Rigid-flexible Coupling Dynamic Model Research Articles

Investigation on the fusion reliability and cluster consistency of multivariable entropy method

Recent researches have shown that the multivariable entropy based feature extraction method can obtain better diagnosis results for fault diagnosis of planetary gearbox. However, the nature properties of multivariable entropy have still not been deeply explored: the reliability of multi-source information fusion and cluster consistency for the same fault signal. These two properties will affect the accuracy of fault diagnosis based on multivariate entropy. This paper aims to reveal the nature properties of multivariate entropy. Firstly, a rigid-flexible coupling dynamic model of a planetary gearbox is conducted to establish a pure test environment. Then the generated vibration signals are used to evaluate the fusion reliability and cluster consistency of multivariable entropy. Additionally, a new multivariable entropy feature extraction method called variational embedding refined composite multiscale diversity entropy (veRCMDE) is proposed. Finally, the simulation and experiment results show that high fusion reliability and high cluster consistency enable multivariate entropy to extract more valuable features, and the proposed veRCMDE performs the best in all experiments.

Theoretical research on dynamic modeling of rigid–flexible coupling system with double joint folded wing

For meeting the requirements of tactical missiles seeking miniaturized launch devices for storage, transportation, and launch, a tube-launched missile wing is adopted, which folds before launch and quickly unfolds after launch. As a structure installed on the missile body to generate the required aerodynamic force for manipulating the missile, the tube-launched missile wing can effectively stabilize the missile’s flight attitude. At present, most research on the unfolding mechanism of missile folding wings is focused on one-time folding. When the wingspan is large, multiple folding is required to meet the launch requirements of modern tube-launched missiles. Therefore, this article designs a dual-joint folding wing deployment mechanism and studies the rigid–flexible coupling dynamic modeling and related technologies of folding wings based on this structure. Based on the inertial coupling between large-scale rigid body motion and structural flexible deformation, the folding wing breaks through the element convergence of the model and achieves the applicability of the structural model through zero-order approximation model analysis and other technologies. Simulation results show that the hybrid coordinate method can fully and accurately display the vibration information of flexible folding wings. At different speeds, the first-order coupling model is more advanced than the zero-order coupling model. In addition, increasing rotational speed, increasing wing thickness, and reducing wing span length can effectively increase the fundamental frequency of wing flutter. The structural design of folding wings has shown important reference significance.

Dynamics modelling and Layout optimization of CFRP in-situ machining system

The multi-support reconfigurable compliant tooling and robotic in-situ processing method provide a new technical direction for CFRP milling edge processing. Aiming at the layout optimization of CFRP in-situ machining system (CFRPIMS), the dynamics characteristics of the whole system were studied. A rigid-flexible coupling dynamics model of the CFRPIMS was proposed by applying transfer matrix method for multibody systems (MSTMM), treating CFRP as a thin-walled flexible plate and supporting fixtures as rigid bodies. And then the natural frequency and dynamics responses under the different support layout are simulated, which are verified by modal tests and excitation tests. To improve the support rigidity of CFRP workpieces, the optimization model of overall layout of the compliant tooling was established combined with genetic algorithm. Based on the milling test results, compared with the original scheme, the optimization method can effectively reduce the vibration response of the workpiece in the y-direction (along the milling edge direction) and the z-direction (perpendicular to milling edge direction) by more than 60%.

Dynamic Modeling and Optimization Analysis of Rigid–Flexible Coupling Manipulator Based on Assumed Mode Method

Lightweight robotic arms are one of the main technologies to improve the working performance of robotic arms in the future. Focusing on the spatial vibrations issue brought about by the light-weighting of a space robotic arm in this paper, a rigid–flexible coupling dynamics model of a space robotic arm system was established based on the assumed mode method and Lagrange method. Based on the lightweight flexible robotic arm structure, a comparative analysis of the first four mode functions was conducted under different fixed constraints and physical properties to determine the mode order that matches the simulation analysis of this robotic arm, thus, further simplifying the rigid–flexible coupling dynamics equations of the system. The overall rigid model and simplified dynamic model of the robotic arm system were solved by using MATLAB, resulting in a motion trajectory of the flexible arm end in space. The three-dimensional model was validated and simulated using virtual prototype technology under the same joint inputs as the model in MATLAB. The simulation results demonstrated that the trajectory of the end of the flexible arm was basically the same between simplified dynamics model simulation and virtual prototype simulation, and the maximum deviation of the end trajectories of the flexible connecting rods [Formula: see text] and [Formula: see text] was less than 18[Formula: see text]mm and 58[Formula: see text]mm, respectively. Meanwhile, the trajectory trend of the end of the flexible arm in the two aforementioned models was the same as the simulation results of the ideal model (overall rigid model). The above conclusions can verify the correctness of the mathematical model of dynamics obtained from the calculations in this paper. In addition, the research data showed that the maximum vibration deviation of the flexible arm was stabilized within a certain value range under different joint inputs, and this research also provided theoretical support for the late vibration suppression control of the spatial rigid–flexible coupled robotic arm.

Numerical simulation of aircraft arresting process with an efficient full-scale rigid-flexible coupling dynamic model

The arresting process of carrier-based aircraft is widely recognized as a challenging task, characterized by the highest accident rate among all carrier-based aircraft operations. Dynamic simulation plays a crucial role in assessing the intricate responses of the arresting process, favoring the design of carrier-based aircraft. An efficient and accurate rigid-flexible coupling model for analyzing the dynamic response of the arresting process is proposed. By combining the dynamic characteristics of airframe, landing gear, arresting hook and arresting gear system, the rigid-flexible coupling dynamic model is established to reflect the relative motion of the coupling parts and arresting load. The dynamic model is verified through simulations of landing gear landing drops and by comparing the arresting simulation results with corresponding data in the US military standard. Additionally, simulations of the arresting process under different off-center distance and aircraft yaw angle are conducted to obtain the dynamic response of the aircraft during the arresting process. The result indicates that the rigid-flexible coupling dynamic model proposed is effective for analyzing the arresting dynamics response of carrier-based aircraft. The axial force of the arresting cable on both sides of the hook engagement point, pitch and yaw angle of aircraft are inconsistent under yaw and off-center arresting. The analysis method and obtained results provide valuable references for assessing the dynamic responses of carrier-based aircraft during arresting process and offer valuable in-sights in the design of carrier-based aircraft.

A Rigid-Flexible Coupling Dynamic Model for Robotic Manta with Flexible Pectoral Fins

The manta ray, exemplifying an agile swimming mode identified as the median and paired fin (MPF) mode, inspired the development of underwater robots. Robotic manta typically comprises a central rigid body and flexible pectoral fins. Flexible fins provide excellent maneuverability. However, due to the complexity of material mechanics and hydrodynamics, its dynamics are rarely studied, which is crucial for the advanced control of robotic manta (such as trajectory tracking, obstacle avoidance, etc.). In this paper, we develop a multibody dynamic model for our novel manta robot by introducing a pseudo-rigid body (PRB) model to consider passive deformation in the spanwise direction of the pectoral fins while avoiding intricate modeling. In addressing the rigid-flexible coupling dynamics between flexible fins and the actuation mechanism, we employ a sequential coupling technique commonly used in fluid-structure interaction (FSI) problems. Numerical examples are provided to validate the MPF mode and demonstrate the effectiveness of the dynamic model. We show that our model performs well in the rigid-flexible coupling analysis of the manta robot. In addition to the straight-swimming scenario, we elucidate the viability of tailoring turning gaits through systematic variations in input parameters. Moreover, compared with finite element and CFD methods, the PRB method has high computational efficiency in rigid-flexible coupling problems. Its potential for real-time computation opens up possibilities for future model-based control.

A novel cable-net buffer device for recovering reusable launch vehicle: Design, dynamic modeling, and performance analysis

At present, reusable launch vehicle technology (RLV) has become a research hotspot in the aerospace field and one of the major development trends in this industry. With reference to the aircraft carrier’s arresting cable technology, this paper puts forward a novel cable-net buffer device for recovering the first stage of launch vehicle. The device can transfer load through a cable-pulley mechanism, and then complete the first stage recovery by losing the kinetic energy and gravitational potential energy of the first stage through hydraulic dampers and preloaded counterweights. In order to analyze the performance of this cable-net buffer device, the finite element software ABAQUS is adopted to establish a rigid-flexible coupling dynamic model. In this model, the cable-pulley mechanism is simulated by connector and shell elements, the damping force of the hydraulic dampers by VUAMP subroutine, and the preloaded counterweights by mass point. And then, performance evaluation indexes of this buffer device are proposed in this paper. Meanwhile, the dynamic simulation, using the established dynamic model, is carried out under different device design parameters and working condition parameters. On the one hand, the simulation results show that the tower span and damping force have remarkable effects on the buffer performance. On the other hand, among all working condition parameters, only the fall point deviation has a significant effect on the buffer performance, but this effect is less than that of the design parameters. Finally, combing the dynamic model and the surrogate model technique, this paper obtains feasible boundaries of design parameters of the device for the subsequent detailed design of it. Researches in this paper will provide new ideas for the development of RLV.

Hybrid control of attitude maneuver and structural vibration for a large phased array antenna satellite

This paper focuses on the study about hybrid control strategy of attitude maneuver and structural vibration for a large phased array antenna satellite. The satellite system is equipped with cable actuators in the antenna structure and control moment gyros on the central satellite. Firstly, the rigid-flexible coupling dynamic model of the entire satellite system is established based on the hybrid coordinate method. Then a control strategy is presented which could realize the ideal attitude maneuver of satellite while suppressing the structural vibration simultaneously. The proposed strategy is contained of two parts: the attitude controller is designed based on the computed torque method, and the vibration controller is achieved by using a piecewise cost function which could ensure the unidirectional and saturated constraints of cable actuators. Finally, numerical simulations of a large antenna satellite model demonstrate that the structural vibration during the attitude maneuver process can be suppressed effectively by applying the proposed control strategy.

Research of rigid-flexible coupling dynamics model for riser-LMRP/BOPs-wellhead system

The deepwater drilling riser system is the most vulnerable part of the offshore drilling operation. Understanding its dynamic response under complex marine environment is crucial for ensuring drilling safety. However, the coupling mechanism between the riser and LMRP/BOPs is not well understood in existing analysis models of riser system dynamic response. In this paper, a theoretical model for the rigid-flexible coupling dynamics of multi-scale riser-LMRP/BOPs-wellhead system is proposed to reveal the coupling mechanism between the riser and LMRP/BOPs. Considering the characteristics of flexible riser and rigid LMRP/BOPs as well as the nonlinear coupling effect between conductors and soil, a rigid-flexible coupling dynamics model of the riser-LMRP/BOPs-wellhead system is established based on the theory of rigid-flexible coupling dynamics and Lagrange equation, which is numerically solved by the Newmark method. To verify the correctness of the proposed model, a simulation model of the riser-LMRP/BOPs-wellhead system is applied, which is modelled by the combination of pipe and mass elements. The research results demonstrate that the numerical results of the proposed theoretical model agree with the simulation results of the coupling system, thus verifying the correctness of the proposed model and revealing the rigid-flexible coupling mechanism between the riser and LMRP/BOPs.

Analysis of Catapult-Assisted Takeoff of Carrier-Based Aircraft Based on Finite Element Method and Multibody Dynamics Coupling Method

Catapult-assisted takeoff is the initiation of flight missions for carrier-based aircrafts. Ensuring the safety of aircrafts during catapult-assisted takeoff requires a thorough analysis of their motion characteristics. In this paper, a rigid–flexible coupling model using the Finite Element Method and Multibody Dynamics (FEM-MBD) approach is developed to simulate the aircraft catapult process. This model encompasses the aircraft frame, landing gear, carrier deck, and catapult launch system. Firstly, reasonable assumptions were made for the dynamic modeling of catapult-assisted takeoff. An enhanced plasticity algorithm that includes transverse shear effects was employed to simulate the tensioning and release processes of the holdback system. Additionally, the forces applied by the launch bar and holdback bar, nonlinear aerodynamics loads, shock absorbers, and tires were introduced. Finally, a comparative analysis was conducted to assess the influence of different launch bar angles and holdback bar fracture stain on the aircraft’s attitude and landing gear dynamics during the catapult process. The proposed rigid–flexible coupling dynamics model enables an effective analysis of the dynamic behavior throughout the entire catapult process, including both the holdback bar tensioning and release, takeoff taxing, and extension of the nose landing gear phases. The results show that higher launch bar angle increase the load and extension of the nose landing gear and cause pronounced fluctuations in the aircraft’s pitch attitude. Additionally, the holdback bar fracture strain has a significant impact on the pitch angle during the first second of the aircraft catapult process, with greater holdback bar fracture strain resulting in larger pitch angle variations.

NVH Analysis and Optimization of Construction Hoist Drive System

The construction hoist drive system is a critical component of the construction hoist, and high speed and low vibration noise are essential development directions. In order to improve the NVH level of the construction hoist drive system, this paper carries out research and analysis of construction hoist drive system excitation, establishes the drive system rigid-flexible coupling dynamics model, and completes the establishment of the vibration and noise model of the drive system, simulation analysis, and optimization work. Ansys Motor CAD 2020 was used to establish the parametric model of the asynchronous motor and it was combined with the virtual work method to calculate Maxwell’s electromagnetic force to arrive at the radial electromagnetic force as the main cause of electromagnetic noise. For the mechanical excitation generated by the gearbox, the time-varying stiffness excitation, mesh shock excitation, and transmission error excitation are considered, and the transmission error of helical gears under different working conditions is calculated by combining it with Romax software 2020. The rigid-flexible coupling model of the construction hoist drive system is established. The load distribution analysis of the unit length of the tooth surface is completed for the first- and third-stage helical gears under different working conditions. The primary source of the drive system excitation is the tooth surface bias load. Based on the dynamic response analysis theory of the vibration superposition method, the maximum vibration speed of the drive system was analyzed by Romax. The maximum noise value of 78.8 dB was calculated from the acoustic power simulation of the drive system using Actran acoustic software 2022 in combination with acoustic theory, and the magnetic density amplitude of the stator teeth of the asynchronous motor was optimized based on the microscopic shaping design of the helical gear by Romax. The vibration and noise simulation of the optimized drive system shows that the vibration value is reduced to 0.75 mm/s, and the maximum noise is reduced to 70.2 dB, which is 10.9% lower than before the optimization. The overall NVH level has been improved. The optimization method to reduce the vibration noise of the drive system is explored, which can be used for vibration noise prediction and control during the development of the construction hoist drive system.

Influence of wheelset structural flexibility on dynamic properties of a wide-gauge six-axle heavy-haul locomotive

Wheelset structural flexibility, that is the elastic deformation of the wheelset as a structure, has an important influence on the dynamic properties of railway locomotive vehicles at medium and high frequencies. Based on the practical structural parameters, this paper proposes a multi-degree of freedom rigid-flexible coupling dynamic model of a wide-gauge freight electric locomotive with C0-C0 bogies with an axle suspension driving system. The wheelset with the interference-fit large gear is made flexible using the finite element method, and then the rigid-flexible coupling vehicle model with elastic wheelsets is established in the software SIMPACK 2020. A short-wave irregularity superposed on the American fifth-grade track irregularity is used as the track excitation to study the performance at higher frequencies. From the modal analysis of the vehicle, it is obtained that the lowest frequency at which the elastic deformation of the wheelset occurs is 24.631 Hz. The lateral vibration responses of the vehicle with elastic wheelsets are reduced mainly in the frequency range of 30-150 Hz. There are two resonances in the lateral vibration responses at the mode frequencies of the vehicle over 50 Hz, which are close to the wheelset’s first mode frequency. Taking the ГОСТ standard of wide-gauge countries as the main reference, simulations are separately taken in straight-line and curved-line cases. Results show that the wheelset structural flexibility mainly influences the vehicle lateral stability and safety.

Dynamic Simulation Analysis of Truck Crane Based on ADAMS

Background: With a reduction in the weight of telescopic boom crane and an increase in its lifting capacity, the contradiction between its speed, stability and safety becomes more prominent. The telescopic arm also has flexible deformation during operation, which will cause vibration of the whole vehicle system. Therefore, in order to ensure safety, accuracy, and efficiency in the working process, it is necessary to accurately predict the dynamic characteristics of the telescopic boom load in the working process. Objective: The purpose of this study is to establish a rigid-flexible coupling dynamic model of the crane, which can accurately reflect the dynamic characteristics of the telescopic boom during its operation in the simulation test. Methods: In theory, this study analyzes the characteristics of a truck crane and simplifies it as a cantilever beam. Based on the Euler-Bernoulli beam theory, the vibration differential equation of the mobile masscantilever beam system is established. In the aspect of simulation, the three-dimensional modeling software Solidworks is used to establish the solid model of the truck telescopic boom, the finite element analysis software is used to establish the finite element model of the telescopic boom, and the modal neutral file is generated and imported into ADAMS to establish the dynamic model of the truck crane multi-level flexible telescopic boom. The dynamic simulation of the virtual prototype model of the truck telescopic boom crane is carried out in ADAMS software to obtain the dynamic characteristics of the key components of crane under specific working conditions. Results: The vibration differential equation derived in theory can be used to solve the dynamic response of the crane jib under specific conditions by MATLAB programming. In the aspect of simulation, the error fluctuation and its causes in the key components of the crane in the working state are analyzed, and the rationality of the virtual prototype model is verified. Finally, through the trajectory planning of the crane under typical working conditions, the purpose of stable control of the telescopic boom system of the truck crane is realized. Conclusion: The derived equation is universal for solving the vibration of crane jib in general cases. The rigid-flexible coupling model also provides a reference for the dynamic modeling, analysis, design, and manufacture of a multi-stage flexible telescopic boom. The findings of this study can provide a reference for related patent research and development.

Dynamical modeling and characteristics analysis of tooth spalling in gear system with weight reduction structure

Focusing on gear transmission systems having thin web and hole structures for energy saving and weight reduction, this work aims to propose an effective method for dynamical modeling and characteristics identification of spalling in lightweight gear systems. A novel three-dimensional (3D) spalling morphology modeling method is developed by the optical scanner. Subsequently, an analytical-finite element (AFE) model is established to calculate the mesh stiffness with weight reduction structures and spalled teeth. Additionally, the discrete tooth surfaces from coordinate measuring machines (CMMs) are used to calculate the no-load static transmission error (NLSTE). A rigid-flexible coupling dynamic model is introduced into the gear-rotor-bearing system considering the lightweight rotor and friction characteristics. The effects of spalling fault levels, the number and distribution form of spalled teeth on dynamic characteristics of the lightweight gear system are investigated. The numerical and experimental results demonstrate the existence of coupling modulation between spalling and holes, but it can still be identified by time and frequency domain characteristics. The proposed model and analysis results provide important references for identifying spalling in lightweight gear systems.

Dynamic modeling and control of a solar sail considering large-amplitude nonlinear vibration

The solar sail spacecraft utilizes Solar Radiation Pressure (SRP) to achieve propulsion, which can realize long-term acceleration without fuel consumption, making it an appealing option for deep space exploration and polar-sitter observation. However, because of the large-scale and high-flexibility of the membrane structure, the solar sail poses challenging dynamic and control issues. Precise dynamic modeling and effective control design can provide theoretical guidance for the efficient functioning of solar sail, which are of great significance and urgently need to be studied. In this paper, a dynamic model that can describe the large-amplitude vibrations of the solar sail is established. Additionally, an attitude tracking controller and a cable-based nonlinear vibration controller are designed to control the attitude motion and flexible vibration of the solar sail. The results show that the established nonlinear rigid-flexible coupling dynamic model is more accurate compared to the linear dynamic model. The polynomial fitting method can characterize the nonlinear dynamics of the solar sail extremely effectively while cutting the program runtime to 5% of the original. Two controllers designed in this paper can make the solar sail maneuver follow the desired trajectory accurately while reducing the sail surface vibration by more than 40%. The research outcomes of this paper can provide references for the dynamic study and active control of large-scale membrane spacecraft.

Vibration response mechanism of fixed-shaft gear train with cracks based on rigid-flexible coupling dynamics and signal convolution model

Affected by external flexible transfer path of fixed-shaft gear train, internal gear meshing vibration signals that representing the healthy state of gear will convolve with modal information of gearbox housing and become much more complicated. Moreover, gear crack fault features of fixed-shaft gear train are relatively weak and complex, which are difficult to diagnose. Therefore, to reveal the origination mechanism of crack fault, a rigid-flexible coupling dynamics model of fixed-shaft gear train with full consideration of flexible housing is firstly established, then a signal convolution model is proposed to solve housing vibration response signal by combining internal excitation and external transfer path. Thereinto, as internal influence factor, time-varying meshing stiffness that drives excitation forces is used to reflect excitation characteristics under normal and crack state; as external influence factor, flexible transfer path that includes modal characteristics of gearbox housing is calculated by finite-element-method. Through the established models, modulation sideband features of housing vibration response signals are selected as crack fault indicator. Corresponding vibration response mechanism is revealed clearly under normal and different crack degrees in simulations. Experimental results keep good consistency at crack fault features with simulation signals and verify the effectiveness of the proposed models.

Parameter sensitivity analysis under failure condition of lifting device mechanism

The sensitivity of each influencing parameter in the selected range of the complex multi-hinge space flap mechanism under typical fault conditions is studied, and the influence degree of each parameter and its dispersion on the driving torque of the mechanism is determined. Firstly, the rigid-flexible coupling dynamic model of the mechanism is established considering the flap deformation, and then the influence of four parameters that may cause mechanism failures, such as hinge friction, aerodynamic load, driving speed and assembly error, on the driving torque of the mechanism is explored. Then, the drive torque of the mechanism under each parameter value is given, finally, the sensitivity of each selected parameter is obtained by the direct de rivation method. The results show that the parameters are positively correlated with the driving torque, the aerodynamic load coefficient and hinge friction parameters are the most sensitive to the driving performance of the mechanism, while the driving speed is the smallest. After the aerodynamic load increased by 30%, the maximum driving torque of the inner mechanism increased by 28.8%; when the hinge friction parameter was in the range of 0~0.05, the maximum torque of the inner and outer mechanisms increased by 8.6% and 8.4% respectively. In engineering applications, the lubrication of each spherical hinge should be increased, the driving speed should be reduced, and the manufacturing and assembly accuracy should be improved.To a certain extent, it can prevent failures and improve the reliability of the flap mechanism.

Research on causes and countermeasures of wheel polygon wear based on Kik-Piotrowiski contact model

In order to study the wheel polygon wear problems in high-speed trains, an iterative model of wheel wear was established based on 1 ) the train-track rigid-flexible coupling dynamics model, 2 ) Kik-Piotrowiski + Fastsim wheel-rail contact model, and 3 ) Archard wear model to predict the developing process of wheel polygon. Taking a certain type of high-speed train in China as an example, the developing process of the 20-order wheel polygon is simulated. Compared with the Hertz model, the results of the Kik-Piotrowiski model are more consistent with the actual situation, and the prediction of the wheel polygon is more accurate. The results show that with the increase of vehicle running speed, the dominant order of the final wheel polygon decreases gradually, while the excitation frequency always locates between 550 and 600 Hz, which verifies the ‘frequency fixed’ mechanism. By comparing the development of wheel polygon wear results under three working conditions 1 ) flexible wheelset + flexible rail, 2 ) rigid wheelset + flexible rail, and 3 ) flexible wheelset + rigid rail), and by analysing the harmonic response of rail, it is concluded that the third-order bending modal vibration of rail plays an important role in the forming of wheel polygon. .

Research on Body Tube Vibration Response of Small Combat Robots Motion

As a hot topic in military research, small combat robots are always in a dynamic process when traveling, causing the body tube to vibrate which affects its firing accuracy. Different from the traditional two-degree-of-freedom combat robot, this paper establishes a rigid-flexible coupling dynamics model for the new three-degree-of-freedom combat robot to study the response characteristics of its body tube during travel. To accurately reflect the driving conditions of the mobile robot, a road surface unevenness model was established using the sine wave superposition method. The firing accuracy of a small combat robot can be affected by the speed and road conditions, as shown in numerous studies. The effects of arm structure, arm mounting position, and firing angle on the vibration response of the body tube are analyzed in this paper. The results show that a reference for improving the design of small combat robots can be found in a correlation between the structure, mounting position, and firing angle of the robotic arm, and the body tube’s vibration response.

Dynamic modeling and analysis of planetary gear train system considering structural flexibility and dynamic multi-teeth mesh process

The structural flexibility of planetary gear trains (PGTs) is a significant factor that affects tooth loads and system vibrations, especially in heavy-duty wind turbine gearboxes. Therefore, it is crucial to investigate the influence mechanisms of complex structural deformations on tooth loads and system vibrations. In this work, a dynamic modeling approach is proposed for the complex carrier and ring gear based on the condensation theory of finite elements. The dynamic model of the sun shaft is modeled using the Euler-Bernoulli beam element, and the planetary gear set is modeled using the lumped parameter method. Then, the dynamic multi-teeth mesh process is developed using variable-speed characterization variables and virtual vibration line displacements. Lastly, the rigid-flexible coupling dynamic model of PGT is established and validated. The results indicate that treating components as rigid solids may lead to an underestimation of the impact of input torque variation on system vibrations. When the input torque remains stable, the tooth stiffness can be used to assess the overall change trend of tooth loads. However, when the input torque varies significantly, it is necessary to take into account the comprehensive structural deformations.