a three-dimensional space, the displacement vectors are obtained, the speed vectors are obtained by carrying out differential calculation on the change of the displacement vectors along with time, the acceleration vectors are obtained by carrying out secondary differential calculation on the displacement vectors, and in addition, the collection time of each part is synchronous during collection.
In this embodiment, when external force vectors of the respective functional parts are generated, acceleration vectors, velocity vectors and displacement vectors corresponding to the input shaft part 10, the output shaft part 20, the gear set part 30 and the housing bracket part 40 are collected by the sensors respectively, and the external force vectors corresponding to the input shaft part 10, the output shaft part 20, the gear set part 30 and the housing bracket part 40 can be generated by combining weight data, damping coefficients and local stiffness data of the corresponding input shaft part 10, the output shaft part 20, the gear set part 30 and the housing bracket part 40 in the mass matrix M, the damping matrix C and the stiffness matrix K of the gearbox and inputting the data to a second differential equation of vibration of the corresponding functional parts.
When the external force vectors corresponding to the input shaft part 10, the output shaft part 20, the gear set part 30 and the housing bracket part 40 are generated, the external force vectors of all the parts are equivalent to variables in a second-order differential equation of vibration of all the parts, the acceleration vector, the speed vector and the displacement vector which are acquired and measured are independent variables, and a Newmark-beta method or a Runge-Kutta method can be adopted for solving the second-order differential equation.
Step 4: according to the digital twin model of the gear box, generating an optimal external force vector of the work of the gear box, decomposing the optimal external force vector, and generating components in the three directions of x, y and z in a Cartesian coordinate system.
In this embodiment, when the external force vector is decomposed along three directions of x, y and z, the x direction is the axial direction of the input shaft of the gearbox, the y direction is in the plane formed by the axes of the input shaft and the output shaft of the gearbox, the y direction is perpendicular to the x direction, and the z direction is perpendicular to the plane formed by the y direction and the x direction.
When the digital twin model of the gear box generates the optimal external force vector of the work of the gear box, the optimal external force vector represents the normal work of the gear box, and the direction and the magnitude of the overall bearing external force which is externally represented by the corresponding gear box when the efficiency is highest are obtained through simulation of the digital twin model.
Step 5: according to the external force vectors of all functional parts of the gear box, data analysis is carried out by combining preset vibration thresholds of the external force vectors of all functional parts to generate a functional vibration vector index, comprehensive analysis is carried out on comprehensive external force components of the functional parts along the x, y and z directions and components of the optimal external force vectors along the x, y and z directions to generate the comprehensive vibration vector index.
Further, according to the external force vector of each functional part of the gear box, a specific calculation formula according to which the functional vibration vector index is generated is as follows:
GNzd＝α*e(|FSR|-FSRy)+β*e(|FSC|-FSCy)+γ*e(|FCL|-FCLy)+δ*e(|FWK|-FWKy)
Where GN zd denotes a functional vibration vector index, FSRy, FSCy, FCLy and FWKy denote external force vector vibration thresholds set in advance for the input shaft portion 10, the output shaft portion 20, the gear train portion 30 and the housing bracket portion 40, respectively, α, β, γ and δ denote an input shaft weight, an output shaft weight, a gear train weight and a housing bracket weight, respectively, and α > β > γ > δ >0, α+β+γ+δ=1.
The vibration of the gear box is transmitted along with the operation of the gear box, for example, the vibration of the input shaft portion 10 of the gear box can cause the vibration of the output shaft portion 20 to be aggravated, so in this embodiment, the weight of the input shaft, the weight of the output shaft, the weight of the gear set and the weight of the housing bracket can be gradually reduced, in the function vibration vector index, the vibration of the input shaft portion 10 can cause the vibration of the input shaft portion itself and can be transmitted to other portions, therefore, the influence on the function vibration vector index is the greatest, the vibration threshold of the external force vectors of the input shaft portion 10, the output shaft portion 20, the gear set portion 30 and the housing bracket portion 40 are all constants, the external force vector of the function portion is a vector with a direction, and the calculation of the function vibration vector index takes the modulus of the external force vector for calculation.
The function vibration vector index is constantly positive, when the modulus of the external force vector FSC of the output shaft portion 20 is greater than the external force vector vibration threshold of the input shaft portion 10, at which time e (|FSR|-FSRy) is greater than 1 and increases with the increase of the modulus of FSC, at which time the greater the function vibration vector index is, the stronger the vibration of the gear box is indicated, which may cause damage to the gear box, and when the modulus of the external force vector FSC of the output shaft portion 20 is less than the external force vector vibration threshold of the input shaft portion 10, at which time e (|FSR|-FSRy) is less than 1 and decreases with the decrease of the modulus of FSC, at which time the smaller the function vibration vector index is, the weaker the vibration of the gear box is indicated, the less damage is caused to the gear box, and the influence principle of the external force vector of the input shaft portion 10, the external force vector of the gear set portion 30 and the external force vector of the housing bracket portion 40 on the function vibration vector index is the same as the analysis method described above.
In this embodiment, when generating the comprehensive external force components of the functional part along the x, y and z directions, the four external force vectors of the external force vector FSR of the input shaft part 10, the external force vector FSC of the output shaft part 20, the external force vector FCL of the gear set part 30 and the external force vector FWK of the housing bracket part 40 are decomposed along the x, y and z directions, and the vectors in each direction are superimposed to generate the comprehensive external force component in the x direction, the comprehensive external force component in the y direction and the comprehensive external force component in the z direction, respectively, and calibrated as: zw x、Zwy and Zw z.
For example: the components of the four external force vectors along the x-axis of the input shaft portion 10 external force vector FSR, the output shaft portion 20 external force vector FSC, the gear set portion 30 external force vector FCL, and the housing bracket portion 40 external force vector FWK are respectively: FSR (x), FSC (x), FCL (x) and FWK (x), then:
Zwx＝FSR(x)+FSC(x)+FCL(x)+FWK(x)
The calculation principle of the y-direction comprehensive external force component and the z-direction comprehensive external force component is the same as that of the x-direction comprehensive external force component.
In this embodiment, the optimal external force vector is calibrated to be Zj, and after the optimal external force vector is decomposed along the x, y and z directions, components in the three directions are respectively calibrated as follows: zj x、Zjy and Zj z;
the specific formula according to which the integrated vibration vector index is generated is as follows:
Where ZH zd represents the integrated vibration vector index.
The integrated vibration vector index represents the sum of distances between the integrated external force components in the three directions and the components in the three directions of the optimal external force vector, and when the integrated external force components in the three directions are larger, the direction of the external force vector indicates that the gearbox is far from the working state with the highest efficiency, and at the moment, the larger the integrated vibration vector index is, the higher the probability of occurrence of problems or faults of the gearbox is.
Further, the logic on which the vibration evaluation index is generated by integrating the vibration vector index and the functional vibration vector index is:
Where ZH pg represents a vibration evaluation index, GN zd represents a functional vibration vector index, ε 1 and ε 2 represent a functional weight coefficient and a comprehensive weight coefficient, respectively, and ε 1>ε2 >1.
The vibration evaluation index comprehensively considers the functional vibration vector index and the comprehensive vibration vector index, when the functional vibration vector index or the comprehensive vibration vector index is larger, the vibration evaluation index is higher, which indicates that the current vibration of the gear box can be abnormal, and because the comprehensive vibration vector index considers the whole external force vector of the gear box, each functional part can be coupled together, so that the comprehensive vibration vector index is smaller, but the state of the gear box cannot be completely reflected, and the comprehensive weight coefficient is smaller than the functional weight coefficient.
According to the embodiment, a high-precision digital model of the gear box is established by utilizing a digital twin technology, an optimal external force vector for work is generated, a second-order differential equation of vibration of each functional part of the gear box is generated according to a quality matrix, a damping matrix and a rigidity matrix of the gear box, data are acquired by adopting sensors arranged on actual gear box parts, the second-order differential equation of vibration of each functional part of the gear box is combined, a functional vibration vector index is generated by combining the generated external force vectors, the vibration condition of each functional part of the gear box can be reflected through the functional vibration vector index, the external force vectors of each functional part are decomposed and overlapped, the combined optimal external force vector for work is combined to generate a comprehensive vibration vector index, and the difference between the current gear box working state and the optimal working state is reflected on the whole through the comprehensive vibration vector index;
Step 6: and generating a vibration evaluation index by integrating the vibration vector index and the functional vibration vector index, comparing the vibration evaluation index with a preset abnormal evaluation index threshold, and sending or not sending an early warning signal according to a comparison result.
When the vibration evaluation index is larger than or equal to a preset abnormal evaluation index threshold value, the vibration of the gear box is indicated to be abnormal, an early warning signal is sent out at the moment, and when the vibration evaluation index is smaller than the preset abnormal evaluation index threshold value, the vibration of the gear box is indicated to be in a normal range, and the early warning signal is not sent out at the moment.
In the embodiment, the data is acquired through the sensors arranged on the actual gear box component, and the external force vector is generated for decomposition, so that a dynamic and real-time monitoring and analyzing means is provided, the vibration characteristics under the actual working condition can be reflected more accurately, because the vibration characteristics are based on the data acquired in real time rather than just theoretical calculation or preset assumption, the method has the advantages that the accuracy and timeliness of analysis are remarkably improved, the method is not single analysis, external force vectors of all parts of the gearbox and the whole external force vector are combined, the working state of the gearbox is analyzed by adopting a part and whole and finally fusion mode, so that the assessment of the vibration of the gearbox is closer to the actual working condition, and powerful data support is provided for maintenance and optimization.
The above formulas are all formulas with dimensions removed and numerical values calculated, the formulas are formulas with a large amount of data collected for software simulation to obtain the latest real situation, and preset parameters in the formulas are set by those skilled in the art according to the actual situation.
The above embodiments may be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented in software, the above-described embodiments may be implemented in whole or in part in the form of a computer program product. Those of skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein can be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed over a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present application.
Claims (2)
1. A simulation analysis method for vibration response of a gear box is characterized by comprising the following specific steps:
according to a design drawing of the gear box, using CAD software to create the geometric shape of each component of the gear box, assembling the components according to the design drawing to form a three-dimensional model of the gear box, importing the three-dimensional model into a digital twin platform, inputting structural parameters of each structure of the three-dimensional model, and generating the digital twin model of the gear box, wherein the structural parameters comprise material properties and geometric dimensions;
Dividing a digital twin model of the gear box into a plurality of functional parts according to the structure and the function, generating a mass matrix, a damping matrix and a rigidity matrix of the gear box according to the material attribute and the geometric dimension of each part, and generating a second-order differential equation of vibration of each functional part of the gear box according to the mass matrix, the damping matrix and the rigidity matrix of the gear box;
Setting a sensor at each functional part of an actual gear box, collecting displacement vectors, speed vectors and acceleration vectors of each functional part of the gear box, generating external force vectors of each functional part according to a second-order differential equation of vibration of each functional part, decomposing the external force vectors of each functional part, generating components in three directions of x, y and z in a Cartesian coordinate system, and superposing the components to generate comprehensive external force components of the functional part along the three directions of x, y and z;
generating an optimal external force vector of the work of the gear box according to a digital twin model of the gear box, decomposing the optimal external force vector, and generating components in three directions of x, y and z in a Cartesian coordinate system;
according to the external force vectors of all functional parts of the gear box, carrying out data analysis by combining preset vibration thresholds of the external force vectors of all functional parts to generate a functional vibration vector index, carrying out comprehensive analysis on comprehensive external force components of the functional parts along the x, y and z directions and components of the optimal external force vectors along the x, y and z directions to generate a comprehensive vibration vector index;
generating a vibration evaluation index by integrating the vibration vector index and the functional vibration vector index, comparing the vibration evaluation index with a preset abnormal evaluation index threshold, and sending or not sending an early warning signal according to a comparison result;
The material properties of each structure of the three-dimensional model comprise material density, elastic modulus, rigidity data and weight, the geometric dimensions of each structure of the three-dimensional model comprise shape dimension and installation position data, and the functional parts divided according to the digital twin model of the gear box comprise an input shaft part, an output shaft part, a gear set part and a shell bracket part;
The mass matrix M of the gear box generated is:
Wherein m 1、m2、m3 and m 4 represent the weights of the input shaft portion, the output shaft portion, the gear set portion, and the housing bracket portion, respectively;
the damping matrix C of the gear box is generated as follows:
Wherein c 1、c2、c3 and c 4 are damping coefficients of the input shaft portion, the output shaft portion, the gear set portion and the housing bracket portion, respectively;
the stiffness matrix K of the gearbox is generated as:
Wherein k 1、k2、k3 and k 4 are the local stiffness of the input shaft portion, the output shaft portion, the gear set portion and the housing bracket portion, respectively;
the second differential equation of the generated input shaft partial vibration is:
wherein FSR represents an external force vector of the input shaft portion, AndAn acceleration vector, a velocity vector, and a displacement vector, respectively, representing the input shaft portion;
The second differential equation of the generated output shaft partial vibration is:
wherein FSC represents an external force vector of the output shaft portion, AndRespectively representing an acceleration vector, a velocity vector and a displacement vector of the output shaft portion;
the second differential equation for the generated gear set partial vibrations is:
wherein FCL represents an external force vector of the gear set portion, AndRespectively representing an acceleration vector, a velocity vector and a displacement vector of the gear set part;
the second differential equation of the generated housing bracket part vibration is:
wherein FWK represents an external force vector of the housing bracket portion, AndRespectively representing an acceleration vector, a velocity vector and a displacement vector of the housing bracket part;
When external force vectors of all the functional parts are generated, acceleration vectors, speed vectors and displacement vectors corresponding to the input shaft part, the output shaft part, the gear set part and the shell support part are respectively acquired through sensors, and the external force vectors corresponding to the input shaft part, the output shaft part, the gear set part and the shell support part can be generated by combining weight data, damping coefficients and local rigidity data of the corresponding input shaft part, the output shaft part, the gear set part and the shell support part in a quality matrix M, a damping matrix C and a rigidity matrix K of the gear box and inputting the weight data, the damping coefficients and the local rigidity data into a second-order differential equation corresponding to the vibration of the functional parts;
According to the external force vector of each functional part of the gear box, a specific calculation formula according to which the functional vibration vector index is generated is as follows:
GNzd＝α*e(|FSR|-FSRy)+β*e(|FSC|-FSCy)+γ*e(|FCL|-FCLy)+δ*e(|FWK|-FWKy)
Wherein GN zd represents a functional vibration vector index, FSRy, FSCy, FCLy and FWKy represent external force vector vibration thresholds of the input shaft portion, the output shaft portion, the gear set portion and the housing bracket portion, respectively, α, β, γ and δ represent an input shaft weight, an output shaft weight, a gear set weight and a housing bracket weight, respectively, and α > β > γ > δ >0, α+β+γ+δ=1;
When the external force vector is decomposed along three directions of x, y and z, the x direction is the axial direction of an input shaft of the gear box, the y direction is in a plane formed by the axial lines of the input shaft and an output shaft of the gear box, the y direction is vertical to the x direction, and the z direction is vertical to the plane formed by the y direction and the x direction;
When generating comprehensive external force components of the functional part along three directions of x, y and z, decomposing four external force vectors of an input shaft part external force vector FSR, an output shaft part external force vector FSC, a gear group part external force vector FCL and a shell support part external force vector FWK along the three directions of x, y and z, superposing vectors in each direction, respectively generating an x-direction comprehensive external force component, a y-direction comprehensive external force component and a z-direction comprehensive external force component, and respectively calibrating the four external force vectors as follows: zw x、Zwy and Zw z;
The optimal external force vector is marked as Zj, and after the optimal external force vector is decomposed along the three directions of x, y and z, the components in the three directions are respectively marked as follows: zj x、Zjy and Zj z;
the specific formula according to which the integrated vibration vector index is generated is as follows:
wherein ZH zd represents the integrated vibration vector index;
the logic on which the vibration evaluation index is generated by integrating the vibration vector index and the functional vibration vector index is as follows:
Where ZH pg represents a vibration evaluation index, GN zd represents a functional vibration vector index, ε 1 and ε 2 represent a functional weight coefficient and a comprehensive weight coefficient, respectively, and ε 1>ε2 >1.
2. The method for simulating analysis of vibration response of a gearbox according to claim 1, wherein: when the vibration evaluation index is larger than or equal to a preset abnormal evaluation index threshold value, the vibration of the gear box is indicated to be abnormal, an early warning signal is sent out at the moment, and when the vibration evaluation index is smaller than the preset abnormal evaluation index threshold value, the vibration of the gear box is indicated to be in a normal range, and the early warning signal is not sent out at the moment.
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| CN117592332A (en) * | 2023-11-21 | 2024-02-23 | 江苏省特种设备安全监督检验研究院 | Digital twinning-based gearbox model high-fidelity method, system and storage medium |
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