2-DOF System Research Articles

Design and optimization of large range 2-DOF micro-positioning clamping system

Design and optimization of large range 2-DOF micro-positioning clamping system

Design, Development, and Testing of an Intelligent Wearable Robotic Exoskeleton Prototype for Upper Limb Rehabilitation.

Neuromotor rehabilitation and recovery of upper limb functions are essential to improve the life quality of patients who have suffered injuries or have pathological sequels, where it is desirable to enhance the development of activities of daily living (ADLs). Modern approaches such as robotic-assisted rehabilitation provide decisive factors for effective motor recovery, such as objective assessment of the progress of the patient and the potential for the implementation of personalized training plans. This paper focuses on the design, development, and preliminary testing of a wearable robotic exoskeleton prototype with autonomous Artificial Intelligence-based control, processing, and safety algorithms that are fully embedded in the device. The proposed exoskeleton is a 1-DoF system that allows flexion-extension at the elbow joint, where the chosen materials render it compact. Different operation modes are supported by a hierarchical control strategy, allowing operation in autonomous mode, remote control mode, or in a leader-follower mode. Laboratory tests validate the proper operation of the integrated technologies, highlighting a low latency and reasonable accuracy. The experimental result shows that the device can be suitable for use in providing support for diagnostic and rehabilitation processes of neuromotor functions, although optimizations and rigorous clinical validation are required beforehand.

Efficient modal-based method for analyzing nonlinear aerostatic stability of long-span bridges

An efficient method for analyzing the nonlinear aerostatic stability of long-span bridges using a modal formulation is proposed. First, a simplified linear version defined as modal-based approach is introduced, which evaluates the bridge displacements using the modal properties of the bridge and speeds up the assessment of the critical velocity by applying a root-finding algorithm. Then, this scheme is further developed to identify the instability limit point in nonlinear structures by combining nonlinear FEM analyses with the linear version of the modal-based approach and a root-finding algorithm in an outer loop. The effects of considering the three components of the wind loads, the stays sag effect, structural nonlinearities, aerodynamic nonlinearities, and the initial wind angle of attack, are analyzed and discussed. The computational advantages of the proposed method and its accuracy are demonstrated through three application examples, including a simplified linear 1 DoF system, and linear and nonlinear FEM models of a full cable-stayed bridge. The collapse mechanism of the cable-stayed bridge is driven by the stiffness degradation of the stays caused by the deck vertical upward displacements. It has been found that the influence of the nonlinear aerodynamic features is very low when the structural nonlinearities control the bridge collapse.

Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping, and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

On the Zeros of an Undamped Three Degrees-of-Freedom Flexible System

Abstract This paper presents an investigation of zeros in the SISO dynamics of an undamped three degrees-of-freedom (3DOF) linear time invariant (LTI) flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros—marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP), and complex non-minimum phase (CNMP)—that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. Consequently, the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a 3DOF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped 3DOF system considered in this paper comprised one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros, (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero, and (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system.

Detailed modelling and LQG\LTR control of a 2-DOF radial active magnetic bearing for rigid rotor

The paper presents detailed modelling of rotor, electro-magnetic actuators, and accompanying electronics of an in-house-developed active magnetic bearing (AMB) test rig in a unified manner. The work is the extension of our previous work on a 1-degree-of-freedom (DOF) cantilever beam while in here, the challenging problem of levitating and spinning a 2 DOF rotor on a pair of opposing EMs is investigated. Classical three-term PID controllers are designed as a benchmark controllers, in frequency domain to stabilize the 2-DOF open-loop unstable system, and the performance is compared with the modern state-space control strategies, namely Linear Quadratic Gaussian (LQG) and combined LQG-Loop Transfer Recovery (LQG\LTR) compensators. The tuned robust controllers are deployed on a custom-designed hardware using Simulink Real-Time software. Dual axes controllers performed reasonably well when subjected to static and dynamic tests both in simulation and in experimentation. The key time domain performance objectives such as reference tracking, disturbance rejection, and minimal control efforts as well as frequency domain stability margins are accomplished. The validity of the developed model is thus confirmed through successful synthesis and implementation of both PID and LQG\LTR controllers, wherein the robust controller (LQG\LTR) outperformed the benchmark controller in terms of performance, i.e. minimal overshoot, superior disturbance rejection capabilities, and improved loop gain characteristics. The AMB actuator also showed reasonable dynamic behaviour when the levitated rotor was spun at 1000 r/min. The dynamic performance was evaluated through a two-dimensional rotor orbit plot. The study goes beyond theory and underscores practical design considerations and demonstrates real-time controller implementation.

On discontinuous dynamics of a 2-DOF system with bilateral rigid constraints and nonlinear friction

In this paper, the discontinuous dynamic analysis of a two-degree-of-freedom system with bilateral rigid constraints in the coexistence of nonlinear friction and external excitations with negative feedbacks is presented through the theory of flow switchability and flow barrier in discontinuous dynamical systems, where the nonlinear friction force is approximated by a piecewise linear, kinetic friction model with static friction. Considering inequality of coefficients of static and kinetic friction, the flow barriers on velocity boundaries are introduced. Based on friction and collisions, different domains and boundaries are defined in phase plane. The analytical conditions of motion switching at separation boundaries are explored through the force criteria and the flow barrier’s criteria based on the analysis of vector fields in domains. Finally, the numerical simulations of several typical motions are given for a better understanding of switching conditions between different motions. The results obtained in this paper are of great significance to the optimization design of mechanical system with bilateral rigid constraints and negative feedbacks.

Experimental investigation of the effects of vibration parameters on ultrasonic vibration-assisted tip-based nanofabrication

The experimental investigation of the effects of key vibration parameters including vibration mode, frequency, and amplitude on vibration-assisted tip-based nanofabrication (VTBN) is presented in this paper. To analyze the detailed effects, the experiments were specifically designed with the general factorial method. The experiments are conducted with a self-developed 3D ultrasonic VTBN system, which integrates a 3-DOF tip-based nanofabrication system and a 3D ultrasonic vibration platform. According to the experimental results, three parameters are all significant factors of the responses of single scratch. On the whole, the fabricated grooves with 2D vibration in x−y plane have the largest depth and widest width. Moreover, the vibrations with 1D vibration in x-axis and 2D vibration in x−y plane add to the width controllability of single scratch by tuning the amplitude of the component in the x-axis. The vibration amplitude has an almost linear relationship between the responses and the factors. Finally, to verify the accuracy and effectiveness of the established model, a validation test is conducted. The results show that the maximum error for the depth and the width between the model and the result is less than 8%, which validates the effectiveness of the method.

Improvement study of modal analysis for offshore structures based on reconstructed displacements

Compared with traditional acceleration-based modal analysis, displacement can serve as a more reliable and robust identification parameter for operational modal analysis (OMA). However, for offshore structures operating in the marine environment, it is difficult to find a fixed reference point for measuring structural displacements. Additionally, when displacements are reconstructed by integrating measured accelerations, unrealistic drifts are inevitably generated due to the unknown initial velocity and displacement as well as the influence of noise. Aiming at providing more accurate and stable results for identifying the modal parameters of offshore structures, this paper developed a displacement-based OMA strategy based on displacement reconstruction and stochastic subspace identification (SSI) techniques. The strategy starts from integration of the measured accelerations, and removes the drift terms by employing Chebyshev polynomials to fit the integrated displacements. Then, the reconstructed displacement-based SSI is applied to offshore structures for modal parameter identification. To demonstrate the differences between results obtained by using the reconstructed displacements and accelerations for OMA, two numerical examples are used, i.e., a synthesized ideal acceleration signal and a two-degree-of-freedom (2-DOF) system. Numerical results show that the low-frequency components in the reconstructed displacements can be more easily identified than those in the accelerations, which implies that the developed strategy may be more suited to offshore structures with low-frequency characteristics. To further investigate the performance of the developed displacement-based strategy, experimental data of a cantilever beam with similar structural properties to a monopile offshore wind turbine (OWT) is then analysed. The results show that the displacement-based strategy can produce more accurate modal parameters than using accelerations. Finally, two sets of accelerations from field tests of an OWT at difference installation stages are used: one set of data is measured from a foundation before a turbine is installed, and the other is collected from a completed OWT. Reference results are calculated by performing the eigensystem realization algorithm (ERA) on measured accelerations under ship collision excitations and the OMA results show that for low-frequency dominated structures like OWTs, the developed displacement-based OMA strategy is more stable and accurate than traditional acceleration-based modal analysis.

Multi-degree-of-freedom systems with a Coulomb friction contact: analytical boundaries of motion regimes

This paper proposes an approach for the determination of the analytical boundaries of continuous, stick-slip and no motion regimes for the steady-state response of a multi-degree-of-freedom (MDOF) system with a single Coulomb contact to harmonic excitation. While these boundaries have been previously investigated for single-degree-of-freedom (SDOF) systems, they are mostly unexplored for MDOF systems. Closed-form expressions of the boundaries of motion regimes are derived and validated numerically for two-degree-of-freedom (2DOF) systems. Different configurations are observed by changing the mass in contact and by connecting the rubbing wall to: (i) the ground, (ii) the base or (iii) the other mass. A procedure for extending these results to systems with more than 2DOFs is also proposed for (i)–(ii) and validated numerically in the case of a 5DOF system with a ground-fixed contact. The boundary between continuous and stick-slip regimes is obtained as an extension of Den Hartog’s formulation for SDOF systems with Coulomb damping (Trans Am Soc Mech Eng 53: 107–115, 1931). The boundary between motion and no motion regimes is derived with an ad hoc procedure, based on the comparison between the overall dynamic load and the friction force acting on the mass in contact. The boundaries are finally represented in a two-dimensional parameter space, showing that the shape and the extension of the regions associated with the three motion regimes can change significantly when different physical parameters and contact configurations are considered.

Analysis of Structural Vibrations of Vertical Axis Wind Turbine Blades via Hamilton’s Principle — Part 3: Pitch Angle and Equilibrium State

Pitch angle is one of the most important parameters of wind turbine blade. This study is aimed to investigate the effect of the pitch angle on the deformation of a VAWT. Lagrangian mechanics and Euler’s beam theory are used to derive the motion equations of linear structural vibration for straight blade vertical axis wind turbine blade with the pitch angle [Formula: see text]. The complete equations of motion take account of the 4-DOF deformation of flexural–flexural–torsion–extension as well as the material damping. Vibration analysis of generalized displacement about the equilibrium state (GDAES) is carried out with respect to the displacement of the equilibrium state (DOES), which is separated from the motion of vibration. After simplifying the equilibrium equation of 4-DOF into 1-DOF system, the exact solution of displacement [Formula: see text] of the equilibrium state is derived. The correction [Formula: see text] of [Formula: see text] due to the pitch angle and the characteristics of [Formula: see text] with constant linear speed are analyzed. Furthermore, we investigate the coupling effect of lateral bending and axial extension of the blade on [Formula: see text] is analyzed. Finally, the exact solution of [Formula: see text] is verified by the central difference method.

Seismic modal identification using a new approach based on weighted transmissibility

AbstractIn recent years, the transmissibility‐based operational modal analysis has attracted the attention of many researchers due to its effective applications in output‐only modal identification. However, the present research indicates that the application of this approach is not so appropriate for the ambient vibration records with short length and high spectral leakage, such as seismic records. The existence of nonperiodic frequency components in the records leads to an increase in the spectral leakage and dispersion. In this paper, an effective approach called weighted transmissibility‐based operational modal analysis is proposed to properly identify the structural modal parameters using the seismic records. The proposed method identifies the natural frequencies and mode shapes based on weighed transmissibility, so that it combines the single‐reference weighted transmissibility functions associated with different transferring outputs obtained from single or multiple loading conditions in a unique matrix formulation. Then, it extracts the vibration modes using the efficient spectra obtained from the singular value decomposition of weighted transmissibility matrices. In this paper, a theoretical example (5DOF system) is provided to indicate the capabilities of the proposed approach for identifying the modal parameters of structural systems.

Experimental and Analytical Investigation of a RC Wall with a Gabion Cushion Subjected to Boulder Impact

An experimental investigation involving the use of a full-scale pendulum device to deliver solid object impact on a reinforced concrete (RC) barrier specimen that was fitted with a layer of gabion cushion is reported in this paper. The deflection behaviour of the stem wall of the RC barrier including the tensile strains developed in the longitudinal reinforcement was of interests. Results recorded from the tests are compared with results from control experiments which were without the protection of any cushion materials. The introduction of a layer of cushion is shown to be able to have the contact force reduced by more than 95% and deflection demand reduced by about 70%. An analytical procedure employing the Hunt and Crossley contact model, Swiss code model and two-degrees-of-freedom (2DOF) system modelling technique is presented for calculating the flexural response behaviour of the cushioned barrier and validated by comparison with experimental measurements. An important outcome from the study is a simple hand calculation procedure featuring the use of a closed form expression along with a design chart which is illustrated by a worked example, to facilitate uptake in design practices.

Mitigation of Stick-Slip Vibrations in Drilling Systems With Tuned Top Boundary Parameters

Abstract Aiming at preventing stick-slip oscillations in drilling systems for oil and gas explorations, a reduced-order model is proposed to capture the nonlinear torsional dynamics of drilling operations. In this model, the drill string structure is simplified as a single-degree-of-freedom (DOF) system suffering from dry frictions at the drill bit, while the electromechanical boundary generated by the top drive system is modeled as another tunable DOF used for stick-slip suppression. To simplify and parameterize the problems, a normalized 2DOF system with negative damping and tunable parameters is deduced via nondimensionalization and linearization. Based on this system, stability criteria are obtained analytically in the five-dimensional parametric space. Stable regions and the optimized boundary parameters are found analytically. The results suggest that the system can be stabilized by an optimally tuned boundary when and only when the magnitude of the negative damping is no greater than 2. It also reveals that the stability deteriorates if the inertia on the top is huge and nonadjustable, which is the commonest scenario for commercial drilling rigs nowadays. Finally, applications of the tuned boundary in a typical drilling system for stick-slip mitigation are conducted and verified numerically. The results indicate that the control performance can be potentially enhanced by three to five times, via an additional virtual negative inertia generated by the top drive motor. This research provides an alternative approach to fully optimize the top boundary for curing stick-slip vibrations in drilling systems.

Residual vibration reduction in back-and-forth moving systems driven by slider-crank mechanisms working through a dead point configuration

This study proposes an algorithm to construct back-and-forth motion profiles to reduce residual vibrations of 1-dof linear oscillatory systems, driven through a transmission chain made up of a 1-dof linkage mechanism. This set can be advantageous for high transmission ratios, when multistage drive trains are discouraged to prevent a build-up of backlash nonlinearities. We assume that the mechanism: i) is moved by a conventional electric actuator and, ii) is working through a dead point configuration. The solution focuses on the continuity degree Cn of the motion profile to guarantee its feasibility by means of the mentioned actuators. We aim to provide an algorithm to design these profiles. The development meshes several conclusions from other studies: the classical strategies of residual vibration reduction together with an analytical solution, with regard to Cn, of the inverse kinematic problem at a dead point configuration. The development includes an analytical approach to some methods of residual vibration reduction, in addition to numerical simulations. Finally, we present experimental results on a slider-crank mechanism test bed, with a pendulum acting as the oscillatory system.

NHERI@UC San Diego 6-DOF Large High-Performance Outdoor Shake Table Facility

Since its commissioning in 2004, the UC San Diego Large High-Performance Outdoor Shake Table (LHPOST) has enabled the seismic testing of large structural, geostructural and soil-foundation-structural systems, with its ability to accurately reproduce far- and near-field ground motions. Thirty-four (34) landmark projects were conducted on the LHPOST as a national shared-use equipment facility part of the National Science Foundation (NSF) Network for Earthquake Engineering Simulation (NEES) and currently Natural Hazards Engineering Research Infrastructure (NHERI) programs, and an ISO/IEC Standard 17025:2005 accredited facility. The tallest structures ever tested on a shake table were conducted on the LHPOST, free from height restrictions. Experiments using the LHPOST generate essential knowledge that has greatly advanced seismic design practice and response predictive capabilities for structural, geostructural, and non-structural systems, leading to improved earthquake safety in the community overall. Indeed, the ability to test full-size structures has made it possible to physically validate the seismic performance of various systems that previously could only be studied at reduced scale or with computer models. However, the LHPOST's limitation of 1-DOF (uni-directional) input motion prevented the investigation of important aspects of the seismic response of 3-D structural systems. The LHPOST was originally conceived as a six degrees-of-freedom (6-DOF) shake table but built as a single degree-of-freedom (1-DOF) system due to budget limitations. The LHPOST is currently being upgraded to 6-DOF capabilities. The 6-DOF upgraded LHPOST (LHPOST6) will create a unique, large-scale, high-performance, experimental research facility that will enable research for the advancement of the science, technology, and practice in earthquake engineering. Testing of infrastructure at large scale under realistic multi-DOF seismic excitation is essential to fully understand the seismic response behavior of civil infrastructure systems. The upgraded 6-DOF capabilities will enable the development, calibration, and validation of predictive high-fidelity mathematical/computational models, and verifying effective methods for earthquake disaster mitigation and prevention. Research conducted using the LHPOST6 will improve design codes and construction standards and develop accurate decision-making tools necessary to build and maintain sustainable and disaster-resilient communities. Moreover, it will support the advancement of new and innovative materials, manufacturing methods, detailing, earthquake protective systems, seismic retrofit methods, and construction methods. This paper will provide a brief overview of the 1-DOF LHPOST and the impact of some past landmark projects. It will also describe the upgrade to 6-DOF and the new seismic research and testing that the LHPOST6 facility will enable.

A Kinetic Simulator For Distributed Mechanically Linked Marine Vehicles

Abstract The possibility of performing high-level simulations based on a kinetic model is an important step in the implementation of navigation, guidance, and control systems for marine robots. In the framework of the EUMR TNA project DINGOS, we strive to enhance a simulation tool under MATLAB/Simulink for the CNR catamaran-like vehicle SWAMP (Shallow Water Autonomous Multipurpose Platform) ASV. The vehicle can be separated into two hull vessels that can operate independently, but also with different physical connection between them (like fixed pole or rubber band). In the paper, we will describe the physical modelling of the different connection types in a 3DOF system, the implementation into the existing simulation tool for the whole vehicle, and show the results achieved in simulation runs where different connection types can be chosen and parameterized.

Influence of mass ratio on characteristics of vibration suppression of two DOF Frahm damper for two DOF system

Influence of mass ratio on characteristics of vibration suppression of two DOF Frahm damper for two DOF system

Compact 2DOF liner based on a long elastic open-neck acoustic resonator for low frequency absorption

Passive acoustic liners, used in aeronautic engine nacelles to reduce radiated fan noise, have a quarter-wavelength behavior. The simplest systems are SDOF-type (single degree of freedom), consisting of a perforated sheet backed with a honeycomb, whose absorption ability is limited to frequencies near the Helmholtz frequency. Thus, to widen the absorption frequency range, manufacturers use a 2DOF (double degree of freedom) system, with an internal layer over another honeycomb (stack of two resonators). However, one constraint is the limited thickness of the overall system, which reduces the space allotted to each honeycomb. A possible approach, based on a previous concept called LEONAR (long elastic open-neck acoustic resonator), could be to link each perforated layer to hollow tubes inserted in each honeycomb layer, in order to shift resonance frequencies to lower frequencies by extending the air column lengths. The presence of an empty chamber on both sides of the internal perforated layer also allows the tube length to be increased through tubes crossing both cavities, preserving the liner thickness. The main aim of this article is to mathematically describe the principle of a 2DOF LEONAR and to show the relevance of the mathematical model through FEM simulations and experiments performed in an impedance tube. Moreover, its behavior is analyzed through a parametric study, in order to explore its potential for an aeronautic application. A remarkable feature of 2DOF LEONAR-type materials with insertion of bottom tubes in the higher cavity is the possibility of maintaining the low frequency band provided by the original LEONAR concept, while adding a second absorption peak at a higher frequency, by the second layer and the accompanying tubes. There is a fundamental difference from classical SDOF/2DOF resonators, for which the thicknesses are obviously different.

Modelling, control and robustness analysis of a 2-DoF exoskeleton-upper limb system

Modelling, control and robustness analysis of a 2-DoF exoskeleton-upper limb system