Multibody Research Articles

Optimal Design and Dynamic Characteristic Analysis of Double-Link Trapezoidal Suspension for 3WPYZ High Gap Self-Propelled Sprayer

A fast spraying speed, wide working area, and easy operation are the operational advantages of high-clearance boom sprayers. To address the issue of spray boom mechanical vibration affecting the spraying effect, a double-link trapezoidal boom suspension is designed for the 3WPYZ sprayer. This suspension can achieve passive vibration reduction, active balance, and ground profiling. The kinematic model of the boom suspension is established based on D’Alembert’s principle and the principle of multi-body dynamics, and the design factors affecting the stability of the boom are determined. Through orthogonal experimental design and virtual kinematics simulation, the influence of the boom length and orifice diameter of each part on the swing angle and the natural frequency of the boom suspension is investigated. Design-Expert 8.0.6 software is used to analyze and optimize the test results. The optimization results show that, when the connecting boom length LAB is 265 mm, the inner boom suspension boom length LAD is 840 mm, the outer boom suspension boom length LBC is 1250 mm, and the throttle hole diameter d is 4 mm; the maximum swing angle of the boom suspension is reduced by 53.02%. In addition, the natural frequency of the boom is reduced from 1.3143 rad/s to 1.1826 rad/s, and the dynamic characteristic optimization effect is remarkable. The modal analysis results show that the first sixth-order vibration test frequency of the boom sprayer suspension designed in this paper meets the requirements and avoids the influence of external factors. Field tests show that, when the sprayer is excited by the environment at 3.5° to 4°, the boom suspension can reduce the vibration transmitted by the body to a reasonable range. The static analysis shows that the structural design of this study reduces the stress at the connection of the end boom suspension, the maximum displacement, and the maximum stress of the inner boom suspension. The test results of the dynamic characteristics of the implement are basically consistent with the virtual model simulation test results, thus achieving the optimization objectives.

Two-Way Coupling Simulation of Fluid-Multibody Dynamics for Estimating Power Generation Performance of Point Absorber Wave Energy Converters

The objective of the present study is to develop and validate a two-way coupling simulation method between viscous fluid and multibody dynamics to estimate the power generation performance of point absorber wave energy converters. For numerical analysis of fluid dynamics, an enhanced density correction model was proposed to improve the accuracy and stability of the pressure calculation in DualSPHysics, an open-source code based on smoothed particle hydrodynamics (SPH). Through 2D hydrostatic and wave generation simulations, it was seen that the relative error in the average pressure was reduced from 11.81% to 1.64%. In addition, an interaction interface was developed to enable coupling simulation with RecurDyn, a commercial software for the simulation of multibody dynamics. Simulations were performed for a 3D single-body cylinder with a simple shape and a two-body floating wave energy converter (WEC) in regular waves, varying the linear damping coefficient of the power take-off (PTO) system to verify the proposed coupling simulation method for fluid-multibody dynamics. The results were benchmarked against experimental data, revealing a relative error of 1.05% with the experimental results when employing a high damping coefficient for the PTO system. Furthermore, to improve the efficiency of the two-body WEC, two design modifications were suggested; their impact on power generation performance improvement was examined. The developed method is anticipated to contribute to research aiming to enhance the power generation efficiency of various wave power devices with multiple elements and joints, pending further validation and refinement of the simulation approach.

Predictive analysis of the precision remaining useful life of CNC machine tools based on meta-action unit

Taking into consideration the dynamic characteristics of motion error propagation in CNC machine tools, in order to enhance the accuracy of PRUL (precision remaining useful life) prediction analysis, this paper presents a precision degradation modeling approach based on MAU (meta-action unit) for CNC machine tools. Firstly, from the perspective of motion, the CNC machine tool is divided into the smallest unit by the decomposition of FMA (Function-Motion-Action). Secondly, the MBS (multi-body systems) theory is used to topologically describe the motion relationship between the MAU, and the spinor theory is used to model the motion error. Thirdly, considering the influence of multiple error sources on the PRUL of the CNC machine tool MAU, the motion transmission ratio is used to synthesize multiple error sources, and combined with the constructed error model, the precision degradation model of MAU is constructed, and its PRUL is accurately predicted. Finally, the CNC turntable is selected as the experimental subject to compare the proposed method with commonly used methods in terms of rationality, applicability, and simplicity, and the results verify the applicability and correctness of the method proposed in this paper.

Dynamic Modeling, Dynamic Characteristics, and Slight Self-Guidance Ability at High Speeds of Independently Rotating Wheelset for Railway Vehicles

For better small-radius curve negotiation performance, the independently rotating wheelset has the potential to be equipped in urban rail transit. As a crucial part of the running gear, its dynamic characteristics directly affect the railway vehicle’s stability and curve negotiation ability. This study follows a model–simulation–experiment method to delve into the dynamic process and steady convergent process of the independently rotating wheelset. An improved mathematical dynamic model of the independently rotating wheelset is established, considering the gravitational restoring forces of the wheelset and different creepages between the left and right wheels. In addition, the gyroscopic effects on the independently rotating wheelset with positive wheel tread conicity and at high speeds are introduced and analyzed. With variations in the longitudinal speed and yaw suspension coefficients, three kinds of motions, derailment, hunting, and offset running, occur on the independently rotating wheelset. We find that the gyroscopic effects contribute to the slight self-guidance ability of the independently rotating wheelset, causing a hunting motion at high speeds. Through sufficient simulations, the improved mathematical dynamic model is verified to be closer to the dynamic model built in the general multibody system simulation software SIMPACK 2018 than the classical mathematical dynamic model. Further, we perform experiments on a scaled independently rotating wheelset experiment system. The dynamic characteristics derived from theoretical analysis, especially the slight self-guidance ability at high speeds, are verified.

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.

A Planar Cable-Driven Under-Sensing Model to Measure Forces and Displacements

This paper presents a planar cable-driven model of a simple mechanism that is able to measure forces and displacements. Recently, a preliminary study based on a cable-driven sensitive mechanism was presented to the research community, underlining the innovative characteristics of the model in under-actuation and under-sensing. The core of the research work was to conceive a compliant system able to measure forces and displacements from a point located in a different zone with respect to the one where the force is applied, and this is possible thanks to cable-driven systems. In this paper, a new simplified model with respect to our published work is presented, reducing the number of cables and including the calculation of friction in the developed test bench. The formulation to calculate the displacement of the point of the applied force and the formulation to calculate the force are presented and validated with a simulation and by using a real test bench for experimentation. A multi-body system is used for the simulation, and the results are compared and discussed. Four cases are analysed to test the formulation, including the friction in pulleys and in the joint connection between the mobile part and the fixed part of the mechanism. Future works will be oriented toward reducing the dimensions of the conceived mechanism in order to implement the model in minimally invasive robotic surgery instruments.

Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-α Time Integration

In this paper, the direct differentiation of generalized-α time integration is derived, equations are introduced and results are shown. Although generalized-α time integration has found usage, the derivation and the resulting equations for the analytical sensitivity analysis via direct differentiation are missing. Thus, here, the sensitivity equations of generalized-α time integration via direct differentiation are provided. Results with generalized-α are compared with Newmark-β time integration and their sensitivities with numerical sensitivities via forward finite differencing in terms of accuracy and performance. An example is shown for each linear structural dynamics and flexible multibody dynamics.

Simulation of a control method for active kinesiotherapy with an upper extremity rehabilitation exoskeleton without force sensor

Exoskeleton-aided active rehabilitation is a process that requires sensing and acting upon the motion intentions of the user. Typically, force sensors are used for this. However, they increase the weight and cost of these wearable devices. This paper presents the methodology for detecting users’ intentions only with encoders integrated with the drives. It is unique compared to other algorithms, as enables active kinesiotherapy while adding no sensory systems. The method is based on comparing the measured motion with the one computed with the idealised model of the multibody system. The investigation assesses the method’s performance and its robustness to model and measurement inaccuracies, as well as patients’ unintended motions. Moreover, the PID parameters are selected to provide the optimal regulation based on the dynamics requirements. The research proves the presented concept of the control approach. For all the tests with the final settings, the system reacts to a change in the user’s intention below one second and minimises the changes in proportion between the system’s acceleration and the generated user’s joint torque. The results are comparable to those obtained by EMG-based systems and significantly better than low-cost force sensors.

Computational Fluid Dynamics Simulation Study on Aerodynamic Characteristics under Unfavorable Conditions during Flight Phase in Ski Jumping

Objective: The stability of the flight phase in ski jumping is crucial for athletes’ performance and safety. This study aims to investigate the influence of unfavorable conditions on aerodynamic characteristics and flight stability through computational fluid dynamics (CFD) numerical simulations. Methods: The ski jumper and the skis are considered a multi-body system. A detailed three-dimensional (3D) model of this multi-body system under a commonly observed posture during flight is established. The Partially Averaged Navier–Stokes (PANS) turbulence model is employed, and CFD simulations are conducted to predict the aerodynamic characteristics of the multi-body system under lateral environmental wind and asymmetric postures during the flight phase. The conditions of asymmetric postures include yaw rotation and roll rotation. Results: (1) Lateral environmental wind generated a yaw force, yaw moment, and roll moment, which influenced the lift, drag, and pitch moment of the athlete. These forces and moments were relatively small at lower wind speeds (less than 3 m/s) and became more significant at higher wind speeds (greater than 4.5 m/s). (2) Under the influence of yaw rotation or roll rotation, the multi-body system exhibited a noticeable yaw force, yaw moment, and roll moment, all showing a monotonic increasing trend. Moreover, they had a significant impact on the lift, drag, and pitch moment of the multi-body system. Conclusion: (1) The influence of unfavorable conditions was complex, resulting in a significant yaw force, yaw moment, and roll moment on the multi-body system. The adverse effects of roll rotation were generally greater than those of yaw rotation. (2) The multi-body system exhibited self-stabilizing tendencies in yaw and roll. This phenomenon can provide a solution to maintain flight stability by employing appropriate yaw or (and) roll rotation angles, effectively compensating for or even eliminating the adverse effects of lateral environmental wind. (3) Understanding the mechanisms of how unfavorable conditions affect aerodynamic characteristics and stability during flight in ski jumping can provide valuable assistance for real-time prediction and decision making during competitions, as well as scientific guidance for training athletes’ stable flight control and techniques for improving their sport performance.

A Kinematic Variable for Analyzing Snake Robot Dynamics

This paper presents a modern mathematical method to analyze snake robot dynamics. The method is rooted in three facets of contemporary mathematics: Cartan’s concept of endowing all moving bodies with their own reference frames, Lie group theory with its associated algebra, and a compact notation. Building upon previous work with cranes, this paper presents a new kinematic variable for determining the equations of motion for any number of rigid bodies linked in a tree structure with revolute joints. The core equations simplify the analysis and introduce a notation for the coordinate transformation matrix that directly ports to coding. The resulting equations can be readily applied using symbolic math packages and direct numerical solvers. In addition to its primary role as a research document, this paper also serves as an expository educational resource, presenting the methodology in a semi-tutorial format. The culmination of this work yields a comprehensive 3D forward-kinematics analytical model for analyzing the multi-body dynamics of a snake robotic system.

An improved methodology to restrict the range of motion of mechanical joints

Joints with rotational degrees of freedom, for instance, revolute, spherical, or universal joints, are commonly utilized in real-world scenarios. In the multibody systems methodology, mechanical joints usually are formulated as classical kinematic constraints such that there is no restriction of the range of motion (RoM) of the joint. Thus, the formulation must include additional restrictions to prevent the joints from performing unacceptable movements and to avoid unrealistic configurations of the connected bodies. Therefore, the aim of this work is to propose a methodology to restrict the RoM of mechanical joints. Joint resistance moments are applied to the bodies connected by the joint to mimic the dissipative behavior of the materials constituent of joints and to prevent unacceptable configurations of those bodies. The proposed methodology aims to extend and improve a previously published study, specifically in the definition of the RoM limits, calculation of the penalty moments, and establishment of their direction of application. Enhanced methods to deal with the detection of unacceptable joint configurations, namely the elliptical and polynomial approaches, are proposed. A parametrization procedure is described to correctly calculate the direction of the penalty moments to apply to the connected bodies. The methodology is investigated in the dynamic modeling and simulation of one demonstrative example of application, namely a simple pendulum. A parametric analysis is performed to assess the influence of the methodology parameters in the response of the model. The methodology allows the correct restriction of the RoM of joints, while preserving the mechanical energy of the system.

Co-simulation of drag reduction of placoid scale oscillation driven by micro Stewart mechanism

To reduce the drag of underwater vehicles during navigation, this paper proposes a skin imbricated with bionic placoid scale based on micro-Stewart mechanism. The skin is composed of bionic shark placoid scales and Stewart structure with multi-dimensional motion characteristics, which can well simulate the multi-dimensional oscillation motion of shark scales during swimming. A co-simulation platform of computational fluid dynamics and multi-body dynamics is established to investigate the impact of oscillating parameters (heave and pitch) on the drag reduction performance of the skin. The novel skin shows a remarkable drag reduction performance, with a relative drag reduction rate over 20% (up to 33%) in the range of Re = 105 ∼ 106. It is found that the oscillation motion generated by the placoid scales can cause the fluid inside the skin to spray upward, which can increase the thickness of the fluid boundary layer, revealing the drag reduction mechanism of the skin to some extent. Moreover, the pitching motion of the placoid scale is more effective in drag reduction than the heaving motion in the condition of Re = 105. It is expected that applying this skin to underwater vehicles can achieve satisfactory drag reduction effects.

Adapting geometry-based polygonal contacts for simulating faulty rolling bearing dynamics

Rolling bearings are a leading cause of equipment breakdowns in electrical machines, underscoring the significance of predictive maintenance strategies. However, the given methods require high-quality big data, which is challenging to acquire, especially for faulty cases. Simulation models offer an alternative by generating large datasets to complement experimental data. However, bearings involve complex contact-related phenomena, such as slipping and clearance. Therefore, generating realistic data comparable to the real-world necessitates accuracy. Our study presents a multibody simulation system of a motor bearing, incorporating a geometry-based polygonal contact method (PCM), which accurately captures nonlinear bearing dynamics and allows for the simulation of various contact geometries. We introduce a systematic approach to adjust the PCM contact properties for rolling bearings, referencing the well-established Hertzian theory. Both healthy and faulty bearings with a local outer ring fault were simulated. The simulated output was a relative shaft displacement, experimentally validated using a capacitive sensor. Our model successfully demonstrates the potential to employ geometry-based contacts for generating realistic data on faulty bearings with the aim of predictive maintenance.

Multiple Working Mode Control of Robotic Operations on Mechanisms With Unmodelled Constraints With Online Mode Switching

Robotic operations such as opening doors in an unstructured environment pose a challenge for robot control due to unmodelled constraints. In this article, a multiple working mode approach is proposed to control a mobile serial robot manipulator to perform operations on mechanisms with unmodelled constraints. The multiple working mode control switches the working mode of a number of active joints during the operation to relax the problem of over-actuation of the constrained robot manipulator when modeling errors cause excessive internal and external reaction forces. Three practical criteria are derived for the assignment of active and passive control modes; two based on the coordinate partitioning method for multibody dynamics, and another based on minimizing task friction forces. The proposed control method has been implemented on a mobile reconfigurable robot, performing constrained motion along an elliptical trajectory, similar to a door-opening task. Simulation and experimental results are presented to show the effectiveness of the proposed control approach.

Optimizing and designing upper-stage separation spring of lifting-body rocket

Because the upper-stage separation of a lifting-body rocket is difficult under the low-altitude and high-speed flight environments, an upper-stage separation scheme based on the separation spring is proposed. The integration of ADAMS and MATLAB realizes the multi-body dynamics simulation analysis of upper-stage separation. The experimental design method is used to carry out the target simulation and calculation of the upper-stage separation process, with the separation condition deviation and the separation spring deviation considered at the same time, thus ensuring the reliability of the separation scheme. In order to further optimize the separation scheme, an upper-stage separation optimization model is established with the Isight software, and the mass of separation spring is optimized with the multi-island genetic algorithm and significantly reduced by 48.87% under the condition that the upper-stage separation process satisfies all constraints, thereby effectively improving the performance of the lifting-body rocket.

Numerical Simulation Research on Aerodynamic Characteristics during Take-Off Phase in Ski Jumping

In view of the inability to directly and accurately obtain an athlete’s aerodynamic force during the take-off phase through the wind tunnel test, the athlete’s aerodynamic force and surrounding flow field form under different take-off postures are obtained through numerical simulation research, and the effects of different take-off modes on the aerodynamic characteristics during take-off in ski jumping are discussed. The multi-body system composed of the athlete and skis was selected as the research object. By using a partially averaged Navier–Stokes (PANS) turbulence model and a 3D numerical simulation of computational fluid dynamics (CFD), the aerodynamic characteristics of the athlete under different take-off postures were predicted. The take-off modes include the knee-push-hip (KPH) mode and hip-drive-knee (HDK) mode, and the hip joint angle of the HDK mode is significantly greater than that of the KPH mode. First, the aerodynamic force ratio of the athlete’s torso and legs is obviously large. Although the aerodynamic forces of arms themselves are not obvious, they have a great impact on the overall aerodynamic characteristics of the athlete, so the posture of the arms cannot be ignored. The total drag and moment of the HDK mode are significantly higher than that of the KPH mode, and the lift-to-drag ratio of the HDK mode is significantly lower than that of the KPH mode. At first, the total lift of the HDK mode is higher than that of the KPH mode, but in the last attitude, the total lift of the HDK mode does not rise but fall, and finally, the total lift of the HDK mode is lower than that of the KPH mode. The aerodynamic characteristics change dramatically during the take-off phase, and the aerodynamic characteristics of the two take-off modes are quite different, and these changes and differences are difficult to observe during real training and at the competition site. The KPH mode has an obvious aerodynamic advantage over the HDK mode. During the take-off process, the athlete should increase the force generated by the knee joint extension and appropriately reduce the speed of the hip joint extension, control the using force order of the lower limb joints, and push the hip joint extension by the knee joint extension in order to avoid issues, such as the hip joint angle being too large, the hip joint extension angle being too fast, the center of gravity being too far back, and other problems. Studying the aerodynamic characteristics during the take-off phase provides valuable insights for athletes to achieve favorable flight postures after take-off, offering scientific guidance to improve their training strategies and enhance their competitive performance.

Research on the dynamics of a heavy mechanized bridge in the deployment phase of the lifting frame

This article presents a dynamic model of the TMM-3M heavy mechanized bridge during the frame lifting stage, which is driven by a hydraulic system, constituting the initial phase of the bridge erection process. The model is constructed as a multi-body dynamic system, taking into account the elastic deformation of the rear outriggers, front tires, and front suspension system. The research model integrates a mechanical system controlled by hydraulic cylinders, with pressure being considered as a variable reacting to external loads during the system's operation. Lagrangian equations of the second kind are utilized to establish a system of differential equations describing the oscillations of the system and form the basis for investigating the dynamics of the frame lifting process. The system of differential equations is solved numerically using MATLAB simulation software based on the Runge-Kutta algorithm. The study has revealed laws regarding the displacement and velocity of components within the system, evaluating the stability of the TMM-3M heavy mechanized bridge during operation. This research paves the way for a comprehensive understanding of the working process of the TMM-3M heavy mechanized bridge, aiming for practical improvements to minimize deployment or retrieval time, reduce the number of deployment team members, enhance the automation of the operation process to reduce the workload for operators

A discrete adjoint gradient approach for equality and inequality constraints in dynamics

The optimization of multibody systems requires accurate and efficient methods for sensitivity analysis. The adjoint method is probably the most efficient way to analyze sensitivities, especially for optimization problems with numerous optimization variables. This paper discusses sensitivity analysis for dynamic systems in gradient-based optimization problems. A discrete adjoint gradient approach is presented to compute sensitivities of equality and inequality constraints in dynamic simulations. The constraints are combined with the dynamic system equations, and the sensitivities are computed straightforwardly by solving discrete adjoint algebraic equations. The computation of these discrete adjoint gradients can be easily adapted to deal with different time integrators. This paper demonstrates discrete adjoint gradients for two different time-integration schemes and highlights efficiency and easy applicability. The proposed approach is particularly suitable for problems involving large-scale models or high-dimensional optimization spaces, where the computational effort of computing gradients by finite differences can be enormous. Three examples are investigated to validate the proposed discrete adjoint gradient approach. The sensitivity analysis of an academic example discusses the role of discrete adjoint variables. The energy optimal control problem of a nonlinear spring pendulum is analyzed to discuss the efficiency of the proposed approach. In addition, a flexible multibody system is investigated in a combined optimal control and design optimization problem. The combined optimization provides the best possible mechanical structure regarding an optimal control problem within one optimization.

Passive Safety Assessment of Railroad Trains in Moose Herd Collision Scenarios

Moose herd–train collisions represent one of the potential hazards that railway operations must contend with, making the assessment of passive train safety in such scenarios a crucial concern. This study analyzes the responses of bullet trains colliding with moose herds and investigates the influence of various factors under these conditions. To achieve this goal, a multibody (MB) model was developed using the MADYMO platform. The displacement of the moose’s center of gravity (CG) was employed to assess the safety boundaries, while the relative positions between the wheels and rails were used to evaluate the risk of derailment. The findings revealed that the collision forces exhibited multi-peak characteristics that were subsequently transmitted to the wheel–rail contact system, resulting in disturbances in the relative positions of the wheels and rails. However, these disturbances did not reach a level that would induce train derailment. Furthermore, larger moose herds exhibited higher throw heights, although these heights remained within safe limits and did not pose a threat to overhead lines. The primary safety risk in moose–train collisions stemmed from secondary collisions involving moose that had fallen onto the tracks and oncoming trains. This study offers valuable insights for enhancing the operational safety of high-speed trains and safeguarding wildlife along railway corridors.

Integration of brake block thermal equations within a railway vehicle multibody model: a multiphysics approach

ABSTRACT The paper shows the development of a finite-difference (FD) railway brake block thermal model and its integration within the multibody (MB) formalism of the Simpack commercial code. The block nodal temperatures are included among the dynamic states computed by the MB solver, through the definition of a user-defined force element, which determines the braking torque based on the applied brake cylinder pressure. The proposed approach overcomes the main limitations of existing detailed railway vehicle models, which solve the thermal and vehicle dynamics equations in different computational environments. Furthermore, the new strategy can thrust the development of models able to account for the coupling between the wheel and block thermal behaviour and the whole vehicle dynamics. Preliminary simulations of drag and stop braking operations of a reference European freight waggon prove that the proposed model is able to effectively consider the main heat fluxes and nonlinearities involved in tread braking operations.