Electric servo mechanism multidisciplinary digital twin modeling method and device

Abstract

A multidisciplinary digital twinning modeling method and device for an electric servo mechanism belongs to the field of digital twinning technology and mechatronics systems, and is characterized in that static stiffness analysis is performed on a planetary gear reducing mechanism and a ball screw transmission mechanism to obtain gear pair torsional stiffness and screw pair axial stiffness; then, based on a multi-degree-of-freedom kinetic model and a Lagrange equation, establishing a linearization motion equation including gap nonlinear stiffness; constructing a complete electromechanical control missile multidisciplinary dynamic model; through multidisciplinary coupling modeling, multi-scale analysis and fault model integration, mechanical transmission characteristics, motor and control characteristics and fault mechanisms of the electric servo mechanism can be completely reflected, and corresponding mathematical and simulation models are constructed. The constructed digital twinborn simulation platform can provide solid theoretical basis and technical support for design optimization, performance improvement, fault diagnosis and health assessment of the servo system, and has important application value and popularization significance.

Description

Technical Field

[0001] This invention belongs to the field of digital twin technology and mechatronics systems, and particularly relates to a multidisciplinary digital twin modeling method and device for electric servo mechanisms. Background Technology

[0002] Electric servo mechanisms are widely used in aerospace, robotics, and automated equipment. They drive mechanical transmission systems via motors, converting control signals into precise displacement, velocity, or force outputs. However, under the design requirements of high precision and high reliability, traditional modeling methods struggle to comprehensively consider the coupling characteristics of control, mechanics, and electrical systems, and are insufficient in characterizing important factors such as backlash nonlinearity and fault mechanisms. Furthermore, with the development of digital twin technology, combining high-fidelity simulation models of servo mechanisms with real-time test data to achieve online performance evaluation and fault prediction has become a trend. Current technologies lack multi-scale digital twin modeling methods for electric servo mechanisms and have not yet formed a complete solution encompassing electromechanical coupling, nonlinear backlash, fault mode modeling, and health assessment. Therefore, a multi-disciplinary modeling method based on digital twin technology is needed to organically combine mechanical structure, dynamics, electrical control, and fault models to construct a high-fidelity servo mechanism simulation platform to improve system performance and reliability. Summary of the Invention

[0003] The present invention aims to solve the above problems and provides a multidisciplinary digital twin modeling method and apparatus for electric servo mechanisms.

[0004] In a first aspect, the present invention provides a multidisciplinary digital twin modeling method for an electric servo mechanism, comprising the following steps: Step 1: Static stiffness modeling. The static stiffness of the gear reduction mechanism and the ball screw transmission mechanism is calculated using the finite element analysis method. For gear pairs, a finite element model of the gear pair is established after simplifying the three-dimensional model, and the torsional stiffness of the gear pair is obtained through contact nonlinear analysis. For ball screw pairs, a finite element model of the ball screw pair is established after simplifying the three-dimensional model. The nut, screw and balls are equivalently segmented, a preload is applied and the load is applied in steps to obtain the axial stiffness of the screw pair. Step 2: Based on the torsional stiffness of the gear pair and the axial stiffness of the lead screw pair obtained in Step 1, the kinetic and potential energy equations of the electric servo mechanism transmission system are listed using the rotational angular displacement of the sun gear and the displacement of the ball screw as generalized coordinates. Using the second kind of Lagrange equations, a dynamic model of the electric servo mechanism transmission system is established by simultaneously solving the kinetic and potential energy equations; by applying a constant force load to the output end of the ball screw, a linear dynamic model of the electric servo mechanism transmission system is obtained.

[0005] In the formula, J A This is the rotational inertia of the gear pair equivalent to the motor output. i 1 represents the output angle of the planetary carrier of the gear pair. K t1 For the overall torsional stiffness of the gear pair, K 2 represents the contact stiffness of the ball screw. i 3 represents the transmission ratio of the ball screw pair. x The ball screw pair nut outputs displacement. M nut For the quality of ball screw nuts, F A constant force load applied to the output end of the ball screw; Step 3: Establish a servo motor model, including establishing the voltage equation and torque balance equation of the servo motor; establish a servo motor controller model based on the three-loop control principle of the servo motor; Step 4: Couple the dynamic model of the transmission system, the servo motor model, and the servo motor controller model to establish an overall electromechanical coupled dynamic model, and complete the multidisciplinary digital twin modeling of the electric servo mechanism.

[0006] Furthermore, in the multidisciplinary digital twin modeling method for electric servo mechanisms described in this invention, there are gaps in the gear pairs and lead screw bearings in the dynamic model of the transmission system described in step two. The nonlinear dynamic model of the electric servo mechanism transmission system, which integrates gaps in multiple components, is as follows:

[0007] In the formula, f N ( i 1) This refers to the nonlinear restoring force caused by the gap; N It is a non-linear subscript; When establishing a nonlinear dynamic model of a transmission system with clearance, the clearance between the gear pair and the lead screw is considered. A dynamic equation with nonlinear stiffness containing clearance is used to consider the clearance effect in the transmission chain. A nonlinear restoring force term caused by clearance is added to the right side of the dynamic model. Specifically, a restoring force based on the nonlinear stiffness of the center clearance is added to the right side of the dynamic equation. The nonlinear restoring force is described by a piecewise function to realize the modeling of the clearance effect.

[0008] Furthermore, in the multidisciplinary digital twin modeling method for electric servo mechanisms described in this invention, step three, establishing a servo motor controller model based on the three-loop control principle of the servo motor, includes: defining the controller input as a position command. x 0, the output is the voltage value that drives the motor to rotate. U aThe control method is a three-loop control, including a position loop, a speed loop, and a current loop; the position loop uses P control, and the control parameter is the proportional parameter of the position loop. The speed loop uses PI control, and the control parameter is the proportional parameter of the speed loop. Integral parameters K I The current loop uses P control, and the control parameter is the proportional parameter of the current loop. ; The input-output relationship of the controller is represented as follows:

[0009] In the formula, x 0、 x feedback These are position commands and position feedback, respectively; Ω ref Ω and Ω represent the speed reference value and speed feedback, respectively. I ref , I These are the current reference value and the current feedback, respectively.

[0010] Furthermore, in the multidisciplinary digital twin modeling method for electric servo mechanisms described in this invention, step three, establishing the servo motor model, includes: establishing the servo motor model through the voltage equation and torque balance equation of the servo motor, with the input being the voltage value output by the servo motor controller and the reaction torque transmitted by the gear pair, and the output being the angular displacement of the servo motor shaft; The voltage equation is expressed as:

[0011] In the formula, U a This is the input voltage for the motor. L It is the q-axis inductance. R For phase resistance, i For armature current, i 0 represents the rotor angular displacement. K e The back electromotive force constant is... t Indicates time; The torque balance equation is expressed as:

[0012] In the formula, K T The electromagnetic torque constant is T e For the electromagnetic torque of the motor, J The moment of inertia of the motor rotor. B This is the motor damping coefficient. T 0 represents the reaction torque of the gear pair on the motor; The input-output relationship of the servo motor model is represented as follows:

[0013] In the formula, J The moment of inertia of the motor rotor. K T The electromagnetic torque constant is R For phase resistance, K e is the back electromotive force constant.

[0014] In model building, the servo motor and motor control system are incorporated into the mechanical model to construct a complete electromechanical-control coupled digital twin model. The servo system comprises four functional units: a motor controller, a motor body, a mechanical transmission mechanism, and sensors. The motor controller adopts a three-loop control structure (position loop P control, speed loop PI control, and current loop P control); the servo motor body uses a permanent magnet synchronous motor model, establishing its voltage equation and torque balance equation; the mechanical transmission chain adopts the dynamic model obtained in step two. Through the coupling connection of torque and displacement, the interaction between the motor, electronic control, and mechanical transmission is realized, forming the electromechanical-control-spring coupled dynamic model of the entire electric servo mechanism.

[0015] Furthermore, in the multidisciplinary digital twin modeling method for electric servo mechanisms described in this invention, step four, which involves coupling the dynamic model of the transmission system, the servo motor model, and the servo motor controller model, includes: connecting the output torque of the servo motor to the input torque of the gear pair; simultaneously connecting the output rotation angle of the servo motor to the input rotation angle of the gear pair; connecting the output rotation angle of the gear pair to the input rotation angle of the ball screw-bearing pair model; and feeding back the output torque of the ball screw pair to the input torque of the gear pair.

[0016] Secondly, the present invention provides a multidisciplinary digital twin modeling system for electric servo mechanisms, including a transmission system analysis module, a basic model modeling module, and a digital twin modeling module; The transmission system analysis module is used to perform static stiffness modeling of the electric servo mechanism. It employs finite element analysis to calculate the static stiffness of the gear reduction mechanism and the ball screw transmission mechanism. For the gear pair, a finite element model is established after simplifying the three-dimensional model, and the torsional stiffness of the gear pair is obtained through contact nonlinear analysis. For the ball screw pair, a finite element model is established after simplifying the three-dimensional model. The nut, screw, and balls are equivalently segmented, a preload is applied, and the load is applied in stages to obtain the axial stiffness of the screw pair. The basic modeling module is used to establish the dynamic model, servo motor model, and servo motor controller model of the electric servo mechanism transmission system. Based on the gear pair torsional stiffness and screw pair axial stiffness parameters obtained from the transmission system analysis module, the kinetic and potential energy equations of the electric servo mechanism transmission system are listed using the sun gear rotational angular displacement and ball screw displacement as generalized coordinates. Using the second kind of Lagrange equation, the dynamic model of the electric servo mechanism transmission system is established by simultaneously solving the kinetic and potential energy equations. A constant force load is applied to the output end of the ball screw to obtain the linear dynamic model of the electric servo mechanism transmission system. Since there are gaps in the gear pair and screw bearings in the dynamic model, considering the load effect, a nonlinear dynamic model of the electric servo mechanism transmission system integrating the gaps of multiple links is constructed. The digital twin modeling module is used to couple the dynamic model of the transmission system, the servo motor model, and the servo motor controller model to establish an overall electromechanical coupling dynamic model, and complete the multidisciplinary digital twin modeling of the electric servo mechanism.

[0017] Furthermore, in the multidisciplinary digital twin modeling system for electric servo mechanisms described in this invention, the coupling of the dynamic model of the transmission system, the servo motor model, and the servo motor controller model includes: connecting the output torque of the servo motor to the input torque of the gear pair; simultaneously connecting the output rotation angle of the servo motor to the input rotation angle of the gear pair; connecting the output rotation angle of the gear pair to the input rotation angle of the ball screw-bearing pair model; and feeding back the output torque of the ball screw pair to the input torque of the gear pair.

[0018] Furthermore, in the multidisciplinary digital twin modeling system for electric servo mechanisms described in this invention, the servo motor model is established through the voltage equation and torque balance equation of the servo motor. The inputs are the voltage value output by the servo motor controller and the reaction torque transmitted by the gear pair, and the output is the angular displacement of the servo motor shaft. The servo motor controller model is established based on the three-loop control principle of the motor.

[0019] Thirdly, the present invention provides a multidisciplinary digital twin modeling device for an electric servo mechanism, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the multidisciplinary digital twin modeling method for an electric servo mechanism as described in the first aspect when the computer program is executed.

[0020] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the multidisciplinary digital twin modeling method for electric servo mechanisms as described in the first aspect.

[0021] The multidisciplinary digital twin modeling method and apparatus for electric servo mechanisms described in this invention, through multidisciplinary coupled modeling, multi-scale analysis, and fault model integration, can comprehensively reflect the mechanical transmission characteristics, motor and control characteristics, and fault mechanisms of electric servo mechanisms, and construct corresponding mathematical and simulation models. The constructed digital twin simulation platform can provide a solid theoretical foundation and technical support for servo system design optimization, performance improvement, fault diagnosis, and health assessment, and has significant application value and promotional significance. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the multidisciplinary digital twin modeling method for electric servo mechanisms described in an embodiment of the present invention; Figure 2 A 3D schematic diagram of the finite element model of the gear pair of the transmission mechanism of an electric servo mechanism; Figure 3 A 3D schematic diagram of the finite element model of the ball screw pair of the transmission mechanism of an electric servo mechanism; Figure 4 This is a block diagram model of the electromechanical coupling of the electric servo mechanism described in an embodiment of the present invention. Detailed Implementation

[0023] The multidisciplinary digital twin modeling method and apparatus for electric servo mechanisms described in this invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0024] Example 1 This embodiment discloses a multidisciplinary digital twin modeling method for electric servo mechanisms, such as... Figure 1 As shown, the specific steps include: Step 1: Perform static stiffness modeling on the mechanical transmission components of the electric servo mechanism. Create a gear pair model using SolidWorks, such as... Figure 2 The model shown has 5 gears and 1 planet carrier. A 3D model including the sun gear, planet gears, internal gear ring, and planet carrier is created. The number of gear teeth is simplified to the actual number of teeth involved in meshing.

[0025] In this embodiment, non-coordinated elements (C3D8I) are used to discretize the model in the finite element software, and the mesh is refined in the tooth contact area to improve accuracy. Contact pairs are set and torsional loads are applied. The solution is obtained by progressively loading the loads in multiple analysis steps to obtain the torsional stiffness of the gear pair. Mesh convergence analysis shows that the change in the support reaction moment-rotation angle curve obtained by adjusting the mesh density is very small, indicating that the calculation has reached convergence. The calculated torsional stiffness of the gear pair is 1.64198 × 10⁻⁶. 7 N·mm / rad.

[0026] For ball screw pairs, a 3D model is also created using SolidWorks, such as... Figure 3 As shown, the ball screw pair model in the electric servo mechanism in this embodiment includes a screw, a nut, and balls. The model is cut off by 1 / 15 using rotational symmetry.

[0027] In this embodiment, the model is discretized using a three-dimensional solid 8-node non-coordinated element C3D8I, and a preload step is set: the first step simulates ball preload, followed by two steps of applying axial working load. Mesh convergence analysis shows that as the mesh size decreases, the axial deformation-axial force curve gradually approaches and changes very little after the mesh size is less than 0.2 mm, indicating that the calculation results have converged. The axial stiffness of the ball screw pair is 1.71522 × 10⁻⁶. 6 N / mm.

[0028] Finite element stiffness analysis revealed the nonlinear stiffness characteristics of the gear mechanism and ball screw pair under working load, providing parameter basis for dynamic modeling.

[0029] Step 2: Based on the torsional stiffness of the gear pair and the axial stiffness of the ball screw pair obtained in Step 1, a linear dynamic model of the electric servo mechanism transmission system is established, taking the sun gear rotation angle and the axial displacement of the ball screw as generalized coordinates, considering motor rotor lock-up, and neglecting nonlinear elements. The kinetic energy and potential energy of the system are then derived.

[0030] The potential energy equation is expressed as:

[0031] In the formula, K t1 For the overall torsional stiffness of the gear pair, K 2 represents the contact stiffness of the ball screw. i 1 represents the output angle of the planetary carrier of the gear pair. x The ball screw pair nut outputs displacement. i 3 represents the transmission ratio of the ball screw pair.

[0032] The kinetic energy equation can be expressed as:

[0033] In the formula, J A This is the rotational inertia of the gear pair equivalent to the motor output. m nut For the quality of the ball screw nut.

[0034] The moment of inertia of the gear pair equivalent to the motor output. J A The calculation method is as follows:

[0035] In the formula,J 1 represents the moment of inertia of the sun gear. J 2. Moment of inertia of a single planetary gear J H For the planetary carrier's moment of inertia, z 1 represents the number of teeth on the sun gear. z 2 represents the number of teeth on a single planetary gear. z 3 represents the number of teeth on the gear ring. m 2 represents the mass of a single planetary gear. m It is the modulus.

[0036] Substituting the second kind of Lagrange equations, and assuming negligible damping, we derive the linear dynamic model of the electric servo mechanism transmission system:

[0037] For linear servo mechanisms, the dynamic equations already include the linear restoring force of the nonlinear stiffness of the gear pair backlash. f L ( i 1). Therefore, the restoring force of the nonlinear part f L ( i 1) Adding this to the right-hand side of the linear dynamics equation of the servo mechanism, and rearranging the equations, we obtain the nonlinear dynamics model of the electric servo mechanism transmission system that incorporates the backlashes of multiple links: .

[0038] In this embodiment of the disclosure, when modeling the transmission system, the input to the gear pair model is the angular displacement of the motor rotation angle. i 0 and the reaction torque applied by the ball screw T sg The output is the reaction torque applied to the motor. T 0 and the rotational angular displacement of the ball screw i 1. Other model parameters are the gear pair transmission ratio. i 1. Moment of inertia of the gear pair J A Torsional stiffness of gear pairs K t1 Ball screw pair transmission ratio i 3; The input-output relationship of the gear pair is as follows:

[0039] Can be written as:

[0040] After Laplace transform, the input-output relationship is obtained as follows:

[0041] The input to the ball screw pair model is the rotational angular displacement of the ball screw. i 1 and external torque T load The output is linear displacement. x Other model parameters are the ball screw pair transmission ratio. i 3. Contact stiffness of ball screw pair K 2. Nut quality M B ; The input-output relationship of the ball screw pair is as follows:

[0042] Can be written as:

[0043] After Laplace transform, the input-output relationship is obtained as follows: .

[0044] Step 3: Establish the servo motor model, including establishing the voltage equation and torque balance equation of the servo motor; establish the servo motor controller model based on the three-loop control principle of the servo motor; in this embodiment, a permanent magnet synchronous motor model is used.

[0045] In this embodiment, a three-loop closed-loop control strategy is used to construct the servo controller model: the position loop uses proportional P control, the speed loop uses proportional-integral PI control, and the current loop uses proportional P control. Based on the control parameters (position loop proportional...),... Speed ​​ring ratio and points K I Current loop ratio Establish the input-output transmission relationship of the controller, as shown in the following expression:

[0046] In the formula, x 0、 x feedback These are position commands and position feedback, respectively; Ω ref Ω and Ω represent the speed reference value and speed feedback, respectively. I ref , I These are the current reference value and the current feedback, respectively.

[0047] When establishing the servo motor model, a permanent magnet synchronous motor model is also used, with the input being the voltage value output from the motor controller. Ua and the reaction torque transmitted by the gear pair T The output is the angular displacement of the motor shaft. i0. By combining the motor voltage equation and torque balance equation, a motor model is established, and a Laplace transform is performed to obtain the input-output relationship of the motor module as follows:

[0048] In the formula, J The moment of inertia of the motor rotor. K T The electromagnetic torque constant is R For phase resistance, K e is the back electromotive force constant.

[0049] Step 4: Couple the dynamic model of the transmission system, the servo motor model, and the servo motor controller model to establish an overall electromechanical coupled dynamic model, and complete the multidisciplinary digital twin modeling of the electric servo mechanism.

[0050] In the electromechanical coupling model, the gear pair model and the motor model are coupled through torque transmission, connecting the output torque of the servo motor to the input torque of the gear pair; simultaneously, the output rotation angle of the servo motor is connected to the input rotation angle of the gear pair. The output rotation angle of the gear pair is connected to the input rotation angle of the ball screw-bearing pair model; the output torque of the ball screw pair is fed back and connected to the input torque of the gear pair. This constitutes the electromechanical coupling model of the electric servo mechanism described in this embodiment, as follows. Figure 4 As shown, this illustrates the process of establishing a multidisciplinary digital twin model of the electric servo mechanism, in which... i 13 This indicates the total transmission ratio of the electric servo mechanism's transmission system.

[0051] By using the digital twin model established in this embodiment for simulation and combining it with actual measurement data, the performance indicators of each functional unit of the servo mechanism can be evaluated online, and the system performance can be tested and analyzed, providing a technical solution for the health evolution analysis of the servo mechanism.

[0052] The multidisciplinary digital twin modeling method described in this embodiment can fully reflect the static stiffness, dynamics, electronic control, and fault characteristics of electric servo mechanisms. This method not only improves the electromechanical coupling dynamics modeling theory of electric servo mechanisms, but also establishes a systematic fault modeling framework based on this model, providing a theoretical foundation and technical support for the performance optimization and reliability analysis of servo systems.

[0053] Example 2 Based on Embodiment 1, this embodiment discloses a multidisciplinary digital twin modeling system for electric servo mechanisms, including a transmission system analysis module, a basic model modeling module, and a digital twin modeling module; The transmission system analysis module is used to perform static stiffness modeling of the electric servo mechanism. It employs finite element analysis to calculate the static stiffness of the gear reduction mechanism and the ball screw transmission mechanism. For the gear pair, a finite element model is established after simplifying the three-dimensional model, and the torsional stiffness of the gear pair is obtained through contact nonlinear analysis. For the ball screw pair, a finite element model is established after simplifying the three-dimensional model. The nut, screw, and balls are equivalently segmented, a preload is applied, and the load is applied in stages to obtain the axial stiffness of the screw pair. The basic modeling module is used to establish the dynamic model, servo motor model, and servo motor controller model of the electric servo mechanism transmission system. Based on the gear pair torsional stiffness and screw pair axial stiffness parameters obtained from the transmission system analysis module, the kinetic and potential energy equations of the electric servo mechanism transmission system are listed using the sun gear rotational angular displacement and ball screw displacement as generalized coordinates. Using the second kind of Lagrange equation, the dynamic model of the electric servo mechanism transmission system is established by simultaneously solving the kinetic and potential energy equations. A constant force load is applied to the output end of the ball screw to obtain the linear dynamic model of the electric servo mechanism transmission system. Since there are gaps in the gear pair and screw bearings in the dynamic model, considering the load effect, a nonlinear dynamic model of the electric servo mechanism transmission system integrating the gaps of multiple links is constructed. The digital twin modeling module is used to couple the dynamic model of the transmission system, the servo motor model, and the servo motor controller model to establish an overall electromechanical coupling dynamic model, and complete the multidisciplinary digital twin modeling of the electric servo mechanism.

[0054] In this embodiment, the servo motor model is established using the voltage equation and torque balance equation of the servo motor. The inputs are the voltage value output by the servo motor controller and the reaction torque transmitted by the gear pair, and the output is the angular displacement of the servo motor shaft. The servo motor controller model is established based on the three-loop control principle of the motor. Coupling the dynamic model of the transmission system, the servo motor model, and the servo motor controller model includes: connecting the output torque of the servo motor to the input torque of the gear pair; simultaneously connecting the output rotation angle of the servo motor to the input rotation angle of the gear pair; connecting the output rotation angle of the gear pair to the input rotation angle of the ball screw-bearing pair model; and feeding back the output torque of the ball screw pair to the input torque of the gear pair.

[0055] The specific operation steps of the multidisciplinary digital twin modeling system for electric servo mechanisms described in this embodiment are the same as those of the multidisciplinary digital twin modeling method for electric servo mechanisms described in Embodiment 1 above, and will not be repeated here.

[0056] Example 3 This embodiment discloses a multidisciplinary digital twin modeling device for an electric servo mechanism, including a memory and a processor; the memory is used to store a computer program; the processor is used to implement the multidisciplinary digital twin modeling method for an electric servo mechanism as described in Embodiment 1 when the computer program is executed. The specific modeling method steps are the same as those in Embodiment 1, and will not be repeated here.

[0057] Example 4 This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the multidisciplinary digital twin modeling method for electric servo mechanisms as described in Embodiment 1. The specific modeling method steps are the same as those in Embodiment 1, and will not be repeated here.

[0058] The computer described in this application embodiment can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. The computer-readable storage medium can be any usable medium that a computer can read, or a data storage device such as a server or data center that integrates one or more usable media. The usable medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., digital versatile optical disc (DVD)), or a semiconductor medium (e.g., solid-state drive (SSD)). The software formed by the computer's stored code can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other storage media that are mature in the art.

[0059] In the various embodiments of this application, the functional modules can be integrated into one processing unit or module, or each module can exist physically separately, or two or more modules can be integrated into one unit or module. In the above embodiments, they can be implemented entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated.

[0060] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multidisciplinary digital twin modeling method for an electric servo mechanism, characterized in that, Includes the following steps: Step 1: Static stiffness modeling. The static stiffness of the gear reduction mechanism and the ball screw transmission mechanism is calculated using the finite element analysis method. For gear pairs, a finite element model of the gear pair is established after simplifying the three-dimensional model, and the torsional stiffness of the gear pair is obtained through contact nonlinear analysis. For ball screw pairs, a finite element model of the ball screw pair is established after simplifying the three-dimensional model. The nut, screw and balls are equivalently segmented, a preload is applied and the load is applied in steps to obtain the axial stiffness of the screw pair. Step 2: Based on the torsional stiffness of the gear pair and the axial stiffness of the lead screw pair obtained in Step 1, the kinetic and potential energy equations of the electric servo mechanism transmission system are listed using the rotational angular displacement of the sun gear and the displacement of the ball screw as generalized coordinates. Using the second kind of Lagrange equations, a dynamic model of the electric servo mechanism transmission system is established by simultaneously solving the kinetic and potential energy equations; by applying a constant force load to the output end of the ball screw, a linear dynamic model of the electric servo mechanism transmission system is obtained. ； In the formula, J A This is the rotational inertia of the gear pair equivalent to the motor output. θ 1 represents the output angle of the planetary carrier of the gear pair. K t1 For the overall torsional stiffness of the gear pair, K 2 represents the contact stiffness of the ball screw. i 3 represents the transmission ratio of the ball screw pair. x The ball screw pair nut outputs displacement. M nut For the quality of ball screw nuts, F A constant force load applied to the output end of the ball screw; Step 3: Establish a servo motor model, including establishing the voltage equation and torque balance equation of the servo motor; establish a servo motor controller model based on the three-loop control principle of the servo motor; Step 4: Couple the dynamic model of the transmission system, the servo motor model, and the servo motor controller model to establish an overall electromechanical coupled dynamic model, and complete the multidisciplinary digital twin modeling of the electric servo mechanism.

2. The multidisciplinary digital twin modeling method for electric servo mechanisms according to claim 1, characterized in that, In the dynamic model of the transmission system described in step two, there are gaps in the gear pairs and lead screw bearings. The nonlinear dynamic model of the electric servo mechanism transmission system, which incorporates gaps in multiple components, is as follows: ； In the formula, f N ( θ 1) The nonlinear restoring force caused by the gap; N It is a non-linear subscript.

3. The multidisciplinary digital twin modeling method for electric servo mechanisms according to claim 1, characterized in that, Step three, establishing the servo motor controller model based on the three-loop control principle of the servo motor, includes: defining the controller input as a position command. x 0, the output is the voltage value that drives the motor to rotate. U a The control method is a three-loop control, including a position loop, a speed loop, and a current loop; the position loop uses P control, and the control parameter is the proportional parameter of the position loop. The speed loop uses PI control, and the control parameter is the proportional parameter of the speed loop. Integral parameters K I The current loop uses P control, and the control parameter is the proportional parameter of the current loop. ; The input-output relationship of the controller is represented as follows: ； In the formula, x 0、 x feedback These are position commands and position feedback, respectively; Ω ref Ω and Ω represent the speed reference value and speed feedback, respectively. I ref , I These are the current reference value and the current feedback, respectively.

4. The multidisciplinary digital twin modeling method for electric servo mechanisms according to claim 3, characterized in that, Step 3, establishing the servo motor model, includes: establishing the servo motor model through the voltage equation and torque balance equation of the servo motor, with the input being the voltage value obtained from the output of the servo motor controller and the reaction torque transmitted by the gear pair, and the output being the angular displacement of the servo motor shaft; The voltage equation is expressed as: ； In the formula, U a This is the input voltage for the motor. L It is the q-axis inductance. R For phase resistance, i For armature current, θ 0 represents the rotor angular displacement. K e The back electromotive force constant is... t Indicates time; The torque balance equation is expressed as: ； In the formula, K T The electromagnetic torque constant is T e For the electromagnetic torque of the motor, J The moment of inertia of the motor rotor. B This is the motor damping coefficient. T 0 represents the reaction torque of the gear pair on the motor; The input-output relationship of the servo motor model is represented as follows: ； In the formula, J The moment of inertia of the motor rotor. K T The electromagnetic torque constant is R For phase resistance, K e is the back electromotive force constant.

5. The multidisciplinary digital twin modeling method for electric servo mechanisms according to claim 1, characterized in that, Step four involves coupling the dynamic model of the transmission system, the servo motor model, and the servo motor controller model, which includes: connecting the output torque of the servo motor to the input torque of the gear pair; simultaneously connecting the output rotation angle of the servo motor to the input rotation angle of the gear pair; connecting the output rotation angle of the gear pair to the input rotation angle of the ball screw-bearing pair model; and feeding back the output torque of the ball screw pair to the input torque of the gear pair.

6. A multidisciplinary digital twin modeling system for electric servo mechanisms, characterized in that: It includes a transmission system analysis module, a basic modeling module, and a digital twin modeling module; The transmission system analysis module is used to perform static stiffness modeling of the electric servo mechanism. It employs finite element analysis to calculate the static stiffness of the gear reduction mechanism and the ball screw transmission mechanism. For the gear pair, a finite element model is established after simplifying the three-dimensional model, and the torsional stiffness of the gear pair is obtained through contact nonlinear analysis. For the ball screw pair, a finite element model is established after simplifying the three-dimensional model. The nut, screw, and balls are equivalently segmented, a preload is applied, and the load is applied in stages to obtain the axial stiffness of the screw pair. The basic modeling module is used to establish the dynamic model, servo motor model, and servo motor controller model of the electric servo mechanism transmission system. Based on the gear pair torsional stiffness and screw pair axial stiffness parameters obtained from the transmission system analysis module, the kinetic and potential energy equations of the electric servo mechanism transmission system are listed using the sun gear rotational angular displacement and ball screw displacement as generalized coordinates. Using the second kind of Lagrange equation, the dynamic model of the electric servo mechanism transmission system is established by simultaneously solving the kinetic and potential energy equations. A constant force load is applied to the output end of the ball screw to obtain the linear dynamic model of the electric servo mechanism transmission system. Since there are gaps in the gear pair and screw bearings in the dynamic model, considering the load effect, a nonlinear dynamic model of the electric servo mechanism transmission system integrating the gaps of multiple links is constructed. The digital twin modeling module is used to couple the dynamic model of the transmission system, the servo motor model, and the servo motor controller model to establish an overall electromechanical coupling dynamic model, and complete the multidisciplinary digital twin modeling of the electric servo mechanism.

7. The multidisciplinary digital twin modeling system for electric servo mechanisms according to claim 6, characterized in that, The coupling of the dynamic model of the transmission system, the servo motor model, and the servo motor controller model includes: connecting the output torque of the servo motor to the input torque of the gear pair; simultaneously connecting the output rotation angle of the servo motor to the input rotation angle of the gear pair; connecting the output rotation angle of the gear pair to the input rotation angle of the ball screw-bearing pair model; and feeding back the output torque of the ball screw pair to the input torque of the gear pair.

8. The multidisciplinary digital twin modeling system for electric servo mechanisms according to claim 6, characterized in that: The servo motor model is established using the voltage equation and torque balance equation of the servo motor. The inputs are the voltage value output by the servo motor controller and the reaction torque transmitted by the gear pair. The output is the angular displacement of the servo motor shaft. The servo motor controller model is established based on the three-loop control principle of the motor.

9. A multidisciplinary digital twin modeling device for an electric servo mechanism, characterized in that: It includes a memory and a processor; the memory is used to store a computer program; the processor is used to implement the multidisciplinary digital twin modeling method for electric servo mechanisms according to any one of claims 1-5 when the computer program is executed.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, which, when executed by a processor, implements the multidisciplinary digital twin modeling method for electric servo mechanisms as described in any one of claims 1-5.

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