Electromechanically coupled gear dynamics modeling method, apparatus, device, and medium

Abstract

This invention relates to a method, apparatus, device, and medium for modeling the dynamics of electromechanical coupled gears. The method involves: determining the bearing type, motor parameters, and gear parameters in the gear system; based on the determined bearing type, motor parameters, and gear parameters, calculating the time-varying contact stiffness of each bearing, the time-varying meshing stiffness of each gear stage, the motor torque, and the unbalanced magnetic pull of the motor rotor; constructing the motor rotor dynamics equation and the electromechanical coupled gear dynamics equation; establishing a state-space equation by simultaneously solving the motor rotor dynamics equation and the electromechanical coupled gear dynamics equation; and solving the state-space equation to obtain the gear vibration displacement. The electromechanical coupled gear dynamics modeling method of this invention can more accurately calculate the output vibration displacement and vibration acceleration of the gear system in an electric drive assembly, thereby obtaining dynamic response characteristics of the gear system in an electric drive assembly that are more consistent with reality.

Description

Technical Field

[0001] This invention belongs to the field of gear dynamics of electric drive assemblies for pure electric vehicles, and specifically relates to a method for modeling the dynamics of electromechanical coupled gears, a corresponding device, electronic equipment, and a computer-readable storage medium. Background Technology

[0002] With increasingly tight energy supplies and a growing need for ecological improvement, pure electric vehicles have been widely adopted. As a core component of pure electric vehicles, the performance of the electric drive system directly determines the vehicle's power, economy, and reliability. To further improve system efficiency, power density, and operational stability, electric drive systems are iteratively developing towards highly integrated structures and unified control strategies. Simultaneously, the evolution of drive motors towards wider speed ranges, higher speeds, and lighter weights presents new technical challenges and application difficulties for the electric drive system.

[0003] To address the complex electromechanical coupling vibration problem caused by the coaxial arrangement of the motor rotor and reduction gear in current electric drive assemblies, this application proposes a two-way electromechanical coupling dynamics modeling method. This method considers both the eccentricity of the permanent magnet synchronous motor rotor due to machining deviations or assembly errors, which leads to the excitation effect of unbalanced magnetic pull on gear vibration, and the reaction of gear vibration displacement on the motor rotor, causing changes in eccentricity. Ultimately, this alters the two-way influence of the unbalanced magnetic pull. The model is constructed by coupling the stiffness matrix of the unbalanced magnetic pull with the stiffness matrix of the gear dynamics equation. Based on this method, the electromechanical coupling gear dynamics equation can be derived, accurately calculating the vibration displacement and acceleration of the gear under electromechanical coupling.

[0004] Existing electromechanical coupling dynamics modeling methods mostly focus on the individual structure of permanent magnet synchronous motors, neglecting the reverse effects of gear and transmission system vibrations on the motor, resulting in a one-sided modeling problem. For example, invention patent application CN119849264A discloses "a method for electromechanical coupling dynamics modeling of propulsion shaft systems." This method constructs a propulsion shaft system model by coupling the electromagnetic torque of the motor, the unbalanced magnetic pull, and the bearing support force, improving the fit of the shaft system's dynamic response characteristics. However, this method does not fully consider the influence of external loads such as propellers on the unbalanced magnetic pull of the motor. For example, the invention patent application with publication number CN115795877A proposes a "method for calculating the stiffness and transient dynamics of electromechanical coupled modified gears". Its modeling process fully considers the influence mechanism of the base circle and pitch circle dimensions on the time-varying meshing stiffness, which improves the accuracy of meshing stiffness calculation and dynamic analysis. However, the electromechanical coupling method used in this method for calculating the stiffness and transient dynamics of electromechanical coupled modified gears is relatively simplified. It only uses the electromagnetic torque of the motor and the rotor speed as common variables for torque transmission in the motor-gear system, and does not include the electromagnetic stiffness of the motor in the calculation system of vibration displacement of the gear system.

[0005] In summary, due to the pursuit of highly integrated design in current pure electric vehicle electric drive assemblies, the mainstream solution adopts a coaxial arrangement of the motor rotor and gear input shaft to reduce assembly size. In this arrangement, the eccentricity of the motor rotor induces an unbalanced magnetic pull, which acts as an external excitation on the gear, causing a change in its vibration displacement. Simultaneously, the gear vibration displacement is transmitted in the reverse direction to the motor rotor through a rigid connecting shaft, causing dynamic changes in the rotor eccentricity. After continuous interaction, these two forces reach dynamic equilibrium, forming the actual output vibration displacement of the gear. Existing technologies only consider unidirectional electromechanical coupling relationships, such as the influence of bearings on the unbalanced magnetic pull of the motor rotor and the unidirectional effect of electromagnetic excitation on the gear, which cannot meet the gear vibration excitation calculation requirements of highly integrated electric drive assemblies.

[0006] Therefore, there is an urgent need to develop a dynamic modeling method that takes into account both bidirectional electromechanical coupling, so as to accurately calculate the gear output vibration displacement of the electric drive assembly. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide an electromechanical coupling gear dynamics modeling method, corresponding device, electronic device and computer-readable storage medium.

[0008] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0009] A method for modeling the dynamics of electromechanical coupled gears includes the following steps:

[0010] Step 1: Determine the bearing type, motor parameters, and gear parameters of the gear system;

[0011] Step 2: Based on the determined bearing model, motor parameters and gear parameters, calculate the time-varying contact stiffness of each bearing in the gear system, the time-varying meshing stiffness of each gear stage, the motor torque and the unbalanced magnetic pull of the motor rotor.

[0012] Step 3: Construct the dynamic equations of the motor rotor and the electromechanical coupling gear;

[0013] Step 4: Establish the state-space equation by combining the motor rotor dynamics equation and the electromechanical coupled gear dynamics equation, and solve the state-space equation to obtain the gear vibration displacement.

[0014] Preferably, in step 2, based on the determined bearing model, motor parameters, and gear parameters, the time-varying contact stiffness of each bearing is calculated according to national standards. The specific steps are as follows:

[0015] Step 201: Obtain the radial clearance of the bearing and the radial displacement of the bearing shaft, calculate the first ratio of the radial clearance to the fixed value 2, and determine the relationship between the first ratio and the radial displacement of the bearing shaft to determine the value of the radial force on the bearing.

[0016] Step 202: Obtain the first displacement component of the bearing shaft in the X-axis direction, the second displacement component in the Y-axis direction, and the third displacement component in the Z-axis direction, respectively;

[0017] Based on the first displacement component, the radial displacement of the bearing shaft, and the radial force on the bearing, the first radial component of the radial force on the bearing in the X-axis direction is calculated; the second ratio of the first radial component to the first displacement component is calculated and the negative value is taken to obtain the first time-varying contact stiffness in the X-axis direction.

[0018] Based on the second displacement component, the radial displacement of the bearing shaft, and the radial force on the bearing, the second radial component of the radial force on the bearing in the Y-axis direction is calculated; the third ratio of the second radial component to the second displacement component is calculated and taken as negative to obtain the second time-varying contact stiffness in the Y-axis direction.

[0019] Obtain the axial clearance of the bearing, calculate the fourth ratio of the axial clearance to the fixed value 2, determine the relationship between the fourth ratio and the third displacement component, and determine the value of the axial force on the bearing; calculate the fifth ratio of the axial force on the bearing to the third displacement component, and obtain the third time-varying contact stiffness in the Z-axis direction.

[0020] Preferably, in step 201, the rule for determining the value of the radial force on the bearing is as follows:

[0021] When the radial displacement of the bearing shaft is greater than the first ratio, first calculate the first difference between the radial displacement and the first ratio, then raise the first difference to the nth power, and multiply the result by the bearing radial stiffness coefficient. The product is the value of the radial force on the bearing.

[0022] When the radial displacement of the bearing shaft is less than the first ratio, the radial force on the bearing is zero.

[0023] Preferably, in step 2, the motor torque is calculated using the dq model of the permanent magnet synchronous motor.

[0024] Preferably, in step 2, the unbalanced magnetic pull force of the motor rotor includes a first unbalanced magnetic pull force component in the X-axis direction and a second unbalanced magnetic pull force component in the Y-axis direction. The specific calculation steps are as follows:

[0025] Step 211: Determine the mechanical angle on the air gap circumference and the corresponding air gap magnetic flux density distribution at the time. Based on the air gap magnetic flux density distribution and vacuum permeability, calculate the magnetic field energy density at that location.

[0026] Step 212: Determine the area of ​​the micro-element region based on the motor rotor radius, motor rotor axial length, and angular micro-element;

[0027] Step 213: Multiply the magnetic field energy density by the area of ​​the micro-element region, and combine it with the cosine of the mechanical angle on the air gap circumference to obtain the force component of the micro-element region in the X-axis direction; integrate the mechanical angle in the interval [0, 2π], and sum up the force components of all micro-element regions in the X-axis direction to obtain the first unbalanced magnetic pull component in the X-axis direction.

[0028] Step 214: Multiply the magnetic field energy density by the area of ​​the micro-element region, and combine it with the sine value of the mechanical angle on the air gap circumference to obtain the force component of the micro-element region in the Y-axis direction; integrate the mechanical angle in the interval [0, 2π], and sum up the force components of all micro-element regions in the Y-axis direction to obtain the second unbalanced magnetic pull component in the Y-axis direction.

[0029] Preferably, in step 3, the steps for constructing the motor rotor dynamics equations are as follows:

[0030] Calculate the second partial derivative of the first unbalanced magnetic pull component with respect to the first displacement component, and use it as the first electromagnetic stiffness component in the X-axis direction; calculate the second partial derivative of the second unbalanced magnetic pull component with respect to the second displacement component, and use it as the second electromagnetic stiffness component in the Y-axis direction.

[0031] Based on the first electromagnetic stiffness component and the second electromagnetic stiffness component, the electromagnetic stiffness matrix of the motor rotor in the electromagnetic field is calculated.

[0032] By combining the first electromagnetic stiffness component, the second electromagnetic stiffness component, the first displacement component, the second displacement component, the mass of the motor rotor, the mechanical damping coefficient of the motor rotor, and the mechanical stiffness of the motor rotor, the motor rotor dynamic equation is constructed:

[0033] ;

[0034] In the formula: The mass of the motor rotor; This is the mechanical damping coefficient; This is the first displacement component; This is the second displacement component; This is the first electromagnetic stiffness component; This is the second electromagnetic stiffness component; , These are the components of the gear meshing force in the X-axis and Y-axis directions, respectively; This refers to the mechanical stiffness of the motor rotor.

[0035] Preferably, in step 3, the steps for constructing the electromechanical coupling gear dynamics equations are as follows:

[0036] The time-varying meshing stiffness of each gear stage is added to the time-varying contact stiffness matrix of each bearing to construct the eight-degree-of-freedom dynamic equations of the first-stage gear pair.

[0037] The electromagnetic stiffness matrix of the motor rotor is added to the stiffness matrix of the eight-degree-of-freedom dynamic equation of the first-stage gear pair, and the motor torque is introduced as an external excitation term into the excitation part of the eight-degree-of-freedom dynamic equation of the first-stage gear pair to obtain the electromechanical coupled gear dynamic equation.

[0038] ;

[0039] In the formula: , These are the masses of the driving gear and the driven gear, respectively. and These are the mechanical damping coefficients of the driving gear in the X-axis and Y-axis directions, respectively. and These represent the support stiffness of the driving gear in the X-axis and Y-axis directions, respectively. , , These are the components of the gear meshing force in the X-axis, Y-axis, and Z-axis directions, respectively. and These are the radial mechanical damping coefficients of the driving gear and the driven gear, respectively. and These are the radial support stiffnesses of the driving gear and the driven gear, respectively. , These are the moments of inertia of the driving gear and the driven gear, respectively. , These are the base circle radii of the driving gear and the driven gear, respectively. The output torque of the gear system is equal to the output torque of the permanent magnet synchronous motor; This represents the load torque of the gear system.

[0040] An electromechanical coupling gear dynamics modeling device, comprising:

[0041] The parameter identification module is used to determine the bearing model, motor parameters, and gear parameters of the gear system.

[0042] The parameter calculation module is used to calculate the time-varying contact stiffness of each bearing in the gear system, the time-varying meshing stiffness of each stage of gear, the motor torque, and the unbalanced magnetic pull of the motor rotor based on the bearing model, motor parameters, and gear parameters determined by the parameter identification module.

[0043] The model building module is used to construct the motor rotor dynamic equation and the electromechanical coupled gear dynamic equation by calculating the time-varying contact stiffness of each bearing, the time-varying meshing stiffness of each gear, the motor torque and the unbalanced magnetic pull of the motor rotor, which are calculated by the parameter calculation module. The state space equation is established by combining the motor rotor dynamic equation and the electromechanical coupled gear dynamic equation.

[0044] The model solving module is used to solve the state-space equations constructed by the model building module to obtain the gear vibration displacement.

[0045] An electronic device includes a central processing unit and a memory, the central processing unit being configured to invoke and run a computer program stored in the memory to perform the steps of the electromechanical coupling gear dynamics modeling method.

[0046] A computer-readable storage medium stores, in the form of computer-readable instructions, a computer program implemented according to the electromechanical coupling gear dynamics modeling method, which, when called by a computer, executes the steps included in the corresponding method.

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] 1. The electromechanical coupling gear dynamics modeling method of the present invention starts from the perspective of bidirectional electromechanical coupling between the rotor and gear of the permanent magnet synchronous motor, fully considers the unbalanced magnetic pull of the motor rotor, the time-varying meshing stiffness of each gear and the time-varying contact stiffness of each bearing, and establishes the electromechanical coupling gear dynamics equation considering the unbalanced magnetic pull. In this way, the output vibration displacement and vibration acceleration of the gear system in the electric drive assembly can be accurately calculated, thereby obtaining the dynamic response characteristics of the gear system in the electric drive assembly that are more in line with reality.

[0049] 2. The electromechanical coupling gear dynamics modeling method of the present invention takes into account that the motor rotor and the gear input shaft are coaxially arranged, and the two interact with each other and output stable gear vibration displacement after dynamic equilibrium. Therefore, the dynamic equations of the motor rotor and the electromechanical coupling gear are combined, and the final output after dynamic equilibrium is solved by constructing state space equations. In addition, the electromechanical coupling gear dynamics modeling method of the present invention not only introduces the unbalanced magnetic pull as an external input excitation into the model, but also couples the electromagnetic stiffness matrix corresponding to the unbalanced magnetic pull to the eight-degree-of-freedom dynamic equation of the first-stage gear pair, thus better conforming to the actual working conditions.

[0050] 3. The electromechanical coupling gear dynamics modeling method of the present invention is not only applicable to the electric drive assembly of pure electric vehicles, but can also be extended to all electric drive systems that adopt the coaxial scheme of motor rotor and gear input shaft due to high integration requirements. It has a wider range of applications and thus has good versatility and adaptability. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the electromechanical coupling gear dynamics modeling method of the present invention.

[0052] Figure 2 This is a flowchart of the electromechanical coupling gear dynamics modeling method of the present invention.

[0053] Figure 3 This is a structural diagram of a gear system.

[0054] Figure 4 This is a comparison diagram of the vibration acceleration in the X-axis direction of the gear system under two working conditions: "with motor" and "without motor".

[0055] Figure 5 This is a comparison diagram of the vibration acceleration in the Y-axis direction of the gear system under two working conditions: "with motor" and "without motor".

[0056] Figure 6 This is a comparison diagram of the vibration acceleration in the Z-axis direction of the gear system under two working conditions: "with motor" and "without motor". Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0058] Example 1

[0059] like Figures 4-6 As shown, Figure 4 This is a comparison diagram of the vibration acceleration in the X-axis direction of the gear system under two working conditions: "with motor" and "without motor". Figure 5 This is a comparison diagram of the vibration acceleration in the Y-axis direction of the gear system under two working conditions: "with motor" and "without motor". Figure 6 This graph compares the Z-axis vibration acceleration of a gear system under two operating conditions: "with motor" and "without motor." The vertical axis represents vibration acceleration, and the horizontal axis represents time. The red curve represents the vibration acceleration response considering the electromechanical coupling effect of the motor, while the green curve represents the vibration acceleration response without considering the motor's influence (gear transmission only). It shows that the vibration of the gears significantly increases due to the influence of the motor (i.e., the unbalanced magnetic pull reduces the stiffness of the entire gear system). This increased vibration not only causes noise pollution but also accelerates fatigue damage to the gears and transmission components, directly shortening the service life of the gear system. However, traditional pure mechanical gear dynamics modeling focuses only on mechanical factors such as gear meshing and transmission errors, completely ignoring electromagnetic interference such as the unbalanced magnetic pull introduced by the motor. This "separation of mechanical and electromagnetic coupling effects" modeling method cannot accurately reflect the dynamic characteristics of actual electromechanical coupled gear systems, resulting in significant deviations between vibration predictions and life assessments obtained from actual engineering practices. Consequently, it cannot provide reliable support for system vibration reduction design and reliability optimization.

[0060] To address the aforementioned issues, this invention proposes a method for modeling the electromechanical coupling gear dynamics, which not only considers the interaction between the unbalanced magnetic pull of the motor and the vibration displacement of the gear, forming a two-way electromechanical coupling, but also takes into account the eccentricity of the permanent magnet synchronous motor rotor due to processing errors, assembly errors, etc., which in turn triggers the unbalanced magnetic pull.

[0061] The unbalanced magnetic pull acts as a time-varying excitation source on the gear system, causing changes in gear vibration displacement. Since the motor rotor of a pure electric vehicle is coaxially connected to the gear input shaft, the vibration displacement of the gear is transmitted to the motor rotor, thereby dynamically changing the eccentricity of the motor rotor. The change in the eccentricity of the motor rotor, in turn, affects the magnitude of the unbalanced magnetic pull, forming an electromechanical coupling closed loop. At the same time, based on the coaxial structural feature, this invention superimposes / assembles the negative electromagnetic stiffness matrix on the motor side and the time-varying meshing stiffness matrix on the gear side to construct the total electromechanical coupling stiffness matrix under electromechanical coupling action, thereby establishing a gear dynamics model that considers the unbalanced magnetic pull and the electromechanical coupling stiffness.

[0062] See Figures 1-3 The electromechanical coupling gear dynamics modeling method of the present invention includes the following steps:

[0063] Step 1: Determine the bearing model, motor parameters, and gear parameters in the gear system;

[0064] Step 2: Based on the determined bearing models, motor parameters, and gear parameters, calculate the time-varying contact stiffness of each bearing in the gear system, the time-varying meshing stiffness of each gear stage, the motor torque, and the unbalanced magnetic pull of the motor rotor according to national standards. Specifically:

[0065] The calculation steps for the time-varying contact stiffness of each bearing are as follows:

[0066] Step 201: Obtain the radial clearance of the bearing and the radial displacement of the bearing shaft. Calculate the first ratio of the radial clearance to a fixed value 2, and determine the relationship between the first ratio and the radial displacement of the bearing shaft. When the radial displacement of the bearing shaft is greater than the first ratio, first calculate the first difference between the radial displacement and the first ratio, then raise the first difference to the nth power. Multiply the result by the bearing radial stiffness coefficient; the product is the value of the radial force on the bearing. When the radial displacement of the bearing shaft is less than or equal to the first ratio, the radial force on the bearing is zero. Specifically, this can be expressed by the formula:

[0067] ;

[0068] In the formula: This refers to the radial force acting on the bearing. This refers to the radial stiffness coefficient of the bearing. This represents the radial displacement of the bearing shaft. This refers to the radial clearance of the bearing; Depending on the contact type, for rolling bearings, it is generally taken as 1.5;

[0069] Step 202: Obtain the first displacement component of the bearing shaft in the X-axis direction, the second displacement component in the Y-axis direction, and the third displacement component in the Z-axis direction, respectively;

[0070] Based on the first displacement component, the radial displacement of the bearing shaft, and the radial force acting on the bearing, the first radial component of the radial force acting on the bearing in the X-axis direction is calculated:

[0071] ;

[0072] In the formula: This is the first radial component; This is the first displacement component of the bearing shaft;

[0073] Based on the second displacement component, the radial displacement of the bearing shaft, and the radial force acting on the bearing, the second radial component of the radial force acting on the bearing in the Y-axis direction is calculated:

[0074] ;

[0075] In the formula: This is the second radial component; This is the second displacement component of the bearing shaft;

[0076] Calculate the second ratio of the first radial component to the first displacement component and take its negative value to obtain the first time-varying contact stiffness in the X-axis direction; calculate the third ratio of the second radial component to the second displacement component and take its negative value to obtain the second time-varying contact stiffness in the Y-axis direction.

[0077] ;

[0078] In the formula: The first time-varying contact stiffness; This is the second time-varying contact stiffness;

[0079] Obtain the axial clearance of the bearing, calculate the fourth ratio of the axial clearance to the fixed value 2, and determine the relationship between the fourth ratio and the third displacement component to determine the value of the axial force on the bearing.

[0080] ;

[0081] In the formula, This refers to the axial force acting on the bearing. This is the axial stiffness coefficient of the bearing. This is the third displacement component of the bearing shaft. This refers to the axial clearance of the bearing;

[0082] Next, the fifth ratio of the axial force on the bearing to the third displacement component is calculated to obtain the third time-varying contact stiffness in the Z-axis direction;

[0083] ;

[0084] In the formula: The third time-varying contact stiffness;

[0085] The formula for calculating the time-varying meshing stiffness of each gear stage is as follows:

[0086] ;

[0087] In the formula: For time-varying meshing stiffness; This represents the average value of the time-varying meshing stiffness; The meshing angular frequency, and These are the Fourier coefficients. and These represent the amplitude and phase of each harmonic;

[0088] The motor torque is calculated using the dq model of a permanent magnet synchronous motor. The specific calculation formula is as follows:

[0089] ;

[0090] In the formula: For electromagnetic torque, This represents the number of pole pairs of the motor. The fundamental magnetic flux generated by the permanent magnet. and These are direct-axis inductors and quadrature-axis inductors, respectively. , These are the direct-axis current and the quadrature-axis current, respectively.

[0091] The unbalanced magnetic pull force of the motor rotor includes a first unbalanced magnetic pull force component in the X-axis direction and a second unbalanced magnetic pull force component in the Y-axis direction. The specific calculation steps are as follows:

[0092] Step 211: Determine the mechanical angle on the air gap circumference and the corresponding air gap magnetic flux density distribution at the time. Based on the air gap magnetic flux density distribution and vacuum permeability, calculate the magnetic field energy density at that location.

[0093] Step 212: Determine the area of ​​the micro-element region based on the motor rotor radius, motor rotor axial length, and angular micro-element;

[0094] Step 213: Multiply the magnetic field energy density by the area of ​​the micro-element region, and combine it with the cosine of the mechanical angle on the air gap circumference to obtain the force component of the micro-element region in the X-axis direction; integrate the mechanical angle in the interval [0, 2π], and sum up the force components of all micro-element regions in the X-axis direction to obtain the first unbalanced magnetic pull component in the X-axis direction.

[0095] ;

[0096] In the formula: The first unbalanced magnetic pull component in the X-axis direction. To account for the air gap magnetic flux density distribution when the rotor is eccentric, The mechanical angle on the circumference of the air gap. The permeability of free space, The radius of the motor rotor, This refers to the axial length of the motor rotor;

[0097] Step 214: Multiply the magnetic field energy density by the area of ​​the micro-element region, and combine it with the sine value of the mechanical angle on the air gap circumference to obtain the force component of the micro-element region in the Y-axis direction; integrate the mechanical angle in the interval [0, 2π], and sum up the force components of all micro-element regions in the Y-axis direction to obtain the second unbalanced magnetic pull component in the Y-axis direction.

[0098] ;

[0099] In the formula: This represents the second unbalanced magnetic pull component in the Y-axis direction. To account for the air gap magnetic flux density distribution when the rotor is eccentric, The mechanical angle on the circumference of the air gap. The permeability of free space, Let be the radius of the motor rotor. This is the axial length of the motor rotor;

[0100] Step 3: Construct the dynamic equations of the motor rotor and the electromechanical coupling gear. The specific steps are as follows:

[0101] Calculate the second partial derivative of the first unbalanced magnetic pull component with respect to the first displacement component, and use it as the first electromagnetic stiffness component in the X-axis direction; calculate the second partial derivative of the second unbalanced magnetic pull component with respect to the second displacement component, and use it as the second electromagnetic stiffness component in the Y-axis direction.

[0102] Based on the first electromagnetic stiffness component and the second electromagnetic stiffness component, the electromagnetic stiffness matrix of the motor rotor in the electromagnetic field is calculated.

[0103] ;

[0104] In the formula: This is the first electromagnetic stiffness component; This is the second electromagnetic stiffness component; and Since this is a cross-stiffness term, it can be ignored in engineering calculations, therefore we get:

[0105] ;

[0106] By combining the first electromagnetic stiffness component, the second electromagnetic stiffness component, the first displacement component, the second displacement component, the mass of the motor rotor, the mechanical damping coefficient of the motor rotor, and the mechanical stiffness of the motor rotor, the motor rotor dynamic equation is constructed:

[0107] ;

[0108] In the formula: The mass of the motor rotor; This is the mechanical damping coefficient; This is the first displacement component; This is the second displacement component; This is the first electromagnetic stiffness component; This is the second electromagnetic stiffness component; , These are the components of the gear meshing force in the X-axis and Y-axis directions, respectively; This refers to the mechanical stiffness of the motor rotor.

[0109] Furthermore, the steps for constructing the electromechanical coupling gear dynamics equations are as follows:

[0110] The time-varying meshing stiffness of each gear stage is added to the time-varying contact stiffness matrix of each bearing to construct the eight-degree-of-freedom dynamic equations of the first-stage gear pair.

[0111] The electromagnetic stiffness matrix of the motor rotor is added to the stiffness matrix of the eight-degree-of-freedom dynamic equation of the first-stage gear pair, and the motor torque is introduced as an external excitation term into the excitation part of the eight-degree-of-freedom dynamic equation of the first-stage gear pair to obtain the electromechanical coupled gear dynamic equation.

[0112] ;

[0113] In the formula: , These are the masses of the driving gear and the driven gear, respectively. and These are the mechanical damping coefficients of the driving gear in the X-axis and Y-axis directions, respectively. and These represent the support stiffness of the driving gear in the X-axis and Y-axis directions, respectively. , , These are the components of the gear meshing force in the X-axis, Y-axis, and Z-axis directions, respectively. and These are the radial mechanical damping coefficients of the driving gear and the driven gear, respectively. and These are the radial support stiffnesses of the driving gear and the driven gear, respectively. , These are the moments of inertia of the driving gear and the driven gear, respectively. , These are the base circle radii of the driving gear and the driven gear, respectively. The output torque of the gear system is equal to the output torque of the permanent magnet synchronous motor; This represents the load torque of the gear system; subscript 1 represents the driving gear, and subscript 2 represents the driven gear.

[0114] Step 4: Combine the motor rotor dynamics equations with the electromechanical coupled gear dynamics equations to establish the state-space equations. By solving these state-space equations, the gear vibration displacement is obtained. Taking the first or second derivative of the gear vibration displacement yields the gear vibration velocity and acceleration, specifically:

[0115] Define state vector ,in, The gear vibration displacement vector, The gear vibration velocity vector, Given the identity matrix, we obtain the state-space equations:

[0116] ;

[0117] In the formula: For the system matrix, For the input matrix The input vector includes gear meshing force and motor torque. ; The total mass matrix, Here is the total damping matrix. This is the total stiffness matrix (including bearing stiffness, meshing stiffness, and motor electromagnetic stiffness).

[0118] The electromechanical coupling gear dynamics modeling method of this invention starts from the bidirectional electromechanical coupling of the permanent magnet synchronous motor rotor and gears, fully considers the unbalanced magnetic pull of the motor rotor, the time-varying meshing stiffness of each gear stage and the time-varying contact stiffness of each bearing, and establishes the electromechanical coupling gear dynamics equation considering the unbalanced magnetic pull. It can accurately calculate the output vibration displacement and vibration acceleration of the gear system in the electric drive assembly, and thus obtain more realistic dynamic response characteristics of the electric drive assembly gear system.

[0119] Example 2

[0120] The electromechanical coupling gear dynamics modeling device of the present invention includes:

[0121] The parameter identification module is used to determine the bearing model, motor parameters, and gear parameters of the gear system.

[0122] The parameter calculation module is used to calculate the time-varying contact stiffness of each bearing in the gear system, the time-varying meshing stiffness of each stage of gear, the motor torque, and the unbalanced magnetic pull of the motor rotor based on the bearing model, motor parameters, and gear parameters determined by the parameter identification module.

[0123] The model building module is used to construct the motor rotor dynamic equation and the electromechanical coupled gear dynamic equation by calculating the time-varying contact stiffness of each bearing, the time-varying meshing stiffness of each gear, the motor torque and the unbalanced magnetic pull of the motor rotor, which are calculated by the parameter calculation module. The state space equation is established by combining the motor rotor dynamic equation and the electromechanical coupled gear dynamic equation.

[0124] The model solving module is used to solve the state-space equations constructed by the model building module to obtain the gear vibration displacement.

[0125] Example 3

[0126] The electronic device of the present invention includes a central processing unit and a memory, wherein the central processing unit is used to invoke and run a computer program stored in the memory to perform the steps of the electromechanical coupling gear dynamics modeling method in Embodiment 1.

[0127] Example 4

[0128] The computer-readable storage medium of the present invention stores, in the form of computer-readable instructions, a computer program implementing the electromechanical coupling gear dynamics modeling method of Embodiment 1. When the computer program is called and executed by a computer, it performs the steps included in the corresponding method.

[0129] The above are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above content. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for modeling the dynamics of electromechanical coupled gears, characterized in that, Includes the following steps: Step 1: Determine the bearing model, motor parameters, and gear parameters in the gear system; Step 2: Based on the determined bearing model, motor parameters and gear parameters, calculate the time-varying contact stiffness of each bearing in the gear system, the time-varying meshing stiffness of each gear stage, the motor torque and the unbalanced magnetic pull of the motor rotor. Step 3: Construct the dynamic equations of the motor rotor and the electromechanical coupling gear; Step 4: Establish the state-space equation by combining the motor rotor dynamics equation and the electromechanical coupled gear dynamics equation, and solve the state-space equation to obtain the gear vibration displacement.

2. The electromechanical coupled gear dynamics modeling method according to claim 1, characterized in that, In step 2, based on the determined bearing model, motor parameters, and gear parameters, the time-varying contact stiffness of each bearing is calculated according to national standards. The specific calculation steps are as follows: Step 201: Obtain the radial clearance of the bearing and the radial displacement of the bearing shaft, calculate the first ratio of the radial clearance to the fixed value 2, and determine the relationship between the first ratio and the radial displacement of the bearing shaft to determine the value of the radial force on the bearing. Step 202: Obtain the first displacement component of the bearing shaft in the X-axis direction, the second displacement component in the Y-axis direction, and the third displacement component in the Z-axis direction, respectively; Based on the first displacement component, the radial displacement of the bearing shaft, and the radial force on the bearing, the first radial component of the radial force on the bearing in the X-axis direction is calculated; the second ratio of the first radial component to the first displacement component is calculated and the negative value is taken to obtain the first time-varying contact stiffness in the X-axis direction. Based on the second displacement component, the radial displacement of the bearing shaft, and the radial force on the bearing, the second radial component of the radial force on the bearing in the Y-axis direction is calculated; the third ratio of the second radial component to the second displacement component is calculated and taken as negative to obtain the second time-varying contact stiffness in the Y-axis direction. Obtain the axial clearance of the bearing, calculate the fourth ratio of the axial clearance to the fixed value 2, determine the relationship between the fourth ratio and the third displacement component, and determine the value of the axial force on the bearing; calculate the fifth ratio of the axial force on the bearing to the third displacement component, and obtain the third time-varying contact stiffness in the Z-axis direction.

3. The electromechanical coupled gear dynamics modeling method according to claim 2, characterized in that, In step 201, the rule for determining the value of the radial force on the bearing is as follows: When the radial displacement of the bearing shaft is greater than the first ratio, first calculate the first difference between the radial displacement and the first ratio, then raise the first difference to the nth power, and multiply the result by the bearing radial stiffness coefficient. The product is the value of the radial force on the bearing. When the radial displacement of the bearing shaft is less than or equal to the first ratio, the radial force on the bearing is zero.

4. The electromechanical coupled gear dynamics modeling method according to claim 3, characterized in that, In step 2, the motor torque is calculated using the dq model of the permanent magnet synchronous motor.

5. The electromechanical coupled gear dynamics modeling method according to claim 4, characterized in that, In step 2, the unbalanced magnetic pull force of the motor rotor includes a first unbalanced magnetic pull force component in the X-axis direction and a second unbalanced magnetic pull force component in the Y-axis direction. The specific calculation steps are as follows: Step 211: Determine the mechanical angle on the air gap circumference and the corresponding air gap magnetic flux density distribution at the time. Based on the air gap magnetic flux density distribution and vacuum permeability, calculate the magnetic field energy density at that location. Step 212: Determine the area of ​​the micro-element region based on the motor rotor radius, motor rotor axial length, and angular micro-element; Step 213: Multiply the magnetic field energy density by the area of ​​the micro-element region, and combine it with the cosine of the mechanical angle on the air gap circumference to obtain the force component of the micro-element region in the X-axis direction; integrate the mechanical angle in the interval [0, 2π], and sum up the force components of all micro-element regions in the X-axis direction to obtain the first unbalanced magnetic pull component in the X-axis direction. Step 214: Multiply the magnetic field energy density by the area of ​​the micro-element region, and combine it with the sine value of the mechanical angle on the air gap circumference to obtain the force component of the micro-element region in the Y-axis direction; integrate the mechanical angle in the interval [0, 2π], and sum up the force components of all micro-element regions in the Y-axis direction to obtain the second unbalanced magnetic pull component in the Y-axis direction.

6. The electromechanical coupled gear dynamics modeling method according to claim 5, characterized in that, In step 3, the steps for constructing the motor rotor dynamics equations are as follows: Calculate the second partial derivative of the first unbalanced magnetic pull component with respect to the first displacement component, and use it as the first electromagnetic stiffness component in the X-axis direction; calculate the second partial derivative of the second unbalanced magnetic pull component with respect to the second displacement component, and use it as the second electromagnetic stiffness component in the Y-axis direction. Based on the first electromagnetic stiffness component and the second electromagnetic stiffness component, the electromagnetic stiffness matrix of the motor rotor in the electromagnetic field is calculated. By combining the first electromagnetic stiffness component, the second electromagnetic stiffness component, the first displacement component, the second displacement component, the mass of the motor rotor, the mechanical damping coefficient of the motor rotor, and the mechanical stiffness of the motor rotor, the motor rotor dynamic equation is constructed: ； In the formula: The mass of the motor rotor; This is the mechanical damping coefficient; This is the first displacement component; This is the second displacement component; This is the first electromagnetic stiffness component; This is the second electromagnetic stiffness component; , These are the components of the gear meshing force in the X-axis and Y-axis directions, respectively; This refers to the mechanical stiffness of the motor rotor.

7. The electromechanical coupled gear dynamics modeling method according to claim 6, characterized in that, In step 3, the steps for constructing the electromechanical coupling gear dynamics equations are as follows: The time-varying meshing stiffness of each gear stage is added to the time-varying contact stiffness matrix of each bearing to construct the eight-degree-of-freedom dynamic equations of the first-stage gear pair. The electromagnetic stiffness matrix of the motor rotor is added to the stiffness matrix of the eight-degree-of-freedom dynamic equation of the first-stage gear pair, and the motor torque is introduced as an external excitation term into the excitation part of the eight-degree-of-freedom dynamic equation of the first-stage gear pair to obtain the electromechanical coupled gear dynamic equation. ； In the formula: , These are the masses of the driving gear and the driven gear, respectively. and These are the mechanical damping coefficients of the driving gear in the X-axis and Y-axis directions, respectively. and These represent the support stiffness of the driving gear in the X-axis and Y-axis directions, respectively. , , These are the components of the gear meshing force in the X-axis, Y-axis, and Z-axis directions, respectively. and These are the radial mechanical damping coefficients of the driving gear and the driven gear, respectively. and These are the radial support stiffnesses of the driving gear and the driven gear, respectively. , These are the moments of inertia of the driving gear and the driven gear, respectively. , These are the base circle radii of the driving gear and the driven gear, respectively. The output torque of the gear system is equal to the output torque of the permanent magnet synchronous motor; This represents the load torque of the gear system.

8. A device for modeling the dynamics of electromechanical coupled gears, characterized in that, include: The parameter identification module is used to determine the bearing model, motor parameters, and gear parameters of the gear system. The parameter calculation module is used to calculate the time-varying contact stiffness of each bearing in the gear system, the time-varying meshing stiffness of each stage of gear, the motor torque, and the unbalanced magnetic pull of the motor rotor based on the bearing model, motor parameters, and gear parameters determined by the parameter identification module. The model building module is used to construct the motor rotor dynamic equation and the electromechanical coupled gear dynamic equation by calculating the time-varying contact stiffness of each bearing, the time-varying meshing stiffness of each gear, the motor torque and the unbalanced magnetic pull of the motor rotor, which are calculated by the parameter calculation module. The state space equation is established by combining the motor rotor dynamic equation and the electromechanical coupled gear dynamic equation. The model solving module is used to solve the state-space equations constructed by the model building module to obtain the gear vibration displacement.

9. An electronic device comprising a central processing unit and a memory, characterized in that, The central processing unit is used to call and run a computer program stored in the memory to perform the steps of the electromechanical coupling gear dynamics modeling method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores, in the form of computer-readable instructions, a computer program implemented according to the electromechanical coupling gear dynamics modeling method according to any one of claims 1 to 7, which, when called by a computer, executes the steps included in the corresponding method.

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