Single Spur Gear Reducer Optimization Design Mathematical Modeling

2013 ◽  
Vol 273 ◽  
pp. 198-202
Author(s):  
Yu Xia Wang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Optimal Design ◽  
Objective Function ◽  
Optimization Design ◽  
Spur Gear ◽  
Design Parameters ◽  
Constraint Function ◽  
Design Variables ◽  
The Mathematical Model

In a given power P, number of teeth than u, input speed and other technical conditions and requirements, find out a set of used a economic and technical indexes reach the optimal design parameters, realize the optimization design of the reducer, This paper determined unipolar standard spur gear reducer design optimization of the design variables, and then determine the objective function, determining constraint function, so as to establish the mathematical model.

Optimization Research on Dynamic Balance of Spatial Engine under Limiting Shaking Moment

2009 ◽  
Vol 626-627 ◽  
pp. 693-698
Author(s):  
Yong Yong Zhu ◽  
S.Y. Gao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Kinetic Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Dynamic Balance ◽  
Optimized Design ◽  
Design Variables ◽  
The Mathematical Model ◽  
Shaking Moment

Dynamic balance of the spatial engine is researched. By considering the special wobble-plate engine as the model of spatial RRSSC linkages, design variables on the engine structure are confirmed based on the configuration characters and kinetic analysis of wobble-plate engine. In order to control the vibration of the engine frame and to decrease noise caused by the spatial engine, objective function is choosed as the dimensionless combinations of the various shaking forces and moments, the restriction condition of which presents limiting the percent of shaking moment. Then the optimization design is investigated by the mathematical model for dynamic balance. By use of the optimization design method to a type of wobble-plate engine, the optimization process as an example is demonstrated, it shows that the optimized design method benefits to control vibration and noise on the engines and improve the performance practically and theoretically.

Optimization Design of Large-Scale Cross-Roller Slewing Bearing Used in Special Propeller

2011 ◽  
Vol 48-49 ◽  
pp. 787-792 ◽  
Author(s):  
Gang Zhang ◽  
Xue Zhang ◽  
Kai Feng Zhou ◽  
Juan Ruan ◽  
De De Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Objective Function ◽  
Design Process ◽  
Optimization Design ◽  
Large Scale ◽  
Function Optimization ◽  
Design Model ◽  
Slewing Bearing ◽  
The Mathematical Model

According to the working requirement of large-scale cross roller slewing bearing used in special propeller, an optimal design model which includes objective function, optimization variables and constraints is established, and uses genetic toolbox of the Matlab software to solve the mathematical model. An example shows that the bearing’s life is improved significantly by the optimization. It indicates that the optimization design has some guidance significance in the design process of the slewing bearing.

The Effect of Different Optimization Methods on Robustness for Robust Optimization Design

2014 ◽  
Vol 721 ◽  
pp. 464-467
Author(s):  
Tao Fu ◽  
Qin Zhong Gong ◽  
Da Zhen Wang
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Parameters ◽  
Hybrid Particle Swarm Optimization ◽  
Design Variables ◽  
Robust Optimization Design

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

Study of Parameters Optimization on Seismic Isolated Railway Bridges

2011 ◽  
Vol 50-51 ◽  
pp. 135-139
Author(s):  
Tie Yi Zhong ◽  
Chao Yi Xia ◽  
Feng Li Yang
Keyword(s):  
Optimal Design ◽  
Optimization Design ◽  
Seismic Isolation ◽  
Optimization Method ◽  
Relative Displacement ◽  
Parameters Optimization ◽  
Design Parameters ◽  
Isolation System ◽  
Railway Bridges ◽  
Design Variables

Based on optimization theories, considering soil-structure interaction and running safety, the optimal design model of the seismic isolation system with lead-rubber bearings (LRB) for a simply supported railway beam bridge is established by using the first order optimization method in ANSYS, which the parameters of the isolation bearing are taken as design variables and the maximum moments at the bottom of bridge piers are taken as objective functions. The optimal calculations are carried out under the excitation of three practical earthquake waves respectively. The research results show that the ratio of the stiffness after yielding to the stiffness before yielding has important effect on the structural seismic responses. Through the optimal analysis of isolated bridge system, the optimal design parameters of isolation bearing can be determined properly, and the seismic forces can be reduced maximally as meeting with the limits of relative displacement between pier top and beam, which provides efficient paths and beneficial references for dynamic optimization design of seismic isolated bridges.

The Equivalent Variation and Optimization Design of the Operating Mechanism of the Harvester

2013 ◽  
Vol 373-375 ◽  
pp. 7-11
Author(s):  
Lei Lu ◽  
Kang Luo ◽  
Qiang Wang ◽  
Hua Chen
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Optimization Design ◽  
Engineering Problem ◽  
Operating Mechanism ◽  
Brake Pedal ◽  
Optimal Solutions ◽  
The Operating Mechanism ◽  
The Mathematical Model ◽  
Equivalent Mechanism

In this paper, an equivalent mechanism is obtained by means of optimal design to overcome the drawbacks of an existing brake pedal operating mechanism in a harvester. After establishing the mathematical model, we obtain the optimal design model, including the objective and constraint functions. Consequently the local optimal solutions are worked out, resulting in a solution for the applied engineering problem.

A New Approach to Solving Reliability Optimization Design of Gear Box

2011 ◽  
Vol 295-297 ◽  
pp. 1326-1329
Author(s):  
Wen Hui Mo
Keyword(s):  
Objective Function ◽  
Material Properties ◽  
Optimization Design ◽  
Random Variables ◽  
Design Parameters ◽  
Reliability Optimization ◽  
New Approach ◽  
Reliability Calculation ◽  
Design Variables ◽  
Gear Box

Reliability optimization design of the gear box is proposed. It includes an objective function, 30 design variables and 52 constraints. It is important to note that material properties, geometry parameters and applied loads of the structure are assumed to be normal random variables. Reliability calculation adopts the HL-RF method. The comparison of design parameters demonstrates the proposed method.

The Optimization Design on Transmission Mechanism of Tightening Machine

2014 ◽  
Vol 621 ◽  
pp. 227-232
Author(s):  
Quan Ying Sun ◽  
Yi Li Wang ◽  
Xiu Li Meng ◽  
Xiao Dong Yu
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Design ◽  
Optimal Solution ◽  
Planetary Gear ◽  
Transmission Mechanism ◽  
Minimum Volume ◽  
Sqp Method ◽  
Design Variables

This article, to optimize the transmission mechanism of tightening machine, select the involute planetary gear with two teeth differences a research object, determine the design variables about modification coefficient, modulus and tooth thickness, based on the target of having the minimum volume, a mathematical model of optimization was established, the optimal solution of the objective function is obtained by using the SQP method on fmincon function of optimization toolbox of Matlab. The results showed, the volume of pinion decreased 15% after optimizated, the volume of the corresponding gear will also greatly reduced, achieved the optimization goal.

scholarly journals A Two-Round Optimization Design Method for Aerostatic Spindles Considering the Fluid–Structure Interaction Effect

2021 ◽  
Vol 11 (7) ◽  
pp. 3017
Author(s):  
Qiang Gao ◽  
Siyu Gao ◽  
Lihua Lu ◽  
Min Zhu ◽  
Feihu Zhang
Keyword(s):  
Optimal Design ◽  
Optimization Design ◽  
Design Method ◽  
Fluid Structure Interaction ◽  
Design Procedure ◽  
Design Parameters ◽  
Geometrical Parameters ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Aerostatic Spindle

The fluid–structure interaction (FSI) effect has a significant impact on the static and dynamic performance of aerostatic spindles, which should be fully considered when developing a new product. To enhance the overall performance of aerostatic spindles, a two-round optimization design method for aerostatic spindles considering the FSI effect is proposed in this article. An aerostatic spindle is optimized to elaborate the design procedure of the proposed method. In the first-round design, the geometrical parameters of the aerostatic bearing were optimized to improve its stiffness. Then, the key structural dimension of the aerostatic spindle is optimized in the second-round design to improve the natural frequency of the spindle. Finally, optimal design parameters are acquired and experimentally verified. This research guides the optimal design of aerostatic spindles considering the FSI effect.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

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