Tip trajectory control of a flexible manipulator is complex because of the coupled nonlinear dynamics and non-minimum phase nature. The objective of tip trajectory control is to achieve desired tip trajectory tracking and suppress the vibrations of the tip. In this paper, two types of controller for a single link planar flexible manipulator are proposed. The first controller is a stable inversion control which is based on stable inversion technique that converts the non-minimum phase system into stable minimum phase by solving internal dynamics. This controller consists of feed forward compensator derived using stable inversion technique and a robust feedback control to stabilize the unmodeled dynamics. The second controller is based on nonlinear adaptive control derived using sliding mode technique. The analysis of closed loop asymptotic stability of two controllers is performed using Lyapnuov function. A planar single link experimental setup is designed to validate the proposed controllers. The performance of the two controllers is compared with additional payload mass on the tip.
The paper presents the results of a design analysis of a microturbine for a cogeneration micro-power plant working in accordance with organic Rankine cycle. The heat power of the plant is assumed equal to 20 kW and the corresponding available electric output is estimated to be about 3 kW. After the design analysis, the axial turbine with partial admission in all stages was built and tested experimentally. Special attention was paid to the design of the nozzle cascades forming partial admission arcs. The results showed that, for example, remarkable flow separation zones appeared in the nozzle flow channels placed at the edge of the admission segments. The modifycations of these channels reduced the undesirable effect. All the stages were equipped with movable blade shields for reducing windage losses. The effect of the angular position of the shields in the succeeding stages was investigated numerically and experimentally. The examples of the results are shown and discussed in the paper. The proposed micro-turbine has a relatively high efficiency (80%) and the rotor speed of about 8000 rpm which seems to be a low value compared with the other considered variants.
In the paper a design of a multi-stage micro-turbine with partial admission of all the stages is described in detail and the results of particular experimental investigations and numerical calculations are shown, followed by conclusions. The co-generative micro-power plant with the HFE7100 as a working medium was designed and built for experimental investigations. The values of the main cycle parameters were as follows:heat output: 20kW,electric output: 3 kW,rotor speed: 8000 rpm-12000 rpm.The micro-turbine experimental stand was designed to enable the measurement of the electric output, rotor speed, medium mass flow rate and the working medium parameters (pressure, temperature) in nearly 40 points located along the turbine and on its circumference. The turbine performance was calculated for HFE7100 but also for air and nitrogen as a working medium for testing purposes. In the first stage of experiments the turbine behavior was checked using these gases and the results were compared with the calculation data. The details, including the strength and deformation of particular turbine elements, are discussed in the paper. The dynamic behavior of the turbogenerator rotor system was also examined. The changes of a turbine inlet pressure and rotor speed in the case of varying turbine power, emergency shutdown and blackout were measured and presented in the paper in different working conditions.
The dynamic behavior of microcantilever in fluid is strongly influenced by the viscosity of the flowing fluid. The cantilever based microfluidic chips are becoming eminent due to their high sensing accuracy, reduced size for portability, easy fabrication, and low cost. Many MEMS devices such as cantilever based micro flow sensors, micro valves, micro switches, and actuators are influenced by fluid interactions. The performance characterization of MEMS devices submerged in fluid together with application developments is the major motivation to study the microfluid-microstructure interactions. Although, numerous studies have been carried out on fluid viscous loading on the cantilever by the external excitation but the dynamic behavior cantilever under the excitation from fluid flow itself have not been explored yet in micro level. Therefore, the current study presents an experimental study about the dynamic motion of microcantilever under complex harmonic flow of different fluids.
Compared with the coast and the land, the vast deep-water wind resource represents a potential development of better resource. In recent years the Floating Offshore Wind Turbine (FOWT) offers a feasible solution to generate more power with renewable energy. However, the influence of turbulent wind loads is the main cause to the floating offshore wind turbine above the rated wind speed region. Due to the fatigue vibration of the floating platform, the structure damage and the unstable generating system occur inevitably. Therefore the control system needs to concentrate more on reducing fatigue loads and irregular swing to smooth power output to enhance the stability and pull though sudden accidents. This paper proposes an innovative method of individual pitch control for FOWT, which uses an advanced memory-based optimal control strategy, to effectively reduce the asymmetric aerodynamic loads and the platform motion. In this paper, original wind turbine simulation software is developed. Analysis and simulations indicate that the advanced control strategy make a better performance on reducing the fatigue loads including tilt moment and yaw moment, and enhance the stability and reliability of the system.
A crack not detected in time can result in the catastrophic failure and cause injuries and severe damage to machinery. In this paper, a crack identification method for start-up rotor based on Hilbert-Huang Transform (HHT) is addressed. With this method, each Intrinsic Mode Function (IMF) of the vibration signal is obtained by Empirical Mode Decomposition (EMD). Then the spectrum of instantaneous frequency is accordingly calculated via Hilbert transform and is employed to detect the weak crack during the start-up process of the rotor system. To verify the validity of the mentioned method, an experiment with a cracked shaft was conducted on the Bently rotor test rig in the steady accelerating process. The results in the simulation and experiments show that HHT appears to be a more effective tool for the analysis of non-stationary vibration response of the weak cracked rotor compared with Fast Fourier Transform (FFT) and Continue Wavelet Transform (CWT).
The free vibration analysis of moving Timoshenko beam using DTM has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model by using Differential Transform Method (DTM) in this study. In order to use DTM, it is necessary to derive the governing differential equations of motion of the moving beam. At first, the governing differential equations of motion of the moving Timoshenko beam in free vibration are derived using Hamilton's principle. Parameters for the nondimensionalized multiplication factors for the constant velocity and nondimensionalized multiplication factor for the axial tensile force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of the moving Timoshenko beams with various combinations of boundary conditions using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the fundamental mode shapes are presented in graphs.
In this paper, the Homotopy Analysis Method (HAM) is employed to obtain approximate series solution of nonlinear oscillator with real order restoring force. The approximate frequency of the system obtained using HAM is compared with the exact one, and the approximate response of the system using HAM is compared with that obtained from the 4th-order Runge-Kutta Method. The accuracy and efficiency of the proposed procedure are examined by several examples.
To determine the flexural vibration band gaps in functionally graded periodic beam, transfer matrix method is applied. Moreover, a parametric study is also conducted to highlight the influences of material parameters on the gaps. The results show that the method is efficient and accurate and that bandwidth can be enlarged or reduced for different cases.
Modeling viscoelastic materials is interesting as, these materials, store as well as dissipate energy simultaneously under time varying deformation. Two efficient modeling techniques reported in literature, use coupled thermo-mechanical displacements using Augmenting Thermodynamic Fields (ATF) and coupled elastic and anelastic displacements by using Anelastic Displacement Fields (ADF), to represent the linear viscoelastic behaviors in the time domain in terms of viscoelastic parameters. This paper uses a genetic algorithm based minimization process to first find out the viscoelastic ATF as well as ADF parameters from frequency dependent values of storage modulus and loss factor normally reported in literature and next uses these parameters to build the constitutive relationships. The constitutive relationship is then used to obtain the equations of motion of a viscoelastic continuum of a stepped multi-layered cantilevered beam, discretized using finite Raleigh beam elements. Dynamic behavior of a stepped 2-material composite beam is studied as an example by finding out the first natural frequency and the frequency response amplitude. Such a model may be used for modal analysis of a generally viscoelastic beam.
This paper presents the effects of different control strategies on the performance of a six-axis active vibration isolation system based on Stewart platform mechanism and working on a decentralized displacement feedback control. A solid rigid body model with frictionless joints of the Stewart platform was developed in MSC ADAMS 10 software and six independent control loops in each of the six legs were employed for active vibration isolation. The transfer functions defined between the accelerations of the CG of the base platform and moving platform was used to assess the effectiveness of the system with respect to integral and integral plus proportional control laws. An isolation of up to 30 dB with integral control and up to 40 dB with integral plus proportional control is demonstrated along with significant corner frequency variation of the system.
In the present investigation, the geometrically nonlinear free vibration and transient responses of delaminated composite plates in hygrothermal environments are studied using the finite element method. The theoretical formulations are based on the first order shear deformation theory and von Karman type nonlinear kinematics. For modeling the delamination, multipoint constraint algorithm is incorporated in the finite element code. The governing nonlinear equations are solved by using the direct iteration method for the eigenvalue problem for free vibration and Newmark average acceleration method in the time integration in conjunction with modified Newton-Raphson iteration scheme for transient analysis. The validity of the model is demonstrated by comparing the present results with those available in the literature. The effects of delamination size and its location and hygrothermal environments on the nonlinear free vibration and transient responses of delaminated composite plates are studied.
In the present study the detection of the crack in rotor system has been carried out using the statistical features such as kurtosis, skewness and crest factor of vibration response. Such features, mainly kurtosis have been used in literature for identifying bearing and gearbox defects. The simulation results of crack detection have been compared with those of experiments carried out using laser vibrometer. Single and two cracks have been identified. It has been noted that the kurtosis and skewness changes are significant when the crack is closer to the bearing locations. The skewness is mostly negative but as the crack depth increases the positive values of skewness increase beyond the middle part of the shaft. The crest factor deviation curve is developed, which could successfully identify even cracks of small depths.
An analytical method for asymmetrical impact vibration of a beam excited periodically is investigated. As the analytical model of the beam, a cantilever is used. The cantilever collides with a clamped steel stop once in one period of its vibration at arbitral point of a span. In order to consider energy loss in a collision and duration of collision, relation between the force of restitution and the displacement response is modeled as triangular hysteresis loop characteristic. The Fourier series method is applied and approximate solutions of the steady-state responses are obtained. Obtained results are verified experimentally. The analytical results agree well with the experimental results. Applying variation equation, the infinitesimal stabilities are analyzed. It is found that the experimental results are observed at the stable regions of the analytical method.
Dynamic stability behavior of the damped composite beam subjected an action of nonconservative force is intensively investigated based on the finite element model using the Hermitian beam elements. For this, a formal engineering approach of the mechanics of thin-walled composite beams based on kinematic assumptions consistent with Vlasov beam theory is presented. An extended Hamilton's principle is employed to obtain the mass-, elastic stiffness-, geometric stiffness-, and damping matrices. Evaluation procedures for the critical values of flutter and divergence with and without damping effects of the nonconservative system are then briefly introduced. In numerical examples, the influence of various parameters on the dynamic stability of the nonconservative composite systems is newly addressed: 1) variation of the flutter loads with respect to the fiber angle change, 2) influence of external and internal damping on flutter loads by analyzing the instability region of the divergence-flutter system.
Reactobot is a one-wheel robot developed at IIT Bombay. It is balanced by a reaction wheel actuator suspended from its central axis. The Robot can get accelerated in forward or backward direction by pitching the pendulum mass within the wheel body in the same direction. Turns can be executed by tilting the robot to right or left while in motion. In this paper, we describe a multi-body dynamic model of the Reactobot, which is developed by considering seven generalized variables. The Reactobot is assumed to roll on a flat surface without slipping. The system has two nonholonomic constraints as the direction of the forward velocity of the wheel is constrained to be in the direction of wheel heading. The mathematical model of Reactobot is developed using the Lagrangian constrained generalized formulation. Subsequently, the Lagrangian multipliers are eliminated and the model is converted into 5-DOF normal form. The dynamic model is highly nonlinear. The developed mathematical model is validated by numerical simulation for special cases. The behavior of the system is along expected lines. In every simulation case, the potential energy decreases while the total energy remains constant over time since the dynamic model is conservative.
Robots are used in various application such as spot welding, aerospace, hazardous places, nuclear work, paint shop etc. Platform on which robot is mounted may vibrate. These vibrations may be deterministic or random. The effect of these vibrations on end effector (shaky hand) must be studied for the design and control of the robot. In the work the effect of sinusoidal and random excitation of the base on the end effector of single degree of freedom robot is studied. The simplified equation of motion (with rigid arms and flexible joint) is a nonlinear differential equation of Mathieu type. Lindstedt's perturbation is used for the stability analysis of periodic solutions under sinusoidal base excitation. Under sinusoidal base excitation, the solution is generated with the variation of amplitude, frequency of base excitation and stiffness of the joint. Under random excitation, base is excited with white noise having constant spectral density with and without damping.
In the process of NVH design of cavities, accurate vibro-acoustic models are required. Such models at first can be used to obtain an accurate prediction of the sound pressure response due to the structural excitations. Such predictions enable to establish whether the noise levels are within the acceptable limits or not. They can also be used to identify the acoustic and the structural modes and the boundary panels that contribute to the interior noise. These contributions can be quantified effectively via acoustic, structural and boundary panel participation factors (AMPF, SMPF and BPPF). These tools are very important for a quick identification of the trouble spots and for making decisions for modifying the design of a cavity. The structural dynamic modeling errors, which at times are difficult to eliminate in a structural FE model, can affect the accuracy of the vibro-acoustic FE models in analyzing these contributions and arriving at correct design decisions. FE model updating of the vibro-acoustic FE models can be a potential strategy for improving their accuracy and reliability. This aspect however has not been addressed in the literature. In view of this, the objective of this paper is to analyze the influence of structural dynamic modeling errors on the accuracy of participation factors to identify the noise sources and to see how updated models can be used to obtain accurate prediction of these factors and thereby an accurate picture of noise sources in the cavity. It is found that the updated vibro-acoustic models based on both the direct and the iterative method can be used effectively in obtaining an accurate ranking of the contributing sources to the interior noise.
An Active Magnetic Bearing (AMB) is a device that uses electromagnetic forces in a controlled way to support rotors without a mechanical contact. An AMB application often requires formidable control problem to overcome its inherent instability. Characteristics of the AMB depend on the control system directly. The motive of the present paper is to propose a method to optimize controller parameters of a Proportional-Integral-Derivative (PID) controller of a radial AMB in a rotor-bearing system. Theoretical relationships are developed to relate the characteristics of controller transfer-function parameters with performance parameters of the radial AMB and it is used for the tuning of controller parameters. Genetic Algorithm (GA) is adopted for the optimization of PID controller parameters. Controller parameters are bounded in such a way that these are in the acceptable range of the physical controller parameters. The MATLAB SIMULINK tool is used for generation of responses of the four-DOF rotor-bearing system with AMB by using the optimized controlled parameters. The suppression of the vibration is found to be achieved satisfactorily with the application of unbalance force and impact load in the rotor-bearing system.
The main components of a reciprocating machine are a slider, a crank, and a connecting rod. Vibration of the reciprocating machine is induced by the inertia forces resulting from the motion of these machine elements during operation. This unbalanced inertia force consists of a first-order component synchronized with the rotational speed of the crank and even higher-order components. It is impossible to balance not only the first-order component but also the even higher-order harmonic components of the inertia force for a reciprocating machine with a single slider-crank mechanism. In the present paper, in order to reduce the vibration of a reciprocating machine with a single slider-crank mechanism, a very small, lightweight vibration reduction device having a simple mechanism is proposed. The efficiency of the proposed vibration reduction device is verified experimentally. The proposed device is compact and lightweight, has a simple mechanism, and can easily be implemented in practical applications.
