scholarly journals Approximation of a function describing a quality criterion of the thermo-mechanical fusible interfacing process

2020 ◽  
Vol 1 (2) ◽  
pp. 111-120
Author(s):  
Snezhina Andonova ◽  
Silvia Baeva
Keyword(s):  
Linear Approximation ◽  
Complex Function ◽  
Quality Criterion ◽  
Numerical Realization ◽  
Exponential Approximation ◽  
Subjective Factor ◽  
The Mathematical Model ◽  
The Relationship ◽  
Approximation Of A Function ◽  
Effective Approximation

The present work aims to investigate the function describing the relationship between a quality criterion and input factors of the thermo-mechanical fusible /TMF/ interfacing process and to derive its effective approximation. An approximation by interpolation was applied for the purpose of the study. A numerical realization of a linear and exponential approximation of the mathematical model describing the TMF interfacing process was performed. An effective linear approximation of the function connecting the quality criterion with the input factors of the TMF interfacing process was found. This creates conditions for replacing the relatively complex function (describing the TMF interfacing process) with its linear approximation. The linear approximation gives the possibility easier and faster to determine the relationships between the input factors and the quality criterion. This created conditions for ignoring the subjective factor and for optimizing and automating the studied technological process.

Temperature Influence on Performance of Oxidation Ponds

1991 ◽  
Vol 24 (5) ◽  
pp. 85-96 ◽  
Author(s):  
Qingliang Zhao ◽  
Zijie Zhang
Keyword(s):  
Mathematical Model ◽  
Temperature Influence ◽  
Field Scale ◽  
Experiment Data ◽  
Computer Technique ◽  
Oxidation Pond ◽  
Optimum Model ◽  
Oxidation Ponds ◽  
The Mathematical Model ◽  
The Relationship

By means of simulated tests of a laboratory–scale oxidation pond model, the relationship between BOD5 and temperature fluctuation was researched. Mathematical modelling for the pond's performance and K1determination were systematically described. The calculation of T–K1–CeCe/Ci) was complex but the problem was solved by utilizing computer technique in the paper, and the mathematical model which could best simulate experiment data was developed. On the basis of experiment results,the concept of plug–ratio–coefficient is also presented. Finally the optimum model recommended here was verified with the field–scale pond data.

Numerical Simulation on Velocity Profiles of Mill Bearing Lubrication

2010 ◽  
Vol 145 ◽  
pp. 282-286
Author(s):  
Qing Xue Huang ◽  
Jian Mei Wang ◽  
Yu Gui Li ◽  
Li Feng Ma ◽  
Chun Jiang Zhao
Keyword(s):  
Cross Section ◽  
Velocity Profiles ◽  
Flow State ◽  
Oil Film ◽  
Velocity Gradients ◽  
Oil Flow ◽  
The Mathematical Model ◽  
The Relationship ◽  
General Velocity ◽  
Oil Film Pressure

No 460 oil-film bearing oil as the dedicated lubricant is regarded as the incompressible Newtonian fluid. To comprehensively analyze the real oil flow state, the mathematical model on velocity profiles, together with its dimensionless equations, is established, and the calculating program is developed to simulate the 3D velocity profiles and velocity gradients at different oil flow layers. The relationship between velocity profiles and the oil film pressure is discussed, and the velocity tendency is consistent with the general velocity profile of wedge cross section. The conclusions are beneficial to the further study on lubricating performances of heavy contact components and to prolong their service lives.

scholarly journals The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles

2017 ◽  
Vol 14 (133) ◽  
pp. 20170261 ◽  
Author(s):  
Tom Shearer ◽  
Chavaunne T. Thorpe ◽  
Hazel R. C. Screen
Keyword(s):  
Flexor Tendon ◽  
Extensor Tendon ◽  
Mechanical Tension ◽  
Superficial Digital Flexor Tendon ◽  
Microstructural Model ◽  
And Function ◽  
Nonlinear Elastic ◽  
The Mathematical Model ◽  
The Relationship ◽  
Fitting Parameters

A nonlinear elastic microstructural model is used to investigate the relationship between structure and function in energy-storing and positional tendons. The model is used to fit mechanical tension test data from the equine common digital extensor tendon (CDET) and superficial digital flexor tendon (SDFT), which are used as archetypes of positional and energy-storing tendons, respectively. The fibril crimp and fascicle helix angles of the two tendon types are used as fitting parameters in the mathematical model to predict their values. The outer fibril crimp angles were predicted to be 15.1° ± 2.3° in the CDET and 15.8° ± 4.1° in the SDFT, and the average crimp angles were predicted to be 10.0° ± 1.5° in the CDET and 10.5° ± 2.7° in the SDFT. The crimp angles were not found to be statistically significantly different between the two tendon types ( p = 0.572). By contrast, the fascicle helix angles were predicted to be 7.9° ± 9.3° in the CDET and 29.1° ± 10.3° in the SDFT and were found to be statistically highly significantly different between the two tendon types ( p < 0.001). This supports previous qualitative observations that helical substructures are more likely to be found in energy-storing tendons than in positional tendons and suggests that the relative compliance of energy-storing tendons may be directly caused by these helical substructures.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

Design and Implementation of Digital Asthma Diagnosis System

2019 ◽  
Vol 14 (3) ◽  
pp. 1-15
Author(s):  
Qinghua Yao ◽  
Xiantao Yang
Keyword(s):  
Mathematical Model ◽  
Mutation Rate ◽  
Forced Expiratory Volume ◽  
Digital Signals ◽  
Respiratory Parameters ◽  
The Mathematical Model ◽  
The Relationship ◽  
Objective Indicators ◽  
Signal Conditioning Circuit

In this article, the MSP430F149 is the microcontroller (MCU), and a pressure sensor, MPX5100AP, is used to measure body measurement of maximal forced expiratory volume (FEV) and peak expiratory flow rate (PEFR). The two analog signals are processed by the signal conditioning circuit, and then the corresponding digital signals are acquired by the MCU. With the related operations of multiple respiratory parameters, a built-up time of respiration signal mutation rate values and the determination of the mutation rate, a mathematical model is built among FEV, PEFR and the rate of variation. The mathematical model of the system is analyzed, and the relationship between the detection results and the degree of airway obstruction is established. Finally, the patient's condition analysis results are given directly on the LCD, which provided the objective indicators for the medical treatment of the disease.

The Research on the Relationship between Cauchy Integral Theorem and Complex Function Integral in Mechanics of Materials

2012 ◽  
Vol 502 ◽  
pp. 120-123
Author(s):  
Xing Rong Sun
Keyword(s):  
Integral Formula ◽  
Complex Function ◽  
Residue Theorem ◽  
Cauchy Integral ◽  
Integral Theorem ◽  
Mechanics Of Materials ◽  
Cauchy Integral Theorem ◽  
Derivative Formula ◽  
Higher Order Derivative ◽  
The Relationship

This paper is the Cauchy integral theorem and integral of complex function carried out a comparative analysis, summarized in the Cauchy integral theorem and Cauchy integral formula, higher-order derivative formula, residue theorem and the relationship between the derivations to be proved, the formula can be used in these areas, such as mechanics of materials.

scholarly journals Modeling and Optimization of Bidirectional Clamping Forces in Drilling of Stacked Aluminum Alloy Plates

Materials ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 2866
Author(s):  
Jintong Liu ◽  
Anan Zhao ◽  
Piao Wan ◽  
Huiyue Dong ◽  
Yunbo Bi
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Aluminum Alloy ◽  
Clamping Force ◽  
Practical Application ◽  
Element Simulation ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
The Mathematical Model ◽  
The Relationship

Interlayer burrs formation during drilling of stacked plates is a common problem in the field of aircraft assembly. Burrs elimination requires extra deburring operations which is time-consuming and costly. An effective way to inhibit interlayer burrs is to reduce the interlayer gap by preloading clamping force. In this paper, based on the theory of plates and shells, a mathematical model of interlayer gap with bidirectional clamping forces was established. The relationship between the upper and lower clamping forces was investigated when the interlayer gap reaches zero. The optimization of the bidirectional clamping forces was performed to reduce the degree and non-uniformity of the deflections of the stacked plates. Then, the finite element simulation was conducted to verify the mathematical model. Finally, drilling experiments were carried out on 2024-T3 aluminum alloy stacked plates based on the dual-machine-based automatic drilling and riveting system. The experimental results show that the optimized bidirectional clamping forces can significantly reduce the burr heights. The work in this paper enables us to understand the effect of bidirectional clamping forces on the interlayer gap and paves the way for the practical application.

Simulation of Yarn Tension Control System Based on Simulink

2010 ◽  
Vol 426-427 ◽  
pp. 106-108 ◽  
Author(s):  
De Gong Chang ◽  
Zhi Juan Xiao ◽  
Y.H. Liu ◽  
H. Li
Keyword(s):  
Control System ◽  
Dynamic Performance ◽  
Digital Simulation ◽  
Tension Control ◽  
Structure Parameters ◽  
Yarn Tension ◽  
Magnetic Powder Brake ◽  
Tension Control System ◽  
The Mathematical Model ◽  
The Relationship

Based on the analyses of the yarn tension and the mathematical model of the magnetic powder brake, the digital simulation of the yarn tension fuzzy control system was performed by using MATLAB Simulink. The relationship between the structure parameters and the system dynamic performance was then obtained, and the system scheme was justified.

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