Theory Formula Research Articles

High-strength and wear-resistant Babbitt alloy coatings prepared through in-situ alloying

Babbitt alloy, a commonly used wear-resistant coating material, has a low hardness. This causes severe plastic deformation, detachment or heavy wear to easily occur under low speed and heavy-load service conditions, reducing its service life. To solve these problems and improve the bonding strength and wear resistance of the tin-based Babbitt alloy coating, a higher laser cladding power was adopted to achieve in-situ alloying of the cladding layer and enhance the strength of the coating. The increase in strength was verified through the Fleischer theory and Orowan empirical formula to mainly result from the enhancement of solid solution strengthening and dispersion strengthening. Meanwhile, due to dispersion strengthening and the presence of dendritic FeSn, the occurrence of delamination wear was effectively prevented. The bonding strength of the final sample reached 147 MPa, and the wear rate was as low as 4.24 × 10–5 mm3/N・m. Thus, a high-strength and wear-resistant Babbitt alloy cladding layer was obtained.

Effect of limestone powder on mechanical properties of concrete based on Griffith’s microcracking theory

In order to reveal the influence mechanism of limestone powder on the mechanical properties of concrete, the manufactured sand concrete with a water-cement ratio of 0.45 was taken as the research object. The effects of different limestone powder contents (0 %, 5 %, 10 %, 15 %, and 20 %) on the compressive strength of concrete were explored based on Griffith’s microcracking theory. The nano-indentation, ultra-depth-of-field microscopy, LF NMR, and other methods were used for testing. The test results show that with the increase of limestone powder content, the elastic modulus of the Interfacial Transition Zone (ITZ) and the paste increases first and then decreases, the thickness of the ITZ decreases first and then increases, and the total porosity of the paste decreases first and then increases. The microstructure of the ITZ and the paste is the densest, corresponding to the maximum compressive strength of the concrete as the limestone content is 10 %. It is found that the thickness of ITZ can be regarded as the initial crack of concrete. The compressive strength of concrete calculated by Griffith’s microcracking theory formula is the same as the measured value. The research results provide a theoretical reference for the influence mechanism of limestone powder on the mechanical properties of concrete.

Study on Temperature Field Distribution of a High-Speed Double-Helical Gear Pair with Oil Injection Lubrication

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise.

Extreme ATM skew in a local volatility model with discontinuity: joint density approach

This paper concerns a local volatility model in which the volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold. The model is known, and a number of results have been obtained for it. In particular, option pricing formulas and a power-law behaviour of the implied volatility skew have been established in the case when the threshold is taken at the money. In this paper, we derive an alternative representation of option pricing formulas. In addition, we obtain an approximation of option prices by the corresponding Black–Scholes prices. Using this approximation streamlines obtaining the aforementioned behaviour of the skew. Our approach is based on the natural relationship of the model with skew Brownian motion and consists of the systematic use of the joint distribution of this stochastic process and some of its functionals.

Experimental and simulation study on quasi-static and dynamic fracture toughness of 2A12-T4 aluminum alloy using CTS specimen

Based on the study of dynamic fracture toughness of mixed mode I/II fracture crack, using compact tensile shear (CTS) specimen and the method of split Hopkinson tensile bar (SHTB) combined with special fixture, which complete the experiments of complex fracture modes of 2A12-T4 aluminum alloy material under quasi-static and dynamic tensile tests. By combining the results of finite element simulation with experimental–numerical method, the feasibility of Richard’s theory formula in dynamic fracture experiment is discussed. The variation law of fracture toughness under quasi-static and dynamic complex fracture under mixed-mode was analyzed by finite element simulation and experiment. The results show that, in the process of quasi-static and dynamic fracture, the fracture toughness of CTS specimen under mixed mode I/II crack loading is the highest. The conclusion is proved by Richard theorical formula and experimental–numerical methods jointly. When the specimen is subjected to pure mode I fracture, the quasi-static fracture toughness is consistent with that is in condition of dynamic experiment. However, when the specimen is subjected to mode II and mixed mode I/II fracture, the dynamic fracture toughness changes greatly compared with the quasi-static fracture toughness. In addition, in the dynamic fracture experiment, the dynamic fracture toughness of mixed mode I/II depends on the initiation time, and the quasi-static fracture criterion is no longer applicable.

Analysis of lattice deformation originated from residual stress on performance of aluminum nitride-based bulk acoustic wave resonators

With the development of MEMS technology to the nanometer scale, the influence of different process conditions on the performance of nano-devices can be calculated through the microscopic changes of materials. During the manufacturing process, the large residual stress from the film stack significantly influences the performance of devices, thereby reducing the wafer yield. Herein, we apply density functional theory to MEMS processes to reveal the intrinsic mechanism of how residual stress affects the performance of aluminum nitride-based bulk acoustic wave (BAW) resonators on an 8-inch high-resistance silicon wafer. The variation rule of physical properties of piezoelectric material aluminum nitride with different residual stresses is calculated via first-principles calculations. Through theory formula derivation, the piezoelectric-coupling constant (Kt2) of the bulk acoustic wave resonator is positively correlated with tensile residual stress, and the resonant frequency (fp, fs) is negatively correlated with tensile residual stress. The measurement results show that the average shifts of Keff2 is 0.12 % within −137 MPa and 183 Mpa residual stress, which is an excellent match with the theory prediction.

Calculation of Mixed Oil Volume for Sequential Transportation of Crude Oil Pipelines with Variable Temperature and Low Reynolds Number

In order to meet the differentiated demand of oil refiners for crude oil, improve the operating load ratio of long-distance pipelines, and reduce one-time investment, sequential transportation process has been widely used in long-distance crude oil pipelines in China. There are many studies on the calculation method of the mixed oil quantity of sequential transportation of refined oil, but due to its complex influencing factors, there is no general calculation model accepted by everyone. For the sequential transportation of crude oil pipelines, most of them have the characteristics of variable temperature and low Reynolds number, and it is more difficult to accurately calculate the mixed oil quantity than the refined oil pipeline. Through the analysis of the characteristics of oil mixing and hydraulic characteristics of sequential oil transportation, combined with the operation example of an oil pipeline in China, the calculation results of the diffusion theory formula, the Austin-Palfrey empirical formula and the equivalent pipeline length formula were compared and analyzed. The results show that the “equivalent pipeline length method” considers the influence of flow, pipe diameter and conveying distance on oil mixing, and takes into account the oil mixture caused by the change of initial oil mix and Reynolds number, which is more suitable for calculating the mixed oil quantity of sequential transportation of crude oil pipelines. However, for the sequential transportation of crude oil pipelines with low Reynolds number and variable temperature, the amount of oil mixed will be increased. According to the comparative analysis of actual cases, the correction coefficient is increased by 1.5 times on the basis of theoretical calculation, and the calculated value is in good agreement with the actual value, and the deviation is within 5%. It can be used as a reference for the design and operation management of variable temperature and low Reynolds number crude oil sequential transportation pipeline.

Investigation on Disaster Mechanism of Diversion Tunnel Induced by Gripper TBM in Hydrokarst Erosion Stratum and Engineering Measures

In gripper tunnel boring machine (TBM) tunneling through complex geological formations, the safe and efficient recovery from large-scale collapses remains a formidable challenge. In this study, we investigate the causes of a 1246 m3 collapse that occurred during the gripper TBM tunneling in the diversion tunnel in Xinjiang, China. Various techniques including TSP seismic waves, CFC advanced water exploration, laboratory point load tests and packer permeability tests were employed for thorough research. The examination discloses that the water softening in biotite-quartz schist in fractured zones contributes significantly to the loosening and dislocation of rock layers along joints. The gripper TBM’s cutterhead exacerbates this process through cutting action and vibrations, causing large-scale instability and eventual rock mass collapse. To tackle this engineering problem, we propose a three-step treatment scheme comprising “Reinforcement-Backfill-Re-excavation”. Furthermore, we propose a technique to handle TBM collapses by creating a “protective shell” within the cavity. The safety and feasibility of these proposed solutions were thoroughly validated through numerical simulations. Also, we utilized the Hoek-Brown theory and Rostami prediction formula to establish recommended values for the total thrust and total torque of the TBM during the collapsed section. The proposed treatment scheme and estimated parameters were successfully applied, resulting in a comprehensive solution from collapse handling to tunneling. This study offers valuable details on effectively managing large-scale collapses in gripper TBM tunneling, which can be useful for similar tunnel engineering and improve safety and efficiency.

THE EFFECT OF TRAINING, MOTIVATION, AND WORK ENVIRONMENT ON TEACHER PERFORMANCE AT SMA NEGERI 12 PEKANBARU

The purpose of this study is to test and analyze the effect of training, motivation, and work environment on the performance of teachers of SMA Negeri 12 Pekanbaru. The population in this study was a teacher at SMA Negeri 12 Pekanbaru. The sample used in this study was 40 people using the technique of determining the number of samples in this study using the Roscoe theory formula. Roscoe's theory says that if the study will conduct an analysis with multivariate (collation or double regression), then the number of sample members is at least 10 times the number of variables studied (Sugiyono, 2010: 130). So, because this study consists of 4 variables, then the number of samples is 4 x 10 = 40 Respondents. The results of the study obtained that training, motivation, and work environment had a significant and positive effect on the performance of teachers of SMA Negeri 12 Pekanbaru.

Design and Analyses of a Novel Reconfigurable Logging Branch Mechanism

A reconfigurable logging and branch-lopping mechanism has been designed to shorten the production cycle, reduce work intensity, and improve labor survival rate in the logging industry. The mechanism integrating logging and branch-lopping functions can flexibly morph into three con-figurations, namely, series, parallel and mixed, as well as eight structure states to satiate different requirements. Not only does it possess sufficient stiffness to fell large trees but it also offers high flexibility to trim and crop small branches which superior performance has relatively wide engineering application prospects. The kinematics and static stiffness of the mechanism are the key techniques for its engineering application. With the mechanism as the research object, the working principles were analysed and the adjacency matrix of each structure state was presented. The Screw Theory and CGK formula were deployed to calculate the degrees of freedom of some of the structure mechanisms. The kinematics of some of the structure states was analysed and their flexibility matrices were obtained with vector algebra. The static stiffness of two structure states was compared indirectly by contrasting their flexibility matrices before their kinematics was simulated numerically. Engineering application of the mechanism in welding robots, robots that pick up objects, cleaning robots and other fields is demonstrated towards the end of this paper.

Enhanced electron transport and optical properties of experimentally synthesized monolayer Si9C15: a comprehensive DFT study for nanoelectronics and photocatalytic applications.

Two-dimensional silicon-carbide (SixCy) materials stand out for their compatibility with current silicon-based technologies, offering unique advantages in nanoelectronics and photocatalysis. In this study, we employ density functional theory and nonequilibrium Green's function methods to investigate the electronic properties, electron transport characteristics, and optoelectronic qualities of experimentally synthesized monolayer Si9C15. Utilizing the modified deformation potential theory formula, we unveil Si9C15's significant directional anisotropy in electron mobility (706.42 cm2 V-1 s-1) compared to holes (432.84 cm2 V-1 s-1) in the a direction. The electrical transport calculations reveal that configurations with a 3 nm channel length demonstrate an ON state when biased, reaching a peak current of 150 nA. Moreover, this maximum current value escalates to 200 nA under tensile strain, marking an increase of approximately 100 times compared to the 5 nm channel, which remains in an OFF state. Si9C15 exhibits high light absorption coefficients (∼105 cm-1) and suitable band edge positions for water splitting at pH 0-7. Applying 1-5% tensile strain can tune the conduction band minimum and valence band maximum closer to the standard redox potentials, enhancing photocatalytic water splitting efficiency. Remarkably, under illumination at pH 0 and 7, Si9C15 can spontaneously catalyze water splitting, demonstrating its potential as a highly efficient photocatalyst. Our findings emphasize the importance of strain control and device length optimization for performance enhancement in nanoelectronics and renewable energy applications, positioning Si9C15 as a promising material for high-performance field-effect transistors and photocatalytic water splitting.

Exact Large-Scale Fluctuations of the Phase Field in the Sine-Gordon Model.

We present the first exact theory and analytical formulas for the large-scale phase fluctuations in the sine-Gordon model, valid in all regimes of the field theory, for arbitrary temperatures and interaction strengths. Our result is based on the ballistic fluctuation theory combined with generalized hydrodynamics, and can be seen as an exact "dressing" of the phenomenological soliton-gas picture first introduced by Sachdev and Young [Phys. Rev. Lett. 78, 2220 (1997)PRLTAO0031-900710.1103/PhysRevLett.78.2220], to the modes of generalized hydrodynamics. The resulting physics of phase fluctuations in the sine-Gordon model is qualitatively different, as the stable quasiparticles of integrability give coherent ballistic propagation instead of diffusive spreading. We provide extensive numerical checks of our analytical predictions within the classical regime of the field theory by using MonteCarlo methods. We discuss how our results are of ready applicability to experiments on tunnel-coupled quasicondensates.

Convergence in Total Variation for nonlinear functionals of random hyperspherical harmonics

Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit d-dimensional sphere (d≥2). We study the convergence in Total Variation distance for their nonlinear statistics in the high energy limit, i.e., for diverging sequences of Laplace eigenvalues. Our approach takes advantage of a recent result by Bally, Caramellino and Poly (2020): combining the Central Limit Theorem in Wasserstein distance obtained by Marinucci and Rossi (2015) for Hermite-rank 2 functionals with new results on the asymptotic behavior of their Malliavin-Sobolev norms, we are able to establish second order Gaussian fluctuations in this stronger probability metric as soon as the functional is regular enough. Our argument requires some novel estimates on moments of products of Gegenbauer polynomials that may be of independent interest, which we prove via the link between graph theory and diagram formulas.

A floating system integrating a wind turbine with a steel fish farming cage: Experimental validation of the hydrodynamic model

This paper is dedicated to comparing the numerical results of the dynamic responses of a floating offshore wind turbine integrated with a steel fish farming cage (FOWT-SFFC) under wind and waves against the experimental data. FOWT-SFFC's numerical model is built with OrcaFlex where the potential flow theory and quadratic drag formula are used to calculate the hydrodynamic loads on the structural components of the floater, while Morison-type formulation is employed to model the force on fish nets. The numerical model is tuned in terms of the measured data. The simulated motion response amplitude operators and stochastic responses under irregular waves are compared with the experimental results to fathom the influence of drag's modeling on the simulation outcome. The effects of additional damping and 2nd-order wave forces are also investigated to determine the optimal simulation method. With the selected numerical model, the responses of FOWT-SFFC with and without nets under 100-year extreme waves, combined wind and irregular waves are calculated. The simulated response time histories, spectra and statistics are in good agreement with the experimental data. Besides, it is revealed that the effects of 2nd-order wave forces are important for the accurate simulation of low-frequency pitch motion, but unfavorable to the prediction of other responses.

Mechanical predictive modeling of stereolithographic additive manufactured alumina microlattices

Alumina microlattices with stretch- and bending-dominated structures were manufactured to establish the intercorrelation between the quasi-static microlattice mechanical properties and the strut aspect ratio using the stereolithographic additive manufacturing method. In the present work, two kinds of novel mechanical prediction models were calibrated and validated through the experiment and simulation data, aiming to realize the topological optimization and effective design of the weight, strut size, and spatial geometrical structures of the microlattice according to the given load bearing and stiffness demands. First, the mathematical prediction models of the compression strength and Young’s modulus for the microlattices with different aspect ratios were developed based on the modified Gibson and Ashby’s law and Timoshenko beam theory. Then, the prediction models exhibited an excellent prediction achievement of the experiment and simulation results with the assistance of data fitting. Subsequently, the tensile and compressive damage models perfectly reappeared and tracked the actual fracture behaviors of the microlattice, demonstrating different collapse trends for the Simple cubic (SC) and Body-centered cubic (BCC) microlattices. Finally, the quasi-static mechanical properties of SC were far stronger than that of BCC under the same aspect ratio and from the experiment data, simulation results, and theory formulas. This work laid a solid foundation for the microlattice structure design in lightweight engineering.

Geometric error calibration and analysis of rotary axes on a five-axis dispensing machine

Geometric rotary axis errors are one of the main factors affecting the dispensing positioning accuracy of five-axis vision dispensing machines. Hence, the accurate detection and compensation of these error terms is an important and challenging problem. In this study, a decoupling identification method for both position-dependent geometric errors and position-independent geometric errors of a rotary dispensing table is proposed based on vision measurement technology. According to this strategy, the screw theory and exponential product formula are used to establish a kinematic model of the end-effector, followed by the definition of the mapping relationship between position-independent geometric errors and axis posture. Then, to separate the coupling error terms of the rotating axes, a step-by-step identification strategy is proposed based on the least squares method. Furthermore, a coordinate search-based error compensation algorithm is developed, which avoids the inverse singular value problem and is insensitive to the error model. Finally, the effectiveness of the proposed identification algorithm and compensation algorithm is experimentally validated.

Embedding of octonion Fourier transform in geometric algebra of ℝ3 and polar representations of octonion analytic signals in detail

We show how the octonion Fourier transform can be embedded and studied in Clifford geometric algebra of three‐dimensional Euclidean space . We apply a new form of dimensionally minimal embedding of octonions in geometric algebra that expresses octonion multiplication nonassociativity with a sum of up to four (individually associative) geometric algebra product terms. This approach leads to new polar representations of octonion analytic signals and signal reconstruction formulas.

A novel shell‐based hierarchical multiscale model for studying three‐dimensional four‐directional braided composite shafts

AbstractThe mechanical properties of three‐dimensional (3D) braided composites are related to damage evolution. However, the multi‐scale damage mechanism of 3D braided composite shafts remains unclear. The main purpose of this article is to propose a shell‐based multiscale finite element model for effectively predicting the compressive and torsional properties of 3D four‐directional (3D4d) braided composite shafts. Considering the relation between equivalent ply angles and yarn structures, the multiscale model was developed based on a universal tubular unit cell. The equivalent ply angle was derived through the yarns' local braiding and horizontal orientation angles, and the elastic properties of each equivalent ply were derived through the stiffness averaging method. Both derivations were achieved by creatively utilizing deformation gradient theory and Nanson's formula from continuum mechanics. LaRC04 failure criteria and energy‐based damage evolution law were implemented to characterize the equivalent UD‐ply's damage behaviors. The proposed model was validated experimentally, and good agreements were observed between the failure morphologies and load–displacement curves of FEA and experimental results. The results show that the fiber tension and compression damages are the major failure modes of 3D4d braided composite shafts under compressive and torque loads, respectively. Finally, a parametric study was carried out and compared with that from other literature to clarify the meaning of this article in relevant studies. It provides an efficient and useful tool for the design and manufacturing of 3D4d braided composite shafts with desirable mechanical properties.Highlights A shell‐based hierarchical multiscale model is developed for 3D braided composite shafts. An analyzing method is developed to investigate the tubular yarn structures. A large‐scale torsional experimental scheme is developed.

Self-Vibration of a Liquid Crystal Elastomer Fiber-Cantilever System under Steady Illumination.

A new type of self-oscillating system has been developed with the potential to expand its applications in fields such as biomedical engineering, advanced robotics, rescue operations, and military industries. This system is capable of sustaining its own motion by absorbing energy from the stable external environment without the need for an additional controller. The existing self-sustained oscillatory systems are relatively complex in structure and difficult to fabricate and control, thus limited in their implementation in practical and complex scenarios. In this paper, we creatively propose a novel light-powered liquid crystal elastomer (LCE) fiber-cantilever system that can perform self-sustained oscillation under steady illumination. Considering the well-established LCE dynamic model, beam theory, and deflection formula, the control equations for the self-oscillating system are derived to theoretically study the dynamics of self-vibration. The LCE fiber-cantilever system under steady illumination is found to exhibit two motion regimes, namely, the static and self-vibration regimes. The positive work done by the tension of the light-powered LCE fiber provides some compensation against the structural resistance from cantilever and the air damping. In addition, the influences of system parameters on self-vibration amplitude and frequency are also studied. The newly constructed light-powered LCE fiber-cantilever system in this paper has a simple structure, easy assembly/disassembly, easy preparation, and strong expandability as a one-dimensional fiber-based system. It is expected to meet the application requirements of practical complex scenarios and has important application value in fields such as autonomous robots, energy harvesters, autonomous separators, sensors, mechanical logic devices, and biomimetic design.

Research on the Queuing Theory based on M/M/1 Queuing Model

A collection of mathematical theories and models make up queueing theory. The theory, which is derived from several models, makes an effort to recreate numerous typical queue waiting models. The purpose of this study is to do research on the M/M/1 queuing model-based queueing theory. After a brief introduction to the queuing theory, the independent indexes and the dependent variables will be shown. This paper contains some fundamental queuing theory formulas, some of which are specifically derived for the M/M/1 queuing model. This study then presents a simulation of the M/M/1 queuing model. Since some results are attained, this paper revealed some probability distributions and distribution functions of several indexes. The data characteristics displayed by these figures are very consistent with the daily life situation, which also proved the rationality and M/M/1 queuing model's applicability. By investigating this queuing theory, people shall be able to understand, analyze, and predict the phenomenon of waiting in a line.