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Foldable and deployable space structures refer to a broad category of pre-fabricated structures that can be transformed from a compact folded configuration to a predetermined expanded configuration. Such deployable structures are stable and can carry loads. These structures are also mechanisms with one degree of freedom in their entire transformation stages whether in the initial folded form or in the final expanded configuration. Usually, pantograph mechanisms or a scissor-like elements (SLEs) are part of such deployable structures. A new analysis tool to study kinematic and static analyses of foldable and deployable space structures /mechanisms, containing SLEs, has been developed in this thesis. The Cartesian coordinates are used to study the kinematics of large deployable structures. For many deployable structures the degree of freedom derived using the standard Grubler-Kutzback criteria, is found to be less than one even though the deployable structure /mechanism can clearly move. In this work the dimension of nullspace of the derivatives of the constraint equations are used to obtain the correct degrees of freedom of deployable structure. A numerical algorithm has been developed to identify the redundant joints /links in the deployable structure /mast which results in the incorrect degrees of freedom obtained by using the Grubler-Kutzback criteria. The effectiveness of the algorithm has been illustrated with several examples consisting of triangular, box shaped SLE mast and an eighteen-sided SLE ring with revolute joints. Further more the constraint Jacobian matrix is also used to evaluate the global degrees of freedom of deployable masts/structures. Closed-form kinematic solutions have been obtained for the triangular and box type masts and finally, as a generalization, extended to a general n-sided SLE based ring structure. The constraint Jacobian matrix based approach has also been extended to obtain the load carrying characteristics of deployable structures with SLEs in terms of deriving the stiffness matrix of the structure. The stiffness matrix has been obtained in the symbolic form and it matches results obtained from other commonly used techniques such as force and displacement methods. It is shown that the approach developed in this thesis is applicable for all types of practical masts with revolute joints where the revolute joint constraints are made to satisfy through the method of Lagrange multipliers and a penalty formulation. To demonstrate the effectiveness of the new method, the procedure is applied to solving (i) a simple hexagonal SLE mast, and (ii) a complex assembly of four hexagonal masts and the results are presented. In summary, a complete analysis tool to study masts with SLEs has been developed. It is shown that the new tool is effective in evaluating the redundant links /joints there by over coming the problems associated with the well –known Grubler-Kutzback criteria. Closed-form kinematic solutions of triangular and box SLE masts as well as a general n-sided SLE ring with revolute joints has been obtained. Finally, the constraint Jacobian based method is used to evaluate the stiffness matrix for the SLE masts. The theory and algorithms presented in this thesis can be extended to masts of different shapes and for the stacked masts.

In several applications of casting, dendritic microstructure is not desirable as it results in poor mechanical properties. Enhancing fluid flow in the mushy zone by stirring is one of the means to suppress this dendritic growth. Strong fluid flow detaches the dendrites formed at the solid-liquid interface and carries them into the mould to form slurry. When this slurry solidifies, the microstructure is characterized by globular, non-dendritic primary phase particles, separated and enclosed by a near-eutectic lower-melting secondary phase. This property represents a great potential for further processing in semisolid forming (SSF) by various techniques such as pressure die casting and forging. Among all currently available methods, linear electromagnetic (EM) stirring is considered as one of the most suitable routes for large scale production of semisolid feed stock. One of the biggest advantages of EM stirring is that the stirring intensity and direction can be modulated externally and in a non-intrusive manner. With this viewpoint, the primary objective of the present research is to investigate rheocasting using linear electromagnetic stirring. A systematic development of a linear electromagnetic stirrer (LEMS) is the subject of the first part of the thesis. The LEMS consists of a set of six primary coils displaced in space. These coils are excited by a three-phase power supply to produce an axially travelling magnetic field. The metal to be stirred is placed in the annular space of the stirrer. The travelling field induces secondary current in the molten metal. The current and magnetic fields interact to generate a net mechanical force in the metal, commonly termed as the Lorentz force. The molten metal is stirred under the influence of this force. Two prototype stirrers, one for low melting alloys and the other for aluminium alloys are developed. The stirrers are characterized by measuring forces on low melting point alloy and on solid aluminum cylinders placed inside the annular space of the stirrer. As an outcome of these tests, a non-intrusive method of detecting stirring of liquid metal is developed. The development of a rheocasting mould for the LEMS forms the second part of the work presented in the thesis. The mould design and cooling arrangement are such that solidification in the mould is primarily unidirectional. Heat from the solidifying metal is extracted at the bottom of the mould, so that the axisymmetric EM stirring effectively shears the dendrites formed at the solid-liquid interface. The outer surface of the mould is cooled with water or air exiting from 64 jets, each of 4 mm diameter. Such an arrangement provides a high heat transfer coefficient and a wide range of cooling rate in the metal ranging from 0.01 to 10 K/s. Temperature is measured at various depths in the solidifying melt and at other key locations in the mould to assess the various heat transfer mechanisms. The results from the rheocasting experiments using the above mould and LEMS are presented in the third and final part of the thesis. Such studies are required for understanding the solidification process in presence of electromagnetic stirring and for highlighting the important issues connecting solidification, fluid flow, dendrite fragmentation and the resulting microstructure. A series of experiments are performed with A356 (Al-7Si-0.3Mg) alloy. Experiments are conducted with various combinations of operating parameters, and the resulting microstructures and cooling curves at various locations are examined. The key process parameters are stirring current, cooling rate, pouring temperature, and stirring current frequency. The parametric studies also include the case without EM stirring in which liquid aluminium is poured into the rheocast mould without powering the LEMS. It is found that stirring at high currents produces non-dendritic microstructures at all locations of the billet. For lower currents, however, dendritic microstructures are observed in regions outside the zone of active stirring. Stirring also enhances heat loss from the exposed top surface, leading to solid front advancement from the top as well. Without EM stirring, microstructures are found to be dendritic everywhere. The percentage of primary α-Al phase and its number density are found to increase with stirring intensity. With a decrease in cooling rate with air as the coolant, the average grain size of primary α-Al phase increases. Excitation frequency is found to be an important parameter, with lower frequencies generating a more uniform force field distribution, and higher frequencies enhancing induction heating. At higher frequencies, the effect of higher induction heating results in the formation of larger and coarser primary phase grains. This phenomenon has led to the development of a one-step process for rheocasting and heat treatment of billets.

This thesis considers four nonlinear systems with parametric forcing. The first problem involves an inverted pendulum with asymmetric elastic restraints subjected to harmonic vertical base excitation. On linearizing trigonometric terms the pendulum is governed by an asymmetric Mathieu equation. Solutions to this equation are scaleable. The stability regions in the parameter plane are studied numerically. Periodic solutions at the boundaries of stable regions in the parameter plane are found numerically and then their existence is proved theoretically. The second problem involves use of the method of multiple scales to elucidate the dynamics associated with early and delayed ejection of ions from Paul traps. A slow flow equation is developed to approximate the solution of a weakly nonlinear Mathieu equation to describe ion dynamics in the neighborhood of the nominal stability boundary of ideal traps. Since the solution to the unperturbed equation involves linearly growing terms, some care in identification and elimination of secular terms is needed. Due to analytical difficulties, harmonic balance approximations are used within the formal implementation of the method. The third problem involves the attenuation, caused by weak damping, of harmonic waves through a discrete, periodic structure with wave frequency nominally within the Propagation Zone. Adapting the transfer matrix method and using the harmonic balance for nonlinear terms, a four-dimensional map governing the dynamics is obtained. This map is analyzed by applying the method of multiple scales upto first order. The resulting slow evolution equations give the amplitude decay rate in the structure. The fourth problem involves the dynamic response of a strongly nonlinear single-degree-of-freedom oscillator under a constant amplitude, parametric, periodic, impulsive forcing, e.g., a pendulum with strongly nonlinear torsional spring that is periodically struck in the axial direction. Single-term harmonic balance gives an approximate, but explicit, 2-dimensional map governing the dynamics. The map exhibits many fixed points (both stable and unstable), higher period orbits, transverse intersections of stable and unstable manifolds of unstable fixed points, and chaos.

The condition of no relative velocity of fluid past solid is termed as ‘no-slip boundary condition’. This condition is a general observation in fluid mechanics. However, several research groups have recently reported slip of water for surfaces with water repelling chemistry (referred to as hydrophobic surfaces). The effect has been attributed to disruption of H-bonding network of water molecules at such surfaces and resulting nucleation of dissolved gases and even reduced water density locally in absence of dissolved air. Slip of water on hydrophobic surfaces has been demonstrated to get amplified by high degree of roughness and patterning. Trapping of air in the surface asperities has been cited as the possible reason. The present work focuses on the study of effect of surface chemistry and roughness on flow behavior close to solid surfaces. Superhydrophobic surfaces have been generated by novel methods and wet-etching has been used to generate well-defined patterns on silicon surfaces. For flow characterisation, a micrometre resolution Particle Image Velocimetry (micro-PIV) facility has been developed and flow measurements have been carried out with a spatial resolution of less than 4 µm. It has been found from the experiments that flow of water on smooth surfaces, with or without chemical modification, conforms to the no-slip within the resolution limits of experiments. Deviation is observed in case of rough and patterned hydrophobic surfaces, possibly because of trapped air in asperities. Total Internal Reflection experiments, used to visualise the air pockets, confirmed the trapping of air at asperities. Diffusion of air out of the crevices seems to be the limiting factor for the utility of these surfaces in under-water applications.

Hot extrusion of aluminum is widely practiced in industries for economic production of structural components. The surface finish and tolerance of the extruded components, both from design and aesthetic requirement, are important parameters. Hot extrusion involves forcing of aluminum in the form of a billet at a predetermined temperature through a shaped opening called die. Attempts, over time, are made to evolve the die profile to produce quality components. The main geometric feature of the die enables it in imparting plastic deformation and subsequent surface generation of the extrudate. The surface of extrudate is generated on the portion of the die called bearing channel or die land. Aluminum metal which moves relative to bearing channel experiences a different state-of-stress as it passes through the bearing channel. At the entry side of the bearing channel, the stress is compressive which is large in magnitude and this magnitude of compressive stress gets diminished as metal moves towards exit side and eventually becomes zero at the exit. Temperature gradients and its distribution along the bearing channel, similar to stress gradient, are reported. Literature reports formation of the transfer layer on the bearing channel. The transfer layer is of two distinctive types, the one near entry side which virtually leads to contact between aluminum and die steel and the other nearer to exit side which isolates aluminum from die steel. The understanding of the mechanism of formation of transfer layer is most important since it is instrumental in determining the surface finish of the extruded component. All of the previous studies were conducted either in an actual extrusion press or using an instrumented extrusion press in the laboratory. The variables during these experiments could be the temperature of billet, extrusion ratio and speed of ram. Conducting these experiments using extrusion press is expensive and time consuming. To do experiments where the condition in a bearing channel can be simulated would be useful in conducting a more comprehensive study. To simulate the condition in the bearing channel a high temperature vacuum based pin-on-disc machine is designed and built. The fact that in a bearing channel there is virtually metal to metal contact with minimal or no chance of any intervening oxide layer, necessitated studies to be conducted under vacuum. A pin-on-disc test conducted under vacuum and high temperature would almost simulate condition on a bearing channel. Using this specially designed and built experimental setup the parameters influencing the transfer layer formation, temperature, sliding speed, load on the specimen, vacuum level and surface characteristics of the die are studied. Another feature of the test rig is that the configuration of pin and disc setup is vertical, which is different from regular pin on disc tribo-system, where pin and disc are held in horizontal configuration. The advantage of holding in vertical configuration is to eliminate the possibility of trapping the debris which alters the existing friction force and conditions. The test rig is constructed using a cylindrical shell and a matching dome shell. The test rig, to facilitate the isolation of the instrumentations used to measure the forces and wear from the heat source is partitioned into two portions. The cylindrical bottom compartment called test chamber and dome shaped top compartment called sensor chambers are separated by a plate. On the plate in the sensor chamber, a load-cell to pickup friction force, a linear variable differential transformer (LVDT) to measure linear wear and loading lever mechanisms for imparting normal load and measuring friction force are fitted. The lever mechanism, in particular the one which magnifies the normal load is designed to conserve the space in the vacuum chamber. Housing the instrumentation inside the vacuum chamber thereby reducing the number of ports required to sense mechanical signals, increases the efficiency of the pumping system. The cylindrical shell of the testing chamber is a double walled structure and water cooled in order to prevent the exposer of sensors to higher testing temperature. Rubber ‘O’ rings are used, wherever it is required to seal the vacuum. The necessary temperature required at the contact interface in the testing chamber is obtained by an electric resistance furnace, which is configured in such a way in the chamber that the heat generated is completely directed to the area where pin and disc are positioned. The interface temperature is monitored using a chromal-alumal thermocouple which is fixed very close to sliding interface on the pin holder. The power input to the furnace is controlled using PID (proportional integral derivative). The required sliding speed is achieved with the help of direct current (DC) servomotor. The shaft on which the disc or ring is fixed is connected to a timer-pulley. The timer-pulley in turn is connected to servomotor through a timer-belt. The diameter ratio of the driving pulley and driven -timer-pulley is selected in such a way that the rpm of driven-pulley is reduced by four times and the torque increased by four times resulting in a more stable mechanical input to the sliding pair. The necessary high vacuum level in the test chamber is created by using rotary pump and diffusion pump combination. Following tests are carried out. 1. Compression test: The strain rate response of aluminum (6060) under compressive state of loading is studied at strain rates 10-3s-1, 10-2s-1, 10-1s-1, 1s-1, 10s-1 and 102sand temperature ranging from 573 to 823K. The compression specimen is machined out of homogenized aluminum alloy (6060) cast ingots. True stress and true strain are estimated from load-displacement data of compression test. The true stress and true strain data are made use of in predicting the friction coefficient and sliding mode during sliding of aluminum relative to die steel at various temperature and other independent variables in vacuum. 2. The tensile test: A series of tensile tests at different temperatures and 10-1s-1 strain rate are conducted. The temperatures employed are from 423K to 723K. True stress, true strain, ultimate tensile strength and total percentage of elongation are estimated using load displacement data. The estimated ultimate tensile strength and total percentage of elongation are used for qualitatively explaining the morphology of transfer layer formed in the sliding experiments under different independent variables like temperature, speed, normal load, and surface texture of steel surface. 3. Adhesion test: The interaction at different temperature between the die steel (H11) and aluminum (6060) pair under static load is studied by conducting test in vacuum. The pin is made of homogenized aluminum and disc is made of die steel whose surface is generated by polishing on diamond paste until the average surface roughness (Sa) is of the order of 0.1 microns. The test temperatures are varied from 423 to 723K. The result is used in qualitatively explaining the morphology of transfer layer formed during sliding of aluminum and die steel pair in vacuum at various temperature, speeds and, normal load. 4. Sliding experiment: Steel pin and aluminum disc Pin on disc experiments are conducted at different temperatures in vacuum of the order of 4X10-4Pa. The experiments are conducted employing factorial design. The temperature, speed and load are the experimental parameters. The pin and disc are respectively made out of die steel and aluminum. Experiments are carried out with normal loads 20N, 40N, 63N, 80N, and 100N and speeds 0.1ms-1, 0.3ms-1, 0.5ms-1, 1.0ms-1, and 1.5ms-1 and with temperature over a range from 423 to 773K. The sliding distance covered is 500 meters. The friction force during sliding is monitored and used for estimating friction coefficient. Scanning electron microscopic study is carried out on surface, subsurface, wear track. The results, specifically, the friction coefficient and morphology of transfer layer are used to evaluate the influence of independent parameters on transfer mechanisms. The data generated from subsurface study and compression tests are used for estimating friction coefficient using Rigney’s plastic deformation model at 0.1ms-1. 5. Sliding experiment: aluminum pin and Steel disc The experiments reported in the previous paragraph where aluminum disc is slid against die steel pin had developed only the stresses of the order 16MPa. The estimated magnitude of stress level on bearing surface of extrusion die by various methods including numerical analysis is found to be more than 16MPa. In order to achieve a higher magnitude of stress and preserve the transfer layer mechanism, sliding an aluminum pin over the part of the textured surface of die steel ring is carried out. The changed boundary condition resulted in a nominal stress of 28 MPa which is comparatively more at 723K. The experiments are conducted employing factorial design. The other advantage of doing these experiments is that the effect of texture on the die surface can be studied by sliding aluminum pin over various surfaces. Thus temperature and surface texture are the experimental parameters for the present test. Different textured die steel surface is generated by machining process like, milling, electro discharge machining (EDM), wire electro discharge machining, silicon carbide slurry polishing, silicon carbide wheel grinding, CNC-milling and diamond paste polishing. Thus surfaces are basically of two types 1) with a lay on the surface and 2) a random surface. The tests are conducted at ambient temperature, 423, 573, 673, and 723K with a normal load of 56N and speed of 0.129ms-1. The morphology of transfer layer on the die steel ring is studied in scanning electron microscope. The friction coefficient is estimated from monitored friction force. The average surface roughness (Sa), results of compression test, and transfer layer are made use of to identify the sliding mode. The sliding of aluminum pin on diamond polished surface showed interesting results. Hence, another series of experiments using only diamond polished surface are conducted. The surface roughness of the steel surface achieved is 0.05 micro-meters. The load is 47N and speed is 0.043ms-1. The morphology of transfer layer and pin surface is studied using a Scanning Electron Microscope. Results of compression and tensile test: The flow stress is found to decrease with increase in compression test temperature. The SEM micrograph indicates large amount of fragmentation of harder phase with increase in strain rate at all temperature except for 423K. The fractured surface under tensile loading shows both intergranular and transgranular failure. Results of adhesion test: The area covered by the material transfer is found to increase with increase in temperature. The test can be used, to study the adhesive tendency between two pair of contacting surfaces. The area covered by the material transfer is found to be maximum at 723K. Results of sliding of die-steel pin on aluminum disc in vacuum: 1. The ANOVA (analysis of variance) results indicate the existence of transition speed of about 0.5ms-1, more than which the friction coefficient was found constant. The extrusion speeds employed in industries are in the range of 0.1ms-1 to 1.7ms-1 and the transition speed found in the present study is within this range. 2. The magnitude of friction, with a few exceptions, is found to be independent of temperature and sliding speed when the sliding speed is 0.5ms-1and above. The invariance of friction coefficient with temperature and sliding speed beyond 0.5ms-1 is beneficial in that it will not lead to any instability like stick-slip or squeal. 3. Though both ambient temperature and speed influence the morphology of transfer layer and friction coefficient, speed is found to be dominant according to statistical analysis. 4. The observed dependency of friction coefficient and morphology of transfer layer on test temperature and normal load is attributed to decrease in flow stress and increase in friction factor ‘m’, a ratio of interfacial shear stress to shear yield stress of the softer material. Though ANOVA shows the significance of speed and not that of temperature, the observed dependence of friction coefficient on temperature is attributed to the enhanced effect of adhesion at elevated temperature observed in the adhesion test. 5. The state of stress at the contacting surface is found to control the morphology of transfer layer. When the normal load exceeded 40N, it gave rise to higher magnitude of stress state at the contacting surface, resulting in formation of continuous transfer layer and hence the higher magnitude of friction coefficient. 6. Plastic deformation model based on Rigney’s approach for estimating friction coefficient can be used. The estimated friction coefficient is on the higher side. Hence, any design of equipments based on the Rigney’s plastic deformation model is a conservative design. 7. There appears to be a close relation between the morphology of wear track and quantity of wear-loss. The formation of debris and rough track, primarily for low temperature sliding indicate larger magnitude of wear-loss. The parameters, which bring about increased ductility of aluminum as observed in the case of higher temperature of sliding, results in reduced wear-loss due to large scale smearing and back transfer of material. The results of sliding of aluminum pin on die-steel ring in vacuum: 1. The mode of sliding changes from adhesive to abrasive mode depending on depth of penetration, tan(θ) where θ is the base angle of the conical asperity and average roughness parameter Sa ,all of them in turn depend on morphology of die steel surface and test temperature. 2. The friction coefficient and morphology of transfer layer are found to depend on the mode of sliding. The sub-surface plastic deformation, which characterizes the friction coefficient and morphology of transfer layer, is dependent on temperature of sliding. 3. The sliding experiment is capable of simulating the stress state on the bearing channel of the die; elucidating evolution of transfer layer, with change in operating parameters. 4. The ANOVA has clearly indicated the significance in friction coefficient at different temperatures and surface textures. In addition, the complex comparison below and above homogenization temperature (573K) has indicated significance in friction coefficient and thereby recognizing the importance of extrusion of aluminum at a temperature where it is in a single phase. Also, ANOVA indicates the dependency of both friction coefficient and transfer layer on the texture, i.e. either a lay or random. The results of sliding aluminum pin on diamond polished die steel ring: 1. Shearing of the cold welded junction is a probable mechanism involved in the formation of transfer layer up to 423K. 2. The transgranular and intergranular mode of fracture are identified to be the two possible modes of fracture of the asperity at temperatures greater than 573K. The large ductility of the aluminum alloy facilitated smearing resulting in a continuous transfer layer at temperatures greater than 573K. 3. The formation of a continuous transfer layer at temperatures greater than 573K is responsible for the observed high friction coefficient at these temperatures. Scanning electron microscopy observations of the fracture surfaces of the tensile test specimen revealed fracture to be a combination of both transgranular and intergranular modes.

Automobiles have become an integral part of our daily life as more and more mopeds, motor cycles, cars, trucks, busses and trains are being used for transport. The main parts of an automotive engine are cylinder, piston assembly, connecting rod and crank shaft. The piston assembly consists of Piston, Piston rings and Piston Pin. Piston rings are important parts of a piston assembly. Any non-conformance in any quality characteristic of the piston ring leads to deterioration of engine performance. M/S Goetze (India) Limited a medium scale industry and a sister concern of engineering giant M/S Escorts Limited is manufacturing "GOETZE PISTON RINGS" and is producing about 800 varieties of piston rings ranging from 35.00 mm to 228.5 mm nominal diameter. The management was facing serious problem due to high scrap rate in certain types of their manufactured piston rings. Hence instead of trying to handle all of them at the same time, it seemed reasonable to tackle and find a suitable approach to solve the quality problem by taking the most notorious ring first, so that once the methodology is understood, documented and applied to the quality problem of this ring, the same can also be invoked for other rings to improve upon their quality, and thus reducing the scrap rate. One particular ring of 83.0 mm diameter which is delicate and costly, having an average scrap rate of 36.2% in past three years is selected for the study. No systematic effort was made in the past to identify the quality characteristics and the processes which were responsible for this high scrap rate and thus no immediate measure could be recommended. As a matter of fact at the beginning of the study it was not even clear which quality characteristics were mainly responsible for such high rejection. So in July' 1999 a pareto analysis was done for the first time to identify the culpability of each quality characteristic for the rejection of the ring. From the Pareto analysis it was observed that maximum proportion of rejection was due to nonconformity in axial thickness. The scrap rate due to nonconformity in axial thickness were collected for each month from Jul’ 999 to Jan'2000 which averaged at 8.7%. Since in every month the major malefactor for rejection was the nonconformity of axial thickness it was decided to first try to improve the quality of axial thickness, before trying to tackle other quality issues associated with this particular piston ring under study. Once the most problematic quality characteristic namely the axial thickness was identified, as a first step towards the goal of improving the quality of axial thickness, it was necessary to pay attention and isolate the manufacturing processes or operations affecting the axial thickness and study them in detail. So first, the entire manufacturing process flow diagram of the piston ring was studied. From the process flow diagram it appeared that there are 4 operations affecting axial thickness viz. Rough Grinding ,Medium Grinding, First Lapping and Finish Lapping. So each of these processes was critically observed to assess whether they were under statistical control or not. Studies were conducted at each of these 4 operations by collecting samples using the rational subgroup method and control charts were plotted. From the control charts, it was observed that the Rough Grinding and Medium Grinding operations were in statistical control with acceptable Cp, Cpk values. But First Lapping and Finish Lapping operations were not in statistical control. Thus we finally identified the two critical processes namely the First Lapping and Finish Lapping operations which were not in statistical control but were crucially affecting the quality of axial thickness. Since the First and Finish Lapping operations were identified as the major source of the quality problem, an in-depth study was undertaken to analyze these two processes. A brain storming session was conducted with all concerned personnel from production, maintenance, design, quality assurance and tool room to get all possible causes which might be affecting the axial thickness variation at these two processes. During the brain storming session the team suggested that the First Lapping process can be processed in medium grinding machine (DFS machine) instead of Lapping machine. The reasons behind this were two fold. First since the aim of the First Lapping is just to remove excess material which was deposited during chrome plating, the same operation can be performed in DFS machine. Since the required surface finish on axial surface was any way being aimed at the Finish Lapping operation, a similar precursory First Lapping'operation in a Lapping machine was really felt not necessary. Secondly since the performance of the DFS machine was found to be under control, albeit for the grinding operation, it was hoped that the Lapping operation in the same machine would also exhibit a similar performance. For this purpose a study was conducted on the First Lapping operation with the DFS machine. It was found that the process was well within the control limit with decent Cp and Cpk values. Thus this procedure of performing the First Lapping operation in a DFS machine took care of the first one of the two problematic processes affecting the quality of axial thickness. Next for tackling the problem with the other critical process, viz. the Finish Lapping operation, various causes were suggested by the team for axial thickness variation in the Finish Lapping operation. Based on these causes, an Ishikawa diagram (cause and effect diagram) was prepared. This Ishikawa diagram had thrown light into number of possible deficiencies in Man, Machine, Method and Material which were responsible for axial thickness variation at finish Lapping. The Ishikawa diagram was carefully analyzed. The causes were narrowed down to 6 factors. These are Grinding wheel rotating speed, Grinding Time, Grinding pressure, Holding plate, Holes (fixtures) within the holding plate and Positions within a ring. The 3 factors namely grinding wheel speed, time and pressure were identified as the control factors. Holding plate, Hole position within a plate and Checking position within a ring on the other hand were the noise factors whose different levels might exhibit a variability of axial thickness. Since there were only 3 control factors, it was decided to conduct a full factorial experiment with each control factor at 3 levels. Hence altogether there were 27 experiments at a fixed given combination of speed, time and pressure. There were 4 holding plates with each plate having 6 slotted holes leading to machining 24 rings at a time during the finish lapping operation. Next 3 measurements were taken for each one of these 24 rings. Thus altogether there were 72 observations for one of these experiments. Each experiment was replicated twice by taking measurements for 2 consecutive batches of rings. From the analysis of variance of the results of these experiments for both S/N ratio and mean it was observed that all the three main factors and their interactions were significant. The Normality assumption of standardized residuals for the S/N ratio and mean was validated by normal probability plot and Kolmonogorov-Smirnoff test. The homoscedasticity assumption was validated through Bartlett’s test and residual plots. It was found that the experiment no. 23 (Speed 84 RPM, Time 10 sees and Pressure 300 daN) yielded highest S/N ratio (η) with mean within the specification limit. That the mean and S/N ratio for the experiment no.23 were significantly different from others was established by means of Tukey's multiple comparison test. Next control charts for experiment no. 23 were plotted and was found to be well within control with acceptable Cp and Cpk values. Hence we concluded that the non-conformance in axial thickness can be substantially reduced by using the following optimal setting of factors i.e. grinding speed with 84 RPM, grinding pressure with 300 daN and grinding time with 10 seconds. Using this optimal setting the earlier average rejection rate of 8.7% due to non-conformance in axial thickness was reduced to 0.05%. Under this optimal setting, the process capability index (Cpk) of finish Lapping operation was estimated to be 2.5, which is well above acceptable standard. Due to this reduction in rejection rate in one quality characteristics of one particular ring out of 800 types, the net savings to the organization is approximately Rs. 10,44,000 per year.

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