ASME Conference Presenter Attendance Policy and Archival Proceedings

2014;():V006T00A001. doi:10.1115/DETC2014-NS6.

This online compilation of papers from the ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2014) represents the archival version of the Conference Proceedings. According to ASME’s conference presenter attendance policy, if a paper is not presented at the Conference, the paper will not be published in the official archival Proceedings, which are registered with the Library of Congress and are submitted for abstracting and indexing. The paper also will not be published in The ASME Digital Collection and may not be cited as a published paper.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Biomechanics

2014;():V006T10A001. doi:10.1115/DETC2014-34231.

Sit-to-stand (STS) is a common activity in daily lives which requires relatively high joint torques and a robust coordination of lower and upper extremities with postural stability. Many elderly, people with lower limb injuries, and patients with neurological disorders or musculoskeletal abnormalities have difficulties in accomplishing this task. In contrast to the literature on numerous experimental studies of STS, there are limited studies that were carried out through simulations. In literature, mostly bilateral symmetry was assumed for STS tasks, however even for healthy people, it is more difficult to perform STS tasks with a perfect bilateral symmetry. The goal of this research is to develop a three-dimensional unassisted STS motion prediction formulation for healthy young individuals. Predicted results will be compared with experimental results found in literature for the validation of the proposed formulation.

Topics: Simulation
Commentary by Dr. Valentin Fuster
2014;():V006T10A002. doi:10.1115/DETC2014-34430.

Carbon nanotubes (CNTs) are capable to absorb and encapsulate some molecules to create new hybrid nano-structures providing a variety of functionally useful properties. CNTs functionalized by encapsulaitng single-stranded deoxy-ribonucleic acid (ssDNA) promise great potentials for applications in nanotechnology and nano-biotechnology. In this paper, buckling instability of ssDNA@CNT i.e. hybrid nano-structure composed of ssDNA encapsulated inside CNT has been investigated using the nonlocal elasticity theory. The nonlocal elasticity theory is capable to capture the small scale effects due to the discontinuity of nano-structures at atomic scales. The nonlocal elastic rod and shell equations are derived for modeling ssDNA and CNT respectively. Providing numerical examples, it is predicted that, ssDNA@(10,10) CNT is more resistant than the pristine (10,10) CNT against the buckling instability under radial pressure due to the inter-atomic van der Waals interactions between DNA and CNT. Furthermore, nonlocal elasticity theory predicts lower critical buckling pressure than does the local elasticity theory.

Commentary by Dr. Valentin Fuster
2014;():V006T10A003. doi:10.1115/DETC2014-34479.

This work presents a parametric dynamic model of a helicopter collective control inceptor that includes the biodynamics of the pilot. The biodynamic feedthrough and neuromuscular admittance of a helicopter pilot are characterized using a detailed multibody analysis of the pilot’s left arm holding the inceptor as a ‘virtual experiment’ to produce the results required to identify the parameters of the coupled system. The goal is to develop an analytical model of the dynamics of the coupled pilot-device system and gain insight into the effect of several design parameters on the characteristics of the coupled system. The effect of device inertia, damping, stiffness and friction on the stability margins of the coupled system with respect to the collective bounce instability phenomenon are analyzed and discussed. The analytical model is verified using it in place of the detailed multibody model of the pilot’s arm in the fully detailed multibody simulation of the coupled system. It is then used in linearized analysis of the complete system in support of the vehicle design.

Commentary by Dr. Valentin Fuster
2014;():V006T10A004. doi:10.1115/DETC2014-34521.

A realistic driver model can support the development of new steering technologies by reducing the time-consuming trial and error process of designing products. A neuromuscular driver model, by offering physiologically realistic steering maneuvers can provide insights into the task performance and energy consumption of the driver, including fatigue and muscle co-contraction. Here, two muscles are used in a simplified neuromuscular driver model. To study the effect of driver’s characteristics such as age, gender and physical ability on steering, the muscle parameters are adjusted to represent a particular population. Then, this modified driver model is used to to tune the Electric Power Steering (EPS) assist curves for that particular population.

Commentary by Dr. Valentin Fuster
2014;():V006T10A005. doi:10.1115/DETC2014-34835.

The army has a vision for using autonomous micro ground vehicles (MGV) for soldier support in the last 100 meters of operations in urban and natural environments. These MGVs are expected to typically fit in a human palm and weigh in the order of 30–50 grams. Robust mobility is a necessary condition to ensure operations. Given the severe challenge of size, weight and power (SWAP) of the MGVs, significant uncertainties currently remain in quantifying micro ground vehicle mobility. In this paper we describe a research methodology and representative results for understanding legged MGV mobility in different types of terrain. Our methodology is based on a synergy of novel experimental setup and high-fidelity computational methods. We report the use of a novel “single-leg” test rig that uses tactile sensors to measure ground interaction loads. We also report the use of high speed imaging and use of particle image velocimetry to understand soil deformation during legged interactions with terrain. Finally, we report on the use of multibody dynamics and High Performance Computing (HPC) based granular media simulations. This conference paper emphases more on the overall approach based on synergistic use of high fidelity modeling and experimental methods supported by representative results rather than presenting a detailed analyses of the results.

Commentary by Dr. Valentin Fuster
2014;():V006T10A006. doi:10.1115/DETC2014-34920.

This paper presents a new and simple fall detection concept based on detailed experimental data of human falling and Activities of Daily Living (ADL). Establishing appropriate fall algorithms compatible with MEMS sensors requires detailed data on falls and ADL that indicate clearly the variations of the kinematics at the possible sensor node location on the human body, such as hip, head, and chest. Currently, there is a lack of data on the exact direction and magnitude of each acceleration component associated with these node locations. This is crucial for MEMS structures, which have inertia elements very close to the substrate and are capacitively biased, and hence, are very sensitive to the direction of motion whether it is toward or away from the substrate. This work presents detailed data of the acceleration components on various locations on the human body during various kinds of falls and ADL. An algorithm for fall detection based on MEMS switches is then established. A new sensing concept based on the algorithm is proposed. The concept is based on employing several inertia sensors, which are triggered simultaneously, as electrical switches connected in series, upon receiving a true fall signal. In the case of everyday life activities, some or no switches will be triggered resulting in an open circuit configuration, thereby preventing false positive. Lumped-parameter model is presented for the device and preliminary simulation results are presented illustrating the new device concept.

Commentary by Dr. Valentin Fuster
2014;():V006T10A007. doi:10.1115/DETC2014-35487.

DNA is a long flexible polymer and is involved in several fundamental cellular processes such as transcription, replication and chromosome packaging. These processes induce forces and torques in the DNA which deform it. These deformations in turn affect the structure and function of DNA. However, understanding of the dynamic response of DNA to the various forces that act on it is still far from complete. Several experiments have been carried out to study these responses most of which use a micron sized magnetic bead attached to the DNA molecule to both manipulate it and to observe its dynamics. One limitation of this approach is that the dynamics of the DNA molecule has mostly been characterized “indirectly” by observing the dynamics of the magnetic bead. It is also reasonable to expect that, because of the size of the bead relative to that of the DNA, the magnetic bead dynamics will obscure that of the DNA. We adapt existing coarse-grained Brownian dynamics models of DNA to develop a model capable of representing the dynamics of DNA without any of the artifacts inherent to the experiments. This model accounts for bending, torsion, extension, electrostatics, hydrodynamics and the random thermal forces acting on DNA in an electrolyte solution. We then carry out Brownian dynamics simulations with our model to benchmark with well established theoretical results of a stretched polymer in solution. Finally, we employ our model to predict the relaxation time scale for single molecule experiments which sets the framework for future studies in which we plan to further shed light on the dynamics of DNA over long length and time scales.

Commentary by Dr. Valentin Fuster
2014;():V006T10A008. doi:10.1115/DETC2014-35582.

Human gait studies have not been applied frequently to the prediction of the performance of medical devices such as prostheses and orthoses. The reason is most biomechanics simulations require experimental data such as muscle activity or joint moment information a priori. In addition, biomechanical models are normally too complicated to be adjusted and these simulations normally take a long period of time to be performed which makes testing of various possibilities time consuming; therefore they are not suitable for prediction purpose. The objective of this research is to develop a control oriented human gait model that is able to predict the performance of prostheses and orthoses before they are experimentally tested. This model is composed of two parts. The first part is a seven link nine degree-of-freedom (DOF) plant to represent the forward dynamics of human gait. The second part is a control system which is a combination of Model Predictive Control (MPC) and Proportional-Integral-Derivative (PID) control. The purpose of this control system is to simulate the central nervous system (CNS). This model is sufficiently simple that it can be simulated and adjusted in a reasonable time, while still representing the essential principles of human gait.

Topics: Simulation
Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Computational Methods in Multibody Systems and Nonlinear Dynamics

2014;():V006T10A009. doi:10.1115/DETC2014-34142.

The similarity transformation and direct ansatz are applied to obtain rogue wave solutions of nonlinear Schrödinger equation with varying coefficients. These obtained solutions can be used to describe the possible formation mechanisms for optical rogue wave phenomenon in optical fibres. Moreover their dynamical behaviors are exhibited for chosen different functions. This will further excite the possibility of relative researchers and potential applications of rogue waves in other related fields.

Commentary by Dr. Valentin Fuster
2014;():V006T10A010. doi:10.1115/DETC2014-34322.

In this article, the non-smooth contact dynamics of multi-body systems is formulated as a complementarity problem. Minimal coordinates operational space formulation is used to derive the dynamics equations of motion. Depending on the approach used for modeling Coulomb’s friction, the complementarity problem can be posed either as a linear or a nonlinear problem. Both formulations are studied in this paper. An exact modeling of the friction cone leads to a nonlinear complementarity problem (NCP) formulation whereas a polyhedral approximation of the friction cone results in a linear complementarity problem (LCP) formulation. These complementarity problems are further recast as non-smooth unconstrained optimization problems, which are solved by employing a class of Levenberg-Marquardt algorithms. The necessary theory detailing these techniques is discussed and five schemes are implemented to solve contact dynamics problems. A simple test case of a sphere moving on a plane surface is used to validate these schemes, while a twelve-link pendulum example is chosen to compare the speed and accuracy of the schemes presented in this paper.

Commentary by Dr. Valentin Fuster
2014;():V006T10A011. doi:10.1115/DETC2014-34476.

The analysis of thin structural components integrated within a general-purpose multibody system dynamics formulation is presented. An original inverse finite element solution procedure is developed to reconstruct the deformed shape of a membrane from in-plane membrane strain measurements, and eventually indirectly estimate the distributed loads. A direct solution approach is used in co-simulation with fluid-dynamics solvers to predict the configuration of the system under static and unsteady loads. Numerical validation of the inverse solution is performed considering the results of direct solution analysis. The direct and inverse solutions are validated considering experimental displacement and strain measurements obtained using digital image correlation. Moving Least Squares are used to smooth and remap measurements as needed by the inverse solution meshing. Utilizing surface strain measurements from strain sensors, the methodology enables the accurate computation of the three-dimensional displacement field.

Commentary by Dr. Valentin Fuster
2014;():V006T10A012. doi:10.1115/DETC2014-34511.

Any description of rigid body motions requires body-fixed RFRs since the latter kinematically represent the bodies and are necessary to define their inertia properties. Consequently there is no formulation without RFR. Nevertheless this does not necessarily mean that the definition of body-fixed RFRs is an indispensable step in MBS modeling.

A formulation without body-fixed reference frames is one that does not involve explicit definition of body-fixed frames to express the kinematics and the inertia data of an MBS. In this paper a formulation is presented that only requires a single spatial inertial frame to model all kinematic and dynamic properties of the MBS. It only requires the joint kinematics (axis and position vector) as well as the inertia tensors w.r.t. the spatial inertial frame in a reference configuration the MBS. That is, the inertia tensors of all rigid bodies are expressed w.r.t. a virtual body-fixed references frame that coincides with the spatial inertia frame in the reference configuration.

Avoiding the explicit introduction of body-fixed reference frames significantly simplifies the MBS modeling. This is not only beneficial for manual modeling but also gives rise to much simpler MBS codes. The approach is discussed for tree-topology MBS as well as for closed loop systems. It is demonstrated for a planar slider-crank examples.

Commentary by Dr. Valentin Fuster
2014;():V006T10A013. doi:10.1115/DETC2014-34606.

Large-scale contact problems with impacts and Coulomb friction arise in the simulation of rigid body dynamics treated within the non-smooth contact dynamics approach using set-valued force and impact laws. In this paper the parallelization of two popular numerical methods for solving such contact problems on the GPU, being the projected over-relaxed Jacobi (JOR Prox) and projected Gauss-Seidel iteration (SOR Prox), is studied in detail. Performance tests for the parallel JOR and SOR Prox iterations are conducted and a speedup factor of up to 16, depending on the problem size, can be achieved compared to a sequential implementation. This work forms the stepping stone to the simulation of granular media on a computer cluster.

Commentary by Dr. Valentin Fuster
2014;():V006T10A014. doi:10.1115/DETC2014-34737.

A simple mathematical model of friction in speed reducers is presented and discussed. A rigid body approach, typical for multibody simulations, is adopted. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms.

The first version of the model is purely rigid, i.e. no deflections of the mechanism bodies are allowed. Constraints are introduced to maintain the ratio between input and output velocity. It is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, coefficient of friction and inertial parameters) two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints and Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Examples of all indicated paradoxical situations are provided and discussed.

The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input-output velocity ratio are introduced). In non-paradoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previously paradoxical situations no multiple solutions of friction force are found, however, the amended model does not solve all problems. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. Numerical examples showing behavior of the model are provided and analyzed.

Topics: Friction , Coulombs , Modeling
Commentary by Dr. Valentin Fuster
2014;():V006T10A015. doi:10.1115/DETC2014-34899.

The stabilization of geometric constraints is vital for an accurate numerical solution of the differential-algebraic equations (DAE) governing the dynamics of constrained multibody systems (MBS). Although this has been a central topic in numerical MBS dynamics using classical vector space formulations, it has not yet been sufficiently addressed when using Lie group formulations. A straightforward approach is to impose constraints directly on the Lie group elements that represent the MBS motion, which requires additional constraints accounting for the invariants of the Lie group. On the other hand, most numerical Lie group integration schemes introduce local coordinates within the integration step, and it is natural to perform the stabilization in terms of these local coordinates. Such a formulation is presented in this paper for index 1 formulation. The stabilization method is applicable to general coordinate mappings (canonical coordinates, Cayley-Rodriguez, Study) on the MBS configuration space Lie group. The stabilization scheme resembles the well-known vectors space projection and pseudo-inverse method consisting in an iterative procedure. A numerical example is presented and it is shown that the Lie group stabilization scheme converges normally within one iteration step, like the scheme in the vector space formulation.

Commentary by Dr. Valentin Fuster
2014;():V006T10A016. doi:10.1115/DETC2014-35041.

The underlying dynamic model of multibody systems takes the form of a differential Complementarity Problem (dCP), which is nonsmooth and thus challenging to integrate. The dCP is typically solved by discretizing it in time, thus converting the simulation problem into the problem of solving a sequence of complementarity problems (CPs). Because the CPs are difficult to solve, many modelling options that affect the dCPs and CPs have been tested, and some reformulation and relaxation options affecting the properties of the CPs and solvers have been studied in the hopes to find the “best” simulation method. One challenge within the existing literature is that there is no standard set of benchmark simulations.

In this paper, we propose a framework of Benchmark Problems for Multibody Dynamics (BPMD) to support the fair testing of various simulation algorithms. We designed and constructed a BPMD database and collected an initial set of solution algorithms for testing. The data stored for each simulation problem is sufficient to construct the CPs corresponding to several different simulation design decisions. Once the CPs are constructed from the data, there are several solver options including the PATH solver, nonsmooth Newton methods, fixed-point iteration methods for nonlinear problems, and Lemke’s algorithm for linear problems. Additionally, a user-friendly interface is provided to add customized models and solvers.

As an example benchmark comparison, we use data from physical planar grasping experiments. Using the input from a physical experiment to drive the simulation, uncertain model parameters such as friction coefficients are determined. This is repeated for different simulation methods and the parameter estimation error serves as a measure of the suitability of each method to predict the observed physical behavior.

Commentary by Dr. Valentin Fuster
2014;():V006T10A017. doi:10.1115/DETC2014-35118.

Redundancy-free computational procedure for solving dynamics of rigid body by using quaternions as the rotational kinematic parameters will be presented in the paper. On the contrary to the standard algorithm that is based on redundant DAE-formulation of rotational dynamics of rigid body that includes algebraic equation of quaternions’ unit-length that has to be solved during marching-in-time, the proposed method will be based on the integration of a local rotational vector in the minimal form at the Lie-algebra level of the SO(3) rotational group during every integration step. After local rotational vector for the current step is determined by using standard (possibly higher-order) integration ODE routine, the rotational integration point is projected to Sp(1) quaternion-group via pertinent exponential map. The result of the procedure is redundancy-free integration algorithm for rigid body rotational motion based on the rotational quaternions that allows for straightforward minimal-form-ODE integration of the rotational dynamics.

Commentary by Dr. Valentin Fuster
2014;():V006T10A018. doi:10.1115/DETC2014-35226.

In this paper the mathematical framework of an advanced algorithm is presented to efficiently form and solve the equations of motion of a multibody system involving uncertainty in the system parameters and/or the excitations. The uncertainty is introduced to the system through the application of the polynomial chaos expansion. In this scheme, states of the system, nondeterministic parameters, and the constraint loads are expanded using modal values as well as orthogonal basis functions. Computational complexity of the application of traditional methods to solve the stochastic equations of motion of a multibody system drastically grows as a cubic function of the number of the states of the system, uncertain parameters and the maximum degree of the polynomial chosen for the basis function. The presented method forms the equation of motion of the system without forming the entire mass and Jacobian matrices. In this strategy, the stochastic governing equations of motion of each individual body as well as the one associated with the kinematic constraint at the connecting joint are developed in terms of the basis functions and modal coordinates. Then sweeping the system in two passes assembly and disassembly, one can form and solve the stochastic equations of motion. In the assembly pass the non-deterministic equations of motion of the assemblies are obtained. In the disassembly process, these equations are then recursively solved for the modal values of the spatial accelerations and the constraints loads. In the serial and parallel implementations, computational complexity of the method increases as a linear and logarithmic functions of the number of the states of the system, uncertain variables, and the maximum degree of the basis functions used in the expansion.

Commentary by Dr. Valentin Fuster
2014;():V006T10A019. doi:10.1115/DETC2014-35550.

Substructuring techniques have been widely used in model reduction of large structures. In these methods a large structure is partitioned into several components and reduced components are built. Boundary degrees-of-freedom (DoF) at the interfaces between components are used to assemble the reduced components and to form a reduced model of the original structure. In the current substructuring methods the boundary DoF or a transformation of these DoF remain in the reduced model. In this paper a methodology is suggested that could eliminate the boundary DoF from the reduced model which in turn leads to having even a smaller reduced model. This method which uses a different partitioning of the DoF of the structure is illustrated for a two-component structure. An example on a simple structure shows how the method can be implemented. The results show that the same level of accuracy compared to a standard substructuring can be obtained with fewer number of DoF in the reduced model.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Contact and Interface Dynamics

2014;():V006T10A020. doi:10.1115/DETC2014-34159.

Friction draft gears are the most widely used draft gears. Modeling and prediction of their dynamic behavior are of significant assistance in addressing various concerns. Longer, heavier and faster heavy haul trains mean larger in-train forces and more complicated force patterns, which require further improvements of dynamic modeling of friction draft gears to assess the longitudinal train dynamics. In this paper a force-displacement characteristics model named “base model” was described. The base model was simulated after the analyses of a set of field-test data. Approaches to improve the base model to a full advanced draft gear model were discussed; preliminary simulation results of an advanced draft gear model were also presented.

Commentary by Dr. Valentin Fuster
2014;():V006T10A021. doi:10.1115/DETC2014-34399.

The influence of the revolute joint model on the dynamic response of planar multibody mechanical systems is studied in this work. In the sequel of this process, under the framework of the multibody formalisms, a general methodology for modeling the main kinematic aspects of dry revolute joint clearances is revisited. The numerical models for normal and tangential contact forces developed at the clearance joints are also discussed, which are based on the Hertzian contact theory and dry Coulomb’s friction law, respectively. The fundamental kinematic and dynamic issues of the modeling lubricated revolute joints are presented in this work in order to compare them with the dry revolute joint approach. In a simple manner, the lubrication forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation corresponding to the dynamic regime. The intra-joint forces developed for both dry and lubricated cases are evaluated based on the state of variable of the system and subsequently included into the dynamic equations of motion of the multibody system as external generalized forces. The main assumptions and procedures adopted throughout this work are demonstrated through simulations of a planar slider-crank mechanism, which includes dry and lubricated revolute joint with clearance. Finally, some experimental data is also presented and analyzed.

Commentary by Dr. Valentin Fuster
2014;():V006T10A022. doi:10.1115/DETC2014-34709.

One method for modeling idealized contact between two bodies in mechanical system is based on the constraint approach, where Lagrange multipiers are introduced, which serve as constraint forces. In the usage of this formulation, there exists a linear dependancy between the Lagrange multipliers. Moreover, it has been observed that some Lagrange multipliers are always identical to zero. This sort of contradicts the basic notion that Lagrange multipliers in mechanical systems act as constraint forces which, when constraints are violated, push the system back in the desired configuration. In this paper it will be shown, by theory and example, that the above-mentioned linear dependency of the Lagrange multipliers, together with specific entries in the Jacobian of the constraint equations, results in some Lagrange multipliers being identical to zero.

Commentary by Dr. Valentin Fuster
2014;():V006T10A023. doi:10.1115/DETC2014-35231.

We present a contact model for rigid-body simulation that considers the local geometry at points of contact between convex polyhedra in order to improve physical fidelity and stability of simulation. This model formulates contact constraints as sets of complementarity problems in a novel way, avoiding or correcting the pitfalls of previous models. We begin by providing insight into the special considerations of collision detection needed to prevent interpenetration of bodies during time-stepping simulation. Then, three fundamental complementarity based contact constraints are presented which provide the foundation for our model. We then provide general formulations for 2D and 3D which accurately represent the complete set of physically feasible contact interactions in six unique configurations. Finally, experimental results are presented which demonstrate the improved accuracy of our model compared to four others.

Topics: Simulation
Commentary by Dr. Valentin Fuster
2014;():V006T10A024. doi:10.1115/DETC2014-35390.

This work analyzes the effects of the stick-slip transition of planar rigid body systems undergoing simultaneous, multiple point impact with Coulomb friction. A discrete, algebraic approach is used in conjunction with an event-driven scheme which detects impact events. The system equations of motion for the examples considered are indeterminate with respect to the impact forces. Constraints consistent with rigid body assumptions are implemented to overcome the indeterminacy. The post-impact velocities of a system are determined by exploiting the work-energy relationship of a collision and using an energetic coefficient of restitution to model energy dissipation. These developments lead to a unique and energetically consistent solution to the post-impact velocities. A frictionless rocking block example is analyzed as a benchmark case and compared to experimental results to demonstrate the accuracy of the proposed method. Simulation results are also presented for a planar ball example with friction.

Topics: Friction , Coulombs
Commentary by Dr. Valentin Fuster
2014;():V006T10A025. doi:10.1115/DETC2014-35421.

In the analysis of multibody system (MBS) dynamics, contact between two arbitrary rigid bodies is a fundamental feature in a variety of models. Many procedures have been proposed to solve the rigid body contact problem, most of which belong to one of two categories: off-line and on-line contact search methods. This investigation will focus on the development of a contact surface model for the rigid body contact problem in the case where an on-line three-dimensional non-conformal contact evaluation procedure, such as the elastic contact formulation - algebraic equations (ECF-A), is employed. It is shown that the contact surface must have continuity in the second order spatial derivatives when used in conjunction with ECF-A. Many of the existing surface models rely on direct linear interpolation of profile curves which leads to first order spatial derivative discontinuities. This, in turn, leads to erroneous spikes in the prediction of contact forces. To this end, an absolute nodal coordinate formulation (ANCF) thin plate surface model is developed in order to ensure second order spatial derivative continuity to satisfy the requirements of the contact formulation employed. A simple example of a railroad vehicle negotiating a turnout, which includes a variable cross-section rail, is tested for the cases of the new ANCF thin plate element surface, an existing ANCF thin plate element surface with first order spatial derivative continuity, and the direct linear profile interpolation method. A comparison of the numerical results reveals the benefits of using the new ANCF surface geometry developed in this investigation.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Emerging Frontiers

2014;():V006T10A026. doi:10.1115/DETC2014-34374.

A state-of-the-art simulation technique that solves the equations of motion together with the set-valued contact and impulse laws by the time-stepping scheme of Moreau is introduced to the legged robotics community. An analysis is given that shows which of the many variations of the method fits best to legged robots. Two different methods to solve the discretized normal cone inclusions are compared: the projected over-relaxed Jacobi and Gauss-Seidel iteration. The methods are evaluated for an electrically-driven quadrupedal robot in terms of robustness, accuracy, speed and ease of use. Furthermore, the dependence of the simulation speed on the choice of the generalized coordinates is examined. The proposed technique is implemented in C++ and compared to a fast and simple approach based on compliant contact models. In conclusion, the introduced method with hard contacts is very beneficial for the simulation of legged robots.

Topics: Robots , Simulation
Commentary by Dr. Valentin Fuster
2014;():V006T10A027. doi:10.1115/DETC2014-34618.

Motion control of a three link underactuated manipulator, whose first joint has an actuator and a sensor and second and third joints do not have actuator or sensor, is theoretically proposed without feedback control with respect to the motion of the free links. By using high-frequency vertical excitation, so called Kapitza pendulum is stabilized at the upright position without state feedback control. The phenomenon can be regarded as a subcritical pitchfork bifurcation. On the other hand, it is known that the horizontal excitation causes supercritical pitchfork bifurcation in a pendulum. Also, the inclination of excitation from the horizontal and vertical directions produces the perturbation of the complete supercritical and subcritical pitchfork bifurcations, respectively. In this paper, we apply the method of multiple scales to obtain the averaged equations governing the motion of the free links. We perform the bifurcation analysis of the free links and clarify the equilibrium points in the free links and their stability. Then, we propose a strategy to swing up the free links and to stabilize them at the upright position by actuating the perturbation of the pitchfork bifurcations based on the change of the inclination of excitation.

Commentary by Dr. Valentin Fuster
2014;():V006T10A028. doi:10.1115/DETC2014-35345.

We consider the hydrogen molecular ion with time-dependent magnetic field strength. We discretize the corresponding Schroedinger equation with the Hamiltonian written in prolate spheroidal coordinates. We formulate a control problem and give an example of steering a restricted initial state to a restricted terminal state.

Commentary by Dr. Valentin Fuster
2014;():V006T10A029. doi:10.1115/DETC2014-35425.

The state space reconstruction technique was recognized by Edward N. Lorenz as “one of the most surprising developments in nonlinear dynamics” [1]. Nowadays, the technique is applied in various scientific areas for prediction, analysis and diagnostics. This paper aims to discuss the possibility of using the embedding dimension of a reconstructed state space of time series as a tool for preliminary diagnostics. After a short description and illustration of the method, the paper considers two case studies: a single degree of freedom (DOF) and a 2 DOF system. The results of the analysis help detect a class of structural defects, including defects connected to a coupling mechanism. There is clearly a huge potential of such an approach for diagnostics of complex machinery.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Flexible Multibody Dynamics

2014;():V006T10A030. doi:10.1115/DETC2014-34355.

A viscoelastic beam model is presented based on SE(3) group theory. We discretize a rod with beams between finite frames on the rod and regard the configurations of these frames as elements of the SE(3) Lie group. Two subsequent frames are connected by a beam. The curvatures and strains are assumed to be constant on the trajectory between them. If the deflection curve of the beam is modeled as a helix, the resulting beam model is geometrical exact for large bending deformations. The stiffness matrices of the discrete beam elements result from the potential extensional and shearing energy as well as from the potential bending and torsion energy. The benefit of this SE(3) modeling for translational elastic coordinates and for translational forces in comparison to an SO(3) × ℝ3 variant is demonstrated.

Topics: Modeling
Commentary by Dr. Valentin Fuster
2014;():V006T10A031. doi:10.1115/DETC2014-34392.

In the large rotation vector formulations (LRVF), two independent interpolations are used in the nonlinear large displacement analysis of beams. This kinematic description leads to a fundamental redundancy problem. This paper examines this fundamental issue and demonstrates that the use of two geometrically independent meshes can lead to coordinate and geometric invariant redundancy that cannot be solved using constraints or forces. It is demonstrated in this paper that the two geometry meshes can define different space curves, which can differ by arbitrary rigid body displacements. The material points of the two meshes occupy different positions in the deformed configuration, and as a consequence, the geometries of the two meshes can differ significantly. Simple examples are presented in order to shed light on these fundamental issues.

Commentary by Dr. Valentin Fuster
2014;():V006T10A032. doi:10.1115/DETC2014-34444.

In this investigation, a three dimensional gradient deficient beam element (BEAM9) using the absolute nodal coordinate formulation (ANCF) is introduced. This element has nine coordinates per node, this includes the position vector and the two gradient vectors rx and ry. Like most of the ANCF elements, this element has constant mass matrix and zero centrifugal and Coriolis inertia forces. The plane strain elastic force model and the elastic line approach are two elastic force models presented in this paper in order to simulate the element internal resistance. Both models support resistance to the general bending and twist moments. The possibilities of employing nonlinear material models will be discussed in future work. Furthermore, the proposed element has the advantage of easy integration over general cross section area that is not easy to perform using the fully parameterized ANCF beam element (BEAM12). Comparing to the ANCF cable element (BEAM6), the proposed element can resist general bending and twist loads. Moreover, shear deformations in the xy plane due to shear force and in the yz plane due to twist moment are considered with the gradient deficient beam element proposed in this work. However, no shear deformations are considered with the ANCF cable element. Comparing to the fully parameterized ANCF beam element, the gradient deficient beam element (BEAM9) avoids some locking issues, shows better computational efficiency and offers better convergency characteristics. Numerical examples are presented in order to validate the proposed gradient deficient beam element and to compare with other ANCF beam elements.

Commentary by Dr. Valentin Fuster
2014;():V006T10A033. doi:10.1115/DETC2014-34473.

This paper discusses the formulation and implementation of a 4-node C0 shell element within a general-purpose multibody formulation. A geometrically consistent set of strains and curvatures, defined in a co-rotational framework, is augmented by Enhanced Assumed Strains (EAS) and Assumed Natural Strains (ANS), to alleviate shear and membrane locking. The shell element formulation is validated by solving several static and dynamic problems from the open literature. The proposed element has been successfully used for the coupled structural and fluid-dynamics analysis of flapping wing micro-aerial vehicles.

Commentary by Dr. Valentin Fuster
2014;():V006T10A034. doi:10.1115/DETC2014-34635.

The absolute nodal coordinate formulation (ANCF) is a finite element procedure that has been developed specifically for the dynamic analysis of large deformation problems. This study concerns compatibility problems in thin rectangular ANCF shell elements, which have been reported in a recent study revealing that these elements lead to a loss of inter-element connectivity when used to discretize non-rectangular structures. This study presents an easily implementable extension to the already used formulae that reduces the inter-element connectivity problems significantly. The new approach is based on using a set of element specific parameters that corresponds to the initial shape of the element. The ability of both the standard and the proposed methods to express curved structures are compared as well as their respective numerical performance.

Commentary by Dr. Valentin Fuster
2014;():V006T10A035. doi:10.1115/DETC2014-34961.

In this paper, the procedure of construction of geometrical and structural matrices of plate finite elements employing absolute nodal coordinate formulation (ANCF) is studied. The kinematic and topological properties of an arbitrary plate finite element are described using universal digital code dncm that provides systematic enumeration of finite elements. This code is formed using the element’s dimension d, the number of nodes it possesses n, the number of scalar coordinates per node c, and a multiplier describing the process of transforming a conventional finite element to an ANCF element m. The detailed generation of a new type of triangular plate finite element 2343 using numerical computation of shape functions is discussed in the paper. The new triangular element employs position vectors and slope vectors up to second order mixed-derivative slope vector. A detailed derivation of the equations of motion of the element is provided; the examples of numerical simulation and validation are presented. The features of creating the models and numerical methods as well as results obtained by applying both approaches are discussed in the paper.

Topics: Computation , Shapes
Commentary by Dr. Valentin Fuster
2014;():V006T10A036. doi:10.1115/DETC2014-34974.

In this paper, we investigate the absolute nodal coordinate finite element (FE) formulations for modeling multi-flexible-body systems in a divide-and-conquer framework. Large elastic deformations in the individual components (beams and plates) are modeled using the absolute nodal coordinate formulation (ANCF). The divide-and-conquer algorithm (DCA) is utilized to model the constraints arising due to kinematic joints between the flexible components. We develop necessary equations of the new algorithm and present numerical examples to test and validate the method.

Commentary by Dr. Valentin Fuster
2014;():V006T10A037. doi:10.1115/DETC2014-35113.

Two approaches for simulation of dynamics of complex beam structures such as drill strings are considered.

In the first approach, the drill string is presented as a set of uniform beams connected via force elements. The beams can undergo arbitrary large displacements as absolutely rigid bodies but its flexible displacements due to elastic deformations are assumed to be small. Flexibility of the beams is simulated using the modal approach. Thus, each beam has at least twelve degrees of freedom: six coordinates define position and orientation of a local frame and six modes are used for modeling flexibility.

The second approach is dynamic simulation of the drill string using nonlinear finite element model. The proposed beam finite element uses Cartesian coordinates of its nodes and node rotation angles around axis of Cartesian coordinate system as generalized coordinates. The nonlinear finite element is developed based on method of large rotation vectors. Rotation angles in the nodes can be arbitrary large.

Equations of motion of beam structure are derived in the paper. The number of degrees of freedom is decreased by factor two as compared with the modal approach. Thereby, computational efficiency under simulation of dynamics of long drill strings is considerably increased.

The features of creating the models and numerical methods as well as results obtained by applying both approaches are discussed in the paper.

Topics: Drilling , Simulation
Commentary by Dr. Valentin Fuster
2014;():V006T10A038. doi:10.1115/DETC2014-35224.

Bucket-Wheel excavators (BWE) represent a specific type of complex machine system used in mining technology. During operation, the system is exposed to a number of external forces and disturbances like digging resistances on the Bucket-Wheel that cause transverse, longitudinal, and torsional vibrations. All vibrations will affect to normal working conditions, operational effectiveness, and may under specific conditions also effect the stability of the BWE. To increase working conditions advanced control systems can be applied controlling the dynamics, especially induced structural vibrations. In order to analyze and synthesize a controller for the above mentioned system, adequate modeling to describe the dynamical behavior of the system under real operating conditions is necessary. In a previous investigation, it was assumed that the Bucket-Wheel boom can be modeled as a flexible beam using the Euler-Bernoulli beam theory. Additionally it is assumed that the boom is attached to the excavator turning platform. The nonlinear modeling of the three-dimensional elastic boom considering the elasticity of suspending cables and also couplings resulting from geometrical nonlinear deformations is presented. Here the known modeling approach of higher order is used and extended to model the Bucket-Wheel boom of a Bucket-Wheel-Excavator including guided rotating motion in combination with digging resistance forces. The dynamic phenomena resulting from the higher-order modeling including higher-order geometrical couplings as well as the external excitations on the dynamic behavior of the Bucket-Wheel boom are analyzed in detail. Intensive simulation studies are realized demonstrating the effect of higher-order couplings as well as resulting destabilizing effects from the modeling.

Commentary by Dr. Valentin Fuster
2014;():V006T10A039. doi:10.1115/DETC2014-35229.

Bucket-Wheel excavators (BWE) represent a specific type of complex machine system used in mining technology. During operation, the system is exposed to a number of external forces and disturbances like digging resistances on the Bucket-Wheel that cause transverse, longitudinal, and torsional vibrations. All vibrations will be affected to normal working conditions, operational effectiveness, and may under specific conditions also effect the stability of the BWE. Taking into account nonlinear effects due to the higher-order geometrical and dynamical couplings of flexible deformations modeled under guided motions in combination with digging resistance forces result to the adequately dynamic behavior of the Bucket-Wheel boom, introduced in the first part. Additionally, it also leads to difficulties controlling the nonlinear dynamic system. To overcome these difficulties here the nonlinear dynamical system is approximated by an equivalent linear system linearized for suitable working points of remaining and not considered additive nonlinear parts of the system. In this contribution, based on the nonlinear characteristic of the system, the time behavior of nonlinearities (as additive effects in relation to the linearized system) is estimated in combination with related system states using a high-gain extended state observer. Then the well-known disturbance rejection control approach is used for vibration control of this nonlinear mechanical system. Simulation examples are included to illustrate the efficient suppression of vibrations as well as stabilization of the system during the digging process of Bucket-Wheel Excavator.

Commentary by Dr. Valentin Fuster
2014;():V006T10A040. doi:10.1115/DETC2014-35349.

In this investigation, a bi-linear shear deformable shell element is developed using the absolute nodal coordinate formulation for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the mid-plane and the position vector gradient at a material point in the element are interpolated by bi-linear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element locking exhibited in this type of element can be eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the bi-linear shear deformable ANCF shell element proposed in this investigation.

Commentary by Dr. Valentin Fuster
2014;():V006T10A041. doi:10.1115/DETC2014-35573.

By integrating the procedures of wear prediction with multibody dynamics, this paper proposed a numerical approach for the modeling and prediction of wear at revolute clearance joint in flexible multibody mechanical systems. In the approach, the flexible component was modeled by using absolute nodal coordinate formulation (ANCF)-based element. The clearance joint was modeled as a dry contact pair, in which the continuous contact force model proposed by Lankanrani and Nikravesh was applied to evaluate the normal contact force, and the friction effect was considered using the LuGre friction model. The calculation of wear was performed by an iterative wear prediction procedure based on Archard’s wear model. Using this approach, a planar slider-crank mechanism including a flexible rod and clearance joint was numerically investigated as a demonstrative example. Furthermore, the effects of the flexibility of the mechanism and the clearance size on the wear at clearance joint were also studied.

Commentary by Dr. Valentin Fuster
2014;():V006T10A042. doi:10.1115/DETC2014-35590.

This paper studies the problem of the motion of a classical model of modern analytical multibody dynamics — a chain of gyrostats coupled by ideal spherical joints. The chain moves about a fixed point in a central Newtonian force field. The paper develops the equations of chain’s motion and then establishes and analyzes the conditions for existence of some classes of precessional motions of the chain, under the assumption that the barycenter of each gyrostat is located on the line connecting the points where it is attached to other gyrostats. The findings of the paper extend corresponding results in the dynamics of a single gyrostat to a case of the multibody chain as well as generalize some of the known properties of precessional motions in the dynamics of many bodies.

Topics: Chain
Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Formulations for Real-Time Simulation

2014;():V006T10A043. doi:10.1115/DETC2014-35609.

Researchers simulate robot dynamics to optimize gains, trajectories, and controls and to validate proper robot operation. In this paper, we focus on this latter application, which allows roboticists to verify that robots do not damage themselves, the environments they are situated within, or humans. In current simulations, robot control code runs in lockstep with the dynamics integration. This design can result in code that appears viable in simulation but runs too slowly on physical systems. Addressing this problem requires overcoming significant challenges that arise due both to the speed of dynamic simulation running time (simulations may run 1/10 or 1/100 of real-time or slower) and to the variability of the running times (e.g., the speed of collision detection algorithms depends on pairwise object proximities). These difficulties imply that one must not only slow the control software but also scale controller running speeds dynamically. We describe the numerous architectural and OS-level technical challenges that we have overcome to yield temporally consistent simulation for modeling robots that use only real-time processes, and we show that our system is superior to the status quo using simulation-based experiments.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Modeling, Simulation, and Validation of Vehicle Dynamics

2014;():V006T10A044. doi:10.1115/DETC2014-34400.

This paper describes a modeling, simulation, and visualization framework aimed at enabling physics-based analysis of ground vehicle mobility. This framework, called Chrono, has been built to leverage parallel computing both on distributed and shared memory architectures. Chrono is both modular and extensible. Modularity stems from the design decision to build vertical applications whose goal is to reduce the end-to-end time from vision-to-model-to-solution-to-visualization for a targeted application field. The extensibility is a consequence of the design of the foundation modules, which can be enhanced with new features that benefit all the vertical applications. Two factors motivated the development of Chrono. First, there is a manifest need of modeling approaches and simulation tools to support mobility analysis on deformable terrain. Second, the hardware available today has improved to a point where the amount of sheer computer power, the memory size, and the available software stack (productivity tools and programming languages) support computing on a scale that allows integrating highly accurate vehicle dynamics and physics-based terramechanics models. Although commercial software is available nowadays for simulating vehicle and tire models that operate on paved roads; deformable terrain models that complement the fidelity of present day vehicle and tire models have been lacking due to the complexity of soil behavior. This paper demonstrates Chrono’s ability to handle these difficult mobility situations through several simulations, including: (i) urban operations, (ii) muddy terrain operations, (iii) gravel slope operations, and (iv) river fording.

Commentary by Dr. Valentin Fuster
2014;():V006T10A045. doi:10.1115/DETC2014-34423.

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the CPU times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (Non-Uniform Rational B-Spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some MBS application, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

Commentary by Dr. Valentin Fuster
2014;():V006T10A046. doi:10.1115/DETC2014-34470.

The objective of this investigation is to develop a low order continuum-based liquid sloshing model that can be successfully integrated with multibody system (MBS) algorithms. The liquid sloshing model proposed in this investigation allows for capturing the effect of the distributed inertia and viscosity of the fluid. The fluid viscous forces are defined using the Navier-Stokes equations. In order to demonstrate the use of the approach presented in this study, the assumption of an incompressible Newtonian fluid is considered with a total Lagrangian approach. Fluid properties such as the incompressibility condition are formulated using a penalty method. The low order model that captures the effect of the distributed fluid inertia on the vehicle dynamics is developed in this investigation using the floating frame reference (FFR) formulation. The use of this approach allows for developing an inertia-variant fluid model that accounts for the dynamic coupling between different modes of the fluid displacements. The matrix of position vector gradients and its derivative are formulated using the FFR kinematic description. The position and velocity gradient tensors are used to define the Navier-Stokes stress forces. The proposed liquid sloshing model is integrated with a MBS railroad vehicle model in which the rail/wheel interaction is formulated using a three-dimensional elastic contact formulation that allows for the wheel/rail separation. Several simulation scenarios are used to examine the effect of the distributed liquid inertia on the motion of the railroad vehicle. The results, obtained using the sloshing model, are compared with the results obtained using a rigid body vehicle model. The comparative numerical study presented in this investigation shows that the effect of the sloshing tends to increase the possibility of wheel/rail separation as the forward velocity increases, thereby increasing the possibility of derailments at these relatively high speeds.

Commentary by Dr. Valentin Fuster
2014;():V006T10A047. doi:10.1115/DETC2014-34831.

Offline multibody dynamics based modeling and simulation of vehicle dynamics has been pursued with varying levels of success for more than two decades. This has been used in design, controls, training, and other technical and programmatic objectives. Over the last decade, autonomous vehicle dynamics has become an important area of research. This has resulted in a growing need for onboard vehicle model that works with the vehicle controller and path planner. Typically, kinematic models have largely been used for these objectives. Use of dynamics models for onboard motion planning is a relatively new topic of research with only a handful of prior work. In this paper we report our attempts at addressing the need for onboard vehicle dynamics models for motion planning in relatively fast autonomous mobility scenarios. We present the idea of using adaptive motion models that trade fidelity and cost of simulation to enable a motion planner to select an adequate model. Towards this, we present representative simulation results that demonstrate the need for adaptivity. We then present some technical challenges with onboard vehicle models and our attempts at addressing these challenges. Finally, we present some results that compare raw vehicle data with model predictive results.

Commentary by Dr. Valentin Fuster
2014;():V006T10A048. doi:10.1115/DETC2014-34833.

Use of simulation in the initial assessment and testing of a rail vehicle has gained popularity in recent years with the advancement of computational power and software. However, there is a lack of guidance and approved methodologies for simulation in standards around the world. Though simulation is considered a vital tool, the use of physical tests for the acceptance/certification of a vehicle design still plays the most significant part. A better understanding of simulation methodology can reduce the requirement for costly, time consuming and potentially risky physical tests. In this paper, a new three stage methodology for investigating a wagon concept has been proposed to achieve the most suitable design in line with any mandatory requirements. The three stages are the development of the multibody model of the concept wagon, a train operation simulation to obtain the critical external forces acting on the wagon and a wagon dynamics simulation. A case study has been added to demonstrate the implementation of the proposed methodology. The simulated case study shows that simulation of wagon dynamic behaviour in multibody software, combined with data obtained from longitudinal train simulation, is not only possible, but it can identify issues with a wagon design that can otherwise be overlooked.

Topics: Simulation , Design
Commentary by Dr. Valentin Fuster
2014;():V006T10A049. doi:10.1115/DETC2014-35053.

As vibration based condition monitoring requires a good understanding of the dynamic behaviour of the structure, a good model is needed. At the TU Delft a train borne monitoring system is being developed which currently focusses on crossings. Crossings are prone to very fast degradation due to impact loading. In this paper a finite element model of a free floating frog is presented and validated up to a 100 Hz using dynamic impact measurements. The mode shapes of the free floating frog are then also compared to some preliminary results from an in-situ test. This comparison shows that the in-situ frequencies can be up to twice the free floating frequency.

Commentary by Dr. Valentin Fuster
2014;():V006T10A050. doi:10.1115/DETC2014-35146.

Multibody dynamics and the discrete element method (DEM) are integrated into one solver for predicting the dynamic response of ground vehicles which run on wheels and/or tracks on cohesive soft soils (such as mud and snow). Multibody dynamics techniques are used to model the various vehicle components and connect those components using various types of joints and contact surfaces. A penalty technique is used to impose joint and normal contact constraints. An asperity-based friction model is used to model joint and contact friction. A soft cohesive soil material model (that includes normal and tangential inter-particle force models) is presented that can account for soil compressibility, plasticity, fracture, friction, viscosity, cohesive strength and flow. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between the particles and polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. Numerical simulations of a typical vehicle going over a slopped soft soil terrain are presented to demonstrate the integrated solver. The solver can be used in vehicle design optimization.

Commentary by Dr. Valentin Fuster
2014;():V006T10A051. doi:10.1115/DETC2014-35191.

Multibody dynamics and smoothed particle hydrodynamics (SPH) are integrated into one solver for predicting the dynamic response of tanker trucks. Multibody dynamics techniques are used to model the various vehicle components and connect those components using various types of joints and contact surfaces. A penalty technique is used to impose joint and normal contact constraints (between the tires and ground, and between the tank and the fluid particles). An asperity-based friction model is used to model joint and contact friction. The liquid in the tanks is modeled using an SPH particle-based approach. A contact search algorithm that uses a moving Cartesian Eulerian grid that is fixed to the tank is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between polygonal contact surfaces and the fluid particles. The governing equations of motion for the solid bodies and the fluid particles are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The integrated solver is used to predict the dynamic response of a typical tanker truck performing a braking test with an empty, half-full and full tank. The solver can be used in vehicle design optimization to simulate and evaluate various vehicle designs.

Commentary by Dr. Valentin Fuster
2014;():V006T10A052. doi:10.1115/DETC2014-35615.

Computation of common normal between a pair of wheel and rail surface is an important sub problem in railroad simulations. In this study, it is shown that there are special position and orientation of every wheelset that makes the governing equation for computation of the common normal degenerate. This condition leads to divergence of the Newton’s iterate. To develop a procedure that can successfully compute the common normal between a straight rail and a wheelset, first parametric equation for the rail and wheel surface in track coordinate system is developed. Then four nonlinear equations whose solution is location of common normal are constructed. Three of the equations are used to eliminate three unknown in fourth equation. The resulting equation has only one unknown. A hybrid procedure based on Newton method and bisection method is used to solve the roots of the last equation. The utility of this approach is demonstrated by reporting the common normal for a pair of wheel and rail surface at singular position.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Nonlinear Dynamics of Structures

2014;():V006T10A053. doi:10.1115/DETC2014-34109.

In this paper, a z-shaped planar inextensible beam with harmonic foundation excitations is considered. The linear frequencies and modes of the beam with various folding angles are obtained through analytical formulations, and validated by numerical simulations. The continuous system is truncated into a system of ordinary differential equations with quadratic nonlinear terms by using the Galerkin method based on the modes obtained under a special folding angle, which may bring about modal interactions. The nonlinearities of the system are researched under the combined resonances, such as primary and internal resonances.

Commentary by Dr. Valentin Fuster
2014;():V006T10A054. doi:10.1115/DETC2014-34461.

Localization phenomena, also referred to as intrinsic localized modes (ILMs), are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are connected with each other by weak linear springs. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for frequency response curves for the principal parametric resonances, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N=2 and 3 are shown to examine the patterns of ILMs, and the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constant results in the appearance of Hopf bifurcation. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs) including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

Topics: Pendulums
Commentary by Dr. Valentin Fuster
2014;():V006T10A055. doi:10.1115/DETC2014-34484.

The complex nonlinear dynamic behaviors of the composite bi-stable plates with piezoelectric patch are analyzed. Based on the Vo n Karman hypothesis and Hamilton’s principle, the nonlinear dynamic model is derived. Temperature and piezoelectric effect are also considered in the model. Numerical simulations are performed to study the nonlinear vibration response of the composite bi-stable plate using the Runge-Kutta method. The analysis of the phase portrait, waveforms and bifurcation diagrams of numerical simulations shows that the period, multi-period and chaotic responses can be observed with the variation of the excitation in frequency and amplitude.

Commentary by Dr. Valentin Fuster
2014;():V006T10A056. doi:10.1115/DETC2014-34916.

We present modeling and simulation of the nonlinear dynamics of a MEMS resonator to two-source excitation. The resonator is composed of a clamped-clamped beam excited by a DC voltage load superimposed to two AC voltage loads of different frequencies. One frequency is chosen to be close to the first natural frequency of the beam and the other close to the third (second symmetric) natural frequency. A multi-mode Galerkin procedure is applied to extract a reduced-order model, which forms the basis of the numerical simulations. Time history response, Poincare’ sections, Fast Fourier Transforms FFT, and bifurcation diagrams are used to reveal the dynamics of the system. The results indicate complex nonlinear phenomena, which include quasi-periodic motion, torus bifurcations, and modulated chaotic attractors.

Commentary by Dr. Valentin Fuster
2014;():V006T10A057. doi:10.1115/DETC2014-35144.

A nonlinear characterization based on modern methods of nonlinear dynamics is performed to identify the effects of a multi-segmented nonlinearity on the response of an aeroelastic system. This system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The multi-segmented nonlinearity is associated with the pitch degree of freedom and contains two different boundaries. The results show that the presence of this multi-segmented nonlinearity results in the presence of a subcritical instability. It is also shown that there are four main transitions or sudden jumps in the system’s response when increasing the freestream velocity. It is demonstrated that the first and second sudden jumps are accompanied by the appearance and disappearance of quadratic nonlinearity induced by discontinuity and static positions. The results show that the first transition is due to a near grazing bifurcation that occurs near the first boundary of the multi-segmented nonlinearity. As for the second transition, it is demonstrated that the sudden jump at this transition is associated with a tangential contact between the trajectory and the first boundary of the multi-segmented nonlinearity and with a zero-pitch velocity incidence which is a characteristic of a grazing bifurcation. In the third and fourth transitions, it is demonstrated that there are changes in the response of the system from simply periodic to two periods having the main oscillating frequency and its superharmonic of order 3 and from chaotic to two periods having the main oscillating frequency and its superharmonic of order 3. Using modern methods of nonlinear dynamics, it is shown that this transition is due to a grazing bifurcation at the second boundary of the multi-segmented nonlinearity.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Nonlinear Energy Transfers and Harvesting

2014;():V006T10A058. doi:10.1115/DETC2014-34088.

In this computational study, a light-weight dynamic device is investigated for passive energy reversal from the lowest frequency mode to the high frequency modes of a large-scale frame structure for rapid shock mitigation. The device is based on the single-sided vibro-impact mechanism. It has two functions for passive energy transfer: a nonlinear energy sink (NES) for local energy dissipation and an energy pump to high frequency modes where a significant amount of the shock energy is rapidly dissipated. As a result, a significant portion of the shock energy induced into the linear dynamic structure can be passively reversed from the lowest frequency mode to the high frequency modes and rapidly dissipated by their modal damping. The amount of the energy dissipated by the modal damping of the high frequency modes can be controlled by the amount of inherent damping in the device. Ideally, the device can passively reverse up to 80% of the input shock energy from the lowest frequency mode to the high frequency modes when its damping is assumed to be zero and its impact coefficient of restitution is equal to unity. The shock energy redistribution between this device and the high frequency modes is found to be efficient for rapid shock mitigation in the considered 9-story dynamic structure.

Commentary by Dr. Valentin Fuster
2014;():V006T10A059. doi:10.1115/DETC2014-34134.

We develop performance criteria for the objective comparison of different classes of single-degree-of-freedom oscillators under stochastic excitation. For each family of oscillators, these objective criteria take into account the maximum possible energy harvested for a given response level, which is a quantity that is directly connected to the size of the harvesting configuration. We prove that the derived criteria are invariant with respect to magnitude or temporal rescaling of the input spectrum and they depend only on the relative distribution of energy across different harmonics of the excitation. We then compare three different classes of linear and nonlinear oscillators and using stochastic analysis tools we illustrate that in all cases of excitation spectra (monochromatic, broadband, white-noise) the optimal performance of all designs cannot exceed the performance of the linear design.

Commentary by Dr. Valentin Fuster
2014;():V006T10A060. doi:10.1115/DETC2014-34397.

To improve the broadband transduction capabilities of vibratory energy harvesters (VEHs) under random and non-stationary excitations, many researchers have resorted to purposefully introducing nonlinearities into the restoring force of the harvester. While performing this task, it is often very challenging to maintain a perfectly symmetric restoring force which usually yields a VEH with an asymmetric potential energy function. This paper investigates the influence of potential function asymmetries on the performance of nonlinear VEHs under white noise inputs. To that end, a quadratic nonlinearity is introduced into the restoring force of the harvester and its influence on the mean power for both mono- and bi-stable potentials is investigated. It is shown that, for VEHs with a mono-stable potential function, the mean output power increases with the degree of potential function asymmetry. On the other hand, for energy harvesters with a bi-stable potential function, asymmetries in the restoring force appear to worsen performance especially for low to moderate noise intensities. When the noise intensity becomes sufficiently large, the influence of the potential function’s asymmetry on the mean power diminishes. Results also reveal that a VEH with a symmetric bi-stable potential function produces higher mean power levels than the one with the most asymmetric mono-stable potential. As such, it is concluded that a VEH with a bi-stable symmetric potential is most desirable to improve performance under white noise.

Commentary by Dr. Valentin Fuster
2014;():V006T10A061. doi:10.1115/DETC2014-34524.

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

Commentary by Dr. Valentin Fuster
2014;():V006T10A062. doi:10.1115/DETC2014-34834.

This paper specifies the configuration of a harvester for absorbing energy from ambient oscillation with broadband frequencies. Two major methodologies for broadband harvesting have been developed, one is the use of a nonlinear oscillator, and the other is the use of multiple resonators. We focus on the traditional way of assembling multiple resonators but suggest some nontrivial improvements in the configuration. In order to make a variety of resonant frequencies, resonators can be connected in series, in the form of a tree-like structure. The energy absorption of the tree configuration harvester under broadband frequency excitation is tested, and additionally the placement of multiple resonators is also considered. The numerical results indicate that our proposal of the tree configuration might be useful under broadband frequency excitation.

Commentary by Dr. Valentin Fuster
2014;():V006T10A063. doi:10.1115/DETC2014-34859.

This paper aims at an analytical and numerical analysis of a bistable Duffing equation. One purpose lies in the identification of suitable oscillations for a robust energy harvesting device, i.e. a system that is well suited for a broad bandwidth excitation. A map is constructed illustrating the dependence of the harvested energy on the predominant oscillation type. It shows that inter-well oscillations lead to the highest energy harvest compared to intra-well and cross-well oscillations under harmonic excitation. The determination of the critical excitation parameters necessary to maintain inter-well oscillations is essential for the design of bistable energy harvesters. Therefore, investigations are made to attain an analytical description of the inter-well oscillation region. On this basis, a design criterion is derived for nonlinear energy harvesters.

Commentary by Dr. Valentin Fuster
2014;():V006T10A064. doi:10.1115/DETC2014-34958.

In this paper, cantilevered beam with piezoelectric layers are considered as the mechanical model of vibration energy harvesters. This paper aims to investigate the complicated dynamics behavior of the nonlinear vibrations of the cantilevered piezoelectric beam. The base excitation on the harvester beam is assumed to be harmonic load. Based on the third-order shear deformation theory and the Hamilton’s principle, the nonlinear equations of motion for the cantilevered piezoelectric beam are derived. The Galerkin’s approach is employed to discretize the partial differential equations to the ordinary differential equations with one-degree-of-freedom. The method of multiple scales is used to obtain the averaged equations in the polar form. Based on the actual work situation of the cantilevered piezoelectric beam, it is known that the base excitation plays an important role in the nonlinear vibration of the cantilevered piezoelectric beam. From the averaged equations obtained, numerical simulations are presented to investigate the effects of parameters on the steady-state responses of the cantilevered piezoelectric beam. We analyze the influences of the excitation magnitude, the excitation frequency, the piezoelectric material parameter and the damping parameter on the steady-state responses of the cantilevered piezoelectric beam. In addition, it is observed that the base excitation has significant influence on the nonlinear dynamical behavior of the cantilevered piezoelectric beam.

Commentary by Dr. Valentin Fuster
2014;():V006T10A065. doi:10.1115/DETC2014-35375.

Rotational nonlinear energy sinks (NESs) have been proposed to mitigate the response of underlying primary structures subjected to shock loading. This type of NES, which is composed of a passive mass that is free to rotate, has the potential to be easier to realize and more compact than other types of NESs. Like other types of NESs, these devices engage in targeted energy transfer, which allows for the broadband transfer of energy from the primary structure to the NES where it can be rapidly dissipated. Additionally, these devices can couple the dynamics of the primary structure and facilitate the transfer of energy from lower modes to higher modes, where it can be dissipated at a faster rate. This paper experimentally investigates the performance of this type of NES by using the results from tests of a rotational NES attached to a small-scale two-story structure. For these experiments, a shock load is provided to the primary structure using a shake-table-produced impulse-like ground motion. Additionally, by varying the amplitude of the input ground motion, the energy dependency of the performance of these devices can be investigated. The results of these experiments show that this type of NES can attenuate the response of a structure by responding in a highly effective rotational mode.

Commentary by Dr. Valentin Fuster
2014;():V006T10A066. doi:10.1115/DETC2014-35480.

This paper presents the relation between uncertainty in the excitation and parameters of vibrational energy harvesting systems and their power output. Nonlinear vibrational energy harvesters are very sensitive to the frequency of the base excitation. If the excitation frequency does not match with the resonance frequency of the energy harvester, the power output significantly deteriorates. The mismatch can be due to the inherent changes of the ambient oscillations. The fabrication errors or gradual changes of material properties also result in the mismatch. This paper quantitatively shows the probability density function for the power as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the energy harvester, and design parameters. Recently developed the conjugated unscented transformation methodology is used in conjunction with the principle of maximum entropy to compute the probability distribution for the base response and power. The computed nonlinear density functions are validated against Monte Carlo simulations.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Nonlinear Rotordynamics and Rotating Systems

2014;():V006T10A067. doi:10.1115/DETC2014-34336.

Passive control of flapwise vibrations of a wind turbine blade is investigated when a single tuned mass damper (TMD) is attached to the blade. The blade is subjected to a wind pressure which changes linearly with height from the ground level due to the wind shear. The vibrations of the wind turbine blade are theoretically and numerically analyzed to determine the natural frequency diagrams, frequency responses, stationary time histories and their FFT results. It is found that several peaks appear near the specific rotational speeds in the response curves for the blade because of both the wind pressure and the parametric excitation terms. It is also demonstrated that the optimal single TMD can suppress the resonance peaks if the fixed point theorem is used to determine the optimal values of the parameters of the TMD. The influences of the mass and install position of the TMD on its performance are also examined.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Optimization, Sensitivity Analysis, and System Design

2014;():V006T10A068. doi:10.1115/DETC2014-34162.

Evidence gathered from industry indicates that railway coupling system failures have become a limitation for further developments of heavy haul trains. Friction draft gears have implications for both longitudinal train dynamics and rolling stock fatigue; therefore, optimization of friction draft gears could be a possible solution to conquer the limitation. In this paper, a methodology for optimization of friction draft gear design based on an advanced friction draft gear model is proposed. The methodology proposes using simulation techniques such as longitudinal train dynamics simulation and a Genetic Algorithm to develop improved parameters.

Commentary by Dr. Valentin Fuster
2014;():V006T10A069. doi:10.1115/DETC2014-34193.

Generating the motion of redundant systems under general constraints within an optimization framework is a problem not yet solved, as there is, so far, a lack of completely predictive methods that concurrently solve for the optimal trajectory and the contact status induced by the given constraints. A novel approach for optimal motion planning of multibody systems with contacts is developed, based on a Sequential Quadratic Programming (SQP) algorithm for Nonlinear Programming (NLP). The objective is to detect and optimize the contact status and the relative contact force within the optimization sequential problem, while simultaneously optimizing a trajectory. The novelty is to seek for the contact information within the iterative solution of the SQP algorithm and use this information to sequentially update the resulting contact force in the system’s dynamic model. This is possible by looking at the analytical relationship between the dual variables resulting from the constrained NLP and the Lagrange multipliers that represent the contact forces in the classical formulation of constrained dynamic systems. This approach will result in a fully predictive algorithm that doesn’t require any a priori knowledge on the contact status (e.g., time of contact, point of contact, etc.) or contact force magnitude. A preliminary formulation is presented, as well as numerical experiments on simple planar manipulators, as demonstration of concepts.

Commentary by Dr. Valentin Fuster
2014;():V006T10A070. doi:10.1115/DETC2014-34269.

Planetary gear transmission system is one of the primary parts of the wind turbine drive train. Due to the assembly state, lubrication conditions and wear, the mesh stiffness of the planetary gear system is an uncertain parameter. In this paper, taking the uncertainty of mesh stiffness into account, the dynamic responses of a wind turbine gear system subjected to wind loads and transmission error excitations are studied. Firstly, a lumped-parameter model is extended to include both the planetary and parallel gears. Then the fluctuation ranges of dynamic mesh forces are predicted quantitatively and intuitively based on the combined Chebyshev interval inclusion function and numerical integration method. Finally, examples of gear trains with different interval mesh stiffnesses are simulated and the results show that tooth separations are becoming more obvious at the resonant speed by considering the fluctuating mesh stiffness of the second parallel gear stage. The nonlinear tooth separations are degenerated obviously as the fluctuation error of the mesh stiffness of the second parallel gear set is increased.

Commentary by Dr. Valentin Fuster
2014;():V006T10A071. doi:10.1115/DETC2014-34885.

The aim of this work is to develop an optimization methodology for the design of the arm of a small-sized working machine. The workspace and a reference maneuver are firstly defined together with a pre-defined redundant kinematic topology. The kinematic synthesis is framed as a constrained multi-objective problem with respect to link length variables. The constraints consider the capability of the machine to follow the assigned trajectory and to fulfill the joint limits. The cost function incorporates the solution of the inverse kinematics and uses several indices, e.g., total link lengths, manipulability, energy consumption. The multi-objective optimization problem is solved employing the weighting method, converting the initial problem into a single-objective one. The final scalar cost function is minimized by the Nelder-Mead method. On the basis of the outcomes of numerical simulations, the effectiveness and versatility of the developed procedure for the design of novel working machine arms is verified.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Software Tools for Computational Dynamics in Industry and Academia

2014;():V006T10A072. doi:10.1115/DETC2014-34545.

This paper describes a web-enabled tool capable of generating high quality videos and images from multibody dynamics simulation results. This tool, called Chrono::Render, uses the Blender modeling software as the front end with Pixars RenderMan used to create high quality images. Blender is a free and open source tool used to create and visualize 3D content and provides a robust plugin framework which Chrono::Render leverages. To produce the final image, the Blender front end passes data to a RenderMan compliant rendering engine. Along with Pixars PhotoRealistic RenderMan (PRMan), several open source options such as Aqsis, JrMan, or Pixie can be used. Preprocessing is performed on the client side, where the front end generates a work order for the RenderMan compliant rendering engine to process. This work order, which contains several scripts that define the visualization parameters, along with the pre-processed simulation data and other user-defined geometry assets is uploaded to a remote server hosted by the Simulation Based Engineering Lab. This server contains more than a thousand CPU cores used for high performance computing applications, which can be used to render many frames of an animation in parallel. Chrono::Render is free and open source software released under a BSD3 license.

Commentary by Dr. Valentin Fuster
2014;():V006T10A073. doi:10.1115/DETC2014-34817.

This paper describes an analog actuation circuit for a novel frequency-modulated MEMS gyroscope. The circuit provides an amplitude-modulated (AM) signal as the input into a RLC resonant drive circuit, which drives the gyroscope. The actuation system is composed an automatic gain control (AGC) loop, a low pass filter, an amplitude modulation component and a resonant drive circuit. The AM signal is composed of a modulating signal that excite a natural frequency of gyroscope drive mode and a carrier signal with a frequency corresponding to the electrical resonant frequency of the RLC circuit. Both feedforward and feedback AGC configurations are used to stabilize the envelope of the signal. However, the breadboard implementations of the feedforward and feedback circuits in their current configurations have similar signal to noise ratio to that of the function generator. To improve the actuation circuit performance, we plan to include the resonant drive circuit within the AGC feedback loop and implement the actuation circuit on PCB.

Commentary by Dr. Valentin Fuster
2014;():V006T10A074. doi:10.1115/DETC2014-34898.

This work presents the development of a kinematic model of a spur gear pair and the implementation of a hydrodynamic bearing in a multidisciplinary multibody dynamics software. Both models are employed to simulate the behavior of a planetary gear set typically adopted in wind turbines. Geared transmissions have been a popular choice to transmit the rotation of the main rotor to the electrical generator in this type of turbine. Compared to other kinds of transmission, a gearbox is more compact, robust and require low maintenance over its lifetime, which is interesting, since these turbines are usually installed in remote places. The gearbox of a wind turbine is normally composed by a set of spur gears and bearings, assembled in arrangement known as epicyclic. Spur gears generally have an involute profile, which allows a constant transmission of the angular speed. This kinematic constraint between gears is defined by the angle that the surface of their teeth is in contact with. This angle is known as pressure angle and, by design, it should remain constant during operation. However, a variation of the distance between gears changes this angle, which also changes the direction of the transmission of the movement. To account for this effect, the joint is described by the projection of the absolute velocity of the contact point of each gear on the line of action, which is calculated from their position. Another important group of elements are the bearings that support gear and shafts. They can absorb part of the vibration, and compensate misalignments and teeth surface failures. Hydrodynamic bearings are widely employed in turbomachinery, due to their simplicity, long life and good damping properties, which are features that wind turbines can benefit from. Most of the hydrodynamic bearing models are two dimensional, so they have to be adapted to be implemented in a multibody dynamics software. The development of these modifications is also described in this work, so any other hydrodynamic bearing model can be easily adapted using the same procedure. Finally, a model of the wind turbine gearbox is presented, and some of the features of using the aforementioned elements inside a multibody dynamics software can be highlighted.

Commentary by Dr. Valentin Fuster

10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control: Time-Varying and Time-Delay Systems

2014;():V006T10A075. doi:10.1115/DETC2014-34894.

The paper is devoted for the analysis of the dynamics effect on the 5-axis milling process of flexible details. The integrated model of milling dynamics composed by block principle in the paper is presented. The model consist of: 1) dynamical model of tool; 2) dynamical model of machined detail based on Finite Element Method (FEM); 3) phenomenological model of cutting forces and 4) algorithm of geometry modeling for instant machined chip thickness calculation. Regeneration mechanism of cutting and calculation of the machined surface are into this algorithm embedded. The elaborated model is adapted for 5-axis processing of the profiled details with 3-D complex geometry. Alteration of workpiece dynamic characteristics while the allowance removal is considered by the special algorithm of FEM grid changing based on the results of cutting geometry modeling. The results of modeling give us opportunity determine cutting forces, estimate the machined surface quality, calculate the magnitude and the character of tool and detail vibrations under the specified cutting conditions. The conception of increasing the process quality and the machinability for 3-D shaped details machining is offered in the paper. Applying the specified efficient conditions the undesired dynamical effects can be excluded on the base of the results of multi-variant simulation for milling dynamics varying the technological parameters at the different region of the processing route.

Commentary by Dr. Valentin Fuster
2014;():V006T10A076. doi:10.1115/DETC2014-34896.

The examples of multi-variant simulation of 5-axis milling dynamics while the machining of 3-D shaped detail in the paper are presented. The simulation model takes into account tool and detail vibrations. The regeneration mechanism is embedded into the model. The diagram of tool speed influence on the vibration amplitudes and cutting forces magnitudes for the different area of the tool path are determined. The system dynamic parameters and the vibrations behavior and their effect on the machined surface shape for favourable and unwanted regimes are analyzed. The effect of the dynamic characteristics alteration of the workpiece while stock removal on the process behavior is considered. Some recommendations for the efficient cutting conditions setting on the base of the model application and the obtained results in the conclusion are discussed.

Commentary by Dr. Valentin Fuster
2014;():V006T10A077. doi:10.1115/DETC2014-34923.

We present an investigation of the dynamics of a clamped-clamped microbeam excited electrostatically near its third mode. To maximize the response at the third mode, a partial electrode configuration is utilized. A multi-mode Galerkin method is used to develop a reduced order model (ROM) of the beam. A shooting method to find the periodic motion is utilized to generate frequency response curves. The curves show hardenining behavior and dynamic pull-in. We show that the dynamic amplitude of the partial configuration is higher than that of a full electrode configuration. These results are promising for the use of higher-order modes for mass detection and for ultra sensitive resonant sensors.

Commentary by Dr. Valentin Fuster
2014;():V006T10A078. doi:10.1115/DETC2014-35139.

In this paper the dynamics and stability of a linear system with stochastic delay are investigated. We assume that the delay may take finitely many different values and its dynamics are modeled by a continuous-time Markov chain. Semi-discretization is used to derive the dynamics of the second moment which leads to necessary and sufficient stability conditions for the trivial solution. We apply these results to investigate the stability of the steady state of an auto-regulatory gene-protein network. We demonstrate that stochastic delay may stabilize the system when the corresponding deterministic system with average delay is unstable.

Topics: Stability , Circuits , Delays
Commentary by Dr. Valentin Fuster
2014;():V006T10A079. doi:10.1115/DETC2014-35473.

In this paper, analytical solutions of period-1 motions in a time-delayed Duffing oscillator with a periodic excitation are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed by eigenvalue analysis. The symmetric and asymmetric period-1 motions in such time-delayed Duffing oscillator are obtained analytically, and the frequency-amplitude characteristics of period-1 motions in such a time-delayed Duffing oscillator are investigated. Numerical illustrations of period-1 motions are given by numerical and analytical solutions.

Commentary by Dr. Valentin Fuster

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