The primary barrier to the production of better machined parts is machine tool error. Present day applications are requiring closer machine part tolerances. The errors in dimensional part accuracy derive from the machine, in this case, a vertical two axis CNC lathe. A two axis vertical lathe can be utilized to produce a variety of parts ranging from cylindrical features to spherical features. A vertical lathe requires a spindle to rotate the work at speeds reaching 3000rpm, while simultaneously requiring the machine tool to be positioned in such a manner to remove material and produce an accurate part. For this to be possible, the machine tool must be precisely controlled in order to produce the correct contours on the part. There are many sources of errors to be considered in the two axis vertical lathe. Each axis of importance contains six degrees of freedom. The machine has linear displacement, angular, spindle thermal drift, straightness, parallelism, orthogonal, machine tool offset and roundness error. These error components must be measured in order to determine the resultant error. The characterization of the machine addresses thermal behavior and geometric errors. This thesis presents the approach of determining the machine tool errors and using these errors to transform the actual tool path closer to the nominal tool path via compensation schemes. One of these schemes uses a laser interferometer in conjunction with a homogenous transformation matrix to construct the compensated path for a circular arc, facing and turning. The other scheme uses a ball bar system to directly construct the compensated tool path for a circular arc. Test parts were created to verify the improvement of the part accuracy using the compensated tool paths.

The creep models of Sn/3.0Ag/0.5Cu solder material under tensile and shear loads are investigated in this study. The creep test results for Sn/3.0Ag/0.5Cu solder material with four operating temperatures, i.e. 120o, 135 o, 150 o and 165 oC are presented. The experimental results reveal that different creep equations are derived for the Sn/3.0Ag/0.5Cu solder material under tensile and shear loadings. The creep parameters, i.e. stress exponent, material constant and activation energy are curve fitted for the tensile and shear loading tests. The concept of failure toughness of solder ball joints is proposed and studied. The effects of high temperature aging and the thermal cycling loading on the failure toughness of different solder materials and ball sizes have also been explored. The difference between failure toughness values of traditional Sn/37Pb eutectic solder ball joints and the lead free Sn/3.0Ag/0.5Cu solder are compared and discussed. The results simulated from finite element method and experiment measurements under the ball shear test (BST) have been compared and studied. The variation stress, strain distributions and failure toughness during the ball shear testing are studied. The fracture behaviors of different ball joints under the high temperature aging and thermal cycles testing are examined and studied. The ball shear test results measured for the same size Sn/37Pb and Sn/3.0Ag/0.5Cu solder ball joints reveal different load-displacement variations. The relative ductility results are measured for the joint of Sn/37Pb solder ball. However, a high peak load and larger deformation are measured for Sn/3.0Ag/0.5Cu solder ball joints. Based on the definition of failure toughness proposed in this study, the higher failure toughness values are observed for the same size lead free Sn/3.0Ag/0.5Cu solder joints. The variation of failure toughness of different ball joints reveals that the high temperature aging and thermal cyclic loading reduce the failure toughness significantly. However, the measured failure toughness values indicate that the Sn/3.0Ag/0.5Cu solder joints have better ductility for the joints undergoing the high temperature aging and the thermal cycle loadings. Based on the measured results, the better reliability for the Sn/3.0Ag/0.5Cu ball joints is expected, due to the aging and cycling load testing.

Bismuth telluride based compounds is known to be the best thermoelectric materials within the low temperature regime. In this study, the P-type Bi0.5Sb1.5Te3 thermoelectric alloy was synthesized by ceramic processing method. The Bi0.5Sb1.5Te3 thermoelectric materials were prepared via the ball milling, cold pressing, and sintering processes. The effects of sintering time and temperature on the microstructures and thermoelectric properties were investigated and discussed. The X-ray diffraction patterns of Bi0.5Sb1.5Te3 reveal that the compounds have the oxides after the sintering processes and the heat treatment process causes grain growth by the increased sintering temperature and time. The results of thermoelectric properties show that the optimal Seebeck coefficient 300(£gV/K) was obtained as the sample was sintered at 350¢XC for 3h and the resistivity will reach the maximum. The figure of merit of 0.15 was obtained at room temperature as the sample was sintered at 375¢XC for 3h.

The cutter is a fundamental machine tool used extensively throughout manufacturing industries. The performance and quality of the cutter have a direct influence upon the cutting precision, product quality and production rate. Invigorating the domestic cutter industry and establishing a characteristic syscxtem of cutter technology requires that new technology be imported, the constraints of previous experience be overcome, a fundamental research and development capability be developed and new machine tool materials be adopted Two basic approaches exist when considering geometrical models of the cutter. In the first approach, developing new cutters and establishing an optimal set of cutter design parameters is performed in accordance with general cutting theory and the operational functions of the machine tool. Meanwhile, in the second approach, the structural requirements and design parameters of an ideal cutter are used to establish a geometrical cutter model which describes the various contours of the cutter. Developing an accurate geometrical model is an essential prerequisite to realizing the com-puter-aided design of a cutter, and is necessary in order to apply the theory of cutter design and manufacturing theory to the practical manufacturing proc-ess. Moreover, the geometrical model provides the basis for interference checking and manufacturing error analysis. Modern cutter design and manufacturing technologies integrate the results from a diverse range of previous studies, including those performed within the fields of fundamental mathematical theory, computer-aided ap-plication technology, modern design technology, material science and manufacturing technology. In each field, technological progress is reliant upon the development of mathematical theory. In the present study, differen-tial geometry, conjugate theory, engagement relationship theory, coordinate transfer and numerical methods are used to develop a systematic method for the design, simulation, manufacturing and compensation of special revolving cutters. Using the proposed mathematical models, this paper presents real-izable and effective manufacturing models for these revolving cutters. Fur-thermore, the Taguchi method and power signal analysis techniques are em-ployed to investigate the effects of different cutting-edge curves on the cut-ting characteristics of Inconel tool material. The basic research activities performed within the present study can be summarized as follows: 1.The study develops geometrical models for the cutting-edge curves and flute designs of ball-end cutters, truncated-cone ball-end cutters and toroid-cone shape cutters. Applying the inverse-envelope theory, a geometrical model for the cross-section of the grinding wheel used to grind the required helical groove on the cutter is developed. Further-more, the relative positions and velocities of the grinding wheel and workpiece during the NC manufacturing of the cutter are developed and investigated via a process of computer simulation. Finally, a compensation method is developed which resolves the problems of residual revolution surface and localized non-existence of the cutting-edge. The theoretical models and results provide a valuable source of reference for the NC manufacturing of revolving cutters. 2.A series of experiments are performed to investigate the effects of the cutting-edge geometry on the machining performance when machining Inconel 718. The Taguchi method is adopted to determine the set of optimal machining parameters for a variety of cutting-edge types, in-cluding those of the truncated-cone ball-end cutter, the plane type, the S type and the traditional type. The results of these experiments serve as a valuable reference for the automated machining of aero-materials. 3.Study the design and manufacture of the cutting-edge curve, flute sur-face and the coning angle of the grinding wheel for both the rotating burr and the revolving cutter, and discuss the difference of the related geometrical models. Also, the practical cutting-edge curve and the feeding rate of the relative movement for the cutter of the two and half axes processes of the NC machine have been discussed.

A general closed-form analytical solution is derived for the lapping tracks with its kinematics for the concentric V-groove lapping system. The lapping tracks on the ball surface for the three contact points are fixed circles, and their lengths of the lapping tracks are linearly proportional to , , and , respectively. In practice, if the orientation is randomized as the ball enters the lap again, then the distribution of the lapping tracks are dense after many cycles, and the larger the lapping length in each cycle, the smaller is the number of cycles required achieving the maximum lapped area ratio. In the geometry design of ball lapping, the V-groove half-angle should be larger than 45¢X, but to prevent the splash of abrasives, it should be less than 75¢X. Since the spin angular speed with its angle continuously varies with time for the eccentric lapping system, lapping tracks are not fixed circles. In practice, the lapped areas are complementary at the contact points of A and B. The total lapped area ratio is higher than 87% for a slip ratio less than 0.5. Hence, it is possible to lap all the surface of a ball by changing the slip ratio during the lapping process. Moreover, the larger the V-groove half-angle, the less is the eccentricity to achieve the optimum lapped area ratio. In order to understand the ball motion and ball lapping mechanism in the magnetic fluid lapping system, the forces and moments equilibrium equations are derived and numerical methods are analyzed. As the balls traveling in a train are assumed to be the same size, only one ball is considered in the dynamic analysis. Results show that as the ball separates from the shaft and the float, the spin angle increases quickly and approaches to 90¢X. Hence, the ball changes its attitude and thereby generates a new lapping tracks on the ball surface. Consequently, after repeating many cycles, lapping tracks would be scoping out more space and this is one of the spherical surface generation mechanisms. Surface waviness of ball causes a variation in the lapping load. When , it is possible to cause the ball separated from float and the lapping load is zero during the separation period. No matter how the ball separates from float, the spin angle always varies in a small range. Hence, only a very small region can be grounded due to the effect of the surface waviness. Therefore, it is not the main lapping mechanism of the spherical surface generation. In fact, during the lapping process, many balls with different diameters are lapped. To understand the ball¡¦s lapping mechanism of the spherical surface generation, it is necessary to consider a batch of balls. For a batch of balls with different diameters, the applied load on each should be different from each other. Generally, the larger the diameter of a ball, the larger is the friction force between the ball and shaft and the ball circulation speed. Therefore, it is possible to cause the collision between the larger and the smaller balls. To understand the interaction between balls traveling in a train, the dynamic analysis of multiple balls is developed. As the ball interacts with each other, it is possible to change the spin angle, and thereby to achieve the larger variation range of the lapping tracks. During the lapping process of a batch of balls, it is also possible to cause the separation between the shaft and the ball, and it causes the ball to change its attitude and to achieve more uniform lapping tracks.

Abstract This thesis is mainly aimed to the study the basic physical properties of different flux, and the combination with semiconductor packaging of 0.6mm Sn96.5/Ag3.0/Cu0.5 (SAC305) big solder ball, and 0.3mm Sn98.5/Ag1.0/Cu0.5 (SAC105) small solder ball. Big solder ball was proceeded with shear stress test, pull ball test, and tray drop test. However small solder ball was proceeded with shear stress test, pull ball test, zone shear solder balls test and board level drop test. After experiments, samples of different flux, the effect of solder strength and mechanical properties were received and discussed. And failure modes were observed by high-power microscope, SEM and OM. The experimental result shows that the flux doesn¡¦t have direct relationship with the point of welding strong and weak, the point of welding strong and weak is determined by the metal¡¦s characteristics. However, the less of residual flux is, the higher the solder balls shearing force as well as pulling force are. As for the more of residual more of flux, after aged processing, some solder balls have the phenomenon of missing from the IMC layer. And the difference of the residual flux will affect the various failure modes of zone shear solder balls. From board level drop test, the majority of failure modes is pad peeling at the corner of test board side for all test flux, and the remaining failure modes exhibit solder fractured and IMC layer broken. Therefore, the judgement of the residual flux is a very important key factor for the semiconductor packaging. It doesn¡¦t have the direct correlation with the reliability of final products. Keywords: Lead Free, Solder Ball, Flux, Semiconductor Packaging, Tests.

ABSTRACT Wireless communication products require thinner and small packaging to allow for reductions in Cell Phone and PDA product sizes. Currently, the Film-BGA (Ball Grid Array) package is in production for thinner and small case. The Film-BGA package is a thin package that uses polyimide tape as a substrate to reduce the overall package profile to 1 mm and ball pitch is 0.5 mm. The Film substrate can reach 0.11 mm thick or less. Analysis the Film-BGA model consists of a sequentially coupled thermal- mechanical analysis considering epoxy curing, post molding compound and IR-Reflow by MARC. After these processes Film-BGA will occur warpage and residual stress, we will study the sizes of materials on the warpage and residual stress by Taguchi Method. From the MARC analysis, it is found that due to the coefficient of thermal expansion (CTE) mismatch between solder ball, die, molding compound, epoxy and substrate, there exists very high stress near the interfaces of epoxy and results the maximum warpage (y-displacement) that occurs at the edge of the substrate after IR-Reflow. By means of the Taguchi Method, it is found that die size greatly affect the warpage of Film-BGA more than epoxy size and molding compound size. It is also found that epoxy size has more effect than die size and molding compound size on the residual stress of Film-BGA.

This study aims to investigate the effect of a 96 I/O Film-BGA package of surface mounted components on the thermal induced nonlinear viscoplastic deformation of solder balls during temperature cyclic loading between -40¢J to 125¢J. Specifically, it aims to study the trend effect of the joint fatigue life with respect to four control factors of the PI (Polyimide) thickness, die size, die thickness, and the upper copper trace thickness. Then, two different package types of Fan-in and Fan-out design in terms of the joint fatigue life are discussed. Due to the structure/loading symmetry, a three-dimension octant finite element structure was modeled to capture the entire package structural behaviors and a formulation of Modified Coffin-Manson was used to predict the joint fatigue life. Under temperature cyclic loading, the study results show that the die size, die thickness, and PI thickness had significant impact on the solder joint fatigue life, especially the effect of applying die size to the joint, but the upper copper trace thickness had little effect on the joint fatigue life. The study results also show that the package type of Fan-out design had higher joint fatigue life than that the package type of Fan-in design did for this Film-BGA package. In addition, by using the Taguchi method, the research could find the intensity of affected fatigue life due to the selected four control factors, and determine the optimized design by means of the optimized dimensions of the control factors. Then, the use of the ANOVA (analysis of variance) method helped the researcher predict the optimized joint fatigue life in comparison with the study results by using ANSYS finite element software analysis.

This thesis presents a visual servo control scheme for a ball-and-plate system with a maze. The maze built on the plate forms obstacles for the ball and increases variety and complexity of its environment. The ball-and-plate system is a two degrees-of-freedom robotic wrist with an acrylic plate attached as the end effector. By using image processing techniques, the ball¡¦s position is acquired from the visual feedback, which was implemented with a webcam and a personal computer. A fuzzy controller, which provides dexterity of the robotic wrist, is designed to decide the slope angles of the plate to guide the ball to a designated target spot. Using the method of distance transform, the path planning based on the current position of the ball is conducted to find the shortest path toward the target spot. Besides, a relaxed path, appears to be more suitable for actual applications, is provided by the obstacle¡¦s expansion approach. Experimental results show that the presented control framework successfully leads the ball to pass through the maze and arrive at target spot. The visual servo control scheme works effectively in both stabilization and tracking control. Based on this preliminary achievement, further improvement and deeper exploration on related research topics can be carried on in the future.

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