A two-mass model with a spring and a damper in the vertical direction, accounting for vertical translational motion and a torsional spring and a damper connecting the rotational motion of two masses is used to simulate the dynamics of a tennis ball as it comes into contact with a flat surface. The model is supposed to behave as a rigid body in the horizontal direction. The model is used to predict contact of the ball with the ground and applies from start of contact to end of contact. The springs and dampers for both the vertical and the rotational direction are linear. Differential equations of motion for the two-mass system are formulated in a plane. Two scenarios of contact are considered: Slip and no-slip. In the slip case, Coulomb??s law relates the tangential contact force acting on the outer mass with the normal contact force, whereas in the no-slip case, a kinematic constraint relates the horizontal coordinate of the center of mass of the system with the rotational coordinate of the outer mass. Incorporating these constraints in the differential equations of motion and applying initial conditions, the equations are solved for kinematics and kinetics of these two different scenarios by application of the methods for the solutions of second-order linear differential equations. Experimental data for incidence and rebound kinematics of the tennis ball with incidence zero spin, topspin and backspin is available. The incidence angles in the data range from 17 degrees up to 70 degrees. Simulations using the developed equations are performed and for some specific ratios of inner and outer mass and mass moments of inertia, along with the spring-damper coefficients, theoretical predictions for the kinematics of rebound agree well with the experimental data. In many cases of incidence, the simulations predict transition from sliding to rolling during the contact, which is in accordance with the results obtained from available experimental measurements conducted on tennis balls. Thus the two-mass model provides a satisfactory approximation of the tennis ball dynamics during contact.

A two-mass model with a spring and a damper in the vertical direction, accounting for vertical translational motion and a torsional spring and a damper connecting the rotational motion of two masses is used to simulate the dynamics of a tennis ball as it comes into contact with a flat surface. The model is supposed to behave as a rigid body in the horizontal direction. The model is used to predict contact of the ball with the ground and applies from start of contact to end of contact. The springs and dampers for both the vertical and the rotational direction are linear. Differential equations of motion for the two-mass system are formulated in a plane. Two scenarios of contact are considered: Slip and no-slip. In the slip case, Coulomb??s law relates the tangential contact force acting on the outer mass with the normal contact force, whereas in the no-slip case, a kinematic constraint relates the horizontal coordinate of the center of mass of the system with the rotational coordinate of the outer mass. Incorporating these constraints in the differential equations of motion and applying initial conditions, the equations are solved for kinematics and kinetics of these two different scenarios by application of the methods for the solutions of second-order linear differential equations. Experimental data for incidence and rebound kinematics of the tennis ball with incidence zero spin, topspin and backspin is available. The incidence angles in the data range from 17 degrees up to 70 degrees. Simulations using the developed equations are performed and for some specific ratios of inner and outer mass and mass moments of inertia, along with the spring-damper coefficients, theoretical predictions for the kinematics of rebound agree well with the experimental data. In many cases of incidence, the simulations predict transition from sliding to rolling during the contact, which is in accordance with the results obtained from available experimental measurements conducted on tennis balls. Thus the two-mass model provides a satisfactory approximation of the tennis ball dynamics during contact.

Some seabirds (such as Northern Gannets and Brown Boobies) can dive from heights as high as 30 m reaching speeds of up to 24 m/s as they impact the water surface. It is perceived that physical geometry, particularly of the beak, allows them to endure relatively high impact forces that could otherwise kill non-diving birds. Acceleration data from simplified models of diving birds agree with simulated data for one species (Northern Gannet), however, no reliable experimental data with real bird geometries exist for comparison purposes. This study utilizes eleven 3D printed diving birds (five plunge-diving, five surface-diving and one dipper) with embedded accelerometers to measure water-entry impact accelerations for impact velocities ranging between 4.4 - 23.2 m/s. Impact forces for all bird types are found to be comparable under similar impact conditions and well within the safe zone characterized by neck strength as found in recent studies. However, the time each bird requires to reach maximum impact acceleration and its effect represented here by the derivative of acceleration (i.e., jerk), is different based on its beak and head shape. We show that surface diving birds cannot dive at high speeds as the non-dimensional jerk experienced exceeds a safe limit estimated from human impact analysis, whereas those by plunge divers do not.

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One of the most complicated issues the aerospace and aviation industries are dealing with is aircraft icing. The impact and freezing process of a water droplet on a cold surface has been investigated over time in order to develop preventative methods for avoiding icing. In the present study, we examined the behavior of a water droplet impacting on an aluminum plate with a surface roughness of 0.01µm and surface temperature variation from room temperature to 0oC, −5oC, −10oC and −15oC. The effect of droplet impact Reynolds number along with surface temperature variation on non-dimensional parameters like spread factor, retraction rate, and spread velocity is analyzed. The increase in impact Reynolds number and droplet spread factor is observed with a rise in the initial height of the droplet. At a higher Reynolds number, inertial forces are dominant over viscous and capillary forces, while at a lower Reynolds number, surface temperature shows a significant effect. The graphical representation of droplet retraction rate indicates a decrease with lower surface temperature and a rise with higher Reynolds numbers. Moreover, the spread velocity of the droplet is higher with an increased Reynolds number, and surface temperature does not have a notable effect on it. A rapid transition of momentum from vertical to horizontal direction occurs, and droplet dissipates energy in overcoming the viscous effects. The effect of surface roughness variation coupled with surface temperature is investigated in detail for three different surface roughness of aluminum and glass. The increase in surface roughness and temperature enhance hydrophobic behavior by repelling the droplet, while reduced surface temperatures show hydrophilic behavior by causing adhesion of the droplet on surface. / Master of Science / The supercool water droplets exist in the atmosphere and whenever these droplets come in contact with a cold surface, ice is formed. This ice accretion phenomena is observed not only on aircraft's control surfaces, but also on jet engines, power transmission lines and wind turbine blades. Research is on going to understand the impact and freezing process of water droplets on different cold surfaces and subsequently devise methods for avoiding this phenomena. In the current research work, the droplet impact is analyzed on an aluminum plate with surface roughness of 0.01µm. The spread factor of the droplet indicates the liquid surface contact area, and an increase is observed at larger heights in spread factor, impact velocity, and Reynolds number due to high inertia. Then, the surface temperature is varied from 0oC to −5oC, −10oC and −15oC, and it is observed that as the viscous effects are higher at lower surface temperatures, the droplet dissipates more energy in overcoming the high viscous effects and the spread factor decreases . Moreover, the spread velocity of the droplet is the measure of rate at which the liquid-solid contact area increases. Initially the droplet has vertical momentum, and on impact it shifts from vertical to horizontal direction, as the velocity rises drastically after impact. Surface roughness is another important factor that affects the ability of a surface to repel (hydrophobic) and attract (hydrophilic) the droplet by affecting its spread rate. The more the surface roughness, the droplet spread factor reduces and droplet rebounds indicating the hydrophobic nature. While adhesion is observed at the lower surface temperature, even with high roughness, showing the hydrophilic nature.

The research topic of liquid drop interaction with solid surfaces is being actively pursued to gain in-depth understanding of several practical cases such as the impingement of fuel spray droplets on surfaces like combustion chamber walls and piston top of an I.C. engine, heat transfer via spray impingement, ink-jet printing, etc. In most of the cases, the physical and flow properties of the liquid drop/spray may be fixed whereas it may be possible to tune the physical and chemical properties of the solid surface thereby enabling to control the interaction process. The present work belongs to the study of liquid drop-solid surface interaction process with special focus on the physical characteristics of solid surface. The thesis reports an experimental study of the dynamics of millimetric water drops impacted onto the junction of dual-textured substrates made of stainless steel. The dual-textured substrates consisted of hydrophobic (textured) and hydrophilic (smooth) portions. The entire textured portion comprised of parallel groove-like structures separated by solid posts/pillars. Two dual-textured substrates, which differ only in the geometry of their textured portions, were employed. Surface topography features of the dual-textured substrates were characterized using scanning electron microscopy (SEM) and optical surface profilometer. The wetting behavior of the textured and smooth portions of the substrates, quantified in terms of the equilibrium, advancing, and receding contact angles adopted by a water drop on the surface portions, was characterized experimentally through the methods of sessile drop formation, captive needle volume addition, and drop evaporation under ambient conditions. Free-falling water drops were impacted from a height onto the junction between the hydrophobic (textured) and hydrophilic (smooth) portions of the dual-textured substrates. A set of twelve different impact experiments were conducted on each of the target substrates with drop impact velocity (Uo) ranging from 0.37 to 1.50 m/sec. The dynamics of drop impact were captured using a high speed camera with frame rate ranging from 3000 to 10000 frames per second. From the captured frames, the temporal variations of the impacting drop parameters were measured using a MATLAB-assisted program. A systematic analysis of experimental data revealed the existence of four distinct regimes of drop dynamics on the dual-textured substrate: (a) early inertia driven drop spreading, (b) primary drop receding, (c) secondary spreading on the hydrophilic portion, and (d) final equilibrium regimes. It is shown that the drop impact dynamics during the early inertia driven impact regime remains unaffected by the dual-texture feature of the substrate. A larger retraction speed of impacting drop liquid observed on the hydrophobic portion of the substrate makes the drop liquid on the higher wettability/hydrophilic portion to advance further (secondary drop spreading). The net horizontal drop velocity towards the hydrophilic portion of the dual-textured substrate decreases with increasing drop impact velocity. The available experimental results suggest that the movement of bulk drop liquid away from the impact point during drop impact on the dual-textured substrate is larger for the impact of low inertia drops. A semi-empirical model, based on the balance of the wettability gradient, contact angle hysteresis, and viscous forces acting on impacted drop liquid on the substrate, is formulated to predict the movement of bulk drop liquid away from the impact point (ξ). A satisfactory comparison between the model predictions and the experimental measurements is reported for the variation of ξ with Uo.

The thesis is concerned with the contact mechanics behaviour of non-conforming solids. The geometry of the solids considered gives rise to various contact configurations, from concentrated contacts with circular and elliptical configuration to those of finite line nature, as well as those of less concentrated form such as circular flat punches. The radii of curvature of mating bodies in contact or impact give rise to these various nonconforming contact configurations and affect their contact characteristics, from those considered as semi-infinite solids in accord with the classical Hertzian theory to those that deviate from it. Furthermore, layered solids have been considered, some with higher elastic modulus than that of the substrate material (such as hard protective coatings) and some with low elastic moduli, often employed as tribological coatings (such as solid lubricants). Other bonded layered solids behave in viscoelastic manner, with creep relaxation behaviour under load, and are often used to dampen structural vibration upon impact. Analytic models have been developed for all these solids to predict their contact and impact behaviour and obtain pressure distribution, footprint shape and deformation under both elastostatic and transient dynamic conditions. Only few solutions for thin bonded layered elastic solids have been reported for elastostatic analysis. The analytical model developed in this thesis is in accord with those reported in the literature and is extended to the case of impact of balls, and employed for a number of practical applications. The elastostatic impact of a roller against a semi-infinite elastic half-space is also treated by analytic means, which has not been reported in literature. Two and three-dimensional finite element models have been developed and compared with all the derived analytic methods, and good agreement found in all cases. The finite element approach used has been made into a generic tool for all the contact configurations, elastic and viscoelastic. The physics of the contact mechanical problems is fully explained by analytic, numerical and supporting experimentation and agreement found between all these approaches to a high level of conformance. This level of agreement, the development of various analytical impact models for layered solids and finite line configuration, and the development of a multi-layered viscoelastic transducer with agreed numerical predictions account for the main contributions to knowledge. There are a significant number of findings within the thesis, but the major findings relate to the protective nature of hard coatings and high modulus bonded layered solids, and the verified viscoelastic behaviour of low elastic modulus compressible thin bonded layers. Most importantly, the thesis has created a rational framework for contact/impact of solids of low contact contiguity.

A very short and disagreeable audible and tactile response from a vehicle driveline may be excited when the throttle is abruptly applied or released, or when the clutch is rapidly engaged. The condition is most noticeable in low gear and in slow moving traffic, when other background engine and road noise levels are low. This phenomenon is known as clonk and is often associated with the first cycle of shuffle response, which is a low frequency longitudinal vehicle movement excited by throttle demand. It is often reported that clonk may coincide with each cycle of the shuffle response, and multiple clonks may then occur. The problem is aggravated by backlash and wear in the drivetrain, and it conveys a perception of low quality to the customer. Hitherto, reported investigations do not reveal or discuss the mechanism and causal factors of clonk in a quantitative manner, which would relate the engine impulsive torque to the elastic response of the driveline components, and in particular to the noise radiating surfaces. Crucially, neither have the issues of sensitivity, variability and non-linearity been addressed and published. It is also of fundamental importance that clonk is seen as a total system response to impulsive torque, in the presence of distributed lash at the vibro-elastic impact sites. In this thesis, the drivetrain is defined as the torque path from the engine flywheel to the road wheels. The drivetrain is a lightly damped and highly non-linear dynamic system. There are many impact and noise emitting locations in the driveline that contribute to clonk, when the system is subjected to shock torque loading. This thesis examines the clonk energy paths, from the initial impact to many driveline lash locations, and to the various noise radiating surfaces. Both experimental and theoretical methods are applied to this complex system. Structural and acoustic dynamics are considered, as well as the very important frequency couplings between elastic structures and acoustic volumes. Preliminary road tests had indicated that the clonk phenomenon was a, very short transient impact event between lubricated contacts and having a high frequency characteristic. This indicated that a multi-body dynamics simulation of the driveline, in conjunction with a high frequency elasto-acoustic coupling analysis, would be required. In addition, advanced methods of signal analysis would be required to handle the frequency content of the very short clonk time histories. These are the main novelties of this thesis. There were many successful outcomes from the investigation, including quantitative agreement between the numerical and experimental investigations. From the experimental work, it was established that vehicle clonk could be accurately reproduced on a driveline rig and also on a vehicle chassis dynamometer, under controlled test conditions. It then enabled Design of Experiments to be conducted and the principal causal factors to be identified. The experimental input and output data was also used to verify the mathematical simulation. The high frequency FE analysis of the structures and acoustic cavities were used to predict the dynamic modal response to a shock input. The excellent correlation between model and empirical data that was achieved, clearly established the clonk mechanism in mathematical physics terms. Localised impact of meshing gears under impulsive loads were found to be responsible for high frequency structural wave propagation, some of which coupled with the acoustics modes of cavities, when the speed of wave propagation reached supersonic levels. This finding, although previously surmised, has been shown in the thesis and constitutes a major contribution to knowledge.

The development of improved numerical methods for computer simulation of high velocity impact dynamics is of importance in a variety of science and engineering fields. The growth of computing capabilities has created a demand for improved parallel algorithms for high velocity impact modeling. In addition, there are selected impact applications where experimentation is very costly, or even impossible (e.g. when certain bioimpact or space debris problems are of interest). This dissertation extends significantly the class of problems where particle-element based impact simulation techniques may be effectively applied in engineering design. This dissertation develops a hybrid particle-finite element method for a general hexahedral mesh. This work included the formulation of a numerical algorithm for the generation of an ellipsoidal particle set for an unstructured hex mesh, and a new interpolation kernel for the density. The discrete model is constructed using thermomechanical Lagrange equations. The formulation is validated via simulation of published impact experiments. / text

Dynamic behavior of impacting water drops on superhydrophobic solid surfaces provides important details on the stability/durability of such solid surfaces. Multi-scale surface roughness combined with a layer of low energy chemical is an essential surface modification process followed to create superhydrophobic capabilities on solid surfaces. The present work aims at studying the effect of low energy surface coating on droplet impact dynamics by carrying out experiments of water drop impacts on rough solid surfaces with and without chemical modification. A group of six aluminium alloy (Al6061) surfaces (three pairs) are prepared. Roughness, characterized in terms mean surface roughness, Ra, is introduced to these metallic surfaces using sand-paper polishing, electric discharge machining (EDM), and chemical based surface etching process. Low energy surface layer is laid on the rough surfaces by coating NeverWet hydrophobic solution, octadecyl-trichloro-silane (OTS), and perfluorodecyltricholorosilane (FAS-17). The impact dynamics of water drops is analyzed by capturing high speed videos for a range of drop Weber number from 1 to 570 and the salient features of drop impact process on the coated rough surfaces are compared with the corresponding uncoated rough surfaces. A one-to-one comparison on the spreading, fingering, receding, and final equilibrium of impacting drops on the coated and uncoated target surfaces is presented. Upon coating NeverWet, the original surface features of the base aluminium surface are completely covered by the hydrophobic coating material resulting in a fresh top surface layer. The outcomes as well as the bounce-off characteristics of impacting water drops on the coated surface are comparable to those observed on lotus leaf. The surface morphology features of rough aluminium surfaces coated with OTS and FAS-17 are comparable to those of the corresponding uncoated surfaces. The quantitative measurements on primary spreading and maximum spread factor of impacting drops are largely unaffected by the presence of low energy chemical coating. The dominant effect of surface coating is seen on the receding of impacting drops and hence the final drop configuration. This behavior is more prominently seen on EDM fabricated rough surface (larger Ra) combined with OTS coating than that on etching based rough surface (smaller Ra) combined with FAS-17 coating highlighting the dependence of coating effect with roughness features.