Limit Values Of Parameters Research Articles

Flutter and divergence instability regions of a column subjected to the load realized by means of a jet engine with an additional guiding structure

In this paper, a new slender system is considered — a column that is subjected to a compressive follower load. The studied structure uses a system of rigid transoms guiding the loaded end of the column with the limitation of their mutual rotation by means of rotational springs. This additional element does not transfer the compressive load but affects guidance of the loaded end of the column. In the presented form, the solution used to guide the end of the column was not previously taken into account. The boundary problem was formulated on the basis of Hamilton’s principle, taking into account (due to the non-linearity) the small parameter method. The theoretical, numerical, and experimental studies were conducted by determining an influence of the system parameters (in particular the element guiding the loaded end) on the instability type. On the basis of the kinetic stability criterion, critical divergence and flutter loads as well as limit values of parameters in the system were determined, at which instability occurs. The research was limited to the determination of the first linear component of vibration frequency. As a part of numerical research, detailed considerations were made on characteristic curves. It has been shown that with an appropriate selection of the parameters of the guiding system, a new shape of the characteristic curves can be obtained. This new feature shows that in the boundary case (instability change from flutter to divergence) the critical divergence load is greater than the critical flutter. In order to confirm the correctness of the mathematical model and thus the results of numerical tests concerning the occurrence of flutter and divergence areas the experimental tests were carried out consisting of recording the behavior of the system with a quick camera when it was loaded with a model jet engine. The correctness of the shape of characteristic curves was confirmed by the experimental frequency analysis of considered columns at different jet engine thrust magnitudes. The conducted research may be of great importance in the control of the flutter phenomenon of slender systems exposed to follower forces, including those resulting from the action of the wind.

Metric and ultrametric inequalities for directed graphs

Consider an electrical network modeled by a digraph G each directed edge e of which is a semiconductor with a monomial conductance function ye∗=fe(ye)=yes/μer if ye≥0 and ye∗=0 if ye<0. Here ye is the potential difference (voltage), ye∗≥0 is the current in e, and μe>0 is the resistance of e; furthermore, r>0 and s>0 are two real parameters common for all edges. In particular, case r=s=1 corresponds to the Ohm law, while r=12,s=1 may be interpreted as the square law of resistance, which is typical of hydraulics and gas dynamics. We show that for every ordered pair of nodes a,b of the network, the effective resistance μa,b is well-defined. In other words, any two-pole network with poles a and b can be effectively replaced by two oppositely directed edges: from a to b of resistance μa,b and from b to a of resistance μb,a. Furthermore, for every three nodes a,b,c the inequality μa,cs/r+μc,bs/r≥μa,bs/r holds, in which the equality is achieved if and only if every directed path from a to b in G contains c. In addition to case (i) s=r=1, some limit values of parameters s and r are also of interest being related to classic triangle inequalities. Namely, (ii) the length/time of a shortest directed path, (iii) the inverse width of a bottleneck path, (iv) the inverse capacity (maximum flow per unit time) from a terminal a to a terminal b correspond to: (ii) r=s→∞, (iii) r=1,s→∞, (iv) r→0,s=1, respectively. These results generalize ones obtained in 1987 for monomial isotropic networks, which are modeled by undirected graphs. In this special case, effective resistances form a metric space when s≥r and an ultrametric one when s/r→∞. Of course, for anisotropic networks, which are modeled by directed graphs, the symmetry μa,b=μb,a may fail. For the linear isotropic networks triangle inequality is known since 1967 and it was extended to the linear anisotropic case in 2016.

СРАВНИТЕЛЬНЫЙ АНАЛИЗ ДВУХ МЕТОДОВ ЭЛЕКТРОЭРОЗИОННОЙ ПРОШИВКИ ГЛУХИХ МИКРООТВЕРСТИЙ

The paper presents the results of experimental studies of the significance of differences in the technological parameters of electroerosive micro-hole firmware for two variants of the micro-hole firmware series process: without facing the tool electrode and with the tool electrode facing after processing each hole. The significance of differences in the technological parameters of the firmware process is established: by the wear of the electrode-tool, by the productivity of the process and the efficiency of the process as a whole. Detailed statistical processing of data from two samples of eight duplicate (parallel) experiments in each sample is performed to accurately assess the significance of the differences between the two variants of the process of electroerosive firmware of microholes. Calculations are made of the limit values of parameters of the microholes' electroerosion firmware: the relative linear wear of the electrode-tool and the process performance. They allow identifying and excluding doubtful experiments (artifacts) from the results, i.e. experiments with sharply distinguished results. The results of such experiments should be excluded from the statistical series, since they significantly affect the results of the experiment. The paper uses an exact method for determining the required number of duplicate experiments developed at BSTU named after V. G. Shukhov. The conducted research clearly shows the feasibility of introducing the electrode-tool in manufacturing to reduce the wear of the electrode-tool and, therefore, increase the quality of products with deaf microholes, for example, in the mass production of atraumatic surgical needles, the volume of production of which is millions of pieces per year.

Ensuring Reliable Operation of Machine Parts with a New System of Variable Tolerances

Introduction. The article describes an algorithm for determining the system of tolerances for ensuring reliable operation of parts on the section. The block diagram of the program for determining the variable tolerances is demonstrated. There determined blocks of initial information − broken and smooth curves of the controlled parameter, histogram and graph of resource distribution and definition of active area of control, and blocks of building graphs of “marginal fan curves of wear” and systems of admissions for objects of study of two types: for universal fuel pump (UTN-5) and four-section small-sized fuel pump with mechanical regulator. Two ways of determining the system of tolerances are suggested. Variant 1 is a graphical way through constructing “limit fan curves of wear” and determining tolerances by the value of ordinates in the control points. Variant 2 is an analytical way. There is created a formula to replace the graphical method for determining system tolerances. Materials and Methods. Two models of high-pressure pump were selected as objects of the study. Nominal and limit values of parameters were known for the pumps. Schedules for checking and equation of wear curves are determined. Dependencies describing the pump plunger pair wear curves are determined. A histogram and graph for determining pump life cycles are drawn. The active area of control is determined with a given failure probability coefficient. Results. As a result of the study the values for the tolerances system of two types of high pressure fuel pumps are obtained. Reliability values for one pump type are determined. Graphic and analytical algorithms for determining the system of tolerances by the formula are developed. Discussion and Conclusion. The study approves the possibility of using the variable tolerance as a basis for determining the system of tolerances and reliability indicators of the diagnostic object.

Establishment of Engine Condition Monitoring Alarm System Based on Fuzzy Neural Network

In order to overcome the defect of traditional engine condition monitoring only depending on single parameter, this paper establishes the five-level condition monitoring alert system with fuzzy neural network (FNN) which is good at settling uncertain and complicated problems. Firstly, optimal monitoring parameters are selected from three aspects of ferrography, vibration and performance parameters. With sufficient historical data, limit values of parameters and reliable five-level condition monitoring standards are maintained and established by statistical analysis. Then fuzzy membership functions are applied to transform practical data into fuzzy data. Finally the structure of neural network is designed and trained by sample data. The model is tested with original data and proved to be more effective and reliable to engine condition monitoring.

Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems

In this paper we prove the continuity of stable subspaces associated to parabolic-hyperbolic boundary value problems, for limiting values of parameters. The analysis is based on the construction performed in [MZ] of Kreiss' type symmetrizers.

Local Sounding of the Earth Due to Interference of Electromagnetic Waves Near Earth's Surface

The theory of electromagnetic sounding of the earth, based on interference effects in the spatial structure of a pair of coupled waves, propagating along the earth's surface with the same frequency but different wavelengths, is proposed. A hitherto unknown heterogeneous structure of surface impedance, the conductivity being constant, is analysed by means of new exact analytical solutions of Maxwellian equations, described by the propagation of coupled waves from the source along the boundary between two media, the complex dielectric permittivities of both media being arbitrary. The classical formulae for Biot-Savart law and VLF impedance of conducted surface prove to be the private causes of obtained interference structure, related to the limit values of parameters. The perspectives of use of amplitude-phase effects of interference pattern, generated by direct and lateral waves, for earth sounding, especially for undersea sounding, are illustrated.