Investigation of the Dynamics of a Clamped-Clamped Microbeam Near the Third Mode Using a Partial Electrode

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.

Multi-Variant Simulation of Milling of 3-D Shaped Detail Considering Changing of Workpiece Rigidity While Cutting

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.

Dynamic Impact Measurements on Crossings, in Free Floating and In-Situ Conditions

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.

Shock Mitigation by Energy Reversal to the High Frequency Modes

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.

Performance Barriers for Single-Degree-of-Freedom Energy Harvesters Under Generic Stochastic Excitation

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.

Modeling and Experimental Validations of a Piezoelectric Energy Harvester Under Combined Galloping and Base Excitations

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.

A Framework for Problem Standardization and Algorithm Comparison in Multibody System

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.

Dynamic Response Analysis of Wind Turbine Planetary Gear System With Interval Stiffness Parameters

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.

Temporally Consistent Simulation of Robots and Their Controllers

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.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Speed Reducers

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.