Steve Feng

This thesis presents a novel voxel representation that employs tetrahedron as its basic voxel elements. The modeling method is intended to achieve high computational efficiency while maintaining reasonable modeling accuracy. The modeling method is developed on the basis of the traditional cubic voxel by dividing it into 40 tetrahedrons to provide sub-voxel accuracy. Thus, to achieve a desired level of accuracy, the modeling method requires a low resolution. To enhance its modeling efficiency, a tetrahedron-based lookup table is derived to cover all the possible tetrahedral decomposition shapes in a cubic voxel. The use of a lookup table avoids complicated geometric calculations, resulting in a fast modeling process. Furthermore, each voxel is assigned a signed distance field and a control scheme that allows morphing of the tetrahedron shapes into the target input model, which leads to a higher level of accuracy. Various legacy geometry models are tested with the developed tetrahedron-based voxel model. Acquired modeling times are compared with the traditional cubic voxel multi-level method. As both modeling methods achieve similar levels of accuracy, the tetrahedron-based method shows an up to four times improvement in modeling time. This level of computational efficiency obtained makes it a suitable candidate for modeling scenarios involving frequent model updates.

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A dual-material model has been developed for wire-arc additive manufacturing (WAAM), focusing on strategies to embed secondary material elements uniformly in the surface layers of engineering parts. The embedment should distribute within the top surface layer of a component in a controlled manner, while enabling the fulfilment of specified minimum spacing requirement between any two adjacent elements. To optimize the locations of embedded elements, a new surface sub-sampling algorithm has been developed, for sampling the points that are uniformly distributed according to the specified requirements. The research workflow involves processing of the input 3D model, surface decomposition, a hexagon-based surface sub-sampling, and the generation of the dual-material model. The model is validated first using different prototypical geometries, and then tested using several real engineering parts. Finally, the WAAM toolpath is generated by slicing the dual-material model and converting the resultant 3D printing toolpath into robotic welding path code. Utilizing electric arc as the heat source and metal wire as feedstock, WAAM is a promising metal additive manufacturing technology capable of fabricating large-scale components with high buy-to-fly ratio and with exceptional deposition rate, However, the high heat input associated with the welding process can result in high thermal and residual stresses, leading to cracking of the deposited parts; especially, cracking susceptibility is extremely high while depositing brittle materials. The proposed model can enhance structural integrity and, at the same time, ensure functionality of the additively manufactured parts by embedding brittle elements of suitable sizes into a ductile material matrix.

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Multi-axis machine tools are used to machine parts with complex, curved surfaces. With additional rotary axes, multi-axis machine tools have a higher risk to have collisions compared with traditional three-axis machine tools. Collision during machining often causes damages to the machine and workpiece, which in turn leads to loss of productivity and extra costs. It can occur between the cutter, workpiece, and machine. Machining simulation with moving machine axis links becomes essential to detecting collisions prior to physical machining. In order to simulate machine movements, it is necessary to attain the kinematic chain of a given machine tool and to group machine components for each link in the kinematic chain. Existing methods to group link components require many inputs from users and follow an error-prone and lengthy manual process.This thesis presents an automatic method to group link components for each machine axis of a given multi-axis machine tool. The method is able to generate the kinematic chain of the multi-axis machine tool with only basic user inputs. As the first step, interference detection by voxel modeling is used to get contact relationships between components. Link-interface features between components are then identified and used to generate the link groups. The process of generating the link groups may be accompanied with uncertainties that can result in incorrect link groups. As a result, if there is an uncertainty, the generated link groups need to be validated to be free of link collision within the travel span of each axis. If there is collision, the collision is to be resolved by examining the uncertainty causing the specific link collision. The iterative step of validation and resolution continues until no link collision exists. The link collision is detected also by voxel modeling. The output of the automatic grouping method is the kinematic chain of the machine tool and the geometric model of each link for machining simulation. The presented method has been implemented on five commercial Haas five-axis machine tools with varying configurations. Correct kinematic chains for these machine tools have been generated and ready to be used for simulation of machine movements.

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Additive manufacturing (AM) is renowned for its flexibility and low upfront costs. Amongst the variety of AM technologies, fused filament fabrication (FFF) is by far the most prevalent. FFF printers work by extruding molten polymer in a series of planar layers according to directions derived from computer-aided design (CAD) data. While FFF provides a low-cost alternative to conventional manufacturing for small-batch prototyping, it’s hindered by its time-intensive nature and high unit cost of production. One contributing factor to the manufacturing time and material costs of FFF is the requirement to print additional supporting structures in order to facilitate the construction of inclined surfaces. In absence of these structures, the forces acting on the unsupported (overhanging) portion of the molten extrusions are liable to cause deformation or collapse. As per the universally-quoted heuristic, any surface that is inclined by more than 45 degrees from the vertical should be supported. However, to date, there has been little justification provided to support this heuristic and, in fact, components with surface angles exceeding 45 degrees are routinely produced without support using FFF printers. In this work we present a theory to explain the limiting phenomena in the printing of inclined surfaces via FFF. We also develop a model to predict a component’s printability based on its geometry, the process parameters and the material properties of the filament. Experimental validation is provided to verify the appropriateness of the model. The results indicate that the phenomena limiting the maximum surface angle are scale-dependent. For large-scale FFF printing, the angle is limited by gravity, which tends to cause the extruded filament to deflect downwards, limiting the vertical progression of the structure. For small-scale printing, the angle is limited by surface tension, which tends to cause the extruded filament to contract, limiting the structure’s horizontal progression. At small scales the maximum surface angle was found to depend solely on the geometry of the print bead and the number of perimeters, whereas at large scales it also depends on the process parameters and material properties.

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For complex sheet metal parts, multiple stamping stages are needed in a sequence. In today’s industry, intermediate parts are transferred between stages automatically by feeding as a strip (progressive die) or a blank (transfer die). Although progressive/transfer dies are highly automated, transfer system parameters need to be predefined. These parameters must ensure that the part is transferred to next stage quickly and safely. However, due to highly complex geometry and motion in the die system, these parameters are conventionally finalized manually according to designers’ experience. In this thesis, algorithms are proposed to optimize transfer system parameters in transfer die, according to the geometry and motion restrictions of the entire system. Two algorithms are proposed to complete a two-step optimization process. In the first step, the geometry of the die set and parts are analyzed. Based on Siemens NX software and customized kinematic model, motions of die components are simulated, an “Obstacle Map” is generated to record the potential collisions between parts (and grippers) and die set during the part transfer process. Obstacle map can be regarded as an inherent property of the entire die system geometry, which can be utilized not only for the optimization algorithm proposed in the second step, but also for future research. In the second step, with obstacle map, motions of the transfer system are analyzed. According to system motion capacity and freedom of modification in practice, transfer system parameters are optimized. The core of the algorithm in this step is to apply overlap between motions to reduce the transfer duration. Lift stroke and press stroke are also optimized when modifications are allowed. The optimized transfer system parameters result in improved strokes per minute, while all the obstacles in the obstacle map are bypassed. One case study for a typical transfer die system with 14 initial SPM is performed to show the effectiveness of the proposed algorithms. Four levels of optimization are conducted with increasing freedom of modification: initial speed -> maximum speed -> allow lift stroke modification -> allow press stroke modification. The results show that the proposed algorithms are valid, SPM can be improved (22.9 -> 26.52 -> 26.61 -> 27.99) in different situations. Some topics can be further addressed based on the works in this thesis, future works can focus on algorithm expansion to progressive die, and algorithm improvements for more complex cases.

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A new method is presented to generate ball-end milling tool paths for the efficient three-axis machining of sculptured surfaces. The fundamental principle of the presented method is to generate the tool paths according to a preferred feed direction (PFD) field derived from the surface to be machined. In this work, the PFD at any point on the surface is the feed direction that maximizes the machining strip width. Theoretically, tool paths that always follow the direction of maximum machining strip width at each cutter contact point on the surface would maximize material removal, which leads to the shortest overall tool path length. Scallops are generated when a surface is machined using three-axis ball-end mills. There is no redundant machining if the scallop height is always maximized and the neighboring machining strips do not overlap. Unfortunately, these overlaps commonly exist for tool paths always following the preferred directions. Such redundant machining can be reduced via iso-scallop tool paths. Nonetheless, iso-scallop tool paths do not in general follow the preferred feed directions. To attain maximum machining efficiency via generating the shortest overall tool path length, the presented method analyzes the PFD field of the surface and segments the surface into distinct regions with similar PFD's by identifying the degenerate points and generating their separatrices. The tool paths of each region are generated by the iso-scallop method to mitigate redundant machining. Since a sequential approach is employed to generate the iso-scallop tool paths, an initial tool path is selected in such a way that the growing deviations of the subsequent tool paths from the PFD's are not significant. The proposed method has been validated with numerous case studies, showing that the generated tool paths have a shorter overall length compared with those generated by the existing methods.

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This thesis presents a novel geometric modeling methodology of cutter-workpiece engagement extraction for general milling processes. Cutter-workpiece engagement (CWE) geometry is the instantaneous contact area between the cutter and the in-process workpiece. It defines how the cutting edge enters and exits the workpiece. It plays a crucial role for process simulation and directly effects the calculation of cutting force, torque and et cetera. Based on the result of physical simulation, the milling process can be optimized and the machining performance can be improved. Successful optimization depends on the accuracy of the extracted CWE.The difficulty and challenge of CWE extraction comes from various types of cutters, changing geometry of in-process workpiece and multi-axis tool path of cutter movement. Existing methods confront difficulty to be available for general milling processes, which means for any type of cutter, any shape of in-process workpiece and any tool path, even with self-intersections. To fulfill the requirement of generality, this thesis proposes to model all geometries as triangle meshes throughout the simulation and certain strategy of CWE extraction is applied. Our methodology adopts ball pivoting algorithm for cutter swept volume generation. Octree space partition method is applied to speed up triangle-to-triangle intersection calculation which is used for Boolean operation between meshes. The reported method has been tested on several case studies of different complexity. The effectiveness of the proposed methodology shows its potential for further applications.

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Airfoil is the basic profile geometry of impeller and turbine blades. The operational efficiency of these blades is governed by stringent tolerance specifications on the airfoils. The specified tolerances are commonly evaluated from discrete coordinate data collected in sections by a touch-probe coordinate measuring machine (CMM). These measurement data are subject to inspection inaccuracies associated with CMM measurement operation. Apart from well-known inspection parameters like profile tolerance, profile thickness and edge radius, the leading edge (LE) and trailing edge (TE) are specified with a unique set of geometric parameters like the maximum linear segment length restriction and the minimum curvature radius restriction. This thesis focuses on evaluating these two localized geometric restrictions along the leading edge and trailing edge of an airfoil.This thesis first presents a robust algorithm to identify the longest linear segment. The main feature of the proposed algorithm is the explicit consideration of measurement uncertainty. The algorithm starts by detecting relatively small linear segments and then merges these segments to determine the longest feasible linear segment under given measurement uncertainty. The effect of measurement uncertainty and data point resolution on the performance of the presented algorithm is demonstrated through case studies. Once the linear segments are identified and excluded, the remaining data points only belong to the non-linear segments. As minimum radius can occur at any location, curvature radius at each point along the non-linear segments is evaluated. Curvature radius at a specific point can only be estimated from its neighborhood. The chosen neighborhood size needs to be balanced between capturing local curvature attribute and effectively considering the effect of measurement uncertainty. An algorithm is thus proposed to evaluate radius via a rolling scheme of five consecutive data points in order to retrieve the local curvature information of the mid-point. A statistical approach is employed where all feasible radii are considered in order to reliably estimate the desired radius. Biarc construction is used as a tool to calculate radius. Compared with existing radius estimation methods, the proposed method has demonstrated to yield better accuracy with varying measurement uncertainty and data point resolution.

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This thesis presents geometric computing algorithms for the evaluation of geometric errors on the pressure and suction sides of an airfoil section. Airfoil blades such as those in an impeller have a complex freeform geometry which poses significant challenges to the geometric error evaluation tasks. Reliable error evaluation is critical to the impellers as wrongful rejections will lead to significant financial losses. In practice, touch-probe coordinate measuring machines are employed to acquire measurement data points on the impeller blade surface along pre-specified sections. The measurement data points are then used to evaluate against the specified geometric tolerances including the profile tolerance and airfoil thickness control. Profile tolerances can be defined in three ways: bilateral asymmetric, bilateral symmetric, and unilateral. Existing methods for profile error evaluation are not capable of evaluating all three possible types of profile tolerance. These methods are not adaptive with respect to the specified tolerance zone boundaries. This thesis proposes a novel Scaled Minimax Method which is able to address all types of profile tolerance. The proposed method builds on the conventional Minimax Method and utilizes a scaling constant to control the relative positioning of the evaluated profile error zone boundaries. Thickness control is a less-known tolerance specification for airfoil sections. It controls the overall shape deviation of an airfoil section between the pressure and suction sides. The proposed evaluation method is based on determining a minimum error zone via simultaneously shrinking the outer boundary and growing the inner boundary for the involved measurement data points. Numerous case studies have been performed to validate the effectiveness of the proposed geometric error evaluation methods.

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Layer manufacturing has emerged as a highly versatile process to produce complex parts compared to conventional manufacturing processes, which are either too costly to implement or just downright not possible. However, this relatively new manufacturing process is characterized by a few outstanding issues that have kept the process from being widely applied. The most detrimental is the lack of a reliable method on a computational geometry level to predict the resulting part error. Layer setup with regard to the contour profile and thickness of each layer is often rendered to operator-deemed best. As a result, the manufactured part accuracy is not guaranteed and the build time is not easily optimized. Even with the availability of a scheme to predict the resulting finished part, optimal layer setup cannot be determined. Current practice generates the layer contours by simply intersecting a set of parallel planes through the computer model of the design part. The volumetric geometry of each layer is then constructed by extruding the layer contour by the layer thickness in the part building direction. This practice often leads to distorted part geometry due to the unidirectional bias of the extruded layers. Because of this, excessive layers are often employed to alleviate the effect of the part distortion. Such form of the distortion, referred to as systematic distortion, needs to be removed during layer setup. This thesis proposes methods to first remove the systematic distortion and then to determine the optimal layer setup based on a tolerance measure. A scheme to emulate the final polished part geometry is also presented. Case studies are performed in order to validate that the proposed method. The proposed scheme is shown to have significantly reduced the number of layers for constructing an LM part while satisfying a user specified error bound. Therefore, accuracy is better guaranteed due to the existence of error measure and control. Efficiency is greatly increased.

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