Study On Energy Dissipation Mechanism of an Impact Damper System

The objective of this paper is to investigate how higher damping is achieved by energy dissipation as high-frequency vibration due to the addition of impact mass. In an impact damper system, collision between primary and impact masses cause an exchange of momentum resulting in dissipation of energy. A numerical model is developed to study the dynamic behaviour of an impact damper system using a MDOF system with Augmented Lagrangian Multiplier contact algorithm. Mathematical modelling and numerical simulations are carried out using ANSYS FEA package. Studies are carried out for various mass ratios subjecting the system to low-frequency high amplitude excitation. Time responses obtained from numerical simulations at fundamental mode when the system is excited in the vicinity of its fundamental frequency are validated by comparing with experimental results. Magnification factor evaluated from numerical simulation results is comparable with those obtained from experimental data. The transient response obtained from numerical simulations is used to study the behaviour of first three modes of the system excited in vicinity of its fundamental frequency. It is inferred that dissipation of energy is a main reason for achieving higher damping for an impact damper system in addition to being transformed to heat, sound, and/or those required to deform a body.

A Hybrid Ale Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

The present work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two dimensional beam finite element is presented, based on the Absolute Nodal Coordinate Formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as the case of (continuously) distributed mass.

Numerical and Experimental Investigations On Cross-sensitivity Characteristics of Instrumented Wheelset Associated with Longitudinal Force and Lateral Contact Position

It is crucial to grasp wheel-rail contact forces in the evaluation of running safety and curving performance of railway vehicles. To measure the wheel-rail contact forces, instrumented wheelset, which has the strain gauges on the wheel surface, is widely used. The purpose of this research is to increase the measurement accuracy of the wheel-rail contact forces by understanding the detailed characteristics of the instrumented wheelset. Although the various research works on the instrumented wheelset have been carried out to increase the measurement accuracy of wheel-rail contact forces, there are few works considering the longitudinal force and the lateral shift of the wheel-rail contact point. However, sometimes the longitudinal force has a non-negligible influence on the measurement accuracy on the instrumented wheelset. In this paper, the authors clarify the cross-sensitivity characteristics of the instrumented wheelset when the longitudinal force is applied to the various lateral position on the wheel tread through the FEM analysis and the static load test. The authors also propose a method to approximate the cross-sensitivity as an analytical function of the lateral and circumferential contact positions.

Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled with Piecewise Nonlinear Energy Sink

The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to a piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding to nonlinear targeted energy transfer (TET) by the PNES. The attached PNES to the considered linear dynamical systems incorporates a symmetrical clearance zone of zero stiffness content where the boundaries of the zone are coupled with the linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during the PNES mass oscillation. The underlying nonlinear dynamical behaviour of the considered structure-PNES systems is investigated by generating the fundamental backbone curves of the FEP and the bifurcated subharmonic resonance branches using numerical continuation methods. Accordingly, interesting dynamical behaviour of the nonlinear normal modes (NNMs) of the structure-PNES system on different backbones and subharmonic resonance branches has been observed. In addition, the imposed wavelet transform frequency spectrums on the FEPs have revealed that the TET takes place in multiple resonance captures where it is dominated by the nonlinear action of the PNES.

A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

In this paper, the stability of a waveboard, a human propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels, is analysed. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a Differential-Algebraic system of equations (DAE system), are linearized along the steady forward motion resorting to a recently validated linearization procedure, which allows the maximum possible reduction of the linearized equations of motion of constrained multibody systems. The approach enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of spurious null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.

An Alternative Formulation for Modeling Self-Excited Vibrations of Drillstring with PDC Bits

This work describes an alternative formulation of a system of nonlinear state-dependent delay differential equations (SDDDEs) that governs the coupled axial and torsional vibrations of a 2 DOF drillstring model considering a Polycrystalline Diamond Compact (PDC) bit with realistic cutter layout. Such considerations result in up to 100 state-dependent delays due to the regenerative effect of the drilling process, which renders the computational efficiency of conventional solution strategies unacceptable. The regeneration of the rock surface, associated with the bit motion history, can be described using the bit trajectory function, the evolution of which is governed by a partial differential equation (PDE). Thus the original system of SDDDEs can be replaced by a nonlinear coupled system of a PDE and ordinary differential equations (ODEs). Via the application of the Galerkin method, this system of PDE-ODEs is transformed into a system of coupled ODEs, which can be readily solved. The algorithm is further extended to a linear stability analysis for the bit dynamics. The resulting stability boundaries are verified with time-domain simulations. The reported algorithm could, in principle, be applied to a more realistic drillstring model, which may lead to an in-depth understanding of the mitigation of self-excited vibrations through PDC bit designs.

Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models described in terms of Standard Absolute Coordinates

A classical approach to the MBS modeling is to use absolute coordinates, i.e. a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies w.r.t. to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as alternative approach to the singularity-free time integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. A framework for interfacing Lie group integrators to standard EOM formulations is presented in this paper. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. The direct product group SO(3)xR3; and the semidirect product group SE(3) are use for representing rigid body motions. The key element of this method is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations. This embedding of Lie group integration methods allows for interfacing with standard vector space integration methods.

Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model

Dynamic response of a gear pair subjected to input and output torque or velocity fluctuations is examined analytically. Such motions are commonly observed in various powertrain systems and identified as gear rattle or hammering motions with severe noise and durability consequences. A reduced-order torsional model is proposed along with a computationally efficient piecewise-linear solution methodology to characterize the system response including its sensitivity to excitation parameters. Validity of the proposed model is established through comparisons of its predictions to measurements from a gear rattle experimental set-up. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincaré maps, and bifurcation diagrams. The severity of the resultant impacts on the noise outcome is also assessed through a rattle severity index defined by using the impact velocities.

Nussbaum-type Neural Network-based Control of Neuromuscular Electrical Stimulation with Input Saturation and Muscle Fatigue

Neuromuscular electrical stimulation is a promising technique to actuate the human musculoskeletal system in the presence of neurological impairments. The closed-loop control of NMES systems is non-trivial due to their inherent uncertain nonlinearity. In this paper, we propose a Nussbaum-type neural network-based controller for the lower leg limb NMES systems. The control accounts for model uncertainties and external disturbances in the system and, for the first time, provides a solution with rigorous stability analysis to the adaptive NMES tracking problem with input saturation and muscle fatigue. The proposed controller guarantees a uniformly ultimately bounded tracking for the knee joint angular position. To evaluate the control performance, a simulation study is taken, where the adaptation mechanism of the Nussbaum-type gain and the controller's robustness to muscle fatigue and input saturation are discussed.

Boosting the Model Discovery of Hybrid Dynamical Systems in An Informed Sparse Regression Approach

We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identifying discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In a two-stages approach, we first locate the switches between separate vector fields. Then, the dynamics among the manifolds are regressed, in this case by making use of the existing algorithm of Brunton et al. [1]. The reconstruction of the discontinuity surfaces comes as the outcome of a statistical analysis implemented via symbolic regression with small clusters (micro-clusters) and a rigid library of models. These allow to classify all the feasible discontinuities that are clustered and to reduce them into the actual discontinuity surfaces. The performances of the sparse regression hybrid model discovery are tested on two numerical examples, namely, a canonical spring-mass hopper and a free/impact electromagnetic energy harvester, engineering archetypes characterized by the presence of a single and double discontinuity, respectively. Results show that a supervised approach, i.e. where the number of discontinuities is preassigned, is computationally efficient and it determines accurately both discontinuities and set of governing equations. A large improvement in the time of computation is found with the maximum achievable reliability. Informed regression-based identification offers the prospect to outperform existing data-driven identification approaches for hybrid systems at the expense of instructing the algorithm for expected discontinuities.