Rigid-flexible Coupling Dynamic Model Research Articles

Launching dynamic analysis for tank on the move based on dynamic simulation

Achieving high firing accuracy of tank on the move is challenging. For improving firing accuracy, better understanding launching dynamic behavior of tank firing on the move is required. This study established a rigid-flexible coupling dynamic model of tank firing on the move. Thereinto, the barrel flexibility was considered based on the FFlex body technology, and the contact-impact algorithm was used to describe the projectile-barrel interaction. With the sinusoid superposition method, a three-dimensional road surface spectrum file considering the coherence of left and right tracks was created. Based on the results obtained in simulation, this study discussed the dynamic behaviors of a tank gun system such as the barrel curvature and the influence of projectile-barrel interaction on firing accuracy of tank firing on the move, in which the factors including projectile type, driving speed and road roughness were taken into consideration. The results indicated that the barrel curvature and the muzzle vibration do not increase simply with the increase of road roughness and driving speed as common sense.

Parameterization dynamics visual design platform for missile launching system

The missile launching system is a typical complex mechanical system, which is becoming increasingly larger in scale and more complicated in structure. Designing these types of products often requires repeated complex and time-consuming model design, calculation, and analysis of the dynamics of the system. The most time-consuming is repeatedly modifying the geometric and dynamics models. In this article, we put forward a new method for bidirectional-driving parameter between CAD and CAE, by changing the geometric model parameters, which directly changes the dynamics model. A parameterized multibody system dynamics modeling and analysis software for missile launching system are proposed, which gathered modeling, solving, visual simulation as a whole, and realized design parameters seamless transfer between geometric models and dynamics models for missile launching system. In order to examine the correctness of the simulation results, a parameterized experimental platform for missile launching system is designed, which can modify the key parameters as designed in simulation software. Finally, a missile launching system simulation and test examples are given, and the simulation analysis and experiment results demonstrate that the overall trend of the simulation results of multi-rigid and rigid-flexible coupling dynamics model is consistent with the experiment results.

Study on the dynamic modeling and natural characteristics of wind turbine drivetrain considering electromagnetic stiffness

As the wind turbine starts running, the drivetrain would suffer a significant impact load, which severely endangers the safety of the wind turbine. Therefore, ensuring the capacity of the drivetrain to resist the impact load is critical to prevent wind turbine downtime. Most of the drivetrain models fail to balance the efficiency and accuracy, and lack the concern on the responses of the drivetrain at start-up. In this paper, a rigid-flexible coupling dynamic modeling method and an experiment method are proposed to study the modal characteristics of the doubly-fed wind turbine drivetrain at start-up. The drivetrain model is constructed applying the electromagnetic (EM) stiffness and the mesh deformation of the multistage gear transmission as well as the flexibility of bearings, main shaft and parallel stage shafts. The proposed model is validated by the professional software. A new measuring point is discovered to record the experimental data influenced by the electromagnetic stiffness. An efficient method is further developed to calculate the electromagnetic stiffness. The modal shape, modal energy and amplitude-frequency responses of the drivetrain are investigated considering the electromagnetic stiffness. The proposed method can be used to guide the drivetrain optimization and the experiment.

Rigid-flexible coupling dynamic model of a flexible planar parallel robot for modal characteristics research

The increasing applications of flexible parallel robots in industrial production have presented the advantages of light weight and high speed, but at the same time, the elastic vibration problem has emerged. By investigating the modal features of flexible parallel robots so as to suppress the elastic vibration, with pinned-pinned as flexible intermediate links boundary conditions, this article analyzes the rigid-flexible coupling dynamic mathematical model of the 3-RRR (3-Rotate-Rotate-Rotate) flexible planar parallel robot with flexible intermediate links. The effect of the extremity concentrated rotation inertia of flexible intermediate links is considered in the mathematical model. Besides, the effect of inertia and coupling force on the dynamic model and the first three-order vibration responses of flexible intermediate links were discussed based on the established model. The corresponding spectrum characteristics were studied using fast Fourier transform. Comparing the frequency characteristics obtained by theoretical model and modal experiment, it was found that the results obtained by the dynamic mathematical model are quite close to the test results. Less dynamic parameters make it convenient to carry out the control program.

Dynamics Study of Straddle-Type Monorail Vehicle With Single-Axle Bogies-Based Full-Scale Rigid-Flexible Coupling Dynamic Model

The longitudinal drawbar and the lateral stabilizer bar of straddle-type monorail vehicle with the single-axle bogies have relatively long structure size. The multibar system leads to deformation during the driving process due to impact loads, even leads to influence on the dynamic characteristic of the hauling mechanism as well as the riding comfort of the whole vehicle. To evaluate the dynamic behavior of straddle-type monorail vehicle with single-axle bogies accurately, a full-scale rigid-flexible coupling multibody dynamics method is proposed based on multibody dynamics and finite element (FE) theory. The modal synthesis method is adopted to establish flexible multibody dynamics of the single-axle bogies. And then rigid-flexible coupling dynamic model of the straddle-type monorail vehicle is established with the ADAMS software. The validity of the full-scale model is verified. Finally, the influences of vehicle velocity, passenger mass, curve radius and the number of axles on dynamic characteristics are discussed.

Influence of Vibration Isolator Failure on Vehicle Operation Performance and Floating Slab Track Structure Vibration Reduction Effectiveness

At present, steel‐spring floating slabs have been widely used in urban rail transit to reduce the influence of ground vibration caused by vehicle operation on the surrounding environment. As a core part of vibration reduction for floating slab track, the steel‐spring vibration isolator may fail in different forms during operation. In order to study the influence of vibration isolator failure on vehicle operation performance and floating slab track structure vibration reduction effectiveness, a rigid‐flexible coupling dynamic model of vehicle‐rail‐floating slab track is established by multibody dynamics and finite element simulation, and the rationality of the model and its parameters is verified by comparing the theoretical calculation results with the measured data. Based on the model, the failure conditions of steel spring are simulated, considering the failure position and number of steel springs. The results show that the failures of steel‐spring vibration isolators have a significant impact on operating safety and stability of vehicle, and the failure at end is more dangerous than that at midspan. In addition, it also changes the local restraint state of floating slab, resulting in the local vibration mode, which reduces the floating slab track structure vibration reduction effectiveness, mainly within 10 Hz. The different numbers of steel‐spring failures will change the natural modal frequency of floating slab to varying degrees, which may cause the resonance of a certain frequency of the vehicle‐track coupling system, leading to other track structure diseases.

Simulation and analysis of wheel wear prediction with rigid flexible couple wheelset

Wheel wear problem of high-speed train is one of the important factors that affect the dynamic performance of the train, from the angle of wear prediction, combined with the Hertz vehicle dynamics model, rolling contact model, wheel wear model, analyzed the main influencing factors of wheel wear. The rigid flexible coupling dynamic model is established to calculate the wheel rail contact relationship considering the wheel elastic deformation, and the Fastsim algorithm is used to calculate the creep force and contact parameters on the wheel rail contact spot. Combining the Fastsim algorithm and the Zobory wear model, the wear rate of the contact surface between the rigid wheel and the elastic wheel is obtained. The results show that in a straight section considering wheel elastic model to increase the width of the rigid model of wear, wear depth of the amplitude is also increasing. The maximum wear depth of rigid model is 9.23e-4mm, the maximum wear depth of the rigid flexible couple model is 1.019e-3mm, and the maximum depth of rigid flexible couple model increased 9.4%. The effects of the velocity and the longitudinal stiffnesss of the two models are analyzed. When the velocity and the longitudinal stiffness of the system are increased, the wear depth of the flexible wheelset model is more obvious than that of the rigid wheelset model.

Rigid-flexible coupling dynamic modeling and vibration control for flexible spacecraft based on its global analytical modes

In this study, we used global analytical modeswfny (GAMs) to develop a rigid-flexible dynamic modeling approach for spacecraft with large flexible appendages (SwLFA). This approach enables the convenient and precise calculation of the natural characteristics for designing an attitude control law for the spacecraft while simultaneously suppressing the active vibration of its flexible appendages. We simplify the flexible spacecraft as a rigid-flexible coupling hub-beam system with tip mass and derive the system’s governing equations of motion based on Hamilton’s principle. By solving the linearized form of those equations with their associated boundary conditions, we obtain the frequencies as well as the corresponding GAMs of flexible spacecraft, which we use to discretize the equations of motion. Using this approach, we performed numerical simulations to investigate the system’s global modes and assess the performance of the controller based on the GAM model. The results reveal that the GAM model can be used to directly calculate the exact global modes of SwLFAs and that the controller based on the discrete GAM model can achieve a control-index for a SwLFA in a shorter time with less input energy than other methods.

Observer-based continuous finite-time attitude control for rigid–flexible coupling satellites

ABSTRACTIn this paper, a novel finite-time attitude control law is proposed for rigid–flexible coupling satellites in large angle manoeuver. First, the rigid–flexible coupling dynamic model is set up to reflect the coupling effect between the deformation of flexible appendages and the spatial movement of the rigid hub. Then an extended state observer (ESO) is designed to estimate and compensate the total perturbation including high-order flexible coupling terms, external disturbances and uncertain inertia. Following this, a continuous finite-time attitude controller is designed based on non-singular fast terminal sliding mode (NFTSM) and fast power reaching law, which is introduced to smooth the control input and eliminate the chattering. Numerical simulation is designed to verify the finite-time stability, high accuracy, disturbance rejectionand vibration damping of the proposed control scheme and then a ground experimental system is set to further test the controller's practicability.

Analysis of Flexible Car Body of Straddle Monorail Vehicle

Based on the finite element model of straddle monorail vehicle, a rigid-flexible coupling dynamic model considering vehicle body’s flexibility is established. The influence of vertical stiffness and vertical damping of the running wheel on the modal parameters of the car body is analyzed. The effect of flexible car body on modal parameters and vehicle ride quality is also studied. The results show that when the vertical stiffness of running wheel is less than 1 MN / m, the car body bounce and pitch frequency increase with the increasing of the vertical stiffness of the running wheel, when the running wheel vertical stiffness is 1MN / m or more, car body bounce and pitch frequency remained unchanged; When the vertical stiffness of the running wheel is below 1.8 MN / m, the vehicle body bounce and pitch damping ratio increase with the increasing of the vertical stiffness of the running wheel; When the running wheel vertical stiffness is 1.8MN / m or more, the car body bounce and pitch damping ratio remained unchanged; The running wheel vertical damping on the car body bounce and pitch frequency has no effect; Car body bounce and pitch damping ratio increase with the increasing of the vertical damping of the running wheel. The flexibility of the car body has no effect on the modal parameters of the car, which will improve the vehicle ride quality index.

Nonlinear Vibration of Ladle Crane due to a Moving Trolley

The structural vibration of the main beam of a crane causes fatigue damage and discomfort to the driver. The swing of the payload has an effect on positioning precision, especially for a ladle crane, and this directly affects production safety. To study the influence of system parameters on the vibration of a crane’s main beam and the angle of the payload, a system consisting of the main beam, trolley, payload, and cabin was constructed. A rigid-flexible coupling dynamic model of a moving trolley with a hanging payload that moves on the flexible main beam with a concentrated cabin mass is established, and the direct integration method is used to solve the nonlinear differential equations of system vibration, which are obtained through Lagrange’s equation. Then, the time domain responses of the flexible main beam, payload angle, and cabin vibration are obtained. The influences of the trolley running speed, quality of the payload, and quality and position of the cabin on the vibration of the main beam and payload angle are analyzed. The results indicate that the amplitude of the main beam is directly proportional to the quality of the trolley, payload, and cab; the position of the cabin is closer to the mid-span; the amplitude of the main beam is larger; the structural damping has some influence on the vibration of the main beam; and the swing angle of the payload is related to the maximum running speed of the trolley, acceleration time, and length of the wire rope. In order to reduce the vibration of the main beam and cabin, the connection stiffness of the cabin should be ensured during installation.

The rigid–flexible coupling dynamic model and response analysis of bearing–wheel–rail system under track irregularity

As the main bearing components of vehicle wheel/rail systems, railway bearings take on the main load of wheel/rail system. These bearings can be easily damaged after a long-term load, which causes vibrations and significant deterioration of force distribution and directly affects the driving stability of the locomotive. Current systems available for modeling the dynamics of wheel/rail systems rarely consider nonlinear contact load bearing, which causes errors in the calculation of wheel/rail system dynamics. According to the bearing structure characteristics and working features of a specific system, this paper thoroughly evaluates the flexible deformation of shaft and bearing, time-varying nonlinear contact load, track irregularity, and bearing to establish a wheel/rail system coupling dynamics model. Then, based on the coupling dynamics theoretical model, the wheel/rail system’s coupling nonlinear dynamic characteristics are studied under random load. Then, this theoretical model of the wheel–bearing–rail system dynamics is verified using the railway bearing as an example. Finally, the model is applied to the process of rail/wheel low force design. Results show that under irregular stimulation, the maximum contact load increased by 71.2% and the maximum contact stress increased by 19.6%. After moderate wear, the wheel/rail system vibration and loading condition deteriorate rapidly. Under the low rail/wheel force, the wheel tread and diameter had significant effects on wheel/rail contact force distribution. The rail specifications are found to affect the wheel/rail system’s vibration significantly. This paper has important theoretical value and practical significance for developing reliable railway bearings and wheel/rail systems with good static/dynamic characteristics that can withstand dynamic impact load.

Dynamic modeling and hierarchical compound control of a novel 2-DOF flexible parallel manipulator with multiple actuation modes

Abstract This paper addresses the problem of rigid-flexible coupling dynamic modeling and active control of a novel flexible parallel manipulator (PM) with multiple actuation modes. Firstly, based on the flexible multi-body dynamics theory, the rigid-flexible coupling dynamic model (RFDM) of system is developed by virtue of the augmented Lagrangian multipliers approach. For completeness, the mathematical models of permanent magnet synchronous motor (PMSM) and piezoelectric transducer (PZT) are further established and integrated with the RFDM of mechanical system to formulate the electromechanical coupling dynamic model (ECDM). To achieve the trajectory tracking and vibration suppression, a hierarchical compound control strategy is presented. Within this control strategy, the proportional-differential (PD) feedback controller is employed to realize the trajectory tracking of end-effector, while the strain and strain rate feedback (SSRF) controller is developed to restrain the vibration of the flexible links using PZT. Furthermore, the stability of the control algorithm is demonstrated based on the Lyapunov stability theory. Finally, two simulation case studies are performed to illustrate the effectiveness of the proposed approach. The results indicate that, under the redundant actuation mode, the hierarchical compound control strategy can guarantee the flexible PM achieves singularity-free motion and vibration attenuation within task workspace simultaneously. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and efficient controller design of other flexible PMs, especially the emerging ones with multiple actuation modes.

Planar rigid-flexible coupling spacecraft modeling and control considering solar array deployment and joint clearance

Based on Nodal Coordinate Formulation (NCF) and Absolute Nodal Coordinate Formulation (ANCF), this paper establishes rigid-flexible coupling dynamic model of the spacecraft with large deployable solar arrays and multiple clearance joints to analyze and control the satellite attitude under deployment disturbance. Considering torque spring, close cable loop (CCL) configuration and latch mechanisms, a typical spacecraft composed of a rigid main-body described by NCF and two flexible panels described by ANCF is used as a demonstration case. Nonlinear contact force model and modified Coulomb friction model are selected to establish normal contact force and tangential friction model, respectively. Generalized elastic force are derived and all generalized forces are defined in the NCF-ANCF frame. The Newmark-β method is used to solve system equations of motion. The availability and superiority of the proposed model is verified through comparing with numerical co-simulations of Patran and ADAMS software. The numerical results reveal the effects of panel flexibility, joint clearance and their coupling on satellite attitude. The effects of clearance number, clearance size and clearance stiffness on satellite attitude are investigated. Furthermore, a proportional-differential (PD) attitude controller of spacecraft is designed to discuss the effect of attitude control on the dynamic responses of the whole system.

Research on the Influence of Straddle-Type Monorail\u2019s Pantograph Head Parameter on Power Collection Quality

At present, the coupling relationship between the pantograph and catenary is not ideal for straddle-type monorail. The power collection quality is poor, and the wear of the contact strip of a pantograph is uneven. Therefore, the key problem of coupling relation between the pantograph and catenary is the dynamics of a pantograph–catenary system. This paper analyzed the modal of catenary through simulation with finite element model and the vibration modal of pantograph multi-rigid-body dynamic model by simulation in multi-body danamics software ADAMS. A rigid-flexible coupling dynamic model of pantograph–catenary system is established. Finally, extensive research has been made on the influence of pantograph head parameters on the power collection quality.

Rigid-Flexible Coupling Dynamic Modeling and Vibration Control for a Three-Axis Stabilized Spacecraft

An approach is proposed to obtain the global analytical modes (GAMs) and establish discrete dynamic model with low degree-of-freedom for a three-axis attitude stabilized spacecraft installed with a pair of solar arrays. The flexible spacecraft is simplified as a hub–plate system which is a typical rigid-flexible coupling system. The governing equations of motion and the corresponding boundary conditions are derived by using the Hamiltonian principle. Describing the rigid motion and elastic vibration of all the system components with a uniform set of generalized coordinates, the system GAMs are solved from those dynamic equations and boundary conditions, which are used to discretize the equations of motion. For comparison, another discrete model is also derived using assumed mode method (AMM). Using ansys software, a finite element model is established to verify the GAM and AMM models. Subsequently, the system global modes are investigated using the GAM approach. Further, the performance of GAM model in dynamic analysis and cooperative control for attitude motion and solar panel vibration is assessed by comparing with AMM model. The discrete dynamic model based on GAMs has the capability to carry out spacecraft dynamic analysis in the same accuracy as a high-dimensional AMM model. The controller based on GAM model can suppress the oscillation of solar panels and make the control torque stable in much shorter time.

Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes

A systematic dynamic modeling methodology is presented to develop the rigid-flexible coupling dynamic model (RFDM) of an emerging flexible parallel manipulator with multiple actuation modes. By virtue of assumed mode method, the general dynamic model of an arbitrary flexible body with any number of lumped parameters is derived in an explicit closed form, which possesses the modular characteristic. Then the completely dynamic model of system is formulated based on the flexible multi-body dynamics (FMD) theory and the augmented Lagrangian multipliers method. An approach of combining the Udwadia-Kalaba formulation with the hybrid TR-BDF2 numerical algorithm is proposed to address the nonlinear RFDM. Two simulation cases are performed to investigate the dynamic performance of the manipulator with different actuation modes. The results indicate that the redundant actuation modes can effectively attenuate vibration and guarantee higher dynamic performance compared to the traditional non-redundant actuation modes. Finally, a virtual prototype model is developed to demonstrate the validity of the presented RFDM. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and controller design of other planar flexible parallel manipulators, especially the emerging ones with multiple actuation modes.

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

ABSTRACTIn particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel–rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid–flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel–rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.

Nonlinear dynamic modeling and performance analysis of a redundantly actuated parallel manipulator with multiple actuation modes based on FMD theory

A novel redundantly actuated parallel manipulator (PM) with multiple actuation modes was developed recently by the author. In this paper, the further research is implemented and a systematic methodology is proposed to develop the rigid–flexible coupling dynamic model (RFDM) of the novel PM based on the flexible multi-body dynamics theory. Firstly, under the floating frame of reference, an arbitrary flexible link of the novel PM is regarded as an Euler–Bernoulli beam and the finite element approach is employed to discretize the flexible beam. Then, one kind of planar beam element with lumped masses and moments of inertia at both ends is presented and a corresponding dynamic model is deduced based on the Lagrangian formulation. On this basis, the RFDM of system is formulated by virtue of the augmented Lagrangian multipliers approach. Given the stiff characteristic of system dynamic model, the hybrid TR-BDF2 numerical algorithm combined with Baumgarte stabilization approach is employed to address the nonlinear RFDM so as to balance the solution efficiency and precision. Based on the RFDM and its degradation model, i.e., the rigid dynamic model, one dynamic simulation experiment is designed to investigate the dynamic performance of the PM. Numerical results indicate that the practical motion of the PM manifests rigid–flexible coupling characteristic, and the redundant actuation modes can attenuate the effect of link flexibility and improve the trajectory tracking precision of end-effector in comparison with the non-redundant actuation modes. Finally, to validate the presented methodology, the obtained numerical results are compared with a virtual prototype model developed based on SimMechanics. The results will be helpful for structure optimization and efficient controller design of the PM with multiple actuation modes.

A Method of Energy-Optimal Trajectory Planning for Palletizing Robot

In this work, the energy-optimal trajectory planning and initial pick point searching problem for palletizing robot with high load capacity and high speed are studied, in which the pick point and place point of the robot are fixed to a desired location for each single task. These optimization problems have been transformed to ternary functional extremum problem and parameters optimal selection problem in which the performance index of the problems the rigid-flexible coupling dynamics model of the robot, and the constraint and boundary conditions of the robot are given. The fourth-order Runge-Kutta method, multiple shooting method, and traversing method are used to solve these specific mathematical problems. The effectiveness of the trajectory planning method is validated by the experimental and simulating results; thus the research work done here provides important support for subsequent palletizing robot research.