Department of Mechanical Engineering

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IIT Jodhpur

The nonlinear behavior of a rotating system with large elastic deformation subjected to harmonically varying ground disturbance has been investigated numerically. The Euler-Bernoulli beam theorem has been adopted in order to derive the partial differential equation governing the dynamics characteristics of the rotating system using extended Hamilton’s principle. Method of multiple scales has been selected in approximately finding the nonlinear dynamic characteristics of the system for possible resonance conditions. The effect of nonlinearities and other variations in the values of different parameters like amplitude of external excitation, position of disk along the span, and mass of the disk on the system performance has been investigated. The outcome from the present work will furnish a proper guidance to the designers in the vicinity of the limitation and safe range of operational speed of rotor shaft under the variation of other control parameters. © Springer International Publishing Switzerland 2015.

World University root node

Mechanisms and Machine Science

Numerical studies of a nonlinear flexible rotating system under harmonic ground motion

The blind hole drilling technique, utilized for measuring residual stress by using strain gauge rosette, is associated with plastic deformation of material that is removed from the hole and also with stress concentration effect of multi point cutting tool. Further, the plasticity effect is also induced in presence of high applied stress which may lead to local yielding of the hole boundary. The present paper describes the plasticity and stress concentration effects of blind hole drilling technique on the calculation of residual stresses for SS 304L and modified Cr-Mo Grade 91 alloys. For uniaxial loading, the responses of strain gauge rosettes were investigated experimentally through tensile testing and for biaxial loading through numerical modeling. Correlations were developed to directly calculate the corrected values of residual stresses from the experimental strain data obtained through the strain gauge rosette and from stress values as per ASTM E837-13. © 2015 Elsevier Ltd. All rights reserved.

Measurement: Journal of the International Measurement Confederation

On the estimation of error in measuring the residual stress by strain gauge rosette

Several methods have been proposed in the literature for solving the Black-Scholes equation for European Options. The method proposed in the current study achieves spectral accuracy in both space and time. The method is based on minimization of a functional given in terms of the sum of squares of the residuals in the partial differential equation and initial condition in different Sobolev norms, and a term which measures the jump in the function and its derivatives across inter-element boundaries in appropriate fractional Sobolev norms. To obtain values of the solution and its derivatives the initial condition is mollified and the computed solution is post processed. Error estimates are obtained for this method. Specific numerical examples are given to show the efficiency of this method. © 2015 Elsevier Ltd.

Fulltext

Computers and Mathematics with Applications

Nonconforming least-squares spectral element method for european options

Design of a rotorcraft is a very challenging task due to its inherent complex aerodynamics and structural coupling. It is inevitable that the response characteristics and handling qualities should be analyzed in the earlier stage of design itself. Most of the handling qualities such as quickness parameters, agility parameters, bandwidth and phase delay are defined based on the control response characteristics. The flight dynamic model is needed to analyse the response characterstics of rotorcraft. The aim of the present study is to develop relatively simple flight dynamic model. It should have the ability to analyze trim, stability and response characteristics of a rotorcraft under various maneuvering conditions. This study further addresses the influence of numerical aspects of perturbation step size in linearized model and integration time step on nonlinear model response. A new updated Drees model is proposed in this study and the applicability of this approach in rotorcraft flight dynamics is studied. The effects of inflow models on the linearized model response and nonlinear model response are anlysed. © 2015 by the Asian-Australian Rotorcraft Forum. All rights reserved.

ARF 2015 - 4th Asian-Australian Rotorcraft Forum

Influence of flight dynamic modeling on control response characteristics of a rotorcraft

A crucial step in the design of rotorcraft is the prediction of oscillatory loads produced by the periodic aerodynamic environment of the helicopter rotor. These oscillatory loads cause vibrations in the helicopter. The vibrations normally pervade both the rotor and the airframe and can seriously degrade service life as well as ride qualities. Accurate prediction of helicopter oscillatory/dynamic loads and response requires the development of multidisciplinary comprehensive analysis program which combines structure, aerodynamic and inertial operators. In this study, one such comprehensive analysis model is described.The model includes elastic flap-lag-torsion and axial blade deformations, modified ONERA dynamic stall theory for airloads calculation, and Peters-He dynamic wake theory for inflow computation. In the present study the number of state variables representing the inflow are varied from 3 states to 45 states by increasing the number of harmonics and radial functions, and their effects on helicopter trim, rotor loads and control response are analysed. Results indicate that there is a clear redistribution of inflow with the increase in number of inflow states. In general there is an increase in the inflow from forward to the aft of the rotor disk with the increase in number of states. It is important to note that there is no significant change in the trim variables with the increase in number of inflow states. However with the inclusion of higher harmonic inflow states, the harmonic content increase in sectional loads and blade root loads. Higher inflow states are seen to affect helicopter control response to longitudinal input at high speeds.

41st European Rotorcraft Forum 2015, ERF 2015

Influence of inflow states of dynamic wake model on trim, rotor loads and control response of a helicopter in forward flight

An Economical Version of SAKSHAR-IDVT: Image-projective Desktop Varnamala Trainer

In the present experiment we study turbulent moist air convection, where the turbulence is buoyancy driven and characterized by gradient Rayleigh number g(1/ρ0)(Δρ/l)d4/αν ∼ 108, in a square tube of aspect ratio 8. Hot moist air is provided at the bottom of the tube, while the top of the tube is open and is exposed to cold air reservoir. In the statistically steady state, a constant temperature gradient of -6.7 0C/m is obtained in the tube excluding some distance from the tube ends. Away from the tube ends width of the tube d is found to be relevant length scale indicating homogeneity of turbulence in the axial direction. Temperature profile is obtained from measurements. Calculations are shown that explain some features of the temperature curve. Heat fluxes are estimated. © 2015 Published by Elsevier B.V.

Procedia IUTAM

Buoyancy Driven Turbulence of Moist Air

Abstract: Column reactor models of volume size 3,000 and 1,500 cm3 are made using organic materials such as sawdust and immature (drumstick) Moringa oleifera and other natural materials such as gravels (6 mm size) and ball clay available locally at Jodhpur, India. Water is passed through these porous reactors under gravity at once. The experiments were aimed at finding low-cost solutions for wastewater or sewage disposal at point of use. The change in pH during water filtration experiments is measured and modelled as functions of X1 (column height), X2 (flow rate), X3 (cumulative percolation time) and X4 (change in electrical conductivity). The parameters X1, X2, X3 and X4 are found to be highly correlated to each other irrespective of materials used for making the bioreactors. There is a hyperbolic relationship between temperature gradient within the porous material column bed through which water is percolating and time taken during that process. The temperature distribution in the gravel or sawdust media reactors is not influenced by the inflow rate or height of the reactor column used for experimentation. Distinct temperature distribution exists at each depth of the heterogeneous reactors. The multi-parameter model developed and the hyperbolic relationships help to characterize the efficacy of bioreactors. The effect of the materials on the wastewater treatment can now be individually evaluated using the multi-parameter approach presented in this paper. © 2014 Balaban Desalination Publications. All rights reserved.

Desalination and Water Treatment

Empirical models for change in pH and temperature within gravity-based reactor columns

In this paper, we propose a better planning technique of the standard walking gaits for a quadruped robot than the conventional successive gait transition method to realize omnidirectional static walking. The technique involved planning the sequence as well as motion of the swinging and supporting legs. The relationship between the stability margin, the stride length and the duty factor are also formulated mathematically. The proposed modified crawl gait is compared to the conventional method with respect to the above parameters geometrically as well as mathematically and is shown to have positive stability margin at all times. The successive gait transition is demonstrated on the modified crawl and rotation gaits. Computer simulations of a model quadruped robot were performed to validate the theory proposed. Experiments were performed on an actual quadruped robot to realize the omnidirectional static walking with increased stability margin. © 2015 ACM.

ACM International Conference Proceeding Series

Implementation of Gaits for Achieving Omnidirectional Walking in a Quadruped Robot

In this paper we consider the motion planning problem of humanoid with articulated-spine for object manipulation in double support phase. Complexity of motion planning increases due to higher degrees-of-freedom (DOF), redundancy arising due to articulated spine, inherent underactuation and stability constraint. Additionally, loop-closure constraints arise during double-support phase, and self-collision constraints exist independent of the task to be performed. These problems make motion planning of humanoids a challenging task. In this work, we address the above issues by proposing a sampling based approach for planning the motion of the humanoid. Our approach to the problem is based on RRT∗ which can generate asymptotically optimal paths. The proposed approach deals with the stability constraints by rejective sampling approach which divides random configurations generated into valid and invalid configurations. Additionally, the loop-closure constraints are tackled by separating the humanoid into two open-kinematic sub-chains, and then generating random configurations in one sub-chain whereas the remaining sub-chain uses inverse kinematics for closure. Efficacy of the proposed approach is demonstrated for wholebody motion planning of a 25-DOF humanoid in generating asymptotically optimal end-effector paths. © 2015 ACM.