Flexible Multi-body Dynamic Model Research Articles

The use of an artificial neural network for assessing tone perception in electric powertrain noise, vibration and harshness

The transition from internal combustion engines to electric powertrains brings new challenges for the Noise, Vibration, and Harshness (NVH) analysis of these vehicles. The tonal nature of the electromagnetic excitations and of the gear meshing mechanism are reflected in the radiated noise of electric powertrains, often leading drivers and passengers to rate the noise from electric vehicles with an increased nuisance even if they are quieter than internal combustion driven powertrains. In this paper, a flexible multi-body dynamics model is developed to calculate the vibration and forces transmitted from the bearings to the housing of an electric powertrain. Acceleration, force and sound spectra data are used to train an artificial neural network to assess the prominence of tones in the noise based on the results of the structural simulation. The results show it is possible to identify psychoacoustic metrics from the multibody dynamics simulation alone. With this new approach, it is feasible to quickly investigate how changes in the powertrain will affect the tonal perception of the noise without the need of new acoustic simulations and experiments. For the tonal perception analysis, the Prominence Ratio is used as a metric. This framework of combining multibody dynamics simulation with initial acoustic data and neural networks can be also applied to different NVH metrics as appropriate.

Rigid-flexible coupling multi-body dynamics modeling of a semi-submersible floating offshore wind turbine

A 14-degree-of-freedom (14-DOF) flexible multibody dynamics model is developed and verified for a semi-submersible floating offshore wind turbine (FOWT). The model considers the coupled dynamics of the platform, tower, nacelle, blades, and mooring subjected to external wind and wave loads. The platform is simplified as a rigid body connected to the seabed by the mooring system. The tower and blade are modeled as flexible cantilever beams. The energy method is used to derive the governing equations of motion, where the kinetic energy, potential energy, and work done by external wind-wave forces are all deduced in a global coordinate system. The 5-MW baseline semi-submersible FOWT is used to verify the derived model against the results simulated from FAST developed by the US National Renewable Energy Laboratory (NREL) at two scenarios: free decay state and different wind-wave load cases. Results show that the established FOWT model can well reflect the vibration characteristics of FAST model. The application of the model to the control of platform pitch with a tuned mass damper is studied. The simplified model could provide a low-order method for the structural dynamics analysis and advanced vibration control design for the multi-body components of the semi-submersible FOWT in the future.

Influence of clearance and structural coupling parameters on shimmy stability of landing gear

AbstractThere are many factors causing the shimmy of the aircraft landing gear and structural clearance of landing gear is a typical factor. Some aircraft in service or operation did not shimmy before, but suddenly appeared after a period of use. To solve the problem of clearance shimmy during the service of a certain aircraft, we established a dynamic model of rotating gear with clearance based on the flexible multi-body dynamics model of landing gear and L-N contact theory. We defined different types of clearance and established a mechanical model of aircraft pendulum vibration considering the clearance of landing gear structure for dynamic simulation, and studied the effects of different clearance types, clearance size of motion pair and different clearance positions on the stability of pendulum. The results show that the axial clearance has little effect on the shimmy performance of landing gear; the radial clearance has a certain effect on the shimmy performance of medium speed running, which slightly improves the shimmy damping required by medium speed running; the rotational clearance affects the shimmy performance of the nose landing gear by affecting the force transmission of structural components. The required shimmy damping coefficient increases at low speed and decreases at high speed. The main reason for the return clearance is that during the return, the shimmy damper does not work, which leads to the decrease of the shimmy damping performance and the increase of the required shimmy damping coefficient in the whole speed range. Meanwhile, the structural clearance will increase the shimmy frequency of the nose landing gear. By analysing the yaw angle of the nose landing gear and the time domain curve of the yaw angle of the yaw damper, we can determine which structure of the landing gear and which type of clearance is the cause of the yaw. Finally, the coupling effect caused by the main structural parameters of the landing gear in “gap shimmy” was analysed according to different mechanical stability distances and strut stiffness of the nose landing gear, providing reference for aircraft anti-shimmy design, nose landing gear fault diagnosis and nose landing gear maintenance support.

A semi-analytical approach to sensitivity analysis with flexible multibody dynamics of a morphing forward wing section

In the present paper, semi-analytical design sensitivity analysis of a morphing forward wing section modeled as a flexible multibody system is developed. The flexible multibody dynamics model consists of a flexible external wing skin and an actuation mechanism with rigid bodies. The floating frame of reference formulation is used for the formulation of the equations of motion, while time integration is carried out with the generalized-alpha method and Newton–Raphson iterations for the nonlinear analysis. These steps are considered in both the primal analysis and the developed efficient design sensitivity analysis. The calculation of the design sensitivities is based on direct differentiation and carried out with a semi-analytical approach. The responses of interest include the deviations of the wing profile from the targeted morphed geometry and the resulting stresses in the wing skin. The design variables considered in this work are geometric parameters, material parameters and loading parameters. The calculations with the shown method provide reliable and accurate results combined with high computational efficiency. The visualization of the computed sensitivity values gives an easy interpretation of the sensitivities and facilitates the understanding of the design engineer on how to change the design variables to improve the design of the system. The introduced sensitivity analysis enables future investigations, including the application of the method to gradient-based design optimization and uncertainty analysis.

Prediction and Accuracy verification of Machine tool Using a Coupling Analysis of Flexible Multibody Dynamics and Control Model

Prediction and Accuracy verification of Machine tool Using a Coupling Analysis of Flexible Multibody Dynamics and Control Model

Fast flexible multibody dynamic analysis of machine tools using modal state space models

Digital twins of machine tools are widely used for the validation and optimization of part programs. However, implementing flexible body dynamics in digital twins is challenging due to low computational efficiency. This study presents a flexible multibody dynamic model of a machine tool using modal state space representation of a finite element model. Simulation using the model is twice as fast as actual machining, enabling vibration analysis of flexible body machines in parallel with the machining process. Experiments using a horizontal machine tool confirm that the model predicts residual vibration under various acceleration conditions with an average accuracy of 88%.

Spin dynamics of a long tethered sub-satellite system in geostationary orbit

A long tethered sub-satellite system (LTSS) has a promising application for earth observation, which requires that the LTSS spins towards the earth. Due to the long flexible tethers and the spinning of the LTSS, the system exhibits dynamics of high nonlinearity and high complexity. While most previous studies did not consider more than three satellites in a tethered satellite system, the computational method developed in this work allows considering an arbitrary number of satellites as demonstrated by the numerical examples presented. First of all, a nonlinear flexible multibody dynamic model of the spinning LTSS in the orbital coordinate frame is established and the corresponding dynamic analysis is studied. Here, the absolute nodal coordinate formulation (ANCF) and the natural coordinate formulation (NCF) are used to accurately describe the large deformations and large overall motions of the flexible tethers and rigid satellites, respectively. Afterwards, through coordinate transformation, the orbital dynamics of the LTSS is obtained and the effects of Coriolis force, centrifugal force, and gravity gradient are analytically derived. Finally, several numerical examples are presented, and the vibrations and stabilities of the LTSS are analyzed via parameter study.

Research on self-propelled performance of multi-body system of wave-driven robot

wave-driven robot is a flexible multi-body dynamic system driven by ocean waves. Self-propelled performance is an important index of wave-driven robot, which includes propulsion performance, resistance performance and rapidity of wave-driven robot, as well as its ability to capture and utilize ocean wave energy. However, the wave-driven robot belongs to flexible multi-body structure, whose dynamic model is more complex compared with conventional ocean vehicle, and the motion of wave-driven robot is completely driven by waves. It is difficult to predict its dynamic response and kinematic performance. In this paper, a numerical method is developed to solve the self-propelled process of wave-driven robot by coupling flexible multi-body dynamics and computational fluid dynamics. Firstly, the flexible multi-body dynamic model of the whole wave-driven robot is established. Secondly, the numerical flow field which can simulate regular waves is established. Finally, the dynamic model is combined with the numerical flow field, and the self-propelled process of the wave-driven robot is simulated by overlapping grid under typical wave parameters, and the propulsion performance, resistance performance and rapidity of wave-driven robot are analysed in depth. Through the test in water pool, it is found that the prediction accuracy of the velocity of float can reach 92.52%.

Dynamic characteristics of high-speed gasoline engine turbocharger based on thermo-elasto-hydrodynamic lubrication bearing model and flexible multibody dynamics method.

A flexible multibody dynamic calculation model based on thermo-elasto-hydrodynamic lubrication bearing model was established. This numerical simulation method provided a more realistic turbocharger calculation model and a more reliable theoretical support for studying the dynamic vibration characteristics of the floating ring bearing turbocharger system. In order to fully consider the dynamic characteristics of each component, the behavior of the floating ring bearing was described by generalized incompressible Reynolds equation in thermo-elasto-hydrodynamic lubrication model. The flexible body substructure models were established by the modal synthesis method. Based on this model, the direct mathematical model of the relationship between the eccentricity of the rotor and the oil film clearance on the turbocharger's surface vibration was established. The influence of eccentricity and oil film thickness on the surface vibration of the turbocharger body was calculated by transient dynamics method. The results showed that the eccentricity of the rotor and the vibration of turbocharger housing were monotonic functions, but the interaction between the whirl of internal and external oil films made the mechanism of the influence of the oil film thickness on the turbocharger body's vibration complicated. The research provided a new idea for the structural vibration and synchronous noise control of the supercharger.

Dynamic Analysis of the Deployment for Mesh Reflector Antennas Driven With Variable Length Cables

Abstract This paper addresses the deployment dynamic analysis of antennas mainly composing of deployable truss and cable net. The antennas are deployed by retracting driving cables, which pass through pulleys fixed on the deployable truss successively. An analytical model is first proposed for the driving cable system where the nodal position and the transmission lengths of the cable segment between two adjacent pulleys are selected as the generalized coordinates. This model could simulate the dynamics of the driving cables with time-varying length. Then, the flexible multibody dynamic model of the deployable antenna including the flexible deployable truss and cable net is established. The absolute nodal coordinate formulation is employed to model the flexible deformation of the truss and the tension of the cable net. The method is demonstrated by analyzing the deployment of a cylindrical mesh antenna. The deployment experiment of the antenna shows that the proposed method can correctly predict the driving force and length variation of the driving cables, the bending deformation of the flexible truss, and the deployment process.

Calculation of the Hinge Moments of a Folding Wing Aircraft during the Flight-Folding Process

A folding wing morphing aircraft should complete the folding and unfolding process of its wings while in flight. Calculating the hinge moments during the morphing process is a critical aspect of a folding wing design. Most previous studies on this problem have adopted steady-state or quasi-steady-state methods, which do not simulate the free-flying morphing process. In this study, we construct an aeroelastic flight simulation platform based on the secondary development of ADAMS software to simulate the flight-folding process of a folding wing aircraft. A flexible multibody dynamic model of the folding wing structure is established in ADAMS using modal neutral files, and the doublet lattice method is developed to generate aerodynamic influence coefficient matrices that are suitable for the flight-folding process. The user subroutine is utilized, aerodynamic loading is realized in ADAMS, and an aeroelastic flight simulation platform of a folding wing aircraft is built. On the basis of this platform, the flight-folding process of the aircraft is simulated, the hinge moments of the folding wings are calculated, and the influences of the folding rate and the aircraft’s center of gravity (c.g.) position on the results are investigated. Results show that the steady-state method is applicable to the slow folding process. For the fast folding process, the steady-state simulation errors of the hinge moments are substantially large, and a transient method is required to simulate the flight-folding process. In addition, the c.g. position considerably affects the hinge moments during the folding process. Given that the c.g. position moves aft, the maximum hinge moments of the inner and outer wings constantly increase.

Solar ray collection rate fluctuation analysis with Monte Carlo Ray Tracing method for space solar power satellite

According to the ideal optical design, the spherical concentrator made by the semi-transparent and semi-reflecting thin film is used in SSPS-OMEGA system. To obtain the continuous power, the PV array should rotate around the spherical concentrator to point the sun when SSPS-OMEGA rotate around the earth on GEO. However, considering the in-orbit assembly, the concentrator is assembled by many planar elements to be approximate to the ideal spherical concentrator. The solar ray collection rate fluctuates in certain scope because the original solar ray path is changed. In addition, planar element is deformed easily by the rotating PV array, which also lead to the fluctuation because the position of the planar element is changed. In this paper, the spherical concentrator is divided into many planar elements by using equal latitude and longitude method. It is studied that the relationship between the number of division layers and the collection rate fluctuation by using Monte Carlo Ray Tracing method. The simulation results indicate that with increasing dividing layers, the collection rate increases and the fluctuation amplitude decreases, which ranges 80.72–83.70% (2.98%) of 24-layers concentrator, ranges 88.45–89.91% (1.47%) of 48-layers concentrator, and ranges 92.46–93.80% (1.33%) of 72-layers concentrator. To solve the deformation of the concentrator, the flexible multibody dynamics model of SSPS-OMEGA is established. Combing the deformation and Monte Carlo Ray Tracing method, it is studied that the relationship between the deformation of the concentrator and the collection rate. The simulation results indicate that the stiffness of 72-layers concentrator is better than 24-layers concentrator and 48-layers concentrator, and the reduction of the collection rate of 72-layers concentrator, which is 0.4%, is less than 24-layers concentrator (1.57%) and 48-layers concentrator (0.81%).

Multi-body dynamics modeling and TMD optimization based on the improved AFSA for floating wind turbines

Compared to the onshore or fixed-bottom offshore wind turbines, floating wind turbines experience larger loads and displacements under combined effects of wind and waves. Therefore, it is necessary to control the structural vibration of floating wind turbines. First, a flexible multi-body dynamics model of a spar-type floating wind turbine is established in SIMPACK. Second, to perform the TMD parameter optimization, a simplified model of the wind turbine is constructed, and unknown parameters in the model are estimated using the Levenberg–Marquardt method. Third, the global optimization ability of the artificial fish swarm algorithm (AFSA) is improved to optimize TMD parameters. Fourth, in order to examine the vibration suppression performance of the designed TMD, a new aero-hydro-elastic-servo model of the wind turbine is built to perform simulations. The simulation results show that the optimized TMD system obtained by the improved AFSA has significant vibration control performance for the floating wind turbine.

Neural Network Control of Space Manipulator Based on Dynamic Model and Disturbance Observer

Space flexible manipulators are convenient for performing on-orbit service; however, the vibration of the end effector is becoming increasingly serious because of the excessive length and mass of the arm. To solve this problem, in this paper, neural network control based on a flexible multibody dynamic model and disturbance observer is proposed. The dynamics model is based on the Lagrangian equation and assumed mode method, and also considers the position and attitude constraint equations of the flexible joint. The combination of a neural network controller and adaptive controller is introduced in detail, and a switching mechanism is added to improve the global stability of the system. Considering the joint module as an independent control system, a disturbance observer is added to the current loop of the control system, and a filter is combined to effectively suppress the influence of friction and dynamic coupling on joint control performance. The effectiveness of the proposed dynamic model and control scheme in terms of vibration suppression is verified in experiments on the self-designed space flexible redundant arm.

Multi-body Dynamic Analysis of the Braking Process for Megawatt Wind Turbine Disc Brake

The dynamic characteristics of brake during the braking process are studied by the method of multi-body dynamics, in order to reduce the vibration of disc brake in the emergency braking process, improving the braking efficiency of the brake of the megawatt wind turbine. The flexible multi-body dynamics model of the mechanical assembly for the whole megawatt wind turbine disc brake is built, including the brake spring, active brake caliper, passive brake caliper and compensatory mechanism. The simulation results under the common working conditions are compared with the test results under the same working condition to verify the model. The influence trends of braking parameters, such as initial braking speed, spring braking force and friction coefficient between the brake pairs, on the dynamic characteristics of the brake are analyzed, which provides the theoretical basis for reducing the severe vibration during the emergency braking process in this paper.

Kriging Model Based Optimization of MacPherson Strut Suspension for Minimizing Side Load using Flexible Multi-Body Dynamics

In a MacPherson strut suspension, which is one of the most popularly used vehicle suspension type, the side load is inevitably generated at the damper when wheel moves in the vertical direction. Since the side load causes friction at the damper and reduces riding comfort, it is important to reduce the side load for improving riding comfort. In this paper, an optimal design is performed to minimize the side load by using Kriging model. Before performing the optimal design, a flexible multi-body dynamics (FMBD) analysis, which can consider both multi-body dynamics and finite element method, is performed to verify the side load generated at the top of damper rod. As a result of optimal design, spring setting positions that minimize the side load are obtained and by using optimal spring setting positions, the suspension FMBD model was constructed.

Flexible multibody dynamics modelling of point-absorber wave energy converters

Abstract As an inexhaustible and environmentally-friendly energy resource, ocean wave power, which is extracted from ocean waves through WECs (wave energy converters), is highly valued by coastal countries. Compared to other types of WECs, point-absorber WECs, the main body of which can be fixed on a platform (e.g. ship), save on installation costs and therefore have concentrated significant interest among researchers and technology developers. In the development of point-absorber WECs, it is crucial to develop a reliable structural model to accurately predict the structural dynamic responses of WECs subjected to wave loadings. In this work, a FMBD (flexible multibody dynamics) model, which is a combination of MBD (multibody dynamics) and FEA (finite element analysis), has been developed for point-absorber WECs. The FMBD model has been applied to the structural modelling of the NOTC (National Ocean Technology Centre) 10 kW multiple-point-absorber WEC. The floater arm tip displacement and velocity obtained from the FMBD model are validated against the values obtained from an analytical model, which is also developed in this work. The results from the FMBD model show reasonable agreement with those from the analytical model, with a relative difference of 10.1% at the maximum value of the floater arm tip displacement. The FMBD model is further used to calculate the stress distributions, fatigue life, deformations, modal frequencies and modal shapes of the structure. The results indicate that WECs are prone to experience fatigue failure, with the shortest fatigue life (2 years) observed in the floater arm. The FMBD model developed in this work is demonstrated to be capable of accurately modelling point-absorber WECs, providing valuable information for designers to further optimise the structure and assess the reliability of WECs.

Research on The Construction of Flexible Multi-body Dynamics Model based on Virtual Components

Focus on the harsh operation condition of space manipulator, which cannot afford relative large collision momentum, this paper proposes a new concept and technology, called soft-contact technology. In order to solve the problem of collision dynamics of flexible multi-body system caused by this technology, this paper also proposes the concepts of virtual components and virtual hinges, and constructs flexible dynamic model based on virtual components, and also studies on its solutions. On this basis, this paper uses NX to carry out model and comparison simulation for space manipulator in 3 different modes. The results show that using the model of multi-rigid body + flexible body hinge + controllable damping can make effective control on amplitude for the force and torque caused by target satellite collision.

Sequential Approximate Optimization of MacPherson Strut Suspension for Minimizing Side Load by Using Progressive Meta-Model Method

In a MacPherson strut suspension, the side load is inevitably generated and it causes friction at the damper reducing riding comfort. In this paper, to solve this problem, progressive meta-model based sequential approximate optimization (SAO) is performed to minimize the side load. To calculate the side load, a wheel travel analysis is performed by using flexible multi-body dynamics (FMBD) model of suspension, which can consider both finite element method (FEM) and multi-body dynamics (MBD). In the optimal design process, meta-model is generated by using extracted sampling points and radial basis function (RBF) method. As a result of optimal design, spring setting positions that minimize the side load are obtained and by using optimal spring setting positions, the suspension FMBD model was constructed.

Noise source identification and transmission path optimisation for noise reduction of an axial piston pump

Reduction of the radiated noise of an axial piston pump by modifying the piston pump shell structure has previously been achieved. However, the main noise sources and transmission paths have scarcely been investigated. In this study, the flexible multi-body dynamic (FMBD) model of an axial piston pump was established, and the main noise source and transmission path were determined. Then, a set of programs to improve the sound quality of the piston pump was developed. Firstly, the finite element analysis method was adopted to numerically analyse the natural modes of the shell, which was verified by an experimental modal analysis using the multiple input and single output technology. Then, AMEsim and Virtual.lab were used to establish the FMBD model of the axial piston pump considering the bearing dynamics and fluid dynamics. The simulated vibration acceleration level from the shell surface was consistent with the experimental test. The finite element method (FEM) and Automatically Matched Layer (AML) technique were employed to acquire the radiated noise from the shell surface in the frequency range of interest, and the noise transmission path was analysed. From the results, it was determined that the excitation force of the swash plate to the cover Y direction is the main noise source. Finally, the main noise transmission path was optimised, and the optimised piston pump radiated noise is reduced by 1.26 dB(A) of the main noise frequency. This research can provide theoretical guidance for engineers to design low noise piston pumps.