Mathematical model of an inadvertent stall

2018 ◽  
Vol 123 ◽  
pp. 111-120
Author(s):  
Patrycja Pacak
Keyword(s):  
Mathematical Model ◽  
Safety Concern ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Loss Of Control ◽  
Flight Phase ◽  
Rigid Plane ◽  
Basic Equations ◽  
Aircraft Accident ◽  
The Mathematical Model

This paper contains the mathematical model of an inadvertent stall as the incipient phase of a spin. Some further simplifications were included. Representation of a rigid plane was modeled as the three-dimensional movement of center of gravity. The equations of motion were presented, as well as the basic equations for the LLT method. The aerodynamic stall as the specific flight phase and the Loss of Control in Flight cause of aircraft accident sets the global safety concern that needs further actions. The created mathematical model shall be used for creating simulation algorithms for an inadvertent stall.

Research on cargo-loading optimization based on genetic and fuzzy integration

2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Distribution Center ◽  
Long Time ◽  
Low Efficiency ◽  
Decision Making Model ◽  
The Mathematical Model ◽  
Loading Scheme

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.

Simulation Investigation on Environment-Induced Pitting Corrosion on the Metal Surface

2021 ◽  
Vol 13 (5) ◽  
pp. 820-828
Author(s):  
Wei Zhang ◽  
Shengli Lv ◽  
Leijiang Yao ◽  
Xiaoyan Tong
Keyword(s):  
Mathematical Model ◽  
Pitting Corrosion ◽  
Three Dimensional ◽  
Corrosion Damage ◽  
Sudden Onset ◽  
Ion Concentration ◽  
Two Dimensional Image ◽  
Aging Aircraft ◽  
Efficient Calculation ◽  
The Mathematical Model

The prediction of corrosion damage is one of effective research methods in the safety inspection of aging aircraft structures. A mathematical model for quantifying corrosion damage is used in this paper to predict the onset of corrosion on structural surfaces exposed to aggressive environments. Based on the finite difference technique, the evolution process of local pitting corrosion on the surface of aluminum alloy in the medium is simulated, which can consider the sudden onset and the randomness of pitting corrosion. The effect of local ion concentration and oxide film damage on subsequent pitting nucleation was analyzed. Based on the efficient calculation program, the effectiveness of the mathematical model is verified by the comparison between the corrosion damage morphology and the experimental data in the literature. The results show a more widespread distribution of subsequent pits because of stronger aggressive ions are released during the life cycle of active pits and the higher diffusion coefficient of the aggressive ions. The three dimensional morphology is generated by image processing method based on the gray value of the two dimensional image of pits.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Mathematical modeling of a generic multi-profile form milling cutter

2012 ◽  
Vol 227 (5) ◽  
pp. 1036-1046 ◽  
Author(s):  
Mohammed Rajik Khan ◽  
Puneet Tandon
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Sculptured Surfaces ◽  
Three Dimensional Model ◽  
Machining Time ◽  
Milling Cutter ◽  
Machined Parts ◽  
Rotary Cutting ◽  
Three Dimensional Models ◽  
The Mathematical Model

In order to machine multiple sculptured surfaces with reduced machining time and high accuracy of the machined parts, shape design of a customised multi-point rotary cutting tool needs to be evolved. In the present work, a novel design of a generic multi-profile form milling cutter is developed for machining various multiple sculptured surfaces. This article describes in detail the mathematical model to design an accurate three-dimensional geometry of a generic multi-profile form milling cutter. Use of non-uniform rational B-spline curve(s) and sweep surfaces enables to control the shape of cutting flutes of the generic multi-profile form milling cutter. The article also discusses the methodology to develop a variety of cutters lying in the same conceptual family of multi-profile form milling cutter. To physically visualise the cutter and to show one of the downstream applications once a three-dimensional model of the cutter is available, one of the multi-profile form milling cutters is fabricated. The proposed methodology offers an intuitive high-quality mathematical model for a generic family of multi-profile form milling cutters, which is different from the traditional three-dimensional models.

Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 326-336 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
D. B. Spalding
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Combustion Process ◽  
Three Dimensional ◽  
Solution Algorithm ◽  
Physical Models ◽  
Turbulence Energy ◽  
Experimental Conditions ◽  
Diffusion Controlled ◽  
The Mathematical Model

The paper presents a mathematical model for three-dimensional, swirling, recirculating, turbulent flows inside can combustors. The present model is restricted to single-phase, diffusion-controlled combustion, with negligible radiation heat-transfer; however, the introduction of other available physical models can remove these restrictions. The mathematical model comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy, its dissipation rate, and the mean square of concentration fluctuations. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variables at all internal grid nodes. The prediction procedure, composed of the mathematical model and its solution algorithm, is applied to predict the fields of variables within a representative can combustor; the results are compared with corresponding measurements. The predicted results give the same trends as the measured ones, but the quantitative agreement is not always acceptable; this is attributed to the combustion process not being truly diffusion-controlled for the experimental conditions investigated.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

Modeling and Simulation Analysis of the Twist Drill Conical Grinding Method Based on Pro/E Software

2010 ◽  
Vol 160-162 ◽  
pp. 1680-1684
Author(s):  
Xing Jun Gao ◽  
Qing Liu ◽  
Ping Zou ◽  
Jian Song ◽  
Ping Li
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Fundamental Principle ◽  
Drilling Process ◽  
Twist Drill ◽  
Three Dimensional Modeling ◽  
Grinding Method ◽  
Dimensional Modeling ◽  
The Mathematical Model

The fundamental principle of the twist drill conical grinding method was introduced. The mathematical model of the twist drill was established. Mathematical model to establish drill bit is the geometric design, manufacture, cutting analysis and modeling on the basis of the drilling process. According to the twist drill grinding principle, using Pro/E the three-dimensional modeling of the twist drill was completed, and the feature of the conical grinding method was analyzed.

Updating the Mathematical Model of a Structure Using Vibration Data

2005 ◽  
Vol 11 (12) ◽  
pp. 1469-1486 ◽  
Author(s):  
Ashutosh Bagchi
Keyword(s):  
Mathematical Model ◽  
Model Updating ◽  
Three Dimensional ◽  
Field Tests ◽  
Mode Shapes ◽  
Actual Structure ◽  
Shell Elements ◽  
Vibration Data ◽  
The Difference ◽  
The Mathematical Model

Model updating is an important step for correlating the mathematical model of a structure to the real one. There are a variety of techniques available for model updating using dynamic and static measurements of the structure’s behavior. This paper concentrates on the model updating techniques using the natural frequencies or frequencies and mode shapes of a structure. An iterative technique is developed based on the matrix update method. The method hasbeenappliedtothefiniteelement models of a three span continuous steel free deck bridge located in western Canada. The finite element models of the bridge have been constructed using three-dimensional beam and facet shell elements and the models have been updated using the measured frequencies. From the study it is clear that the initial model needs to be built such that it represents the actual structure as closely as possible. The results demonstrate that the difference between the modal parameters from the model and field tests affect the quality of the model updating process.

scholarly journals Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

2021 ◽  
Vol 24 (4) ◽  
pp. 17-24
Author(s):  
V.M. Churkin ◽  
T.Yu. Churkina ◽  
A.M. Girin
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Body ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Spatial Motion ◽  
Mathematical Task ◽  
Spatial Movement ◽  
Elastic Thread ◽  
The Mathematical Model

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main parachute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main parachute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main parachute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and partial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

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