Analysis Method, Device, Equipment and Medium for Spur Gear and Rolling Bearing Transmission System

Abstract

The present invention relates to the technical field of gear mechanics calculation, and in particular to an analysis method, device, equipment and medium for a spur gear and rolling bearing transmission system, including: obtaining the design and working condition parameters of the spur gear, analyzing the meshing process to obtain the initial meshing stiffness; constructing a transmission dynamics model, introducing the initial stiffness to solve for the initial dynamic response; based on the response, analyzing the meshing process under bearing deformation to obtain the corrected meshing position; based on this position, analyzing the tooth force and tooth surface lubrication state to obtain the corrected meshing stiffness and tooth surface friction coefficient; introducing the parameters to solve for the corrected dynamic response; determining whether the iteration stop condition is satisfied, if not, replacing the initial response with the corrected response and repeating the above analysis; this method dynamically corrects the meshing position, stiffness and friction coefficient through an iterative mechanism, considers the coupling effect of bearing deformation and tooth surface friction, and effectively improves the analysis accuracy of the spur gear-rolling bearing transmission system.

Description

Technical Field

[0001] The present invention relates to the technical field of gear mechanics calculation, and particularly to an analysis method, device, equipment and medium for a spur gear and rolling bearing transmission system. Background Art

[0002] With the development of gear transmission systems towards high speed and high power density, how to reduce their vibration and noise levels has become a key issue in the current research and development of high-serviceability and high-reliability gear transmission systems. Previous studies have shown that conducting dynamic modeling research on gear transmission systems can provide a theoretical reference for gear transmission vibration analysis and optimization design. Generally, internal excitations such as gear pair stiffness excitation are important reasons for the vibration and noise of gear transmission systems. Therefore, studying the meshing stiffness and dynamic characteristics of spur gear transmissions has important engineering value and scientific significance for vibration control of spur gear transmissions, etc.

[0003] However, existing research has not considered the coupling effect between tooth surface friction, bearing deformation and gear meshing and its influence on the dynamic characteristics of spur gear-rolling bearing transmissions, which limits the analysis accuracy of spur gear-rolling bearing transmission systems.

[0004] It can be seen that the existing technology still needs to be improved. Summary of the Invention

[0005] In order to overcome the deficiencies of the prior art, the purpose of the present invention is to provide an analysis method, device, equipment and storage medium for a spur gear and rolling bearing transmission system, which can analyze the meshing process of spur gears under the condition of bearing deformation and improve the analysis accuracy of spur gear-rolling bearing transmission systems.

[0006] The first aspect of the present invention provides an analysis method for a spur gear and rolling bearing transmission system, including: analyzing the meshing process of the spur gear based on the obtained design parameters and working condition parameters of the spur gear to obtain the initial meshing stiffness; constructing a spur gear transmission dynamic model and introducing the initial meshing stiffness into the spur gear transmission dynamic model for model solution to obtain the initial dynamic response; analyzing the meshing process of the spur gear under bearing deformation based on the initial dynamic response to obtain the corrected meshing position of the spur gear pair; analyzing the tooth force state of the spur gear pair based on the corrected meshing position to obtain the corrected meshing stiffness; analyzing the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain the tooth surface friction coefficient; introducing the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamic model for model solution to obtain the corrected dynamic response; judging whether the preset iteration stop condition is satisfied based on the corrected dynamic response, and if not, using the corrected dynamic response to replace the initial dynamic response and returning to execute the analysis of the meshing process of the spur gear under bearing deformation based on the initial dynamic response.

[0007] Optionally, in the first implementation manner of the first aspect of the present invention, the constructing a spur gear transmission dynamics model and introducing the initial meshing stiffness into the spur gear transmission dynamics model for model solution to obtain the initial dynamic response includes: constructing a spur gear transmission system dynamics model; introducing the initial meshing stiffness into the spur gear transmission dynamics model to obtain the initial spur gear and rolling bearing transmission dynamics equations; and solving the initial spur gear and rolling bearing transmission dynamics equations to obtain the initial dynamic response.

[0008] Optionally, in the second implementation manner of the first aspect of the present invention, the analyzing the spur gear meshing process under bearing deformation based on the initial dynamic response to obtain the corrected meshing position of the spur gear pair includes: constructing a spur gear pair meshing model under bearing deformation based on the initial dynamic response to determine the meshing line and meshing point of the driving gear and the driven gear under bearing deformation; constructing a spur gear pair meshing tooth cantilever beam model and constructing a local coordinate system in the spur gear pair meshing tooth cantilever beam model based on the meshing line; and converting the meshing point to the local coordinate system to obtain the corrected meshing position.

[0009] Optionally, in the third implementation manner of the first aspect of the present invention, the analyzing the tooth force state of the spur gear pair based on the corrected meshing position to obtain the corrected meshing stiffness includes: analyzing the force direction of the spur gear pair based on the corrected meshing position to obtain the tooth load angle; and calculating the meshing stiffness based on the tooth load angle to obtain the corrected meshing stiffness.

[0010] Optionally, in the fourth implementation manner of the first aspect of the present invention, the analyzing the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain the tooth surface friction coefficient includes: constructing a tooth surface lubrication model; obtaining the mixed lubrication model parameters based on the corrected meshing position; and solving the tooth surface lubrication model based on the mixed lubrication model parameters to obtain the tooth surface friction coefficient.

[0011] Optionally, in the fifth implementation manner of the first aspect of the present invention, the introducing the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamics model for model solution to obtain the corrected dynamic response includes: introducing the tooth surface friction coefficient and the meshing stiffness into the spur gear transmission dynamics model to obtain the corrected spur gear and rolling bearing transmission dynamics equations; and solving the corrected spur gear and rolling bearing transmission dynamics equations to obtain the corrected dynamic response.

[0012] Optionally, in the sixth implementation manner of the first aspect of the present invention, it is determined whether a preset iteration stop condition is satisfied based on the corrected dynamic response. If not, the corrected dynamic response is used to replace the initial dynamic response, and the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response is returned to execute, including: if the current iteration time is less than the preset maximum iteration time, the preset iteration stop condition is not satisfied; the corrected dynamic response is used to replace the initial dynamic response, and the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response is returned to execute.

[0013] The second aspect of the present invention provides an analysis device for a spur gear and rolling bearing transmission system, including: a first acquisition module, configured to analyze the meshing process of the spur gear based on the acquired design parameters and working conditions of the spur gear to obtain an initial meshing stiffness; a first solution module, configured to construct a spur gear transmission dynamics model and introduce the initial meshing stiffness into the spur gear transmission dynamics model for model solution to obtain an initial dynamic response; a second acquisition module, configured to analyze the meshing process of the spur gear under bearing deformation based on the initial dynamic response to obtain a corrected meshing position of the spur gear pair; a force analysis module, configured to analyze the tooth force state of the spur gear pair based on the corrected meshing position to obtain a corrected meshing stiffness; a lubrication analysis module, configured to analyze the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain a tooth surface friction coefficient; a second solution module, configured to introduce the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamics model for model solution to obtain a corrected dynamic response; an iteration module, configured to determine whether a preset iteration stop condition is satisfied based on the corrected dynamic response. If not, the corrected dynamic response is used to replace the initial dynamic response, and the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response is returned to execute.

[0014] The third aspect of the present invention provides an analysis device for a spur gear and rolling bearing transmission system. The analysis device for the spur gear and rolling bearing transmission system includes: a memory and at least one processor, wherein instructions are stored in the memory; at least one of the processors calls the instructions in the memory so that the analysis device for the spur gear and rolling bearing transmission system executes each step of the analysis method for the spur gear and rolling bearing transmission system described in any one of the above.

[0015] The fourth aspect of the present invention provides a computer-readable storage medium, on which instructions are stored, and when the instructions are executed by a processor, each step of the analysis method for the spur gear and rolling bearing transmission system described in any one of the above is implemented.

[0016] In the technical solution of the present invention, first, the initial meshing stiffness is obtained by analyzing the meshing process based on the design parameters and operating conditions of the spur gear. Then, a dynamic model of the spur gear transmission is constructed to obtain the initial dynamic response. Using the initial dynamic response as a basis, the meshing process of the spur gear under bearing deformation is iteratively analyzed to correct the meshing position, meshing stiffness, tooth surface friction coefficient, and dynamic response, more accurately revealing the influence of the meshing line offset and friction state change caused by bearing deformation on the spur gear-rolling bearing transmission system, and effectively improving the analysis accuracy of the spur gear-rolling bearing transmission system. Description of the Drawings

[0017] Figure 1 It is a logic flowchart of the analysis method for the spur gear and rolling bearing transmission system provided by an embodiment of the present invention;

[0018] Figure 2 It is a schematic structural diagram of the analysis device for the spur gear and rolling bearing transmission system provided by an embodiment of the present invention;

[0019] Figure 3 It is a schematic structural diagram of the analysis equipment for the spur gear and rolling bearing transmission system provided by an embodiment of the present invention;

[0020] Figure 4 It is a diagram of the dynamic model of the spur gear transmission;

[0021] Figure 5 It is a model diagram of the meshing relationship between the driving and driven wheels of the spur gear under the influence of bearing deformation;

[0022] Figure 6 It is a model diagram of the meshing position of the gear pair under bearing deformation;

[0023] Figure 7 It is a model diagram of the cantilever beam of the meshing teeth of the spur gear pair;

[0024] Figure 8 It is a dynamic simulation diagram of the meshing stiffness of the gear pair;

[0025] Figure 9 It is a dynamic simulation diagram of the dynamic transmission error of the gear pair. Detailed Embodiments

[0026] In the description, claims and the above-mentioned drawings of the present invention, the terms "first", "second", "third", "fourth", etc. (if any) are used to distinguish similar objects and do not necessarily describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the term "comprising" or "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, device, product or equipment comprising a series of steps or units does not necessarily limit to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or equipment.

[0027] For ease of understanding, the specific process of the embodiments of the present invention will be described below. Please refer to Figure 1 , an embodiment of the analysis method of the spur gear and rolling bearing transmission system in the embodiments of the present invention includes:

[0028] 101. Analyze the meshing process of the spur gear based on the obtained design parameters and working condition parameters of the spur gear to obtain the initial meshing stiffness;

[0029] In this embodiment, the initial meshing stiffness can be solved first according to the gear meshing theory analysis and calculation methods in the prior art (such as the common potential energy method, finite element method, and Ishikawa method);

[0030] Please refer to Table 1, which shows the design parameters and working condition parameters of the spur gear pair studied in this embodiment;

[0031]

[0032] Taking the potential energy method as an example, based on the Hertz contact principle, it quantifies the relationship between the elastic deformation and load in the gear contact area through the geometric characteristics (i.e., the module, number of teeth, normal pressure angle, and tooth width in Table 1) and material characteristics (i.e., the elastic modulus and Poisson's ratio in Table 1) of the gear contact area, so as to realize the solution of the gear meshing stiffness; specifically, it first solves the radius of curvature of the meshing point based on the module, number of teeth of the driving and driven wheels, and normal pressure angle, and then substitutes the elastic modulus, Poisson's ratio, radius of curvature, and tooth width into the Hertz contact theory to quantify the relationship between the elastic deformation and load in the gear contact area, so as to obtain the calculation of the initial meshing stiffness of the gear pair at a certain moment ; The initial meshing stiffness is the meshing stiffness calculated based on the gear geometric dimensions and material characteristics under the ideal meshing state when the bearing deformation has not occurred, and it is used as the initial input for the subsequent spur gear transmission dynamics model.

[0033] 102. Construct a dynamic model of spur gear transmission, and introduce the initial meshing stiffness into the dynamic model of spur gear transmission for model solution to obtain the initial dynamic response.

[0034] In this embodiment, referring to Figure 4 , first, based on the multi-body dynamics theory, construct a 6-degree-of-freedom dynamic model (i.e., the dynamic model of spur gear transmission) including spur gears and rolling bearings, and input the initial meshing stiffness as the meshing stiffness of the gear pair into the dynamic model of spur gear transmission, and solve the model by numerical solution methods (such as the Runge-Kutta method) to obtain the initial dynamic response of the system in the initial state; the initial dynamic response includes dynamic parameters such as the displacement, velocity, acceleration, rotation angle, and meshing force of the driving and driven wheels. These parameters can reflect the dynamic characteristics of the system under the initial meshing stiffness and constitute the initial conditions for subsequent analysis, participating in the calculation of the meshing position, load angle, tooth surface friction coefficient, and meshing stiffness.

[0035] 103. Analyze the meshing process of spur gears under bearing deformation based on the initial dynamic response to obtain the corrected meshing position of the spur gear pair.

[0036] 104. Analyze the force state of the teeth of the spur gear pair based on the corrected meshing position to obtain the corrected meshing stiffness.

[0037] 105. Analyze the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain the tooth surface friction coefficient.

[0038] In this embodiment, the tooth surface friction coefficient is of great significance for studying the dynamic characteristics, energy loss, and wear of the spur gear transmission system. Different meshing positions will cause changes in parameters such as the relative motion speed, contact pressure, and oil film thickness between the tooth surfaces, thereby affecting the tooth surface friction coefficient. Therefore, after obtaining the corrected meshing position of the spur gear pair, the tooth surface lubrication state of the spur gear pair can be analyzed based on the corrected meshing position to obtain the tooth surface friction coefficient.

[0039] 106. Introduce the tooth surface friction coefficient and the corrected meshing stiffness into the dynamic model of spur gear transmission for model solution to obtain the corrected dynamic response.

[0040] In this embodiment, the tooth surface friction coefficient reflects the friction characteristics between the tooth surfaces, and the corrected meshing stiffness takes into account the influence of factors such as bearing deformation on gear meshing. These two parameters will significantly affect the dynamic behavior of the spur gear and rolling bearing transmission system. Therefore, introducing them into the model can more accurately simulate the actual operation of the system. By solving the model after introducing these two parameters, we can obtain the corrected dynamic response, which can better reflect the true dynamic characteristics of the system considering actual factors such as tooth surface friction and bearing deformation.

[0041] 107. Determine whether the preset iteration stop condition is satisfied based on the corrected dynamic response. If not, replace the initial dynamic response with the corrected dynamic response, and return to perform the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response.

[0042] In this embodiment, due to the coupling effect between tooth surface friction, bearing deformation and gear meshing, an iterative algorithm is required to gradually correct the model parameters to approximate the true dynamic response, forming a closed-loop iteration of "parameter correction - model solution" to solve the modeling error problem caused by the traditional method not considering the coupling effect.

[0043] In the embodiment of the present invention, the initial meshing stiffness is obtained by analyzing the meshing process based on the design parameters and working conditions of the spur gear. Then, a dynamic model of the spur gear transmission is constructed to obtain the initial dynamic response, and based on the initial dynamic response, an iterative analysis of the spur gear meshing process under bearing deformation is carried out to correct the meshing position, meshing stiffness, tooth surface friction coefficient and dynamic response, more accurately revealing the influence of the meshing line offset and friction state change caused by bearing deformation on the spur gear - rolling bearing transmission system, and effectively improving the modeling accuracy of the spur gear - rolling bearing transmission dynamics.

[0044] Two embodiments of the analysis method for the spur gear and rolling bearing transmission system in the embodiment of the present invention include:

[0045] 201. Construct a dynamic model of the spur gear transmission system.

[0046] In this embodiment, refer to Figure 4 , first construct a 6 - degree - of - freedom dynamic model of the spur gear transmission system (i.e., the dynamic model of the spur gear transmission system), which considers the deformation of the driving and driven wheels in three degrees of freedom directions such as x, y, and θ; in the actual spur gear and rolling bearing transmission system, the movement of the gear is not a simple unidirectional movement, but there are dynamically correlated changes in multiple directions. The dynamic model of the spur gear transmission system can accurately describe the force and movement conditions of the driving and driven wheels in different directions, thus providing a basis for in - depth analysis of the dynamic characteristics of the entire transmission system.

[0047] Figure 4 In and ( = or , which respectively represent the driving and driven wheels) are the stiffness of the support bearings of the gear on the positive semi - axes of x and y, and are respectively the damping of the support bearings of the gear on the positive semi - axes of x and y. is the gear is the transmitted torque is the meshing damping of the spur gear pair is the meshing stiffness of the spur gear pair

[0048] 202. Introduce the initial meshing stiffness into the dynamic model of spur gear transmission to obtain the dynamic equations of the initial spur gear and rolling bearing transmission;

[0049] In this embodiment, by introducing the initial meshing stiffness into the dynamic model of spur gear transmission and combining the force conditions of the spur gear pair and Newton's second law, the dynamic equations of the initial spur gear transmission system can be obtained as follows:

[0050] (1)

[0051] In Equation (1), and are the deformations of the driving and driven wheels in the x direction, which are equal to the deformations of the bearings in the x direction; and are the deformations of the driving and driven wheels in the y direction, which are equal to the deformations of the bearings in the y direction; and are the deformations of the driving and driven wheels in the direction; and are the masses of the driving and driven wheels respectively; and are the base circle radii of the driving and driven wheels respectively; and are the polar moments of inertia of the driving and driven wheels respectively;

[0052] is the dynamic meshing force (DMF) of the spur gear pair, and the calculation formula is:

[0053] (2)

[0054] In the formula, is the dynamic transmission error of the spur gear pair, takes the value of the initial meshing stiffness of the gear pair at time ; The calculation formula of

[0055] (3)

[0056] These equations clearly describe the relationship between the motions of the driving and driven wheels in each degree of freedom and the external forces, stiffness, damping, and dynamic meshing force they receive; through these equations, the internal mechanical interaction mechanism of the spur gear transmission system can be comprehensively understood.

[0057] 203. Solve the dynamic equations of the initial spur gear and rolling bearing transmission to obtain the initial dynamic response;

[0058] In this embodiment, the above equations are solved by a numerical solution method (such as the Runge-Kutta method) to obtain the initial dynamic response, which includes dynamic parameters such as the displacement, velocity, acceleration, rotation angle, and meshing force of the driving and driven wheels.

[0059] The initial dynamic response can understand the basic dynamic characteristics of the system when the bearing deformation is not considered. On this basis, the spur gear-rolling bearing system under bearing deformation is further analyzed. By comparing the dynamic responses before and after considering the bearing deformation, the influence degree of the bearing deformation on the performance of the spur gear and rolling bearing transmission system can be accurately evaluated.

[0060] The three embodiments of the analysis method for the spur gear and rolling bearing transmission system in the embodiments of the present invention include:

[0061] 301. Based on the initial dynamic response, construct a meshing model of the spur gear pair under bearing deformation to determine the meshing line and meshing points of the driving and driven wheels under bearing deformation;

[0062] In this embodiment, as Figure 6 shown, under the influence of bearing deformation, the meshing point of the gear pair moves from point X to (meshing point of the driving wheel) and (meshing point of the driven wheel), and and are respectively the intersection points of the elastic cylinders of the driving and driven wheels and the actual meshing line ; and are respectively the radii of curvature of the driving and driven wheels at the original meshing point X; and are the deformation amounts of the driving and driven wheels in the x direction; , ;

[0063] It can be seen from Figure 6 that the bearing deformations and in the initial dynamic response will cause the curvature centers of the driving and driven wheels to change from A1 and B1 to A1' and B1' (i.e., the actual meshing line ), resulting in the meshing point changing from X to and .

[0064] 302. Construct a cantilever beam model of the meshing teeth of the spur gear pair, and construct a local coordinate system in the cantilever beam model of the meshing teeth of the spur gear pair based on the meshing line;

[0065] In this embodiment, in order to more conveniently analyze and model the meshing process of the spur gear pair, a cantilever beam model of the meshing teeth of the spur gear pair is first constructed (see Figure 7 ), and a local coordinate system with the origin at point and the y-axis perpendicular to the actual meshing line is established in the model .

[0066] 303. Convert the meshing point to the local coordinate system to obtain the corrected meshing position;

[0067] In this embodiment, after determining the local coordinate system , it is necessary to convert the previously determined meshing points and to this local coordinate system.

[0068] In order to solve for the coordinates of the meshing points and in the local coordinate system , it is necessary to construct a meshing relationship model of the driving and driven wheels of the spur gear under the influence of bearing deformation (see Figure 5 ); Figure 5 In and are the tangent points of the theoretical meshing line of the gear pair after bearing deformation and the gear base circle;

[0069] According to the geometric relationship of the gear pair, the following equations can be established:

[0070] (4)

[0071] (5)

[0072] Equation (4) is the equation of the straight line and the equivalent elastic cylinder equation of the driving wheel; Equation (5) is the equation of the straight line and the equivalent elastic cylinder equation of the driven wheel; In Equations (4) and (5), and can respectively correspond to the coordinates of point and point in the local coordinate system ;

[0073] According to Equations (4)-(5), the coordinates of the meshing points and in the local coordinate system can be obtained.

[0074] Through the calculation of the above formulas, we can obtain the meshing points and The coordinates in the coordinate system are the corrected meshing positions. The corrected meshing positions take into account the influence of bearing deformation on gear meshing and are more in line with the actual transmission situation compared to the theoretical meshing positions without considering bearing deformation.

[0075] The four embodiments of the analysis method for the spur gear and rolling bearing transmission system in the embodiments of the present invention include:

[0076] 401. Analyze the force direction of the spur gear pair based on the corrected meshing position to obtain the tooth load angle;

[0077] In this embodiment, after obtaining the corrected meshing position, based on the spur gear pair meshing tooth cantilever beam model (see Figure 5 ), the force analysis of the spur gear can be carried out;

[0078] Among them, the tooth load angle of the driving side meshing tooth of the driving gear at time t is , which can be obtained from Equation (6):

[0079] (6)

[0080] In Equation (6), is the pressure angle of the driving gear at the meshing point, and are the number of teeth of the driving gear and the pressure angle of the driving side pitch circle respectively. If < , the plus sign is taken in Equation (6). If ≥ , the minus sign is taken in Equation (6); and are the tooth center distance and the pitch circle radius at the meshing point respectively, and the tooth center distance at the meshing point can be calculated based on the corrected meshing position.

[0081] 402. Calculate the meshing stiffness based on the tooth load angle to obtain the corrected meshing stiffness;

[0082] In this embodiment, during the meshing process, the meshing stiffness of the meshing teeth of the jth (j = 1, 2,..., n, n is the total number of meshing tooth pairs) meshing tooth pairs of the driving gear includes four parts: the Hertz contact stiffness , the bending stiffness , the radial compression stiffness and the shear stiffness , which can be obtained from the mechanics of materials:

[0083] (7)

[0084] (8)

[0085] (9)

[0086] (10)

[0087] In the formula, E i and v i ( i = p or g , respectively representing the driving and driven wheels) are the gear i elastic modulus and Poisson's ratio, B is the gear tooth width, is the Hertz contact radius at the meshing position; G is the gear shear modulus, is the polar moment of inertia at the microelement, is the cross-sectional area at the microelement dx, E = Ei is the elastic modulus of gear i; d is the tooth height at the meshing point, h is the half tooth thickness at the meshing point X, x is the distance of the microelement dx from the meshing point, dx is the microelement width, h x is the tooth thickness at the microelement dx;

[0088] In the formula, since each meshing tooth pair j of the driving wheel corresponds to a contact point (refer to Figure 5 ), and the contact points of each meshing tooth pair j of the driving wheel are different, so each meshing tooth pair j of the driving wheel corresponds to a different tooth load angle , that is, the tooth load angle is also a parameter related to the meshing tooth pair j of the driving wheel.

[0089] The meshing stiffness of the tooth pair j (j = 1, 2,..., n, n is the total number of meshing tooth pairs) is as shown in formula (11):

[0090] (11)

[0091] The parameters in the formula can be obtained from formulas (8)-(10).

[0092] In addition, during the gear meshing process, the gear matrix of the driving wheel will also have a certain deformation, and the stiffness corresponding to this part of the deformation is the matrix stiffness , which can be obtained from the following formula:

[0093] (12)

[0094] In the formula, is the distance from the focus of the meshing line and the tooth symmetry line to the root circle, is the base circle arc corresponding to the entire tooth profile. , , and is a coefficient, which can be obtained from the following polynomial:

[0095] (13)

[0096] wherein, is , , and any one of A, B′, C, D, E′ and F′. Details of A, B′, C, D, E′ and F′ are shown in Table 2. , is the root circle radius of the driving gear, is the radius of the gear shaft hole of the driving gear, is the center angle of the tooth profile of the driving gear tooth.

[0097]

[0098] It can be seen from Equation (7) that the Hertz contact stiffness of the tooth pair j (j = 1, 2, …, n, where n is the total number of meshing tooth pairs) is related to the load it bears; the load borne by the tooth pair j (j = 1, 2, …, n, where n is the total number of meshing tooth pairs) can be obtained from the load distribution equation:

[0099] (14)

[0100] wherein, and are respectively the load borne by the tooth pair j (j = 1, 2, …, n, where n is the total number of meshing tooth pairs) and the meshing error, is the dynamic meshing force of the spur gear pair. In this embodiment, Equation (14) is used to determine the numbers of the meshing tooth pairs and the corresponding loads borne; the specific method is as follows: First, substitute the initial load distribution information, the tooth pair meshing stiffness, and the meshing error of each tooth pair into this load distribution equation, and the meshing forces F j of each tooth pair can be obtained; when F j < 0, it indicates that the j th tooth pair does not participate in meshing. That is, the corresponding parameters are removed from this load distribution equation, and recalculation is performed until the numbers of the finally participating meshing tooth pairs are determined.

[0101] The meshing stiffness of the gear pair can be obtained from Equation (15):

[0102] (15)

[0103] wherein, is the matrix deformation correction coefficient, generally 1.1; k j is the meshing stiffness of the participating meshing tooth pairs,k fi is the gear i of the matrix stiffness.

[0104] That is the modified meshing stiffness, hereinafter referred to as .

[0105] The five embodiments of the analysis method for the spur gear and rolling bearing drive system in the embodiments of the present invention include:

[0106] 501. Construct a tooth surface lubrication model;

[0107] In this embodiment, considering that in the actual operation of spur gears, the lubrication state between tooth surfaces is usually in the mixed lubrication region, that is, there are both fluid lubrication and boundary lubrication states, so a mixed lubrication model is required to describe the lubrication situation of the tooth surface;

[0108] Specifically, the following formula is used to represent the friction coefficient in the mixed lubrication model:

[0109] Generally, the lubrication state of the tooth surface of the gear pair is mixed lubrication, which is composed of full-film lubrication and boundary lubrication. The tooth surface friction coefficient in this state can be expressed as:

[0110] (16)

[0111] In formula (16), is the friction coefficient in the boundary lubrication state, which is a constant between 0.1 and 0.2; is the friction coefficient in the full-film lubrication state, which can be obtained from the following formula:

[0112] (17)

[0113] In formula (17), is the normal load per unit tooth width, and R are the relative sliding speed and the composite curvature radius at the meshing point X respectively, ; n is the dynamic viscosity of the lubricating oil, is the pitch circle radius of the driving wheel, is the composite roughness of the gear pair;

[0114] is the load distribution percentage coefficient under mixed lubrication conditions, which can be obtained from the following formula:

[0115] (18)

[0116] In the formula, is the minimum oil film thickness of the gear pair.

[0117] 502. Obtain the parameters of the mixed lubrication model based on the corrected meshing position;

[0118] In this embodiment, based on the corrected meshing position, the parameters required in the mixed lubrication model are obtained based on the corrected meshing position, such as and \(R\) are the relative sliding velocity and the comprehensive curvature radius at the meshing point \(X\), respectively.

[0119] 503. Solve the tooth surface lubrication model based on the parameters of the mixed lubrication model to obtain the tooth surface friction coefficient;

[0120] In this embodiment, after obtaining the parameters of the mixed lubrication model, we can solve the tooth surface lubrication model to obtain the tooth surface friction coefficient.

[0121] The six embodiments of the analysis method for the spur gear and rolling bearing transmission system in the embodiments of the present invention include:

[0122] 601. Introduce the tooth surface friction coefficient and the meshing stiffness into the spur gear transmission dynamics model to obtain the corrected spur gear and rolling bearing transmission dynamics equations;

[0123] In this embodiment, when introducing the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamics model, the original equations need to be modified accordingly;

[0124] During the spur gear transmission process, the tooth surface friction force will generate an additional torque, thus affecting the rotation of the gear; at the same time, the corrected meshing stiffness will change the magnitude and characteristics of the dynamic meshing force of the spur gear pair; after considering these factors, the corrected spur gear and rolling bearing transmission dynamics equations are as follows:

[0125] (19)

[0126] 602. Solve the corrected spur gear and rolling bearing transmission dynamics equations to obtain the corrected dynamic response;

[0127] In this embodiment, the above equations are solved by a numerical solution method (such as the Runge - Kutta method) to obtain the corrected dynamic response; the corrected dynamic response takes into account the influence of the tooth surface friction coefficient and the corrected meshing stiffness, and can more accurately reflect the actual dynamic characteristics of the spur gear and rolling bearing transmission system under bearing deformation.

[0128] The seven embodiments of the analysis method for the spur gear and rolling bearing transmission system in the embodiments of the present invention include:

[0129] 701. If the current iteration time is less than the preset maximum iteration time, the preset iteration stop condition is not satisfied;

[0130] In this embodiment, the upper limit of the simulation time is set according to the engineering requirements. After each iteration, the system reads the current simulation time and compares it with the upper limit of the simulation time If < , the iterative loop is triggered.

[0131] 702. Replace the initial dynamic response with the corrected dynamic response, and return to perform the analysis of the spur gear meshing process under the bearing deformation based on the initial dynamic response.

[0132] Please refer to Figure 8 . There are significant differences between the meshing stiffness curve calculated by the method of the present invention and the calculation results of the traditional energy method; this is because the present invention incorporates the coupling effects of spur gear pair bearing deformation, tooth surface friction and gear meshing into the modeling, and the dynamic meshing excitation causes the load distribution at each meshing point to change, while the traditional energy method does not consider the coupling effect and calculates the stiffness only based on static geometric parameters, so it cannot reflect the dynamic modulation effect of the meshing line offset and friction state change caused by bearing deformation in the actual working conditions.

[0133] Please refer to Figure 9 . There is a large error between the dynamic transmission error of the gear pair calculated by the present invention and the results of the traditional method (without considering the coupling effect). The fluctuation amplitude of the dynamic transmission error curve of the traditional method is smaller, while the results of the present invention more truly reflect the dynamic meshing characteristics of the gear pair under the coupling action of bearing deformation and tooth surface friction (such as high-frequency vibration components).

[0134] Figure 8 and Figure 9 show that: the coupling effects between spur gear pair bearing deformation, tooth surface friction and gear meshing have a significant impact on the meshing mechanism and dynamic response. The traditional modeling method will cause the analysis results to be distorted due to ignoring this coupling effect. The present invention realizes the accurate capture of the coupling effect through the iterative algorithm, and its calculation results are closer to the actual working conditions, providing a necessary theoretical basis for the design of high-precision gear transmission systems, and also verifying the necessity of considering the multi-physical field coupling effect in subsequent modeling.

[0135] The above describes the analysis method of the spur gear and rolling bearing transmission system in the embodiment of the present invention. Next, the analysis device of the spur gear and rolling bearing transmission system in the embodiment of the present invention will be described. Please refer to Figure 2 . An embodiment of the analysis device of the spur gear and rolling bearing transmission system in the embodiment of the present invention includes:

[0136] The first acquisition module 801 is used to analyze the meshing process of the spur gear based on the acquired design parameters and working condition parameters of the spur gear to obtain the initial meshing stiffness;

[0137] The first solving module 802 is configured to construct a spur gear transmission dynamics model, introduce the initial meshing stiffness into the spur gear transmission dynamics model for model solving, so as to obtain an initial dynamic response;

[0138] The second obtaining module 803 is configured to analyze the spur gear meshing process under bearing deformation based on the initial dynamic response, so as to obtain the corrected meshing position of the spur gear pair;

[0139] The force analysis module 804 is configured to analyze the tooth force state of the spur gear pair based on the corrected meshing position, so as to obtain the corrected meshing stiffness;

[0140] The lubrication analysis module 805 is configured to analyze the tooth surface lubrication state of the spur gear pair based on the corrected meshing position, so as to obtain the tooth surface friction coefficient;

[0141] The second solving module 806 is configured to introduce the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamics model for model solving, so as to obtain a corrected dynamic response;

[0142] The iteration module 807 is configured to determine whether a preset iteration stop condition is satisfied based on the corrected dynamic response. If not, the corrected dynamic response is used to replace the initial dynamic response, and the process returns to execute the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response;

[0143] In this embodiment, the first obtaining module 801 analyzes the meshing process based on the design parameters and operating conditions of the spur gear to obtain the initial meshing stiffness. Then, the first solving module 802 constructs a spur gear transmission dynamics model to obtain the initial dynamic response, and the second obtaining module 803 uses the initial dynamic response as a basis to analyze the spur gear meshing process under bearing deformation to correct the meshing position. Subsequently, the force analysis module 804 and the lubrication analysis module 805 calculate the corrected meshing stiffness and the tooth surface friction coefficient based on the corrected meshing position. The second solving module 806 introduces the tooth surface friction coefficient and the corrected meshing stiffness to obtain the corrected dynamic response. Then, the iteration module 807 continuously repeats the above analysis process, gradually approaching the true dynamic response of the spur gear-rolling bearing transmission system considering the bearing deformation, tooth surface friction, and gear meshing coupling effect. The present invention more accurately reveals the influence of the meshing line offset and friction state change caused by the bearing deformation on the spur gear-rolling bearing transmission system, and effectively improves the modeling accuracy of the spur gear-rolling bearing transmission dynamics.

[0144] Figure 3FIG. 0 is a schematic structural diagram of an analysis device for a spur gear and rolling bearing transmission system provided by an embodiment of the present invention. The analysis device 900 for the spur gear and rolling bearing transmission system may vary greatly due to different configurations or performances, and may include one or more processors (central processing units, CPUs) 910 (for example, one or more processors) and a memory 920, and one or more storage media 930 (for example, one or more mass storage devices) storing application programs 933 or data 932. Among them, the memory 920 and the storage media 930 may be transient storage or persistent storage. The program stored in the storage media 930 may include one or more modules (not shown in the figure), and each module may include a series of instruction operations on the analysis device 900 for the spur gear and rolling bearing transmission system. Further, the processor 910 may be configured to communicate with the storage media 930 and execute a series of instruction operations in the storage media 930 on the analysis device 900 for the spur gear and rolling bearing transmission system to implement the steps of the analysis method for the spur gear and rolling bearing transmission system provided in the above method embodiments.

[0145] The analysis device 900 for the spur gear and rolling bearing transmission system may further include one or more power supplies 940, one or more wired or wireless network interfaces 950, one or more input / output interfaces 960, and / or one or more operating systems 931, such as Windows Serve, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art can understand that Figure 9 the shown structural diagram of the analysis device for the spur gear and rolling bearing transmission system does not limit the analysis device for the spur gear and rolling bearing transmission system, and it may include more or fewer components than shown in the figure, or combine some components, or have different component arrangements.

[0146] The present invention also provides a computer-readable storage medium. The computer-readable storage medium may be a non-volatile computer-readable storage medium, and may also be a volatile computer-readable storage medium. Instructions are stored in the computer-readable storage medium. When the instructions run on a computer, the computer is caused to execute the steps of the analysis method for the spur gear and rolling bearing transmission system.

[0147] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described device or device and unit can refer to the corresponding processes in the foregoing method embodiments and will not be described herein again.

[0148] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs.

[0149] Finally, it should be noted that the above are only preferred examples of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for analyzing a spur gear and rolling bearing transmission system, characterized in that Including: Analyze the meshing process of the spur gear based on the obtained design parameters and operating conditions of the spur gear to obtain the initial meshing stiffness; Construct a dynamic model of the spur gear transmission, and introduce the initial meshing stiffness into the dynamic model of the spur gear transmission for model solution to obtain the initial dynamic response; Analyze the meshing process of the spur gear under bearing deformation based on the initial dynamic response to obtain the corrected meshing position of the spur gear pair; Analyze the tooth force state of the spur gear pair based on the corrected meshing position to obtain the corrected meshing stiffness; Analyze the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain the tooth surface friction coefficient; Introduce the tooth surface friction coefficient and the corrected meshing stiffness into the dynamic model of the spur gear transmission for model solution to obtain the corrected dynamic response; Judge whether the preset iteration stop condition is satisfied based on the corrected dynamic response. If not, replace the initial dynamic response with the corrected dynamic response, and return to execute the analysis of the meshing process of the spur gear under bearing deformation based on the initial dynamic response; The constructing a dynamic model of the spur gear transmission, and introducing the initial meshing stiffness into the dynamic model of the spur gear transmission for model solution to obtain the initial dynamic response includes: constructing a dynamic model of the spur gear transmission system; introducing the initial meshing stiffness into the dynamic model of the spur gear transmission to obtain the dynamic equations of the initial spur gear and rolling bearing transmission; solving the dynamic equations of the initial spur gear and rolling bearing transmission to obtain the initial dynamic response; The calculation formula of the initial dynamic equations of the spur gear transmission system is as follows: ； Wherein, and are the deformations of the driving and driven wheels in the x direction, which are equal to the deformations of the bearings in the x direction; and are the deformations of the driving and driven wheels in the y direction, which are equal to the deformations of the bearings in the y direction; and are the deformations of the driving and driven wheels in the direction; and are the masses of the driving and driven wheels respectively; and are the base circle radii of the driving and driven wheels respectively; and are the polar moments of inertia of the driving and driven wheels respectively; and are the stiffnesses of the supporting bearings of the driving and driven wheels on the positive x semi-axis, and are the stiffnesses of the supporting bearings of the driving and driven wheels on the positive y semi-axis; and are the dampings of the supporting bearings of the driving and driven wheels on the positive x semi-axis, and are the dampings of the supporting bearings of the driving and driven wheels on the positive y semi-axis; and are the torques transmitted by the driving and driven wheels; is the dynamic meshing force of the spur gear pair, and its calculation formula is as follows: ； is the dynamic transmission error of the spur gear pair, is the meshing damping of the spur gear pair, is the meshing stiffness of the spur gear pair; The calculation formula is as follows: ； The introducing the tooth surface friction coefficient and the corrected meshing stiffness into the dynamic model of the spur gear transmission for model solution to obtain the corrected dynamic response includes: introducing the tooth surface friction coefficient and the meshing stiffness into the dynamic model of the spur gear transmission to obtain the corrected dynamic equations of the spur gear and rolling bearing transmission; solving the corrected dynamic equations of the spur gear and rolling bearing transmission to obtain the corrected dynamic response; The corrected dynamic equations of the spur gear and rolling bearing transmission are as follows: ； where is the tooth surface friction coefficient.

2. The analysis method of the spur gear and rolling bearing drive system according to claim 1, wherein The analyzing the meshing process of the spur gear under bearing deformation based on the initial dynamic response to obtain the corrected meshing position of the spur gear pair includes: Construct a meshing model of the spur gear pair under bearing deformation based on the initial dynamic response to determine the meshing line and meshing point of the driving gear and the driven gear under bearing deformation; Construct a cantilever beam model of the meshing teeth of the spur gear pair, and construct a local coordinate system in the cantilever beam model of the meshing teeth of the spur gear pair based on the meshing line; Convert the meshing point to the local coordinate system to obtain the corrected meshing position.

3. The analysis method of the spur gear and rolling bearing transmission system according to claim 1, characterized in that The analyzing the tooth force state of the spur gear pair based on the corrected meshing position to obtain the corrected meshing stiffness includes: Analyze the force direction of the spur gear pair based on the corrected meshing position to obtain the tooth load angle; Conduct meshing stiffness calculation based on the tooth load angle to obtain the corrected meshing stiffness.

4. The method for analyzing a spur gear and rolling bearing drive system according to claim 1, wherein The analyzing the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain the tooth surface friction coefficient includes: Construct a tooth surface lubrication model; Obtain the parameters of the mixed lubrication model based on the corrected meshing position; Solve the tooth surface lubrication model based on the parameters of the mixed lubrication model to obtain the tooth surface friction coefficient.

5. The method for analyzing a spur gear and rolling bearing drive system according to claim 1, characterized in that Judge whether the preset iteration stop condition is satisfied based on the corrected dynamic response. If not, replace the initial dynamic response with the corrected dynamic response and return to execute the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response, including: If the current iteration time is less than the preset maximum iteration time, the preset iteration stop condition is not satisfied. Replace the initial dynamic response with the corrected dynamic response and return to execute the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response.

6. An analysis device for a spur gear and rolling bearing transmission system, characterized in that, Including: The first acquisition module is used to analyze the meshing process of the spur gear based on the obtained design parameters and working conditions of the spur gear to obtain the initial meshing stiffness. The first solution module is used to construct a spur gear transmission dynamics model and introduce the initial meshing stiffness into the spur gear transmission dynamics model for model solution to obtain the initial dynamic response. The construction of the spur gear transmission dynamics model and the introduction of the initial meshing stiffness into the spur gear transmission dynamics model for model solution to obtain the initial dynamic response include: constructing a spur gear transmission system dynamics model; introducing the initial meshing stiffness into the spur gear transmission dynamics model to obtain the initial spur gear and rolling bearing transmission dynamics equations; solving the initial spur gear and rolling bearing transmission dynamics equations to obtain the initial dynamic response; the calculation formula of the initial spur gear transmission system dynamics equations is as follows: ； In the formula, and are the deformations of the driving and driven wheels in the x direction, which are equal to the deformations of the bearings in the x direction; and are the deformations of the driving and driven wheels in the y direction, which are equal to the deformations of the bearings in the y direction; and are the deformations of the driving and driven wheels in the direction; and are the masses of the driving and driven wheels respectively; and are the base circle radii of the driving and driven wheels respectively; and are the polar moments of inertia of the driving and driven wheels respectively; and are the stiffnesses of the supporting bearings of the driving and driven wheels on the positive x semi-axis, and are the stiffnesses of the supporting bearings of the driving and driven wheels on the positive y semi-axis; and are the dampings of the supporting bearings of the driving and driven wheels on the positive x semi-axis, and are the dampings of the supporting bearings of the driving and driven wheels on the positive y semi-axis; and are the torques transmitted by the driving and driven wheels; is the dynamic meshing force of the spur gear pair, and its calculation formula is as follows: ； is the dynamic transmission error of the spur gear pair, is the meshing damping of the spur gear pair, is the meshing stiffness of the spur gear pair; The calculation formula of ； The second acquisition module is used to analyze the meshing process of the spur gear under bearing deformation based on the initial dynamic response to obtain the corrected meshing position of the spur gear pair. The force analysis module is used to analyze the tooth force state of the spur gear pair based on the corrected meshing position to obtain the corrected meshing stiffness. The lubrication analysis module is used to analyze the tooth surface lubrication state of the spur gear pair based on the corrected meshing position to obtain the tooth surface friction coefficient. The second solution module is used to introduce the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamics model for model solution to obtain the corrected dynamic response; the introduction of the tooth surface friction coefficient and the corrected meshing stiffness into the spur gear transmission dynamics model for model solution to obtain the corrected dynamic response includes: introducing the tooth surface friction coefficient and the meshing stiffness into the spur gear transmission dynamics model to obtain the corrected spur gear and rolling bearing transmission dynamics equations; solving the corrected spur gear and rolling bearing transmission dynamics equations to obtain the corrected dynamic response; the corrected spur gear and rolling bearing transmission dynamics equations are as follows: ； where is the tooth surface friction coefficient; The iteration module is used to judge whether the preset iteration stop condition is satisfied based on the corrected dynamic response. If not, replace the initial dynamic response with the corrected dynamic response and return to execute the analysis of the spur gear meshing process under bearing deformation based on the initial dynamic response.

7. An analysis device for a spur gear and rolling bearing transmission system, characterized in that, The spur gear and rolling bearing transmission system analysis device includes: a memory and at least one processor, and instructions are stored in the memory; At least one of the processors invokes the instructions in the memory to cause the spur gear and rolling bearing transmission system analysis device to perform each step of the spur gear and rolling bearing transmission system analysis method according to any one of claims 1-5.

8. A computer-readable storage medium having instructions stored thereon, characterized in that, When the instructions are executed by the processor, each step of the spur gear and rolling bearing transmission system analysis method according to any one of claims 1-5 is implemented.

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