DESTROYING EFFECTS OF TRUCK TIRES ON THE DESIGN OF ROADWEAR

The article presents a mathematical model of the destructive effect of a wide-profile tire on the roadway. The mathematical model makes it possible to adequately reproduce the effect of a wide-profile tire on the road surface, taking into account the load and parameters of the tire, as well as the structure of the road surface and the temperature state.

Algorithmic solutions to the problem of assessing the information impact on the electorate during election campaigns

In the article, to solve the problem of assessing the information impact on the electorate during election campaigns, algorithmic solutions, including a mathematical model, a numerical scheme and algorithmic implementations, are formed. This assessment is reduced to determining the instantaneous values of the number of voters who prefer a candidate (party), taking into account: the positive or negative stochastic nature of the impact of mass media; interpersonal interaction; two-step assimilation of information; the presence of a variety of mass media, social groups and a list of candidates. The mathematical model is based on a generalized model of information confrontation in a structured society and, with the introduction of stochastic components in the intensity of agitation, it is reduced to solving the FokkerPlanckKolmogorov equation. For its study in the formulation of the Galerkin method, a numerical scheme is proposed and the order of its convergence is determined. In relation to the basic procedures of the numerical scheme, the features of the algorithmic implementation are clarified.

Recovering Heat Source from Fourth-Order Inverse Problems by Weighted Gradient Collocation

The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution based on a priori assumptions is considered herein. In view of the fourth-order partial differential equation (PDE) in the mathematical model, the high-order gradient reproducing kernel approximation is introduced to efficiently untangle the problem without calculating the high-order derivatives of reproducing kernel shape functions. The weights of the weighted collocation method for high-order inverse analysis are first determined. In the benchmark analysis, the unclear illustration in the literature is clarified, and the correct interpretation of numerical results is given particularly. Two mathematical formulations with four examples are provided to demonstrate the viability of the method, including the extreme cases of the limited accessible boundary.

Overlapping optimization of hybrid deposited and micro-rolling additive manufacturing

Purpose This paper aims to summarize the influence law of hybrid deposited and micro-rolling (HDMR) technology on the bead morphology and overlapping coefficient. A better bead topology positively supports the overlapping deposited in multi-beads between layers while actively assisting the subsequent layer's deposition in the wire and arc additive manufacturing (WAAM). Hybrid-deposited and micro-rolling (HDMR) additive manufacturing (AM) technology can smooth the weld bead for improved surface quality. However, the micro-rolling process will change the weld bead profile fitting curve to affect the overlapping coefficient. Design/methodology/approach Weld bead contours for WAAM and HDMR were extracted using line lasers. A comparison of bead profile curves was conducted to determine the influence law of micro-zone rolling on the welding bead contour and fitting curve. Aiming at the optimized overlapping coefficient of weld bead in HDMR AM, the optimal HDMR overlapping coefficient curve was proposed which varies with the reduction based on the best surface flatness. The mathematical model for overlapping in HDMR was checked by comparing the HDMR weld bead contours under different rolling reductions. Findings A fitting function of the bead forming by HDMR AM was proposed based on the law of conservation of mass. The change rule of the HDMR weld bead overlapping spacing with the degree of weld bead rolling reduction was generated using the flat-top transition calculation for this model. Considering the damming-up impact of the first bead, the overlapping coefficient was examined for its effect on layer surface flatness. Originality/value Using the predicted overlapping model, the optimal overlapping coefficients for different rolling reductions can be achieved without experiments. These conclusions can encourage the development of HDMR technology.

Robust sideslip angle observer of commercial vehicles based on cornering stiffness estimation using neural network

Accurate estimation of sideslip angle is essential for vehicle stability control. For commercial vehicles, the estimation of sideslip angle is challenging due to severe load transfer and tire nonlinearity. This paper presents a robust sideslip angle observer of commercial vehicles based on identification of tire cornering stiffness. Since tire cornering stiffness of commercial vehicles is greatly affected by tire force and road adhesion coefficient, it cannot be treated as a constant. To estimate the cornering stiffness in real time, the neural network model constructed by Levenberg-Marquardt backpropagation (LMBP) algorithm is employed. LMBP is a fast convergent supervised learning algorithm, which combines the steepest descent method and gauss-newton method, and is widely used in system parameter estimation. LMBP does not rely on the mathematical model of the actual system when building the neural network. Therefore, when the mathematical model is difficult to establish, LMBP can play a very good role. Considering the complexity of tire modeling, this study adopted LMBP algorithm to estimate tire cornering stiffness, which have simplified the tire model and improved the estimation accuracy. Combined with neural network, A time-varying Kalman filter (TVKF) is designed to observe the sideslip angle of commercial vehicles. To validate the feasibility of the proposed estimation algorithm, multiple driving maneuvers under different road surface friction have been carried out. The test results show that the proposed method has better accuracy than the existing algorithm, and it’s robust over a wide range of driving conditions.

Selected Mathematical Models Describing Flow in Gas Pipelines

The main aim of simulation programs is to study the behavior of gas pipe networks in certain conditions. Solving a specified set of differential equations describing transient (unsteady) flow in a gas pipeline for the adopted parameters of load and supply will help us find out the value of pressure or flow rate at selected points or along selected sections of the network. Transient gas flow may be described by a set of simple or partial differential equations classified as hyperbolic or parabolic. Derivation of the mathematical model of transient gas flow involves certain simplifications, of which one-dimensional flow is most important. It is very important to determine the conditions of pipeline/transmission network operation in which the hyperbolic model and the parabolic model, respectively, should be used. Parabolic models can be solved numerically in a much simpler way and can be used to design simulation programs which allow us to calculate the network of any structure and any number of non-pipe elements. In some conditions, however, they describe the changes occurring in the network less accurately than hyperbolic models do. The need for analysis, control, and optimization of gas flows in high-pressure gas pipelines with complex structure increases significantly. Very often, the time allowed for analysis and making operational decisions is limited. Therefore, efficient models of unsteady gas flows and high-speed algorithms are essential.

Influence of circumferential annular grooving design of impeller on suspended fluid force of axial flow blood pump

Aiming at insufficient suspension force on the impeller when the hydraulic suspension axial flow blood pump is start at low speed, the impeller suspension stability is poor, and can’t quickly enter the suspended working state. By establishing the mathematical model of the suspension force on the impeller, then the influence of the circumferential groove depth of the impeller on the suspension force is analyzed, and the annular groove depth on the impeller blade in the direction of fluid inlet and outlet was determined as (0.26, 0.02 mm). When the blood pump starts, there is an eccentricity between the impeller and the pump tube, the relationship between the suspension force and the speed of the impeller under different eccentricities is analyzed. Combined with the prototype experiment, the circumferential annular grooving design of the impeller can make the blood pump rotate at about 3500 rpm into the suspension state, when the impeller is at 8000 rpm, the impeller can basically achieve stable suspension at the eccentricity of 0.1 mm in the gravity direction, indicating that the reasonable circumferential annular grooving design of the impeller can effectively improve the suspension hydraulic force of the impeller and improve the stability of the hydraulic suspension axial flow blood pump.

Simulation of oscillatory processes in the MVSTUDIUM package

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

Fuzzy fractional mathematical model of COVID-19 epidemic

In this paper, we develop a mathematical model with a Caputo fractional derivative under fuzzy sense for the prediction of COVID-19. We present numerical results of the mathematical model for COVID-19 of most three infected countries such as the USA, India and Italy. Using the proposed model, we estimate predicting future outbreaks, the effectiveness of preventive measures and potential control strategies of the infection. We provide a comparative study of the proposed model with Ahmadian’s fuzzy fractional mathematical model. The results demonstrate that our proposed fuzzy fractional model gives a nearer forecast to the actual data. The present study can confirm the efficiency and applicability of the fractional derivative under uncertainty conditions to mathematical epidemiology.