Uncharted Stable Peninsula for Multivariable Milling Tools by High-Order Homotopy Perturbation Method

In this work, a new method for solving a delay differential equation (DDE) with multiple delays is presented by using second- and third-order polynomials to approximate the delayed terms using the enhanced homotopy perturbation method (EMHPM). To study the proposed method performance in terms of convergency and computational cost in comparison with the first-order EMHPM, semi-discretization and full-discretization methods, a delay differential equation that model the cutting milling operation process was used. To further assess the accuracy of the proposed method, a milling process with a multivariable cutter is examined in order to find the stability boundaries. Then, theoretical predictions are computed from the corresponding DDE finding uncharted stable zones at high axial depths of cut. Time-domain simulations based on continuous wavelet transform (CWT) scalograms, power spectral density (PSD) charts and Poincaré maps (PM) were employed to validate the stability lobes found by using the third-order EMHPM for the multivariable tool.This research was funded by Tecnológico de Monterrey through the Research Group of Nanotechnology for Devices Design, and by the Consejo Nacional de Ciencia y Tecnología de México (Conacyt), Project Numbers 242269, 255837, 296176, and National Lab in Additive Manufacturing, 3D Digitizing and Computed Tomography (MADiT) LN299129

Semi-Active Magnetorheological Damper Device for Chatter Mitigation during Milling of Thin-Floor Components

The productivity during the machining of thin-floor components is limited due to unstable vibrations, which lead to poor surface quality and part rejection at the last stage of the manufacturing process. In this article, a semi-active magnetorheological damper device is designed in order to suppress chatter conditions during the milling operations of thin-floor components. To validate the performance of the magnetorheological (MR) damper device, a 1 degree of freedom experimental setup was designed to mimic the machining of thin-floor components and then, the stability boundaries were computed using the Enhance Multistage Homotopy Perturbation Method (EMHPM) together with a novel cutting force model in which the bull-nose end mill is discretized in disks. It was found that the predicted EMHPM stability lobes of the cantilever beam closely follow experimental data. The end of the paper shows that the usage of the MR damper device modifies the stability boundaries with a productivity increase by a factor of at least 3.This research was funded by Tecnológico de Monterrey through the Research Group of Nanotechnology for Devices Design, and by the Consejo Nacional de Ciencia y Tecnología de México (Conacyt), Project Numbers 242269, 255837, 296176, and National Lab in Additive Manufacturing, 3D Digitizing and Computed Tomography (MADiT) LN299129

A Knowledge Gradient Policy for Sequencing Experiments to Identify the Structure of RNA Molecules Using a Sparse Additive Belief Model

We present a sparse knowledge gradient (SpKG) algorithm for adaptively selecting the targeted regions within a large RNA molecule to identify which regions are most amenable to interactions with other molecules. Experimentally, such regions can be inferred from fluorescence measurements obtained by binding a complementary probe with fluorescence markers to the targeted regions. We use a biophysical model which shows that the fluorescence ratio under the log scale has a sparse linear relationship with the coefficients describing the accessibility of each nucleotide, since not all sites are accessible (due to the folding of the molecule). The SpKG algorithm uniquely combines the Bayesian ranking and selection problem with the frequentist $\ell_1$ regularized regression approach Lasso. We use this algorithm to identify the sparsity pattern of the linear model as well as sequentially decide the best regions to test before experimental budget is exhausted. Besides, we also develop two other new algorithms: batch SpKG algorithm, which generates more suggestions sequentially to run parallel experiments; and batch SpKG with a procedure which we call length mutagenesis. It dynamically adds in new alternatives, in the form of types of probes, are created by inserting, deleting or mutating nucleotides within existing probes. In simulation, we demonstrate these algorithms on the Group I intron (a mid-size RNA molecule), showing that they efficiently learn the correct sparsity pattern, identify the most accessible region, and outperform several other policies

Thin-Wall Machining of Light Alloys: A Review of Models and Industrial Approaches

Thin-wall parts are common in the aeronautical sector. However, their machining presents serious challenges such as vibrations and part deflections. To deal with these challenges, di erent approaches have been followed in recent years. This work presents the state of the art of thin-wall light-alloy machining, analyzing the problems related to each type of thin-wall parts, exposing the causes of both instability and deformation through analytical models, summarizing the computational techniques used, and presenting the solutions proposed by di erent authors from an industrial point of view. Finally, some further research lines are proposed

Eco-efficient process based on conventional machining as an alternative technology to chemical milling of aeronautical metal skin panels

El fresado químico es un proceso diseñado para la reducción de peso de pieles metálicas que, a pesar de los problemas medioambientales asociados, se utiliza en la industria aeronáutica desde los años 50. Entre sus ventajas figuran el cumplimiento de las estrictas tolerancias de diseño de piezas aeroespaciales y que pese a ser un proceso de mecanizado, no induce tensiones residuales. Sin embargo, el fresado químico es una tecnología contaminante y costosa que tiende a ser sustituida. Gracias a los avances realizados en el mecanizado, la tecnología de fresado convencional permite alcanzar las tolerancias requeridas siempre y cuando se consigan evitar las vibraciones y la flexión de la pieza, ambas relacionadas con los parámetros del proceso y con los sistemas de utillaje empleados. Esta tesis analiza las causas de la inestabilidad del corte y la deformación de las piezas a través de una revisión bibliográfica que cubre los modelos analíticos, las técnicas computacionales y las soluciones industriales en estudio actualmente. En ella, se aprecia cómo los modelos analíticos y las soluciones computacionales y de simulación se centran principalmente en la predicción off-line de vibraciones y de posibles flexiones de la pieza. Sin embargo, un enfoque más industrial ha llevado al diseño de sistemas de fijación, utillajes, amortiguadores basados en actuadores, sistemas de rigidez y controles adaptativos apoyados en simulaciones o en la selección estadística de parámetros. Además se han desarrollado distintas soluciones CAM basadas en la aplicación de gemelos virtuales. En la revisión bibliográfica se han encontrado pocos documentos relativos a pieles y suelos delgados por lo que se ha estudiado experimentalmente el efecto de los parámetros de corte en su mecanizado. Este conjunto de experimentos ha demostrado que, pese a usar un sistema que aseguraba la rigidez de la pieza, las pieles se comportaban de forma diferente a un sólido rígido en términos de fuerzas de mecanizado cuando se utilizaban velocidades de corte cercanas a la alta velocidad. También se ha verificado que todas las muestras mecanizadas entraban dentro de tolerancia en cuanto a la rugosidad de la pieza. Paralelamente, se ha comprobado que la correcta selección de parámetros de mecanizado puede reducir las fuerzas de corte y las tolerancias del proceso hasta un 20% y un 40%, respectivamente. Estos datos pueden tener aplicación industrial en la simplificación de los sistemas de amarre o en el incremento de la eficiencia del proceso. Este proceso también puede mejorarse incrementando la vida de la herramienta al utilizar fluidos de corte. Una correcta lubricación puede reducir la temperatura del proceso y las tensiones residuales inducidas a la pieza. Con este objetivo, se han desarrollado diferentes lubricantes, basados en el uso de líquidos iónicos (IL) y se han comparado con el comportamiento tribológico del par de contacto en seco y con una taladrina comercial. Los resultados obtenidos utilizando 1 wt% de los líquidos iónicos en un tribómetro tipo pin-on-disk demuestran que el IL no halogenado reduce significativamente el desgaste y la fricción entre el aluminio, material a mecanizar, y el carburo de tungsteno, material de la herramienta, eliminando casi toda la adhesión del aluminio sobre el pin, lo que puede incrementar considerablemente la vida de la herramienta.Chemical milling is a process designed to reduce the weight of metals skin panels. This process has been used since 1950s in the aerospace industry despite its environmental concern. Among its advantages, chemical milling does not induce residual stress and parts meet the required tolerances. However, this process is a pollutant and costly technology. Thanks to the last advances in conventional milling, machining processes can achieve similar quality results meanwhile vibration and part deflection are avoided. Both problems are usually related to the cutting parameters and the workholding. This thesis analyses the causes of the cutting instability and part deformation through a literature review that covers analytical models, computational techniques and industrial solutions. Analytics and computational solutions are mainly focused on chatter and deflection prediction and industrial approaches are focused on the design of workholdings, fixtures, damping actuators, stiffening devices, adaptive control systems based on simulations and the statistical parameters selection, and CAM solutions combined with the use of virtual twins applications. In this literature review, few research works about thin-plates and thin-floors is found so the effect of the cutting parameters is also studied experimentally. These experiments confirm that even using rigid workholdings, the behavior of the part is different to a rigid body at high speed machining. On the one hand, roughness values meet the required tolerances under every set of the tested parameters. On the other hand, a proper parameter selection reduces the cutting forces and process tolerances by up to 20% and 40%, respectively. This fact can be industrially used to simplify workholding and increase the machine efficiency. Another way to improve the process efficiency is to increase tool life by using cutting fluids. Their use can also decrease the temperature of the process and the induced stresses. For this purpose, different water-based lubricants containing three types of Ionic Liquids (IL) are compared to dry and commercial cutting fluid conditions by studying their tribological behavior. Pin on disk tests prove that just 1wt% of one of the halogen-free ILs significantly reduces wear and friction between both materials, aluminum and tungsten carbide. In fact, no wear scar is noticed on the ball when one of the ILs is used, which, therefore, could considerably increase tool life

Towards Faster-than-real-time Power System Simulation Using a Semi-analytical Approach and High-performance Computing

This dissertation investigates two possible directions of achieving faster-than-real-time simulation of power systems. The first direction is to develop a semi-analytical solution which represents the nonlinear dynamic characteristics of power systems in a limited time period. The second direction is to develop a parallel simulation scheme which allows the local numerical solutions of power systems to be developed independently in consecutive time intervals and then iteratively corrected toward the accurate global solution through the entire simulation time period. For the first direction, the semi-analytical solution is acquired using Adomian decomposition method (ADM). The ADM assumes the analytical solution of any nonlinear system can be decomposed into the summation of infinite analytical expressions. Those expressions are derived recursively using the system differential equations. By only keeping a finite number of those analytical expressions, an approximation of the analytical solution is yielded, which is defined as a semi-analytical solution. The semi-analytical solutions can be developed offline and evaluated online to facilitate the speedup of simulations. A parallel implementation and variable time window approach for the online evaluation stage are proposed in addition to the time performance analysis. For the second direction, the Parareal-in-time algorithm is tested for power system simulation. Parareal is essentially a multiple shooting method. It decomposes the simulation time into coarse time intervals and then fine time intervals within each coarse interval. The numerical integration uses a computational cheap solver on the coarse time grid and an expensive solver on the fine time grids. The solution within each coarse interval is propagated independently using the fine solver. The mismatch of the solution between the coarse solution and fine solution is corrected iteratively. The theoretical speedup can be achieved is the ratio of the coarse interval number and iteration number. In this dissertation, the Parareal algorithm is tested on the North American eastern interconnection system with around 70,000 buses and 5,000 generators

Fast chatter stability prediction for variable helix milling tools

Regenerative chatter is a well-known form of self-excited vibration that limits the productivity of machining operations, in particular for milling. Variable helix tools have been previously proposed as a means of avoiding regenerative chatter, and although recent work has analysed the stability of such tools there has not always been a strong agreement with experimentally observed behaviour. Furthermore, the analysis of variable helix tool stability can be tedious and numerically slow, compared to standard tools. Consequently it has been difficult to gain insight into the potential advantages of variable helix tools. The present work attempts to address these issues, by first developing an efficient approach to variable helix tool stability based upon the Laplace transform. Then, this new analysis method is used to demonstrate the importance of multi-frequency effects and nonlinear cutting stiffness. The work suggests that whilst variable-helix tools can have more operating regions that are stable, un-modelled behaviour (such as nonlinearity and multi-frequency effects) can have a critical influence on the accuracy of model predictions

Equiconvergence in summation associated with elliptic polinomial

We compare the Fourier integral with the Fourier series in summation associated with elliptic polinomial

A reliable turning process by the early use of a deep simulation model at several manufacturing stages

The future of machine tools will be dominated by highly flexible and interconnected systems, in order to achieve the required productivity, accuracy, and reliability. Nowadays, distortion and vibration problems are easily solved in labs for the most common machining operations by using models based on the equations describing the physical laws of the machining processes; however, additional efforts are needed to overcome the gap between scientific research and real manufacturing problems. In fact, there is an increasing interest in developing simulation packages based on "deep-knowledge and models" that aid machine designers, production engineers, or machinists to get the most out of the machine-tools. This article proposes a methodology to reduce problems in machining by means of a simulation utility, which uses the main variables of the system and process as input data, and generates results that help in the proper decision-making and machining plan. Direct benefits can be found in (a) the fixture/ clamping optimal design; (b) the machine tool configuration; (c) the definition of chatter-free optimum cutting conditions and (d) the right programming of cutting toolpaths at the Computer Aided Manufacturing (CAM) stage. The information and knowledge-based approach showed successful results in several local manufacturing companies and are explained in the paper.The work presented in this paper was supported in some sections within the project entitled MuProD-Innovative Proactive Quality Control System for In-Process Multi-Stage Defect Reduction- of the Seventh Framework Program of the European Union [FoF.NMP.2011-5] and UPV/EHU under program UFI 11/29. Thanks are given to Tecnalia, for collaboration in testing, and especially to Ainhoa Gorrotxategi and Ander Jimenez for the sound work in the project. Thanks to Gamesa Eolica and Guruzpe, for the time, technical advices, and efforts during the analysis in examples

Optimum selection of variable pitch for chatter suppression in face milling operations

Cutting capacity can be seriously limited in heavy duty face milling processes due to self-excited structural vibrations. Special geometry tools and, specifically, variable pitch milling tools have been extensively used in aeronautic applications with the purpose of removing these detrimental chatter vibrations, where high frequency chatter related to slender tools or thin walls limits productivity. However, the application of this technique in heavy duty face milling operations has not been thoroughly explored. In this paper, a method for the definition of the optimum angles between inserts is presented, based on the optimum pitch angle and the stabilizability diagrams. These diagrams are obtained through the brute force (BF) iterative method, which basically consists of an iterative maximization of the stability by using the semidiscretization method. From the observed results, hints for the selection of the optimum pitch pattern and the optimum values of the angles between inserts are presented. A practical application is implemented and the cutting performance when using an optimized variable pitch tool is assessed. It is concluded that with an optimum selection of the pitch, the material removal rate can be improved up to three times. Finally, the existence of two more different stability lobe families related to the saddle-node and flip type stability losses is demonstrated