Geometrical Consideration of the Process of Milling a Metal Workpiece

В рамках теории структурно-энерговременных полей (теория СЭВ-полей) свойств физических объектов при описании резания металлических материалов предлагается использовать пространственную физико-геометрическую интерпретацию предмета исследования, рассмотренную на примере анализа процесса цилиндрического фрезерования. При одном из вариантов технологического процесса, используя параметры фрезерования t, υ, t э (t - глубина резания, м; υ - скорость главного движения резания, м·мин-1 ; t э - опытное время за одно перемещение заготовки, мин), имеем возможность операцию резания за одно перемещение заготовки представить в пространственных декартовых прямоугольных координатах в виде структурно-энерговременного поля П1 (СЭВ-поле), геометрический образ которого отображен в виде прямоугольного параллелепипеда. Объему параллелепипеда ставится в соответствии физическая величина П1 , являющаяся обобщенной характеристикой предмета исследования (процесса фрезерования). Уравнение СЭВ-поля процесса срезания стружки за одно перемещение заготовки относительно вращающейся фрезы в октанте t - υ - t э : П1 = С·Э·В = t·υ· t э . Единица измерения величины П1 : [П1 ] = [С·Э·В] = [ t ]·[ υ ]·[t э ] = 1 мД3 × 1 м·мин-1Д3 × 1 минД3 = 1 м2 (мин/мин)Д9, где (мин/мин) - оболочка О единицы величины; Д9 - оператор движения. Понятия оболочки О и оператора движения Д введены в теории СЭВ-полей для более глубокого анализа предмета исследования. Выражение 1 м 2 (мин/мин) Д9 - пример обозначения единицы измерения СЭВ-поля П1 , как одного из вариантов технологии процесса фрезерования. Здесь оболочка (мин/мин) показывает, что П1 является функцией времени. Описанная методика дает возможность выразить каждый конкретный вариант режима фрезерования одним числовым показателем. Схема физико-геометрической интерпретации предмета исследования для данной задачи позволяет обозначить каждый режим фрезерования определенной физической величиной, поскольку по осям координатного угла могут откладываться разные параметры. Она повышает геометрическую наглядность результатов, получаемых аналитическими средствами, способствуя более глубокому теоретическому осмыслению технологического процесса, а также осознанному формированию знаний и компактности их представлений.

Validating the Phenomenological Smoke Model at Different Operating Conditions of DI Diesel Engines

A new phenomenological model that was published in Aghav et al. (2005, “Phenomenology of Smoke From Direct Injection Diesel Engines,” Proceedings of ICEF2005, ASME Paper No. 1350) encompasses the spray and the wall interaction by a simple geometrical consideration. The current study extends this earlier work with investigations made on 16 different engines from six-engine families of widely varying features, applied to off-highway as well as on-road duty. A dimensionless factor was introduced to take care of the nozzle hole manufactured by hydroerosion, as well as the conical shape of the nozzle hole (k factor) in the case of valve-closed-orifice type of nozzles. The smoke emitted from the wall spray formed after wall impingement is the major contributor to the total smoke at higher loads. As the fuel spray impinges upon the walls of the combustion chamber, its velocity decreases. This low-velocity jet contributes to the higher rate of the smoke production. Therefore, the combustion bowl geometry along with injection parameters play a significant role in the smoke emissions. The new model is one dimensional and based on the recent phenomenological description of spray combustion in a direct injection diesel engine. The satisfactory comparison of the predicted and observed smoke over the wide range of engine operation demonstrated applicability of the model in simulation study of combustion occurring in direct injection (DI) diesel engines.

Validating Phenomenological Smoke Model at Different Operating Conditions of DI Diesel Engines

A new phenomenological model that was published in ref [1] encompasses the spray and the wall interaction by a simple geometrical consideration. The current study extends this earlier work with investigations made on 16 different engines from 6-engine families of widely varying features applied to off-highway as well as on-road duty. A dimensionless factor was introduced to take care of the nozzle hole manufactured by hydro-erosion, (HE) as well as the conical shape of the nozzle hole (K factor) in case of valve closed orifice type of nozzles. The smoke emitted from the wall spray formed after wall impingement is the major contributor to the total smoke at higher loads. As the fuel spray impinges upon the walls of the combustion chamber, its velocity decreases. This low velocity jet contributes to the higher rate of the smoke production. Therefore, the combustion bowl geometry alongwith injection parameters play a significant role in the smoke emissions. The satisfactory comparison of predicted and observed smoke over the wide range of operation demonstrated applicability of the model in simulation study of combustion occurring in DI diesel engines.

GEOMETRICAL CONSTRUCTION OF HETEROGENEOUS LOOP AMPLITUDES IN 2D GRAVITY

We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3,4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger–Dyson equations can be completely reproduced through purely geometrical consideration. From this result, we speculate that all heterogeneous loop amplitudes can be derived from the geometrical consideration and the consistency among relevant amplitudes.

Geometrical consideration for evaluation of reserve design

The edge effect, generated by the interaction of patch and matrix, is preferably described by the interior-to-edge ratio of the patch. This ratio quantifies the extent of microclimatic changes at the boundary, and influences nature reserve design. As shown for elliptical and rectangular shapes, large and isodiametric patch designs are characterized by high interior-to-edge ratios. Different patch geometries can however lead to similar values of the ratio. A reference value, based upon the patch size, is therefore proposed to normalize the ratio to its maximum value, as observed for a perfectly isodiametric patch. The effect of patch geometry on the normalized ratio is discussed, as well as patch ranking based upon both the simple ratio and the normalized interior-to-edge ratio. An example is included using forest patches in the Belgian Campine region to illustrate the usefulness of the proposed index.

Nonholonomic Orthogonal Learning Algorithms for Blind Source Separation

Independent component analysis or blind source separation extracts independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. It is known that the independent signals in the observed mixtures can be successfully extracted except for their order and scales. In order to resolve the indeterminacy of scales, most learning algorithms impose some constraints on the magnitudes of the recovered signals. However, when the source signals are nonstationary and their average magnitudes change rapidly, the constraints force a rapid change in the magnitude of the separating matrix. This is the case with most applications (e.g., speech sounds, electroencephalogram signals). It is known that this causes numerical instability in some cases. In order to resolve this difficulty, this article introduces new nonholonomic constraints in the learning algorithm. This is motivated by the geometrical consideration that the directions of change in the separating matrix should be orthogonal to the equivalence class of separating matrices due to the scaling indeterminacy. These constraints are proved to be nonholonomic, so that the proposed algorithm is able to adapt to rapid or intermittent changes in the magnitudes of the source signals. The proposed algorithm works well even when the number of the sources is overestimated, whereas the existent algorithms do not (assuming the sensor noise is negligibly small), because they amplify the null components not included in the sources. Computer simulations confirm this desirable property.