Analytical Model For Calculation Research Articles

Modeling of fuel combustion processes in a steam boiler when replacing standard burners

To date, most of Ukraine's thermal power equipment has exhausted its factory resource and is physically and morally obsolete. One of the ways to solve this problem is to modernize it with the introduction of modern fuel-using equipment. The decisive direction in this situation is the focus on domestic technologies, which differ from imported counterparts due to better adaptability to domestic equipment, as well as a more favorable price policy for domestic manufacturers. The presented work was carried out in order to check the feasibility of replacing standard burners with burners built on the basis of jet-niche technology in power boilers, for example, such as the GМ-50 (Е-50-3,9-440GМ) steam boiler. For this, a computer model of a steam boiler and regular burners was developed. The research was carried out using the ANSYS Student software package. The application of the numerical modeling method using the ANSYS Student software complex made it possible to perform a detailed analysis of the fuel combustion process in a steam boiler, evaluate its efficiency and study the impact on environmental indicators. The object of the research was the processes that take place during the combustion of gaseous fuel and their influence on the performance indicators of the GМ-50 power boiler. The subject of the study was a CFD fuel model of the GМ-50 boiler, whose regular burners are capable of working on both liquid and gaseous fuel. Methane was used as fuel. Both regular axial burners and burners built on the basis of jet-niche technology, which are more environmentally friendly, were used as burners. Verification of the CFD model, which took place using a known analytical technique, shows that the discrepancy between the values of analytical calculations and model calculations does not exceed 6.7 %. The average temperature of flue gases in the festoon window was selected as a comparison parameter. The temperature value of 1117 С was obtained analytically. Calculation using the CFD model developed in the ANSYS-CFX environment shows that the temperature value should be 1042 С. It was determined that regular burners are less environmentally friendly than, for example, modern jet-niche ones. So, for the coefficient of excess air  = 1.2, the average value of nitrogen oxides at the fuel outlet is 187 ppm. It makes sense to replace standard burners, for example, with jet-niche ones, which are most suitable for replacing standard ones.

Determination of Chip Compression Ratio for the Orthogonal Cutting Process

The chip compression ratio is the most important characteristic of various machining processes with chip generation. This characteristic enables the determination of kinetic and other energy loads on the tool and the machined material. This provides an overall evaluation of the machining process and the possibility of its subsequent optimization. This paper presents the results of determining this cutting characteristic by experimental method, analytical calculation, and numerical modeling. For the analytical calculation of the chip compression ratio, an analytical cutting model developed based on the variational principle of the minimum potential energy was used. A finite element model of orthogonal cutting was used for the numerical simulation of the above process characteristic. Experimentally, the chip compression ratio was determined by the ratio of the chip thickness to the cutting depth (undeformed cutting thickness). The chip thickness was determined by direct measurement using chip slices obtained during the cutting process. The Johnson–Cook constitutive equation was used as the machined material model and the Coulomb model was used as the friction model. The generalized parameters’ determination of the constitutive equation was performed through a DOE (Design of Experiment) sensitivity analysis. The variation range of these parameters was chosen based on the analysis of the effect of individual parameters of the constitutive equation on the chip compression ratio value. The largest deviations between the experimental and analytically calculated values of the chip compression ratio did not exceed 21%. At the same time, the largest deviations of simulated values of the indicated cutting characteristic and its experimental values did not exceed 20%. When comparing the experimental values of the chip compression ratio with the corresponding calculated and simulated values, the deviations were within 22%.

Fuzzy random sensitivity analysis for the overall structure reliability of reinforced concrete freezing wellbores in deep alluvium based on hidden Markov model

To address the shortcomings of traditional reliability theory in characterizing the stability of deep underground structures, the advanced first order second moment of reliability was improved to obtain fuzzy random reliability, which is more consistent with the working conditions. The traditional sensitivity analysis model was optimized using fuzzy random optimization, and an analytical calculation model of the mean and standard deviation of the fuzzy random reliability sensitivity was established. A big data hidden Markov model and expectation-maximization algorithm were used to improve the digital characteristics of fuzzy random variables. The fuzzy random sensitivity optimization model was used to confirm the effect of concrete compressive strength, thick-diameter ratio, reinforcement ratio, uncertainty coefficient of calculation model, and soil depth on the overall structural reliability of a reinforced concrete double-layer wellbore in deep alluvial soil. Through numerical calculations, these characteristics were observed to be the main influencing factors. Furthermore, while the soil depth was negatively correlated, the other influencing factors were all positively correlated with the overall reliability. This study provides an effective reference for the safe construction of deep underground structures in the future.

A setup and analytical dose calculation model for solid-state sample irradiation using a microtron type e-beam accelerator

A setup and analytical dose calculation model for solid-state sample irradiation using a microtron type e-beam accelerator

Design and Analysis of 5-DOF Compact Electromagnetic Levitation Actuator for Lens Control of Laser Cutting Machine.

In laser beam processing, the angle or offset between the auxiliary gas and the laser beam axis have been proved to be two new process optimization parameters for improving cutting speed and quality. However, a traditional electromechanical actuator cannot achieve high-speed and high-precision motion control with a compact structure. This paper proposes a magnetic levitation actuator which could realize the 5-DOF motion control of a lens using six groups of differential electromagnets. At first, the nonlinear characteristic of a magnetic driving force was analyzed by establishing an analytical model and finite element calculation. Then, the dynamic model of the magnetic levitation actuator was established using the Taylor series. And the mathematical relationship between the detected distance and five-degree-of-freedom was determined. Next, the centralized control system based on PID control was designed. Finally, a driving test was carried out to verify the five-degrees-of-freedom motion of the proposed electromagnetic levitation actuator. The results show it can achieve a stable levitation and precision positioning with a desired command motion. It also proves that the proposed magnetic levitation actuator has the potential application in an off-axis laser cutting machine tool.

Glulam frame corner joints built of birch plywood and mechanical fasteners: An experimental, analytical, and numerical study

This study investigates frame corner joints built of birch plywood plates and glulam elements connected via self-tapping screws. Analytical calculations based on the fastener group’s torsional moment resistance, the proposed fastener group’s elastic and post-elastic load-bearing criteria, and the design formulas in Eurocode 5 were performed to predict the connection capacity in both elastic and post-elastic stages. A combined action check formula was adopted to predict the capacity of birch plywood plates and glulam elements. Frame corner specimens constructed with three different plywood thicknesses were planned to study the influence on global behavior and rotational stiffness. The specimens were intentionally designed so that failure occurred either in plywood or in glulam, in order to examine the robustness and validity of analytical calculation models. Another supplementary test group with 21 mm plywood and fewer fasteners was also designed and tested, in which the plastic yield of fasteners was expected. The test results of this supplementary group served to calibrate the analytical model that predicts the elastic and post-elastic capacity of the connection group. As a result of the comparison, the analytical calculations gave reasonable predictions on the failure of plywood, glulam, and the capacity of the fastener group. Only when the exposed moment exceeded the post-elastic limit of the fastener group did the plastic yielding of fasteners become observable. Moreover, numerical finite element models adopting the foundation zone-modeling scheme were constructed, which were proven to capture all test configurations' linear loading stiffness satisfactorily.

Experimental investigation and numerical study on evolution of surface roughness caused by ultrasonic shot peening of 2024 aluminum alloy sheet

Ultrasonic shot peening (USP) is widely used for materials surface strengthening and metal sheet forming as a novel mechanical surface treatment technology. The USP-caused surface roughness is usually viewed as an unfavorable factor influencing the service performance of the mechanical components treated by USP. Taking advantages of the experimental investigation, analytical calculation and finite element simulation, the correlation between the USP-caused surface roughness and the USP-induced metal sheet forming deformation is studied comprehensively. Firstly, the USP intensity was experimentally tested by USP of Almen strips. In accordance with the USP intensity, the experimental investigations on the evolutions of surface roughness caused by USP of 2024 aluminum alloy sheets with the thicknesses of 1 mm, 2 mm and 3 mm were carried out, respectively. An analytical calculation model (ACM) was then proposed to account for the effects of the USP-induced metal sheet forming deformation on the USP-caused surface roughness. The analytically-calculated results are in good agreement with the experimentally-measured surface roughness caused by USP of 2024 aluminum alloy sheets. Lastly, linking the finite element simulation of the USP-induced metal sheet forming with the analytical calculation model, an innovative FEM-ACM coupling approach was presented for predicting the evolutions of surface roughness caused by USP of metal sheets. It has been experimentally validated with USP of 2024 aluminum alloy sheets, and would be of great significance for the development and industrial application of USP technology.

Analytical calculation model for elastic modulus and strength of foamed concrete

Foamed concrete has gained increasing attention for its excellent engineering performance. Endeavors have been made to experimentally and numerically elucidate the mechanism of foamed concrete, while few theoretical methods are used to analytically calculate mechanical properties. This paper proposes a theoretical framework to describe the elastic behavior of foamed concrete by combining Eshelby’s equivalent inclusion theory with the Mori–Tanaka method. In the analytical model, foamed concrete is regarded as a two-phase composite comprising a homogeneous cement matrix and randomly oriented ellipsoidal air void. During derivation, the elastic modulus, strength, bulk modulus, shear modulus, and Poisson ratio are measured. A good agreement is established between the proposed method and experimental data.

Numerical Study on Cable Force Adjustment System for Replacing Slings of In-Service Suspension Bridges

To conduct a systematic investigation on the replacement scheme for slings in service of suspension bridges, five feasible tensioning schemes were determined based on numerical simulation and analytical methods using the sling replacement project of an existing bridge as a case study. The safety performance of the bridge was evaluated by considering parameters such as sling position, quantity, order, and force value. According to the coupling relationship between different slings during the tensioning process, a precise analytical calculation model for adjusting cable force of the suspender is determined. The findings demonstrate that the dynamic performance of the completed bridge solely depends on its final state and remains unaffected by the intermediate tensioning process of suspension. The research findings suggest that symmetrically batch or stepwise tensioning can be applied to the suspension bridge slings with cable adjustment sequence from both ends to middle span replacement scheme to minimize structural response and optimize mechanical properties.

Analytical analysis of the thermal comfort of the occupants inside a truck cabin

Thermal comfort inside a truck cabin is a parameter that influences the well-being of the driver and passengers. From the very first steps of designing the driver’s seat of a vehicle, the driver’s well-being is taken into account through ergonomic parameters. To analyze the ultimate comfort inside a truck cabin, a simplified sketch of the cabin will be proposed. The three-dimensional analytical calculation model is solved using the Ansys program in the Fluid Flow (CFX) module. Through modeling and numerical simulations, the temperature inside a truck cabin, the mode of movement of the air flow and the speed of the air flow are determined. Following these tests, it is checked whether the thermal comfort conditions for the driver and passengers in a truck cabin are respected and fulfilled. These term comfort conditions are evaluated based on some comfort indices available in specialized literature.

Mechanism analysis and optimal design of sound-absorbing metastructure constructed by slit-embedded Helmholtz resonators

<sec>Low-frequency noise has always been a thorny problem in the field of noise control. In recent years, the development of sound-absorbing metastructures has provided new ideas for controlling low-frequency noise. In this work, we propose a low-frequency sound-absorbing metastructure constructed by Helmholtz resonators with embedded slit. Analytical and numerical models are established to analyze the sound absorption performance and mechanism of the proposed sound-absorbing metastructure, and optimization design is conducted to achieve low-frequency wideband absorption performance. The analytical modeling method and the performance of the proposed sound-absorbing metastructure are also experimentally verified. The main conclusions are summarized as follows.</sec><sec>1) By using transfer matrix method and finite element method, analytical and numerical models for calculating sound absorption coefficient are established. It is shown that analytical predictions are in good agreement with numerical calculations. It is demonstrated that a typical design of a 30-mm-thick single-cell metastructure can achieve a sound absorption coefficient of 0.88 at 404 Hz. Typical designs of two-cell parallel structure and the four-cell parallel structure (both with a thickness of 50 mm) can achieve two and four nearly perfect low-frequency sound absorption peaks in a frequency band of 200–400 Hz, respectively.</sec><sec>2) The low-frequency sound absorption mechanisms of the proposed metastructures are explained from four aspects: simplified equivalent model parameters, normalized acoustic impedance, complex-plane zero/pole distribution, and sound pressure cloud image and particle velocity field distribution. It is demonstrated that the main sound absorption mechanism is related to the thermal viscous loss of sound waves, caused by the inner wall of embedded slit.</sec><sec>3) The design for broadband low-frequency absorption performance is optimized by using differential evolution optimization algorithm. An optimized parallel-multi-cell coupled metastructure with multiple perfect sound absorption peaks below 500 Hz is realized. For a thickness of 90 mm, the sound absorption coefficient curve of an optimized metastructure exhibits 8 almost perfect sound absorption peaks and an average sound absorption coefficient of 0.86 in a frequency range of 170－380 Hz.</sec><sec>4) Experimental samples are fabricated to test sound absorption. Experimental results are basically consistent with the analytical predictions. The results from analytical model, numerical calculations and experimental measurements are mutually verified.</sec><sec>In summary, the sound-absorbing metastructures with a thickness of sub-wavelength, proposed in this work, exhibit outstanding sound absorption performance at low frequencies. We demonstrate that they are suitable for low frequency broadband sound absorption below 500 Hz. Owing to their thin thickness and relatively simple construction, they have broad application prospects in practical noise control engineering.</sec>

Analytical calculation model for radial-axial coordinated feed strategy in large-scale flat ring rolling based on ultimate bending moment

Analytical calculation model for radial-axial coordinated feed strategy in large-scale flat ring rolling based on ultimate bending moment

A coupled matrix-fracture productivity calculation model considering low-velocity non-Darcy flow in shale reservoirs

The flow behavior of shale reservoirs is extremely complex. The mainly used development method of large-scale volume fracturing of horizontal wells is associated with a series of problems such as low productivity in general, fast decrease in productivity, and difficulty to increase productivity. Therefore, it is necessary to evaluate the productivity of shale oil wells and determine the key control factors. Considering low-velocity non-Darcy flow, this paper establishes an analytical solution model for productivity calculation of multi-fracture shale oil horizontal wells with coupled matrix-fracture flow. Calculating the oil production rate by considering low-velocity non-Darcy flow in shale oil reservoirs obtains values closer to the actual oil production rate on site. The average relative error of the oil production rate of the H8 shale oil well is 4.27%. The average relative error of the oil production rate of the TMS shale oil wells is 34.97%, which exceeds the rate of the semi-analytical model by 47.84%. Sensitivity analysis shows that the oil production rate of multi-fracture shale oil horizontal wells is most sensitive to fracture cluster spacing and flowing bottom hole pressure. With decreasing fracture cluster spacing and flowing bottom hole pressure, both the matrix pressure gradient and the apparent permeability of the matrix increase. These increases not only increase the oil production rate but also reduce the influence of the non-Darcy effect on the oil production rate caused by boundary effect. In addition, the limits of the impact of non-Darcy effects caused by boundary effect on oil production rate have been clarified. The results enable not only the prediction of the oil production rate, cumulative oil production, and recovery factor of multi-fracture horizontal shale oil wells, but also the finding of the shale oil sweet spot according to the influence of matrix permeability and crude oil viscosity on the oil production rate.

Analytical Calculation Model of the TV3-117 Turboshaft Working Regimes Based on Experimental Data

The paper presents a practical and relevant analytical calculation model for free turbine turboshaft working regimes and engine performance. The analytical calculation model is based on a post-processing method that analyzes a series of experimental data, specifically focusing on the percentage variations of the engine’s main parameters from the minimum to the takeoff working regime. The experimental data were acquired from three different types of engines: TV2-117A turboshaft, AI-20K turboprop, and Viper 632-41 turbojet. The analysis method aimed to identify, through calculations, certain similarity parameters that exhibit nearly constant variations or variations within tight limits. These parameters can then be used as approximate constants in the calculation model. By utilizing these constants related to similarity parameters, a mathematical connection between different engine regimes is established; more exactly, for the engine data from a known to unknown regime. In the current case, only the engine data from the takeoff regime are requested to be known, and in this way, the other working regimes of several engines can be calculated.

Very high-energy electron dose calculation using the Fermi-Eyges theory of multiple scattering and a simplified pencil beam model.

Very high-energy electrons (VHEE) radiotherapy, in the energy range of 100-200 MeV is currently considered a promising technique for the future of radiation therapy and could benefit from the promises of ultra-high dose rate FLASH therapy. However, to our knowledge, no analytical calculation models have been tested for this type of application and the approximations proposed for multiple scattering with electron beams have not been extensively evaluated at these high energies. In this work, we discuss the derivation of a simple and fast algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for fast dose calculation for VHEE beams (up to 200 MeV). Similar to the Gaussian pencil beam models used for electron or proton beams, this pencil beam kernel is separated into a central and an off-axis term. Monte Carlo simulations are performed to compare the analytical calculations with simulations and to determine the parametrizations used in the model at the highest electron energies. The normalized electron planar fluence distribution is described in water according to the Fermi-Eyges theory of multiple Coulomb scattering and a double Gaussian distribution model. The main quantities used in the model and their calculation (mass angular scattering power, mean energy, range straggling) are discussed and tested for electron energies up to 200 MeV. The TOPAS/Geant4 Monte Carlo (MC) toolkit is used to compare analytical calculations with MC simulations for a theoretical pencil beam irradiation and to find the best parameters describing the range straggling. The model is then tested on a realistic simulation of a pencil beam scanning beamline with treatment field dimensions up to 15×15cm2 and for deep-seated targets. Radial dose distributions of a pencil beam in water were calculated with the model and compared with the results of a complete Monte Carlo simulation. A good agreement (within 2%/2mm gamma passing rate superior to 90%, and a mean deviation between calculated and simulated pencil beam radial spread smaller than 0.6mm) was observed between analytical dose distributions and simulations for energies up to 200 MeV and field sizes up to 15×15cm2 . A parameterization of an electron source and an analytical pencil beam model were proposed in this work, thereby allowing a suitable reproduction of the lateral fluence of a VHEE beam and good agreement between calculations and simulated data. Further improvement of the method would require the consideration of a model describing the large-angle scattering of the electrons. The results of this work could support future research into VHEE radiotherapy and might be of interest for use together with VHEE broad beams produced by scanned narrow pencil beams.

Analytical calculation of mesh stiffness for spiral bevel gears with an improved global tooth deformation model

The paper proposes an efficient and accurate analytical calculation model of time-varying mesh stiffness (TVMS) for the spiral bevel gear. Firstly, an enhanced numerical loaded tooth contact analysis (NLTCA) model that considers both the global tooth and local contact deformations is developed. Based on Tredgold's approximation, spiral bevel gears are sliced into a series of spur gears. An improved global tooth deformation model is developed by accounting for axial tooth deformation and the effect of non-contacting tooth slices. The influence coefficient method is utilized to determine the local contact deformation. Subsequently, based on the results of the NLTCA model, a detailed calculation procedure for determining the TVMS of spiral bevel gears is described. Finally, some numerical examples are provided to illustrate the efficiency and accuracy of the proposed model through comparisons to finite element analysis (FEA) results. The proposed model can achieve satisfactory accuracy without FEA modification. Furthermore, ignoring the effects of the non-contacting tooth slices will lead to excessive elastic deformation when the length of the contact area across the tooth width is significantly shorter than the tooth width.

Radial–axial feeding process design for large-scale flat ring by quantitative estimation of ring roundness error

Due to the large size and thin wall characteristics, the large-scale ring is prone to plastic instability, resulting in loss of ring roundness. An analytical calculation model of roundness error is proposed to design the feeding process. This model is established by analytically deriving the relationships between feeding process, ring geometry, contact arc length, rolling force, ring vibration angle, ring bending angle, contact arc length increment and ring roundness error at different rolling stages. Compared with numerical calculation and production trial, the analytical model can predict the roundness error with reasonable accuracy and high efficiency and guide feeding process design.

Axial Crushing Behaviors of Metal Density Gradient Foam-Filled Square Taper Tubes: Analytical Model and Numerical Calculation

Abstract Metal tube is a traditional energy-absorbing structure, and metal foam is a lightweight material with advantages, i.e., high energy absorption and high specific strength. The foam-filled square tube can improve crashworthiness and has better energy absorption, which is higher than the sum of the energy absorption of the tube and foam. Axial crushing behaviors of metal density gradient foam (DGF) filled square taper tubes are studied analytically and numerically in this paper. An analytical model is presented to study the crushing behavior of DGF-filled square taper metal tube under axial loading, in which the interaction between square taper tube and DGF is considered. The numerical calculation is conducted, and the deformation mode is obtained. The analytical predictions are well consistent with the experimental and numerical results. The influences of taper angle, foam strength, maximum relative density, and minimum relative density of gradient foam on the compressive behavior of metal DGF-filled square taper tubes under axial loading are considered. It is demonstrated that when the taper angle is less than 85 deg, the average crushing force increases as the minimum density of the DGF increases. However, when the taper angle is greater than 85 deg, the average crushing force decreases with the increase of the minimum density of the gradient. This proposed analytical model can effectively predict the axial crushing behaviors of metal DGF-filled square taper tubes.

A methodology for data-driven modeling and prediction of the drag losses of wet clutches

AbstractIn wet clutches, load-independent drag losses occur in the disengaged state and under differential speed due to fluid shearing. The drag torque of a wet clutch can be determined accurately and reliably by means of costly and time-consuming measurements. As an alternative, the drag losses can already be precisely calculated in the early development phase using computing-intensive CFD models. In contrast, simple analytical calculation models allow a rough but non-time-consuming estimation. Therefore, the aim of this study was to develop a methodology that can be used to build a data-driven model for the prediction of the drag losses of wet clutches with low computational effort and, at the same time, sufficient accuracy under consideration of a high number of influencing parameters. For building the model, we use supervised machine learning algorithms. The methodology covers all relevant steps, from data generation to the validated prediction model as well as its usage. The methodology comprises six main steps. In Step 1, the data is generated on a suitable test rig. In Step 2, characteristic values of each measurement are evaluated to quantify the drag loss behavior. The characteristic values serve as target values to train the model. In Step 3, the structure and quality of the dataset are analyzed and, subsequently, the model input parameters are defined. In Step 4, the relationships between the investigated influencing parameters (model input) and the characteristic values (model output) are determined. Symbolic regression and Gaussian process regression have both been proven to be suitable for this task. Lastly, the model is used in Step 5 to predict the characteristic values. Based on the predictions, the drag torque can be predicted as a function of differential speed in Step 6, using an approximation function. The model allows a user-oriented prediction of the drag torque even for a high number of parameters with low computational effort and sufficient accuracy at the same time.

Analysis of the Bearing Capacity of Reinforced Concrete Dapped-End Beams

The dapped-end beam is a widely utilized structural component that offers many benefits in real-world applications. However, abrupt changes in the geometry result in complex stress flows, rendering conventional calculation methods unreliable. The estimation of the bearing capacity becomes particularly challenging when such elements are designed with prestressed reinforcement. Previous studies have identified that prestressing can have a negative impact on the behavior of dapped-end beams in specific configurations; however, this effect remains inadequately studied. This study employed both analytical and numerical parametric analyses to compare the behavior of prestressed and non-prestressed dapped-end beams. The results show that prestressing has a significant impact on the crack formation and bearing capacity of dapped-end beams. The intensity of this effect is dependent on various parameters, including shear reinforcement, concrete strength, height of the dap, and the distance between the support and the re-entrant corner. A reduction of approximately 50% in the cracking load was observed when the compressive stress ratio fell within the 0.20–0.25 range. At elevated prestressing levels, cracks emerged in the re-entrant corner prior to the beam being subjected to an external load. The analysis conducted revealed a decline of up to 8.81% in load-bearing capacity attributable to prestressing. The study highlights the importance of assessing reductions in bearing capacity and proposes an analytical calculation model for evaluating such reductions.