General Formula For Calculation Research Articles

The Safe Load-Bearing Capacity of Railway Tunnel Linings under High-Pressure and Water-Rich Conditions

High water pressure has been identified as the direct cause of water seepage problems in tunnels. Consequently, it is imperative to ascertain the safety load-bearing limits of tunnel linings in high-pressure, water-rich strata. In this study, FLAC3D (V5.0) numerical simulation software was employed to establish seepage models of tunnels under high-pressure, water-rich conditions, taking an actual engineering project as a reference. The hydrostatic pressure on tunnel linings under various conditions, including different permeability coefficients of the surrounding rock, grouting rings, levels of the water table, and coordinates of lining positions, was computed. By extracting the results of these simulations, correlations between lining water pressure and various parameters were analyzed, and preliminary hydrostatic pressure calculation formulas were deduced. Through regression analysis using SPSS (19.0) software, a general calculation formula for lining water pressure was derived. Given similar surrounding rock conditions, it was revealed that railway tunnel lining types adhere to a universal standard. The calculation formula for lining water pressure, when integrated with lithostatic pressure in the seepage model, facilitates the computation of the maximum pressure head that the tunnel lining can withstand under different conditions. A tabulation summarizing safe water head heights under various conditions is also presented, which enables rapid consultation of the safe load-bearing range of tunnel lining under corresponding conditions. This study provides a new calculation method for the lining water pressure of a water-rich railway tunnel, filling the literature gap. The safe tunnel head query table provides a new research approach for the design of water-rich tunnels. The research method in this article is rare in the literature, and the research approach has obvious innovations. The findings of this study have the potential to provide a theoretical foundation and data reference for the structural design of tunnel linings and the remediation of related issues.

Novel Meshing Stiffness Model for Spur Gear Pairs considering the Temperature Effect

This work studied the effect of temperature on gear stiffness in the full temperature range which contained thermal expansion and cold shrinkage. Considering the temperature effect, a meshing stiffness model for spur gear pairs in the full temperature range was established based on the conservation of energy. The general calculation formula for the gear pair’s temperature meshing stiffness in the full temperature range was derived. The influence of addendum modification and gear temperature distribution on gear stiffness was studied. Thereafter, the proposed model was verified experimentally. The results revealed that the temperature stiffness was smaller than the standard stiffness of the gears in the full temperature range. When the temperature of the gears increased from an initial temperature, which was lower than the standard temperature, the temperature stiffness of the gear first increased and then decreased. Moreover, the obtained results could provide theoretical support for an accurate dynamic analysis of gear transmission systems in the full temperature range.

Research on fast matching method of suspension stiffness and damping based on unmanned special vehicle

At present, the domestic research on the matching of stiffness and damping of the suspension system of unmanned special vehicles mainly adopts the empirical method and experimental method. This method is time-consuming and laborious, which prolongs the development cycle of unmanned special vehicles. In order to improve the vehicle ride comfort and reduce the research and development time, based on the single wheel two degree of freedom driving vibration model, this paper analyzes the influence of suspension stiffness and damping on the acceleration response of vehicle body, deduces the general calculation formulas of acceleration, suspension dynamic deflection and root mean square value of wheel dynamic load, and establishes the mathematical model of the optimal damping ratio of suspension system based on driving safety and comfort, The damping ratio design of the suspension system of an unmanned special vehicle is completed. The results show that this method can quickly and accurately complete the stiffness and damping matching design of suspension system, and shorten the time of vehicle design and development.

CRITICAL ANALYSIS OF EXISTING METHODS FOR CALCULATING CHANNELS WITH HETEROGENEOUS ROUGHNESS

This article examines the application of their methods, critically analyzing the data obtained as a result of many years of research when calculating the roughness channels of the actual work performed. The value of the reduced roughness coefficient when the flow is moving is always higher than one of the largest values of the roughness coefficients that make up the channel. According to the cross-section of the channels, the general calculation formula should be generalized, taking into account the possibility of different roughness of the sole.

ПРОЦЕССЫ КОММУТАЦИИ ВЕНТИЛЬНЫХ ТОКОВ ПОЛУПРОВОДНИКОВОГО ВОЛЬТОДОБАВОЧНОГО УСТРОЙСТВА

One of the main tasks of a railway power supply system is the provision of increased traffic volumes especially on direct current railway sections. For this reason the personnel of traction substations uses various means and methods of power supply strengthening including boosters representing two parallel thyristor bridges shunted by diodes. The paper considers three processes of commutation of rectifier currents arising in boosters: between two thyristors, between a shunt diode and thyristors and between thyristors and a shunt diode. The paper presents a detailed mathematical description of these processes. As a result, the authors gained a general formula for calculation of all three angles of commutation, with the use of which the authors have carried out all calculations. Reliability of gained expressions is confirmed on a physical model.

Study on the Influence of Internal Water Pressure on the Internal Force of Circular Hydraulic Tunnel Lining

The internal water pressure condition influences the internal force of the circular hydraulic tunnel lining. However, calculating the lining’s internal force of this type of tunnel still lacks practical theory. Based on the modified routine method and the theory of structural mechanics, the internal stress model of the tunnel section is established in this paper. The general calculation formula of lining internal force is deduced by considering arbitrary water level height and different water conveyance pressures. The formula is used to calculate the internal force of the lining under the action of internal water pressure and the influence laws of water level height and water conveyance pressure are explored, respectively. In addition, case analysis was carried out for several typical projects. The results show that the maximum internal force of the lining increases with the increase of water pressure and inner radius and the maximum internal force is in a fixed special position when the water is conveyed under pressure. When the water is conveyed without pressure, the internal force of the lining will increase with the increased water level. However, the maximum bending moment and axial force will reduce at the special water level. This calculation theory considering different working conditions of internal water pressure solves the calculation problem of the internal force of a circular hydraulic tunnel. It improves the design theory of tunnel structure and provides a theoretical basis for this type of tunnel’s structural design and safe operation.

Research on braking dynamics of multi-axle vehicle

Braking dynamics is an important part of longitudinal dynamics. Through the analysis of braking performance of multi-axle vehicles, we can deepen our understanding of longitudinal dynamics. Starting from the braking dynamics analysis of the whole vehicle, this paper proposes to establish the braking dynamics model of multi-axle vehicle by using the suspension deformation coordination equation, so as to calculate the general calculation formula of ground reaction force of multi-axle vehicle when braking. The brake force distribution of 4-axle brake is analyzed to verify its rationality and provide basis for multi-axle brake design.

A Series-Connected 40-Pulse Rectifier With DC Link Passive Harmonic Reduction Circuit

This article is focused on power quality improvement of the series-connected multipulse rectifiers (MPRs). For the dc side passive harmonic reduction method, the optimum design of the harmonic injection transformer is the key point to achieve the optimal harmonic elimination effect. First, a novel method for determining the optimum turns ratio of the harmonic injection transformer is proposed. Then, in combination with a five-phase bridge-rectifier-based MPR, the correctness of the general calculation formula is verified. In the verification processes, the operation principle and harmonic reduction mechanism are clearly analyzed before and after using the harmonic reduction circuit (HRC). The optimum turns ratio of the harmonic injection transformer obtained from the view point of minimizing the input voltage total harmonic distortion (THD) value is consistent with that calculated from general formula. Under the optimum design, the kVA rating of the HRC is only 0.87% of the load power. In experimental, the THD values of the input voltages in the 20-pulse rectifier and 40-pulse rectifier are 3.32% and 2.07%, respectively. The proposed method greatly reduces the complexity of the design processes and helpful for the development of the super-MPR. The proposed 40-pulse rectifier has high reliability, easy realization, considerable harmonic reduction ability, and quite a low load voltage ripple coefficient.

A contrast improved OR and XOR based ([formula omitted]) visual cryptography scheme without pixel expansion

Visual cryptography scheme (VCS) is a branch of secret sharing, in which a secret image is encrypted into n noise-like shares. In the recovering phase, the secret image can be reconstructed by stacking sufficient shares. It’s obvious that VCS with multiple decryptions can further widen the range of application. However, the investigations on the existing scheme with multiple decryptions are not sufficient. In this paper, we develop a novel contrast improved OR and XOR based (k,n)-VCS without pixel expansion. Significantly, we give a general simplified calculation formula to compute the theoretical contrast of the proposed scheme. In addition, if there are no computing devices, then we can reconstruct the secret image by stacking the shares directly. Meanwhile, we recover the secret image perfectly by performing XOR operation when computing devices are available. Since the proposed scheme is based on the parity basis matrices, our scheme has no pixel expansion. Finally, Theoretical analysis and experimental results are conducted to evaluate the efficiency and security of the proposed scheme.

The Mechanism Analysis on Open-Circuit Back EMF in Fractional-Slot Concentrated Winding Permanent Magnet Machines Using Air-Gap Field Modulation Theory

This article investigates the production mechanism of the open-circuit back-electromotive force (back EMF) in fractional-slot concentrated winding permanent magnet (FSCW-PM) machines based on the air-gap field modulation (AFM) theory. The relationship between spatial PM field harmonics and temporal back EMF harmonics is discovered by using a general model, which is suitable for both stator-PM and rotor-PM machines. The analysis results reveal that the FSCW-PM machines produce their open-circuit back EMF on the basis of AFM, which means that each back EMF harmonic is induced not only by a specific single spatial field harmonic but also by several different spatial field harmonics. Furthermore, a general winding factor calculation formula for FSCW-PM machines is derived together with the general calculation formula of all back EMF harmonics. Finally, the analysis is verified numerically by the finite element method and experimentally.

СУТНІСТЬ ДОХОДІВ ТА ПРИБУТКУ НЕПРИБУТКОВИХ УСТАНОВ ТА ПІДХОДИ ДО ЇХ ВИЗНАЧЕННЯ

The key characteristic of the XXI century is the rapid development of productive resources and information technologies. This feature results in the fast development of new and existing forms of entities and to the globalization of their activities. Non-profit organizations, regardless of organizational and legal form, are beginning to play a significant role in the socio-political and economic life of modern states. Such organizations promote the development of civil society and freedom of speech, and they can be a tool for achieving both the long-term and short-term goals of the state, or a group of people united on a certain basis. That is why the legal and tax regulation of non-profit organizations is an important factor in their development and serves as a tool to control the activities of non-profit institutions by the state. By regulation of the kinds of non-profit activity, the state may promote concepts of national development as, for example, an increase of life term through granting non-profit status to sports clubs and defined hospitals. Such an approach, in the long-term perspective, may result in economic growth through an increase of lifecycle of productive resources. As of today, one of the most discursive categories related to accounting and taxation of non-profit organizations is the concept of profit which appears as a result of excess revenue of the non-profit organization over expenses related to the execution of the statutory activity. In this article, the approaches to the definition of the concept of profit and income of a non-profit institution were analyzed through the analysis of existing approaches to its definition applied to classical business entities, also the definition of a profit of a non-profit organization was proposed. Additionally, possible sources of income of a non-profit institution in accordance with current legislation, and the peculiarities of payment of remuneration to employees of non-profit institutions were analyzed. Moreover, based on the normative requirements of the Ukrainian state authorities the general formula for calculation of the taxable income of non-profit organizations was designed.

Parametric Design on Solving the Maximum Deformation of Traction Helical Gear on Locomotive

The helical gear for locomotive traction has a popular application in the locomotive transmission system due to its excellent transmission performance. The maximum amount of deformation needs to be taken into consideration when performing the tooth profile modification on helical gear. The tooth profile design and corresponding calculation process tend to be tedious since the variation of the contact ratio of gear might lead to the change of logarithm in meshing tooth. In this paper, starting from the effect of the contact ratio on the logarithm of meshing teeth, the mesh-stiffness of helical gear can be solved by cross-section deformation formula based on the similarity of helical gear and spur gear. And then the general calculation formula governing the variation on the length of contact line is derived regarding the moment when gear tooth just engages. On the basis of actual production requirements, the solution equation for inter-tooth load distribution coefficient is derived. As a result, the general mathematical model for maximum deformation of helical gear which can perform parameterized calculation is established. The theory provides a significant theoretical guide in the field of tooth profile modification on locomotive traction helical gear.

Local correlation buckling analysis of double lipped channel cold-formed steel column

In this paper, the double lipped channel cold-formed steel column is analyzed by finite element method. Compared with the code both at home and abroad, convenient and practical design formulas have been figured out. The finite element model in this paper was compared with existing data analysis, and the results show that the model precision can meet the needs of the analysis. Through finite element analysis of double lipped channel cold-formed steel column, we can get the influence of a relative size, the plate width, on the bearing capacity of the local stability. The specification about plate buckling under the influence of the common effect of the different types of adjacent panel has no clear rules. Under even pressure, we get the general calculation formula under certain conditions. The conclusion can be used for reference in the standard revision.

Measurement error analysis of a cross correlation algorithm with a threshold centroiding method

The measurement error of a cross correlation algorithm with a threshold centroiding method, which is not only related to the background noise variance, the image spatial variance, the size of the reference image, and the image sensor parameters, but also concerned with the half width at half maximum and the threshold value of the cross correlation function, is derived theoretically in detail. Our general calculation formula of the measurement error of the cross correlation algorithm with the optimal normalized threshold value of 0.6035 is fit for the arbitrary sampling condition and extended target. Furthermore, the experimental results of the measurement error of the cross correlation algorithm using different sunspots taken by the correlating Shack-Hartmann wave-front sensor are compared with the theoretical measurement error. The experiment results agree well with the theoretical results.

The buckling strength of plexiglass protective shield under static water pressure

The protective shield of PMT (photon multiplier tubes) is a typical spherical-cylindrical thin-walled shell structure which works in the environment of deep water pressure with the material of plexiglass and character of low Young's Modulus. Therefore, it is significant to analyze the stability of the structure. The validity of eigenvalue buckling prediction and arc length method was verified by classic buckling theory of rotation shell firstly. Then the stability of plexiglass shield was researched by these two methods and a general calculation formula of shallow shell was fitted. The results show that the critical stress of plexiglass shield decreases with the reduction of section roundness; if the height of cylindrical shell is less than 0.3R, there is no influence on sphere-cylindrical shell structure, but when the height is more than 0.3R, the structure stability decreases with the increasing of cylindrical shell height. If the influence of exhaust orifice is considered, the geometry of shell is the main factor for the stability of shell when the orifice radius is less than 0.3 times of orifice spacing. Otherwise, orifice is the main factor for the stability of shell. There is a significant influence of initial imperfection on the critical stress of the protective shield and the critical stress decreases with the increasing of initial deformation. The research of this paper can provide useful guidance for the design of PMT plexiglass shield.

On Problem of Efficient Determination of Elastic Critical Moment of Beams with Selected Types of Cross-Sections

Assessment of the lateral-torsional buckling resistance of slender metal beams with no intermediate restraints requires the determination of the critical moment. Nowadays, its magnitude can be found using numerical analysis e.g. by means of widely used finite element method but also available derived formulae for the calculation of the critical moment based on the mathematical solution of the eigenvalue problem of differential equations of bending are still of considerable importance. For some common cases of support and load conditions and some specific types of cross-sections of metal beams, they allow to calculate the desired magnitude of the critical moment required for the buckling resistance check practically and reliably. The paper focuses on problem of derivation of the elastic critical moment of beams of double symmetrical cross-sections and channels loaded perpendicularly to the axis of symmetry. Starting with the Vlasov’s theory of stability of thin-walled members and variational methods, the process of derivation of the critical moment is briefly described. Whereas in case of beams of prismatic cross-sections the application of this method can subsequently result in general formula for calculation of the critical moment for various support and load conditions, the solution for members with variable cross-sections is much more complex and requires application of specific methods. The paper deals with application of selected methods of numerical mathematics on problem of determination of the elastic critical moment of metal beams and, when possible, compares the obtained values with analytical solution. Special attention is paid to members with variable cross-sections where primarily numerical methods can be used. Based on comparison of results, suitability of the utilized methods applied on problem of lateral-torsional buckling of metal beams is evaluated with significant emphasis on members with variable cross-sections.

The Vertex-gutman Index of k-Caterpillars with Equal Length Hairs

Caterpillars are often used to describe the structure of benzene molecules in chemical graph theory. In this paper, we studied the vertex-Gutman index and Gutman index of a class of k-Caterpillars with hairs of equal length mainly, and the general calculation formula was given in this paper.

The establishment of a mechanics model of multi-strand wire rope subjected to bending load with finite element simulation and experimental verification

In view of lack of a general mechanics model and theoretical calculation formulas for the bending state of a wire rope at present, a new mechanics modeling method for wire rope under bending is put forward. Firstly, the change law of the secondary helix angle is analyzed, and the reasonable assumptions for the mechanics model are put forward. According to the elastic thin rod theory of Love and the conservation of energy principle, the mechanics model of multi-strand wire rope in bending state is established, and the theoretical formulas of bending stiffness and equivalent elastic modulus are derived. Taking 6 × 7 and 6 × 19 wire ropes as examples, theoretical formulas are applied for calculation, meanwhile, the finite element simulation is carried out using ABAQUS and a special deflection measuring device is designed and manufactured to measure the large deformation deflection of the wire ropes. The theoretical calculation results are compared with the finite element simulation results and the measurement results. The contrast results show that the theoretical results are closer to the measurement results than the finite element simulation results. The maximum deformation error of the wire ropes free end between the theoretical results and the measurement results is 11.16%, which verifies the correctness of the mechanics model.

Theoretical and experimental investigation on internal gear pair with small sliding ratio

Aiming at the issue of sliding ratio, an internal gear pair is proposed which consists of an involute internal gear and a pinion with quadratic curve teeth. Particularly, the contact pattern is point contact and the pinion is generated based on an involute gear. The generation method and mathematical models of the gear pair are presented. The sliding ratio is calculated and the general calculation formulas of sliding ratios are developed. Also, the comparison between the involute gear and proposed gear is made. The adaptability of center distance and contact stress are also discussed. In addition, the gear pair was manufactured and inspected according to the exactitude solid model of the gear pair. In order to confirm this model to be effective, the efficiency experiment and the contrast experiment with the involute gear pair were performed. Furthermore, these two types of pinions were analyzed by scanning electron microscope and wear depths were measured by measuring center. The experiment results show that the efficiency of the internal gear pair is stable at a range about 97.1% to 98.6% and wear depth is less than 50% of the involute gear pair. The internal gear pair is expected to have excellent transmission performance.

Air Traffic Forecasting Using Optimization for Econometric Models

Forecasting has always been playing an important role for any company or organization. Air traffic forecasting is no exception. Accurate air traffic forecasting is essential for planning of future projects, management decisions, such as how much investment is needed, which projects to develop, which projects to postpone, etc. This paper proposes the new way of forecasting of air traffic combining the optimization model with the econometric model. General formulas for calculation of the aircraft volume and passenger volume in airports have been proposed. Using these formulas, an econometric model for passenger volume in Changi airport has been obtained. Furthermore, by using this model, Singapore air traffic passenger numbers have been predicted for 2016-2021.