multi-DOF System Research Articles

A study on a novel two-body floating wave energy converter

This paper proposes a novel wave energy converter (WEC), which is needed for monitoring the marine environment. The converter is composed of two oscillating bodies: a floating sphere connected to a heavy submerged sphere using a tight rope and a power take off (PTO) system mounted in the floater. Energy is converted from the relative motion between the differently oscillating bodies caused by the action of the waves. The model was first tested in the frequency domain to optimize the geometry and mechanical parameters, and subsequently, a time domain model was built for simulation of a multi-DOF motion system. In the frequency domain research, a constraint was first added to the two-body WEC to address the problem of the small value of the optimized PTO damping. The state space approximation method was employed during the time domain simulation, and external forces acting on the bodies due to the tight rope were deduced. The motions of the system and power absorbed by the converter under regular and irregular waves were analyzed in detail. Finally, experiments were conducted on a scaled model, and the results show that the total power efficiency was more than 20%.

Bifurcation analysis of reduced rotor model based on nonlinear transient POD method

The singularity theory is applied to study the bifurcation behaviors of a reduced rotor model obtained by nonlinear transient POD method in this paper. A six degrees of freedom (DOFs) rotor model with cubically nonlinear stiffness supporting at both ends is established by the Newton's second law. The nonlinear transient POD method is used to reduce a six-DOFs model to a one-DOF one. The reduced model reserves the dynamical characteristics and occupies most POM energy of the original one. The singularity of the reduced system is analyzed, which replaces the original system. The bifurcation equation of the reduced model indicates that it is a high co-dimension bifurcation problem with co-dimension 6, and the universal unfolding (UN) is provided. The transient sets of six unfolding parameters, the bifurcation diagrams between the bifurcation parameter and the state variable are plotted. The results obtained in this paper present a new kind of method to study the UN theory of multi-DOFs rotor system.

Adapted linear decimation procedures for TFR analysis of non-stationary vibration signals of vehicle suspensions

The paper addresses the adaptation of linear decimation procedures (LDP) for time-frequency representation (TFR) analysis of non-stationary vibration signals of vehicle suspension. It is extremely important for designing suspensions elements to achieve proper characteristics in term of propagation of vibration. One of the major factors for the identification of defined frequency components in terms of resonance phenomena. Given that a car is a multi-DOF dynamic system, the meaning of suspension becomes even more important due to its functions such as: isolating and damping vibrations and assuring constant contact of wheel to road. Many of the important information of the vibration phenomena and dynamic system properties refer to the frequency domain. Given the volatile nature of vibrations resulting from the nonlinear characteristics of suspension elements of the vehicle and the random nature of dynamic interactions, determining the frequency characteristics is a very complex issue. For non-stationary signals the time-frequency transformation methods are recommended. But applying transformation algorithms during signal processing is not time-effective. Thus the new method, developed in AGH University of Science and Technology, for transferring non-stationary signals into pseudo-stationary signals has been tested on vibrations recorded on a real car suspension system. The paper presents the research aimed at examining the possibility of adapting the linear decimation procedure for identification of characteristic components of non-stationary vibration signals in a car. Also presented is the effect of applying of the LDP for the analysis of TFR of the vibration signal on examples of vehicle suspension and gear-meshing. There is also short description of hardware implementation of the LDP.

Investigation on chatter stability of thin-walled parts in high-speed milling based on relative transfer functions

High-speed milling of thin-walled part is a common application for aerospace industry, automotive, computer hardware and bioengineering industries. Aiming at the small-stiffness frequency response characteristics of thin-walled parts, the dynamic model and critical condition of stability was proposed by the relative transfer functions between cutter subsystem and thin-walled part subsystem in this paper. The stability critical domain was predicted by semi-discretization (SD) method based on the dynamic behavior of the multi-DOF system. It can be shown that the chatter condition in high-speed milling is closely related to both cutter speed and depth of cut, besides cutter geometry, engagement conditions, relative frequency response function, material property of thin-walled part and so on. This conclusion provides a theoretical foundation and reference for the milling mechanism research.

Design and Calibration of a Soft Multiple Degree of Freedom Motion Sensor System Based On Dielectric Elastomers

Abstract Soft robots use active deformable structures to provide highly capable yet simple and robust robotic systems. Motion sensors for soft robots must, therefore, be able to provide joint position sensing on deformable, multiple degrees of freedom (DOFs) joints often found in soft robot architectures and whose kinematics are not accurately described by closed-form mathematical models. This article proposes a method for designing dielectric elastomer sensor systems for such soft robots. The method is presented as a case study of a soft sensor system for an existing robotic manipulator designed for magnetic resonance image-guided surgery to the prostate. A calibration method based on support vector regression (SVR) is proposed to calibrate the coupled, multi-DOFs sensor system without a model. A prototype sensor system is built and is shown to reach a precision of 0.3 mm root mean square/1.2 mm maximum when calibrated with SVR. These results show sufficient precision for many applications and suggest th...

Characteristics Analysis of a 2-D Differentially Coupled Magnetic Actuator

In multi-degree-of-freedom (multi-DOF) systems, a number of motors are used to achieve a multi-DOF motion. However, these systems have problems, such as heavy weight, large size, and no back drivability due to the large number of motors. In order to solve these problems, there has been much work on multi-DOF motion using one actuator. In this paper, a novel 2-DOF differentially coupled magnetic actuator is proposed, and its structure and operating principle are described. A 2-D motion can be realized with the conventional motor control circuits.

Prediction and mitigation analysis of ground vibration caused by running high-speed trains on rigid-frame viaducts

In this study a 3D numerical analysis approach is developed to predict the ground vibration around rigid-frame viaducts induced by running high-speed trains. The train-bridge-ground interaction system is divided into two subsystems: the train-bridge interaction and the soil-structure interaction. First, the analytical program to simulate bridge vibration with consideration of train-bridge interaction is developed to obtain the vibration reaction forces at the pier bottoms. The highspeed train is described by a multi-DOFs vibration system and the rigid-frame viaduct is modeled with 3D beam elements. Second, applying these vibration reaction forces as input external excitations, the ground vibration is simulated by using a general-purpose program that includes soil-structure interaction effects. The validity of the analytical procedure is confirmed by comparing analytical and experimental results. The characteristics of high-speed train-induced vibrations, including the location of predominant vibration, are clarified. Based on this information a proposed vibration countermeasure using steel strut and new barrier is found effective in reducing train-induced vibrations and it satisfies environmental vibration requirements. The vibration screening efficiency is evaluated by reduction VAL based on 1/3 octave band spectral analysis.

Human-inspired motion model of upper-limb with fast response and learning ability – a promising direction for robot system and control

Purpose – Human movement system is a Multi-DOF, redundant, complex and nonlinear system formed by coordinating combination of neural system, bones, muscles and joints, which is robust and has fast response and learning ability. Imitating human movement system can improve robustness, fast response and learning ability of the robots. Design/methodology/approach – In this paper, we propose a new motion model based on the human motion pathway, especially the information propagation mechanism between the cerebellum and spinal cord. Findings – The proposed motion model proves to have fast response and learning ability through experiments, which matches the features of human motion. Originality/value – The proposed model in this paper introduces the habitual theory in kinesiology and neuroscience into robot control, and improves robustness, fast response and learning ability of the robots. This paper proves that introduction of neuroscience has an important guiding significance for precise and adaptive robot control, such as assembly automation.

Investigation for Synchronization of a Rotor-Pendulum System considering the Multi-DOF Vibration

This work is a continuation for our published literature for vibration synchronization. A new mechanism, two rotors coupled with a pendulum rod in a multi-DOF vibration system, is proposed to implement coupling synchronization, and the dynamics equation of mechanism is derived by Lagrange equation. In addition, the coupling relationship between the vibrobody and the pendulum rod is ascertained with the Laplace transformation method, based on the dimensionless equation of the dynamics system. The Poincare method is employed to study the synchronization state between the two unbalanced rotors, which is converted into that of existence and the stability of solutions for synchronization-balance equations. The obtained results are supported by computer simulations. It is demonstrated that the values of the spring stiffness coefficient, the length of the pendulum, and the angular installation of the pendulum are important parameters with respect to the synchronous behavior in the rotor-pendulum system.

Influential parameter analysis on vibration responses of rigid-frame viaducts induced by running high-speed trains

This study is intended to clarify the parametric influence for the vibration responses of rigid-frame viaducts in both vertical and lateral directions caused by running high-speed trains. A developed 3D numerical analysis approach considering trainbridge interaction is applied to investigate the vibration characteristics of rigid-frame viaducts. The analytical model is composed of the high-speed train model with multi-DOFs vibration system for each car and the rigid-frame viaduct model with three bridge blocks. They are linked by an assumed wheel-rail relation through the rail model considering the simulated track irregularities. By using the analytical model, the parametric study is carried out. The impact factors including train speed, train type, track irregularity, rail type and damping are investigated and identified as significant variables. The analytical results are significant and give some instructive information regarding the impact factors of the train-bridge system which could be much helpful for the mitigation of vibration and the maintenance in the high-speed railway.

Design of Torque Actuator in Hybrid Multi-DOF System Considering Magnetic Saturation

In this paper, it is proposed to substitute the tilting operation device of hybrid multi-degree-of-freedom (DOF) system from three-phase surfaced permanent-magnet motor (SPM) to single-phase torque actuator. When performing a tilting operation with a three-phase SPM which is appropriate for continuous rotary operations, there are disadvantages such as low efficiency and difficulty in control. On the other hand, a single-phase torque actuator is suitable for sequential tilt control, and the efficiency of the actuator is higher than that of a three-phase SPM. Thus, this actuator will greatly influence the development and practical usage of multi-DOF system. This paper shows a single-phase torque actuator design, considering of magnetic saturation. In addition, the proposed method was verified by the experimental results of the manufactured torque actuator.

Characteristic analysis on train-induced vibration responses of rigid-frame RC viaducts

A three-dimensional (3D) numerical analysis for the train-bridge interaction (TBI) system is actively developed in this study in order to investigate the vibration characteristics of rigid-frame reinforced concrete (RC) viaducts in both vertical and lateral directions respectively induced by running high-speed trains. An analytical model of the TBI system is established, in which the high-speed train is described by multi-DOFs vibration system and the rigid-frame RC viaduct is modeled with 3D beam elements. The simulated track irregularities are taken as system excitations. The numerical analytical algorithm is established based on the coupled vibration equations of the TBI system and verified through the detailed comparative study between the computation and testing. The vibration responses of the viaducts such as accelerations, displacements, reaction forces of pier bottoms as well as their amplitudes with train speeds are calculated in detail for both vertical and lateral directions, respectively. The frequency characteristics are further clarified through Fourier spectral analysis and 1/3 octave band spectral analysis. This study is intended to provide not only a simulation approach and evaluation tool for the train-induced vibrations upon the rigid-frame RC viaducts, but also instructive information on the vibration mitigation of the high-speed railway.

A wavelet-based method for the forced vibration analysis of piecewise linear single- and multi-DOF systems with application to cracked beam dynamics

The present investigation outlines a method based on the wavelet transform to analyze the vibration response of discrete piecewise linear oscillators, representative of beams with breathing cracks. The displacement and force variables in the governing differential equation are approximated using Daubechies compactly supported wavelets. An iterative scheme is developed to arrive at the optimum transform coefficients, which are back-transformed to obtain the time-domain response. A time-integration scheme, solving a linear complementarity problem at every time step, is devised to validate the proposed wavelet-based method. Applicability of the proposed solution technique is demonstrated by considering several test cases involving a cracked cantilever beam modeled as a bilinear SDOF system subjected to a harmonic excitation. In particular, the presence of higher-order harmonics, originating from the piecewise linear behavior, is confirmed in all the test cases. Parametric study involving the variations in the crack depth, and crack location is performed to bring out their effect on the relative strengths of higher-order harmonics. Versatility of the method is demonstrated by considering the cases such as mixed-frequency excitation and an MDOF oscillator with multiple bilinear springs. In addition to purporting the wavelet-based method as a viable alternative to analyze the response of piecewise linear oscillators, the proposed method can be easily extended to solve inverse problems unlike the other direct time integration schemes.

An efficient method for seismic analysis of structures

Purpose – The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions. Design/methodology/approach – The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis. Findings – Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations. Research limitations/implications – No limitation. Practical implications – Swift analysis has become possible. Originality/value – Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.

Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque

Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.

Multi-DOF rotor model based measurement of stiffness and damping for active magnetic bearing using multi-frequency excitation

To represent the support characteristic of active magnetic bearings (AMB), the commonly used parameters are the equivalent stiffness and the equivalent damping, which inherit the parameters of the stiffness and the damping from traditional mechanical bearings. First, by analyzing the diversity and the similarity between traditional mechanical bearing and AMB, the prior condition for applying the parametric representation of equivalent stiffness and equivalent damping to AMB is illuminated. Then, a method for measuring the equivalent stiffness and the equivalent damping of AMB-rotor system is proposed with multi-frequency excitation. One of its outstanding features is that the proposed method is based on the multi-degree of freedom (DOF) rotor model, not the single- DOF model, because the single DOF model cannot be suitably applied to the multi-DOF AMB-rotor systems. Otherwise, in order to decrease the identification error, the multi-frequency excitation can achieve the lowest peak value by means of appropriate selection for the relative phasing of each component, so that the possibility of the rotor displacement exceeding clearances of AMB and the magnetic force reaching saturation is minimized. Finally, the experiments, which are carried out on an AMB-rotor test rig with a vertical shaft, indicate that the proposed method can efficiently reduce the peak value for the superimposed multi-frequency excitation and correctly identify the equivalent stiffness and equivalent damping of AMB-rotor system.

Task space control considering passive muscle stiffness for redundant robotic arms

In service robotics, control systems allowing for skillful manipulation and dexterity constitute one of the most valuable technologies. Recently, control approaches inspired by humans or animals have attracted widespread attention, due to their merit of allowing various tasks to be performed naturally without precisely calculating their behaviors. This work, thus, focuses on the embodiment of a notable control method for a multi-DOF robotic system considering a human physical activity. In contrast to the traditional approaches, in the proposed control, the linear superposition of four control terms is exploited. These consist of joint spring-damping and virtual spring-damper terms in the joint and Cartesian spaces, respectively. Remarkably, the joint spring term is newly designed for the consideration of the simple passive muscle stiffness effect under gravity to guarantee motion repeatability and avoid the problem of ill-posedness. In the experiment, various abilities with respect to position control and compliant behavior are exposed through a real robot. Additional experiments are performed for the verification of the motion repeatability and energy-efficient motion under DOF redundancy.

A modified nonlinear POD method for order reduction based on transient time series

In this paper, a modified nonlinear proper orthogonal decomposition (POD) method based on transient time series on account of approximate inertial manifold method is proposed to reduce the order of the multiple degrees of freedom (DOFs) of a rotor system. A model of 23 DOFs rotor system comprising a pair of liquid-film bearing with pedestal looseness at one end is established by using the Newton’s second law. The multi-DOFs system is reduced to a two-DOFs model by using the modified POD method, which preserves the original dynamics behaviors. The comparison between the modified and the traditional POD method shows that the modified POD method is more effective especially in finding the bifurcation point and detecting the bifurcation diagrams and the mean square error of amplitudes curves. Finally, a relative error analysis is also carried out to evaluate the accuracy of the proposed order reduction method, indicating that the relative error is below 5 % excluding the interval between original bifurcation point and the shift of the reduced system.

A Novel Design of Manipulator Arm Control System Based on STM32

This paper presents a novel design of multi dof and multifunctional manipulator arm control system. It uses 32 bit microcontroller STM32 as the core control unit, by controlling the pulse width modulation to control the manipulator arm of the steering gear. It consists of a mechanical model, the control core module, operation module, power supply module. The manipulator arm can greatly improve labor productivity, accelerate the realization of industrial production mechanization and automation, it can replace human labor in order to realize the mechanization and automation of production, and protect the personal safety in harmful environment. It has the advantages of light weight, simple operation, and low production cost etc.

Control-Configured Design of Spheroidal, Appendage-Free, Underwater Vehicles

A highly maneuverable, spheroid-shaped, underwater robot using appendage-free, multi-degree of freedom (DOF) propulsion technologies is presented. The vehicle is hydrodynamically unstable due to the Munk moment. The vehicle is stabilized by feedback control, rather than passive fins, which facilitates rapid turns and agile motions. The new design was motivated by nuclear reactor inspection and other applications where external appendages must be avoided. Two technical challenges are addressed in this paper. One is the development of a compact, multi-DOF propulsion system that generates multiaxis water jets and switches them rapidly. The other is the design of a jet configuration and control system that augments stability and achieves high maneuverability. A nonlinear hydrodynamic model is formulated, and its linearized dynamics are analyzed to attain insights into how jet direction influences controllability and stability. A prototype vehicle is built and used to verify these concepts. The integrated design method is implemented and shown to achieve stable motions, high maneuverability, and multidirectional capability.