Rigid-flexible Coupling Research Articles

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.

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.

Design of a robotic gripper for casting sorting robots with rigid–flexible coupling structures

Design of a robotic gripper for casting sorting robots with rigid–flexible coupling structures

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

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

Reliability analysis of 50000 kN hydraulic support test bench under shrinkage test conditions

The large mining-height hydraulic support test-bed serves as a crucial tool for heavy hydraulic support factory inspections and type testing. With the successful development of the ZY29000/45/100D hydraulic support, the need for a large high-mining hydraulic support test-bed has become evident. This paper combines the theory of rigid-flexible coupling in virtual prototypes and ADAMS multi-body dynamic simulation technology to analyze the strength of the 50,000 kN hydraulic support test-bed. ANSYS classic modules were employed to address the flexibility of key components within the test-bed. The fatigue life of the test-bed was analyzed using NSOFT software, the von Mises yield criterion, and the Goodman modified curve. The S-N curve of material parameters for the test-bed components was used to conduct a shrinkage test. The results indicate that the lowest position is the most vulnerable during the shrinkage test. Among the key components, the stress on the pin bearing is 356.6 MPa, which is 167.9 %, 123.3 %, and 41.6 % higher than that of the pillar, movable beam, and base, respectively. The fatigue life of the base under low, medium, and high shrinkage conditions is1.1×107, 4.0×108, and 1.7×108, with damage values of 8.8×10-8, 2.5×10-9, and 5.7×10-9, respectively. The base’s life under low shrinkage conditions is the shortest, followed by that under high shrinkage conditions. These research findings provide technical guidance and an optimization foundation for the successful development of a 50000 kN hydraulic support test-bed. They also offer a new method and approach for analyzing and predicting the fatigue life of key components in large-scale industrial and mining equipment operating under complex conditions, with promising practical applications.

Vibration-attitude integrated control of large membrane diffraction space telescope

The development of telescopes with large apertures is driven by the increasing demand for higher imaging resolution and coverage. Large membrane diffraction space telescopes are particularly attractive due to their lightweight nature, ease of folding and unfolding, and high-precision imaging capabilities. However, their substantial size and flexibility make them susceptible to long-duration, low-frequency vibrations during attitude maneuvers, which degrade attitude and imaging accuracy and risk instrument damage. Consequently, an urgent need exists for a high-precision integrated control scheme. In this paper, the integrated control of vibration and attitude in a large space telescope is studied using cable actuators and control moment gyroscopes (CMGs). Since cables can only withstand limited tension, the unilateral and constrained characteristics of the control input are taken into account during the control design process. Firstly, a rigid-flexible coupling dynamic model of the space telescope is established using the velocity variation principle with hybrid coordinates. Additionally, a two-body astrodynamic model is developed to assess the impact of gravity gradient torque. Next, combining the computational torque method and H∞ control theory, an integrated control scheme is proposed, which achieves vibration and attitude control during maneuvers. Then, this paper optimizes the cable actuator positions via the discrete particle swarm optimization (PSO) algorithm and plans various attitude maneuver paths. Finally, numerical simulations are adopted to demonstrate the effectiveness of the control scheme. The results show that this integrated control scheme swiftly suppresses structural vibrations during attitude maneuvers, enabling high-precision attitude control of the space telescope.

Development and investigation for rigid-flexible coupling dynamic performances of the morphing wing with clearance joints

Morphing wings have enjoyed much research interest due to their advantages in improving aircraft adaptability to various service environments. A single drive and continuous variable bending morphing mechanism with multiple configurations is proposed. The morphing wing designed based on this mechanism can have the advantages of lightweight, multiple configurations and smooth morphing shapes. Transient aerodynamic loads will destroy the dynamic performance of the wing during the multi-mode morphing process. Therefore, it is crucial to analyze the vibration characteristics for the reliability of the morphing wing. However, it is difficult to obtain its dynamic model and solution because of the complex configuration and the multi-mode morphing. In this paper, a mathematical model for the multi-mode morphing of the morphing mechanism based on lockable joints is described using the constraint equation firstly. Then, a rigid-flexible coupling dynamic model of the morphing wing with clearance joints is established. Finally, the influence of the infective joint and the flexible link on the vibration properties of the morphing wing is analyzed in detail. Moreover, differences in the dynamic parameters between rapid and regular actuation are discussed. The results obtained in this paper have an important engineering value for the design and manufacture of the morphing wing.

Pantograph-Catenary Coupling System Dynamics Analysis with Rigid-Flexible Pantograph for Straddle-Type Monorail

The flexible pantograph of straddle-type monorail has influence on the dynamics performance of pantograph-catenary system. This paper established a rigid-flexible pantograph-catenary-vehicle coupling dynamics model of monorail. By embedded the rigid-flexible pantograph into the vehicle dynamic analysis model, the rigid-flexible pantograph-catenary coupling dynamics model that could consider the random irregularity of track beam ultimately established. The validity of model has been approved by the pantograph dynamics test of Chongqing monorail line 3. The dynamic performance of the pantograph-catenary system, calculated by the dynamics models with rigid and rigid-flexible pantograph are compared in detail. The results show that the pantograph flexibility affects the vibration characteristics and the current collection quality of pantograph-catenary system.

Evolution Characteristics of Aluminum Thermal Weld Irregularity and Damage in Heavy-Haul Railway under Different Service Conditions

Aluminum thermal welding joints are widely used in the maintenance welding of heavy-haul railways due to their easy handling and high efficiency. However, due to their inherent welding characteristics, welding results in certain differences in the material’s physical properties at the welding zone compared to adjacent base materials, leading to the occurrence of short-wave irregularity under long-term wheel–rail interactive forces. In order to explore the evolution characteristics of weld irregularity, dynamic characteristics, and plastic deformation under long-term wheel–rail impact, a detailed tracking test was conducted on a normal aluminum weld, and the process from being put on the track to being damaged and replaced was evaluated. At the same time, a rigid–flexible coupling model was established for subsequent analysis, and plastic damage was analyzed using the finite element model. The results show that the service life of the weld can be divided into three different stages: the initial stage, the intermediate stage, and the damage stage. In the damage stage, a temporary separation occurred between the wheel and rail, leading to a sudden change in the wheel–rail interaction. The weight of 250 MT at the weld reached the repairment control limit. The concentration effect of equivalent plastic deformation was most serious at 2~5 mm below the rail head.

Rigid–flexible coupling design and reusable impact mitigation of the hierarchical-bistable hybrid metamaterials

Mechanical metamaterials with multistable unit cells featured by negative stiffness or quasi-zero stiffness is attracting increasing attention owing to their unique mechanical properties and reusable potential. In this paper, a hierarchical-bistable hybrid metamaterial with rigid–flexible coupling design is proposed, demonstrating excellent mitigation performance and protection against multiple impacts. The metamaterial consists of a multi-layer bistable beams with a central honeycomb and is manufactured by 3D printing. Firstly, the negative stiffness characteristics of the curved beams in the metamaterial are theoretically determined, and the convergence of the finite element model under different mesh sizes is analyzed. And the quasi-zero stiffness characteristics of the metamaterial have been confirmed, along with its more stable and uniform deformation pattern, through the quasi-static compression experiment. Then the buffering performance of the metamaterial is studied in ball impact tests, showing an average improvement of about 65% compared to the rigid control group, while verifying the accuracy of the finite element model. With the analysis of the deformation modes and strain energy, the mitigation mechanism of metamaterials is demonstrated to extend the contact time and disperse the impact load through the layered deformation to reduce the peak response, instead of relying on plastic strain. Finally, the reusability of the metamaterial is explored by the ten-times plate impacts simulation. The results demonstrate that the metamaterial decreases the plastic strain of its structure by 60% while reducing impact response, thereby preventing the premature failure of core components. These results demonstrate the great potential of the proposed metamaterials for various engineering applications, including aircraft or spacecraft landing protection, vehicle pedestrian protection, and the transportation protection of fragile objects or precision instruments.

Rigid-flexible coupling multistage carbon composite materials based on hybrid crosslinking as anodes for ultra long-cycling lithium-ion batteries

Graphene have garnered considerable attention owing to their disordered structure, wide layer spacing, and cost-effectiveness. The hierarchical porous structure of porous reduced graphene oxide (rGO) nanosheets with hollow carbon nanospheres offers advantages such as an intact conductive network and a robust structure. However, since the hollow carbon nanospheres are physically in contact with rGO, they are randomly dispersed on the graphene surface, severely impeding fast electron transport and resulting in poor electrochemical performance. In this study, we introduced a third layer of a polypyrrole (PPy) -derived carbon film on the basis of porous rGO sheets and hollow carbon nanospheres. The HCGP-200 anode was successfully prepared to effectively encapsulate hollow carbon nanospheres on rGO sheets through the synergistic effect of rGO and the PPy-derived carbon film. The HCGP-200 anode exhibits robust cycling performance (780 mAh g−1 after 2200 cycles at 5 A g−1) and excellent rate capacity. Additionally, it demonstrates outstanding cycling stability and remarkable capacity retention (450 mAh g−1 after 3000 cycles) even at ultra-high current densities of 20 A g−1. The ingenious design and preparation of HCGP-200 is of great significance in guiding the application of high-power appliances.