Gear dynamics modeling method considering influence of meshing position change

Abstract

The application relates to the technical field of mechanical dynamics, and discloses a gear dynamics modeling method considering the influence of meshing position change. The gear dynamics modeling method realized by the method adopts a gear meshing stiffness model which no longer simplifies the meshing stiffness between a driving wheel and a driven wheel into equivalent meshing stiffness acting on a node with a fixed spatial position and only a change in amplitude, but truly considers the change of the instantaneous meshing position between the driving wheel and the driven wheel, that is, the gear meshing stiffness model considers the change of the stiffness amplitude in the time dimension and the change of the stiffness position in the space dimension, and the gear meshing stiffness model is more in line with the actual meshing state of the gear.

Description

Technical Field

[0001] This invention relates to the field of mechanical dynamics, and in particular to a gear dynamics modeling method that takes into account the influence of changes in meshing position. Background Technology

[0002] Gears are commonly used transmission components in aerospace, transportation, and machinery manufacturing. The dynamic behavior of gears mainly depends on the alternating meshing between gear teeth. Establishing a gear dynamic model that can accurately reflect the actual meshing state of gears is the key to the dynamic analysis and evaluation of gear transmission systems.

[0003] Currently, most common gear dynamics models simplify the alternating meshing behavior between gear teeth into time-varying meshing stiffness. The time-varying meshing stiffness of gears is often treated as the stiffness whose amplitude changes with time at the meshing node, and the influence of gear meshing position changes is generally not considered. The corresponding gear dynamics models also do not consider the influence of gear meshing position changes.

[0004] With the trend towards high power density in gear manufacturing, lightweight heavy-duty gears are being used more and more widely. The lightweight, thin-walled characteristics and heavy-load bearing capacity of these gears result in complex vibration characteristics, exhibiting significant elastic vibration properties. This means that traditional gear dynamics modeling methods that do not consider changes in meshing position are no longer sufficient to meet the needs of analyzing and evaluating the dynamic behavior of lightweight heavy-duty gears. Therefore, there is an urgent need to establish a gear dynamics modeling method that considers the influence of changes in meshing position to meet the requirements of analyzing and evaluating the dynamic behavior of lightweight heavy-duty gears. Summary of the Invention

[0005] This invention addresses the problem that existing gear dynamics models cannot adequately meet the needs of analyzing and evaluating the dynamic behavior of lightweight, heavy-duty gears, and provides a gear dynamics modeling method that considers the influence of changes in meshing position.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A gear dynamics modeling method that considers the influence of changes in meshing position, the method comprising:

[0008] The time-varying meshing stiffness K of the i-th pair of meshing teeth is calculated using the local tangent method of the force-deformation curve at the instantaneous meshing position. mi (t), the calculation formula is as follows:

[0009]

[0010] Where t is the time variable, and F is the total meshing force between all meshing teeth of the gear pair. i (·) represents the meshing force between the i-th pair of meshing teeth, ΔF is the small increment of the meshing force, and ei (·) is the transmission error between the i-th pair of meshing teeth.

[0011] The time-varying meshing stiffness k mi (t) is the instantaneous meshing deformation between the master and driven gears at each time instant mi (t) is calculated as follows:

[0012]

[0013] where t is the time variable, θ is the angle variable, u p,ci and v p,cii are the radial and tangential deformations of the master gear dedendum circle at the instantaneous meshing position angle of the i-th pair of meshing teeth, u g,ci and v g,ci are the radial and tangential deformations of the driven gear dedendum circle at the instantaneous meshing position angle of the i-th pair of meshing teeth, θ p,ci( t) and θ g,ci (t) are the instantaneous meshing position angles of the i-th pair of meshing teeth of the master and driven gears, respectively, α is the theoretical pressure angle, Γ p,ci (t) and Γ g,ci (t) are the radial distances from the instantaneous meshing position of the i-th pair of meshing teeth of the master and driven gears to the dedendum circle, R p,r and R g,r are the dedendum circle radii of the master and driven gears, respectively;

[0014] Using the Hamilton principle, the kinetic energy, potential energy, elastic support strain energy, meshing potential energy, and virtual work of external forces of the master and driven gears are calculated to obtain the gear dynamics control equation considering the influence of meshing position changes,

[0015]

[0016] where t is the time variable, M is the mass operator, G is the gyroscopic effect operator, C is the centripetal effect operator, K is the stiffness operator excluding the meshing stiffness effect, K m (t) is the meshing stiffness operator considering the influence of meshing position changes, Ω is the master gear rotational speed, q is the degree of freedom column vector of the master and driven gears, and F is the excitation force column vector;

[0017] Solving the above equation and its corresponding eigenvalue problem, the gear dynamics behavior considering the influence of meshing position changes, including modal characteristics and vibration response characteristics, is obtained.

[0018] As a preferred embodiment: the total meshing force F between all meshing teeth of the gear pair is calculated as follows:

[0019]

[0020] where T g is the load torque on the driven gear, R g,b is the base radius of the driven gear.

[0021] As preferred: the radial distance Γ p,ci (t) from the instantaneous meshing position of the i-th pair of meshing teeth of the driving gear to the root circle. g,ci (t) is calculated as follows:

[0022]

[0023] where t is the time variable, R p,b and R g,b are the base radii of the driving and driven gears, respectively, R p,r and R g,r are the root circle radii of the driving and driven gears, respectively, θ p,ci (t) and θ g,ci (t) are the instantaneous meshing position angles of the driving and driven gears, respectively, and a is the theoretical pressure angle.

[0024] As preferred: the dynamic model includes a driving gear dynamic model, a driven gear dynamic model, and an engagement stiffness model considering the influence of the change of the meshing position;

[0025] The driving gear dynamic model includes radial deformation u p , tangential deformation v p , and axial deformation w p ; the driven gear dynamic model includes radial deformation u g , tangential deformation v g , and axial deformation w g ;

[0026] The engagement stiffness model considering the influence of the change of the meshing position includes the instantaneous meshing position angle θ p,ci (t) of the driving gear and the instantaneous meshing position angle θ g,ci (t) of the driven gear of the i-th pair of meshing teeth, and the time-varying engagement stiffness K mi (t) of the i-th pair of meshing teeth.

[0027] As preferred: the instantaneous meshing position angle θ p,ci (t) of the driving gear is the angle of the radial line of the instantaneous meshing position of the i-th pair of meshing teeth of the driving gear relative to the line connecting the axes of the driving and driven gears, and when the radial line is in the counterclockwise direction of the line connecting the axes of the driving and driven gears, θ p,ci (t) is positive, and vice versa;

[0028] The instantaneous meshing position angle θ g,ci(t) is the angle of the radial line of the instantaneous engagement position of the ith pair of meshing teeth relative to the axis connecting the main and driven gears, and is positive when the radial line is in the counterclockwise direction of the axis connecting the main and driven gears, and is negative otherwise g,ci (t) is positive, and is negative otherwise;

[0029] The time-varying engagement stiffness K of the ith pair of meshing teeth mi (t) is uniformly distributed in the meshing tooth width direction; The time-varying engagement stiffness K of the ith pair of meshing teeth mi (t) is calculated using the local tangent method of the force and deformation curve at the instantaneous engagement position.

[0030] To solve the above technical problems, the application further provides an electronic device comprising a memory and a processor, the memory being used to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement the gear dynamics modeling method considering the influence of the change of the engagement position as described.

[0031] To solve the above technical problems, the application further provides a computer readable storage medium storing a computer program, which, when executed by a computer, implements any one of the gear dynamics modeling methods considering the influence of the change of the engagement position. The application has the following technical effects:

[0032] The gear dynamics modeling method considers the influence of the change of the instantaneous engagement position of the gear teeth, can more truly reflect the internal engagement characteristics of the heavy-duty lightweight gear, and thus obtains more accurate dynamics behavior prediction.

[0033] The gear dynamics modeling method of the application does not simplify the engagement stiffness between the main and driven gears into the engagement stiffness acting on the node with fixed spatial position and only amplitude change, but truly considers the change of the instantaneous engagement position between the gear teeth, that is, the gear engagement stiffness model considers the change of the stiffness amplitude in the time dimension and the change of the stiffness position in the space dimension, and the gear engagement stiffness model is more consistent with the actual engagement state of the gear. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 The application is a gear dynamics model considering the influence of the change of the engagement position;

[0035] Figure 2 The application is a gear engagement stiffness considering the influence of the change of the engagement position and a comparison diagram of the conventional gear engagement stiffness;

[0036] Figure 3The application is a comparison chart of gear radial deformation response under the influence of meshing position change and gear radial deformation response without considering the influence of meshing position change.

[0037] Figure 4 The application is a comparison chart of gear axial deformation response under the influence of meshing position change and gear axial deformation response without considering the influence of meshing position change. DETAILED DESCRIPTION

[0038] The application will be further described in detail below in combination with the drawings and embodiments.

[0039] Embodiment 1

[0040] A gear dynamics modeling method considering the influence of meshing position change, the method comprising:

[0041] The time-varying meshing stiffness K of the i pair of meshing gear teeth is calculated by using the local tangent method of the force and deformation curve at the instantaneous meshing position mi (t), and the calculation formula is as follows:

[0042]

[0043] Wherein, t is a time variable, F is the total meshing force between all meshing gear teeth of the gear pair, F i (·) is the meshing force between the i pair of meshing gear teeth, ΔF is a small increment of the meshing force, e i (·) is the transmission error between the i pair of meshing gear teeth.

[0044] The time-varying meshing stiffness K mi (t) of the i pair of meshing gear teeth is calculated, and the instantaneous meshing deformation Δ mi (t) between the master and driven gear at each time instant is calculated, and the calculation formula is as follows:

[0045]

[0046] Wherein, t is a time variable, θ is an angle variable, u p,ci and v p,cii are the radial and tangential deformations of the gear tooth root circle of the driving gear at the instantaneous meshing position angle of the i pair of meshing gear teeth, u g,ci and v g,ci are the radial and tangential deformations of the gear tooth root circle of the driven gear at the instantaneous meshing position angle of the i pair of meshing gear teeth, θ p,ci (t) and θ g,ci (t) are the instantaneous meshing position angles of the i pair of meshing gear teeth of the driving gear and the driven gear respectively, α is the theoretical pressure angle, Γ p,ci (t) and Δ g,ci(t) is the radial distance from the instantaneous meshing position of the ith pair of meshing teeth of the driving gear and the driven gear to the dedendum circle, R p,r and R g,r are the dedendum circle radii of the driving gear and the driven gear, respectively;

[0047] By using the Hamilton principle, the kinetic energy, potential energy, elastic support strain energy, meshing potential energy and virtual work of external forces of the driving gear and the driven gear are calculated to obtain the gear dynamics control equation considering the influence of meshing position change,

[0048]

[0049] where t is the time variable, M is the mass operator, G is the gyroscopic effect operator, C is the centripetal effect operator, K is the stiffness operator not containing the meshing stiffness effect, K m (t) is the meshing stiffness operator considering the influence of meshing position change, Ω is the rotational speed of the driving gear, q is the column vector of degrees of freedom of the driving gear and the driven gear, and F is the column vector of excitation forces;

[0050] Solving the above equation and the corresponding eigenvalue problem, the gear dynamics behavior considering the influence of meshing position change, including the modal characteristics and vibration response characteristics, is obtained.

[0051] The total meshing force F between all meshing teeth of the gear pair is calculated according to the following formula:

[0052]

[0053] where T g is the load torque on the driven gear, R g,b is the base circle radius of the driven gear.

[0054] As preferred: the radial distance Γ p,ci (t) from the instantaneous meshing position of the ith pair of meshing teeth of the driving gear and the driven gear to the dedendum circle, g,ci (t) is calculated according to the following formula:

[0055]

[0056] where t is the time variable, R p,b and R g,b are the base circle radii of the driving gear and the driven gear, respectively, R p,r and R g,r are the dedendum circle radii of the driving gear and the driven gear, respectively, θ p,ci (t) and θ g,ci (t) are the instantaneous meshing position angles of the driving gear and the driven gear, respectively, and α is the theoretical pressure angle.

[0057] As preferred: the dynamic model comprises a driving wheel dynamic model, a driven wheel dynamic model and a mesh stiffness model considering the influence of mesh position variation;

[0058] The driving wheel dynamic model comprises a radial deformation u p , a tangential deformation v p and an axial deformation w p ; the driven wheel dynamic model comprises a radial deformation u g , a tangential deformation v g and an axial deformation w g ;

[0059] The mesh stiffness model considering the influence of mesh position variation comprises a driving gear instantaneous mesh position angle θ p,ci (t) and a driven gear instantaneous mesh position angle θ g,ci (t) of the i-th pair of meshing teeth, and a time-varying mesh stiffness K mi (t) of the i-th pair of meshing teeth.

[0060] The driving wheel instantaneous mesh position angle θ p,ci (t) is an angle of a radial line of the instantaneous mesh position of the i-th pair of meshing teeth of the driving wheel relative to the line connecting the axes of the driving wheel and the driven wheel, and when the radial line is in the counterclockwise direction of the line connecting the axes of the driving wheel and the driven wheel, θ p,ci (t) is positive, and vice versa;

[0061] The driven wheel instantaneous mesh position angle θ g,ci (t) is an angle of a radial line of the instantaneous mesh position of the i-th pair of meshing teeth of the driven wheel relative to the line connecting the axes of the driving wheel and the driven wheel, and when the radial line is in the counterclockwise direction of the line connecting the axes of the driving wheel and the driven wheel, θ g,ci (t) is positive, and vice versa;

[0062] The time-varying mesh stiffness K mi (t) of the i-th pair of meshing teeth is uniformly distributed in the meshing tooth width direction; the time-varying mesh stiffness K mi (t) of the i-th pair of meshing teeth is obtained by using a local tangent line method of force and deformation curves at the instantaneous mesh position.

[0063] Embodiment 2

[0064] On the basis of Embodiment 1, the embodiment is an electronic device comprising a memory and a processor, the memory being configured to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement a gear dynamic modeling method considering the influence of mesh position variation as described.

[0065] Embodiment 3

[0066] On the basis of the above-mentioned embodiments, the present embodiment is a computer readable storage medium storing a computer program, which, when executed by a computer, implements any one of the above-mentioned gear dynamic modeling methods considering the influence of the change of the meshing position.

[0067] Embodiment 4

[0068] On the basis of the above-mentioned embodiments, the present embodiment combines Figure 1 the above-mentioned gear dynamic modeling methods considering the influence of the change of the meshing position, which is applied to a gear pair with a gear ratio greater than 1 and less than 2, and the dynamic model includes a driving gear dynamic model, a driven gear dynamic model, and a meshing stiffness model considering the influence of the change of the meshing position. The driving gear dynamic model considers the three-dimensional deformation of the driving gear, including radial deformation u p , tangential deformation v p , and axial deformation w p ; the driven gear dynamic model considers the three-dimensional deformation of the driven gear, including radial deformation u g , tangential deformation v g , and axial deformation w g .

[0069] The meshing stiffness model considering the influence of the change of the meshing position includes: the instantaneous meshing position angle θ p,c1 (t) of the driving gear and the instantaneous meshing position angle θ g,c1 (t) of the driven gear of the first pair of meshing teeth, the time-varying meshing stiffness k m1 (t) of the first pair of meshing teeth, the instantaneous meshing position angle θ p,c2 (t) of the driving gear and the instantaneous meshing position angle θ g,c2 (t) of the driven gear of the second pair of meshing teeth, and the time-varying meshing stiffness k m2 (t) of the second pair of meshing teeth. The time-varying meshing stiffness k m1 (t) and k m2 (t) are uniformly distributed in the meshing tooth width direction. Taking the first pair of meshing teeth as an example, the instantaneous meshing position angles θ p,c1 (t) and θ g,c1 (t) are the angles of the radial lines of the driving gear and the driven gear at the instantaneous meshing position of the first pair of meshing teeth relative to the connecting line of the driving gear and the driven gear.

[0070] In combination with Figure 2 , Figure 3 and Figure 4 , the above-mentioned gear dynamic modeling methods considering the influence of the change of the meshing position are applied to a gear pair with a gear ratio greater than 1 and less than 2, and include the following specific steps:

[0071] Step 1: Calculate the time-varying mesh stiffness K of the 1st pair of meshing teeth using the local tangent method of force and deformation curve at the instantaneous meshing position m1 (t) and the time-varying mesh stiffness K of the 2nd pair of meshing teeth m2 (t) as follows:

[0072]

[0073] Where t is the time variable, F is the total meshing force between all meshing teeth of the gear pair (determined by the driven wheel load torque divided by the driven wheel base circle radius), F1(·) and F2(·) are the meshing forces between the 1st and 2nd pair of meshing teeth respectively, ΔF is the small increment of meshing force, e1(·) and e2(·) are the transmission errors between the 1st and 2nd pair of meshing teeth respectively.

[0074] The time-varying mesh stiffness considering the influence of meshing position change obtained by the above formula is compared with the traditional stiffness as shown in Figure 2 .

[0075] Step 2: Calculate the instantaneous meshing deformation Δ between the driving and driven gears corresponding to the time-varying mesh stiffness K m1 (t) of the 1st and 2nd pair of meshing teeth m2 (t) as follows: m1 (t) and Δ m2 (t) are the time-varying meshing deformations of the 1st and 2nd pair of meshing teeth respectively.

[0076]

[0077] Where t is the time variable, θ is the angle variable, u p,c1 and u p,c2 are the radial deformations of the driving gear root circle at the instantaneous meshing position angles of the 1st and 2nd pair of meshing teeth respectively, v p,c1 and v p,c2 are the tangential deformations of the driving gear root circle at the instantaneous meshing position angles of the 1st and 2nd pair of meshing teeth respectively, u g,c1 and u g,c2 are the radial deformations of the driven gear root circle at the instantaneous meshing position angles of the 1st and 2nd pair of meshing teeth respectively, v g,c1 and vg, c2 are the tangential deformations of the driven gear root circle at the instantaneous meshing position angles of the 1st and 2nd pair of meshing teeth respectively, θ p,c1 (t) and θ p,c2 (t) are the instantaneous meshing position angles of the driving gear of the 1st and 2nd pair of meshing teeth respectively, θ g,c1 (t) and θ g,c2 (t) are the instantaneous meshing position angles of the driven gear of the 1st and 2nd pair of meshing teeth respectively, α is the theoretical pressure angle, Γ p,c1 (t) and Γp,c2 (t) are the radial distances from the instantaneous meshing position of the 1st and 2nd pair of meshing teeth to the root circle of the driver, respectively, Γ g,c1 (t) and Γ g,c2 (t) are the radial distances from the instantaneous meshing position of the 1st and 2nd pair of meshing teeth to the root circle of the driver, respectively, Γ p,r and R p,r are the root circle radii of the driver and the driven, respectively. Γ p,c1 (t), Γ p,c2 (t), Γ g,c1 (t) and Γ g,c2 The calculation formulas of Γ

[0078]

[0079] where t is the time variable, R p,b and R g,b are the base circle radii of the driver and the driven, respectively, R p,r and R g,r are the root circle radii of the driver and the driven, respectively, θ p,c1 (t) and θ p,c2 (t) are the instantaneous meshing position angles of the 1st and 2nd pair of meshing teeth of the driver, respectively, θ p,c1 (t) and θ p,c2 (t) are the instantaneous meshing position angles of the 1st and 2nd pair of meshing teeth of the driven, respectively, and α is the theoretical pressure angle.

[0080] Step 3: Using the Hamilton principle, the kinetic energy, potential energy, elastic support strain energy, meshing potential energy and virtual work of external forces of the driver and the driven are calculated to obtain the gear dynamics control equation considering the influence of meshing position change, as follows

[0081]

[0082] where t is the time variable, M is the mass operator, G is the gyroscopic effect operator, C is the centripetal effect operator, K is the stiffness operator excluding the meshing stiffness effect, K m (t) is the meshing stiffness operator considering the influence of meshing position change, Ω is the rotational speed of the driver, q is the freedom column vector of the driver and the driven, and F is the excitation force column vector.

[0083] Solving the above equation and the corresponding eigenvalue problem can obtain the gear dynamics behavior considering the influence of meshing position change, including the modal characteristics and vibration response characteristics.

[0084] The radial deformation and axial deformation results of the heavy-duty light-weight gear obtained based on the modeling method of the application and the traditional modeling method are compared as follows Figure 3 and Figure 4As shown, according to the figure, for the heavy load light gear, the response obtained by the traditional modeling method misses some important resonance responses, and the gear dynamics modeling method provided by the application considers the influence of the change of the instantaneous meshing position of the gear teeth, can more truly reflect the internal meshing characteristics of the heavy load light gear, and thus more accurate dynamics behavior is obtained.

Claims

1. A method for modeling gear dynamics considering the influence of meshing position variation, the method comprising: The time-varying meshing stiffness K of the ith pair of meshing teeth is calculated by using the local tangent method of force and deformation curve at the instant meshing position mi (t), and the calculation formula is as follows: where t is the time variable, F is the total meshing force between all the meshing teeth of the gear pair, F i (·) is the meshing force between the i-th pair of meshing teeth, ΔF is a small increment of the meshing force, e i (·) is the transmission error between the i-th pair of meshing teeth; calculating the time-varying mesh stiffness K of the ith pair of meshing teeth mi (t) the instantaneous mesh deformation Δ between the master and driven gears at each time instant mi (t), the calculation formula is as follows: where t is the time variable, θ is the angular variable, u p,ci and v p,cii are the radial and tangential deformations of the driving tooth root circle at the instant of engagement of the i-th pair of engaging teeth, u g,ci and v g,ci are the radial and tangential deformations of the driven tooth root circle at the instant of engagement of the i-th pair of engaging teeth, θ p,ci (t) and θ g,ci (t) are the instant of engagement angular positions of the i-th pair of engaging teeth of the driving wheel and of the driven wheel, respectively, a is the theoretical pressure angle, Γ p,ci (t) and Γ g,ci (t) are the radial distances of the instant of engagement of the i-th pair of engaging teeth of the driving wheel and of the driven wheel, respectively, from the tooth root circle, R p,r and R g,r are the driving wheel and driven wheel tooth root circle radii, respectively. calculating the kinetic energy, potential energy, elastic support strain energy, meshing potential energy and virtual work of external forces of the driving gear and the driven gear by using Hamilton principle to obtain the gear dynamics governing equations considering the influence of meshing position variation, where t is the time variable, M is the mass operator, G is the gyroscopic operator, C is the centripetal operator, K is the stiffness operator excluding the effect of mesh stiffness, K m (t) is the mesh stiffness operator considering the effect of mesh position variation, Ω is the driving wheel rotational speed, q is the column vector of degrees of freedom of the driving and driven wheels, and F is the column vector of excitation forces. solving the above equations and corresponding eigenvalue problems to obtain the gear dynamics behavior considering the influence of meshing position variation, including modal characteristics and vibration response characteristics.

2. The gear dynamics modeling method considering the influence of mesh position variation according to claim 1, characterized in that: The total meshing force F between all meshing teeth of the gear pair is calculated according to the following formula: where T g is the load torque on the driven wheel, R g,b is the base circle radius of the driven wheel.

3. The gear dynamics modeling method considering the influence of mesh position variation according to claim 1, characterized in that: the radial distance Γ of the instantaneous meshing position of the meshing toothing of the master-slave gear pair i to the root circle p,ci (t) and Γ g,ci The formula for calculating (t) is as follows: where t is the time variable, R p,b and R g,b are the base circle radii of the driving and driven gears, respectively, R p,r and R g,r are the root circle radii of the driving and driven gears, respectively, θ p,ci (t) and θ g,ci (t) are the instantaneous angles of the driving and driven gears, respectively, and α is the theoretical pressure angle.

4. The gear dynamics modeling method considering the influence of mesh position variation according to claim 1, characterized in that: The dynamics model includes the driving gear dynamics model, the driven gear dynamics model and the meshing stiffness model considering the influence of meshing position variation; The driving wheel dynamics model comprises a radial deformation u p , a tangential deformation v p and an axial deformation w p ; the driven wheel dynamics model comprises a radial deformation u g , a tangential deformation v g and an axial deformation w g ; The meshing stiffness model considering the influence of meshing position changes includes the instantaneous meshing position angle θ of the driving gear of the i-th pair of meshing teeth. p,ci (t) and the instantaneous meshing position angle θ of the driven gear g,ci (t) and the time-varying meshing stiffness K of the i-th pair of meshing teeth. mi (t). 5.The method according to claim 4, characterized in that: instantaneous engagement position angle θ of the driving wheel p,ci (t) is the angle between the radial line of the instantaneous engagement position of the i-th pair of meshing teeth of the driving wheel and the line connecting the axes of the driving and driven wheels. When this radial line is in the counterclockwise direction of the line connecting the axes of the driving and driven wheels, θ p,ci (t) is positive, and vice versa; Instantaneous meshing position angle of driven wheel θ g,ci (t) is the angle of the radial line of the instantaneous meshing position of the i-th pair of meshing teeth of the driven wheel relative to the line connecting the axes of the primary and driven wheels, θ g,ci (t) is positive, and vice versa. Time-varying engagement stiffness K of the ith pair of meshing teeth mi (t) is uniformly distributed in the meshing tooth width direction; Time-varying engagement stiffness K of the ith pair of meshing teeth mi (t) is calculated using the local tangent method of the force-deformation curve at the instantaneous engagement position.

6. An electronic device, comprising: a memory and a processor, the memory being configured to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement the method according to any one of claims 1-5.

7. A computer readable storage medium storing a computer program, characterized in that, The computer program is executed by a computer to implement the method according to any one of claims 1-5.

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