Multibody System Dynamics Research Articles

Computational dynamics of soft machines

Soft machine refers to a kind of mechanical system made of soft materials to complete sophisticated missions, such as handling a fragile object and crawling along a narrow tunnel corner, under low cost control and actuation. Hence, soft machines have raised great challenges to computational dynamics. In this review article, recent studies of the authors on the dynamic modeling, numerical simulation, and experimental validation of soft machines are summarized in the framework of multibody system dynamics. The dynamic modeling approaches are presented first for the geometric nonlinearities of coupled overall motions and large deformations of a soft component, the physical nonlinearities of a soft component made of hyperelastic or elastoplastic materials, and the frictional contacts/impacts of soft components, respectively. Then the computation approach is outlined for the dynamic simulation of soft machines governed by a set of differential-algebraic equations of very high dimensions, with an emphasis on the efficient computations of the nonlinear elastic force vector of finite elements. The validations of the proposed approaches are given via three case studies, including the locomotion of a soft quadrupedal robot, the spinning deployment of a solar sail of a spacecraft, and the deployment of a mesh reflector of a satellite antenna, as well as the corresponding experimental studies. Finally, some remarks are made for future studies.

Study on Coupling Dynamics Theory and Simulation of Advance Support and Tunnel Surrounding Rock

In order to study the dynamic coupling problem of tunnel advance support equipment and surrounding rock, the roof dynamics model based on thin plate theory is established in this paper; Advance support equipment is simplified, and the differential equations of motion of each component to establish the dynamic model of the whole; finally considering multi support conditions of advanced support roof system coupling dynamic model. The dynamic response of the coupling dynamic model under various working conditions is studied by using multi-body system dynamics simulation software RecurDyn. Through simulation we get the advance support top beam and retaining plate in dynamic response of collateral roadway conditions. The research conclusions of this paper can provide a theoretical basis for the research and design of advance support equipment in fully mechanized roadway.

Influences of system uncertainties on the numerical transfer path analysis of engine systems

Practical mechanical systems operate with some degree of uncertainty. In numerical models uncertainties can result from poorly known or variable parameters, from geometrical approximation, from discretization or numerical errors, from uncertain inputs or from rapidly changing forcing that can be best described in a stochastic framework. Recently, random matrix theory was introduced to take parameter uncertainties into account in numerical modeling problems. In particular in this paper, Wishart random matrix theory is applied on a multi-body dynamic system to generate random variations of the properties of system components. Multi-body dynamics is a powerful numerical tool largely implemented during the design of new engines. In this paper the influence of model parameter variability on the results obtained from the multi-body simulation of engine dynamics is investigated. The aim is to define a methodology to properly assess and rank system sources when dealing with uncertainties. Particular attention is paid to the influence of these uncertainties on the analysis and the assessment of the different engine vibration sources. Examples of the effects of different levels of uncertainties are illustrated by means of examples using a representative numerical powertrain model. A numerical transfer path analysis, based on system dynamic substructuring, is used to derive and assess the internal engine vibration sources. The results obtained from this analysis are used to derive correlations between parameter uncertainties and statistical distribution of results. The derived statistical information can be used to advance the knowledge of the multi-body analysis and the assessment of system sources when uncertainties in model parameters are considered.

Dynamics and Precision Control of Uncertain Tumbling Multibody Systems

This paper deals with the precision control of tumbling multibody systems with uncertainties present in the descriptions of their mathematical models. A generic tumbling multibody system consisting of a rigid body with internal degrees of freedom is used. A two-step control methodology is developed. First, a nominal system is conceived that best approximates the actual physical system. An analytical dynamics-based control methodology is used to obtain the nominal control force that ensures that this nominal system satisfies the control requirements. This is done using the control methodology proposed by Udwadia (“Optimal Tracking Control of Nonlinear Dynamical Systems,” Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 464, 2008, pp. 2341–2363). Second, an additional compensating generalized control force is designed to ensure that the actual controlled (uncertain) system tracks the trajectories of the nominal system so that the control requirements are also met by the actual system. This paper deals primarily with the second step and its combination with the first. Uncertainties in both the description of the system as well as the forces acting on it are considered. No linearizations or approximations are made in either of the steps, and the full nonlinear dynamical system is considered. The efficacy of the control methodology is demonstrated by applying it to two tumbling uncertain multibody dynamical systems.

System-Based Approaches for Structural Optimization of Flexible Mechanisms

This paper reviews the state-of-the-art methods to perform structural optimization of flexible mechanisms. These methods are based on a system-based approach, i.e. the formulation of the design problem incorporates the time response of the mechanism that is obtained from a dynamic simulation of the flexible multibody system. The system-based approach aims at considering as precisely as possible the effects of nonlinear dynamic loading under various operating conditions. Also, the optimization process enhances most existing studies which are limited to (quasi-) static or frequency domain loading conditions. This paper briefly introduces flexible multibody system dynamics and structural optimization techniques. Afterwards, the two main methods, named the weakly and the fully coupled methods, that couple both disciplines are presented in details and the influence of the multibody system formalism is analyzed. The advantages and drawbacks of both methods are discussed and future possible research areas are mentioned.

New Developments in Multibody System Dynamics and Its Applications 2015

New Developments in Multibody System Dynamics and Its Applications 2015

The Kalker book of tables for non-Hertzian contact of wheel and rail

ABSTRACTA new regularisation of non-elliptical contact patches has been introduced, which enables building the look-up table called by us the Kalker book of tables for non-Hertzian contact (KBTNH), which is a fast creep force generator that can be used by multibody dynamics system simulation programs. The non-elliptical contact patch is regularised by a simple double-elliptical contact region (SDEC). The SDEC region is especially suitable for regularisation of contact patches obtained with approximate non-Hertzian methods for solving the normal contact problem of wheel and rail. The new regularisation is suitable for wheels and rails with any profiles, including worn profiles.The paper describes the new procedure of regularisation of the non-elliptical contact patch, the structure of the Kalker book of tables, and parameterisation of the independent variables of the tables and creep forces.A moderate volume Kalker book of tables for SDEC region suitable for simulation of modern running gears has been computed in co-simulation of Matlab and program CONTACT.To access the creep forces of the Kalker book of tables, the linear interpolation has been applied.The creep forces obtained from KBTNH have been compared to those obtained by program CONTACT and FASTSIM algorithm. FASTSIM has been applied on both the contact ellipse and the SDEC contact patch. The comparison shows that KBTNH is in good agreement with CONTACT for a wide range of creepage condition and shapes of the contact patch, whereas the use of FASTSIM on the elliptical patch and SDEC may lead to significant deviations from the reference CONTACT solutions.The computational cost of calling creep forces from KBTNH has been estimated by comparing CPU time of FASTSIM and KBTNH. The KBTNH is 7.8–51 times faster than FASTSIM working on 36–256 discretisation elements, respectively.In the example of application, the KBTNH has been applied for curving simulations and results compared with those obtained with the creep force generator employing the elliptical regularisation. The results significantly differ, especially in predicted creepages, because the elliptical regularisation neglects generation of the longitudinal creep force by spin creepage.

Active Vibration Control Design Method Based on Transfer Matrix Method for Multibody Systems

AbstractThe efficient vibration control of complex multibody systems is an important issue in engineering design and has drawn substantial attention in the field of multibody system dynamics and co...

Application of hyper-dual numbers to rigid bodies equations of motion

This paper formulates the equations of motion of a rigid body in a hyper-dual number form. By introducing the hyper-dual Jacobian matrix, hyper-dual velocity, hyper-dual momentum and the hyper dual inertia operator, while taking advantage of the “automatic differentiation” feature of the dual numbers, rigid body equations of motion are derived in a compact form with no need for further time differentiation. An open kinematic chain robot manipulator is presented as an exemplary application of the hyper-dual scheme to multi-body system dynamics.

SMA actuator material model with self-sensing and sliding-mode control; experiment and multibody dynamics model

Shape memory alloys (SMA) can be used to create actuators that are simple, high strength, and inexpensive. These benefits come at the cost of low electrical efficiency, moderate lifetime, and complex mechanical behavior that makes them difficult to design into new applications and products. To improve the integration of SMA actuators—in particular thin SMA wires heated by passing electric current through them—into modern mechanical applications, we have created tools for modeling SMA mechanical and thermal behavior in dynamic systems and under feedback controls. Thermo-electro-mechanical constitutive models are implemented in a multibody dynamics software where they are easily applied to an actuator emplaced in a multibody dynamic system. Mechanical behavior is modeled with 1D constitutive equations. The material state determines the electrical resistivity of the material which drives ohmic heating, while thermal cooling is based on a heat transfer analysis of thin cylinders. These models contain states which are very difficult to measure experimentally (such as crystal phase fraction) and thus provide insight into the material behavior and design that experimental results cannot offer. This thermomechanical model is used in conjunction with sliding mode control—historically difficult to simulate in numerically integrated models—to develop a working ball-on-a-beam setup in which the ball position is controlled via current passed through an SMA wire and with application of an original self-sensing method. The constitutive model is developed in the multibody dynamics software MSC ADAMS and validated through the simulation of the same system.

Accuracy of Wearable Sensors for Estimating Joint Reactions

Miniature wireless inertial measurement units (IMUs) hold great promise for measuring and analyzing multibody system dynamics. This relatively inexpensive technology enables noninvasive motion tracking in broad applications, including human motion analysis. This paper advances the use of an array of IMUs to estimate the joint reactions (forces and moments) in multibody systems via inverse dynamic modeling. In particular, this paper reports a benchmark experiment on a double-pendulum that reveals the accuracy of IMU-informed estimates of joint reactions. The estimated reactions are compared to those measured by high-precision miniature (6 degrees-of-freedom) load cells. Results from ten trials demonstrate that IMU-informed estimates of the three-dimensional reaction forces remain within 5.0% RMS of the load cell measurements and with correlation coefficients greater than 0.95 on average. Similarly, the IMU-informed estimates of the three-dimensional reaction moments remain within 5.9% RMS of the load cell measurements and with correlation coefficients greater than 0.88 on average. The sensitivity of these estimates to mass center location is discussed. Looking ahead, this benchmarking study supports the promising and broad use of this technology for estimating joint reactions in human motion applications.

Application of Multibody System Dynamics in Marine Machinery

The multibody system dynamics is to establish mathematical model suitable for computer program to solve the kinematics and dynamics analysis, and seek the efficient and stable numerical method, its fundamental purpose is computer application technology for dynamic analysis and simulation of complex mechanical system. Through the computer to solve the multibody system dynamics problems, engineers the main work only need to according to the reality of the situation build suitable dynamics model, and submit to the computer solution. Moreover, the computer can also provide the results analysis, the extremely difficult complex mechanical problems which cannot even solve can now use computer calculation function to facilitate the solution. In the early days, the multi-body system dynamics is only applicable to the aviation machinery and robot, and now, with the continuous deepening of its theory, multibody system dynamics has a wide range of applications in the ship mechanical design. Below, we first briefly introduce the basic theory of multi-body system dynamics, and then focus on the application of multi-body system dynamics in the ship mechanical design.

基于高斯最小拘束原理的广义质量矩阵奇异性问题研究

高斯最小拘束原理为含约束的多体系统动力学提供了一种新的建模思路：将以求解微分代数方程为主的动力学问题引入到求函数最小值的优化问题的框架中。质量矩阵奇异性问题是在常规多体系统动力学求解框架下经常遇到的难点问题。本文从建模方式出发研究了经典动力学框架下的难点问题，通过引入广义逆，建立了广义质量矩阵奇异情形下的高斯最小拘束原理，研究了针对奇异性问题的优化方法的数值求解策略。算例中分别采用了优化方法及第一类拉格朗日方程进行了建模及数值模拟。算例表明了文中方法在解决该类奇异性问题时的有效性。 Gauss principle of least constraints provides a new modeling method for dynamics of multibody systems, which changes dynamical problem of mainly solving differential-algebra equation into the frame of solving minimum. The problem of the mass singular matrix is the difficulty in tradi-tional dynamics of multibody systems. We start with new modeling method for solving the singular problems. By introducing the generalized inverse, the Gauss principle of least constraints for matrix singular matrix and solving strategies for optimization method are established. In the example, the optimization and the Lagrange equation of the first kind are used to model and calculate. The example validates the optimization method for this kind of singular problems.

Integration of ANCF continuum-based soil plasticity for off-road vehicle mobility in multibody system dynamics

In this paper, we outline the formulation and implementation of an inelastic continuum-based soil model in a multibody system (MBS) simulation environment. The generality of the approach allows for the simulation of general vehicle manoeuvres over unprepared terrain. Unlike other approaches, both the material and vehicle in this investigation can be altered independently. This ability allows for a greater degree of freedom in the design of computational models for the evaluation of off-road tracked vehicles. In this investigation, the soil model is developed using a hexahedral absolute nodal coordinate formulation (ANCF) finite element. The Drucker-Prager plastic material is used to model the behaviour of the soil and offers a good starting point for computational plasticity in terramechanics applications. A convergence study for a single link interacting with ANCF soil is provided. The capabilities and generality of this implementation is demonstrated using an armoured personnel carrier (APC) model.

Integration of ANCF continuum-based soil plasticity for off-road vehicle mobility in multibody system dynamics

Integration of ANCF continuum-based soil plasticity for off-road vehicle mobility in multibody system dynamics

Application of Hilber-Hughes-Taylor- method to dynamics of flexible multibody system with contact and constraint

Numerical characteristics of the Hilber-Hughes-Taylor- (HHT-) method for the differential-algebraic equations (DAEs) in impact dynamics of flexible multibody systems are investigated. The research is based on a dynamic process of a flexible beam rotating about a fixed axis, whichis under the action of gravity and collides with a rigid plane. Therefore, the dynamic transformation and solution of flexible multibody system are divided into two parts. The Lagrange's equations of the second kind are used to derive the dynamic equations before and after impact, whereas the contact constraint method (CCM) is adopted to simulate the contact process. Compared with other methods, the CCM can describe the contact process accurately and avoid choosing the additional parameters. A set of the differential equations are transformed into a set of the DAEs due to the added constraint equations into impact process. Normally the dynamic equations of the flexible multibody system are index-3 DAEs. Solving a system of the index-3 DAEs directly by an integration algorithm would be subject to ill-conditioning and poor global convergence properties, so it is reasonable to find the methods that avoid both drawbacks and dependence on the constraint information. In order to solve this complex process, the HHT- method is used in the impact dynamic simulation by introducing the Gear-Gupta-Leimkuhler formulation. The coefficient of the HHT- method can be used to control the numerical dissipation, and it also represents asymptotic annihilation of the high frequency response. The smaller the value of , the more the damping is induced in the numerical solution. The Baumgarte's stabilization method is the most famous one for index-3 DAEs. Unfortunately, no general way can be adopted to determine the coefficients of the Baumgarte's stabilization method. It is the main reason for the numerical stability problems. It is necessary to study the influences of coefficients of the former two methods. Simultaneously, the simulation results from the HHT- method are compared with those from the Baumgarte's stabilization method to calculate the CCM model, and the Newmark method is used to solve the ODEs by using the continuous contact force model. The influence of the modal truncation N on the numerical method is also taken into account. Furthermore, the influences of N and the coefficient of HHT- method on the velocity and acceleration constraints in the multibody system are analyzed. Results have shown that the choice of the stabilization coefficients exerts a greater influence on the simulation results, such as the dynamic responses and the constraints, than that of the coefficient . Meanwhile, the HHT- method has an influence on the choice of coefficient and numerical damping properties. This numerical damping property can reduce the effect of high order modes induced by impact. Finally, the increase of N causes the sharpening default of both velocity and acceleration constraints.

Maneuver and Active Vibration Suppression of Free-flying Space Robot

This work studies the maneuver control and vibration suppression of a flexible free-flying space robot using variable-speed control moment gyros as actuators. A novel flexible space manipulator is designed. The dynamics of the flexible multibody system is derived by using Kane method. Based on the singular perturbation approach, the dynamics of the flexible manipulator is decoupled into a slow subsystem and a fast subsystem. The slow subsystem is associated with the rigid motion dynamics, and the fast subsystem is related to the link flexible dynamics. A composite control strategy is proposed as a combination of two controllers for these subsystems. An adaptive sliding mode controller is designed for the slow subsystem, and an adaptive controller is designed for the fast subsystem. Uncertainty estimation can be achieved by the adaptive terms of the composite controller. A weighted robust pseudo-inverse steering law is proposed for the variable-speed control moment gyros. Numerical results demonstrate that the proposed composite controller is robust to parameter uncertainties and external disturbances.

Coupling multibody system and granular dynamics application to a 2D benchmark

We present a benchmark to experimentally validate the method we have developed to simulate mechanical devices interacting with granular media. Consequently the method we develop is able to solve problems involving bilateral and unilateral constraints. The mechanical device is modelled with the multibody system approach and is described by the use of relative coordinates. With these coordinates, the bilateral constraints are mainly due to loop-closure conditions (or specific bilateral constraints such as imposed screw-joint motion). The bilateral constraints are solved thanks to the coordinate partitioning method. The problem of contact dynamics, which introduces the unilateral constraints, is solved by a non-linear Gauss-Seidel procedure applied in the contacts coordinates. The procedure accounts for the constrained motion of the mechanism because the coordinate partitioning is also applied to the mapping between the contacts coordinates and the generalized coordinates. Consequently the solution of the unilateral constraints problem is locally compatible with the set of bilateral constraints coming from the mechanical system. The proposed planar benchmark consists of a modified four-bar mechanism blending a set of disks contained in a vibrating box. The numerical results reveals the influence of the vibration frequency on the granular compactness and thus the mechanism motion.

Soft Machines: Challenges to Computational Dynamics

The paper surveys the recent studies of authors on the dynamic modeling and simulation of soft machines in the frame of multibody system dynamics. The studies focus on the geometric nonlinearity of coupled overall motion and large deformation of a soft body, the physical nonlinearity of a soft body made of hyper-elastic or elastoplastic materials, the frictional impacts and contacts of soft bodies, and the efficient dynamic computation algorithm of soft multibody systems governed by a set of differential-algebraic equations of very high dimensions. The paper presents the validation of proposed approach through three case studies, including the locomotion of a soft quadrupedal robot, the spinning deployment of a solar sail of spacecraft, and the deployment of a mesh reflector of satellite antenna, as well as the corresponding experimental studies. Finally, the paper gives some remarks on future researches.

Instantaneous Metabolic Cost of Walking: Joint-Space Dynamic Model with Subject-Specific Heat Rate.

A subject-specific model of instantaneous cost of transport (ICOT) is introduced from the joint-space formulation of metabolic energy expenditure using the laws of thermodynamics and the principles of multibody system dynamics. Work and heat are formulated in generalized coordinates as functions of joint kinematic and dynamic variables. Generalized heat rates mapped from muscle energetics are estimated from experimental walking metabolic data for the whole body, including upper-body and bilateral data synchronization. Identified subject-specific energetic parameters—mass, height, (estimated) maximum oxygen uptake, and (estimated) maximum joint torques—are incorporated into the heat rate, as opposed to the traditional in vitro and subject-invariant muscle parameters. The total model metabolic energy expenditure values are within 5.7 ± 4.6% error of the measured values with strong (R2 > 0.90) inter- and intra-subject correlations. The model reliably predicts the characteristic convexity and magnitudes (0.326–0.348) of the experimental total COT (0.311–0.358) across different subjects and speeds. The ICOT as a function of time provides insights into gait energetic causes and effects (e.g., normalized comparison and sensitivity with respect to walking speed) and phase-specific COT, which are unavailable from conventional metabolic measurements or muscle models. Using the joint-space variables from commonly measured or simulated data, the models enable real-time and phase-specific evaluations of transient or non-periodic general tasks that use a range of (aerobic) energy pathway similar to that of steady-state walking.