scholarly journals Multi-Objective Optimization of Two-Stage Helical Gear Train Using NSGA-II

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. C. Sanghvi ◽  
A. S. Vashi ◽  
H. P. Patolia ◽  
R. G. Jivani
Keyword(s):  
Bending Strength ◽  
Gear Train ◽  
Design Parameters ◽  
Uniform Motion ◽  
Nsga Ii ◽  
Surface Fatigue ◽  
Face Width ◽  
Design Variables ◽  
Load Carrying ◽  
Do So

Gears not only transmit the motion and power satisfactorily but also can do so with uniform motion. The design of gears requires an iterative approach to optimize the design parameters that take care of kinematics aspects as well as strength aspects. Moreover, the choice of materials available for gears is limited. Owing to the complex combinations of the above facts, manual design of gears is complicated and time consuming. In this paper, the volume and load carrying capacity are optimized. Three different methodologies (i) MATLAB optimization toolbox, (ii) genetic algorithm (GA), and (iii) multiobjective optimization (NSGA-II) technique are used to solve the problem. In the first two methods, volume is minimized in the first step and then the load carrying capacities of both shafts are calculated. In the third method, the problem is treated as a multiobjective problem. For the optimization purpose, face width, module, and number of teeth are taken as design variables. Constraints are imposed on bending strength, surface fatigue strength, and interference. It is apparent from the comparison of results that the result obtained by NSGA-II is more superior than the results obtained by other methods in terms of both objectives.

Design Study of Dovetail Geometries of Turbine Blades Using Abaqus and Isight

2012 ◽  
Author(s):  
Youngwon Hahn ◽  
John I. Cofer
Keyword(s):  
Surrogate Model ◽  
High Reliability ◽  
Turbine Blades ◽  
Optimization Methods ◽  
Nonlinear Static Analysis ◽  
Design Parameters ◽  
Second Step ◽  
Nsga Ii ◽  
Python Script ◽  
Design Variables

Blades in gas and steam turbines continually face more challenging requirements for high reliability and efficiency. In order to meet these challenges in an increasingly competitive marketplace, blade design engineers are always looking for more efficient ways to design the blades in the shortest possible time and at the lowest possible cost while meeting multiple design objectives. In this paper, several design studies are performed using Abaqus and Isight to optimize the minimum contact pressure and stress around the dovetail of a typical turbine blade in order to achieved desired goals for stress levels. First, nine design parameters describing the dimensions of the dovetail are set up in a Python script which can be executed in Abaqus/CAE. The Python script generates the entire finite element model including boundary and loading conditions in Abaqus/CAE. A nonlinear static analysis considering centrifugal loading is performed in this work. After setting up the workflow using the Python script and Abaqus/CAE, Isight is used to automate the process to achieve the optimized dimensions of the dovetail. The optimization is performed in two steps. First, a surrogate model using the Optimal Latin Hypercube approximation method is created using tools in Isight. In this step, the surrogate model is used to determine the optimum values of the design variables, as well as the sensitivity of the design to the selected design variables. It also can be observed that the design is especially sensitive to five of the design variables. In the second step of the optimization, the five design variables to which the design is most sensitive are selected for further optimization by setting the other design variables to the optimized values obtained in the first step of the optimization. In this second step, several different optimization methods supported in Isight are used, including the NSGA-II non-dominated sorting genetic algorithm, Downhill Simplex, and an evolutionary optimization algorithm. Results from these methods are compared with those obtained using other common optimization methods in Isight.

Geometric displacement optimization of external helical gear pumps

2009 ◽  
Vol 223 (9) ◽  
pp. 2191-2199 ◽  
Author(s):  
K J Huang ◽  
C C Chen ◽  
Y Y Chang
Keyword(s):  
Optimization Problems ◽  
Influence Factors ◽  
Flow Characteristics ◽  
Flow Property ◽  
Helical Gear ◽  
Design Parameters ◽  
Face Width ◽  
Design Variables ◽  
Gear Pumps ◽  
Tooth Number

An approach to geometric displacement optimization of external helical gear pumps is presented. In addition, relations of pump flow property and its influence factors are also investigated. During that, only the pumps with transverse contact ratios of not less than one are discussed. First, using the involute property, an analytic representation for flowrates is deduced, by which displacements and fluctuation coefficients of helical gear pumps can be calculated accurately and efficiently. Then, by incorporating several design considerations, optimization problems for maximum geometric displacement are formulated and solved integrally by an optimization code, Multifunctional Optimization System Tool, with which various types of design variables including real, integer, and discrete can be simultaneously dealt with. Finally, the desired pumps with optimal displacement can be obtained. The proposed approach facilitates the design optimization of helical gear pumps. Moreover, influences of design parameters on the displacement and flow characteristics of the optimal pumps by assigning individual parameters are investigated. The result also concludes that the pump with a larger module, larger face width, or smaller tooth number has bigger displacement but may cause more severe flowrate fluctuation.

scholarly journals Multi-Objective Optimization of Deep Groove Ball Bearings Using Fatigue-Wear-Thermal Considerations Through Genetic Algorithms

2021 ◽  
Author(s):  
Raghavendra Rohit Dabbara ◽  
Rajiv Tiwari
Keyword(s):  
Genetic Algorithm ◽  
Dynamic Load ◽  
Maximum Temperature ◽  
Fatigue Wear ◽  
Nsga Ii ◽  
Design Variables ◽  
Deep Groove ◽  
Wide Range ◽  
Metal Metal ◽  
Load Carrying

Abstract Bearings are the key components in a wide range of machines used in different sectors of industries. Consequently, any improvement in the performance of bearings would be a step forward to extract better performance from those machines. With this motivation in mind, we selected the most common type of bearing, the Deep Groove Ball Bearing (DGBB), for optimizing its performance. Obviously, the first and foremost performance characteristic would be the dynamic load carrying capacity (CD), whose improvement directly leads to the increased service life of the bearing. We have considered two more characteristics of bearings, which we thought would have an impact on the bearings’ performance. They are elasto-hydrodynamic film thickness (hmin) and maximum temperature developed (Tmax) inside the bearing. Maximization of the lubricant thickness decreases the damage to the rolling elements and the raceways due to metal-metal contact. And minimization of temperature is desirable in every machine element. Later, we would also see that the three objective functions chosen are conflicting in nature and hence mutually independent. For the current optimization problem, a genetic algorithm, Elitist Non-dominating Sorting Genetic Algorithm (NSGA-II) is chosen. And the bearing dimensions, which could be controlled during manufacturing are chosen as the design variables. Multiple constraints are chosen based on the design space and strength considerations. The optimization algorithm is used on a set of commercially available bearings. Pareto fronts are drawn to give the designer a multitude of optimal solutions to choose from. However, in this paper, the knee-point solution is presented, which is one of the optimum solutions. When compared with the commercial bearings, the bearings with optimized dimensions have higher dynamic load carrying capacities and hence longer life. Also, the sensitivity analysis is done to check the robustness of the bearings to manufacturing tolerances in the design variables. Finally, for visualization and as a check for physical plausibility, the radial dimensions of one of the optimized bearings have been shown.

scholarly journals Optimal weight design problem of spur gears

2021 ◽  
Vol 4 (1) ◽  
pp. first
Author(s):  
Minh Nguyen ◽  
Nguyen Anh My ◽  
Le Quang Phu Vinh ◽  
Vo Thanh Binh
Keyword(s):  
Design Problem ◽  
Bending Strength ◽  
Grey Wolf Optimizer ◽  
Spur Gears ◽  
Penalty Term ◽  
Optimal Weight ◽  
Shaft Diameter ◽  
Face Width ◽  
Design Variables ◽  
Weight Design

Gear is one of the most common and important components in machinery. Evaluation on durability of gears plays crucial role in the assessment of the whole system reliability and service life. For other parts like shafts, the gears also act as loads. Therefore, dimensions and weight of the gears should be reduced as much as possible, contributing the size and weight reduction of the whole systems, which is essential to be cost-effectiveness. The current research focuses on optimal weight design problem of spur gears, such that the weight is minimized under the constraints taken from working conditions. The weight is a function of six variables, i.e. face width, shaft diameter of pinion, shaft diameter of gear, number of teeth on pinion, module and hardness. Constraints are derived based on AGMA standard and engineering handbooks, including the bending strength, the surface fatigue strength, the interference condition, the condition for uniform load distribution, the torsional strength of shaft on pinion and gear, and the center distance. The set of optimum design variables is determined by the heuristic algorithm Grey Wolf Optimizer (GWO). The accuracy and efficiency of the GWO in the optimal weight design problem of spur gears are assessed based on comparison with other popular methods, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Simulated Annealing (SA). It is noted that in previous works, some of the constraints are still violated. Therefore, a penalty term is taken into the objective function, such that any set of design variables that violates constraints will be considered as ``unfit'' by the algorithm. It is demonstrated that using the proposed approach by current work, the optimal weight and the corresponding set of design variable are very close to reference data. Yet the advantage of the proposed approach is exhibited in the fact that all of the constraints are satisfied.

Optimum design parameters and mechanical properties of polymeric nanocomposites using NSGA-II optimization method

2020 ◽  
pp. 002199832096077
Author(s):  
Mahlatse Rabothata ◽  
Jacob Muthu ◽  
Leon Wegner
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Elastic Modulus ◽  
Optimization Model ◽  
Optimization Method ◽  
Design Parameters ◽  
Published Data ◽  
Polymeric Nanocomposites ◽  
Nsga Ii ◽  
Design Variables

The aim of this work was to develop a method for optimizing both the design parameters and the mechanical properties of polymer-based nanocomposites using multi-objective optimization (MOO) methods. The objective was to maximize both the elastic modulus and the tensile strength of nanocomposites simultaneously by varying the design parameters. The Ji and Zare models were selected as the objective functions for the elastic modulus and tensile strength of polymer nanocomposites, respectively. For this purpose, the NSGA-II approach implemented in MATLAB was used to obtain optimal solutions of the design variables. The optimization model was able to successfully find optimum solutions of the design variables and the overall optimization results were found to be in good agreement with the available published data. In addition, the proposed optimization model was found to be sufficiently accurate in finding the optimum values of the design variables for improving the mechanical properties of nanocomposites.

Reliability Based Optimum Design of Gear Trains

1984 ◽  
Vol 106 (1) ◽  
pp. 17-22 ◽  
Author(s):  
S. S. Rao ◽  
G. Das
Keyword(s):  
Optimum Design ◽  
Bending Strength ◽  
Random Variables ◽  
Kinematic Chain ◽  
Gear Train ◽  
Design Parameters ◽  
Minimum Mass ◽  
Mean Values ◽  
Gear Trains ◽  
The Mean

A reliability based approach is presented for the minimum mass design of gear trains. The gear train is idealized as a weakest link kinematic chain and the optimum design is sought for a specified value of the reliability of the gear train with respect to bending strength and surface wear resistance. The design parameters such as the power transmitted, the geometric dimensions, and the material properties are treated as normally distributed random variables. A linear combination of the mean value and standard deviations of the mass of the gear train is considered as the objective function while treating the mean values of the face widths of the gears as design variables. The reliability based optimization results are compared with those obtained by the deterministic procedure. The effects of variation of parameters like the reliability of the gear train and the coefficients of variation of the random variables are also studied. The minimum mass of the gear trains is found to increase as the specified value of the reliability is increased.

scholarly journals Shear cutting induced residual stresses in involute gears and resulting tooth root bending strength of a fineblanked gear

2021 ◽  
Author(s):  
Daniel Müller ◽  
Jens Stahl ◽  
Anian Nürnberger ◽  
Roland Golle ◽  
Thomas Tobie ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Residual Stresses ◽  
Carrying Capacity ◽  
Bending Strength ◽  
Tooth Root ◽  
Load Carrying Capacity ◽  
Near Surface ◽  
Load Carrying ◽  
Involute Gears ◽  
Cut Surface

AbstractThe manufacturing of case-hardened gears usually consists of several complex and expensive steps to ensure high load carrying capacity. The load carrying capacity for the main fatigue failure modes pitting and tooth root breakage can be increased significantly by increasing the near surface compressive residual stresses. In earlier publications, different shear cutting techniques, the near-net-shape-blanking processes (NNSBP’s), were investigated regarding a favorable residual stress state. The influence of the process parameters on the amount of clean cut, surface roughness, hardness and residual stresses was investigated. Furthermore, fatigue bending tests were carried out using C-shaped specimens. This paper reports about involute gears that are manufactured by fineblanking. This NNSBP was identified as suitable based on the previous research, because it led to a high amount of clean cut and favorable residual stresses. For the fineblanked gears of S355MC (1.0976), the die edge radii were varied and the effects on the cut surface geometry, hardness distribution, surface roughness and residual stresses are investigated. The accuracy of blanking the gear geometry is measured, and the tooth root bending strength is determined in a pulsating test rig according to standardized testing methods. It is shown that it is possible to manufacture gears by fineblanking with a high precision comparable to gear hobbing. Additionally, the cut surface properties lead to an increased tooth root bending strength.

Multiobjective optimization of hard coating parameters designing for damping of the bladed disk

2017 ◽  
Vol 232 (9) ◽  
pp. 1609-1619 ◽  
Author(s):  
Yugang Chen ◽  
Jingyu Zhai ◽  
Qingkai Han
Keyword(s):  
Pareto Front ◽  
Engineering Application ◽  
Front Surface ◽  
Model Material ◽  
Superior Performance ◽  
Hard Coating ◽  
Damping Capacity ◽  
Nsga Ii ◽  
Bladed Disk ◽  
Design Variables

In this paper, the damping capacity and the structural influence of the hard coating on the given bladed disk are optimized by the non-dominated sorting genetic algorithm (NSGA-II) coupled with the Kriging surrogate model. Material and geometric parameters of the hard coating are taken as the design variables, and the loss factors, frequency variations and weight gain are considered as the objective functions. Results of the bi-objective optimization are obtained as curved line of Pareto front, and results of the triple-objective optimization are obtained as Pareto front surface with an obvious frontier. The results can give guidance to the designer, which can help to achieve more superior performance of hard coating in engineering application.

Multi-objective optimization of squirrel cage fan for range hood based on Kriging model

2021 ◽  
pp. 095440622199586
Author(s):  
Qianhao Xiao ◽  
Jun Wang ◽  
Boyan Jiang ◽  
Weigang Yang ◽  
Xiaopei Yang
Keyword(s):  
Flow Rate ◽  
Optimization Design ◽  
Volume Flow Rate ◽  
Kriging Model ◽  
Volume Flow ◽  
Design Parameters ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Squirrel Cage

In view of the multi-objective optimization design of the squirrel cage fan for the range hood, a blade parameterization method based on the quadratic non-uniform B-spline (NUBS) determined by four control points was proposed to control the outlet angle, chord length and maximum camber of the blade. Morris-Mitchell criteria were used to obtain the optimal Latin hypercube sample based on the evolutionary operation, and different subsets of sample numbers were created to study the influence of sample numbers on the multi-objective optimization results. The Kriging model, which can accurately reflect the response relationship between design variables and optimization objectives, was established. The second-generation Non-dominated Sorting Genetic algorithm (NSGA-II) was used to optimize the volume flow rate at the best efficiency point (BEP) and the maximum volume flow rate point (MVP). The results show that the design parameters corresponding to the optimization results under different sample numbers are not the same, and the fluctuation range of the optimal design parameters is related to the influence of the design parameters on the optimization objectives. Compared with the prototype, the optimized impeller increases the radial velocity of the impeller outlet, reduces the flow loss in the volute, and increases the diffusion capacity, which improves the volume flow rate, and efficiency of the range hood system under multiple working conditions.

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