Multibody System Dynamics Research Articles

Simulation of friction and stiction in multibody dynamics model problems

ABSTRACTA continuous model of Coulomb friction is used with a tangent space formulation of differential algebraic equations of motion for simulation of multibody dynamic model problems. Characteristics of the model problems studied are similar to those encountered in broad classes of multibody systems, without the associated geometric and analytical complexities. An implicit trapezoidal numerical solution algorithm is used to simulate dynamic response that includes the onset of stiction, its progression, and its termination, avoiding stiff behavior that is reported in the literature when index 3 formulations are used. Analytical criteria for stiction are derived for a three mass Coulomb friction model problem that defines the onset of and departure from stiction events with redundant equations of constraint. The tangent space formulation with implicit trapezoidal integration is applied to this analytical model to compute dynamic response, determine ranges of constraint forces that may occur during periods of stiction, and demonstrate that dynamic response is a discontinuous function of model parameters when stiction occurs. Accuracy of the continuous model of Coulomb friction is established, through comparison of results with those of the analytical model. Cartesian coordinate models of higher dimension are presented for three and four mass model problems that encounter a higher degree of redundancy in constraints during periods of stiction. Simulation of the Cartesian coordinate models, which have characteristics similar to more general multibody systems, yields accurate solutions, without any indication of stiffness in the tangent space equations of motion. Methods successfully demonstrated in model problems provide a foundation for simulation of spatial multibody dynamic systems with friction.

Screw and Lie group theory in multibody kinematics

After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user-friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this is a holistic geometric approach to the kinematics modeling observing that the general motion of rigid bodies and the relative motion due to technical joints are screw motions. Moreover, screw theory provides the geometric setting and Lie group theory the analytic foundation for an intuitive and compact MBS modeling. The inherent frame invariance of this modeling approach gives rise to very efficient recursive O ( n ) algorithms, for which the so-called “spatial operator algebra” is one example, and allows for use of readily available geometric data. In this paper, three variants for describing the configuration of tree-topology MBS in terms of relative coordinates, that is, joint variables, are presented: the standard formulation using body-fixed joint frames, a formulation without joint frames, and a formulation without either joint or body-fixed reference frames. This allows for describing the MBS kinematics without introducing joint reference frames and therewith rendering the use of restrictive modeling convention, such as Denavit–Hartenberg parameters, redundant. Four different definitions of twists are recalled, and the corresponding recursive expressions are derived. The corresponding Jacobians and their factorization are derived. The aim of this paper is to motivate the use of Lie group modeling and to provide a review of different formulations for the kinematics of tree-topology MBS in terms of relative (joint) coordinates from the unifying perspective of screw and Lie group theory.

A low degree of freedom approach for prediction of friction in finite EHL line contacts

A low degree of freedom (LDOF) approach for expedient prediction of friction in finite EHL line contact is presented. Friction prediction are in good agreement with existing results for all of the reference cases tested. With the present LDOF approach, friction predictions can be obtained thousands of times faster than if using a fully coupled FE-based model. It can, therefore be used to simulated the tribological contacts in multi-body dynamic (MBD) systems with millions of degrees of freedoms. The model was utilised to study edge stress concentrations due to roller tilt. The results confirmed that increasing the tilting angle increases the maximum pressure and shifts its location towards the edge of roller. An increase in total friction was also observed.

Dynamics and lubrication analyses of a planar multibody system with multiple lubricated joints

In order to ensure the mechanical systems a better performance, most of their joints are designed to operate with lubricant. The differently located lubricated joints interact with each other, influencing the total performances of the system. This study proposes a numerical approach for the multibody system modeling with the consideration of the interactions among the multiple lubricated joints to investigate the dynamics and tribological performances of the mechanism. This approach couples the lubrication model of both translational and revolute joints with the dynamics model of the multibody system, and is performed on a four-stroke gasoline engine with the lubricated piston skirt-liner subsystem and lubricated big-end bearing of the connecting rod. The multibody dynamics model is built with Lagrange’s method. The lubrication models are built based on the average Reynolds equation, and solved with finite element method to derive the hydrodynamic forces according to the motion of the system. The piston skirt profile, pin offset and the effects of surface roughness on the lubrication performances are taken into account. The simulation results reveal that there are obvious interactions between the differently located lubricated joints, and the larger clearance can pronounce the interactions.

A Parallel Recursive Hamiltonian Algorithm for Forward Dynamics of Serial Kinematic Chains

This paper presents a novel recursive formulation for the simulation of multibody system dynamics based on Hamilton's canonical equations. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration-based counterparts, it appears that there is a lack of dedicated parallel algorithms for multirigid body system dynamics based on this formulation. Serial kinematic chains are considered in this paper. Initially, the standard set of Hamilton's canonical equations is joined together with constraint equations at the velocity level. The reformulation determines the system's joint velocities and constraint force impulses in a divide and conquer manner resulting in logarithmic numerical cost for parallel implementation. Subsequently, the equations of motion are rearranged in order to obtain the time derivatives of the total joint momenta. In the case of the sequential implementation, the entire algorithm exhibits linear computational cost. Presented numerical method is exact and noniterative. Numerical test cases reveal negligible energy drift without the use of any additional constraint stabilization techniques. The results are compared against more standard acceleration based formulation and the outcome from real-life physical experiment.

Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

The absolute nodal coordinate formulation is a computational approach to analyze the dynamic performance of flexible bodies experiencing large deformations in multibody system dynamics applications...

Development and validation of a simulation-based safety evaluation program for a mega floating crane

The motions of the mega floating crane and the lifted module must be evaluated in advance, to determine whether they satisfy the safety criteria or not. Due to the limitations of the existing dynamic analysis programs, we develop a differentiated program that is dedicated to the mega floating crane. This program is focused on reducing modeling time, while increasing modeling accuracy. Furthermore, it can model the block loader that distributes the tension in wire ropes between the lifted module and the block loader equally, and link beams that are used to connect hooks by hinge joints. The equations of motion based on multibody system dynamics are derived. Wave, wind, and current are included as external environmental loads. A direct volume calculation method below the water plane is adopted to find the buoyant force and center of buoyancy. External loads are verified by commercial program. Finally, the simulation results of the module erection are validated by comparison with the measurement of real operation.

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.