Calculation Of Strength Research Articles

Correlative Theoretical and Experimental Study of the Polycarbonate | X Interfacial Bond Formation (X = AlN, TiN, (Ti,Al)N) During Magnetron Sputtering

AbstractTo understand the interfacial bond formation between polycarbonate (PC) and magnetron‐sputtered metal nitride thin films, PC | X interfaces (X = AlN, TiN, (Ti,Al)N) are comparatively investigated by ab initio simulations as well as X‐ray photoelectron spectroscopy. The simulations predict significant differences at the interface as N and Ti form bonds with all functional groups of the polymer, while Al reacts selectively only with the carbonate group of pristine PC. In good agreement with simulations, experimental data reveal that the PC | AlN and the PC | (Ti,Al)N interfaces are mainly defined by interfacial C─N bonds, whereas for PC | TiN, the interface formation is also characterized by numerous C─Ti and (C─O)─Ti bonds. Bond strength calculations combined with the measured interfacial bond density indicate the strongest interface for PC | (Ti,Al)N followed by PC | AlN, whereas the weakest is predicted for PC | TiN due to its lower density of strong interfacial C─N bonds. This study shows that the employed computational strategy enables prediction of the interfacial bond formation between PC and metal nitrides and that it is reasonable to assume that the research strategy proposed herein can be readily adapted to other organic | inorganic interfaces.

The van der Waals interaction and absorption and electron circular dichroism spectra of two-dimensional bilayer stacked structures

van der Waals (vdW) heterojunctions based on two-dimensional (2D) materials, graphene and transition metal dichalcogenides (TMDs), are a research hotspot for future optoelectronic and exciton devices. Bond-free vdW interactions are key to 2D material heterojunction device reliability and stability. However, most of the current research on 2D stacked materials heterostructures mainly focuses on optical properties and electronic structure. Furthermore, vdW interaction in 2D heterostructures is studied and understood on the basis of qualitative description and energy ranges from the literature. There are few studies on the nature of vdW interaction based on practical calculations of the quantitative strength and microscopic mechanism of vdW interaction between 2D stacked materials. Therefore, this paper explores the vdW interaction between 2D material stacked bilayer structures, including bilayer graphene, graphene/MoS2 and graphene/WS2 heterostructures, focusing on quantitative analysis of the energy components of the vdW interaction. We first visually observed the weak interactions in the three stacked bilayer structures through noncovalent interaction (NCI) analysis, and found that the interactions are concentrated in the binding region between the two-layer structures. We mainly decomposed the weak interaction energy in the three 2D material bilayer heterostructures through energy decomposition analysis based on the force field (EDA-FF) method and obtained the energy values and proportions of the three components-electrostatic energy, exchange repulsion energy and dispersion energy of the total binding energy between the 2D stacked bilayer structures. The vdW interaction energy is the sum of the exchange repulsion energy and dispersion energy, and the dispersion energy of the vdW interaction accounts for more than 60% of the binding energy of the weak interaction between the 2D bilayer stacked structures. The vdW strengths in the bilayer structures are on the order of 177.07, 123.85, and 133.93 kJ/mol, approxmately 1–2 orders of magnitude larger than the classically defined vdW energies of 0.1–10 kJ/mol. Furthermore, we calculate the density of states of the three 2D stacked structures, and further obtained HOMO-LOMO information; to further understand the electronic structures of the graphene/MoS2 and graphene/WS2 heterostructures, we calculated their optical absorption spectra and electron circular dichroism (ECD) spectra. According to the calculation results, the two heterostructures have strong absorption peaks in the visible region, and the charge transfer forms at the strong absorption peak can be determined according to the charge transfer diagram. The ECD spectra indicate that the configurations of the graphene/MoS2 and graphene/WS2 heterostructures have large chirality. Our work contributes to a deeper understanding of the nature of the weak interactions and optical properties in 2D stacked materials, which plays a fundamental role in promoting the construction of stable 2D heterostructure configurations and the development of multifunctional 2D devices. The research is conducive to further promoting the basic research and practical development of strong optoelectronic and excitonic 2D heterojunctions devices.

Study on Rock Failure Criterion Based on Elastic Strain Energy Density

Uniaxial and five conventional triaxial compression tests were conducted on sandstone to obtain the evolution laws of the input energy density, elastic strain energy density, and dissipative energy density. The input and dissipative energy densities increased with increasing axial strain; the elastic strain energy density increased with increasing axial strain at the pre-peak stage and decreased after the peak. According to the linear change rule between the peak elastic strain energy density and confining pressure, the energy density failure criterion of sandstone was established, and the criterion has high precision and few parameters, and the parameters have clear physical meaning. Moreover, the expression of the energy density failure criterion was similar to the classical Hoek-Brown criterion, but its adaptability was more extensive. The strength calculation results for seven different rocks under different confining pressures calculated using the energy density failure criterion were consistent with the experimental values, and the calculation error was smaller than that of the Mohr–Coulomb criterion and Drucker–Prager criterion, verifying the accuracy and applicability of the criterion.

Effects of aspect ratios and strengthening methods on seismic behavior of masonry piers strengthened by using hybrid-fibers modified reactive powder concrete

Piers are the main load-bearing elements of masonry structures. Damage to piers in earthquakes will lead to the collapse of the whole structure, so piers need to be strengthened. In order to study the effectiveness of hybrid-fibers modified reactive powder concrete (HFMRPC) coating strengthening on masonry piers and the influence of different strengthening methods and aspect ratios on the seismic behavior of masonry structures, six masonry walls with different aspect ratios (0.8, 1.0, and 1.4) and strengthened by different methods (unreinforced, single-sided coverage in piers, double-sided coverage in piers, and double-sided cross-bracing) were tested under in-plane quasi-static loading. The test and analysis results showed that the seismic behavior of masonry walls in terms of bearing capacity, displacement ductility, stiffness, and energy dissipation was effectively enhanced by HFMRPC coating. The improvement range of ductility coefficient, initial stiffness, and cumulative energy dissipation were 86.3% ∼ 229.3%, 18.2% ∼ 104.0%, and 57.0% ∼ 139.7%, respectively. The most suitable strengthening method for strengthening piers was double-sided cross-bracing compared with other methods. The strengthening effect of the double-sided coverage in piers was improved with the increased aspect ratio. Additionally, masonry wall shear strength and flexural capacity calculation methods were proposed based on GB 50003-2011, N-M interaction diagrams, and equivalent rectangular stress block.

Characterizing fatigue damage behaviors of concrete beam specimens in varying amplitude load

In this paper, the random and nonlinear mechanical characteristics of the composition distribution of concrete in each phase are investigated to solve the difficulty of fatigue damage test of concrete beam specimens under variable amplitude loading. A three-dimensional (3D) concrete composite random aggregate meso-model of concrete beam specimens is built with Digimat as a composite modeling tool. Subsequently, the bending-tensile strength and fatigue life of the model under four-point bending loading is analyzed and calculated using Abaqus finite element analysis model based on the concrete elastic-plastic damage criterion. The mechanical behaviors of concrete materials under static load failure, multistage fatigue loading, and random fatigue loading are studied. Finally, compared with the test results, the following conclusions are obtained. The random aggregate model and elastoplastic damage mechanics model of concrete composite constructed by concrete in Abaqus and Digimat can better describe the geometric and distribution characteristics of composite structure and aggregate in concrete beams and the mechanical behavior of fatigue and static load failure. The difference is 4.08 % with the experimental results, which verifies the validity and reliability of the numerical simulation model, and the fatigue life of concrete beams under random loading Sra and Srb is 1622 and 164 times, respectively. The research results have certain guiding significance and reference value for accurate calculation of bending and tensile strength of concrete beams under specified raw material and mix ratio and prediction of fatigue damage cracking in airport cement concrete pavement structure.

A proposed method for optimizing coal pillar design using coalfield-specific uniaxial compressive strength

The research described considers whether the variability in coal material strength, as derived through a series of uniaxial compressive strength (UCS) tests, could be used to indicate the variability in coal pillar strength. The aim is to be able to use a distribution of UCS tests as input into the coal pillar strength calculation. This will allow the pillar design to be expressed in terms of a probability of failure rather than as the commonly used safety factor. To achieve this, the bulk strength factor associated with commonly used pillar strength formulae was replaced with a distribution of UCS results divided by an adjustment factor. The factor was determined so as to ensure that the resulting bulk strength does not deviate from the statistically determined bulk strength published in the original formulae. This approach enabled pillar strength distributions to be obtained using industry-accepted strength formulae, subsequently allowing for a probability of failure to be calculated for a specific pillar design. Using a regional coal material strength curve as a baseline, coalfields in which the coal is stronger than the regional mean can be identified and the pillar designs optimized. This is based on the stronger coals achieving lower probabilities of failure at similar safety factors. The research has considered actual UCS data from multiple mines in the Mpumalanga coalfields of South Africa, and has proved that the variability in material strength between coalfields could allow for some optimization using the proposed approach. Based on the data used in the study, a 2.78% increase in extraction could be achieved. However, further research will be required to validate the results of the study in an underground environment.

Designing guiding device of suspension made of aluminum alloys for multi-purpose driverless vehicle using topological optimization method

Introduction (problem statement and relevance). Currently, mobile driverless transport and technological means are widely used for automation of work processes and remote control over a vehicle, excluding immediate human attendance in dangerous areas. Generally, such vehicles feature an electric powerplant while using batteries as energy storage devices. In order to reduce the number of operations during such vehicle driving, it is convenient to use a running gear design that is symmetric relative to its longitudinal and transverse planes. Reducing energy consumption will allow increasing in energy efficiency when performing transport and other technological operations. One of the ways to improve energy efficiency is to reduce the weight of elements of such vehicles. This can be achieved by using materials with high specific strength, such as aluminum alloys, and by developing optimum loading patterns for such element structures. The object of the study is a driverless 4x4 vehicle with the fully loaded weight of 830 kg. The research subject is the methods of optimum designing of vehicle load-bearing structures and their use taking into account the operating conditions. The purpose of the study is to develop the methodology for designing suspension elements for a vehicle with a symmetric design of the running gear made of aluminum alloy taking into account the loading modes.Methodology and research methods. The paper presents a dynamic mathematical model of the wheeled vehicle for determination of loads created in a program for rigid bodies dynamics modeling, the methodology for bringing the loads to one suspension unit (front left wheel), loading patterns for suspension elements obtained with the use of topological optimization and strength calculations performed with application of the finite element method confirming the design functionality.Scientific novelty and results. The paper presents the method for bringing the loads obtained for all suspension elements to the front left point, since the driverless vehicle has a symmetrical running gear design. Taking this into account, a rigid-body dynamic model and an algorithm for processing the obtained loads for a finite element model were developed. Also, typical modes of vehicle loading were selected. The loads were distributed among the following types: operational, extreme and emergency ones. Recommendations were given for the choice of restrictions when conducting topological optimization depending on the mode type. As a result, loading patterns for suspension guiding device elements were obtained. Check calculations were carried out to confirm the design functionality.Practical significance. The obtained results can be used in development of highly loaded elements of wheeled vehicles.

Calculation and Analysis of Short Circuit Strength of Three-Winding Transformer

The transformer is the most important in the entire power system and is also one of the most expensive devices. The operating condition of the transformer affects itself and at the same time concerns the stability and safety of the whole power system. This paper deals with leakage field, short-circuit electromotive force, and other issues in the transformer. The basic data of the SFSZ-40000/110 power transformer is calculated as an example, and then the leakage field of winding and short-circuit electromotive force is calculated and analyzed.

Research of the stress-strain state of the loaded assembly for friction welded device

This article presents the results of the study of methods for friction welding of dissimilar materials and the calculations to determine the structural strength of the most loaded part of a special friction welding device were made. The analysis showed that the friction welding method has wide technological capabilities and it is used in various industries. The designs of existing devices and machines for friction welding were also investigated. It was revealed that the method of friction welding in the conditions of machine-building plants of the Republic of Kazakhstan (RK) has not found application due to the little knowledge and high cost of technological equipment. The authors have developed a special device for friction welding of dissimilar materials. To optimize the parameters of the parts, in particular the bracket part, the stress-strain state calculations were performed using the ANSYS software package and the strength calculation by determining the acting external critical loads. The results of the calculation showed the applicability of the developed design of the bracket part.

Effect of Surface Finishing State on Fatigue Strength of Cast Aluminium and Steel Alloys

The endurance limit of structural mechanical components is affected by the residual stress state, which depends strongly on the manufacturing process. In general, compressive residual stresses tend to result in an increased fatigue strength. Post-manufacturing processes such as shot peening or vibratory finishing may achieve such a compressive residual stress state. But within complex components, manufacturing-process-based imperfections severely limit the fatigue strength. Thus, the interactions of imperfections, residual stress state and material strength are key aspects in fatigue design. In this work, cast steel and aluminium alloys are investigated, each of them in vibratory finished and polished surface condition. A layer-based fatigue assessment concept is extended towards stable effective mean stress state considering the elastic–plastic material behaviour. Murakami’s concept was applied to incorporate the effect of hardness change and residual stress state. Residual stress relaxation is determined by elastic–plastic simulations invoking a combined hardening model. If the effective stress ratio within the local layer-based fatigue strength is evaluated as critical distance value, a sound calculation of fatigue strength can be achieved. Summing up, the layer-based fatigue strength design is extended and features an enhanced understanding of the effective stabilized mean stress state during cyclic loading.

Improvement of the strength calculation of the tube plate of the shell-tube heat exchanger

The purpose of the article is to improve the strength calculation of the tube plate of the shell-and-tube heat exchanger, which is regulated by the interstate standard in force in Ukraine. On the basis of standard tables, dot plots of the change in coefficients were constructed and analyzed, which take into account the supporting effect of pipes Ф1, Ф2, Ф3 depending on the dimensionless parameter of the board-pipe system ω and the dependence of the stiffness coefficient of the perforated board on the coefficient of pressure effect on the tube plate from the side of the tube space ηТ. It is proposed to approximate these dependencies with simple mathematical equations. As a result, it was proposed to use the cubic regression Ф1 = 0,0422ω3 + 0,2305ω2 – 0,2367ω + 2,0179 to describe the dependence of Ф1 = f1(ω) in the range of ω from 0 to 3 and when changing ω from 3 to 11, apply quadratic regression Ф1 = – 0,0286ω2 + 1,8012ω – 0,6171. The dependence of Ф2 = f2(ω) in the range of changing ω from 0 to 0,5 due to a slight change in the function can be described by the linear equation Ф2 = 0.04ω, when changing ω from 0,5 to 2 - by the cubic regression Ф2 = 0,0133ω3 + 0,48ω2 – 0,4033ω + 0,1, and when changing ω from 2 to 11 – by cubic regression Ф2 = 0,0046ω3 – 0,1129ω2 + 1,8692ω – 1,8821. The dependence Ф3 = f3(ω) in the range of ω change from 0 to 0,5 is described by the linear equation Ф3 = 0,38ω, when ω changes from 0,5 to 3 – by cubic regression Ф3 = – 0,2296ω3 + 1,3541ω2 – 0,4884ω + 0,1233, and when ω changes from 3 to 11 – cubic regression Ф3 = – 0,0054ω3 + 0,1060ω2 + 0,7576ω + 1,6129. The discrete tabular dependence of ψ0 on ηТ can be approximated by cubic regression ψ0 = – 0,3419ηТ3 + 1,8834ηТ2 – 0,6915ηТ + 0,1153. The obtained formulas make it possible to abandon the use of standard tables and additional interpolation of intermediate values of the coefficients Ф1, Ф2, Ф3 and ψ0 when performing calculations, which in turn simplifies both the calculation itself and the development of appropriate computer programs. The average value of the errors of the performed approximations is in the range from 0% to 2.05%, which indicates a high level of coincidence of the regression equations with the actual values. The use of the proposed formulas for the dependences of the coefficients Ф1 = f1(ω), Ф2 = f2(ω), Ф3 = f3(ω) and ψ0 = f(ηТ) makes it possible to simplify the calculation of the tube plate of shell-and-tube heat exchangers for strength.

Variation of BCC/B2 coherent microstructure and resultant improvement in strength of Al0.7CrxFe3−xCoNi high-entropy alloys

The effects of Cr and Fe contents on the microstructure and mechanical properties of B2 nanoparticle-enhanced BCC-based Al0.7CrxFe3−xCoNi (x = 1.5–3.0) high-entropy alloys (HEAs) were studied. It was indicated that the addition of Cr and reduction of Fe in the alloys can increase the lattice misfits between the BCC and B2 phases, inducing the variations of BCC/B2 coherent microstructure and the significant improvements of the compressive yield strengths from ∼ 1485 MPa to ∼ 2252 MPa. The calculations of the yield strengths based on the microstructure of the alloys suggested that the improvements of the strengths were mainly due to the enhancements of the precipitation-strengthening effects. The interactions between dislocations and B2 particles with various shapes and sizes were also discussed on the basis of the calculations. It is demonstrated that adjusting the contents of Cr and Fe is an effective way to control BCC/B2 coherent microstructure and improve the mechanical properties of Al–Cr–Fe–Co–Ni HEAs.

Discovery of an extremely intermittent periodic radio source

ABSTRACT We report the serendipitous discovery of an extremely intermittent radio pulsar, PSR J1710−3452, with a relatively long spin period of 10.4 s. The object was discovered through the detection of 97 bright radio pulses in only one out of 66 epochs of observations spanning almost three years. The bright pulses have allowed the source to be localized to a precision of 0.5 arcsec through radio imaging. We observed the source location with the Swift X-ray telescope but did not detect any significant X-ray emission. We did not identify any high-energy bursts or multifrequency counterparts for this object. The solitary epoch of detection hinders the calculation of the surface magnetic field strength, but the long period and the microstructure in the single-pulses resembles the emission of radio-loud magnetars. If this is indeed a magnetar, it is located at a relatively high Galactic latitude (2.9°), making it potentially one of the oldest and the most intermittent magnetars known in the Galaxy. The very short activity window of this object is unique and may point towards a yet undetected population of long period, highly transient radio emitting neutron stars.

Fatigue design of Additive Manufacturing components through Topology Optimization: Comparison of methodologies based on the defect distribution and on the stress gradient

AbstractIn this paper, the fatigue design of AM components is addressed through Topology Optimization. Two defect‐driven methodologies, which model the fatigue response in the finite life range and account for the experimental scatter, are compared. The first approach is based on the defect distribution and the marginal P‐S‐N curves. The second method models the size‐effect by accounting for the stress distribution within the loaded material. The two approaches are used to assess the maximum allowable first principal stress, which causes crack propagation. As the fatigue strength depends on the component volume or the stress distribution, an iterative procedure is necessary to determine the optimal design. The optimal topologies of a cantilever beam and of an engine rod are determined and compared, showing that the defect‐distribution method is the most conservative and the stress‐gradient method can also be reliably applied in the case of uniform stress distribution, as in the engine rod. Furthermore, the choice of the volume to retain for the calculation of the fatigue strength in the defect‐distribution method is critical.

Loads Calculation and Strength Calculation of Landing String during Deepwater Drilling

As an important drilling tool, the landing string will be directly exposed to seawater during surface riserless drilling operations, and it will undergo complex deformation under the action of environmental loads such as ocean currents and waves and the displacement, heave and vibration of the drilling platform. At the same time, with the increase in water depth, the floating weight of drill pipe and casing also increases significantly, and the landing string will bear great tensile loads, which can easily cause accidents. Therefore, in this paper, based on ANSYS software, the finite element analysis models of three stages of the landing string lowering operation were established, and finite element simulations under different combinations of working conditions were carried out. Through theoretical analysis and numerical simulation, the ultimate load and stress distribution of the string under different operating sea conditions were obtained, and the external force requirements for restraining the lateral displacement of the string were proposed according to the existing standards of the industry. Thereby, the recommended safe operating time, safe operating conditions window and the required restraint reaction force of the support mechanism are given for landing string lowering operation throughout the year.

Conversion of a military vessel into a civilian refrigerated vessel

River transport is one of the oldest in the Russian Federation. It is of particular importance for the northern and eastern regions, where the density of railways and highways is not high enough, or they do not exist at all. In these regions, the share of river transport in the total cargo turnover is about four percent. The use of river water transport for military purposes will never be stopped. Since requirements that are more stringent are imposed on military transport, the decommissioning of these vessels is faster than in commercial use. In most cases, the technical condition of the vessel is not critical, and it can be further operated. In view of the fact that recycling is a rather expensive process, ships are idle and are not used for their intended purpose. The way out of this situation can be the use of decommissioned military vessels for commercial purposes by converting them into a refrigerator in order to extend the operational life of the vessel, improve the technical and economic indicators of the vessel and make a profit. From the point of view of the methodological approach, the analysis of existing refrigerated containers was carried out, additional devices for converting electricity were given, the technological process of manufacturing the frame of the refrigerator installation was developed, and its strength calculation was carried out. The economic feasibility of converting the vessel into a refrigerator is shown.

Effect of Void Content on the Mechanical Properties of GFRP for Ship Design

Defects such as voids in composite materials often degrade the mechanical properties of laminates. Even if these materials are manufactured based on the design requirements, there is a possibility of instability occurring in these composite structures. In this study, several prototypes were developed based on changes in composite ship design conditions (glass fiber weight fraction and fabric combination type) using a hand lay-up approach. The fabrication quality was quantitatively defined using the burn-off test, and statistical analysis was performed. A combination of chopped strand mat and woven roving material laminates possessed relatively less void content in the entire glass content (Gc) region (30–70 wt%) compared to a chopped strand mat single-material laminate. The effect was more pronounced in the high-Gc region (50–70 wt%) than that in the normal-Gc region (30–50 wt%). The composite hull plate can be designed seamlessly according to changes in fabrication quality. To ensure safety, the thickness of the laminate must be greater than that specified in the ISO standards, regardless of the combination type in the normal-Gc region. As a result of the void content considered, the flexural strength in the single laminate decreased by 15.02%. Furthermore, 3.33% of the flexural strength calculation decreased in the combined laminate compared to that in the ISO rules. Thus, a single CSM material can be designed to be thicker than a combined-material laminate with the same Gc, while considering the void content on the mechanical properties.

Analysis of safety factors in the calculation of strength by internal pressure of oil and gas field and main pipeline systems

The article is devoted to the analysis of the safety factors used in the calculations for the internal pressure strength of oil and gas pipelines. A number of national, regional and international normative technical documents regulating the design of pipelines were considered. The safety factors provided in these documents in the calculation of the strength of pipelines are analyzed. For a comparative estimation, mathematical models were developed. As a result of the analyzes, the use of a safety factors for the yield strength of pipe material was recognized as more acceptable in calculating the strength of pipelines. The authors give recommendations on the choice of safety factors depending on the mode of operation and the type of transported hydrocarbon products. AzDTN2.2-9 is the only regulatory document in force in the territory of the Republic of Azerbaijan in this sphere. As this document does not meet modern criteria and is morally outdated, it was considered expedient to develop a new regulatory and technical act taking into account the suggestions made.

Experimental and thermal‐structure coupling analysis for oil and water‐swellable packer

AbstractIt has been widely acknowledged that traditional packers will lose their elastic performance in the context of long periods of operation due to plastic deformation. This paper will introduce a swellable packer that can reduce the failure cases of production effectively. The deformation of the packer rubber in different media and temperatures has been analyzed. The pressure test of several packer rubber under different media is carried out in this paper. The reasonable expansion clearance between the rubber tube and the well wall is obtained by strength calculation to ensure the sealing reliability of the packer. Finally, the thermomechanical coupling calculation of the packer with different structural sizes is carried out. Experiments at different temperatures show that the higher saline concentration is associated with a lower expansion rate and a larger expansion rate in clear water. At the same time, the expansion of volume in clear water increases. In addition, the higher the external temperature is, the larger the temperature gradient is. When the temperature of the outer ring is between 100°C and 140°C, the internal temperature rises to 37°C under the thermomechanical coupling effect.

Research on the Strength Calculation Method and Effects of Gear Parameters for High-Coincidence High-Tooth Gears

This article studies the calculation method for the tooth root bending stress of a high-tooth gear pair with a high contact ratio. The boundary point of the double-tooth meshing zone of the high-tooth gear pair is used as the loading point for the load, and the calculation formula for the bending stress at the dangerous section of the tooth root is obtained. By using ANSYS finite element simulation, the effect of the addendum coefficient, pressure angle, and other gear parameters on the bending stress of the tooth root is studied. The analysis shows that increasing the pressure angle will reduce the bending strength of the tooth root. Increasing the coefficient of a tooth’s top height will lead to an increase in the bending strength of the tooth root. Comparing the finite element analysis (FEA) results with the theoretical calculation results, the analysis shows that under low loads, the maximum error of the theoretical calculation values of the driving toothed gear and driven gear shall not exceed 13.53% and 15.42%, respectively. Under high loads, the maximum theoretical errors of the driving toothed gear and driven gear shall not exceed 8.78% and 10.91%, respectively. This verifies the correctness of the calculation method, which is of great significance for improving the load-bearing capacity of high-tooth gears and for guiding tooth shape design.