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Rotordynamics is an important area in mechanical engineering. Many machines contain rotating parts. It is well known that rotating components can develop large amplitude lateral vibrations near certain speeds called critical speeds. This large amplitude vibration is called rotor whirl. This thesis is about rotor whirl. Conventional treatments in rotordynamics use what are called gyroscopic terms and treat the rotor as a one-dimensional structure (Euler-Bernoulli or Timoshenko) with or without rigid masses added to them. Gyroscopic terms are macroscopic inertial terms that arise due to tilting of spinning cross-sections. This approach, while applicable to a large class of industrially important rotors, is not applicable to a general rotor geometry. In this thesis we develop a genuine continuum level three dimensional formulation for rotordynamics that can be used for many arbitrarily shaped rotors. The key insight that guides our formulation is that gyroscopic terms are macroscopic manifestations of the prestress induced due to spin of the rotor. Using this insight, we develop two modal projection techniques for calculating the critical speed of arbitrarily shaped rotors. These techniques along with our prestress based formulation are the primary contributions of the thesis. In addition, we also present two different nonlinear finite element based implementations of our formulation. One is a laborious load-stepping based calculation performed using ANSYS (a commercially available finite element package). The other uses our nonlinear finite element code. The latter two techniques are primarily developed to provide us with an accurate answer for comparison with the results obtained using the modal projection methods. Having developed our formulation and the subsequent modal projection approximations, we proceed to validation. First, we analytically study several examples whose solutions can be easily obtained using routine methods. Second, we consider the problem of a rotating cylinder under axial loads. We use a semi-analytical approach for this problem and offer some insights into the role played by the chosen kinematics for our virtual work calculations. The excellent match with known results obtained using Timoshenko theory validates the accuracy of our formulation. Third, we consider several rotors of arbitrary shape in numerical examples and show that our modal projection methods accurately estimate the critical speeds of these rotors. After validation, we consider efficiency. For axisymmetric rotor geometries, we implement our formulation using harmonic elements. This reduces the dimension of our problem from three to two and considerable savings in time are obtained. Finally, we apply our formulation to describe asynchronous whirl and internal viscous damping phenomena in rotors.

In case of metalworking operations, the purpose of lubrication is served by a complex mixture of two or more phases, these mixtures are known as metalworking fluids (MWFs). For many decades oil-in-water emulsions have been used as metalworking fluids. The particular advantage of using oil-in-water emulsion in metalworking operations is that it combines the cooling property of water and the lubrication property of the oil. To explain the lubrication mechanism for oil-in-water emulsions as metalworking fluids a variety of models and theories has been proposed. To understand the lubrication mechanism, the role of each ingredient in the tribological process needs to be studied. In the present study a model for lubrication which determines force and proximity regimes of droplets based on the droplet size distribution is proposed. Dynamic light scattering (DLS) is used to characterize the emulsions. The small droplets are found to be the ones which enhance lubricity. DLVO (Derjaguin-Landau-Verwey-Overbeek) theory is used to validate the results. The concentration and type of surfactant is found to be the performance controlling parameter. A further analysis of the three interfacial energetics; oil/water, oil/substrate, water/substrate, is studied in the presence and absence of surfactants with the help of a Goniometer, Fourier transform infrared spectroscopy (FTIR), atomic force microscopy (AFM). Such energetics reflects the rate at which the excess surfactant molecules accumulate at the water/oil interface and desorb into the phases. The tribological response is recorded using AFM and the nanotribometer (NTR). Frictional response of the chemisorbed self-assembled monolayer of surfactant (sodium oleate) on the steel substrate reflects that a tribofilm helps in lubricating the contact under boundary lubrication by creating a low shear strength material. Water being the continuous phase in oil/water emulsion a thin water layer adjacent to steel substrate is always present. This thin layer on the solid substrate acts as a barrier to the lubricating oil droplets to reach the metal surface. The focus of the present work is also to investigate conditions which permit the disjoining of the water film to allow the oil to lubricate the metal substrate. AFM is used to study the interaction force between an oil droplet and the steel substrate through water. An oil encapsulated SiO2 colloidal probe used to simulate the oil droplet. The charge regulatory status of the substrates and interfaces are found to be critical in mapping the force characteristics when DLVO interaction is considered. The condition for activation of non-DLVO (hydration, hydrophobic, capillary) forces are also identified and found to be dependent on the physical states of surfaces. Disjoining of the thin film can be controlled by selecting surfactants based on interfacial energetics and attractive force characteristic can be achieved to facilitate lubrication.

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The performance of an acoustic filter (or muffler) is measured in terms of one of the following parameters: Insertion Loss (IL), Level difference (LD) and Transmission loss (TL). All these three parameters may be evaluated in terms of the four-pole or transfer matrix parameters. Appropriate experimental setups have been designed and developed and practical considerations are described. Measured values of TL are compared with the analytically predicted values. It is shown that the Two-Source-Location method is relatively the best. To start with, the matrizant analysis of conical concentric tube resonators is validated experimentally. The effect of mean flow is investigated. The experimental setup is specially designed to measure the pressure transfer function across the test muffler. It is shown that there is reasonably good agreement between the predicted values of the transfer function and the measured ones for incompressible mean flow as well as stationary medium. To measure insertion loss of muffler, one needs to calculate the source impedance. The internal impedance of a sound source can be measured using direct or indirect methods. The four-load SPL measurement method is one such indirect method wherein there are three nonlinear equations in terms of two unknowns which makes one of the equations redundant. This leads to erroneous results. To overcome this inherent weakness, two alternatives multi-load methods have been offered in the literature; namely, the least squares and the direct least squares method, to analyze the measured data used for four (or more) different loads. These two methods produce better results than the four-load SPL measurement method used earlier. These measurement methods have been tested on a loudspeaker to measure its source impedance and the results are validated with a known additional acoustic load. Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss (TL) spectrum which drastically lower the overall TL of the muffler. Many of the present days automobile exhaust systems make use of the extended tube mufflers, often with perforated ducts because of their low back pressure and good acoustic performance. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. However, these cancellations would not occur unless one altered the geometric lengths for the extended tube and perforated tube resonators in order to incorporate the effect of the evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. This is investigated here experimentally as well as numerically (through use of 3-D FEM software) for a moving medium as well as stationary medium. The effect of temperature on the end corrections is also investigated. These tuned extended-tube chambers, however, suffer from the disadvantages of high back pressure and aerodynamic noise generation at the area discontinuities. These two disadvantages can be overcome by means of a perforated bridge between the extended inlet and the extended outlet. One dimensional control volume approach is used to analyze this muffler configuration. It is validated experimentally making use of the two source-location method, which is proven to be the best method available to us. It is thus shown that the inertance of holes plays a role similar to the lumped inertance generated by evanescent 3-D modes at the terminations of the quarter wave resonators in the case of the double-tuned extended tube chambers. The effect of mean flow is also investigated. The resultant transfer matrix is then used to carry out a systematic parametric study in order to arrive at empirical expressions for the differential lengths as well as the end corrections. Thus, an extended concentric tube resonator can be tuned such that the first three troughs that characterize the corresponding simple chamber transmission loss (TL) curve may be eliminated making use of the proposed procedure. In fact, the entire TL curve at low and medium frequencies may be substantially lifted, making the tuned extended concentric tube resonator a viable design option.

This thesis work provides an insight into the design of Force-amplifying Compliant Mechanisms (FaCMs) that are integrated with micromachined resonant accelerometers to increase their sensitivity. An FaCM, by mechanically amplifying the inertial force, enhances the shift in the resonance frequency of the beams used for sensing the acceleration whose effect causes an axial force on the beams. An extensive study on different configurations of resonators namely, single beam resonator, single-ended tuning fork (SETF), and double-ended tuning fork (DETF), is carried out to gain insights about their resonant behavior. The influence of the boundary conditions on the sensor’s sensitivity emerged from the study. We found that not only the force-amplification factor but also the multi-axial stiffness of the FaCM and proof-mass influence the resonance frequency of the resonator as well as the bandwidth of the modified sensor for certain configurations but not all. Thus, four lumped parameters were identified to quantify the effectiveness of an FaCM. These parameters determine the boundary condition of the sensing beams and also the forces and the moment transmitted to them. Also presented in this work is a computationally efficient model, called the Lumped Parameter Model (LPM) for evaluation of the sensitivity. An analytical expression for the frequency-shift of the sensing resonator beams is obtained by considering the FaCM stiffness parameters as well as the lumped stiffness of the suspension of the inertial mass. Various FaCMs are evaluated and compared to understand how the four lumped parameters influence the sensor’s sensitivity. The FaCMs are synthesized using topology optimization to maximize the net amplification factor with the volume constraint. One of the FaCMs outperforms the lever by a factor of six. Microfabrication of resonant accelerometer coupled with FaCM and comb-drive actuator is carried out using a silicon-on-insulator process. Finally, the selection map technique, a compliant mechanism redesign methodology is used for enhancing the amplification of FaCMs. This technique provides scope for further design improvement in FaCMs for given sensor specifications.

This thesis deals with developing Galerkin based solution strategies for several important classes of differential equations involving derivatives and integrals of various fractional orders. Fractional order calculus finds use in several areas of science and engineering. The use of fractional derivatives may arise purely from the mathematical viewpoint, as in controller design, or it may arise from the underlying physics of the material, as in the damping behavior of viscoelastic materials. The physical origins of the fractional damping motivated us to study viscoelastic behavior of disordered materials at three levels. At the first level, we review two first principles models of rubber viscoelasticity. This leads us to study, at the next two levels, two simple disordered systems. The study of these two simplified systems prompted us towards an infinite dimensional system which is mathematically equivalent to a fractional order derivative or integral. This infinite dimensional system forms the starting point for our Galerkin projection based approximation scheme. In a simplified study of disordered viscoelastic materials, we show that the networks of springs and dash-pots can lead to fractional power law relaxation if the damping coefficients of the dash-pots follow a certain type of random distribution. Similar results are obtained when we consider a more simplified model, which involves a random system coefficient matrix. Fractional order derivatives and integrals are infinite dimensional operators and non-local in time: the history of the state variable is needed to evaluate such operators. This non-local nature leads to expensive long-time computations (O(t2) computations for solution up to time t). A finite dimensional approximation of the fractional order derivative can alleviate this problem. We present one such approximation using a Galerkin projection. The original infinite dimensional system is replaced with an equivalent infinite dimensional system involving a partial differential equation (PDE). The Galerkin projection reduces the PDE to a finite system of ODEs. These ODEs can be solved cheaply (O(t) computations). The shape functions used for the Galerkin projection are important, and given attention. Calculations with both global shape functions as well as finite elements are presented. The discretization strategy is improved in a few steps until, finally, very good performance is obtained over a user-specifiable frequency range (not including zero). In particular, numerical examples are presented showing good performance for frequencies varying over more than 7 orders of magnitude. For any discretization held fixed, however, errors will be significant at sufficiently low or high frequencies. We discuss why such asymptotics may not significantly impact the engineering utility of the method. Following this, we identify eight important classes of fractional differential equations (FDEs) and fractional integrodifferential equations (FIEs), and develop separate Galerkin based solution strategies for each of them. Distinction between these classes arises from the fact that both Riemann-Liouville as well as Caputo type derivatives used in this work do not, in general, follow either the law of exponents or the commutative property. Criteria used to identify these classes include; the initial conditions used, order of the highest derivative, integer or fractional order highest derivative, single or multiterm fractional derivatives and integrals. A key feature of our approximation scheme is the development of differential algebraic equations (DAEs) when the highest order derivative is fractional or the equation involves fractional integrals only. To demonstrate the effectiveness of our approximation scheme, we compare the numerical results with analytical solutions, when available, or with suitably developed series solutions. Our approximation scheme matches analytical/series solutions very well for all classes considered.

Aluminum - Silicon alloys are recognized as appropriate materials for high performance cast components used in transportation powertrain applications. A combination of excellent wear resistance, good thermal conductivity and low density make these materials good candidates for engine bore applications. It is well accepted that the tribological properties of these alloys are dictated by the presence of hard eutectic silicon particles and their distribution in the soft aluminum matrix. Three near-eutectic aluminum-silicon engine bore alloys manufactured by different processing routes such as sand casting, chill casting and spray compaction were investigated to determine the influence of solidification on evolution of microstructure of these alloys and to establish correlation of microstructure with tribological properties. The spatial distribution of the silicon particles in aluminum matrix is analyzed using various image analysis techniques and contact distribution studies. The chill cast alloy shows large columnar primary aluminum dendrites interspersed with coarse silicon particles. The sand cast and spray compacted alloys show better spatial distribution of refined silicon particles. Microstructures generated under different solidification modes are found to have varying morphologies. The crystallographic orientations of the dendritic and eutectic aluminum as well as that of the eutectic silicon were studied using electron backscatter diffraction (EBSD). The eutectic silicon nucleating in chill cast alloy is found to exhibit strong orientation relationship with the aluminum matrix. The crystallographic orientation relationship shows that the solidification modes of the eutectics in these three alloys are different, from alloy to alloy, due to their different solidification rates and due to the addition of grain refiners and modifiers. The hardness values of the aluminum matrix and silicon particles of these alloys were found using nanoindentation and micro indentation tests. Preliminary wear studies were carried out on etched and unetched test alloys in dry reciprocating sliding. The results show that of the three test alloys, the alloy in which eutectic regions nucleate heterogeneously from the primary aluminum dendrites gives the best wear resistance and the highest hardness. The very low friction coefficient recorded for the etched alloys is accounted for by the insitu formation of a thin sheet of tribofilm on the protruding silicon particles. The physical and chemical natures of this protective film are being investigated.

A pragmatic method for designing compliant mechanisms is developed in this thesis, by selecting among existing mechanisms one that may be modified as required. This method complements existing techniques by answering questions of the existence and multiplicity of solutions for the given specifications of a practical problem. The premise for the method is a 2D map that juxta- poses the problem-specifications and the characteristics of compliant mechanisms in a database. The selection of the most suitable mechanisms is similar to Ashby's method of material selection. In our method, stuffiness, inertia, and the inherent kinematic characteristics of compliant mechanisms are analogous to material properties in Ashby's method. These characteristics capture the lumped behavior of compliant mechanisms in static and dynamic situations using spring-lever (SL) and spring-mass-lever (SML) models. The work includes the development of computation- ally efficient methods to compute the SL and SML model characteristics of single-input and single-output compliant mechanisms. Also developed in this work is a method to determine a feasible map by solving the governing equations of equilibrium and several inequalities pertaining to problem- specifications. The map helps not only in assessing the feasibility of the specifications but also in re-designing the mechanisms in predetermined ways to nd multiple solutions, all of which account for practical considerations. The method pays due attention to the overall size, strength considerations, manufacturability, and choice of material. It also enables minimal alterations of the problem-specifications when the user prefers a particular mechanism in the database. All these features are implemented in a web-based Java program with a graphical user interface that can be accessed at http://www.mecheng.iisc.ernet.in/ m2d2/CM design. Six case- studies that include micro machined inertial sensors, miniature valve mechanisms, ultra-sensitive force sensors, etc., are documented in detail to demonstrate the usefulness of the method in practice.

In order to meet future emission norms for small carbureted SI engines, such as those used on motorcycles in India, there is a need to study mixture preparation, specifically the two-phase flow exiting the carburetor and entering the inlet manifold. A fully functional, modular experimental rig is designed and erected for performing both qualitative and quantitative flow visualization. The vibrations of the engine are minimized to reduce their effect on the flow. A special, optically accessible tube of square cross-section is added between the carburetor and the inlet manifold, to enable the visualization of flow at the exit of the carburetor. An electronic circuit to obtain a signal for the engine crank angle and convert it to a standard TTL pulse, for use on standard imaging systems to capture cycle resolved-images is also designed. The flow in the optical section is qualitatively visualized using high and low speed cameras. The resulting images and movies show two modes of fuel transport within the inlet manifold, one of which is in the form of a dense cloud of fine fuel droplets during some part of the intake stroke. The second mode is in the form of a film at all times in the cycle, along the lower surface of the inlet manifold during idling and along vertical walls under loaded conditions. Recirculation is seen on the vertical walls of the manifold during idling and under load. Finally, the thickness of the fuel film in the optical section at the exit of the carburetor is measured, using PLIF. This part of the study also reveals that there is a film on upper surface of the optical section, at all loads and speeds. This film is lesser than the resolution of measurement for low loads, and increases to 0.5 mm in the case of highest load and speed attained at full throttle. In contrast to the loaded conditions, during idling, the film occurs on the lower surface of the manifold and its thickness is highest (1 mm.). The film is also present throughout the cycle during idling and all load-speed conditions, suggesting that the mixture that goes into the engine has a significant part of fuel in liquid form.