Modeling method of heavy load isometric forming robot real-time dynamics digital twin system

Abstract

The present application relates to a kind of heavy load equal material forming robot real-time dynamics digital twin system modeling method, comprising the following steps: S1, only considering the dynamics model of heavy load equal material forming robot of link elastic deformation is established;S2, construct multi-sensor distributed force / position interactive measurement system, arrange grating ruler, encoder, pressure sensor, data fusion is carried out in combination with Kalman filter;S3, PID algorithm is embedded into control system, realizes the closed-loop control of motion trajectory tracking and force feedback;S4, establish the digital twin framework including five dimensions of physical entity, virtual entity, digital data, connection and service.The present application realizes the five-dimensional digital twin system of heavy load equal material forming robot, provides the overall view of robot dynamics through the interaction of physical space and network space, overcomes the problems such as large resource consumption and response delay of high-fidelity simulation.

Description

Technical Field

[0001] This invention relates to the field of forming manufacturing equipment, and more specifically, to a method for modeling a real-time dynamic digital twin system of a heavy-duty equal-material forming robot. Background Technology

[0002] As the manufacturing industry moves towards higher precision, higher efficiency, and greater intelligence, heavy-duty equal-material forming robots, with their advantages of high structural rigidity, high motion accuracy, and strong load-bearing capacity, are widely used in aerospace, medical, and precision machining fields. However, heavy-duty equal-material forming robot systems suffer from rigid-flexible coupling and multi-degree-of-freedom motion coupling problems, leading to complex dynamic behavior. Traditional rigid body models struggle to accurately predict dynamic errors under high-speed, heavy loads and suffer from poor online real-time performance. Digital twin technology, through the fusion of data from physical entities and virtual models, provides a new approach for system lifecycle management and state monitoring; however, existing research largely focuses on static or offline simulation, which is insufficient to meet the online dynamic modeling requirements of parallel motion robots. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot, which can improve online prediction and control performance.

[0004] The technical solution adopted by this invention to solve its technical problem is: to construct a real-time dynamic digital twin system modeling method for a heavy-duty equal-material forming robot, including the following steps: S1. Establish a dynamic model of a heavy-load, equal-material forming robot that only considers the elastic deformation of the connecting rod; S2. Construct a multi-sensor distributed force / position interactive measurement system, deploy grating rulers, encoders, and pressure sensors, and perform data fusion using a Kalman filter; S3. Embed the PID algorithm into the control system to achieve closed-loop control of motion trajectory tracking and force feedback; S4. Establish a digital twin framework that includes five dimensions: physical entities, virtual entities, digital data, connections, and services.

[0005] According to the above scheme, the heavy-duty material forming robot includes six sliders, six rigid links, three hydraulic links, and a working platform. The six sliders are arranged symmetrically in a circle and are driven by servo motors, enabling linear motion along a radial track. The six rigid links are connected to the sliders at one end and fixed to the working platform at the other end, converting the linear displacement of the sliders into the spatial motion of the working platform through motion transmission. The platform is connected to the rigid links and hydraulic links through S-joints.

[0006] According to the above scheme, in step S1, the force balance equations for each component are established using the Newton-Euler method; For the slider, the force balance along the axis of the sliding guide simplifies to: (1) in, It is the magnitude of the driving force. It is the constraint force of the upper S joint. It is the unit vector of the entire linkage. It is the mass of the slider. It is time; For six integral connecting rods, the force and moment balance equations are as follows: (2) in, It is the constraint force of the lower S-joint; It refers to the mass of the entire connecting rod; It is the position vector of the entire linkage; These are the Euler angles of the integral connecting rod; neglecting the rotation of the integral connecting rod along its axis, ; It is the inertia tensor of the entire linkage; It is the first Deformation of the entire connecting rod; The geometric constraint equations for the integral link are: (3) in, It is the elastic modulus of the connecting rod material. It is the cross-sectional radius of the integral connecting rod.

[0007] According to the above scheme, the force balance equation of the hydraulic connecting rod is as follows: (4) in, It is the constraint force acting on the lower S joint of the hydraulic linkage; It is the constraint force of the lower S-joint of the hydraulic connecting rod. The z-component is the connecting rod The hydraulic pressure; It is due to the low quality of the hydraulic linkage; It is the position vector of the hydraulic linkage; These are the Euler angles of the hydraulic connecting rod; rotation of the hydraulic connecting rod along its axis is ignored. ; It is the inertia tensor of the hydraulic linkage; The geometric constraint equations for the hydraulic connecting rod are: (5) in, Indicates the position of the hydraulic linkage.

[0008] According to the above scheme, the equilibrium equations for platform forces and moments are as follows: (6) in, For the quality of the platform, For the platform's inertia tensor; and The platform's stance; The position vector of the platform; Let be the Euler angle vector of the platform; and These are the process forces and process torques acting on the platform.

[0009] According to the above scheme, the dynamic equations of the heavy-duty equal-material forming robot are as follows: (7) The geometric constraint equations are: (8)

[0010] According to the above scheme, a dual-position sensor distributed measurement method based on sliders is adopted, with an encoder installed on each servo motor and a grating ruler arranged on each slider.

[0011] According to the above scheme, the dual-position sensor distributed measurement method adopts a data fusion method based on Kalman filtering of encoder and grating ruler, including the following steps: Define the state variable of the slider motion at time t as: ,in The slider's position, velocity, and acceleration are defined, respectively. Then, a state transition relationship is established based on Taylor expansion to describe the change of the slider's motion state over time. (9) In the formula, This is the state noise vector. , T is the state transition matrix, Δt is the sampling time, and its expression is: (10) Measurement equations are established for both the encoder and the grating ruler to distinguish the measurement characteristics of the two sensors: (11) In the formula, , To measure noise, , , , . and For the measurement matrix, , . The transmission ratio of the drive system; The two sub-filters preprocess the encoder and grating ruler data respectively, obtaining preliminary state estimates and covariance matrices: (12) In the formula, , These are the state estimates of encoder data and grating ruler data, respectively. , These are the corresponding covariance matrices. , These are the Kalman gain values ​​for the encoder and the grating ruler, respectively. The main filter combines the outputs of the two sub-filters, and the final fused result is obtained through weighted merging. (13) In the formula, The fused covariance matrix, These are the estimated values ​​of the fused slider state. The fusion weights are determined by the inverse of the sub-filter covariance matrix, with higher-precision sensor data accounting for a larger proportion.

[0012] According to the above scheme, in step S3, the servo motor is controlled by a three-loop PID controller to achieve high-performance motion tracking; the first loop is the position loop, equipped with a PID controller, which is based on the grating ruler data and the set position. Calculate real-time position error Then through gain Adjustments are made and the results are output to the next loop; the second loop is the speed loop, which uses a PI controller based on encoder data and the target speed. Calculate speed error Then through gain The adjustment and output of the result are sent to the next loop; the third loop is the current loop, which uses a PI controller, and it adjusts the current based on encoder data and set force. Calculation of force error Then through gain Adjust and output the result, namely the drive current of the servo motor. In short, the control theorem for each motor is expressed as: (14)

[0013] According to the above scheme, in step S3, for the control of the hydraulic cylinder, the PID controller is based on the data provided by the pressure sensor and the set force value. Calculate real-time force error Then, by adjusting the gain parameters The error is corrected, and the control result, namely the drive current of the proportional valve, is output. The control theorem is expressed as: (15)

[0014] The modeling method for real-time dynamic digital twin system of heavy-duty equal-material forming robot of the present invention has the following beneficial effects: This invention provides a dynamic model for a heavy-duty, equal-material forming robot that considers only the elastic deformation of the connecting links, reducing the system's degrees of freedom and significantly improving computational efficiency to meet real-time dynamic simulation requirements. By arranging grating rulers, encoders, and pressure sensors at key locations and combining them with Kalman filters for data fusion, measurement noise and errors are effectively reduced, improving measurement accuracy and robustness. A PID algorithm is embedded in the control system to achieve closed-loop control of motion trajectory tracking and force feedback, ensuring high accuracy and stability of the system under dynamic conditions. A digital twin framework encompassing five dimensions—physical entity, virtual entity, digital data, connections, and services—is established to achieve bidirectional mapping and real-time interaction between the physical and virtual systems. This invention realizes a five-dimensional digital twin system for a heavy-duty, equal-material forming robot, providing a holistic view of the robot's dynamics through interaction between physical and cyberspace, overcoming the problems of high-fidelity simulation's high resource consumption and slow response. Attached Figure Description

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a schematic diagram of the physical structure of a heavy-duty, equal-material forming robot; Figure 2 This is a schematic diagram of the dynamic model of a heavy-duty equal-material forming robot; Figure 3 This is a diagram showing the dynamic equations and variables; Figure 4 This is a schematic diagram of a closed-loop control system based on PID. Figure 5 This is a schematic diagram of a five-dimensional digital twin model of a heavy-duty equal-material forming robot; Figure 6 This is a schematic diagram of the hardware and software architecture of a digital twin system; Figure 7 This is a schematic diagram of a closed-loop control system based on PID. Figure 8 This is a schematic diagram of the multi-degree-of-freedom forming of an aircraft bevel gear; Figure 9 This is a schematic diagram illustrating the prediction error and accuracy of dynamic errors; Figure 10 This is a force diagram illustrating the multi-degree-of-freedom forming process of aircraft bevel gears; Figure 11This is a schematic diagram of the real-time stress state of a heavy-duty material forming robot; Figure 12 This is a schematic diagram of the dynamic attitude and forming error of an aircraft bevel gear. Detailed Implementation

[0016] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0017] The real-time dynamic digital twin system modeling method for heavy-duty equal-material forming robot of the present invention includes the following steps: S1, Dynamics Model of Heavy-Duty Equal Material Forming Robot: Only the elastic deformation of the link is considered, reducing the system's degrees of freedom, thereby significantly improving computational efficiency and meeting the requirements of real-time dynamic simulation.

[0018] like Figure 1 As shown, this heavy-duty equal-material forming robot adopts a 6-PSS / 3-SPS structure, consisting of 6 drive sliders, 6 rigid connecting rods, 3 hydraulic connecting rods, and a working platform. The 6 sliders are arranged symmetrically on the machine bed and are driven by servo motors, enabling linear motion along radial tracks. The 3 hydraulic connecting rods are connected to the robot base via S-joints, providing both power compensation and enhanced system rigidity. One end of each of the 6 integral connecting rods is connected to a slider via an S-joint, while the other end is fixed to the platform, converting the linear displacement of the sliders into spatial motion of the platform through motion transmission. The platform is then connected to the 6 integral connecting rods and 3 hydraulic connecting rods via S-joints, thus achieving 6 degrees of freedom in translation and rotation. This mechanism layout allows for precise adjustment of the position and orientation of the working platform in three-dimensional space. Tools can be mounted on the platform, and workpieces can be placed on the robot bed, fulfilling multi-degree-of-freedom operation requirements such as complex surface machining, high-precision forming, and heavy-duty manufacturing.

[0019] like Figure 2 The diagram shown is a schematic representation of the dynamic model of a redundant, heavy-duty, equal-material forming robot. Using the Newton-Euler method, the force balance equations for each component are established: (1) Force balance equations of the slider For the slider, the force balance along the axis of the sliding guide can be simplified to: (1) in, It is the magnitude of the driving force. It is the constraint force of the upper S joint. It is the unit vector of the entire linkage. It is the mass of the slider. It's time.

[0020] (2) Force equilibrium equations for rigid rods For six integral connecting rods, the force and moment balance equations are as follows: (2) in, It is the constraint force of the lower S joint. It refers to the mass of the entire connecting rod. It is the position vector of the entire linkage. These are the Euler angles of the entire connecting rod. Ignoring rotation of the entire connecting rod around its axis, we have: . It is the inertia tensor of the entire connecting rod. It is the first Deformation of the entire connecting rod.

[0021] Furthermore, the geometric constraint equations for the integral link can be: (3) in, It is the elastic modulus of the connecting rod material. It is the cross-sectional radius of the integral connecting rod.

[0022] (3) Force balance equation of hydraulic connecting rod Neglecting the upper mass of the hydraulic linkage, the force balance equations will be as follows: (4) in, It is the constraint force acting on the lower S joint of the hydraulic connecting rod. It is the constraint force of the lower S-joint of the hydraulic connecting rod. The z-component is the connecting rod The hydraulic pressure. It is a low-quality hydraulic linkage. It is the position vector of the hydraulic linkage. This is the Euler angle of the hydraulic connecting rod. Ignoring the rotation of the hydraulic connecting rod along its axis, we have... . It is the inertia tensor of the hydraulic linkage.

[0023] Furthermore, the geometric constraint equations for the hydraulic linkage can be: (5) in, Indicates the position of the hydraulic linkage.

[0024] (4) Force balance equations of the platform For this platform, the equilibrium equations for forces and moments are as follows: (6) in, For the quality of the platform, This is the platform's inertia tensor. and This is the platform's stance. This is the platform's position vector. Let be the Euler angle vector of the platform. and These are the process forces and process torques acting on the platform.

[0025] (5) Overall dynamic model Finally, through a comprehensive analysis of equations (1), (2), (4) and (6), the dynamic equations of the heavy-duty equal-material forming robot can be summarized as follows: (7) This contains 6 + 7 × 6 + 9 × 3 + 6 = 81 equations. Furthermore, combining equation (3) with equation (5), the geometric constraint equations become: (8) It contains (3+3+1)×6+(3+3)×3=60 equations.

[0026] Therefore, the total number of equations is 81 + 60 = 141. Unknown force variables include points. ( () constraint force, point ( () constraint force, point ( () constraint force, point ( The constraint force and hydraulic pressure () ), the driving force of the slider ( ) and workload ( The number of force variables is 3×6+3×6+3×3+3×3+3×3+6+6=75. The unknown motion variables include the motion of the slider (…). ), the motion of the entire connecting rod ( ), the movement of the hydraulic linkage ( ), platform movement ( ), sliding position of hydraulic connecting rod Deformation of the integral connecting rod The number of motion variables is 18 + 108 + 54 + 18 + 9 + 6 = 213. The total number of unknown variables is 75 + 213 = 288.

[0027] Therefore, the total number of equations is 141 + 132 = 273, and the number of variables is 288. Figure 3 As shown. Theoretically, as long as there are 15 variables, for example... , , and The dynamic model can be used to solve this problem.

[0028] S2. Multi-sensor distributed force / position interactive measurement system: grating rulers, encoders, and pressure sensors are arranged at key locations, and data fusion is performed using a Kalman filter to effectively reduce measurement noise and errors, and improve measurement accuracy and robustness.

[0029] Theoretically, the ideal method for detecting forming force is to mount a multi-directional force gauge on the tool surface to obtain complete three-dimensional force information. However, in practical engineering, developing a multi-directional force measurement system with a maximum load of 800 tons presents significant technical barriers and cost pressures. On the other hand, in typical heavy-duty parallel structures, the load borne by the slider is only one-third of the total tool load. Therefore, adopting a distributed force measurement strategy, deploying unidirectional force sensors on each slider, not only effectively reconstructs the system load but also offers advantages such as simple structure and ease of implementation. Similarly, achieving high-precision multi-directional measurement of tool displacement under heavy load conditions is also challenging. To address this, this paper introduces a slider-based dual-position sensor distributed measurement method. In addition to six encoders mounted on the motor, six grating rulers are also arranged on the drive slider to measure the slider's motion. This not only effectively solves the problem but also improves measurement accuracy and stability.

[0030] In a dual-position measurement system, a data fusion method based on Kalman filtering of the encoder and grating ruler is adopted to improve the accuracy and robustness of slider displacement estimation. This method not only effectively suppresses measurement noise but also relies on the system dynamic model for predictive compensation when some data is missing. It is particularly suitable for control scenarios in parallel mechanisms where position and force are highly coupled, ensuring continuous and reliable system measurement results.

[0031] Define the state variable of the slider motion at time t as: ,in Let these be the slider's position, velocity, and acceleration, respectively. Then, based on Taylor expansion, a state transition relationship is established to describe the change of the slider's motion state over time: (9) In the formula, This is the state noise vector. , T is the state transition matrix, Δt is the sampling time, and its expression is: (10) Measurement equations are established for both the encoder and the grating ruler to distinguish the measurement characteristics of the two sensors: (11) In the formula, , To measure noise, , , , . and For the measurement matrix, , . This refers to the transmission ratio of the drive system.

[0032] The two sub-filters preprocess the encoder and grating ruler data respectively, obtaining preliminary state estimates and covariance matrices: (12) In the formula, , These are the state estimates of encoder data and grating ruler data, respectively. , These are the corresponding covariance matrices. , These are the Kalman gain values ​​for the encoder and the grating ruler, respectively.

[0033] The main filter combines the outputs of the two sub-filters, and the final fused result is obtained through weighted merging. (13) In the formula, The fused covariance matrix, These are the estimated values ​​of the fused slider state. The fusion weights are determined by the inverse of the sub-filter covariance matrix; the higher the accuracy (the smaller the covariance), the larger the proportion of sensor data.

[0034] S3, PID closed-loop controller integration: The PID algorithm is embedded in the control system to realize closed-loop control of motion trajectory tracking and force feedback, ensuring high precision and stability of the system under dynamic working conditions.

[0035] In real-time digital systems, based on the dynamic state (process force) and process torque The prediction of ) and given the required motion This allows us to obtain the force and motion required during the execution process, i.e. To achieve real-time control of the actuators (servo motors and hydraulic cylinders), a closed-loop proportional-integral-derivative (PID) controller is used to convert the desired force and motion into control states. The gain of the PID controller is set and dynamically adjusted to minimize control error.

[0036] For servo motor control, a three-loop PID control is used to achieve high-performance motion tracking. The first loop is the position loop, equipped with a PID controller, which is based on grating ruler data and the set position. Calculate real-time position error Then through gain Adjustments are made and the results are output to the next loop. The second loop is the speed loop, which uses a PI controller based on encoder data and the target speed. Calculate speed error Then through gain The adjustment and output of the result are sent to the next loop. The third loop is the current loop, which uses a PI controller, and it adjusts the current based on encoder data and the set force. Calculation of force error Then through gain Adjust and output the result, namely the drive current of the servo motor. In short, the control theorem for each motor can be expressed as: (14) For the control of hydraulic cylinders, PID control is used to achieve high-performance force tracking. The PID controller is based on data provided by the pressure sensor and the set force value. Calculate real-time force error Then, by adjusting the gain parameters The error is corrected, and the control result, namely the drive current of the proportional valve, is output. The control theorem can be expressed as: (15) like Figure 4 As shown, this is how data interaction from the digital system to execution is achieved.

[0037] S4. Construction of a five-dimensional digital twin model: Establish a digital twin framework that includes five dimensions: physical entities, virtual entities, digital data, connections and services, to achieve bidirectional mapping and real-time interaction between physical and virtual systems.

[0038] like Figure 5 As shown, a five-dimensional digital twin model of the dynamics of a heavy-duty equal-material forming robot was established, which consists of physical entities, virtual entities, digital data, connections and services.

[0039] The physical entity is a process machine, comprising a parallel motion mechanical structure, actuators, and corresponding force / position sensors. The mechanical structure consists of six sliders, six integral links, three hydraulic links, and corresponding connecting rods, i.e., a 6-PSS / 3-SPS configuration. The actuators consist of six servo systems and three hydraulic systems, driving the corresponding sliders and cylinders. The sensors include six linear scales, six encoders, six force sensors, and three pressure sensors, used to acquire motion and force data.

[0040] The virtual entity consists of four basic models used to build the digital model. The geometric model shows the linkages and pose relationships of the robot's components, i.e., the kinematic constraint equations and schematic diagrams shown in the figure. Based on the above dynamic model, the force, motion, and deformation relationships of the robot's components are given. The behavioral model shows the real-time motion, force, and deformation relationships. The rule model shows the relationship between the robot's computational dynamics and desired dynamics, which is the PID control method given above. In summary, all four basic models are given above, thus modeling the virtual entity.

[0041] Digital data is a real-time, dynamic collection reflected by a display system. Connectivity is the method of data integration. As discussed above, it consists of sensor configuration and placement, data transformation relationships, and data fusion methods.

[0042] Services are applications of digital systems. The basic application is motion planning for state reflection and high-performance control of heavy-duty, equal-material forming robots. Based on dynamics, the system can be extended to many other applications, such as improved accuracy, maintenance prediction, and process optimization.

[0043] S5 Digital Twin System Hardware and Software Architecture: The main processor performs virtual model calculations and control, while the auxiliary processor is responsible for real-time data acquisition and processing. The two are connected via high-speed industrial Ethernet communication to ensure low latency and high-precision control.

[0044] Based on the aforementioned five-dimensional digital twin model, a digital twin system for a heavy-duty, equal-material forming robot was developed. For example... Figure 6 The diagram shows the system's hardware and software architecture. Overall, it consists of a dual central processing system (one master and one slave processor) and multiple distributed edge execution / sensing systems. To handle highly complex tasks such as computation, decision-making, and display, a high-concurrency, highly scalable central master processing system is employed. Simultaneously, to achieve high-speed response tasks for real-time execution / sensing, a central slave processing system with high-speed data processing capabilities is used. Furthermore, edge systems are used for control and data processing to achieve both execution and sensing.

[0045] In terms of hardware, the main processing unit is implemented by an industrial computer consisting of a CPU, GPU, and other storage units. It exhibits excellent performance in parallel iterative computation, data communication, and graphics display when faced with complex and scalable tasks. Pallet processing is implemented via a PCI-based control card with a digital signal processor and corresponding processing circuitry. It demonstrates good real-time performance and multi-source data processing capabilities for complex multi-axis synchronous control and feedback. Distributed sensing is implemented using edge force / position sensors discussed in Section 3. Actuators include six servo motors and their corresponding drivers, and three servo valves and their corresponding drivers. The master and slave processing systems communicate via a PCI bus to achieve high parallelism and large data exchange, while the slave processing system communicates with the actuators via an EtherCAT bus to achieve high-speed synchronous data exchange.

[0046] On the software side, the host computer software runs on an industrial control computer with a Windows operating system. It uses an SQL database for data storage and management, the .NET framework for software development, and integrates a dynamic solver for dynamic model solving, along with OpenGL for 3D display. This enables the interface to be used for motion planning, force display, motion display, historical data display, and even dynamic error display. The digital signal processor chip control software runs on a PCI motion card and includes multiple sub-modules for force / position control, such as a multi-axis synchronization module for each axis of motion coordinates, a motion interpolation module for real-time motion interpolation, and a motion interpolation module for fast motion interpolation. There is also a dynamic solver module for real-time dynamic feedback, a sensor data acquisition module for data calibration, conversion, and caching, and an error correction module for real-time error correction. In addition to the two main central systems mentioned above, different distributed software has been developed to drive the actuators, including a PID motion control module, a force control model, a parameter identification module, and a runtime data acquisition module.

[0047] Based on the aforementioned hardware and software framework, a control system for a digital twin system of a heavy-duty, equal-material forming robot was developed. For example... Figure 7As shown, the system software consists of six basic modules: motion control module, motion planning module, state curve display module, real-time motion status display module, real-time force status display module, and real-time dynamic error display module. The motion control module controls the robot's jogging motion and reflects the motion status of each axis. The motion planning module plans the motion, generating motion codes, adjusting feed modes, and setting motion limits. The state curve display module displays the robot's dynamic state curves, including slider force, process force, and slider position. The real-time motion status display module displays the robot's spatiotemporal configuration using a 3D model, moving synchronously with the real robot to illustrate the posture and spatial relationships of each component. The real-time force status display module displays the robot's spatiotemporal force distribution, where the slider, link, and platform are represented by triangles that move with the real robot, and colors indicate the distribution of forces on each component in real time. The real-time dynamic error display module displays the robot's real-time dynamic errors, where the error distribution at each point on the tool plane is displayed in different colors, and the real-time theoretical and actual trajectories of three points show typical points. In addition to the above six basic software modules, the system can be extended to more applications.

[0048] In summary, a five-dimensional digital twin system for a heavy-duty, equal-material forming robot has been realized, providing a dynamic overall view of the robot through the interaction of physical and cyberspace.

[0049] Based on the above discussion, in order to maintain the real-time performance of digital twin simulation, digital twin systems combine simplified dynamic models, distributed force / position interactions, and corresponding hardware and software architecture actuators / sensors with dual central processors and multiple distributed edges.

[0050] Based on a digital twin system developed for heavy-duty equal-material forming robots, the machine status during the manufacturing process can be acquired in real time, allowing for the development of various applications based on this dynamic state. To evaluate the five-dimensional digital twin model and the developed digital twin system, the application of part error correction in the manufacturing of aircraft spiral bevel gears is taken as an example. As a critical transmission component, the precision of aircraft spiral bevel gears is paramount. In heavy-duty equal-material forming robots, the tooth profile is formed from the blank through a multi-degree-of-freedom plastic forming process, such as... Figure 8 As shown. Using the developed digital twin system, all dynamics during the forming process can be obtained. By detecting the actual dynamic error of the laser ranging platform, the predicted errors of all six axes are obtained, such as... Figure 9As shown, the digital twin system is represented by solid lines of different colors along the X, Y, and Z axes. The corresponding prediction accuracy of the digital twin system is presented by bars of the same color. The magnitude of the prediction error is sinusoidal and increases with the forming process. This sinusoidal prediction error may be caused by the sinusoidal shape of the desired pose. The prediction accuracy can reach up to about 80%, verifying that the accuracy of the digital twin system is acceptable.

[0051] also, Figure 10 Subgraphs (a) and (b) illustrate the real-time processing force and torque. Solid lines of different colors represent the force and torque along the X, Y, and Z axes. It can be seen that all forces and torques increase with processing time. The processing force along the X and Y axes exhibits a sinusoidal shape, changing direction and increasing amplitude, while the processing force along the Z axis generally increases. The processing force along the Z axis is close to 8MN, significantly greater than the processing forces along the X and Y axes. The process torque along the X and Y axes also exhibits a sinusoidal shape, changing direction and increasing amplitude, while the process torque along the Z axis is almost zero. The patterns of these force curves are consistent with the theoretical process forces, demonstrating the correctness of the digital system in terms of force feedback.

[0052] also, Figure 11 The force states of the heavy-duty equal-material forming robot are shown at times 9, 9.25, 9.5, and 9.75 s. Colors represent the force distribution across the robot's sliders, links, and platform. The pink arrows represent the total process force applied to the platform. It can be seen that the forces on the links are significantly greater than those on other components. The force distribution on the links is uneven, with some forces reaching maximum values ​​while others are close to zero. The link experiencing the greatest force varies at different times, exhibiting an alternating load-bearing characteristic across all links. Combined with the process force (pink arrows), it is found that the link with the greatest force is close to the point of application of the process force. These force laws can be used to evaluate the performance and optimize the design of heavy-duty equal-material forming robots.

[0053] Figure 12 The dynamic errors of a heavy-duty equal-material forming robot based on a five-dimensional digital twin system are also shown. Each subplot displays the robot's posture error in different directions. The blue solid line represents the robot's desired posture, the red solid line represents the robot's predicted posture, and the green bar graph represents the posture error between the desired and predicted postures. It can be seen that the predicted posture is completely consistent with the desired posture. Under such large processing forces and torques, the angular error is close to 1.5 mrad, and the positional error is close to 0.6 mm, both increasing with increasing forming load. The prediction error with increasing forming load is consistent with the simplification of dynamics, where the deformation of the forming robot's slider and platform is neglected to improve computational efficiency. Although the prediction error is acceptable, it demonstrates the good performance of the digital twin system.

[0054] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for modeling a real-time dynamic digital twin system of a heavy-duty equal-material forming robot, characterized in that, Includes the following steps: S1. Establish a dynamic model of a heavy-load, equal-material forming robot that only considers the elastic deformation of the connecting rod; S2. Construct a multi-sensor distributed force / position interactive measurement system, deploy grating rulers, encoders, and pressure sensors, and perform data fusion using a Kalman filter; S3. Embed the PID algorithm into the control system to achieve closed-loop control of motion trajectory tracking and force feedback; S4. Establish a digital twin framework that includes five dimensions: physical entities, virtual entities, digital data, connections, and services.

2. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 1, characterized in that, The heavy-duty material forming robot comprises six sliders, six rigid links, three hydraulic links, and a working platform. The six sliders are arranged symmetrically in a circle and are driven by servo motors, enabling linear motion along a radial track. The six rigid links are connected to the sliders at one end and fixed to the working platform at the other end, converting the linear displacement of the sliders into the spatial motion of the working platform through motion transmission. The platform is connected to the rigid links and hydraulic links through S-joints.

3. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 2, characterized in that, In step S1, the force balance equations for each component are established using the Newton-Euler method. For the slider, the force balance along the axis of the sliding guide simplifies to: （1） in, It is the magnitude of the driving force. It is the constraint force of the upper S joint. It is the unit vector of the entire linkage. It is the mass of the slider. It is time; For six integral connecting rods, the force and moment balance equations are as follows: （2） in, It is the constraint force of the lower S-joint; It refers to the mass of the entire connecting rod; It is the position vector of the entire linkage; These are the Euler angles of the integral connecting rod; neglecting the rotation of the integral connecting rod along its axis, ; It is the inertia tensor of the entire linkage; It is the first Deformation of the entire connecting rod; The geometric constraint equations for the integral link are: （3） in, It is the elastic modulus of the connecting rod material. It is the cross-sectional radius of the integral connecting rod.

4. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 3, characterized in that, The force balance equations for the hydraulic connecting rod are shown below: （4） in, It is the constraint force acting on the lower S joint of the hydraulic linkage; It is the constraint force of the lower S-joint of the hydraulic connecting rod. The z-component is the connecting rod The hydraulic pressure; It is due to the low quality of the hydraulic linkage; It is the position vector of the hydraulic linkage; These are the Euler angles of the hydraulic connecting rod; rotation of the hydraulic connecting rod along its axis is ignored. ; It is the inertia tensor of the hydraulic linkage; The geometric constraint equations for the hydraulic connecting rod are: （5） in, Indicates the position of the hydraulic linkage.

5. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 4, characterized in that, The equilibrium equations for the platform forces and moments are as follows: （6） in, For the quality of the platform, For the platform's inertia tensor; and The platform's stance; The position vector of the platform; Let be the Euler angle vector of the platform; and These are the process forces and process torques acting on the platform.

6. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 5, characterized in that, The dynamic equations of the heavy-duty equal-material forming robot are as follows: （7） The geometric constraint equations are: （8）。 7. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 2, characterized in that, In step S2, a dual-position sensor distributed measurement method based on sliders is adopted, with an encoder installed on each servo motor and a grating ruler arranged on each slider.

8. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 7, characterized in that, The dual-position sensor distributed measurement method employs a data fusion approach based on Kalman filtering of an encoder and a linear encoder, and includes the following steps: Define the state variable of the slider motion at time t as: ,in The slider's position, velocity, and acceleration are defined, respectively. Then, a state transition relationship is established based on Taylor expansion to describe the change of the slider's motion state over time. （9） In the formula, This is the state noise vector. , T is the state transition matrix, Δt is the sampling time, and its expression is: （10） Measurement equations are established for both the encoder and the grating ruler to distinguish the measurement characteristics of the two sensors: （11） In the formula, , To measure noise, , , , . and For the measurement matrix, , . The transmission ratio of the drive system; The two sub-filters preprocess the encoder and grating ruler data respectively, obtaining preliminary state estimates and covariance matrices: （12） In the formula, , These are the state estimates of encoder data and grating ruler data, respectively. , These are the corresponding covariance matrices. , These are the Kalman gain values ​​for the encoder and the grating ruler, respectively. The main filter combines the outputs of the two sub-filters, and the final fused result is obtained through weighted merging. （13） In the formula, The fused covariance matrix, These are the estimated values ​​of the fused slider state. The fusion weights are determined by the inverse of the sub-filter covariance matrix, with higher-precision sensor data accounting for a larger proportion.

9. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 8, characterized in that, In step S3, the servo motor is controlled using a three-loop PID control to achieve high-performance motion tracking; the first loop is the position loop, equipped with a PID controller, which is based on the grating ruler data and the set position. Calculate real-time position error Then through gain Adjustments are made and the results are output to the next loop; the second loop is the speed loop, which uses a PI controller based on encoder data and the target speed. Calculate speed error Then through gain The adjustment and output of the result are sent to the next loop; the third loop is the current loop, which uses a PI controller, and it adjusts the current based on encoder data and set force. Calculation of force error Then through gain Adjust and output the result, namely the drive current of the servo motor. In short, the control theorem for each motor is expressed as: （14）。 10. The modeling method for a real-time dynamic digital twin system of a heavy-duty equal-material forming robot according to claim 9, characterized in that, In step S3, for the control of the hydraulic cylinder, the PID controller is based on the data provided by the pressure sensor and the set force value. Calculate real-time force error Then, by adjusting the gain parameters The error is corrected, and the control result, namely the drive current of the proportional valve, is output. The control theorem is expressed as: （15）。

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