Rigid-flexible Coupling Research Articles

Rigid–flexible coupling dynamics of a threaded reusable low-shock spacecraft separation device

Rigid–flexible coupling dynamics of a threaded reusable low-shock spacecraft separation device

Initialization Algorithms of a Rigid–Flexible Coupling Fluid–Structure Interaction System by Considering Length-and-Area Constraints

Rigid–flexible coupling fluid–structure interaction systems are expected to be future solutions for reducing energy lost in water. The dynamics of these systems is usually investigated via numerical simulations. However, in existing numerical works there is no accurate algorithm for the initialization of the flexible filament, which ensures both the length and area constraints, leading to inaccurate results or even severe numerical instabilities. We propose two alternative initialization algorithms, respectively, the “Trapezoidal arrangement” and the “Quartic curve arrangement”. The performances of both of these two algorithms are investigated in numerical simulations by using the immersed boundary method. The motion responses and force characteristics of the flexible filament are analyzed carefully, verifying the capability of the proposed algorithms. Specifically, “Quartic curve arrangement” is further recommended due to its good property of convergence.

Research on coal rock parameter calibration based on discrete element method

To ensure that the discrete element model of the coal wall accurately reflects the actual cutting process of coal and rock during virtual prototype simulation of mining equipment, this study aims to expedite the development of intelligent mining machinery. Using coal samples from the 4602 working face of Yangcun Coal Mine, operated by Yanzhou Coal Mining Group, we conducted coal rock packing experiments and uniaxial compression tests to obtain the packing angle and compressive strength of the coal samples. Based on the experimental results, we designed Plackett–Burman experiments (PB experiments), steepest ascent experiments, and Box-Behnken experiments to study the influence of particle contact mechanics parameters and bonding mechanics parameters on the packing angle and compressive strength, using the packing angle and compressive strength as response variables. Our objective is to minimize the relative error between the simulated packing angle and the measured packing angle. We solved and optimized the parameter calibration model and conducted simulation calibration experiments based on the optimization results. A comparative analysis with the actual test results revealed that the maximum relative errors between the simulated and measured values for the packing angle and compressive strength were only 2.9% and 5.0%, respectively. Additionally, a discrete element model of a typical working face coal wall was established based on the parameters obtained from this calibration method. A bidirectional coupling model of the cutting process between the coal and rock was created using EDEM-RecurDyn to simulate the rigid-flexible coupling of the coal cutter. An experimental coal wall model was constructed based on similarity theory, and both simulation and physical experiments were conducted. The evaluation metrics for comparison were the time-domain and frequency-domain characteristics of the drum’s vibration signals. The maximum relative error for the time-domain signal characteristics between the two experimental setups was only 4.19%, while the maximum relative error for the frequency-domain signal characteristics was 3.75%. This validates the feasibility of the proposed calibration method for the discrete element coal wall model and the accuracy of the calibration results. Furthermore, it demonstrates that the constructed discrete element coal wall accurately represents the actual coal and rock properties. The virtual simulation based on this model effectively replicates the interaction process between mining machinery and coal, providing a safe, efficient, and low-cost technological approach for performance analysis of mining equipment and intelligent control of supporting devices.

ANCF-based modelling of rigid-flexible coupling of helicopter flexible rotor blades

Abstract A high-precision rotor structure dynamic model applicable to a variety of helicopter blade hub structures is established considering rotor blade flexible deformation. The absolute nodal coordinate method is applied to the traditional rotor blade rigid-flexible coupling dynamics model, making the new model applicable to both fully articulated rotor blades and other advanced blade hub structures. No small-volume assumptions were made in the modelling process. Both Green’s strain expression under finite deformation and the geometrical relation of elastic deformation motion based on the absolute nodal coordinate method are used to derive the blade strain energy, kinetic energy, and the external load virtual work. The rotation angle at the articulation constraint at the root of the blade coupled with the elastic deformation degrees of freedom of the blade in three independent rigid body degrees of freedom, respectively. The rotor blade rigid-flexible coupling dynamics equations were established according to the Hamilton action principle. The time-domain simulation is carried out under a free single pendulum and fixed rotational speed/fixed torque for the established flexible blade model, which verifies the validity and high accuracy of the rigid-flexible coupling articulation model of the flexible rotor blade and the blade hub.

Establishing interphase with “rigid-flexible coupling” crosslinking network by supramolecular structure to improve interfacial properties of high modulus carbon fiber reinforced polymer composites

Establishing interphase with “rigid-flexible coupling” crosslinking network by supramolecular structure to improve interfacial properties of high modulus carbon fiber reinforced polymer composites

Research on rigid-flexible coupling nonlinear dynamics of light commercial vehicle considering frame flexibility

Commercial vehicles play a vital role in the transportation industry. Generally, there will present a complex nonlinear dynamic behavior composed of periodic, quasi-periodic, and even chaotic vibration in vehicle vertical system under the continuous speed bump excitation. To explore the nonlinear dynamic behavior of vehicle system, a new rigid-flexible coupling nonlinear dynamic model for light commercial vehicle has been developed theoretically with considering the frame flexibility, suspension stiffness and damping nonlinearity, and rubber bushing nonlinearity. The dynamic model for frame and suspension have been developed with discrete element method and lumped mass method, respectively. Then, the flexible frame model has been verified through the mode shape and frequency calculated by finite element simulation. And the rigid-flexible coupling nonlinear dynamic model of a light commercial vehicle has been verified with Adams simulation and testing results. Furthermore, the influence of vehicle speed and the height of speed bump, suspension stiffness and damping, as well as cargo weight and distribution on vehicle system dynamics is analyzed with bifurcation diagram, time history, frequency, phase diagram and Poincare section. The results show the significant and complex effects on the nonlinear vibration of vehicle system, especially the nonlinear damping and the flexible frame.

Nonlinear dynamics of continuous steady-state tunable mechanical metamaterials based on planetary gears

Mechanical metamaterials with tunable mechanical properties have received extensive attention. In this work, a continuous steady-state metamaterial with tunable mechanical based on planetary gear cells is designed. Firstly, the excellent tunable properties of metamaterials are studied, which shows the designed metamaterials has a wide range of programmable stiffness and a significantly tunning band gap. The configuration relationship between tunability and structural parameters is analyzed. Then, a rigid-flexible coupling nonlinear dynamic model of planetary gear metamaterials is established and the dynamic characteristics of planetary gear metamaterials in the process of dynamic tunning are explored by numerical simulation. Moreover, the distribution characteristics of the system vibration response with the coupling parameter plane are disclosed, and the influence of the system dynamic parameters on its bifurcation characteristics and stability under coupling excitation is explored. Furthermore, an improved non-iterative cell mapping method is used to analyze the dependence of the vibration response of the system on the initial conditions. This work shows that the planetary gear metamaterials have a wide range of stiffness tunability and significantly variable band gap interval. Under the influences of internal and external excitations, the system exhibits various dynamic characteristics. The dynamic characteristics of flexible construction are mainly affected by structural parameters, and the dynamic characteristics of rigid construction are affected by multiple sets of coupling parameters and initial conditions.

Dynamic wheel-rail interaction of a train crossing a turnout under traction/braking behaviour and research on rail wear of the turnout

In order to study the dynamic behaviour of a vehicle passing through turnouts under traction and braking conditions, as well as its influence on the wear of turnout rails, a high-speed vehicle-turnout rigid-flexible coupling dynamic model is established based on the coupling dynamic theory of vehicle and turnout, using China’s No. 18 high-speed turnout and CRH380 high-speed EMU as prototypes. The model is used to analyse wheel-rail creep characteristics, wheel-rail contact mechanics, and wheel-rail wear under traction and braking conditions. The results indicate that when a high-speed train passes through a turnout under traction or braking conditions, the longitudinal creepage of the wheel-rail will change due to the rotative speed difference generated by traction or braking. Furthermore, due to the existence of the lead curve, the longitudinal creep rate of the wheel-rail becomes even more complex when passing through the turnout in the diverging route. The calculations reveal that the traction behaviour of the train leads to a significant increase in wear at the front of the switch rail and nose rail, while the wear number of the switch rail in the heel of the frog after 6m increases significantly under braking conditions. The different impact characteristics of vehicle traction and braking conditions on turnout rail wear obtained in this study can provide guidance for optimizing and grinding the profiles of turnout rails at the throat of railway stations.

Analysis of Force Distribution and Motion Characteristic of Hybrid-Driven Tensegrity Parallel Mechanism

Abstract Tensegrity parallel mechanisms is a novel spatial structure composed of cable-based and rigid-based chains, which is characterized by lightweight, multi-stability, high precision, good stiffness, and high load-bearing capacity. This paper focuses on the six-degree-of-freedom tensegrity parallel mechanism, analyzing its static equilibrium and presenting the force equilibrium equations. A model for cable tension distribution optimization is established, utilizing different P-norm objective functions to optimize the distribution of tension in cables and rigid links, discussing the reasons for unreasonable tensions in the system. Under given constraints on the motion pairs of the mechanism, the workspace of the mechanism is plotted, and factors influencing the size of the workspace are analyzed. Finally, the singularity of the mechanism is addressed based on the Jacobian matrix, demonstrating the feasibility of reaching the space volume by the mechanism. It has certain reference significance for the configuration theory and analysis methods of tensegrity parallel mechanisms and rigid-flexible coupling mechanisms, and provides a reference for the further promotion and application of mechanisms.

Design and kinematics of a novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair

PurposeThis paper aims to present the mechanical design and kinematics of a novel rigid-flexible coupling hybrid robot to develop a promising aeroengine blades in situ repair technology.Design/methodology/approachAccording to requirements analysis, a novel rigid-flexible coupling hybrid robot is proposed by combining a three degrees of freedom (DOF) parallel mechanism with a flexible continuum section. Then the kinematics models of both parallel mechanism and flexible continuum section are derived respectively. Finally, based on equivalent joint method, a two-step numerical iterative inverse kinematics algorithm is proposed for the whole robot: (1) the flexible continuum section is equivalently transformed to a 2-DOF spherical joint, thus the approximate analytical inverse kinematic solution can be obtained; (2) the accurate solution is derived by an iterative derivation of both parallel mechanism and flexible continuum section.FindingsTo verify structure scheme and the proposed kinematics modeling method, numerical simulations and prototype experiments are implemented. The results show that the proposed kinematics algorithm has sufficient accuracy and computational efficiency in the whole available workspace, that is end-effector position error and orientation error are less than 0.2 mm and 0.01° respectively, and computation time is less than 0.22s.Originality/valueA novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair is designed. A two-step numerical iterative inverse kinematics algorithm is proposed for this unique hybrid robots, which has good accuracy and computational efficiency.

Integrated uncertain optimal design strategy for truss configuration and attitude–vibration control in rigid–flexible coupling structure with interval uncertainties

Integrated uncertain optimal design strategy for truss configuration and attitude–vibration control in rigid–flexible coupling structure with interval uncertainties

The influence of elastic pads deterioration in the fastening system on the dynamic characteristics of the vehicle-turnout system

The deterioration of the elastic pads in the fastening system in high-speed turnout areas increases longitudinal stiffness irregularities along the track, posing potential hazards to wheel-rail impact and train running safety. This paper takes the frog area of No. 18 turnout as an example and constructs a vehicle-turnout rigid-flexible coupling model considering the detailed structure of the fastener elastic pads. By increasing the stiffness of the rubber pad under the tie plate to simulate the deterioration of the elastic pads in the turnout area, the study investigates the effects of deterioration location, degree, and number on the dynamic characteristics of the vehicle-turnout system, providing theoretical guidance for stiffness optimization and maintenance of the turnout area. The results indicate that: 1) the deterioration of the elastic pads significantly affects wheel-rail interaction and safety indicators, while having a minor effect on vehicle running stability; 2) the 95th sleeper (point rail with a top width of 60 mm) is identified as the most critical location for the deterioration of elastic pads; 3) comprehensively considering, the stiffness replacement limit for elastic pads in ballastless turnout areas can be set to twice the design stiffness, which is 50 kN/mm.

Rigid-flexible coupling dynamic-assisted imbalanced fault diagnosis for helicopter tail transmission system

Helicopters operate in extreme environments, complicating the balanced and accurate acquisition of operational data. Predicting high-precision failures in helicopter tail-drive systems is particularly challenging due to severe data imbalances. To address this, a fault diagnosis method based on rigid-flexible coupling dynamics is proposed. A high-precision simulation model generates source domain data samples, validated by comparing the frequency domain components and RMS values of simulated and tested vibration responses under healthy conditions. An adaptive Local Maximum Mean Discrepancy (LMMD) mechanism aligns features between simulated and tested data. Additionally, the Coordinate-Separable Convolutional ResNet (CSC-ResNet) network is proposed to efficiently learn high-dimensional feature knowledge. Results show the proposed method outperforms others in fault diagnosis accuracy and smoothness, offering a new perspective for fault diagnosis of helicopter tail transmission systems.

Dynamic characteristics and damage identification with interface damage of slabs in movable point crossing

As the operating density of China’s high-speed railway increases, the phenomenon of interlayer debonding in movable point crossing (MPC) is becoming more prevalent, which can lead to failure of the frog’s slab track. Meanwhile, vehicle impacts and interlayer debonding can exacerbate abnormal vibration of the vehicle and even lead to derailment. Therefore, based on the theory of rigid-flexible coupling dynamics, a vehicle-turnout-slab coupling dynamics model is established for the first time. In this model, the crossing rails with variable cross sections is considered and the interlayer debonding between turnout slabs is modelled by nonlinear springs. Then, the characteristics of the debonding is identified by applying a wavelet transform to the dynamic response of the vehicle. Finally, different types and sizes of debonding between the layers are considered. The results show that different debonding can lead to two types of contact, partial contact and complete voiding, which can further lead to detrimental effects on vehicle safety. And the limit of the defect size that causes the track slab to void is 1 mm. On this basis, it was found that when MPC’s slab tracks were voided, longer debonding can cause high frequency vibration acceleration of approximately 700 Hz in the vehicle axle box. The new insights obtained by this study could provide guidance for the maintenance period and avoid the development of the damage. This study not only obtained a mechanism for the effect of interlayer debonding on the dynamic response of the vehicle-track system, but also provides a theoretical basis of detecting interlayer debonding for future study.

Differential-algebraic equation-based model predictive control for trajectory tracking of spacecraft-mounted continuum manipulators

Spacecraft-mounted continuum manipulators (SMCMs) exhibit great potential for performing dexterous operations in unstructured environments due to their inherent compliance and dexterity. However, the dynamic model of the rigid-flexible coupling SMCM is highly nonlinear and typically formulated as a set of implicit differential-algebraic equations (DAEs), posing significant challenges for precise trajectory tracking control. This paper proposes a novel model predictive control (MPC) framework specifically designed for generic DAEs to achieve precise trajectory tracking of the SMCM under uncertain disturbances and input limitations. The DAE model of the SMCM is discretized into a set of nonlinear algebraic equations. By performing implicit differentiation of these equations with respect to the system state, the state transition matrix (STM) for the DAE model is derived. The optimal control action for the SMCM can be further determined based on the derived STM. Additionally, nonlinear complementary functions are introduced to address the issue of input limitations, allowing the problem of determining the optimal control sequence to be equivalently transformed into a set of nonlinear algebraic equations for solving. Numerical simulations demonstrate that the proposed approach can achieve precise trajectory tracking of the SMCM while strictly adhering to input limitations.

Dynamic Modelling and Performance Analysis of Deployable Telescopic Tubular Mast

AbstractThis work presents the longitudinal and transverse coupling vibrations of a deployable Telescopic Tubular Mast (TTM), a multi-stepped structure integrated into a spacecraft system, while considering the rigid-flexible coupling phenomenon. The model is derived using the principle of virtual work and discretized via the variable separation method. The von Kármán strain is employed to incorporate geometric nonlinear effects. Semi-analytical results for the shape functions and natural frequencies of the quasi-static multi-stepped boom are obtained using the extended transfer matrix method (ETMM). These natural frequencies are validated against results from Nastran, confirming the ETMM's accuracy. In addition, the model accounts for the continuously changing natural frequencies and shape functions during the deployment phase. Finally, the dynamic phenomena of the longitudinal and transverse displacements are analyzed at various deploying states, including locking and restart behaviors. The influence of the structural damping on the vibration evolution is also contained in the numerical analysis.

Dynamics for rigid–flexible coupled solar panel multibody system composed of composite laminated plates

Composite laminates are widely employed in the fabrication of solar panels in modern spacecraft engineering because of their superior durability, mechanical qualities, and cost-effectiveness. This research is dedicated to multibody system dynamics modeling of composite laminate solar panels, specifically the coupling system between the rigid main body and the flexible solar panels. In this study, the rigid body is modeled using the natural coordinate formulation (NCF), and for the flexible solar panel, the absolute nodal coordinate formulation (ANCF) with a 36-DOF reduced-order composite thin shell element is used to accurately capture the coupling effect of the solar panel under large motion and deformation. Compared to a 48-DOF fully parameterized thick plate element, this method efficiently avoids shear locking and improves numerical solution convergence efficiency. Based on the Kirchhoff theory and the constitutive relationship of composite laminates, a dynamic model of the multibody system is developed, taking into account the rigid-flexible coupling effect and the kinematic constraints. This work thoroughly discusses the dynamic behavior of solar panel deployment using a comparative analysis of numerical simulation and virtual prototype simulation, and the accuracy is verified. The findings indicate that the flexible characteristics and fiber orientation of composite laminates have a significant impact on the dynamic response of solar panels during deployment. Furthermore, the bang-bang attitude controller is designed, and the difference in dynamic response between the two modeling methods in controlled and uncontrolled states is studied, providing an important theoretical foundation and technical support for solar panel design and analysis.

Dynamic modeling and trajectory optimization for the rigid-flexible coupled spacecraft with the free-floating manipulator and solar panels

The rigid-flexible coupled spacecraft, composed of flexible solar panels and a multilink manipulator, has gained prominence in on-orbit servicing due to rapid advancements in space technology. However, the intricate effects of rigid-flexible coupling pose significant challenges for dynamic modeling, trajectory planning, and control. This paper aims to develop general dynamic approaches for modeling and trajectory planning in such spacecraft, considering large deformations. The main distinguishing feature is the use of the referenced nodal coordinate formulation to accurately describe the large-deformed solar panels rather than directly treating them as disturbance for the free-floating system. Additionally, the common recursive model for the multilink manipulator is integrated into the same framework. The modal reduction method with modal derivatives techniques is employed to address geometric nonlinearity resulting from large deformations. Polynomial trajectory parameters with different performance characteristics are obtained by defining various optimization objectives. The coupling analysis is conducted based on an accurate reduced-order dynamic model, the results of which can be used for designing manipulator tasks. Coupling values are defined as the objective for trajectory optimization, offering advantages such as insensitivity to dynamic model accuracy and a fast optimization process. After validating the accuracy of the proposed dynamic model through simulations, the performances of different optimized trajectories are demonstrated using numerical examples.

Nonlinear optimal frequency control for dynamic vibration absorber and its application

A principal limitation of passive dynamic vibration absorber (DVA) lies in its intrinsic design constraint, as it is tuned to a specific resonant frequency, rendering it less effective at mitigating vibrations over a variable frequency range. To ensure that the DVA retains its vibration reduction capability under loads with time-varying frequencies, this paper proposes a method for designing the optimal suspension frequency based on the external load frequency. The approach involves altering the stiffness of the DVA through semi-active or active control to achieve the optimal suspension frequency and the best vibration reduction performance. In this study, the ratio R between the optimal suspension frequency and the load frequency is defined, and the nonlinear characteristic of R, based on the lowest vibration transmission rate, is studied using a two degree-of-freedom DVA model. Furthermore, an optimal suspension frequency variation control strategy based on load frequency identification is presented. Combined with the typical load with time-varying frequency encountered in metro vehicles, a multi-body dynamics theoretical model and a rigid–flexible coupling dynamics model are established to verify the effectiveness of the nonlinear optimal frequency control. Finally, the full-size railway vehicle roller rig is used to verify the correctness of the principle of optimal frequency curve. The research results show that when the mass ratio is 0.1, compared with rigid suspension, the nonlinear optimal frequency control can reduce the root mean square (RMS) value of the carbody’s entire time period acceleration during variable speed operation by 62.2%, and the maximum RMS value is reduced by 83.6%. In nonlinear control, unlike passive DVA, the vibration is never higher than that of rigid suspension within a specific velocity range. Compared with linear control strategy, nonlinearity can further reduce the elastic vibration. The test results from roller rig indicate that the semi-active DVA can effectively reduce the elastic vibrations of the carbody, while also validating the correctness of the nonlinear optimal suspension frequency principle. Therefore, the nonlinear frequency control in this study can provide reference for structural vibration control under loads with time-varying frequencies.

Dynamic response of high-speed railway vehicle and welded turnout on large-span bridges based on rigid-flexible coupling system

Welded Turnout on Large-span Bridge (WTLB) is a complex multi-layer heterogeneous system and can significantly influence the service performance of High-Speed Railway (HSR). Understanding the coupling dynamic response of the vehicle and WTLB is essential. Previous research did not consider the dynamic behavior of foundations, leading to an underestimation of the vehicle-turnout-foundation coupling dynamic response, particularly when turnouts were laid on large-span bridges. This study proposes a novel modeling method that includes the foundations, to overcome the previous shortcomings by applying a rigid-flexible coupling system. In this approach, the vehicle was modeled as a rigid body sub-model in a Multi-Body Software (MBS), while WTLB was modeled as a flexible bodies sub-model using Finite Element (FE) software. The modal information from the FE model was imported into the MBS software. The two sub-models were coupled by the wheel-rail contact in the MBS environment and then the Vehicle-turnout-bridge Rigid-flexible Coupling Dynamic (VRCD) calculation model was established and it was discovered that the calculation results showed good agreement with the field test data. Through the VRCD model, the safety of the structure, the stability of the vehicle and the comfort of passengers were investigated, as well as several important infrastructure factors. The results demonstrate that this novel method provides accurate calculations and highlights the complex and significant interactions in the vehicle-turnout-bridge system.