A General Method for Optimum Design of Gear Boxes Through Nonlinear Programming

1989 ◽  
Author(s):  
W. L. Cleghorn ◽  
R. G. Fenton ◽  
J.-F. Fu
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Optimum Design ◽  
Random Search ◽  
Optimization Methods ◽  
Search Method ◽  
Programming Technique ◽  
Tolerance Method ◽  
The Mathematical Model ◽  
General Method

Abstract A general method for the optimum design of gear boxes is presented using a nonlinear programming technique. The mathematical model of the gear box is developed using a symbolic mathematical manipulator. Constraints of the feasible design have been included but reduced to be as few as possible. Identical optimum results were obtained through employing two different optimization methods, the flexible tolerance method and the random search method, for solving an example problem.

Optimum Design of Planar Four-Bar Linkage for Scheduled Tracks

2012 ◽  
Vol 215-216 ◽  
pp. 395-398
Author(s):  
Tian Xiang Liu ◽  
Chun Wang
Keyword(s):  
Mathematical Model ◽  
Optimum Design ◽  
Penalty Function ◽  
Function Method ◽  
Penalty Function Method ◽  
Design Efficiency ◽  
Four Bar Linkage ◽  
The Mathematical Model

The mathematical model was established, the pragram was made to optimize the lengths and angles of each link by means of inner point penalty function method. Involving 12 scheduled points, the track of a certain point on the coupler of a planar four-bar linkage was realized and previewed using Matlab. The optimum program presented here could enhance the design efficiency and insure the design accuracy markedly. By this method the coupler-curve involving more than or less than 12 points could be realized, and more complex multi-linkage could be designed.

On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor

1969 ◽  
Vol 91 (1) ◽  
pp. 115-121 ◽  
Author(s):  
G. N. Sandor ◽  
K. E. Bisshopp
Keyword(s):  
Mathematical Model ◽  
Kinematic Chain ◽  
Higher Order ◽  
Motion Generation ◽  
Rotation Tensor ◽  
Kinematic Synthesis ◽  
Rotation Operator ◽  
Key Concepts ◽  
The Mathematical Model ◽  
General Method

One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

Optimum Design of Motion Curve of Cam Mechanism with Lowest Maximum Acceleration

2011 ◽  
Vol 86 ◽  
pp. 666-669 ◽  
Author(s):  
Chuan Qiong Sun ◽  
Ai Hua Ren ◽  
Guo Xing Sun
Keyword(s):  
Mathematical Model ◽  
Failure Analysis ◽  
Optimum Design ◽  
Design Method ◽  
Maximum Acceleration ◽  
Cold Forming ◽  
Cam Mechanism ◽  
Cam Design ◽  
Set Up ◽  
The Mathematical Model

Taking case of 4500kN automatic multi-station cold forming machine clamp cam design, the mathematical model of motion curve with lowest maximum acceleration of disk cam with oscillation follower is set up on the basis of failure analysis and optimum design is carried out .A modern design method of cam motion curve is proposed in this research.

scholarly journals Optimization methods of operating costs on road transport in international transportation

2020 ◽  
Vol 11 (3) ◽  
pp. 129-133
Author(s):  
S. I. Bondariev ◽  
Keyword(s):  
Mathematical Model ◽  
Optimization Methods ◽  
Road Transport ◽  
Transport Processes ◽  
Road Transportation ◽  
The Road ◽  
Transport Services ◽  
Definition Of ◽  
The Mathematical Model ◽  
Fuel Costs

Transport processes research are closely related to the economic and operational performance of road transport. During planning road transportation, the most important factor is the transport services cost. Known fact that most of the transportation costs are car fuel. The share of car fuel in the transport tariff cost can be 25-50% (depending on the working conditions of vehicles). Therefore, research that is associated with improving the vehicles efficiency by reducing variable costs is appropriate and relevant. The article presents the results of research on the planning of transport processes in the road transport performance in international road transport for the return flight and calculating methods the demand for the amount of fuel purchased in different countries with different prices. The author presents the results of theoretical and experimental research the adequacy of the mathematical model (methodology). The specified mathematical model consists in substantiation of a technique of calculation of quantity of car fuel, definition of the variable factors influencing volumes of fuel expenses, calculation of correction factors (total) received on the basis of technical and operational indicators of vehicles and the influencing factors connected with features of road transport work. . The second part of the research contains the results of the development of an algorithm development to calculate the total cost of automotive fuel, which was purchased at different prices in several countries. Thus, the main purpose of research is the task of substantiating the algorithm (mathematical model – methodology) for determining fuel costs by the criterion of the highest use of fuel in countries at the lowest prices.

scholarly journals Разработка и исследование математической модели проектирования патрульного катера для Союза Мьянма

2020 ◽  
Author(s):  
A.I. Gaikovich ◽  
N.V. Nikitin ◽  
S. Pyae
Keyword(s):  
Mathematical Model ◽  
Search Algorithm ◽  
Load Capacity ◽  
Random Search ◽  
Design Model ◽  
Modular Architecture ◽  
Efficiency Criterion ◽  
Design Problems ◽  
The Mathematical Model ◽  
Mathematical Design

В статье описывается математические модель проектирования для обоснования концепции патрульного катера, предназначенного для Союза Мьянма. Основные кораблестроительные элементы определяются как результаты решения задачи математического программирования (оптимизации). В состав математической модели входят расчеты нагрузки, вместимости, остойчивости, ходкости, запаса плавучести. Критерием эффективности взято отношение вероятности перехвата нарушителя к приведенным годовым затратам. Для решения оптимизационной задачи используется алгоритм случайного поиска. Для реализации разработанной математической модели проектирования создан программный комплекс модульной архитектуры в оболочке DELPHI. В рамках исследования математической модели оценивалась её адекватность, чувствительность и устойчивость. Результаты исследования оказались удовлетворительными, что доказывает возможность применения разработанной математической модели для решения проектных задач на начальных стадиях разработки проекта патрульного катера.The article describes a mathematical design model to substantiate the concept of a patrol boat intended for the Union of Myanmar. The main shipbuilding elements are defined as the results of solving the problem of mathematical programming (optimization). The mathematical model includes calculations of the load, capacity, stability, propulsion, stock of buoyancy. The efficiency criterion is the ratio of the probability of interception of the intruder to the given annual costs. To solve the optimization problem, a random search algorithm is used. To implement the developed mathematical design model, a software package of modular architecture in the DELPHI shell was created. As part of the study of the mathematical model, its adequacy, sensitivity, and stability were evaluated. The research results were satisfactory, which proves the possibility of using the developed mathematical model to solve design problems in the initial stages of the design of a patrol boat project.

scholarly journals DEVELOPING EXPANDED POWELL’S ALGORITHM TO IDENTIFY THE MATHEMATICAL MODEL PARAMETERS FOR TRANSESTERIFICATION OF FISH FAT INTO BIODIESEL FUEL

2011 ◽  
Vol 14 (3) ◽  
pp. 34-48
Author(s):  
Hai Xuan Le ◽  
Anh Huynh Tuyet Le
Keyword(s):  
Mathematical Model ◽  
Random Search ◽  
Equation System ◽  
Optimal Operation ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Biodiesel Fuel ◽  
Model Parameters ◽  
Operation Conditions ◽  
The Mathematical Model

By employing the system approach methodology, this research showed the expansion of Powell’s algorithm to solve the identification of kinetic parameters in the differential equation system which describes the transesterification of fish fat into biodiesel fuel. The expanded Powell’s method is developed on the basis of the algorithm that combines Taxi-Cab method with random search method and gradient method (steepest descent method). The obtained results allow us to simulate and optimize the biodiesel fuel production in order to assess the influence of technological factors on the effect of process and to determine the optimal operation conditions. The expanded Powell’s algorithm can also be advantageously applied to simulation or optimizzation in the cases when the mathematical model of the research object contains several parameters which must be identified.

Enhancing a twist beam suspension system conceptual design using population-based optimization methods

2020 ◽  
Vol 62 (7) ◽  
pp. 672-677 ◽  
Author(s):  
E. İ. Albak ◽  
E. Solmaz ◽  
F. Öztürk
Keyword(s):  
Mathematical Model ◽  
Conceptual Design ◽  
Optimization Methods ◽  
Population Based ◽  
Least Squares Regression ◽  
Stage Design ◽  
Beam Design ◽  
Design Variables ◽  
Optimization Study ◽  
The Mathematical Model

Abstract Twist beam suspension systems are usually used in middle segment vehicles due to certain advantages. Researchers have presented many studies on both lightweight and functional twist beam design. In this paper, an optimization study is presented for enhancing the conceptual design of the twist beam by defining design variables along the twist beam as subject to vehicle handling conditions.Toe and camber angles are essential parameters that determine vehicle behavior during maneuvering. In this study, opposite wheel travel analysis is performed to represent maneuvering behavior. Therefore, while the optimization study is presented in the form of weight reduction, it is aimed to keep the toe and camber angles at certain intervals. Ant lion optimizer and mothflame optimization methods, which are population-based optimization methods, are used in the optimization phase to evaluate the performance of the new algorithms as compared with genetic algorithm in terms of robustness and correctness in the case of twist beam design. A two stage approach is introduced for presenting the optimization model and analysis. In the first stage, design space is created via the Latin hypercube method; the mathematical model is obtained via the least squares regression method. Finally, the mathematical model is solved to enhance twist beam conceptual design using recently developed population based optimization algorithms.

Fixture Optimization for Robotic Belt Grinding System

2011 ◽  
Vol 121-126 ◽  
pp. 2030-2034
Author(s):  
Dong Zhang ◽  
Chao Yun ◽  
Ling Zhang
Keyword(s):  
Mathematical Model ◽  
Optimization Methods ◽  
Belt Grinding ◽  
Robotic Grinding ◽  
The Monte Carlo Method ◽  
New Type ◽  
Set Up ◽  
Robotic Belt Grinding ◽  
The Mathematical Model ◽  
Grinding System

The precision is impacted when the robotic grinding path is discontinuous and the gripper needs to be replaced during manufacturing. In order to solve this problem, a new type PPPRRR grinding robot was proposed. The mathematical model for the robotic grinding paths was set up. The factors including the pose of the workpiece respect to the end joint and the position of contact wheel respect to the robot base frame {O}were analyzed to influence the grinding ability of the system. Base on the Monte Carlo method the posture and position factors above had been optimized, and the grinding ability of the system was increased. The optimization methods were proved right and workable by grinding golf head experiment.

scholarly journals MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS

2019 ◽  
Vol 16 (6) ◽  
pp. 706-716
Author(s):  
D. A. Tikhov-Tinnikov ◽  
V. S. Baradiev ◽  
A. I. Fedotov ◽  
A. V. Alekseev
Keyword(s):  
Mathematical Model ◽  
Optimization Methods ◽  
Force Balance ◽  
Model Description ◽  
Harmonic Mode ◽  
Elastic Suspension ◽  
Power Characteristics ◽  
Operating Modes ◽  
Rubber Bushing ◽  
The Mathematical Model

Introduction. Rubber bushings are important parts of the spring systems of modern vehicles. The properties determine not only the comfort of car movement, but also affect the elastic suspension characteristics. When a bushing is deformed, linear sections appear in characteristics. It is advisable to describe such characteristics using a mathematical model based on the classical elements of Hooke and Saint-Venant. The paper presents a mathematical description of the bushing simulation functioning results, accuracy of approach, areas of application of the mathematical model.Materials and methods. The initial data was the experimental characteristic of a cylindrical automobile rubber bushing, obtained in harmonic mode at the 0.03 to 51 Hz frequency and the 0.4 to 10 mm amplitude. The force balance of the two Hooke elements and one Saint-Venant element interacting with each other determined the mathematical model description. The authors carried out the calculations using numerical and optimization methods.Results. As a result, the authors determined functions characterizing the change in the parameters of the Hooke and Saint-Venant elements from the rubber bushings’ deformation amplitude. Moreover, the authors calculated power characteristics in the form of dependences of the rubber bushing effort and also found quantitative indicators of the reliability of the experimental data approximation by the developed mathematical model.Discussion and conclusions. The analysis of the operating modes shows the possibility of the model application to describe the rubber bushing functioning in a stationary harmonic mode with small and medium strain amplitudes. The simulation results of the Hooke’s and Saint-Venant’s parameters reveals the theoretical prerequisites for the possibility of using the model to calculate the bushing force in an unsteady mode.The authors have read and approved the final manuscript. Financial transparency: the authors have no financial interest in the presented materials or methods. There is no conflict of interest.

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