Infinitesimal Method Research Articles

A stiffness prediction method for variable cross‐section CFRP laminated beam

AbstractTo efficiently design the stiffness of the laminated composite blade‐like structure, an analytical method to assess deformation of variable cross‐section laminated beam under cantilever bending load was developed, in which a local ply density matrix method was introduced to characterize the ply‐up in arbitrary cross‐section after ply drop‐off process and infinitesimal element segment method was used to convert complex variable cross‐section specimen into local equal cross‐section beam structure. The model was validated by the cantilever beam experiment with relative predicted error of stiffness of 5.7%. Inner and outer ply drop‐off models were analyzed using the proposed analytical method. The results show that: (1) stiffness of the outer ply drop‐off model is the highest, at 13.07 N/mm, while that of the inner ply drop‐off model 2 is the lowest, about 17.8% lower than the outer ply drop‐off model; (2) maximum relative deformation difference between the inner ply drop‐off model 2 and outer ply drop‐off model is 21.7% at the free side of the cantilever beam. It indicates that anti‐deformation ability of the variable cross‐section laminated structure can be efficiently designed by the proposed analytical method, especially for the section close to the free side.Highlights Developed a bending stiffness prediction method for composite beam. Variable cross‐section feature of the composite laminate was considered. Local ply density matrix method was introduced to characterize ply drop‐off. Proposed method was validated by cantilever beam bending experiment. Inner and outer ply drop‐off models were compared by the proposed method.

High-Resolution Cross-Layer Scheduling for Low-Latency Communications: When Infinitesimal Method Meets Stochastic Order

High-Resolution Cross-Layer Scheduling for Low-Latency Communications: When Infinitesimal Method Meets Stochastic Order

A Novel Lightning Overvoltage Protection Scheme Using Magnetic Rings for Transmission Line Systems

Overvoltage protection technology is critical to the safe and stable operation of power electronics equipment and power systems. In this study, based on the characteristics of lightning traveling waves, a novel lightning overvoltage protection scheme was proposed using magnetic rings (MRs) for transmission line systems (TLSs). First, the dynamic inductance of the lightning protection scheme using MRs was theoretically derived by combining the ampere loop law and the infinitesimal method. The finite element method (FEM) was then used to verify the theoretical derivation of dynamic inductance (TDDI) of the lightning protection scheme. Furthermore, the TDDI was integrated into the electromagnetic transient program, and the electromagnetic transient model (ETM) of the TLS with the lightning protection scheme was established. Subsequently, the effects of MR characteristics under the influence of various factors on the protection performance of the lightning protection scheme were investigated. Finally, the MR string in the lightning overvoltage protection scheme with optimal physical structure was used for field application. The results confirmed the feasibility of the lightning overvoltage protection scheme and ETM accuracy.

Research on Wear of Micro-Textured Tools in Turning GH4169 during Spray Cooling

In this study, the wear resistance of micro-textured tools was explored. Micro-textured tools with different morphologies were used in turning GH4169 during spray cooling. The tool wear on the rake face of the different micro-texture morphologies was investigated through simulation and experiments. Firstly, based on the existing research on bionics, micro-textures with five different morphologies were designed on the rake face of carbide tools. A simulation model of cutting GH4169 during spray cooling was established, and the tools with designed micro-textures were used in it. The influence of the different micro-texture morphologies on the tool wear was analyzed. Secondly, the designed micro-textured tools with five different morphologies were produced using a femtosecond laser. Cutting experiments were conducted using the micro-textured tools during spray cooling. The wear area of the rake face was measured based on the infinitesimal method, and the optimal morphology with the best anti-wear ability was obtained. This study provides technical support for the design and development of micro-textured tools with an improved cutting performance, and contribute to the promotion and application of micro-textured tools.

A Bearing Fault Diagnosis Method Based on a Residual Network and a Gated Recurrent Unit under Time-Varying Working Conditions.

The diagnosis of bearing faults is an important guarantee for the healthy operation of mechanical equipment. Due to the time-varying working conditions of mechanical equipment, it is necessary to achieve bearing fault diagnosis under time-varying working conditions. However, the superposition of the two-dimensional working conditions of speed and acceleration brings great difficulties to diagnosis via data-driven models. The long short-term memory (LSTM) model based on the infinitesimal method is an effective method to solve this problem, but its performance still has certain limitations. On this basis, this article proposes a model for fault diagnosis under time-varying operating conditions that combines a residual network model (ResNet) and a gate recurrent unit (model) (GRU). Firstly, the samples were segmented, and feature extraction was performed using ResNet. We then used GRU to process the information. Finally, the classification results were output through the output network. This model could ignore the influence of acceleration and achieve high fault diagnosis accuracy under time-varying working conditions. In addition, we used t-SNE to reduce the dimensionality of the features and analyzed the role of each layer in the model. Experiments showed that this method had a better performance compared with existing bearing fault diagnosis methods.

Nonlinear excitation and mesh characteristics model for spiral bevel gears

Accurate and rapid calculation of nonlinear excitation (NE) and loaded mesh characteristics (LMC) of gear pairs is a key to achieving rapid iterative optimization of gear system designs. Therefore, an analytical model (AM) was proposed for the accurate and numerically efficient calculation of NE and LMC for application to spiral bevel gears (SBG). First, a tooth contact analysis of an SBG was completed using Coons surface technology and mesh theory to determine the contact path and unloaded transmission error (UTE). Thus, an AM for the principal and relative normal curvatures of the SBG was derived using the Euler's formula. Based on the traditional calculation method for a Hertz contact ellipse, the relation between the relative curvatures was introduced to derive the formulas for the major and minor axes using the Muller's method, which could improve the programmability and avoid numerical instability of the program. Then, analytical models for the contact ellipse and pressure distribution on the contact tooth surfaces were derived using the Hertz model and geometric theory. Subsequently, based on a single tooth LMC, infinitesimal method, elasticity, and series stiffness model, a single mesh stiffness (SMS) model for SBGs was developed, which incorporates transverse tooth stiffness, transverse gear foundation stiffness, axial tooth stiffness, axial gear foundation stiffness, and Hertz nonlinear contact stiffness. Based on the SMS and UTE, compliance and load matrices were established, and the time-varying mesh stiffness, loaded transmission error, mesh force, and multi-tooth LMC models of the SBG were determined. Finally, the proposed method was validated against nonlinear FE simulations using examples. Compared to FE simulations, the proposed method requires significantly less computational effort and can be further extended to optimization or system analysis problems.

Near-field formation of the UCA-based OAM EM fields and short-range EM power flux profiles

Orbital angular momentum (OAM) multiplexing is a recently considered solution for enhancing wireless and free-space optical communications channel capacity, whether implemented separately or in combination with existing multiplexing techniques. The theoretically infinite number of paraxially propagating and mutually orthogonal OAM modes is expected to increase the channel capacity. However, the orthogonality for different OAM modes has been shown to decrease for far link range distances, and the paraxiality of the OAM beams is not very good for small radiating sources. Based on the current knowledge, OAM beams are most likely to be used for short-range communications. Many models of the electromagnetic (EM) fields carrying the OAM neglect the fact that the OAM beam sources could be electrically large or introduce other approximations that are appropriate for far-field analysis only. An in-depth analysis of the short-range properties of OAM EM fields is still lacking. To address this problem, we propose the use of the infinitesimal (Hertz) dipole method customized for the analysis of the OAM EM fields. This technique can model the positioning and basic radiation properties of separate antennas or antenna sub-arrays that are the building blocks of OAM arrays exactly and efficiently. Similar modeling can represent the OAM sources for free-space optical communications. We focus here on the uniform circular antenna arrays and provide an in-depth analysis of what can and cannot be expected, in the best case, in their utilization. We assume low losses, which is a common assumption for many methods, except for computationally much more demanding full-wave simulations. The obtained results indicate the need to simultaneously optimize the transmission of all planned OAM modes and allow estimates of the link distances that could provide adequate OAM wave reception in various cases.

Investigation of key problems of clustering perforation string running in horizontal well with unconventional oil-gas reservoirs

Currently, there are two main clustering perforation methods: coiled tubing-conveyed perforation (TCP) and cable-conveyed perforation (CCP). To improve the efficiency of CCP strings in wellbore pass-through capacity problems, considering wellbore geometry constraints, pipe string variable cross-section, flexible tool deformation, and other factors, the pass-through capacity analysis model of the perforating tool string was established and solved by geometric analysis and beam-column theory. Aiming at the running depth problem of a TCP string, considering the influence of the buckling effect, a model of coiled tubing running depth was established by the infinitesimal method. The field test data were used to verify the effectiveness of the two models. The effects of well trajectory, perforating string size, casing inner diameter, and coiled tubing size on the pass-through capacity of the CCP string and running depth of the TCP string were explored. The results indicate that with the increase of perforation string size or the reduction of casing inner diameter, the pass-through capacity of CCP string decreases; with the increase of coiled tubing specification, the running capacity of TCP string is improved. The work presented in this paper provides an effective analysis method and theoretical guidance for clustering perforation jobs in the field.

Distribution and Prediction of Incremental Cutter Flank Wear in High-Efficiency Milling

In the milling of titanium alloy workpieces, tool wear seriously affects the surface quality of a workpiece and its tool life. It is of great significance to study the influence of instantaneous contact stiffness on instantaneous friction variables and incremental wear, which is of great significance for the realization of control over the degree of flank wear and improving the service life of cutter teeth. In this paper, an experiment to monitor cutting with a Ti6Al4V workpiece with a high-feed milling cutter was carried out; according to the experimental results, the wear area of the flank face of the cutter tooth was determined. The feature points of the flank were selected, and an instantaneous contact stiffness calculation method for the flank was proposed. The infinitesimal method was used to characterize the distribution of the contact stiffness of the flank, and the evolution characteristics of instantaneous contact stiffness distribution under the influence of vibration were obtained. According to the calculation results, the instantaneous distribution of flank wear depth was calculated. A grey correlation degree was used to reveal the correlation between the instantaneous contact stiffness of the flank face and wear depth, and a positionable wear-prediction model based on the instantaneous contact stiffness of the flank was proposed. Based on a BPNN (back propagation neural network), a prediction model for flank wear was established. The results showed that the above model and method could accurately predict the instantaneous wear of the tool flank.

A Frequency-Domain I/Q Imbalance Calibration Algorithm for Wideband Direct Conversion Receivers Using Low-Cost Compensator

The amplitude and phase imbalances of the in-phase (I) and quadrature (Q) branches inherent in the direct conversion receiver structure cause the generation of image frequency interference signals. In this paper, a frequency-domain I/Q imbalance calibration algorithm is proposed for wideband direct conversion receivers. The I/Q imbalance model is rebuilt by applying the infinitesimal method and FFT algorithm. The mathematical expressions for the exact computation of the I/Q imbalance parameters are derived based on the frequency-domain statistical properties of the baseband signal. The two phase parameters, frequency-dependent I/Q imbalance (FD-IQI) and frequency-independent I/Q imbalance (FI-IQI), are separated according to the parity properties of the imbalance parameter. To avoid the interference from the transmitter, the receiver impairment estimation is performed using a frequency offset (FO) DC training signal, and a low-cost real-valued compensation (RVC) filter is introduced to correct the impairments of the received signal. The performances of the proposed calibration model are evaluated through simulations and experiments. The simulation results show that the image rejection ratio (IRR) is improved to 80-120 dBc and can also exceed 40 dBc at high noise levels. The experimental results based on the CX9261A evaluation board show that the average IRR of the multi-tone signal is increased by 24.99 dB, and the IRR of the wideband signal is increased by 19.08 dB.

SleepMore

The availability of commercial wearable trackers equipped with features to monitor sleep duration and quality has enabled more useful sleep health monitoring applications and analyses. However, much research has reported the challenge of long-term user retention in sleep monitoring through these modalities. Since modern Internet users own multiple mobile devices, our work explores the possibility of employing ubiquitous mobile devices and passive WiFi sensing techniques to predict sleep duration as the fundamental measure for complementing long-term sleep monitoring initiatives. In this paper, we propose SleepMore, an accurate and easy-to-deploy sleep-tracking approach based on machine learning over the user's WiFi network activity. It first employs a semi-personalized random forest model with an infinitesimal jackknife variance estimation method to classify a user's network activity behavior into sleep and awake states per minute granularity. Through a moving average technique, the system uses these state sequences to estimate the user's nocturnal sleep period and its uncertainty rate. Uncertainty quantification enables SleepMore to overcome the impact of noisy WiFi data that can yield large prediction errors. We validate SleepMore using data from a month-long user study involving 46 college students and draw comparisons with the Oura Ring wearable. Beyond the college campus, we evaluate SleepMore on non-student users of different housing profiles. Our results demonstrate that SleepMore produces statistically indistinguishable sleep statistics from the Oura ring baseline for predictions made within a 5% uncertainty rate. These errors range between 15-28 minutes for determining sleep time and 7-29 minutes for determining wake time, proving statistically significant improvements over prior work. Our in-depth analysis explains the sources of errors.

An Ornstein–Uhlenbeck Model with the Stochastic Volatility Process and Tempered Stable Process for VIX Option Pricing

To effectively fit the dynamics and structure of frequent small jumps and sparse large jumps in the VIX time series, we introduce the tempered stable process (the CTS process and CGMY process) into the Ornstein–Uhlenbeck (OU) stochastic volatility model to build an OU model with the stochastic volatility process and tempered stable process. Based on two different assumptions for the underlying assets, we derive the formula of pricing models via two methods. Empirical studies are conducted to prove that our pricing models have a better performance in matching the VIX options. Furthermore, we find that the pricing model via the infinitesimal value method yields better results than pricing models with a measure of change. Overall, our proposed models enrich the derivative pricing theory and help investors understand and hedge risks.

An accurate and numerically efficient time-varying mesh stiffness model for modified straight bevel gear under load

Gear time-varying mesh stiffness (TVMS) plays an important role in the analysis accuracy of a gear transmission mechanism. In previous research, the TVMS of a modified straight bevel gear (SBG) was mainly obtained by the finite element method (FEM), whose computation time is usually long to ensure computational accuracy. By contrast, this work proposes a fast calculation method with high accuracy for the TVMS of a modified SBG. First, B-spline surfaces are introduced to reconstruct a modified SBG using discrete tooth surface points. Next, based on the tooth contact analysis and loaded tooth contact analysis, combined with energy conservation principle and infinitesimal method, a semi-analytical instantaneous single mesh stiffness (SMS) model for the modified SBG is derived. Then, using the additional deformation compatibility condition and principle of force balance, the calculation method of the TVMS of the modified SBG is obtained. Finally, a comparison of the mesh stiffness calculation results between the method of this study and that of FEM is completed. The results show that the semi-analytical TVMS model used in this study can be accurately and quickly solved.

Nonlinear characteristics of semirigid and semiflexible segment joints of submerged floating tunnels under the combined axial force and bending moment

As an important part and a weak link in submerged floating tunnels (SFTs), segment joints are related to the safety of the overall structure. However, there is still a lack of research on joint structural designing and joint characteristics under complex external loads. In this paper, the semirigid and semiflexible SFT segment joint structure is proposed, and the stiffness mathematical model and numerical model of the joint structure are established based on the geometric deformation coordination, mechanical equilibrium conditions and the infinitesimal method. The above model was used to investigate the coupling effects of the axial force and bending moment on the axial displacement, rotation angle and stiffness of the joint, as well as the nonlinear characteristics of the SFT joint under the combined load of the axial force and bending moment. The results show that the nonlinear characteristics of the SFT joints are linked to the nonlinear properties of the materials at the joints as well as the multiple working states of the joints, as reflected in the characteristics of three loading modes and two transition points. Under the axial force-bending moment combined load, the axial force controls the working state and nonlinear characteristics of the joint, while the bending moment affects the working state and nonlinear characteristics of the joint on the basis of the axial force. The research results provide a theoretical basis and technical support for the study of the overall dynamic response of SFTs and the construction of the project.

Surrogate-Assisted Multi-Objective Optimization of a Liquid Oxygen Vacuum Subcooling System Based on Ejector and Liquid Ring Pump

As an important combustion aid for aerospace vehicles, subcooled liquid oxygen of high density can be used to increase loading capacity of a spacecraft. Providing a large amount of cryogenic propellant in a short time with a strict energy consumption limitation is a challenge in the design of the fuel filling system. The authors proposed a vacuumed subcooling system combined with an ejector and liquid ring pump to vacuum a liquid oxygen tank and obtain subcooled liquid oxygen. After the liquid oxygen tank is vacuumed to an intermediate pressure by the ejector, it is further vacuumed to 10 kPa using the liquid ring pump. The infinitesimal method was used to simulate the thermodynamic processes involved. Taking the ejector working fluid mass flow rate, jet pressure, intermediate pressure, initial tank liquid level, and liquid ring pump speed as optimizing variables, optimization was conducted to determine the optimal vacuuming time, remaining liquid level in the tank, pumping speed difference, and nitrogen consumption. The sample set was generated by the optimal Latin sampling algorithm. The surrogate assisted Non-dominated Sorting Genetic Algorithm (NSGA-III) multi-objective algorithm was used to construct a system optimization framework. The non-dominated solutions were added to the sample set to improve the generalization ability of the Gaussian Process Regression (GPR) in the Pareto front. A convergent Pareto solution set was obtained after multiple iterations. The influence of different optimization variables on each optimization objective was analyzed using the Pearson correlation coefficient method. The optimization results show that the trade-off scheme can obtain the subcooled liquid oxygen at 10 kPa and 73 K with a remaining liquid level of 74.84% in a total vacuum time of 19.93 h. The efficiency of the liquid oxygen vacuum subcooling system can be improved significantly.

Equivalence transformations of a generalized fifth-order KdV equation with variable coefficients

By using the infinitesimal method, we firstly obtain the equivalence transformations for a class of generalized fifth-order KdV (gfKdV) equation with variable coefficients. With the application of equivalence transformations, the number of variable coefficients is reduced and the most general form which can be mapped by an equivalence transformation to the constant-coefficient equation is explored. Furthermore, the transformational properties of the gauged subclass are proposed via the direct method. We also construct the transformations that connect the three integrable variable coefficient gfKdV equations obtained before by Painlev e ́ test to their integrable constant-coefficient counterparts.

Simulation Analysis of Combined Mechanics of the Thrust Rotary Guide Drill

The force and deformation analysis of the bottom hole assembly (BHA) is the foundation and essential component of good trajectory control technology. Still, the BHA structure has complexity (multiangle), making it challenging to analyze the force and deformation of the BHA accurately. In this paper, we consider the factors such as well drilling parameters (drill pressure), drill combination structure parameters (multivariable cross section, stabilizer, and flexible short section diameter and position, etc.), a mechanical analysis model of the push-the-bit rotary steering tool is established based on the infinitesimal method and continuous beam-column theory. Taking the push-the-bit rotary steerable drilling assembly as an example, the influence of force and deformation of the rotary guided drilling assembly, such as drill pressure, stabilizer, and flexible short section parameters, was analyzed. The research results of this paper can solve the mechanical modeling problem of the variable cross section in the bottom drill combination, can deal with the combination of infinite multiple stiffnesses according to the actual situation, bring the analysis results closer to the real problem, and provide theoretical support for the design optimization of the bottom drill combination. In addition, edge computing can provide sufficient computing power for the calculation of this paper to ensure operational efficiency. It can realize the online real-time transmission of mechanical analysis results through powerful calculation examples and effectively guide the field operation.

Конструктивное мышление в критической философии Германа Когена

Constructive (productive) thinking in the critical philosophy of Hermann Cohen differs significantly from the seemingly similar speculative thinking in J. G. Fichte’s Science of Knowledge (Wissenschaftslehre) (1794/95). The fundamental characteristics of scientific thinking in Cohen’s teaching include: purity, focus on the “fact of science”, the origin (Ursprung), the infinitesimal method, continuity, movement, production, correlation, intensive magnitude, interrelation of thinking and being. According to Cohen, scientific thinking can only be pure and generated by the origin. The origin is continuous action (movement) of thinking to separate the united and bind the divided content. In this process, thinking and being are correlative. Infinitely small reality contains thinking and being simultaneously as a union and in a divided form. The infinitesimal method is thinking that continuously carries out a) the operations of opposing itself as pure thinking to the results of its own production; b) the coincidence of itself with the products of its own generation. Infinitesimal thinking seeks to eliminate the difference between self and being. Nevertheless, being constantly retains autonomy. Being does not merge with thinking and is not absorbed by it. In Fichte’s Science of Knowledge pure thinking moves in a logical circle, having no access into real being. In an effort to break out of this circle and find its causality, thinking turns not to the being of the world of phenomena, but to the Absolute I. Such a speculative approach to consciousness, thinking and being has little in common with Cohen’s critical position.

Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

Hydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Imbibition of Newtonian Fluids in Paper-like Materials with the Infinitesimal Control Volume Method

Paper-based microfluidic devices are widely used in point-of-care testing applications. Imbibition study of paper porous media is important for fluid controlling, and then significant to the applications of paper-based microfluidic devices. Here we propose an analytical approach based on the infinitesimal control volume method to study the imbibition of Newtonian fluids in commonly used paper-like materials. Three common paper shapes (rectangular paper strips, fan-shaped and circular paper sheets) are investigated with three modeling methods (corresponding to equivalent tiny pores with circle, square and regular triangle cross section respectively). A model is derived for liquid imbibition in rectangular paper strips, and the control equations for liquid imbibition in fan-shaped and circular paper sheets are also derived. The model is verified by imbibition experiments done using the mixed cellulose ester filter paper and pure water. The relation of imbibition distance and time is similar to that of the Lucas−Washburn (L−W) model. In addition, a new porosity measurement method based on the imbibition in circular paper sheets is proposed and verified. Finally, the flow rates are investigated. This study can provide guidance for the design of different shapes of paper, and for better applications of paper-based microfluidic devices.