A new Steiner patch based file format for Additive Manufacturing processes

Additive Manufacturing (AM) processes adopt a layering approach for building parts in continuous slices and use the Standard Tessellation Language (STL) file format as an input to generate the slices during part manufacturing. However, the current STL format uses planar triangular facets to approximate the surfaces of the parts. This approximation introduces errors in the part representation which leads to additional errors downstream in the parts produced by AM processes. Recently, another file format called Additive Manufacturing File (AMF) was introduced by ASTM which seeks to use curved triangles based on second degree Hermite curves. However, while generating the slices for manufacturing the part, the curved triangles are recursively sub-divided back to planar triangles which may lead to the same approximation error present in the STL file. This paper introduces a new file format which uses curved Steiner patches instead of planar triangles for not only approximating the part surfaces but also for generating the slices. Steiner patches are bounded Roman surfaces and can be parametrically represented by rational Bezier equations. Since Steiner surfaces are of higher order, this new Steiner file format will have a better accuracy than the traditional STL and AMF formats and will lead to lower Geometric Dimensioning and Tolerancing (GD&T) errors in parts manufactured by AM processes. Since the intersection of a plane and the Steiner patch is a closed form mathematical solution, the slicing of the Steiner format can be accomplished with very little computational complexity. The Steiner representation has been used to approximate the surfaces of two test parts and the chordal errors in the surfaces are calculated. The chordal errors in the Steiner format are compared with the STL and AMF formats of the test surfaces and the results have been presented. Further, an error based adaptive tessellation algorithm is developed for generating the Steiner representation which reduces the number of curved facets while still improving the accuracy of the Steiner format. The test parts are virtually manufactured using the adaptive Steiner, STL and AMF format representations and the GD&T errors of the manufactured parts are calculated and compared. The results demonstrate that the modified Steiner format is able to significantly reduce the chordal and profile errors as compared to the STL and AMF formats.     

Performance analysis and dimensioning of multi-granular optical networks

Recent years have demonstrated the limited scalability of electronic switching to realize transport networks. In response, all-optical switching has been identified as a candidate solution to enable high-capacity networking in the future. One of the fundamental challenges is to efficiently support a wide range of traffic patterns, and thus emerges the need for equipment that is both practical and economical to construct and deploy. We have previously proposed the use of multi-granular optical cross-connects (MG-OXC), which support switching on both the wavelength and sub-wavelength level. To this end, the MG-OXCs are equipped with cheap, highly scalable slow switching fabrics, as well as a small number of expensive fast switching ports. The goal of this work is two-fold: first to demonstrate that a small number of fast switching ports suffices to support a wide range of traffic requirements, and second that multi-granular optical switching can offer cost-benefits on a network-wide scale. The first objective is studied through simulation analysis of a single switching node, and results indicate that a limited number of fast switching ports can significantly improve burst blocking performance over slow only switches. Furthermore, under certain circumstances, the MG-OXC can even approach the performance of a fast only switch design. Secondly, we introduce an Integer Linear Programming model for the total network installation cost, and our evaluation indicates that multi-granular optical switching can be a cost-effective solution on the network level, in comparison to slow only or fast only approaches. Furthermore, we can achieve reduced costs of individual OXC nodes, which allows us to minimize scalability problems corresponding to emerging fast switching fabrics.     

Computer-aided geometrical dimensioning and tolerancing for process-operation planning and quality control

This paper describes an extension of a model which determines an optimum set of dimensions and tolerances for machining processes at minimum manufacturing cost. This optimisation minimizes the cost of scrap, which is a function of manufacturing tolerances, as the objective function. Requirements of design sizes, geometrical tolerances (including both form and position) and machining allowances are expressed mathematically as constraints for the optimisation. A computerised trace method has been extended to determine the relationships between geometrical tolerances and associated relevant manufacturing dimensions and tolerances. In addition to the manufacturing cost, the model takes into account manufacturing sequence, distribution of manufacturing dimensions, process capabilities, tolerances, design sizes, geometrical tolerances, machining allowances and optimum scrap level. The resulting computerized interactive system can be used not only in process planning, but also in quality control.     

Standardizing the specification, verification, and exchange of product geometry: Research, status and trends

The task of international standardization of product geometry specification, verification and exchange is shared largely by two ISO committees. One is ISO TC 213, which is charged with the standardization of dimensioning, tolerancing, surface finish and related metrological principles and practices. The origin of this standardization dates back to pre-information age, and much effort in the last 20 years has gone into bringing greater mathematical rigour to this work to make it suitable for the information age. The other committee is ISO TC 184/SC 4, which is charged with the standardization of product data models suitable for exchange among various information systems. This effort, commonly known as STEP, is relatively new and is a product of the information age. This paper describes the current state of the interplay between the efforts of these two ISO committees, research work that was undertaken to meet the goals of their standards and plans to address future challenges.     

Scalable dimensioning of optical transport networks for grid excess load handling

Grids consist of the aggregation of numerous dispersed computational and storage resources, able to satisfy even the most demanding computing jobs. An important aspect of Grid deployment is the allocation and activation of installed network capacity, needed to transfer data and jobs to and from remote resources. Due to the data-intensive nature of Grid jobs, it is expected that optical transport networks will play an important role in Grid deployment. As Grids possibly consist of high numbers of resources, and users, solving the network dimensioning problem (i.e. determining the number of wavelength channels per fiber and wavelength granularity required) using straightforward Integer Linear Programs (ILP) does not scale well with increasing number of jobs. Therefore, we propose the use of Divisible Load Theory (DLT) when modeling the OCS (with wavelength translation) dimensioning problem in this context. We compare this approach to both an exact ILP and heuristic (derived from the exact ILP) approach as a function of the job arrival process, network related parameters and the Grid job scheduling strategy on the Grid. Results show the convergence of the DLT-based and the exact ILP approach, which indicates that the DLT-based approach is of practical use in cases where the exact ILP-based problem becomes intractable. We study an excess load scenario and evaluate the network cost for varying wavelength granularity, fiber/wavelength cost models, network topology and traffic demand asymmetry under multiple Grid scheduling strategies. Results indicate the suitability of our DLT-based approach as an Optical Transport Network dimensioning tool to be used by network operators.     

A closed form formula for long-lived TCP connections throughput

In this paper, we study the variation of the throughput achieved by TCP resulting from both the individual behavior of a connection and the interaction with all other connections sharing the same link. In particular, we calculate the tail distribution function (TDF) of the instantaneous throughput seen by one TCP connection in the additive increase multiplicative decrease (AIMD) framework. For the particular case that each TCP connection experiences the same round trip time (RTT) and under the many users approximation we prove that this TDF is given by a closed form formula that solely depends on the network parameters (number of sources, capacity and buffer size of the bottleneck link). This formula can then be used as a dimensioning tool, where throughput is guaranteed to each user to be “larger than a given value for at least a certain percentage of the time”. In the context defined here, this formula plays the same role for the dimensioning of an IP router as the Erlang B formula does for the dimensioning of a PSTN switch.     

Discrete performance model of ATM multiplexer with on-off and CBR sources

The paper addresses the analysis of a single multiplexing node in ATM networks. It presents analytical models for evaluating the performance parameters of a multiplexer that has N independent and identical ON-OFF type input sources, M independent Constant Bit Rate inputs, and an output channel with finite buffer. The channel speed is assumed to be an integer times of the source speed in ON state which equal to speed of the CBR sources. A bidimensional Homogeneous Discrete Time Markov Chain is introduced where the two dimensions describe the number of ON sources and the number of cells in the finite buffer at a given time. Two time scales are defined in order to ensure accurate results in calculating the performance parameters, e.g. cell loss and cell delay. Three alternative models of the cell arrival process are discussed and the performance parameters are derived.