Residual Stresses due to High Temperature Annealing. Mathematical Model and Calculations

2006 ◽  
Vol 524-525 ◽  
pp. 355-360
Author(s):  
O.R. Hachkevych ◽  
V.S. Mykhailyshyn ◽  
A. Ravska-Skotnichna
Keyword(s):  
Mathematical Model ◽  
High Temperature ◽  
Residual Stresses ◽  
Thermal Sensitivity ◽  
High Temperature Annealing ◽  
The Finite Element Method ◽  
Initial Temperature Distribution ◽  
Wide Range ◽  
Thermomechanical Processes ◽  
The Mathematical Model

The mathematical model is developed for description of thermomechanical processes at cooling during high temperature annealing with the known initial temperature distribution (the temperature of holding) and stresses (acquired stresses at the final of a holding). It is taken into account the thermal sensitivity and material hardening at elasto-plastic solid deforming. The methodology based on the finite element method is proposed for solving thermomechanics problems of wide range. The suitable software is developed. At the final stage of annealing a cylindrical solid it is investigated residual stresses being formed on the cooling stage.

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

2022 ◽  
pp. 095440702110724
Author(s):  
Chenyu Zhou ◽  
Liangyao Yu ◽  
Yong Li ◽  
Jian Song
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Stability Control ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Commercial Vehicles ◽  
Sideslip Angle ◽  
The Neural Network ◽  
Wide Range ◽  
The Mathematical Model

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.

Numerical Modeling of Deformation Processes in Rock Pillars

2014 ◽  
Vol 682 ◽  
pp. 202-205 ◽  
Author(s):  
V.V. Aksenov ◽  
S.V. Lavrikov ◽  
Alexander F. Revuzhenko
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Rock Mass ◽  
Deformation Process ◽  
The Finite Element Method ◽  
Sequential Development ◽  
Deformation Processes ◽  
Rock Pillars ◽  
The Mathematical Model ◽  
Loss Of Strength

The mathematical model of rock mass in the context of its internal structure, anisotropy, loss of strength, elastic energy accumulation and release is considered. The numerical solution to the problem of quasistatic deformation in a rock mass pillar is obtained by the finite element method. The sequential development of softening and residual strength zones is considered. It is shown that if the softening modulus is strong enough then the deformation process becomes unstable.

scholarly journals Kinetics of filtration consolidation of water-saturated clay soils

2020 ◽  
pp. 86-95 ◽  
Author(s):  
O. V. Ageikina ◽  
V. V. Vorontsov ◽  
R. R. Sufyanov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Saturated Porous Medium ◽  
Experimental Studies ◽  
Saturated Soils ◽  
Consolidation Process ◽  
Filtration Consolidation ◽  
Wide Range ◽  
Water Saturated ◽  
The Mathematical Model

The relevance of the research processes filtration consolidation due to the place of water-saturated soils in various design solutions related to the exploration, production and transportation of hydrocarbons. It should be noted that the diversity of soils led to the emergence of a wide range of mathematical models, obtained on the basis of generalization of experimental data and various assumptions to simplify engineering calculations. The article presents the results of theoretical and experimental studies of the mathematical model of the consolidation process of a water-saturated porous medium. This model is based on simplifying assumptions that are different from those adopted in well-known solutions. A fundamental approach to the formation of the model was developed on the basis of the kinetic representations of chemical reactions used in solving the environmental problems of epoxidation reactions of olefins. We determined the parameters of the mathematical model of the consolidation process of the saturated porous medium of clayey soil and confirmed its adequacy by the research results. In addition, we established the parameters of the field of non-equilibrium filtration, reducing the nonexistent ability of water-saturated soils.

Design and Modeling of an Experimental ROV with Six Degrees of Freedom

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 113
Author(s):  
Aleksey Kabanov ◽  
Vadim Kramar ◽  
Igor Ermakov
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Experimental Tests ◽  
Underwater Vehicles ◽  
Six Degrees Of Freedom ◽  
Functional Capabilities ◽  
Classical Design ◽  
Wide Range ◽  
Reduced Costs ◽  
The Mathematical Model

With the development of underwater technology, it is important to develop a wide range of autonomous and remotely operated underwater vehicles for various tasks. Depending on the problem that needs to be solved, vehicles will have different designs and dimensions, while the issues surrounding reduced costs and increasing the functionality of vehicles are relevant. This article discusses the development of inspection class experimental remotely operated vehicles (ROVs) for performing coastal underwater inspection operations, with a smaller number of thrusters, but having the same functional capabilities in terms of controllability (as vehicles with traditionally-shaped layouts). The proposed design provides controllability of the vehicle in six degrees of freedom, using six thrusters. In classical design vehicles, such controllability is usually achieved using eight thrusters. The proposed design of the ROV is described; the mathematical model, the results of modeling, and experimental tests of the developed ROVs are shown.

Mathematical modeling of articulated passenger train spatial vibrations

2021 ◽  
Vol 2021 (2) ◽  
pp. 91-99
Author(s):  
O. Markova ◽  
◽  
H. Kovtun ◽  
V. Maliy ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Ride Quality ◽  
Railway Transport ◽  
Passenger Train ◽  
Wide Range ◽  
Random Track Irregularities ◽  
The Mathematical Model

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

Analysis of informative parameters of the magnetoelastic acoustic emission signal

2017 ◽  
Vol 2017 (45) ◽  
pp. 10-13
Author(s):  
Y. P. Pochapskyy ◽  
◽  
B. P. Klym ◽  
I.M. Koblan ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Acoustic Emission ◽  
Residual Stresses ◽  
Pulse Flow ◽  
Emission Signal ◽  
Informative Parameters ◽  
Magnetoelastic Acoustic Emission ◽  
Random Pulse ◽  
The Mathematical Model ◽  
Ferromagnetic Steel

The mathematical model of the magnetoelastic acoustic emission (MAE) signal in the form of a random pulse flow is proposed and substantiated. The pulse and time characteristics of the MAE signal are highlighted. Using the results of the experiment by the MAE method of plate ferromagnetic steel samples an estimation of a number of parameters of the MAE signal is made. As a result, the dependences of the sum of the amplitudes and the final account of the signal from the set threshold for different loads are obtained. The dependence of the final account on the set threshold for the various values of the exponent attached to the sample is approximated. The dependence of the attenuation coefficient of the approximating exponent on the magnitude of the applied to the load sample, which is proposed to be used as a calibration in diagnosing residual stresses in ferromagnetic objects, is constructed.

Simulation of Seepage Flow in Earth Dam with a Free Surface

2012 ◽  
Vol 433-440 ◽  
pp. 1465-1469
Author(s):  
Wen Li Wei ◽  
Hong Zhao ◽  
Pei Zhang ◽  
Y.I. Liu
Keyword(s):  
Mathematical Model ◽  
Seepage Flow ◽  
Earth Dam ◽  
Matrix Equations ◽  
The Finite Element Method ◽  
Curvilinear Boundary ◽  
Seepage Flows ◽  
Large Matrix ◽  
Physical Laws ◽  
The Mathematical Model

The technique of curvilinear boundary-fitted coordinate system is used for the mathematical model of pressure underground seepage flow and the boundary conditions and the method of solving the transformed equations have been presented. The computing example shows that the computed hydraulic parameters conform to the physical laws. Compared with the finite element method, the presented method need not solve the large matrix equations, and the computer memories and the time for computing are less. The mathematical model is effective for numerical solution of seepage flows with complicated boundaries, and can be used in practice hydraulic engineering.

A Material Selection Method Based on Finite Element Method

2014 ◽  
Vol 887-888 ◽  
pp. 1013-1016
Author(s):  
Sheng Bin Wu ◽  
Xiao Bao Liu
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Material Selection ◽  
Selection Method ◽  
Structure Design ◽  
The Finite Element Method ◽  
The Mathematical Model ◽  
Selection Of ◽  
Element Method

A new method for material selection in structure design based on the theory of the finite element method was presented. The method made material selection and structure design working at the same time. The mathematical model was established based on the finite element method. Finally, the material selection of an excavator's boom was verified, the results show that the proposed method is effective and feasible.

A Model for Determining the Asperity Engagement Height in Relation to Web Traction Over Non-Vented Rollers

2002 ◽  
Vol 124 (3) ◽  
pp. 584-594 ◽  
Author(s):  
Brian S. Rice ◽  
Kevin A. Cole ◽  
Sinan Mu¨ftu¨
Keyword(s):  
Mathematical Model ◽  
Optimization Technique ◽  
Peak Height ◽  
Height Distribution ◽  
Gaussian Peak ◽  
Wide Range ◽  
Non Gaussian ◽  
Wide Speed Range ◽  
Air Film ◽  
The Mathematical Model

The traction developed between a thin flexible web, wrapped around a non-vented, rotating cylindrical roller is studied experimentally and theoretically. A series of eight webs representing a wide range of surface roughness characteristics are traction-tested against the same roller over a wide speed range. A mathematical model that couples air film pressure, web deflection, and asperity deformations is used to model the web/roller interface. An optimization technique is used to estimate the asperity compliance function parameters based on the experimental results and the mathematical model. A new model for determining the asperity engagement height, for surfaces with non-Gaussian peak height distribution, is proposed when the roughness of both surfaces is taken into account. Results are presented that indicate the viability and utility of the new methods.

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