Multi-Objective Robust Optimization of Deep Groove Ball Bearings Considering Manufacturing Tolerances Based on Fatigue and Wear Considerations

2021 ◽  
pp. 1-43
Author(s):  
Md Saif Ahmad ◽  
Rajiv Tiwari ◽  
Twinkle Mandawat
Keyword(s):  
Objective Function ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Objective Functions ◽  
Dynamic Capacity ◽  
Multi Objective ◽  
Design Variables ◽  
Deep Groove ◽  
Rolling Element ◽  
Manufacturing Tolerances

Abstract In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein deep groove ball bearings has been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have minimum effect on the objective function, i.e. its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, lubrication, manufacturing accuracy, material quality, etc. and thus the dynamic capacity and elasto-hydrodynamic minimum film thickness has been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter and bearing width for the case of deep groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients and, the number of rolling elements. These five internal geometrical parameters are taken as design variables, moreover five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometrical and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). NSGA-II (non-dominated sorting genetic algorithm) has been used as the optimization tool. Pareto optimal fronts are obtained for one of the bearings. Out of many points on the Pareto-front, only the knee solutions have been presented in the tables. This work shows that geometrically feasible bearings can be designed by optimizing multiple objective functions simultaneously and also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

scholarly journals Multi-objective Informative Frequency Band Selection Based on Negentropy-induced Grey Wolf Optimizer for Fault Diagnosis of Rolling Element Bearings

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1845 ◽  
Author(s):  
Xiaohui Gu ◽  
Shaopu Yang ◽  
Yongqiang Liu ◽  
Rujiang Hao ◽  
Zechao Liu
Keyword(s):  
Frequency Band ◽  
Background Noise ◽  
Grey Wolf Optimizer ◽  
Data Sets ◽  
Rolling Element Bearings ◽  
Grey Wolf ◽  
Objective Functions ◽  
Multi Objective ◽  
Rolling Element ◽  
Envelope Spectrum

Informative frequency band (IFB) selection is a challenging task in envelope analysis for the localized fault detection of rolling element bearings. In previous studies, it was often conducted with a single indicator, such as kurtosis, etc., to guide the automatic selection. However, in some cases, it is difficult for that to fully depict and balance the fault characters from impulsiveness and cyclostationarity of the repetitive transients. To solve this problem, a novel negentropy-induced multi-objective optimized wavelet filter is proposed in this paper. The wavelet parameters are determined by a grey wolf optimizer with two independent objective functions i.e., maximizing the negentropy of squared envelope and squared envelope spectrum to capture impulsiveness and cyclostationarity, respectively. Subsequently, the average negentropy is utilized in identifying the IFB from the obtained Pareto set, which are non-dominated by other solutions to balance the impulsive and cyclostationary features and eliminate the background noise. Two cases of real vibration signals with slight bearing faults are applied in order to evaluate the performance of the proposed methodology, and the results demonstrate its effectiveness over some fast and optimal filtering methods. In addition, its stability in tracking the IFB is also tested by a case of condition monitoring data sets.

Optimum design of rolling element bearings using a genetic algorithm—differential evolution (GA—DE) hybrid algorithm

2010 ◽  
Vol 225 (3) ◽  
pp. 714-721 ◽  
Author(s):  
W Y Lin
Keyword(s):  
Genetic Algorithm ◽  
Differential Evolution ◽  
Objective Function ◽  
Optimum Design ◽  
Dynamic Loads ◽  
Representative Case ◽  
De Algorithm ◽  
Design Variables ◽  
Deep Groove ◽  
Rolling Element

Binary-code genetic algorithms (BGA) have been used to obtain the optimum design for deep groove ball bearings, based on maximum fatigue life as an objective function. The problem has ten design variables and 20 constraint conditions. This method can find better basic dynamic loads rating than those listed in standard catalogues. However, the BGA algorithm requires a tremendous number of evaluations of the objective function per case to achieve convergence (e.g. about 5 200 000 for a representative case). To overcome this difficulty, a hybrid evolutionary algorithm by combining real-valued genetic algorithm (GA) with differential evolution (DE) is used together with the proper handling of constraints for this optimum design task. Findings show that the GA—DE algorithm can successfully find the better dynamic loads rating, about 1.3—11.1 per cent higher than those obtained using the traditional BGA. Moreover, the mean number of evaluations of the objective function required to achieve convergence is about 3011, using the GA—DE algorithm, as opposed to about 5 200 000 for a representative case using the BGA. Comparison shows the GA—DE algorithm to be much more effective and efficient than the BGA.

Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Multi-Objective Design Optimization of a Mixed-Flow Pump

2009 ◽  
Author(s):  
Yumiko Takayama ◽  
Hiroyoshi Watanabe
Keyword(s):  
Performance Characteristic ◽  
Performance Characteristics ◽  
Inverse Design ◽  
Surface Model ◽  
Objective Functions ◽  
Mixed Flow ◽  
Multi Objective ◽  
Design Variables ◽  
Flow Head ◽  
Flow Pump

In most cases of high specific speed mixed-flow pump applications, it is necessary to satisfy more than one performance characteristic such as deign point efficiency, shut-off power/head and non-stall characteristic (no positive slope in flow-head curve). However, it is known that these performance characteristics are in relation of trade-offs. As a result, it is difficult to optimize these performance characteristics by conventional way such as trial and error approach by modifying geometrical parameters. This paper presents the results of the multi-objective optimization strategy of mixed-flow pump design by means of three dimensional inverse design approach, Computational Fluid Dynamics (CFD), Design of Experiments (DoE), response surface model (RSM) and Multi Objective Genetic Algorism (MOGA). The parameters to control blade loading distributions and meridional geometries for impeller and diffuser blades in inverse design were chosen as design variables of the optimization process. Pump efficiency, maximum slope in flow-head curve and shut-off power/head were selected as objective functions. Objective functions of pumps, designed by design variables specified in DoE, were evaluated by using CFD. Then, trade-off relations between objective functions were analyzed by using Pareto fronts obtained by MOGA. Some pumps which have specific performance characteristic (non-stall, low shut-off power, high efficiency etc.) designed along the Pareto front were numerically evaluated.

Optimal design of a parallel robotic gripper using enhanced multi-objective ant lion optimizer with a sensitivity analysis approach

2020 ◽  
Vol 40 (5) ◽  
pp. 703-721
Author(s):  
Golak Bihari Mahanta ◽  
Deepak BBVL ◽  
Bibhuti B. Biswal ◽  
Amruta Rout
Keyword(s):  
Sensitivity Analysis ◽  
Distribution Function ◽  
Design Parameters ◽  
Objective Functions ◽  
Content Type ◽  
Multi Objective ◽  
The Past ◽  
Design Variables ◽  
Pick And Place ◽  
Ant Lion

Purpose From the past few decades, parallel grippers are used successfully in the automation industries for performing various pick and place jobs due to their simple design, reliable nature and its economic feasibility. So, the purpose of this paperis to design a suitable gripper with appropriate design parameters for better performance in the robotic production systems. Design/methodology/approach In this paper, an enhanced multi-objective ant lion algorithm is introduced to find the optimal geometric and design variables of a parallel gripper. The considered robotic gripper systems are evaluated by considering three objective functions while satisfying eight constraint equations. The beta distribution function is introduced for generating the initial random number at the initialization phase of the proposed algorithm as a replacement of uniform distribution function. A local search algorithm, namely, achievement scalarizing function with multi-criteria decision-making technique and beta distribution are used to enhance the existing optimizer to evaluate the optimal gripper design problem. In this study, the newly proposed enhanced optimizer to obtain the optimum design condition of the design variables is called enhanced multi-objective ant lion optimizer. Findings This study aims to obtain optimal design parameters of the parallel gripper with the help of the developed algorithms. The acquired results are investigated with the past research paper conducted in that field for comparison. It is observed that the suggested method to get the best gripper arrangement and variables of the parallel gripper mechanism outperform its counterparts. The effects of the design variables are needed to be studied for a better design approach concerning the objective functions, which is achieved by sensitivity analysis. Practical implications The developed gripper is feasible to use in the assembly operation, as well as in other pick and place operations in different industries. Originality/value In this study, the problem to find the optimum design parameter (i.e. geometric parameters such as length of the link and parallel gripper joint angles) is addressed as a multi-objective optimization. The obtained results from the execution of the algorithm are evaluated using the performance indicator algorithm and a sensitivity analysis is introduced to validate the effects of the design variables. The obtained optimal parameters are used to develop a gripper prototype, which will be used for the assembly process.

Comprehensive Satisfactory Design Method for Product Designs

2001 ◽  
Author(s):  
Eiji Adachi
Keyword(s):  
Decision Making ◽  
Design Method ◽  
Simultaneous Equations ◽  
Objective Functions ◽  
Identification Methods ◽  
Multi Objective ◽  
Sensitivity Coefficients ◽  
Design Variables ◽  
Computer Aided ◽  
Market Needs

Abstract Actual product designs aim to fulfill all product requirements of market needs and wants, which are technical or non-technical, logical or illogical, objective or subjective, and quantitative or qualitative. The actual product designs are objective-aiming designs and can be supposed to be multi-objective satisfactory designs with heterogeneous objective functions and dimensional design variables. To realize computer-aided product designs which can obtain rational and satisfactory solutions, we classify the objective functions and contrive methods to deal with non-theoretical, non-technical, subjective, or illogical objective functions as well. This paper shows all of our methods, including an expression of heterogeneous objective functions which consists of objective and evaluated values, a satisfactory design method by simultaneous equations which searches solutions sequentially, identification methods of non-theoretical or non-technical objective functions and sensitivity coefficients for the simultaneous equations, a decision-making method of promising solutions to fulfill product requirements, and also numerical applications of these methods to actual product designs.

Towards Uniformly Distributed Compliance in Compliant Mechanisms: A Multi-Objective Approach

2006 ◽  
Author(s):  
Stephen L. Canfield ◽  
Daniel L. Chlarson ◽  
Alexander Shibakov ◽  
Patrick V. Hull
Keyword(s):  
Finite Element ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Optimality Criteria ◽  
Optimal Designs ◽  
Limiting Factors ◽  
Objective Functions ◽  
Multi Objective ◽  
Simple Addition ◽  
Current Formulation

Researchers in the field of optimal synthesis of compliant mechanisms have been working to develop tools that yield distributed compliant devices to perform specific tasks. However, it has been demonstrated in the literature that much of this work has resulted in mechanisms that localize compliance rather than distribute it as desired. In fact, Yin and Ananthasuresh (2003) [1] demonstrate that based on the current formulation of optimality criteria and analysis via the finite element (FE) technique, a lumped compliant device will always exist as the minimizing solution to the objective function. The addition of constraints on allowable strain simply moves the solution back from this objective. Therefore, modification to the standard optimality criteria needs to take place. Yin and Ananthasuresh [1] proposed and compared several approaches that include distributivity-based measures within the optimality criteria, and demonstrated the effectiveness of this approach. In this paper, the authors propose to build on this problem. In a similar manner, a general approach to the topology synthesis problem will be suggested to yield mechanisms in which the compliance is distributed throughout the device. This work will be based on the idea of including compliance distribution directly within the objective functions, while addressing some of the potential limiting factors in past approaches. The technique will be generalized to allow simple addition of criteria in the future, and to deliver optimal designs through to manufacture. This work will first revisit and propose several quantitative definitions for distributed compliant devices. Then, a multi-objective formulation based on a non-dominating sort and Pareto set method will be incorporated that will provide information on the nature of the problem and compatibility of employed objective functions.

Sign in / Sign up

Export Citation Format

Share Document