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Effects of Discrete Damping on the Dynamic Behaviour of Rotating Shaft through Extended Lagrangian Formulation

Abstract

The main focus of the paper is touted as effects of discrete damping on the dynamic analysis of rotating shaft. The whole analysis is being carried out through extended Lagrangian formulation for a discrete – continuous system. The variation formulation for this system is possible, considering the continuous system as one-dimensional. The generalized formulation for one dimensional continuous rotary shaft with discrete external damper has been obtained through principle of variation. Using this extended formulation, the invariance of umbra-Lagrangian density through extended Noether’s theorem is achieved. Rayleigh beam model is used to model the shaft. Amplitude equation of rotor is obtained theoretically and validated through simulation results. The simulation results reveal the important phenomena of limiting dynamics of the rotor shaft, which is due to an imbalance of material damping and stiffness of the rotor shaft. The regenerative energy in the rotor shaft, induced due to elasticity/stiffness of the rotor shaft, is dissipated partially through the in-span discrete damper and also through the dissipative coupling between drive and the rotor shaft. In such cases, the shaft speed will not increase with increase in excitation frequency of the rotor but the slip between the drive and the shaft increases due to loading of drive.

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Energy and Transmissibility in Nonlinear Viscous Base Isolators

Abstract

High damping rubber bearings (HDRB) are the most commonly used base isolators in buildings and are often combined with other systems, such as sliding bearings. Their mechanical behaviour is highly nonlinear and dependent on a number of factors. At first, a physical process is suggested here to explain the empirical formula introduced by J.M. Kelly in 1991, where the dissipated energy of a HDRB under cyclic testing, at constant frequency, is proportional to the amplitude of the shear strain, raised to a power of approximately 1.50. This physical process is best described by non-Newtonian fluid behaviour, originally developed by F.H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model used includes a viscous term, that depends on the absolute value of the velocity, raised to a non-integer power. The identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under time-harmonic loads.

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One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets with Face Mating Gears. Part 2: Review of Practical Realization

Abstract

Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid1 and Helicon gear drives. The classical gear drives of this type are Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion has threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three type transmissions with face mating gears and a conic pinion are titled Spiroid and all three type trans- missions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in Part 1: Basic theoretical and CAD experience of this study. The second part of this article is a brief overview of the innovations and inventions created in this field at the Institute of Mechanics – Bulgarian Academy of Sciences in the last three decades. This study is also dedicated on elaboration of the specialized face gear sets for implementation into bio-robot hand. It is based on the application of 3D software technology, using 3D print for the realization of the physical models of the gear drives.

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Solitary-Wave and Periodic Solutions of the Kuramoto-Velarde Dispersive Equation

Abstract

In the present paper, solitary solutions of the Kuramoto- Velarde (K-V) dispersive equation have been found, using the deformation and mapping approach. These exact solutions show the dynamics and the evolution of dispersive solitary waves. In the case α2 = α3, three families of exact periodic solutions have been obtained by employing the bilinear transformation method.

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Study of Heat Transfer with Nonlinear Thermal Radiation on Sinusoidal Motion of Magnetic Solid Particles in a Dusty Fluid

Abstract

In this article, heat transfer with nonlinear thermal radiation on sinusoidal motion of magnetic solid particles in a dust Jeffrey fluid has been studied. The effects of Magnetohydrodynamic (MHD) and hall current are also taken under consideration. The governing equation of motion and energy equation are modelled with help of Ohms law for fluid and dust phases. The solutions of the resulting ordinary coupled partial differential equations are solved analytically. The impact of all the physical parameters of interest such as Hartmann number, slip parameter, Hall parameter, radiation parameter, Prandtl number, Eckert number and particle volume fraction are demonstrated mathematically and graphically. Trapping mechanism is also discussed in detail by drawing contour lines. The present analysis affirms many interesting behaviours, which permit further study on solid particles motion with heat and mass transfer.

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Automatic Bone Drilling – More Precise, Reliable and Safe Manipulation in the Orthopaedic Surgery

Abstract

Bone drilling manipulation often occurs in the orthopaedic surgery. By statistics, nowadays, about one million people only in Europe need such an operation every year, where bone implants are inserted. Almost always, the drilling is performed handily, which cannot avoid the subjective factor influence. The question of subjective factor reduction has its answer - automatic bone drilling.

The specific features and problems of orthopaedic drilling manipulation are considered in this work. The automatic drilling is presented according the possibilities of robotized system Orthopaedic Drilling Robot (ODRO) for assuring the manipulation accuracy, precision, reliability and safety.

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Internal Heat Source in Thermoelastic Microelongated Solid Under Green Lindsay Theory

Abstract

The present study deals with two dimensional deformation, due to internal heat source in a thermoelastic microelongated solid. A mechanical force is applied along the interface of elastic half space and thermoelastic microelongated half space. The problem is in the context of Green Lindsay (GL) theory. The analytic expressions for displacement component, normal force stress, temperature distribution and microelongation have been derived. The effect of internal heat source and microelongation on the derived components have been depicted graphically.

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Mechatronic Scanning System with Integrated Micro Electro Mechanical System Position Sensors

Abstract

In this paper, a study of a mechatronic scanning system for application in the microbiology, microelectronics research, chemistry, etc. is presented. Integrated silicon micro electro mechanical system (MEMS) position sensor is used for monitoring the displacement of the scanning system. The utilized silicon MEMS sensors with sidewall embedded piezoresistors possess a number of key advantages such as high sensitivity, low noise and extremely low temperature dependence. Design of 2D scanning system with a travel range of 22 × 22 μm2 has been presented in present work. This system includes a Compliant Transmission Mechanism, (CTM) designed as a complex elastic mechanism, comprising four parallelograms. Computer aided desigh (CAD) model and finite element analysis (FEA) of the Compliant Transmission Mechanism mechanisms have been carried out. A prototype of the scanning system is fabricated, based on CAD model. An experimental set-up of an optical system and a correlation technique for digital image processing have been used for testing the scanning system prototype. Results of the experimental investigations of the prototyped scanning system are also presented.

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Motion of a Point Mass in a Rotating Disc: A Quantitative Analysis of the Coriolis and Centrifugal Force

Abstract

In Newtonian mechanics, the non-inertial reference frames is a generalization of Newton’s laws to any reference frames. While this approach simplifies some problems, there is often little physical insight into the motion, in particular into the effects of the Coriolis force. The fictitious Coriolis force can be used by anyone in that frame of reference to explain why objects follow curved paths. In this paper, a mathematical solution based on differential equations in non-inertial reference is used to study different types of motion in rotating system. In addition, the experimental data measured on a turntable device, using a video camera in a mechanics laboratory was conducted to compare with mathematical solution in case of parabolically curved, solving non-linear least-squares problems, based on Levenberg-Marquardt’s and Gauss-Newton algorithms.

Open access
One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets With Face Mating Gears. Part 1: Basic Theoretical and Cad Experience

Abstract

Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid and Helicon gear drives. The classical gear drives of this type are the Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion possesses threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three types transmis- sions with face mating gears and a conic pinion are titled Spiroid and all three types transmissions with face mating gears and a cylindrical pinion are titled Helicon.

Principles of the mathematical modelling of tooth contact synthesis are discussed in this study. The presented research shows that the synthesis is realized by application of two mathematical models: pitch contact point and mesh region models. Two approaches for synthesis of the gear drives in accordance with Olivier’s principles are illustrated. The algorithms and computer programs for optimization synthesis and design of the studied hyperboloid gear drives are presented.

Open access