Load Distribution Model Research Articles

Stability Study of Single‐Layer Spherical Shell Roof Under Nonuniformly Distributed Snow Load

ABSTRACTAfter snowfall, the snow load distribution on building roofs is generally nonuniform, and most cases of large‐span structural collapse are related to nonuniform load. The existing regulations provide limited snow distribution coefficients for different roofs, and with the diversification of building forms, they can no longer meet the current calculation requirements for roof snow loads. This article conducts numerical simulations of wind‐induced snow drift on a spherical shell roof, which rise‐span ratio is 1/5. It is found that the friction velocity of the roof is distributed in a band shape and is higher in the windward direction, whereas the friction velocity on the leeward side is lower, which increases the possibility of snow accumulation. Based on this, a simplified snow load distribution model is proposed to improve the economic efficiency of the project. Based on the above research, the stability analysis of K6 single‐layer Kevitt mesh shell was carried out using ABAQUS finite element software. The results show that under uniformly distributed load conditions, the buckling modes of the structure are symmetrical, whereas under nonuniform snow load conditions, the first mode deforms more on the side with higher load, and the position of structural deformation is closer to the edge; when the snow cover range is the same, the larger the extreme snow load, the more unfavorable it is for structural stability; when the extreme snow load is the same, the smaller the snow coverage, the more unfavorable the initial defect is for structural stability.

Методи та засоби оптимізації використання обчислювальних ресурсів в корпоративній мережі закладу вищої освіти

The paper considers the problems of using computing resources in the corporate network of a higher education institution. An approach to assessing the efficiency of the load of computer workstations is proposed, which is based on the indicators of the load of individual computing resources and their implementation in the general system of computing resources for individual applied resource-intensive tasks. It is established that to minimize costs when building a university CM, it is necessary to use non-standard approaches that could dynamically distribute computing resources, in particular terminal and cluster technologies for building corporate networks. A number of experimental studies have been conducted based on data on the functioning of the computer network of a higher education institution. A mathematical model of optimal load distribution on terminal servers has been constructed, which describes the dependence between individual network nodes and the file access system.

Short-term load distribution model for giant cascade serial diversion-type hydropower stations

With the development of complex cascade serial diversion-type hydropower plants (CSDHP) in Southwest China, it has become imperative to study short-term scheduling challenges that are distinctive to this type of hydropower facility. Unlike conventional cascade hydropower stations, which have large reservoirs to regulate the outflow between stations, the CSDHP system consists of several diversion-type hydropower plants connected in series, requiring strict matching of turbine discharge between upstream and downstream facilities. In addition, these plants impose complex operation constraints, such as multiple units sharing one tunnel, which greatly increases the difficulty of short-term scheduling. This paper proposes a short-term optimal scheduling model for CSDHP systems aimed at achieving efficient load distribution among units while minimizing water consumption. The model takes into account the strict matching of turbine discharge and the complex constraints of multiple units sharing one tunnel. Subsequently, the model is transformed into a mixed integer linear programming problem using specified linearization techniques, with complexity further addressed via an iterative resolution method. A case study of a cascade illustrates the model’s efficacy in facilitating effective unit load distribution under complex hydraulic and electrical constraints, which substantially reduces the system’s water consumption by up to 6.1% during the dry season and 1.8% during the flood season, and reducing the number of crossing forbidden zones by 50.0% and 52.0%, respectively. The result shows the models’ potential to enhance day-ahead scheduling for the CSDHP system.

Research on friction and meshing efficiency of ADC12-POM gear pair considering off-line meshing

Metal-plastic gear pairs, due to their combination of the advantages of both materials, have been widely promoted and applied in many industries. However, research on their transmission performance is not yet complete, especially regarding the tribological properties of metal-plastic gear pairs. The study focus on ADC12-POM gear pairs. Based on the principle of potential energy, the study considers significant elastic deformation during POM meshing, resulting in obvious off-line meshing. Consequently, the study establishes a stiffness model for ADC12-POM gear pairs with off-line meshing. Using this stiffness model and a load distribution model, to calculate the tooth surface load distribution coefficient for the gear pairs. Building upon previous research on friction coefficient models, the study develop a friction coefficient model that accounts for off-line meshing and compare it with the friction coefficient model that does not consider off-line meshing. To validate the accuracy of the friction coefficient model, the study design and create an efficiency test rig for ADC12-POM gear pairs, conducting theoretical and experimental studies on gear mesh efficiency. The study analyzes the distribution of mesh efficiency along the meshing line and its relationship with the friction coefficient. By comparing experimental measurements with theoretical calculations, the study verifies the proposed friction coefficient model, providing a theoretical basis for the study of metal-plastic gears.

A bridge dynamic response analysis and load recognition method using traffic imaging

As the primary variable load of bridges, vehicle load is an important parameter for bridge health monitoring. However, traditional Weigh-in-Motion (WIM) systems and the commonly used method of placing sensors on the bridge are challenging to apply in load monitoring for many small and medium-sized bridges. Therefore, this paper proposes a bridge vehicle load identification method based on traffic surveillance video data. Leveraging the surveillance video data on the bridge, without introducing additional hardware devices, the displacement of target points is detected through sub-pixel level image detection algorithms, enabling non-contact measurement of bridge structural response through imaging. A spatiotemporal relationship model of structural displacement, vehicle load, and load distribution is established to solve for vehicle load. Finally, model bridge tests under various loading conditions and engineering practice experiments are conducted to validate the feasibility of the method. The results of the model bridge tests show that the structural displacement measured using traffic video measurement has a deviation of less than 10% compared to the measurements obtained using contact displacement sensors (LVDT), and it can accurately reflect the displacement characteristics of the structure. The results of the field tests demonstrate that the average estimation deviation for heavy vehicle loads ranging from 12 to 18 tons is approximately 18%, meeting the engineering requirements. The proposed method can provide load statistical information for the extensive health monitoring of small and medium-sized bridges and offer a new technical pathway for obtaining bridge load information.

Study on calculation method for dynamic load distribution of thread pair of planetary roller screw mechanism

To reveal the dynamic load distribution characteristics of planetary roller screw mechanism under the high-speed operating conditions, based on the spiral surface equation and deformation coordination relationship, a static contact force calculation method of the roller-screw and roller-nut thread at the contact point is proposed, and a formula for calculating the contact angle after bearing is derived. On this basis, further considering the inertial force generated by using high-speed operation, a dynamic load distribution model for planetary roller screw mechanism thread was established. By comparing with the finite element contact model of planetary roller screw mechansim, the error is below 5%, which verifies the correctness of the model established. Finally, the influence of the parameters such as screw speed, axial load, pitch, and tooth flank angle on the distribution of dynamic load was analyzed. The results show that the inertia force causes the roller to have a tendency to move closer to the nut and away from the screw resulting in a decrease in dynamic contact force on the roller screw side and an increase in dynamic contact force on the roller nut side. The degree of uneven distribution of dynamic load is positively correlated with the screw speed and pitch, and negatively correlated with the tooth side angle. The size of axial load has a significant impact on the distribution of dynamic load.

Short-term load distribution model for cascade giant hydropower stations with complex hydraulic and electrical connections

The cascade giant hydropower station system (CGHSS) has been widely applied in countries with abundant water resources. However, the dense hydropower stations and power grids bring complex hydraulic and power connections, including the backwater effect, multiple hydroplants sharing one reservoir and one-reservoir multiple dispatch power grid, which leads to modelling difficulties and inefficient model solving. To address these challenges, a short-term load distribution (SLD) model considering complicated hydraulic and electricity constraints is developed. First, the discharge of each hydroplant and the downstream forebay water level are used as inputs to construct a multivariate nonlinear function, and the average tailwater levels are obtained. Second, a head constraint considering the shared water level is added to the model to calculate the head of each hydroplant, making the output more accurate. Finally, the nonlinear constraints are linearly reconstructed using the Big-M method, triangulation technique and special ordered sets to reduce the model solution time. The SLD model is applied to the Xiluodu-Xiangjiaba cascade hydropower system in the Jinsha River. The results show that the developed model reduces water consumption by 4.02 %, 4.70 %, 5.79 % and 5.28 % compared to the constant proportional distribution model and the real operation, generating a more executable SLD scheme.

Study on internal load distribution of deep groove ball bearings considering raceway surface waviness

Abstract A full circumferential contact mechanics modeling study considering the effect of waviness mesoscopic profile and rolling element contact relationship on bearing load distribution is carried out. In the model, a sinusoidal function is adopted to simulate the profile of the waviness section. According to the contact tangency condition, a model of the contact deformation relationship between a single rolling element and the raceways is established. On this basis, a full circumferential rolling elements contact load distribution model of the bearing is established by introducing the contact deformation of all rolling elements with the raceway surfaces. Focusing on contact deformation of a full circumferential rolling elements with the raceways, this model can conduct more accurate modeling and reflect the load distribution state inside the bearing more realistically. The correctness of the mechanical analysis model proposed in this paper is proved by an average error of 3.38%, which is the comparison result between the mechanical analysis model and the finite element model. Meanwhile, computational efficiency is improved. Further, based on the model, the influence of the waviness parameters on the load distribution inside the bearing under the action of different types of loads is analyzed.

Optimum management of microgrid generation containing distributed generation sources and energy storage devices by considering uncertainties

In recent years, the financial and energy crises have made the economical and safe operation of distribution microgrids one of the main challenges for operators. In this regard, the optimal distribution of the microgrid, considering the favorable indicators of Generation and consumption, significantly improves the quality of the development and economic operation of electricity grids. On the other hand, distribution microgrids have many problems and complications due to the presence of DG sources and the uncertainties caused by them in Generation and consumption, such as the inability to solve optimal load distribution using common and common calculation methods. Therefore, grid technical indicators such as voltage deviation and losses in solving load distribution add to the complexity of related issues. To solve the challenges raised in the distribution microgrid, this paper proposes an optimal load distribution model that models the uncertainties in the distribution microgrids using the Monte Carlo method. Using meta-heuristic algorithms, the optimal Generation function by modeling grid security constraints such as voltage deviation, losses, and a load limit of the system should be in economic operation mode, and then the power distribution equations should be solved. The battery can supply 1 kW of active power to the system at a cost of 1 unit/kW during the high cost period if it absorbs 1 kW of active power at a cost of 0.92 units/kW during the low cost period. Additionally, the active and reactive power losses have been decreased to 0.3kW and 0.2kW, respectively, by utilizing the suggested methodology. The simulation results show that the proposed method performs satisfactorily and that the modeling is simulated in MATLAB software.

Performance optimization and energy minimization of cloud data center using optimal switching and load distribution model

Cloud computing is an effective computing methodology used in all stages of business. Most of the Cloud Data Centers (CDC) operates on the basis of peak load and huge scales. Hence, it necessitates saving the energy in CDC. This study introduces an energy-efficient strategy based on the fat tree. Here, Taylor-based Manta-Ray Foraging Optimization (Taylor-MRFO) is developed by combining the Taylor series with Manta Ray Foraging Optimization (MRFO) to distribute the load in a CDC. In load distribution, the cloud data switching to the preferred mode is done by the Actor critic neural network (ACNN). Furthermore, the developed Taylor-MRFO+ACNN provided a better outcome than the conventional approaches with the least energy consumption of 0.4930, least load of 0.3631, and least fitness of 0.4343. For setup-1, when the population size is 15, the load value obtained by the proposed method is 23.43 %, 10.19 %, 7.18 %, 5.31 %, 4.43 %, and 2.58 % higher when compared to the existing approaches namely, Artificial Bee colony(ABC), Efficient Load Optimization and Resource Minimization (ELORM), Adaptive Parameter- Ant Colony Optimization (AP-ACO), Multi-Objective Memetic Algorithm-Adaptive Plant Intelligent Behavior Optimization (MOMA-APIBO), Cooling Control Algorithm (CCA), and Minimum Total Power (MinPR).

Modeling load distribution for rural photovoltaic grid areas using image recognition

Expanding photovoltaic (PV) resources in rural-grid areas is an essential means to augment the share of solar energy in the energy landscape, aligning with the “carbon peaking and carbon neutrality” objectives. However, rural power grids often lack digitalization; thus, the load distribution within these areas is not fully known. This hinders the calculation of the available PV capacity and deduction of node voltages. This study proposes a load-distribution modeling approach based on remote-sensing image recognition in pursuit of a scientific framework for developing distributed PV resources in rural grid areas. First, houses in remote-sensing images are accurately recognized using deep-learning techniques based on the YOLOv5 model. The distribution of the houses is then used to estimate the load distribution in the grid area. Next, equally spaced and clustered distribution models are used to adaptively determine the location of the nodes and load power in the distribution lines. Finally, by calculating the connectivity matrix of the nodes, a minimum spanning tree is extracted, the topology of the network is constructed, and the node parameters of the load-distribution model are calculated. The proposed scheme is implemented in a software package and its efficacy is demonstrated by analyzing typical remote-sensing images of rural grid areas. The results underscore the ability of the proposed approach to effectively discern the distribution-line structure and compute the node parameters, thereby offering vital support for determining PV access capability.

The influence of different load distribution considering geometric error on the fatigue life of ball screw

The ball screw pair is a precision drive component that converts rotary motion into linear motion. In practical applications, because the feed system usually has rotational torque and geometric errors, it may increase the contact load of the ball screw pair and reduce the fatigue life. In order to study the influence of different loads and geometric errors on the maximum contact load and fatigue life of ball screw pairs, the following research work was carried out. Firstly, based on the composite load and rotational torque, the ball load distribution model is established, and the accuracy of the model is verified by finite element modeling analysis. Then, the influence of different composite loads, rotation times and geometric errors (including ball size error, lead error and raceway tooth profile error) on the ball load distribution is analyzed. Finally, the influence of compound load, rotating torque and geometric error on the fatigue life of ball screw pairs is studied. The results show that the rotational torque and lead error have a great influence on the load distribution and fatigue life of the ball, and the influence of lead error on load distribution is greater than that of dimension error and tooth profile error. The fatigue life of the ball screw pair with non-uniform load distribution is shorter than that of the ball screw pair with uniform load distribution.

Intelligent Low-Consumption Optimization Strategies: Economic Operation of Hydropower Stations Based on Improved LSTM and Random Forest Machine Learning Algorithm

The economic operation of hydropower stations has the potential to increase water use efficiency. However, there are some challenges, such as the fixed and unchangeable flow characteristic curve of the hydraulic turbines, and the large number of variables in optimal load distribution, which limit the progress of research. In this paper, we propose a new optimal method of the economic operation of hydropower stations based on improved Long Short-Term Memory neural network (I-LSTM) and Random Forest (RF) algorithm. Firstly, in order to accurately estimate the water consumption, the LSTM model’s hyperparameters are optimized using improved particle swarm optimization, and the I-LSTM method is proposed to fit the flow characteristic curve of the hydraulic turbines. Secondly, the Random Forest machine learning algorithm is introduced to establish a load-distribution model with its powerful feature extraction and learning ability. To improve the accuracy of the load-distribution model, we use the K-means algorithm to cluster the historical data and optimize the parameters of the Random Forest model. A Hydropower Station in China is selected for a case study. It is shown that (1) the I-LSTM method fits the operating characteristics under various working conditions and actual operating characteristics of hydraulic turbines, ensuring that they are closest to the actual operating state; (2) the I-LSTM method is compared with Support Vector Machine (SVM), Extreme Learning Machine (ELM) and Long Short-Term Memory neural network (LSTM). The prediction results of SVM have a large error, but compared with ELM and LSTM, MSE is reduced by about 46% and 38% respectively. MAE is reduced by about 25% and 21%, respectively. RMSE is reduced by about 27% and 24%, respectively; (3) the RF algorithm performs better than the traditional dynamic programming algorithm in load distribution. With the passage of time and the increase in training samples, the prediction accuracy of the Random Forest model has steadily improved, which helps to achieve optimal operation of the units, reducing their average total water consumption by 1.24%. This study provides strong support for the application of intelligent low-consumption optimization strategies in hydropower fields, which can bring higher economic benefits and resource savings to renewable energy production.

A multi-objective spatio-temporal pricing method for fast-charging stations oriented to transformer load balancing

To address the challenges posed by the fast-charging demand of electric vehicles, causing feeder load and voltage imbalances during operation, this paper introduces a spatio-temporal pricing strategy tailored to enhance feeder operation equilibrium. This approach facilitates the spatio-temporal guidance of fast-charging loads for electric vehicles in operation. This paper begins by formulating a spatio-temporal distribution model for electric vehicle fast-charging loads, considering owners’ preferences. It further develops a behavioral model for the travel choices of electric vehicles, illustrating the impact of spatio-temporal electricity pricing at fast-charging stations on load distribution. Next, it proposes a multi-objective spatio-temporal pricing model and its solution method specifically designed for feeder-balance-oriented fast-charging stations. This model targets the minimization of the spatio-temporal imbalance in feeder voltage and load. It takes a comprehensive approach, considering the constraints of the spatio-temporal load distribution model and optimal power flow model. The resulting spatio-temporal pricing model for fast-charging stations is effectively solved using the extended Pareto evolutionary algorithm. To validate the effectiveness of the proposed method in achieving feeder balancing, this paper analyzes two examples: a self-built 29-node road network and a 9-node distribution network, as well as a 66-node road network and a 33-node distribution network in the Xinjiang region. The results show that the proposed method can effectively guide the charging of electric vehicles and make the load distribution more balanced.

Spatial distribution model of thermal load for high-speed dry hobbing tool based on probability density function

High-speed dry hobbing is a clean and environmental-friendly gear machining process, but thermal dissipation inefficiency accelerates tool wear and shorten tool life which is difficult to be effectively inhibited due to its complex distribution characteristics. This paper proposes a thermal load distribution model based on probability density function, describing the spatial distribution of thermal load on tool and providing theoretical support for predicting the distribution of thermal load. Firstly, conducting a finite element simulation analysis based on a mathematical model of high-speed dry gear hobbing process; Secondly, the influence of various parameters on the constructed model is analyzed, and the Bayesian optimization algorithm is utilized to optimize the model parameters. Finally, the model is validated at the micro and macro level. The results show that the average coefficient of determination of the model is greater than 0.86 in micro level. And the average fitting error is less than 6 °C in macro level, besides, the average relative error is less than 15%. The description of the uneven thermal distribution on tool is obtained with probability density function, it provides a theoretical support for the prediction and further optimization of thermal load on tool under multiple parameters in the future.

Participation trends, dynamics of results and forecasting of finishing times of athletes specializing in 100 km ultra-marathon

In recent years, there has been an increase in popularity and results in road ultramarathon (running events which includes distances over 42 195 m). Attention to them from athletes, coaches and scientists is increasing. The search for scientifically based approaches to the construction of the training process is relevant. The study of statistical data on the performance of leading athletes at competitions is a source of important information for making recommendations for improving the training process. The purpose of the study was to determine the age and competitive characteristics of qualified ultramarathoners at a distance of 100 km and to develop methodological recommendations for building a training process and predicting the competitive result. The article analyzes statistical data on the performances of qualified ultramarathoners at the 100 km World Championships in 2022 and 2018, and related competition. The obtained results indicate a tendency to improve the finishing time of athletes of various qualifications. Age has a weak correlation with outcome. Qualified ultramarathoners compete in 2 or 3 main competitions during the year, with a period of 12-16 weeks between them. 100 km runners tend to slow down over the distance. More skilled athletes show less reduction in speed. The 100 km performance has a strong correlation with the 50 km performance. You can predict the competitive result at a distance of 100 km using the formula y=788.96 + 2.16x, where y is the result of running 100 km, x is the result of running 50 km in seconds. It is advisable to plan the training process of ultramarathoners based on a two- cycle or three-cycle periodization model. The derived regression equation makes it possible to adjust the training process and plan a rational running pace during the competition. Further research is needed to determine the optimal model of load distribution in the process of training ultramarathon runners.

A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears

As a critical component of the joint gearbox, spur gear pairs play a crucial role in energy conversion, limiting the performance of a collaborative robot. Accurately assessing their instantaneous efficiency and torque fluctuation is essential for developing high-precision robot joint control models. This study proposes a computational model to predict the instantaneous efficiency and torque fluctuation of spur gears under typical operating conditions. The model incorporates a torque balance model, a load distribution model, and a friction model to reflect the relationship between gear meshing position and efficiency. The instantaneous efficiency and torque fluctuation of gear pairs were compared with the Coulomb friction model with an average friction coefficient and the elastohydrodynamic lubrication model with a time-varying friction coefficient. The effect of gear contact ratio on efficiency is analysed, while the instantaneous efficiency and torque fluctuation of gears are studied under varying operating conditions. The results indicate a maximum efficiency difference of 1.86 % between the two friction coefficient models. Under specific operating conditions, the instantaneous efficiency variation of the gear pair can reach 3.34 %, and the torque fluctuation can reach 5.19 Nm. Finally, this study demonstrates the effectiveness and accuracy of the proposed method through comparative analysis.

Influence of Fixed Ring Gear Structural Compliance on the Quasi-Static and Dynamic Response of Epicyclic Gear Sets

Abstract The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets, in fixed ring kinematic configuration. To achieve this objective the current study will incorporate a finite element based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot [1]. The proposed model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Ligata et al. [2]. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears.

Load Distribution Analysis and Contact Stiffness Prediction of the Dual-Drive Ball Screw Pair Considering Guide Rail Geometric Error and Slide Position

The dual-drive ball screw pair serves as a crucial element within the fixed gantry machine tool with cross-rail movement. When in service, the dual-drive ball screw pair experiences variations in axial load, impacting the contact load distribution of the ball screw pair. A calculation model for determining the axial load offset of the dual-drive ball screw pair is proposed to investigate the variation in axial load. The impact of the geometric error associated with the guide rail and the position of the slide are considered. This paper presents the contact load distribution model for the dual-drive ball screw pair. This study investigates the contact load and contact angle distribution of the dual-drive ball screw pair during the machine tool in service. Additionally, based on fractal theory, the stiffness models of individual micro-convex body and contact surfaces have been established. This study provides a comprehensive analysis of the contact stiffness of the ball screw pair, considering the influence of guide rail geometric error and slide position. In addition, the three-dimensional surface morphology of ball screw pair is obtained by experiments. This paper investigates the contact stiffness distribution of dual-drive ball screw pair during service.

Effect of combined geometric errors on static load distribution and deformations for linear rolling guide

Most studies on linear rolling guides usually assume the contact load between the ball and the raceway is uniform, which results in a deviation from the actual conditions. This study aims to establish a load distribution model based on the Hertz contact theory with ball combined interference which is converted from preload, raceway center-distance error, and installation error including ball geometry error. The reliability of the proposed model was verified by a numerical instance for the load distribution and deformation analysis. The result shows that the proposed approach agrees better with the experimental results compared only with the action of the preload. This work can provide an important starting point for studying friction and wear in machine tools.