This thesis presents the use of Computer Numerically Controlled (CNC) machining as a method to manufacture anatomically-shaped synthetic grafts made from Calcium Polyphosphate (CPP) ceramic. Tissue-engineered cartilage is grown on the surface of these implants in vitro followed by in vivo implantation in the host’s body for osteochondral focal defect repair. While most current implants are manufactured from simple geometries and are not specific to one patient’s need, it is believed that custom manufactured implants (from computer tomography data) representing the exact shape of the original bone will be beneficial. This is because custom implants permit an even stress distribution on the cartilage, resulting in increased cartilage survival rates. The present study has successfully manufactured and delivered a custom designed implant with sufficient surface porosity and minimal chipping. This was accomplished by effectively modeling the machinability characteristics and finding the optimal cutting conditions for CPP. CPP’s machinability characteristics were investigated and a cutting force prediction model was developed. This model was verified by a comparison of experimental and predicted forces for a number of ball and flat endmilling tests. The optimal cutting conditions that would result in maximum surface porosity and minimal chipping were established through qualitative investigation of results from varied conditions using Scanning Electron Microscope (SEM) images. Using the established optimal cutting conditions from machinability studies, the multi-axis machining process for producing the designed custom implant was developed and all stages were simulated for accuracy and integrity of the final implant. The designed toolpaths were tested on prototyping wax and verified against the actual Computer Aided Design (CAD) model using an optical microscope. The same toolpaths were executed on a block of CPP and the final implant was again investigated for surface porosity and chipping. After final comparison against the CAD model using an optical microscope, the implant was delivered to surgeons for implantation.

This thesis presents the use of Computer Numerically Controlled (CNC) machining as a method to manufacture anatomically-shaped synthetic grafts made from Calcium Polyphosphate (CPP) ceramic. Tissue-engineered cartilage is grown on the surface of these implants in vitro followed by in vivo implantation in the host’s body for osteochondral focal defect repair. While most current implants are manufactured from simple geometries and are not specific to one patient’s need, it is believed that custom manufactured implants (from computer tomography data) representing the exact shape of the original bone will be beneficial. This is because custom implants permit an even stress distribution on the cartilage, resulting in increased cartilage survival rates. The present study has successfully manufactured and delivered a custom designed implant with sufficient surface porosity and minimal chipping. This was accomplished by effectively modeling the machinability characteristics and finding the optimal cutting conditions for CPP. CPP’s machinability characteristics were investigated and a cutting force prediction model was developed. This model was verified by a comparison of experimental and predicted forces for a number of ball and flat endmilling tests. The optimal cutting conditions that would result in maximum surface porosity and minimal chipping were established through qualitative investigation of results from varied conditions using Scanning Electron Microscope (SEM) images. Using the established optimal cutting conditions from machinability studies, the multi-axis machining process for producing the designed custom implant was developed and all stages were simulated for accuracy and integrity of the final implant. The designed toolpaths were tested on prototyping wax and verified against the actual Computer Aided Design (CAD) model using an optical microscope. The same toolpaths were executed on a block of CPP and the final implant was again investigated for surface porosity and chipping. After final comparison against the CAD model using an optical microscope, the implant was delivered to surgeons for implantation.

Despite the inbuilt advantages offered by 5-axis machining, the manufacturing industry has not widely adopted this technology due to the high cost of machines and insufficient support from CAD/CAM systems. Companies are used to 3-axis machining and the operators are in many cases not yet ready for 5-axis machining in terms of training and programming. An effective solution for this 5 axis problem is a graduated migration through the use of 3+2-axis machining. The objective of this research is to develop and implement a machining technique that uses the simplicity of 3-axis tool positioning and the flexibility of 5-axis tool orientation, to machine complex surfaces. This technique, 3+2-axis machining, divides a surface into patches and then machines each patch using a fixed tool orientation. The tool orientation and section boundaries are determined to minimize the overall machining time. For each section the tool orientation is different but remains constant while machining this section. The number of patches selected for machining has a direct impact on the machining time. If the number of patches is small, the shape of the tool may vary greatly from that of the surface, which can result in smaller side-step distances. In contrast, a large number of patches leads to a better match between the tool and the workpiece, but it also leads to many re-orientations of the part as the tool moves between patches. Also, if the number of patches is large, the size of the patches will be reduced which will result in shorter tool passes that limit the tools ability to achieve the commanded feed rate. The optimum number of patches is a compromise between increasing the side step associated with large patches and the increase in time due to re-orientation of part and tool movement between patches. To find the optimal partition, a series of simulation tests are conducted to find the partition that would lead to the smallest machining time. This work presents the application of well known methods from Pattern Recognition and newly developed methods by the current author that were adapted for surface machining and boundary identification. This work also presents the methodology required to generate tool paths for 3+2-axis machining, which includes an explanation of the procedures required to determine an appropriate tool orientation, feed direction, tool path trajectory and tool parameters for patch-by-patch machining. These parameters are determined independently for each patch and aim at reducing the time required to machine a surface while maintaining the surface specifications. This work presents the surface partitioning scheme and the method of selecting optimum number of partitions along with actual machining experiments. Machining tests on four different surfaces were conducted to demonstrate the efficiency of the proposed technique. The results show that 3+2-axis machine reduced machining times over 3-axis ball nose machining and 5-axis machining using the “Sturz” method. Also, since the tool axis remains fixed during cutting, the tool offers constant feed rates and a better surface finish compared to simultaneous 5-axis.

Despite the inbuilt advantages offered by 5-axis machining, the manufacturing industry has not widely adopted this technology due to the high cost of machines and insufficient support from CAD/CAM systems. Companies are used to 3-axis machining and the operators are in many cases not yet ready for 5-axis machining in terms of training and programming. An effective solution for this 5 axis problem is a graduated migration through the use of 3+2-axis machining. The objective of this research is to develop and implement a machining technique that uses the simplicity of 3-axis tool positioning and the flexibility of 5-axis tool orientation, to machine complex surfaces. This technique, 3+2-axis machining, divides a surface into patches and then machines each patch using a fixed tool orientation. The tool orientation and section boundaries are determined to minimize the overall machining time. For each section the tool orientation is different but remains constant while machining this section. The number of patches selected for machining has a direct impact on the machining time. If the number of patches is small, the shape of the tool may vary greatly from that of the surface, which can result in smaller side-step distances. In contrast, a large number of patches leads to a better match between the tool and the workpiece, but it also leads to many re-orientations of the part as the tool moves between patches. Also, if the number of patches is large, the size of the patches will be reduced which will result in shorter tool passes that limit the tools ability to achieve the commanded feed rate. The optimum number of patches is a compromise between increasing the side step associated with large patches and the increase in time due to re-orientation of part and tool movement between patches. To find the optimal partition, a series of simulation tests are conducted to find the partition that would lead to the smallest machining time. This work presents the application of well known methods from Pattern Recognition and newly developed methods by the current author that were adapted for surface machining and boundary identification. This work also presents the methodology required to generate tool paths for 3+2-axis machining, which includes an explanation of the procedures required to determine an appropriate tool orientation, feed direction, tool path trajectory and tool parameters for patch-by-patch machining. These parameters are determined independently for each patch and aim at reducing the time required to machine a surface while maintaining the surface specifications. This work presents the surface partitioning scheme and the method of selecting optimum number of partitions along with actual machining experiments. Machining tests on four different surfaces were conducted to demonstrate the efficiency of the proposed technique. The results show that 3+2-axis machine reduced machining times over 3-axis ball nose machining and 5-axis machining using the “Sturz” method. Also, since the tool axis remains fixed during cutting, the tool offers constant feed rates and a better surface finish compared to simultaneous 5-axis.

Le processus de réalisation des pièces de formes complexes par usinage est un processus essentiel dans les domaines de l'aéronautique, de l'automobile, des moules et des matrices. Alors que l'usinage 5 axes grande vitesse est maintenant répandu dans les grands groupes industriels, il reste plusieurs problématiques à traiter. L'évitement de collisions le long de la trajectoire outil programmée en alors traité, notamment au niveau des interférences globales représentant une collision entre l'outil et son environnement. Classiquement, l'évitement de collisions dans le domaine de l'usinage 5 axes grande vitesse peut être programmé à l'aide d'une analyse géométrique de la situation. Si une collision est détecté, alors une phase de correction et d'optimisation peuvent être utilisée afin d'obtenir une nouvelle trajectoire hors collision. Le but des travaux est alors d'utiliser une modélisation physique afin d'obtenir une trajectoire corrigée hors collision le plus lisse possible. Pour ce faire le mouvement de l'outil est alors étudié d'un point de vue dynamique afin d'éviter les réorientation brutal post correction. De plus, les éléments constituants les obstacles émettent une action répulsive à distance. Cela permet, au cours de la programmation, d'anticiper l'approche d'un obstacle et ainsi d'entamer les corrections d'orientation outil en prévision d'une possible collision. Cette démarche de modélisation du mouvement étudiée permet alors de réaliser des simulations sur des pièces classiquement usinées dans les domaines énoncés précédemment. Dans le but de généraliser la programmation réalisée, il est alors important de comprendre comment les éléments obstacles sont représentés ainsi que la modélisation retenu pour l'outil utilisé au cours de la simulation. Enfin, la résolution de la dernière problématique mise en avant au cours de cette thèse concerne les temps de calcul obtenus. Il a été montré, après de multiples simulations, que ces derniers peuvent exploser d'un point de vue combinatoire pour des utilisateurs exigeants (modélisation fine de l'outil et de l'environnement). Une méthode de pré calcul est alors présentée utilisant la voxelisation permettant de diminuer les temps de calcul de manière très importante sans pour autant perdre de manière importante sur la solution obtenue. Le dernier objectif présenté est de proposer une approximation permettant de diminuer nettement les temps de calcul tout en conservant une assurance de non-collision. Cette méthode notée voxelisation consiste en utilisant une interpolation à diminuer le temps de calcul. L’important est alors de comprendre quels inconvénients se rattachent à la voxelisation et à partir de quand cette dernière apporte un résultat acceptable / Although 5-axis free form surfaces machining is commonly proposed in CAD/CAM software, several issues still need to be addressed and especially collision avoidance between the tool and the part. Indeed, advanced user skills are often required to define smooth tool axis orientations along the tool path in high speed machining. In the literature, the problem of collision avoidance is mainly treated as an iterative process based on local and geometrical collision tests. In this paper, an innovative method based on potential fields is used to generate 5-axis collision-free smooth tool paths. In the proposed approach, The ball-end tool is considered as a rigid body moving in 3D space on which repulsive force, deriving from a scalar potential field attached to the check surfaces, and attractive forces are acting. The resolution of the differential equations of the tool motion ensure smooth variations of the tool axis orientation. The proposed algorithm is applied on open pocket parts such as an impeller and a pocket corner to emphasize the effectiveness of this method to avoid collision. After that, it is possible to see that de calculation time can be very importante for a delicate mesh. It is for that, a voxelisation method is developed to decrease these.

5軸制御マシニングセンターの運動精度の向上に向けた新たなキャリブレーション手法の開発に取り組んだ．また、直進および旋回軸の各種の運動誤差要因を診断する手法を構築した．さらにサーボ系の位置フィードバックで，サーボ系に起因する運動誤差の診断法も提案した.旋回軸にDDモータ方式を採用することで機械全体のサーボ特性を大きく改善できることも解明した．最後に，複雑形状の実加工により開発機で高い加工精度を確認することができた． / A new calibration method to improve the motion accuracy of a 5-axis control machining center has been developed. A method to diagnose various causes of motion errors on linear and rotary axes has been also established. Furthermore, a diagnosis method of motion errors caused by servo motors using the position feedback function is suggested in this paper. This study also figured out employing the direct drive motor for the rotary axes improved the characteristics of all the servo motors on the machine. Finally, the development test machine proved its high machining accuracy through actual machining of a complex-shaped workpiece. / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University

Although a considerable amount of research exists on geometrical aspects of 5-axis flank milling, the dynamics of this efficient milling operation have not yet been given proper attention. In particular, investigating machining chatter in 5-axis flank milling remains as an open problem in the literature. The axial depth of cut in this operation is typically quite large, which makes it prone to machining chatter. In this thesis, chatter in 5-axis flank milling is studied by developing analytical methods of examining vibration stability, generating numerical simulations of the process, and conducting experimental investigations. The typical application of 5-axis milling includes the machining of thermal resistant steel alloys at low cutting speeds, where the process damping dominates the machining vibration. The results of experimental study in this thesis showed that the effect of process damping is even stronger in flank milling due to the long axial engagement. Accordingly, the first part of the thesis is devoted to studying process damping, and in the second part, the modeling of chatter in flank milling is presented. Linear and nonlinear models have been reported in the literature that account for process damping. Although linear models are easier to implement in predicting stability limits, they could lead to misinterpretation of the actual status of the cut. On the other hand, nonlinear damping models are difficult to implement for stability estimation analytically, yet they allow the prediction of “finite amplitude stability” from time domain simulations. This phenomenon of “finite amplitude stability” has been demonstrated in the literature using numerical simulations. In this thesis, that phenomenon is investigated experimentally. The experimental work focuses on uninterrupted cutting, in particular plunge turning, to avoid unduly complications associated with transient vibration. The experiments confirm that, because of the nonlinearity of the process damping, the transition from fully stable to fully unstable cutting occurs gradually over a range of width of cut. The experimental investigation is followed by developing a new formulation for process damping based on the indentation force model. Then, the presented formulation is used to compute the stability lobes in plunge turning, taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Moreover, the process damping model is integrated into the Multi-Frequency Solution and the Semi Discretization Method to establish the stability lobes in milling. The basic formulations are presented along with comparisons between the two approaches, using examples from the literature. A non-shallow cut is employed in the comparisons. Assessing the performance of the two methods is conducted using time domain simulations. It is shown that the Semi Discretization Method provides accurate results over the whole tested range of cutting speed, whereas higher harmonics are required to achieve the same accuracy when applying the Multi Frequency Solution at low speeds. Semi Discretization method is modified further to calculate the stability lobes in flank milling with tools with helical teeth. In addition to the tool helix angle and long axial immersion, the effect of instantaneous chip thickness on the cutting force coefficients is considered in the modified formulation of Semi Discretization as well. Considering the effect of chip thickness variation on the cutting force coefficients is even more important in the modeling of 5-axis flank milling, where the feedrate, and consequently the chip thickness, varies at each cutter location. It also varies along the tool axis due to the additional rotary and tilt axis. In addition to the feedrate, the tool and workpiece engagement geometry varies at each cutter location as well. The actual feedrate at each cutter location is calculated by the dynamic processing of the toolpath. The tool and workpiece engagement geometry is calculated analytically using the parametric formulation of grazing surface at the previous and current passes. After calculating the instantaneous chip thickness and tool/workpiece engagement geometry, they are integrated into the Semi Discretization Method in 5-axis flank milling to examine the stability of vibration at each cutter location. While the presented chatter analysis results in establishing stability lobes in 3-axis flank milling, it results in developing a novel approach in presenting the stability of the cut in 5-axis flank milling. The new approach, namely “stability maps”, determines the unstable cutter locations of the toolpath at each spindle speed. The accuracy of established 3-axis flank milling stability lobes and 5-axis stability maps is verified by conducting a set of cutting experiments and numerical simulations.

On-the-fly laser drilling provides a highly productive method for producing hole clusters (pre-defined groups of holes to be laser drilled) on freeform surfaced parts, such as gas turbine combustion chambers. Although the process is capable of achieving high throughputs, current machine tool controllers are not equipped with appropriate trajectory functions that can take full advantage of the achievable laser drilling speeds. While the problem of contour following has received previous attention in time-optimal trajectory generation literature, on-the-fly laser drilling presents different technological requirements, needing a different kind of trajectory optimization solution, which has not been studied prior to this thesis. The duration between consecutive hole locations, which corresponds to the laser pulsing period, has to be kept constant, ideally throughout the part program. However, the toolpath between the holes is not fixed and can be optimized to enable the shortest possible segment duration. To preserve the dynamic beam positioning accuracy and avoid inducing excessive vibrations on the laser optics, the axis velocity, acceleration, and jerk profiles need to be limited. Furthermore, to ensure that hole elongation does not violate the given part tolerances, the orthogonal component of part velocity relative to the laser beam needs to be capped. All of these requirements have been fulfilled in the trajectory optimization algorithm developed in this thesis. The hole locations are provided as pre-programmed sequences by the Computer Aided Design/Manufacturing software (CAD/CAM). A time-optimized trajectory for each sequence is planned through a series of time-scaling and unconstrained optimization operations, which guarantees a feasible solution. The initial guess for this algorithm is obtained by minimizing the integral square of the fourth time derivative (i.e. ‘snap’). The optimized trajectories for each cluster are then joined together or looped onto themselves (for repeated laser shots) using a time-optimized looping/stitching (optimized/smooth toolpath to repeat/loop a cluster or connect/stitch between consecutive clusters) algorithm. This algorithm also minimizes the integral square of jerk in the faster axes. The effectiveness of the overall solution has been demonstrated in simulations and preliminary experimental results for on-the-fly laser drilling of a hole pattern for a gas turbine combustion chamber panel. It is shown that the developed algorithm improves the cycle time for a single pass by at least 6% (from kinematic analysis of the motion duration), and more importantly reduces the integral square of jerk by 56%, which would enable the process speed to be pushed up further.

On-the-fly laser drilling provides a highly productive method for producing hole clusters (pre-defined groups of holes to be laser drilled) on freeform surfaced parts, such as gas turbine combustion chambers. Although the process is capable of achieving high throughputs, current machine tool controllers are not equipped with appropriate trajectory functions that can take full advantage of the achievable laser drilling speeds. While the problem of contour following has received previous attention in time-optimal trajectory generation literature, on-the-fly laser drilling presents different technological requirements, needing a different kind of trajectory optimization solution, which has not been studied prior to this thesis. The duration between consecutive hole locations, which corresponds to the laser pulsing period, has to be kept constant, ideally throughout the part program. However, the toolpath between the holes is not fixed and can be optimized to enable the shortest possible segment duration. To preserve the dynamic beam positioning accuracy and avoid inducing excessive vibrations on the laser optics, the axis velocity, acceleration, and jerk profiles need to be limited. Furthermore, to ensure that hole elongation does not violate the given part tolerances, the orthogonal component of part velocity relative to the laser beam needs to be capped. All of these requirements have been fulfilled in the trajectory optimization algorithm developed in this thesis. The hole locations are provided as pre-programmed sequences by the Computer Aided Design/Manufacturing software (CAD/CAM). A time-optimized trajectory for each sequence is planned through a series of time-scaling and unconstrained optimization operations, which guarantees a feasible solution. The initial guess for this algorithm is obtained by minimizing the integral square of the fourth time derivative (i.e. ‘snap’). The optimized trajectories for each cluster are then joined together or looped onto themselves (for repeated laser shots) using a time-optimized looping/stitching (optimized/smooth toolpath to repeat/loop a cluster or connect/stitch between consecutive clusters) algorithm. This algorithm also minimizes the integral square of jerk in the faster axes. The effectiveness of the overall solution has been demonstrated in simulations and preliminary experimental results for on-the-fly laser drilling of a hole pattern for a gas turbine combustion chamber panel. It is shown that the developed algorithm improves the cycle time for a single pass by at least 6% (from kinematic analysis of the motion duration), and more importantly reduces the integral square of jerk by 56%, which would enable the process speed to be pushed up further.

Although a considerable amount of research exists on geometrical aspects of 5-axis flank milling, the dynamics of this efficient milling operation have not yet been given proper attention. In particular, investigating machining chatter in 5-axis flank milling remains as an open problem in the literature. The axial depth of cut in this operation is typically quite large, which makes it prone to machining chatter. In this thesis, chatter in 5-axis flank milling is studied by developing analytical methods of examining vibration stability, generating numerical simulations of the process, and conducting experimental investigations. The typical application of 5-axis milling includes the machining of thermal resistant steel alloys at low cutting speeds, where the process damping dominates the machining vibration. The results of experimental study in this thesis showed that the effect of process damping is even stronger in flank milling due to the long axial engagement. Accordingly, the first part of the thesis is devoted to studying process damping, and in the second part, the modeling of chatter in flank milling is presented. Linear and nonlinear models have been reported in the literature that account for process damping. Although linear models are easier to implement in predicting stability limits, they could lead to misinterpretation of the actual status of the cut. On the other hand, nonlinear damping models are difficult to implement for stability estimation analytically, yet they allow the prediction of “finite amplitude stability” from time domain simulations. This phenomenon of “finite amplitude stability” has been demonstrated in the literature using numerical simulations. In this thesis, that phenomenon is investigated experimentally. The experimental work focuses on uninterrupted cutting, in particular plunge turning, to avoid unduly complications associated with transient vibration. The experiments confirm that, because of the nonlinearity of the process damping, the transition from fully stable to fully unstable cutting occurs gradually over a range of width of cut. The experimental investigation is followed by developing a new formulation for process damping based on the indentation force model. Then, the presented formulation is used to compute the stability lobes in plunge turning, taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Moreover, the process damping model is integrated into the Multi-Frequency Solution and the Semi Discretization Method to establish the stability lobes in milling. The basic formulations are presented along with comparisons between the two approaches, using examples from the literature. A non-shallow cut is employed in the comparisons. Assessing the performance of the two methods is conducted using time domain simulations. It is shown that the Semi Discretization Method provides accurate results over the whole tested range of cutting speed, whereas higher harmonics are required to achieve the same accuracy when applying the Multi Frequency Solution at low speeds. Semi Discretization method is modified further to calculate the stability lobes in flank milling with tools with helical teeth. In addition to the tool helix angle and long axial immersion, the effect of instantaneous chip thickness on the cutting force coefficients is considered in the modified formulation of Semi Discretization as well. Considering the effect of chip thickness variation on the cutting force coefficients is even more important in the modeling of 5-axis flank milling, where the feedrate, and consequently the chip thickness, varies at each cutter location. It also varies along the tool axis due to the additional rotary and tilt axis. In addition to the feedrate, the tool and workpiece engagement geometry varies at each cutter location as well. The actual feedrate at each cutter location is calculated by the dynamic processing of the toolpath. The tool and workpiece engagement geometry is calculated analytically using the parametric formulation of grazing surface at the previous and current passes. After calculating the instantaneous chip thickness and tool/workpiece engagement geometry, they are integrated into the Semi Discretization Method in 5-axis flank milling to examine the stability of vibration at each cutter location. While the presented chatter analysis results in establishing stability lobes in 3-axis flank milling, it results in developing a novel approach in presenting the stability of the cut in 5-axis flank milling. The new approach, namely “stability maps”, determines the unstable cutter locations of the toolpath at each spindle speed. The accuracy of established 3-axis flank milling stability lobes and 5-axis stability maps is verified by conducting a set of cutting experiments and numerical simulations.