Method for analyzing electromechanical coupling dynamics of helical gear transmission system

Abstract

A kind of helical gear transmission system electromechanical coupling dynamics analysis method, comprising: obtaining the basic parameters of electric drive transmission system and helical gear pair;Generation target operation instruction and load boundary timing under different working conditions;Establish motor double closed loop control and electromagnetic torque calculation model;Each slice unit stiffness is calculated, and the helical gear pair comprehensive time-varying mesh stiffness is obtained by accumulating each slice unit stiffness;Establish helical gear pair dynamic mesh displacement calculation model, calculate helical gear pair dynamic mesh force;Establish helical gear transmission system electromechanical coupling dynamics equation;Establish the bending-shaft-torsion-swing coupling dynamics equation of driving gear and driven gear;Iterative solution is carried out using time domain integration method, and the helical gear transmission system electromechanical coupling dynamics calculation result is output.The present application can improve the accuracy of electric drive transmission system multi-working condition dynamics response prediction.

Description

Technical Field

[0001] This invention relates to the field of dynamic analysis technology for electric drive transmission systems, and specifically to a method for electromechanical coupling dynamic analysis of helical gear transmission systems. Background Technology

[0002] Electric drive systems are widely used in new energy vehicles, electric drive reducers, electric drive axles, three-in-one electric drive assemblies, and industrial servo equipment. They typically include a drive motor, control system, gear transmission mechanism, bearing support structure, and load end. As electric drive systems develop towards higher speeds, higher power densities, higher integration, and wider operating conditions, the coupling effect between motor electromagnetic excitation, control system dynamic response, gear meshing excitation, and mechanical structure vibration is becoming increasingly significant, having a major impact on system dynamic load, vibration control, and operational reliability.

[0003] In electric drive transmission systems, drive motors typically employ a dual closed-loop control system consisting of a speed loop and a current loop. The motor's output torque and speed are not ideally constant but are influenced by factors such as target speed, load variations, current regulation, speed feedback, controller parameters, and field weakening control. Especially under conditions such as start-stop, acceleration, deceleration, high-speed field weakening, and sudden load changes, the motor's dual closed-loop control system generates significant time-varying output excitation. This time-varying excitation further acts on the helical gear pair, affecting its dynamic meshing force, transmission error, dynamic load coefficient, bearing support load, and system vibration response.

[0004] In existing methods for calculating the dynamics of electric drive systems, the input excitation at the motor end is often simplified to a constant speed or constant torque. The motor control model and the helical gear pair meshing dynamics model are also usually established separately. This makes it difficult to accurately describe the coupling effect between the time-varying output excitation of the motor's dual closed-loop control and the nonlinear meshing response of the helical gear pair. As a result, the calculated results of dynamic meshing force, dynamic load coefficient, transmission error and system vibration response deviate from the actual operating conditions. Summary of the Invention

[0005] In view of this, the present invention provides an electromechanical coupling dynamics analysis method for helical gear transmission systems to improve the accuracy of predicting the dynamic response of electric drive transmission systems under multiple operating conditions.

[0006] A method for electromechanical coupling dynamic analysis of a helical gear transmission system includes: S1. Obtain the basic parameters of the electric drive transmission system and helical gear pair; S2. Based on the control command parameters and load boundary parameters in the basic parameters, generate target running commands and load boundary timing under different operating conditions; S3. Based on the motor parameters, controller parameters, load boundary parameters and control command parameters generated in step S2, establish a dual closed-loop control and electromagnetic torque calculation model for the motor to obtain the time-varying output torque, time-varying output speed and output angular displacement of the drive motor. S4. Based on the geometric parameters of the helical gear pair in the basic parameters and the time-varying output speed obtained in step S3, the helical gear is discretized into slice elements along the tooth width direction and the stiffness of each slice element is calculated based on the potential energy method. The stiffness of each slice element is accumulated to obtain the comprehensive time-varying meshing stiffness of the helical gear pair. S5. Based on the geometric parameters of the helical gear pair and the bearing support parameters in the basic parameters, establish a dynamic meshing displacement calculation model for the helical gear pair, and calculate the dynamic meshing force of the helical gear pair by combining the comprehensive time-varying meshing stiffness of the helical gear pair. S6. Using the time-varying output torque, time-varying output speed, or output angular displacement of the motor as the system input excitation, and the dynamic meshing force of the helical gear pair as the internal meshing excitation of the system, and combining the mass parameters, damping parameters, stiffness parameters, bearing support parameters, and external load parameters of the transmission system, establish the electromechanical coupling dynamic equation of the helical gear transmission system. S7. Based on the dynamic meshing force of helical gear pairs and the electromechanical coupling dynamic equation of helical gear transmission system, the bending-shaft-torsion-swing coupling dynamic equation of the driving gear and driven gear is established by using the lumped mass method. S8. Based on the dual closed-loop control model of the motor, the comprehensive time-varying meshing stiffness of the helical gear pair, the dynamic meshing force of the helical gear pair, the electromechanical coupling dynamic equation, and the bending-shaft-torsion-swing coupling dynamic equation, the time-domain integration method is used for iterative solution, and the electromechanical coupling dynamic calculation results of the helical gear transmission system are output.

[0007] The electromechanical coupling dynamics analysis method for helical gear transmission systems provided by the present invention has the following beneficial effects: 1. This invention establishes a complete dual-closed-loop control calculation model that includes an outer loop of speed, an inner loop of current, the electromagnetic equations of the motor, and the mechanical motion equations. It incorporates factors such as controller parameters, voltage / current limits, and field weakening control into a unified calculation framework, which can accurately obtain the time-varying output torque, output speed, output angular displacement, and current response of the drive motor under the action of the control system. This overcomes the defect of oversimplification of motor input excitation in the prior art.

[0008] 2. By constructing a time-varying function for the target speed command, a time-varying load torque function, and voltage / current constraints, this invention can generate the target torque timing sequence, target speed timing sequence, and load torque timing sequence of the motor under various operating conditions, such as steady-state operation, start-stop process, continuous acceleration, continuous deceleration, high-speed field weakening, and transient load changes. This achieves accurate generation of transient excitation under multiple operating conditions and provides accurate input excitation boundaries for dynamic response analysis under multiple operating conditions.

[0009] 3. This invention uses the time-varying torque, speed, and angular displacement calculated by the dual closed-loop control model of the motor as the input boundary of the helical gear transmission system, and feeds back the obtained dynamic meshing force of the helical gear pair to the electromechanical coupling dynamic equation. This realizes the bidirectional coupling calculation of the time-varying output excitation of the motor and the nonlinear meshing response of the helical gear pair, thereby truly reflecting the interaction mechanism between the electromagnetic excitation of the motor, the dynamic response of the control system, and the gear meshing excitation.

[0010] 4. This invention establishes a unified coupled electromechanical dynamics model and uses the fourth-order Runge-Kutta method for time-domain iterative solution, which can output complete dynamic responses such as motor electromagnetic torque, mechanical angular velocity, current response, helical gear pair comprehensive time-varying meshing stiffness, dynamic meshing force, dynamic load coefficient, bearing support load, and system vibration displacement, velocity and acceleration, thereby improving the accuracy of multi-condition dynamic response prediction. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the electromechanical coupling dynamics analysis method for helical gear transmission systems. Figure 2 This is a schematic diagram of the helical gear tooth profile; Figure 3 A comparison diagram of dynamic meshing forces of gears with and without electromagnetic torque; Figure 4 The graph shows the calculated results of motor speed, electromagnetic torque, gear dynamic meshing force, and pinion X-axis vibration acceleration under start-stop conditions. Detailed Implementation

[0012] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0013] Please see Figure 1 The present invention provides a method for electromechanical coupling dynamic analysis of a helical gear transmission system, the method comprising steps S1 to S8: S1. Obtain the basic parameters of the electric drive transmission system and helical gear pair.

[0014] The basic parameters include motor parameters, controller parameters, helical gear pair geometric parameters, bearing support parameters, load boundary parameters, and control command parameters. Motor parameters include motor moment of inertia, stator resistance, inductance, flux linkage, number of pole pairs, and electromagnetic torque coefficient. Controller parameters include speed loop control parameters, current loop control parameters, voltage limiting parameters, current limiting parameters, and field weakening control parameters. Helical gear pair geometric parameters include number of teeth, normal module, pressure angle, helix angle, tooth width, base circle radius, and pitch circle radius. Control command parameters include target speed command, target torque command, start / stop command, acceleration command, deceleration command, or load disturbance command.

[0015] Electric angular velocity With mechanical angular velocity The relationship between them is represented as follows:

[0016] in, This represents the number of pole pairs of the motor. Motor mechanical angular displacement Represented as:

[0017] in, For the initial mechanical angular displacement, At the initial moment, To represent the differential, For time.

[0018] The motor dual closed-loop control consists of a speed loop and a current loop. The outer speed loop includes a speed sensor and a speed regulator. MTPA and MTPV control are used between the outer speed loop and the inner current loop. The inner current loop includes a current regulator, Clark transformation, Park coordinate transformation, and voltage vector pulse width modulation. Controller parameters include the proportional coefficient of the outer speed loop. Speed ​​outer ring integral coefficient d-axis current inner loop proportionality coefficient d-axis current inner loop integral coefficient q-axis current inner loop proportionality coefficient q-axis current inner loop integral coefficient Control sampling period Current limiting parameters, voltage limiting parameters, and integral anti-saturation parameters; setting the initial d-axis current of the motor. Initial q-axis current Initial mechanical angular displacement Initial time End time and integral step size .

[0019] S2. Based on the control command parameters and load boundary parameters in the basic parameters, generate target running commands and load boundary timing under different operating conditions.

[0020] This step constructs the target torque timing, target speed timing, load torque timing, and control constraints of the motor under steady-state operation, start-stop process, continuous acceleration, continuous deceleration, high-speed field weakening, and transient load change conditions based on the target speed command, target torque command, start-stop command, acceleration command, deceleration command, load disturbance conditions, voltage limit parameters, current limit parameters, and field weakening control parameters.

[0021] Step S2 specifically includes: S201. Based on the obtained operating condition type identifier, construct the target speed command. Its mechanical angular velocity satisfy: , ,in To represent the rotational speed function that varies with time, different forms are set... The function describes the input requirements of the electric drive axle under start-stop, acceleration, and deceleration conditions; S202. Construct a time-varying load torque command based on the load boundary parameters of the electric drive system. ,in This is a function of the load torque that varies with time. S203. Set voltage constraints during motor closed-loop control. and current constraint ,in The maximum allowable current for the motor. The maximum allowable output voltage of the inverter. , These are voltage commands for the d-axis and q-axis, respectively. , These are the d-axis and q-axis current commands, respectively. S204. Based on the target speed command, target mechanical angular velocity, target torque command, load torque command, voltage constraint condition, and current constraint condition obtained from S201 to S203, construct the motor control input timing sequence. .

[0022] S3. Based on the motor parameters, controller parameters, load boundary parameters and control command parameters generated in step S2, establish a dual closed-loop control and electromagnetic torque calculation model for the motor to obtain the time-varying output torque, time-varying output speed and output angular displacement of the drive motor.

[0023] In this step, the motor dual closed-loop control model includes an outer speed loop and an inner current loop. Based on the deviation between the target speed command and the actual speed, the current setpoint is calculated through the outer speed loop. Based on the deviation between the current setpoint and the actual current, the motor voltage input is calculated through the inner current loop. Combined with the motor electromagnetic equations, voltage limits, current limits, and field weakening control relationships, a control calculation model is formed to characterize the dynamic output characteristics of the drive motor.

[0024] Step S3 specifically includes: S301. Calculate the motor speed deviation based on the target speed command and the motor feedback speed. And generate electromagnetic torque command through speed loop regulation. When the system adopts torque control mode, the electromagnetic torque command is directly given by the target torque command, that is... ; S302. Based on the electromagnetic torque command and the motor operating status, obtain the d-axis current command through the torque-current relationship. and q-axis current command At low speeds and below base speeds, current commands are generated through maximum torque-to-current ratio control. MTPA control is expressed as:

[0025] in, It is a permanent magnet flux chain. , These are the d-axis and q-axis inductances, respectively. When the target speed is higher than the motor base speed or reaches the field weakening start speed threshold At that time, that is When the motor enters the high-speed field weakening condition, the current command is corrected using maximum torque-voltage ratio control. MTPV control is expressed as:

[0026] in, This represents the maximum voltage amplitude. S303, Based on the initial feedback three-phase stator current of the motor , , The feedback d-axis current is obtained through Clark and Park transformations. and feedback q-axis current :

[0027] in, For rotor electrical angle, Indicates transpose; S304. The d-axis and q-axis current commands obtained from S302 and the motor feedback d-axis and q-axis currents from S303 are used as the inner current loop input. The d-axis voltage command is obtained by calculating the current deviation. and q-axis voltage command :

[0028]

[0029]

[0030]

[0031] in, For d-axis current deviation, This refers to the q-axis current deviation. S305, based on rotor electrical angle The d-axis and q-axis voltage commands are subjected to inverse Park transformation to obtain the voltage commands in the two-phase stationary coordinate system:

[0032] in, , The voltages are in a two-phase stationary coordinate system. S306, Based on the voltage in the two-phase stationary coordinate system , and DC bus voltage The three-phase inverter switching control signal is generated by space vector pulse width modulation, and the three-phase stator voltage is output by the three-phase inverter. , , The three-phase stator voltage is equivalently transformed into the voltage input that actually acts on the dq-axis model of the motor. , :

[0033] S307. Based on the d-axis and q-axis voltage inputs from the inner current loop, and combined with the d- and q-axis voltage equations of the permanent magnet synchronous motor, the computer calculates the d-axis and q-axis current responses:

[0034]

[0035] in, The stator winding resistance is used; the d-axis and q-axis current responses at the next time step are obtained through time-domain integration. , :

[0036]

[0037] S308. Based on the d-axis and q-axis current responses and motor parameters obtained in S307, calculate the actual electromagnetic torque of the motor. : .

[0038] S4. Based on the geometric parameters of the helical gear pair in the basic parameters and the time-varying output speed obtained in step S3, the helical gear is discretized into slice elements along the tooth width direction, and the stiffness of each slice element is calculated based on the potential energy method. The stiffness of each slice element is accumulated to obtain the comprehensive time-varying meshing stiffness of the helical gear pair.

[0039] In this step, based on the contact line length of the helical gear pair at different meshing positions, the helical gear is discretized into several slice elements along the tooth width direction. The Hertzian contact stiffness, bending stiffness, shear stiffness, axial compressive stiffness, and base stiffness of the participating slice elements are calculated based on the potential energy method. The meshing stiffness of a single tooth pair is calculated based on the stiffness of each slice element. The meshing stiffness of each tooth pair is superimposed based on the number of tooth pairs participating in meshing at the current moment to obtain the comprehensive time-varying meshing stiffness of the helical gear pair.

[0040] Step S4 specifically includes: S401. Length of the helical gear pair meshing contact line based on gear pair parameters and the angular velocity of the driving gear. Represented as:

[0041] in, This indicates the translational velocity along the transverse cross section. , The radius of the base circle, The base circle helix angle, For tooth width, For end face overlap, For longitudinal overlap, The total overlap is The pitch of the base circle on the end face of the helical gear; S402. Based on the basic parameters of the driving and driven helical gears, the gear teeth are discretized into multiple slice units along the tooth width direction of the helical gear, and the total number of slices is... ,in, This indicates rounding to the nearest integer. The width of each slice; S403. Calculate the distance from the root circle based on the basic parameters of the driving and driven helical gears. Cross-sectional area at the location and moment of inertia of cross section ; S404. Based on the cross-sectional area and moment of inertia of the slice element obtained in S403, approximate a single slice element as a non-uniform cantilever beam, and calculate the Hertzian contact stiffness of the slice element of the gear using the potential energy method. Bending stiffness Axial compressive stiffness Shear stiffness and matrix stiffness :

[0042]

[0043]

[0044]

[0045]

[0046] in, It is the distance from the point of engagement along the tooth height to the root circle. For pressure angle, The Young's modulus of the gear tooth material. The shear modulus of the gear tooth material. Poisson's ratio, The thickness of half a tooth at the meshing point. , , , For polynomial coefficients, , These are the geometric parameters related to the gear base. S405. Based on the contact line length obtained in S401 and the number of meshing slices in S402, the stiffness of each slice unit in S404 is accumulated along the contact line direction to obtain the single-tooth pair meshing stiffness of the helical gear during meshing:

[0047]

[0048]

[0049]

[0050]

[0051] in, For custom angles, , , For the number index of the slice unit, please refer to [link / reference]. Figure 2 , The direction angle of the meshing plane. The gear meshing termination angle, This represents the angular displacement of the gear rotation; S406. Based on the number of gear pairs simultaneously engaging at different meshing positions, calculate the overall meshing stiffness of the helical gear throughout the entire meshing process. :

[0052] in, Indicates the number of gear teeth that mesh simultaneously, subscript. Indicates the active wheel, subscript Indicates the driven wheel, For the first Hertzian contact stiffness of gear teeth, , , , The first The bending stiffness, shear stiffness, axial compressive stiffness, and base stiffness of the driving gear in the gear teeth. , , , The first The bending stiffness, shear stiffness, axial compressive stiffness, and base stiffness of the driven gear in a gear tooth assembly.

[0053] S5. Based on the geometric parameters of the helical gear pair and the bearing support parameters in the basic parameters, establish a dynamic meshing displacement calculation model for the helical gear pair, and calculate the dynamic meshing force of the helical gear pair by combining the comprehensive time-varying meshing stiffness of the helical gear pair.

[0054] In this step, based on the displacement responses of the driving gear and driven gear in the bending direction, axial direction, torsional direction and oscillating direction, the displacements of each degree of freedom are projected onto the meshing line direction of the helical gear pair to obtain the dynamic meshing displacement of the helical gear pair. Combined with the relative velocity in the meshing line direction, the comprehensive time-varying meshing stiffness of the helical gear pair and the meshing damping, the dynamic meshing force calculation relationship of the helical gear pair is established.

[0055] Step S5 specifically includes: S501. When the driving gear rotates clockwise, the relative displacement of the tooth contact point along the meshing line... Represented as:

[0056] in, , , These are the drive gears in , , Vibration displacement in the direction; , , These are the driven gears in , , Vibration displacement in the direction; , , They are the drive gear winding , , Angular displacement of the direction of rotation; , , These are the driven gears winding around , , Angular displacement of the direction of rotation; , These are the base circle radii of the driving gear and the driven gear, respectively. The base circle helix angle, Normal pressure angle; S502. Based on the comprehensive time-varying meshing stiffness obtained in S406 and the relative displacement of the tooth surface obtained in S501, calculate the dynamic meshing force of the helical gear pair. :

[0057] in, For gear pair meshing damping, The relative velocity of the tooth surface contact point along the meshing line direction.

[0058] S6. Using the time-varying output torque, time-varying output speed, or output angular displacement of the motor as the system input excitation, and the dynamic meshing force of the helical gear pair as the internal meshing excitation of the system, and combining the mass parameters, damping parameters, stiffness parameters, bearing support parameters, and external load parameters of the transmission system, establish the electromechanical coupling dynamic equation of the helical gear transmission system.

[0059] In this step, the time-varying output torque, time-varying output speed, or output angular displacement calculated by the motor dual closed-loop control model are used as the system input excitation, the dynamic meshing force of the helical gear pair is used as the internal meshing excitation of the system, and the electromechanical coupling dynamic equation of the helical gear transmission system is established by combining the transmission system mass parameters, damping parameters, stiffness parameters, bearing support parameters and external load parameters obtained by S1.

[0060] Step S6 specifically includes: The electromagnetic torque of the motor is used as a coupling variable to transmit data in real time between the motor and the helical gear transmission system, establishing an electromechanical coupling dynamic model of the helical gear transmission system; the output speed and torque of the motor are correlated with the input speed and torque of the gear pair, and the electromechanical coupling dynamic equation is expressed as follows:

[0061] in, The moment of inertia of the motor. This is the motor damping coefficient. The mechanical angular velocity of the motor. This refers to the torsional stiffness between the motor shaft and the drive gear shaft. This refers to the torsional damping between the motor shaft and the drive gear shaft. For the driving gear to wind around angular displacement of the direction of rotation For the driving gear to wind around Angular velocity of rotation in the direction.

[0062] S7. Based on the dynamic meshing force of helical gear pairs and the electromechanical coupling dynamic equation of helical gear transmission system, the bending-shaft-torsion-swing coupling dynamic equation of the driving gear and driven gear is established by using the lumped mass method.

[0063] In this step, the lumped mass method is used to treat the driving gear and driven gear as lumped mass units. The bearing support stiffness, bearing support damping, gear rotation support stiffness, rotation support damping, dynamic meshing force, and torsional coupling effect between the motor shaft and the driving gear shaft are introduced into the dynamic equilibrium equations of the corresponding degrees of freedom, and the bending-shaft-torsion-swing coupling dynamic equations of the driving gear and driven gear are established.

[0064] Step S7 specifically includes: Based on the dynamic meshing force of the helical gear pair calculated by S502 and the electromechanical coupling model of S601, the dynamic equations of the multi-degree-of-freedom gear pair are established; the driving gear and driven gear are respectively equivalent to lumped mass elements, and the motion of the driving gear and driven gear is mediated by... , , Directional translation and rotation , , Rotation of direction , , To describe, while considering the mechanical angular displacement of the motor. The dynamic equations for the active wheel's bending-axle-torsion-pendulum coupling are as follows:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] The coupled dynamic equations of the driven wheel's bending-shaft-torsion-pendulum motion are:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] in, and These are the masses of the driving gear and the driven gear, respectively. Let be the moment of inertia of the driving gear. Let be the moment of inertia of the driven gear; , , They are respectively , , The support stiffness of the drive gear in the direction of travel; , , They are respectively , , The support stiffness of the driven gear in the direction of travel; , , They are respectively , , Support damping of the drive gear in the direction of travel; , , They are respectively , , Support damping of the driven gear in the direction of movement; , Gear winding , Torsional stiffness and torsional damping of rotational direction; , , The driving gear is wound around , , Moment of inertia in the direction of rotation; , , The driven gears are wound around , , Moment of inertia in the direction of rotation; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; for The second derivative of .

[0077] S8. Based on the dual closed-loop control model of the motor, the comprehensive time-varying meshing stiffness of the helical gear pair, the dynamic meshing force of the helical gear pair, the electromechanical coupling dynamic equation, and the bending-shaft-torsion-swing coupling dynamic equation, the time-domain integration method is used for iterative solution, and the electromechanical coupling dynamic calculation results of the helical gear transmission system are output.

[0078] In this step, the dynamic response of the helical gear transmission system under steady-state operation, start-stop process, continuous acceleration, continuous deceleration, high-speed field weakening, and transient load change conditions is obtained. The dynamic calculation results include motor output torque response, output speed response, current response, time-varying meshing stiffness of the helical gear pair, dynamic meshing force, dynamic load coefficient, bearing support load, system vibration displacement, vibration velocity, vibration acceleration, and dynamic response of key components. The calculation results are then used for parameter design, structural optimization, dynamic load prediction, vibration and noise control, and reliability analysis of the helical gear transmission system.

[0079] Step S8 specifically includes: S801. Based on the control command parameters, the motor dual closed-loop control model, the electromechanical coupling dynamic equation, and the bending-shaft-torsion-swing coupling dynamic equation, the fourth-order Runge-Kutta method is used for iterative solution. In each time step, the motor current response, motor electromagnetic torque, motor mechanical angular velocity and mechanical angular displacement, helical gear pair comprehensive time-varying meshing stiffness, tooth surface relative displacement, dynamic meshing force, and gear pair vibration response are updated synchronously. S802. Based on the time-domain integral solution of S801, output the motor electromagnetic torque, mechanical angular velocity, mechanical angular displacement, and current response. S803. Based on the time-domain integral solution of S801, output the helical gear pair meshing response and gear pair dynamic response; the helical gear pair meshing response includes the helical gear pair's comprehensive time-varying meshing stiffness, the relative displacement of the tooth surface contact point along the meshing line direction, and the dynamic meshing force; the gear pair dynamic response includes the dynamic meshing force of the driving gear and the driven gear in... , , The vibration displacement, vibration velocity, vibration acceleration, and the rotation around the vibration direction. , , Angular displacement, angular velocity, and angular acceleration in the direction of rotation; S804, according to the helical gear pair in , , Vibration displacement and velocity response in the direction of vibration, output bearing support load:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] in, , , The driving gear is respectively in , , The bearing supports the load in the direction of the direction; , , The driven gear is respectively in , , The bearing supports the load in the direction of the direction.

[0086] The present invention will now be subjected to relevant tests. Figure 3 Comparative calculation results of gear dynamic meshing force under steady-state conditions, using constant torque and the electromagnetic torque of this invention as inputs, are presented. Figure 3 It can be seen that the dynamic meshing force of gears under both constant torque and electromagnetic torque conditions exhibits periodic fluctuations. Compared with the constant torque condition, the fluctuation range and spectral amplitude of the dynamic meshing force are increased after adopting electromagnetic torque input. In the frequency domain response, the main frequency components of the constant torque condition are concentrated at the meshing frequency. And its harmonics; after using electromagnetic torque input, the power supply frequency appears in the spectrum. meshing frequency The amplitude at that point increases significantly, while at... Appear on both sides and Sideband components. Figure 3 The comparative results show that the method of the present invention can accurately reflect the power frequency component in the electromagnetic torque of the motor and its modulation effect on the dynamic meshing force of the gear, while the traditional constant torque input method cannot capture this phenomenon, thus verifying the effectiveness and advancement of the method of the present invention.

[0087] Figure 4 The time-domain response curves of motor speed, electromagnetic torque, gear dynamic meshing force, and pinion X-axis vibration acceleration calculated using the method of this invention under start-stop conditions are presented. Figure 4It is evident that during the acceleration, constant speed operation, and deceleration / stopping processes, the method of this invention can accurately capture the time-varying torque characteristics of the motor's dual closed-loop control output and its dynamic evolution during different operating stages. It reveals the short-term overshoot and damped oscillation phenomena of the gear dynamic meshing force when the torque direction reverses, and simultaneously reflects the non-stationary characteristics of the pinion's vibration acceleration being locally enhanced during acceleration and deceleration. This transient response information is completely unattainable by traditional simplified methods using constant speed or constant torque. If traditional methods are used, the transient impact and vibration peak of the dynamic meshing force during start-up and stop will be severely underestimated or omitted. The method of this invention, through full-time-domain electromechanical coupling solution, can accurately predict the transient load and vibration peak during start-up and stop, providing more accurate transient boundary conditions for gear strength assessment and vibration control.

[0088] In summary, the electromechanical coupling dynamics analysis method for helical gear transmission systems according to the above embodiments has the following beneficial effects: 1. This invention establishes a complete dual-closed-loop control calculation model that includes an outer loop of speed, an inner loop of current, the electromagnetic equations of the motor, and the mechanical motion equations. It incorporates factors such as controller parameters, voltage / current limits, and field weakening control into a unified calculation framework, which can accurately obtain the time-varying output torque, output speed, output angular displacement, and current response of the drive motor under the action of the control system. This overcomes the defect of oversimplification of motor input excitation in the prior art.

[0089] 2. By constructing a time-varying function for the target speed command, a time-varying load torque function, and voltage / current constraints, this invention can generate the target torque timing sequence, target speed timing sequence, and load torque timing sequence of the motor under various operating conditions, such as steady-state operation, start-stop process, continuous acceleration, continuous deceleration, high-speed field weakening, and transient load changes. This achieves accurate generation of transient excitation under multiple operating conditions and provides accurate input excitation boundaries for dynamic response analysis under multiple operating conditions.

[0090] 3. This invention uses the time-varying torque, speed, and angular displacement calculated by the dual closed-loop control model of the motor as the input boundary of the helical gear transmission system, and feeds back the obtained dynamic meshing force of the helical gear pair to the electromechanical coupling dynamic equation. This realizes the bidirectional coupling calculation of the time-varying output excitation of the motor and the nonlinear meshing response of the helical gear pair, thereby truly reflecting the interaction mechanism between the electromagnetic excitation of the motor, the dynamic response of the control system, and the gear meshing excitation.

[0091] 4. This invention establishes a unified coupled electromechanical dynamics model and uses the fourth-order Runge-Kutta method for time-domain iterative solution, which can output complete dynamic responses such as motor electromagnetic torque, mechanical angular velocity, current response, helical gear pair comprehensive time-varying meshing stiffness, dynamic meshing force, dynamic load coefficient, bearing support load, and system vibration displacement, velocity and acceleration, thereby improving the accuracy of multi-condition dynamic response prediction.

[0092] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for electromechanical coupling dynamic analysis of a helical gear transmission system, characterized in that, include: S1. Obtain the basic parameters of the electric drive transmission system and helical gear pair; S2. Based on the control command parameters and load boundary parameters in the basic parameters, generate target running commands and load boundary timing under different operating conditions; S3. Based on the motor parameters, controller parameters, load boundary parameters and control command parameters generated in step S2, establish a dual closed-loop control and electromagnetic torque calculation model for the motor to obtain the time-varying output torque, time-varying output speed and output angular displacement of the drive motor. S4. Based on the geometric parameters of the helical gear pair in the basic parameters and the time-varying output speed obtained in step S3, the helical gear is discretized into slice elements along the tooth width direction and the stiffness of each slice element is calculated based on the potential energy method. The stiffness of each slice element is accumulated to obtain the comprehensive time-varying meshing stiffness of the helical gear pair. S5. Based on the geometric parameters of the helical gear pair and the bearing support parameters in the basic parameters, establish a dynamic meshing displacement calculation model for the helical gear pair, and calculate the dynamic meshing force of the helical gear pair by combining the comprehensive time-varying meshing stiffness of the helical gear pair. S6. Using the time-varying output torque, time-varying output speed, or output angular displacement of the motor as the system input excitation, and the dynamic meshing force of the helical gear pair as the internal meshing excitation of the system, and combining the mass parameters, damping parameters, stiffness parameters, bearing support parameters, and external load parameters of the transmission system, establish the electromechanical coupling dynamic equation of the helical gear transmission system. S7. Based on the dynamic meshing force of helical gear pairs and the electromechanical coupling dynamic equation of helical gear transmission system, the bending-shaft-torsion-swing coupling dynamic equation of the driving gear and driven gear is established by using the lumped mass method. S8. Based on the dual closed-loop control model of the motor, the comprehensive time-varying meshing stiffness of the helical gear pair, the dynamic meshing force of the helical gear pair, the electromechanical coupling dynamic equation, and the bending-shaft-torsion-swing coupling dynamic equation, the time-domain integration method is used for iterative solution, and the electromechanical coupling dynamic calculation results of the helical gear transmission system are output.

2. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 1, characterized in that, In step S1, the basic parameters include motor parameters, controller parameters, helical gear pair geometric parameters, bearing support parameters, load boundary parameters, and control command parameters. The motor parameters include motor moment of inertia, stator resistance, inductance, flux linkage, number of pole pairs, and electromagnetic torque coefficient. The controller parameters include speed loop control parameters, current loop control parameters, voltage limiting parameters, current limiting parameters, and field weakening control parameters. The helical gear pair geometric parameters include number of teeth, normal module, pressure angle, helix angle, tooth width, base circle radius, and pitch circle radius. The control command parameters include target speed command, target torque command, start / stop command, acceleration command, deceleration command, or load disturbance command.

3. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 2, characterized in that, In step S1, the electrical angular velocity With mechanical angular velocity The relationship between them is represented as follows: in, This represents the number of pole pairs of the motor. Motor mechanical angular displacement Represented as: in, For the initial mechanical angular displacement, At the initial moment, To represent the differential, For time; The motor dual closed-loop control consists of a speed loop and a current loop. The outer speed loop includes a speed sensor and a speed regulator. MTPA and MTPV control are used between the outer speed loop and the inner current loop. The inner current loop includes a current regulator, Clark transformation, Park coordinate transformation, and voltage vector pulse width modulation. Controller parameters include the proportional coefficient of the outer speed loop. Speed ​​outer ring integral coefficient d-axis current inner loop proportionality coefficient d-axis current inner loop integral coefficient q-axis current inner loop proportionality coefficient q-axis current inner loop integral coefficient Control sampling period Current limiting parameters, voltage limiting parameters, and integral anti-saturation parameters; setting the initial d-axis current of the motor. Initial q-axis current Initial mechanical angular displacement Initial time End time and integral step size .

4. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 3, characterized in that, Step S2 specifically includes: S201. Based on the obtained operating condition type identifier, construct the target speed command. Its mechanical angular velocity satisfy: , ,in To represent the rotational speed function that varies with time, different forms are set... The function describes the input requirements of the electric drive axle under start-stop, acceleration, and deceleration conditions; S202. Construct a time-varying load torque command based on the load boundary parameters of the electric drive system. ,in This is a function of the load torque that varies with time. S203. Set voltage constraints during motor closed-loop control. and current constraint ,in The maximum allowable current for the motor. The maximum allowable output voltage of the inverter. , These are voltage commands for the d-axis and q-axis, respectively. , These are the d-axis and q-axis current commands, respectively. S204. Based on the target speed command, target mechanical angular velocity, target torque command, load torque command, voltage constraint condition, and current constraint condition obtained from S201 to S203, construct the motor control input timing sequence. .

5. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 4, characterized in that, Step S3 specifically includes: S301. Calculate the motor speed deviation based on the target speed command and the motor feedback speed. And generate electromagnetic torque command through speed loop regulation. When the system adopts torque control mode, the electromagnetic torque command is directly given by the target torque command, that is... ; S302. Based on the electromagnetic torque command and the motor operating status, obtain the d-axis current command through the torque-current relationship. and q-axis current command At low speeds and below base speeds, current commands are generated through maximum torque-to-current ratio control. MTPA control is expressed as: in, It is a permanent magnet flux chain. , These are the d-axis and q-axis inductances, respectively. When the target speed is higher than the motor base speed or reaches the field weakening start speed threshold At that time, that is When the motor enters the high-speed field weakening condition, the current command is corrected using maximum torque-voltage ratio control. MTPV control is expressed as: in, This represents the maximum voltage amplitude. S303, Based on the initial feedback three-phase stator current of the motor , , The feedback d-axis current is obtained through Clark and Park transformations. and feedback q-axis current : in, For rotor electrical angle, Indicates transpose; S304. The d-axis and q-axis current commands obtained from S302 and the motor feedback d-axis and q-axis currents from S303 are used as the inner current loop input. The d-axis voltage command is obtained by calculating the current deviation. and q-axis voltage command : in, For d-axis current deviation, This refers to the q-axis current deviation. S305, based on rotor electrical angle The d-axis and q-axis voltage commands are subjected to inverse Park transformation to obtain the voltage commands in the two-phase stationary coordinate system: in, , The voltages are in a two-phase stationary coordinate system. S306, Based on the voltage in the two-phase stationary coordinate system , and DC bus voltage The three-phase inverter switching control signal is generated by space vector pulse width modulation, and the three-phase stator voltage is output by the three-phase inverter. , , The three-phase stator voltage is equivalently transformed into the voltage input that actually acts on the dq-axis model of the motor. , : S307. Based on the d-axis and q-axis voltage inputs from the inner current loop, and combined with the d- and q-axis voltage equations of the permanent magnet synchronous motor, the computer calculates the d-axis and q-axis current responses: in, The stator winding resistance is used; the d-axis and q-axis current responses at the next time step are obtained through time-domain integration. , : S308. Based on the d-axis and q-axis current responses and motor parameters obtained in S307, calculate the actual electromagnetic torque of the motor. : 。 6. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 5, characterized in that, Step S4 specifically includes: S401. Length of the helical gear pair meshing contact line based on gear pair parameters and the angular velocity of the driving gear. Represented as: in, This indicates the translational velocity along the transverse cross section. , The radius of the base circle, The base circle helix angle, For tooth width, For end face overlap, For longitudinal overlap, The total overlap is The pitch of the base circle on the end face of the helical gear; S402. Based on the basic parameters of the driving and driven helical gears, the gear teeth are discretized into multiple slice units along the tooth width direction of the helical gear, and the total number of slices is... ,in, This indicates rounding to the nearest integer. The width of each slice; S403. Calculate the distance from the root circle based on the basic parameters of the driving and driven helical gears. Cross-sectional area at the location and moment of inertia of cross section ; S404. Based on the cross-sectional area and moment of inertia of the slice element obtained in S403, approximate a single slice element as a non-uniform cantilever beam, and calculate the Hertzian contact stiffness of the slice element of the gear using the potential energy method. Bending stiffness Axial compressive stiffness Shear stiffness and matrix stiffness : in, It is the distance from the point of engagement along the tooth height to the root circle. For pressure angle, The Young's modulus of the gear tooth material. The shear modulus of the gear tooth material. Poisson's ratio, The thickness of half a tooth at the meshing point. , , , For polynomial coefficients, , These are the geometric parameters related to the gear base. S405. Based on the contact line length obtained in S401 and the number of meshing slices in S402, the stiffness of each slice unit in S404 is accumulated along the contact line direction to obtain the single-tooth pair meshing stiffness of the helical gear during meshing: in, For custom angles, , , For the number index of the slice unit, The direction angle of the meshing plane. The gear meshing termination angle, This represents the angular displacement of the gear rotation; S406. Based on the number of gear pairs simultaneously engaging at different meshing positions, calculate the overall meshing stiffness of the helical gear throughout the entire meshing process. : in, Indicates the number of gear teeth that mesh simultaneously, subscript. Indicates the active wheel, subscript Indicates the driven wheel, For the first Hertzian contact stiffness of gear teeth, , , , The first The bending stiffness, shear stiffness, axial compressive stiffness, and base stiffness of the driving gear in the gear teeth. , , , The first The bending stiffness, shear stiffness, axial compressive stiffness, and base stiffness of the driven gear in a gear tooth assembly.

7. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 6, characterized in that, Step S5 specifically includes: S501. When the driving gear rotates clockwise, the relative displacement of the tooth contact point along the meshing line... Represented as: in, , , These are the drive gears in , , Vibration displacement in the direction; , , These are the driven gears in , , Vibration displacement in the direction; , , They are the drive gear winding , , Angular displacement of the direction of rotation; , , These are the driven gears winding around , , Angular displacement of the direction of rotation; , These are the base circle radii of the driving gear and the driven gear, respectively. The base circle helix angle, It is the normal pressure angle; S502. Based on the comprehensive time-varying meshing stiffness obtained in S406 and the relative displacement of the tooth surface obtained in S501, calculate the dynamic meshing force of the helical gear pair. : in, For gear pair meshing damping, The relative velocity of the tooth surface contact point along the meshing line direction.

8. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 7, characterized in that, Step S6 specifically includes: The electromagnetic torque of the motor is used as a coupling variable to transmit data in real time between the motor and the helical gear transmission system, establishing an electromechanical coupling dynamic model of the helical gear transmission system; the output speed and torque of the motor are correlated with the input speed and torque of the gear pair, and the electromechanical coupling dynamic equation is expressed as follows: in, For the moment of inertia of the motor, This is the motor damping coefficient. The mechanical angular velocity of the motor. This refers to the torsional stiffness between the motor shaft and the drive gear shaft. This refers to the torsional damping between the motor shaft and the drive gear shaft. For the driving gear to wind around angular displacement of the direction of rotation For the driving gear to wind around Angular velocity of rotation in the direction.

9. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 8, characterized in that, Step S7 specifically includes: Based on the dynamic meshing force of the helical gear pair calculated by S502 and the electromechanical coupling model of S601, the dynamic equations of the multi-degree-of-freedom gear pair are established; the driving gear and driven gear are respectively equivalent to lumped mass elements, and the motion of the driving gear and driven gear is mediated by... , , Directional translation and rotation , , Rotation of direction , , To describe, while considering the mechanical angular displacement of the motor. The dynamic equations for the active wheel's bending-axle-torsion-pendulum coupling are as follows: The coupled dynamic equations of the driven wheel's bending-shaft-torsion-pendulum motion are: in, and These are the masses of the driving gear and the driven gear, respectively. Let be the moment of inertia of the driving gear. Let be the moment of inertia of the driven gear; , , They are respectively , , The support stiffness of the drive gear in the direction of travel; , , They are respectively , , The support stiffness of the driven gear in the direction of travel; , , They are respectively , , Support damping of the drive gear in the direction of travel; , , They are respectively , , Support damping of the driven gear in the direction of movement; , Gear winding , Torsional stiffness and torsional damping of rotational direction; , , The driving gear is wound around , , Moment of inertia in the direction of rotation; , , The driven gears are wound around , , Moment of inertia in the direction of rotation; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; , They are respectively The first and second derivatives; for The second derivative of .

10. The electromechanical coupling dynamics analysis method for helical gear transmission systems according to claim 9, characterized in that, Step S8 specifically includes: S801. Based on the control command parameters, the motor dual closed-loop control model, the electromechanical coupling dynamic equation, and the bending-shaft-torsion-swing coupling dynamic equation, the fourth-order Runge-Kutta method is used for iterative solution. In each time step, the motor current response, motor electromagnetic torque, motor mechanical angular velocity and mechanical angular displacement, helical gear pair comprehensive time-varying meshing stiffness, tooth surface relative displacement, dynamic meshing force, and gear pair vibration response are updated synchronously. S802. Based on the time-domain integral solution of S801, output the motor electromagnetic torque, mechanical angular velocity, mechanical angular displacement, and current response. S803. Based on the time-domain integral solution of S801, output the helical gear pair meshing response and gear pair dynamic response; the helical gear pair meshing response includes the helical gear pair's comprehensive time-varying meshing stiffness, the relative displacement of the tooth surface contact point along the meshing line direction, and the dynamic meshing force; the gear pair dynamic response includes the dynamic meshing force of the driving gear and the driven gear in... , , The vibration displacement, vibration velocity, vibration acceleration, and the rotation around the vibration direction. , , Angular displacement, angular velocity, and angular acceleration in the direction of rotation; S804, according to the helical gear pair in , , Vibration displacement and velocity response in the direction of vibration, output bearing support load: in, , , The driving gear is respectively in , , The bearing supports the load in the direction of the direction; , , The driven gear is respectively in , , The bearing supports the load in the direction of the direction.

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