Method for calculating time-varying meshing stiffness of internal meshing straight toothed spur gear pair by considering bolt loosening fault influence

Abstract

The invention discloses a method for calculating time-varying meshing stiffness of an internal meshing straight spur gear pair by considering bolt loosening fault influence. The method is characterized by comprising the following steps of: obtaining tooth body flexibility and matrix flexibility of a planet gear and tooth body flexibility of a gear ring through an analytical method; establishing a finite element statics analysis model of the gear ring with the bolt loosening fault, performing MLP neural network model training on the extracted data to predict the matrix flexibility of the gear ring under the bolt loosening fault, then establishing a gear bearing contact analysis model, and solving to obtain a time-varying meshing stiffness value; the method has the advantages that deep fusion of the calculation efficiency and the prediction precision of the time-varying meshing rigidity is achieved, the high efficiency and the intelligent level of dynamic simulation of the internal meshing gear transmission system are remarkably improved, and the calculation precision of the time-varying meshing rigidity is further guaranteed.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology in mechanical transmission dynamics, and in particular to a method for calculating the time-varying meshing stiffness of an internal meshing spur gear pair that takes into account the effects of bolt loosening faults. Background Technology

[0002] As a core power component, the efficiency of gear transmission systems directly affects the overall mechanical operation efficiency. When faced with adverse factors such as overload, lubrication loss, and loose bolts, gear transmission systems may experience faults such as cracks, pitting, galling, and even tooth breakage, severely hindering their smooth operation. Given the widespread use of gears in most transmission mechanisms, fault diagnosis of gears is particularly important. Currently, planetary gearbox components widely use bolted connections, and the tightness of these bolts has a significant impact on the time-varying meshing stiffness of the overall gear transmission system. Therefore, in experimental or engineering applications, real-time monitoring of the bolt connection status of planetary gearbox components is a crucial measure. This effectively optimizes the operating conditions of the gear transmission system, promptly identifies and addresses potential problems, and prevents situations that may cause permanent damage to the system. However, the core prerequisite for achieving accurate monitoring and early warning of bolt loosening is establishing a system dynamics model that can accurately characterize fault features, and then deeply analyzing the system response evolution under fault conditions through this model.

[0003] Accurately obtaining the time-varying meshing stiffness curve of a planetary gear transmission system with loose bolts is crucial when constructing a dynamic model of the system, as it determines the accuracy and reliability of the simulation. However, current methods for obtaining this stiffness curve have significant limitations: Firstly, while high-precision finite element simulation models can simulate complex boundaries, they are extremely computationally expensive (requiring significant computation time and hardware resources), inefficient, complex in modeling, have high professional barriers, and are prone to convergence problems in nonlinear solutions, making them unsuitable for the needs of rapid analysis, parametric research, or large-scale dynamic simulation in practical engineering applications. Secondly, while traditional analytical calculation methods are relatively efficient, they are mostly based on the assumption that the gear ring of the planetary gear set is externally rigidly fixed. However, under the condition of loose bolts, the gear ring is fixedly connected to the gearbox housing by bolts, and bolt loosening directly changes the boundary flexibility of the gear ring matrix, which is fundamentally different from the rigid boundary of traditional analytical models. Therefore, existing analytical models cannot accurately characterize the impact of changes in the gear ring matrix flexibility caused by bolt loosening on the time-varying meshing stiffness. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating the time-varying meshing stiffness of an internal meshing spur gear pair that takes into account the effect of bolt loosening failure, which can realize the rapid and accurate acquisition of the time-varying meshing stiffness under bolt loosening failure conditions.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a time-varying meshing stiffness calculation method for internal meshing spur gear pairs considering the influence of bolt loosening faults, including the following specific steps: (1) The tooth body compliance, base compliance and tooth body compliance of the planetary gear are obtained by analytical calculation; (2) Establish a finite element static analysis model of the gear ring with bolt loosening fault; (3) Apply a unit load to the finite element static analysis model of the gear ring and extract the displacement data of the loaded tooth and the adjacent tooth; (4) Calculate the matrix compliance of the gear ring under bolt loosening fault using displacement data; (5) Establish an MLP neural network model, take the measured radius of the load-bearing tooth and the force-bearing point on the adjacent tooth of the gear ring as the input feature, and take the calculated matrix compliance of the gear ring under bolt loosening fault as the output feature. Train the MLP neural network. After training, predict the matrix compliance of the gear ring when the measured radius of the load-bearing point of the load-bearing tooth under bolt loosening fault is taken as the input feature through the MLP neural network. (6) Establish a gear bearing contact analysis model, and input the tooth body flexibility, base flexibility and tooth body flexibility of the planetary gear obtained by analytical method, and the base flexibility of the gear ring under bolt loosening fault into the gear bearing contact analysis model, solve for the time-varying meshing stiffness value of the planetary gear and the gear ring at different meshing positions of the loaded teeth in one meshing cycle, and thus obtain the time-varying meshing stiffness curve.

[0006] Furthermore, in step (1), the analytical method employs the potential energy method.

[0007] Furthermore, in step (1), the matrix compliance of the planetary gear includes matrix-induced tooth body local compliance and matrix-induced tooth body coupling compliance.

[0008] Furthermore, the specific establishment process of step (2) is as follows: (2.1) Establish the finite element static analysis model of the gear ring; (2.2) Set the elastic modulus of the gear body material of the gear ring to 10% of the elastic modulus of the base material of the gear ring. 5 times; (2.3) Apply full-degree-of-freedom constraints to all bolt holes on the base of the gear ring to simulate the assembly boundary conditions under gear ring fastening; (2.4) Release the full degree of freedom of at least one bolt hole to obtain the finite element static analysis model of the gear ring with bolt loosening fault.

[0009] Furthermore, in step (3), the specific extraction process of the displacement data of the loaded tooth and adjacent teeth of the gear ring is as follows: (3.1) Apply along one of the teeth of the finite element static analysis model of the gear ring with bolt loosening fault established in step (2). x direction and y Unit load in the direction; (3.2) Extracting data using a Python script x direction and y Displacement data of the loaded tooth and adjacent teeth under a unit load applied in the direction are generated into a text file.

[0010] Furthermore, in step (4), the matrix compliance of the gear ring includes matrix-induced local compliance of the tooth body and matrix-induced coupled compliance of the tooth body. The relationship between the matrix-induced local compliance of the gear ring under bolt loosening fault is as follows: , in: Indicates unit composite load f The matrix-induced local compliance of the tooth body when acting on the loaded tooth of the gear ring. This represents the unit composite load acting on the loaded tooth. f The angle between its direction and the direction of its tangent on its circumference. and Correspondingly, this indicates the application of force to the loaded teeth of the gear ring. x Under a unit load in the direction, the point of force application on the loaded tooth is at x direction and y Displacement component generated by direction; and Correspondingly, this indicates that an application is made at the same position on the loaded tooth of the gear ring. y Under a unit load in the direction, the point of force application on the loaded tooth is at x direction and y Displacement component generated by direction; The relationship between the matrix-induced tooth coupling compliance of the gear ring under bolt loosening fault is as follows: , in: Indicates unit composite load f When acting on the loaded tooth of the gear ring, the adjacent tooth induces tooth body coupling compliance with the matrix of the loaded tooth; This indicates the angle between the direction of the load on an adjacent tooth and the direction of its circumferential tangent; z Indicates the number of teeth on the gear ring. and Correspondingly, this indicates the application of force to the loaded teeth of the gear ring. x Under a unit load in the direction, the force-bearing point of adjacent teeth is... xdirection and y Displacement component generated by direction; and Correspondingly, this indicates that an application is made at the same position on the loaded tooth of the gear ring. y Under a unit load in the direction, the force-bearing point of adjacent teeth is... x direction and y The displacement component generated by the direction.

[0011] Furthermore, in step (5), when training the MLP neural network, a single-input single-output network based on the measurement point radius of the loaded tooth is established for the matrix-induced local flexibility of the tooth body of the gear ring, and a dual-input single-output network based on the dual measurement point radius of the loaded tooth and the adjacent tooth is established for the matrix-induced coupling flexibility of the tooth body of the gear ring.

[0012] Compared with the prior art, the advantages of the present invention are: (1) Achieving a deep integration of computational efficiency and prediction accuracy for time-varying meshing stiffness; This method breaks through the limitations of traditional analytical methods, establishes a matrix compliance mapping framework for gear rings with bolt holes through finite element simulation, and introduces an MLP neural network to intelligently predict the matrix compliance of the gear ring under bolt loosening fault, effectively capturing the complex boundary deformation characteristics caused by bolt loosening. This fusion scheme of "finite element simulation + analysis" not only significantly improves the efficiency and intelligence level of dynamic simulation of internal meshing gear transmission system, but also ensures the computational accuracy of time-varying meshing stiffness; (2) In the finite element static analysis model of the gear ring, this invention innovatively sets the elastic modulus of the gear body material to 10% of the elastic modulus of the matrix material. 5 This mechanical processing method physically equates the tooth body of the gear ring to an "absolute rigid body," thereby ensuring that after applying a unit load, all displacements at the stress point are purely caused by the elastic deformation of the base body, achieving a complete decoupling of tooth deformation and base body deformation in terms of mechanical mechanism; moreover, it completely locks the flexibility of the tooth body itself, ensuring that the extracted network prediction target (i.e., the base flexibility of the gear ring) is absolute. This allows the prediction results of the neural network to achieve perfect closure of the mechanical boundary when combined with the calculation results of the analytical method, fundamentally guaranteeing the theoretical rigor and numerical reliability of the calculation of the time-varying meshing stiffness curve; (3) The present invention applies a unit load to the rigid tooth body in the orthogonal directions of x and y respectively, and extracts the displacement data of the loaded tooth and the adjacent tooth in the two-dimensional plane. Then, the matrix compliance of the gear ring under bolt loosening fault along the actual meshing line direction is calculated by the displacement data. This principle ensures that the subsequent neural network model can accurately respond to the transient change of the normal load angle. (4) The matrix-induced tooth coupling compliance of the tooth ring of the present invention is separately constructed and predicted. In addition, a dual-input feature mechanism based on the measurement point radius of the load-bearing tooth and the force point on the adjacent tooth is specially designed in the neural network model, which enables the present invention to capture the coupling behavior between adjacent teeth under fault conditions with high precision, filling the gap in the existing fault analysis model in coupling compliance calculation. Attached Figure Description

[0013] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the internal meshing of the planetary gear and the gear ring of the present invention; Figure 3 This is a schematic diagram showing the forces acting on the loaded tooth and adjacent teeth of the gear ring of the present invention; Figure 4 This is a comparison chart of the time-varying meshing stiffness curves obtained by the present invention and the traditional finite element simulation model. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0015] To facilitate understanding of the overall technical solution, the various parts of planetary gear 1 and gear ring 2 are labeled and explained, where: 11 represents the base of the planetary gear, 12 represents the tooth of the planetary gear, 21 represents the base of the gear ring, and 22 represents the tooth of the gear ring.

[0016] like Figure 1-3 As shown, the method for calculating the time-varying meshing stiffness of an internal meshing spur gear pair, taking into account the effects of bolt loosening faults, includes the following specific steps: (1) The tooth compliance of planetary gear 1, the matrix-induced local compliance of planetary gear 1 and the matrix-induced coupled compliance of the tooth, as well as the tooth compliance of gear ring 2, are obtained by calculating the potential energy method. (2) Establish a finite element static analysis model for gear ring 2 with bolt loosening fault, specifically as follows: (2.1) Establish the finite element static analysis model of gear ring 2; (2.2) Set the elastic modulus of the tooth body material of gear ring 2 to 10% of the elastic modulus of the base material of gear ring 2. 5 times; (2.3) Apply full degree of freedom constraints to all bolt holes on the base 21 of the gear ring 2 (i.e. tighten all bolts 3) to simulate the assembly boundary conditions under gear ring fastening. (2.4) Release the full degree of freedom of at least one bolt hole to obtain the finite element static analysis model of the gear ring 2 with bolt loosening fault; (3.1) Apply along the finite element static analysis model of the gear ring 2 with bolt loosening fault established in step (2) to one of the teeth 22. x direction and y Unit load in the direction; (3.2) Extracting data using a Python script x direction and y Displacement data of the loaded tooth 221 and adjacent tooth 222 under a unit load applied in the direction are generated into a text file; (4) Calculate the matrix-induced local compliance and matrix-induced coupled compliance of gear ring 2 under bolt loosening fault using the displacement data extracted in step (3.2). The relationship between the matrix-induced local compliance of gear ring 2 under bolt loosening fault is as follows: , in: Indicates unit composite load f (Right now x direction and y The matrix-induced local compliance of the tooth body when a composite load of unit load in the direction is applied to the loaded tooth 221 of the gear ring 2. This represents the unit composite load acting at the loaded tooth 221. f The angle between its direction and the direction of its tangent on its circumference. and Correspondingly, this indicates that an application is made to the loaded tooth 221 of the gear ring 2. x Under a unit load in the direction, the point of force application of the loaded tooth 221 is at x direction and y Displacement component generated by direction; and Correspondingly, this indicates that an application is made at the same position on the loaded tooth 221 of the gear ring 2. y Under a unit load in the direction, the point of force application of the loaded tooth 221 is at x direction and y Displacement component generated by direction; The relationship between the matrix-induced tooth coupling compliance of gear ring 2 under bolt loosening fault is as follows: , in: Indicates unit composite load f When the load-bearing tooth 221 of the gear ring 2 is subjected to the load-bearing tooth 221, the adjacent tooth 222 induces tooth body coupling compliance with the matrix of the load-bearing tooth 221. This indicates the angle between the direction of the load on adjacent tooth 222 and the direction of its circumferential tangent; z This indicates the number of teeth on gear 2. and Correspondingly, this indicates that when applying force to the loaded tooth 221 of the gear ring 2...x Under a unit load in the direction, the stress point of adjacent tooth 222 is at x direction and y Displacement component generated by direction; and Correspondingly, this indicates that an application is made at the same position on the loaded tooth 221 of the gear ring 2. y Under a unit load in the direction, the stress point of adjacent tooth 222 is at x direction and y The displacement components generated by the direction; each displacement component here is the displacement data extracted in step (3.2); (5) Establish a multilayer perceptron (MLP) neural network model, and measure the radius of the force points on the loaded teeth 221 of the gear ring 2 in step (4). r 1. The measuring radius of the force-bearing point on adjacent tooth 222 r 2. As an input feature, the measuring point radius refers to the distance from the force-bearing point on the tooth body 22 of the gear ring 2 to the center O of the gear ring. The calculated value is then compared with the measuring point radius. r 1. r The matrix-induced local compliance and matrix-induced coupled compliance of the gear ring 2 under bolt loosening fault at the stress point of 2 are used as output features. Furthermore, a measurement point radius based on the loaded tooth 221 is established for the matrix-induced local compliance of the gear ring 2. r A single-input single-output network is used to establish the matrix-induced tooth coupling compliance of gear ring 2 based on the radius of the dual measurement points of the loaded tooth 221 and the adjacent tooth 222. r 1. r The dual-input single-output network of 2 is used to train the MLP neural network. After training, the MLP neural network is used to predict the matrix-induced local compliance and matrix-induced coupling compliance of the tooth ring 2 when the radius of the measuring point of different stress points of the loaded tooth 221 under bolt loosening fault is used as the input feature. (6) Establish a gear bearing contact analysis (LTCA) model, and input the tooth body compliance of planetary gear 1, the base-induced local compliance and base-induced coupling compliance of planetary gear 1, the tooth body compliance of gear ring 2, and the base-induced local compliance and base-induced coupling compliance of gear ring 2 under bolt loosening fault into the LTCA model, solve for the time-varying meshing stiffness values ​​of the loaded tooth 221 at different meshing positions in one meshing cycle between planetary gear 1 and gear ring 2, and thus obtain the time-varying meshing stiffness curve.

[0017] The time-varying meshing stiffness curves obtained using this method (i.e., analytical-finite element simulation model AFEM) are compared with those obtained using the traditional finite element simulation model FEM. Figure 4As shown, the relative error of the time-varying meshing stiffness of the two is no more than 5%, which proves that the method can ensure the accuracy of acquisition while improving the acquisition efficiency of the time-varying meshing stiffness curve, and provides a high-fidelity and fast-response theoretical support for the condition monitoring and dynamic evaluation of planetary gear systems with bolt loosening faults.

[0018] The scope of protection of this invention includes, but is not limited to, the above embodiments. The scope of protection is defined by the claims. Any substitutions, modifications, or improvements to this technology that are easily conceived by those skilled in the art fall within the scope of protection of this invention.

Claims

1. A method for calculating time-varying meshing stiffness of an internally meshing spur cylindrical gear pair considering the influence of bolt loosening failure, characterized in that The method comprises the following specific steps: (1) obtaining the gear body flexibility, base flexibility and gear ring tooth body flexibility of the planetary gear by analytical calculation; (2) establishing a finite element static analysis model of the gear ring with bolt loosening failure; (3) applying a unit load to the finite element static analysis model of the gear ring, and extracting displacement data of the loaded tooth and the adjacent tooth; (4) calculating the base flexibility of the gear ring under bolt loosening failure by using the displacement data; (5) establishing an MLP neural network model, taking the measured point radius of the force point on the loaded tooth and the adjacent tooth of the gear ring as the input feature, taking the calculated base flexibility of the gear ring under bolt loosening failure as the output feature, training the MLP neural network, and after the training is completed, taking the measured point radius of the force point on the loaded tooth under bolt loosening failure as the input feature, predicting the base flexibility of the gear ring; (6) establishing a gear bearing contact analysis model, inputting the gear body flexibility, base flexibility and gear ring tooth body flexibility of the planetary gear calculated by the analytical method, and the predicted base flexibility of the gear ring under bolt loosening failure into the gear bearing contact analysis model, and solving the time-varying meshing stiffness value of the loaded tooth at different meshing positions in one meshing period of the planetary gear and the gear ring, so as to obtain the time-varying meshing stiffness curve.

2. The method for calculating time-varying meshing stiffness of an internal meshing spur cylindrical gear pair considering the influence of bolt loosening failure according to claim 1, characterized in that: In the step (1), the analytical method adopts potential energy method.

3. The method for calculating time-varying meshing stiffness of an internal meshing spur cylindrical gear pair considering the influence of bolt loosening failure according to claim 1, characterized in that: In the step (1), the base flexibility of the planetary gear comprises base-induced gear local flexibility and base-induced gear coupling flexibility.

4. The method for calculating time-varying meshing stiffness of an internal meshing spur cylindrical gear pair considering the influence of bolt loosening failure according to claim 1, characterized in that: The specific establishment process of the step (2) is as follows: (2.1) establishing a finite element static analysis model of the gear ring; (2.2) the modulus of elasticity of the tooth body material of the ring gear is set to be 10 times the modulus of elasticity of the base material of the ring gear 5 ; (2.3) applying full degree of freedom constraint to all bolt holes on the base of the gear ring to simulate the assembly boundary condition under fastening of the gear ring; (2.4) releasing the full degree of freedom of at least one bolt hole to obtain the finite element static analysis model of the gear ring with bolt loosening failure.

5. The method for calculating time-varying meshing stiffness of an internal meshing spur cylindrical gear pair considering the influence of bolt loosening failure according to claim 1, characterized in that: In the step (3), the specific extraction process of the displacement data of the loaded tooth and the adjacent tooth of the gear ring is as follows: (3.1), respectively apply unit load along the direction and the direction on one of the tooth bodies of the finite element static analysis model of the ring gear with bolt loosening fault established in step (2) ; x y direction and the direction.​ (3.2), extract the data of the displacement of the loaded tooth and the adjacent tooth under the unit load in the direction of the tooth surface by the python script x direction and y direction, and form a text file.

6. The method for calculating time-varying meshing stiffness of an internally meshing spur cylindrical gear pair considering the influence of bolt loosening failure according to claim 1, characterized in that: In the step (4), the base flexibility of the gear ring comprises base-induced gear local flexibility and base-induced gear coupling flexibility, the relationship formula of the base-induced gear local flexibility of the gear ring under bolt loosening failure is as follows: ， wherein: represents a unit complex load f a base-induced tooth local flexibility of the loaded tooth acting on the gear ring, represents a unit complex load acting on the loaded tooth f an angle between the direction and a tangential direction of the circumference thereof, and correspondingly represents a force point of the loaded tooth when a unit load in the direction is applied to the loaded tooth of the gear ring x direction generates a displacement component in the x direction and y direction; and correspondingly represents a force point of the loaded tooth when a unit load in the direction is applied to the loaded tooth of the gear ring at the same position y direction generates a displacement component in the x direction and y direction; The relationship formula of the base-induced gear coupling flexibility of the gear ring under bolt loosening failure is as follows: ， in: Indicates unit composite load f When acting on the loaded tooth of the gear ring, the adjacent tooth induces tooth body coupling compliance with the matrix of the loaded tooth; This indicates the angle between the direction of the load on an adjacent tooth and the direction of its circumferential tangent; z Indicates the number of teeth on the gear ring. and Correspondingly, this indicates the application of force to the loaded teeth of the gear ring. x Under a unit load in the direction, the force-bearing point of adjacent teeth is... x direction and y Displacement component generated by direction; and Correspondingly, this indicates that an application is made at the same position on the loaded tooth of the gear ring. y Under a unit load in the direction, the force-bearing point of adjacent teeth is... x direction and y The displacement component generated by the direction.

7. The method for calculating time-varying meshing stiffness of an internal meshing spur cylindrical gear pair considering the influence of bolt loosening failure according to claim 6, characterized in that: In the step (5), when training the MLP neural network, a single-input single-output network based on the measured point radius of the loaded tooth is established for the base-induced gear local flexibility of the gear ring, and a double-input single-output network based on the measured point radius of the loaded tooth and the adjacent tooth is established for the base-induced gear coupling flexibility of the gear ring.

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