Innovative Six Sigma Design Using the Eigenvector Dimension-Reduction (EDR) Method

2007 ◽  
Author(s):  
Lee J. Wells ◽  
Byeng D. Youn ◽  
Zhimin Xi
Keyword(s):  
Taguchi Method ◽  
Dimension Reduction ◽  
Uncertainty Propagation ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Quality Engineering ◽  
Control Factors ◽  
Current Design ◽  
Eigenvector Dimension Reduction ◽  
Mean And Variance

This paper presents an innovative approach for quality engineering using the Eigenvector Dimension Reduction (EDR) Method. Currently industry relies heavily upon the use of the Taguchi method and Signal to Noise (S/N) ratios as quality indices. However, some disadvantages of the Taguchi method exist such as, its reliance upon samples occurring at specified levels, results to be valid at only the current design point, and its expensiveness to maintain a certain level of confidence. Recently, it has been shown that the EDR method can accurately provide an analysis of variance, similar to that of the Taguchi method, but is not hindered by the aforementioned drawbacks of the Taguchi method. This is evident because the EDR method is based upon fundamental statistics, where the statistical information for each design parameter is used to estimate the uncertainty propagation through engineering systems. Therefore, the EDR method provides much more extensive capabilities than the Taguchi method, such as the ability to estimate not only mean and standard deviation of the response, but also the skewness and kurtosis. The uniqueness of the EDR method is its ability to generate the probability density function (PDF) of system performances. This capability, known as the probabilistic “what-if” study, provides a visual representation of the effects of the design parameters (e.g., its mean and variance) upon the response. In addition, the probabilistic “what-if” study can be applied across multiple design parameters, allowing the analysis of interactions among control factors. Furthermore, the implementation of the probabilistic “what-if” study provides a basis for performing robust design optimization. Because of these advantages, it is apparent that the EDR method provides an alternative platform of quality engineering to the Taguchi method. For easy execution by field engineers, the proposed platform for quality engineering using the EDR method, known as Quick Quality Quantification (Q3), will be developed as a Microsoft EXCEL add-in.

Improving the Reliability of Tube Hydroforming Process by the Taguchi Method

2005 ◽  
Author(s):  
Bing Li ◽  
T. J. Nye ◽  
Don R. Metzger
Keyword(s):  
Taguchi Method ◽  
Rapid Development ◽  
Tube Hydroforming ◽  
Design Stage ◽  
Design Parameters ◽  
Forming Parameters ◽  
Hydroforming Process ◽  
Process Output ◽  
Mean And Variance ◽  
The Mean

The tube hydroforming process has undergone extremely rapid development, especially in applications for the automobile industry. In-process variation of forming parameters such as material properties, friction conditions and part geometries will directly affect the quality of forming response by causing variation in the process output. To ensure a reliable hydroforming process at the design stage, applying robust design methodologies becomes crucial to the success of the resulting process. The reliability of the tube hydroforming process based on the tube wall thickness thinning ratio is studied in this paper. In order to improve the reliability of the process, the Taguchi method, which is capable of evaluating the effects of process variables on both the mean and variance of process output, is used to determine the optimal forming parameters for minimizing the variation and average value of the thinning ratio. The Taguchi method is applied to design experimental arrays which incorporate design (i.e., controllable) parameters and noise (i.e., non-controllable) parameters. Finite element simulation is used to analyze the virtual experiments according to the experimental arrays. Through statistical analysis, the influence of each design parameter on both the mean and variance of the thinning ratio is obtained, and is used to find the optimal combination of design parameters for minimum thinning ratio, minimum variance of thinning ratio, and maximum expected process reliability. A cross-extrusion hydroformed tube is employed as an example to illustrate the effectiveness of this approach.

Front steering design guidelines formulation for e-scooters considering the influence of sitting and standing riders on self-stability and safety performance

2021 ◽  
pp. 095440702199217
Author(s):  
Milan Paudel ◽  
Fook Fah Yap
Keyword(s):  
Preventive Measures ◽  
Recent Trend ◽  
Dynamic Performance ◽  
Design Guidelines ◽  
Safety Performance ◽  
Design Parameters ◽  
Single Track ◽  
Standing Posture ◽  
Last Mile ◽  
Current Design

E-scooters are a recent trend and are viewed as a sustainable solution to ease the first and last mile problem in modern transportation. However, an alarming rate of accidents, injuries, and fatalities have caused a significant setback for e-scooters. Many preventive measures and legislation have been put on the e-scooters, but the number of accidents and injuries has not reduced considerably. In this paper, the current design approach of e-scooters has been analyzed, and the most common range of design parameters have been identified. Thereafter, validated mathematical models have been used to quantify the performance of e-scooters and relate them with the safety aspects. Both standing and seated riders on e-scooters have been considered, and their influence on the dynamic performance has been analyzed and compared with the standard 26-in wheel reference safety bicycle. With more than 80% of the accidents and injuries occurring from falling or colliding with obstacles, this paper tries to correlate the dynamics of uncontrolled single-track vehicles with the safety performance of e-scooters. The self-stability, handling, and braking effect have been considered as major performance matrices. The analysis has shown that the current e-scooter designs are not as stable as the reference safety bicycle. Moreover, these e-scooters have been found unstable within the most common range of legislated riding velocity. The results corroborate with the general perception that the current designs of e-scooters are less stable, easy to lose control, twitchy, or wobbly to ride. Furthermore, the standing posture of the rider on the e-scooter has been found dangerous while braking to avoid any disturbances such as potholes or obstacles. Finally, the front steering design guidelines have been proposed to help modify the current design of e-scooters to improve the dynamic performance, hence the safety of the e-scooter riders and the surroundings.

Robust Compressor Blades for Desensitizing Operational Tip Clearance Variations

2014 ◽  
Author(s):  
Pranay Seshadri ◽  
Shahrokh Shahpar ◽  
Geoffrey T. Parks
Keyword(s):  
Robust Design ◽  
Total Pressure ◽  
Pressure Rise ◽  
Side Surface ◽  
Tip Clearance ◽  
Design Parameters ◽  
Compressor Blades ◽  
Robust Designs ◽  
Multi Objective ◽  
Mean And Variance

Robust design is a multi-objective optimization framework for obtaining designs that perform favorably under uncertainty. In this paper robust design is used to redesign a highly loaded, transonic rotor blade with a desensitized tip clearance. The tip gap is initially assumed to be uncertain from 0.5 to 0.85% span, and characterized by a beta distribution. This uncertainty is then fed to a multi-objective optimizer and iterated upon. For each iteration of the optimizer, 3D-RANS computations for two different tip gaps are carried out. Once the simulations are complete, stochastic collocation is used to generate mean and variance in efficiency values, which form the two optimization objectives. Two such robust design studies are carried out: one using 3D blade engineering design parameters (axial sweep, tangential lean, re-cambering and skew) and the other utilizing suction and pressure side surface perturbations (with bumps). A design is selected from each Pareto front. These designs are robust: they exhibit a greater mean efficiency and lower variance in efficiency compared to the datum blade. Both robust designs were also observed to have significantly higher aft and reduced fore tip loading. This resulted in a weaker clearance vortex, wall jet and double leakage flow, all of which lead to reduced mixed-out losses. Interestingly, the robust designs did not show an increase in total pressure at the tip. It is believed that this is due to a trade-off between fore-loading the tip and obtaining a favorable total pressure rise and higher mixed-out losses, or aft-loading the tip, obtaining a lower pressure rise and lower mixed-out losses.

Analysis of tool vibration and surface roughness during turning process of tempered steel samples using Taguchi method

2021 ◽  
pp. 095440892110019
Author(s):  
Menderes Kam ◽  
Mustafa Demirtaş
Keyword(s):  
Surface Roughness ◽  
Taguchi Method ◽  
Cutting Tools ◽  
Cutting Speed ◽  
Machining Parameters ◽  
Turning Process ◽  
Machining Time ◽  
Tool Vibration ◽  
Control Factors ◽  
Tempered Steel

This study analyzed the tool vibration (Vib) and surface roughness (Ra) during turning of AISI 4340 (34CrNiMo6) tempered steel samples using Taguchi Method. In this context, Taguchi design L18 (21 × 32) was used to analyze the experimental results. The vibration amplitude values from cutting tools were recorded for different machining parameters, control factors; two different sample hardness (46 and 53 HRc), three different cutting speeds (180, 220, 260 m.min−1), and feed rates (0.08, 0.14, 0.20 mm.rev−1) were selected. The machining parameters giving optimum Vib and Ra values were determined. Regression analysis is applied to predict values of Vib and Ra. Analysis of variance was used to determine the effects of machining parameters on the Vib and Ra values. The most important machining parameters were found to be the feed rate, sample hardness, and cutting speed for Vib and Ra, respectively. The lowest Vib and Ra values were obtained in 46 HRc sample as 0.0022 gRMS and 0.255 µm, respectively. The surface quality can be improved by reducing the sources of vibration by using appropriate machining parameters. As a result, there is a significant relationship between Ra and Vib. The lower Ra values were found during turning process of tempered steel samples according to the literature studies. It is suggested that the process can be preferred as an alternative process to grinding process due to lower cost and machining time. In application of the turning of experiment samples by ceramic cutting tool, a substantial technological and economical benefit has been observed.

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

The Optimum Cage Position and Orientation on the ALIF with Facet Screw Fixation: A Finite Element Analysis and the Taguchi Method

2011 ◽  
Vol 27 (3) ◽  
pp. 309-320 ◽  
Author(s):  
C.-Y. Fan ◽  
C.-K. Chao ◽  
C.-C. Hsu ◽  
K.-H. Chao
Keyword(s):  
Finite Element ◽  
Taguchi Method ◽  
Screw Fixation ◽  
Three Dimensional ◽  
Element Model ◽  
Lateral Position ◽  
Element Analysis ◽  
Control Factors ◽  
Position And Orientation ◽  
Noise Factors

ABSTRACTAnterior Lumbar Interbody Fusion (ALIF) has been widely used to treat internal disc degeneration. However, different cage positions and their orientations may affect the initial stability leading to different fusion results. The purpose of the present study is to investigate the optimum cage position and orientation for aiding an ALIF having a transfacet pedicle screw fixation (TFPS). A three-dimensional finite element model (ALIF with TFPS) has been developed to simulate the stability of the L4/L5 fusion segment under five different loading conditions. The Taguchi method was used to evaluate the optimized placement of the cages. Three control factors and two noise factors were included in the parameter design. The control factors included the anterior-posterior position, the medio-lateral position, and the convergent-divergent angle between the two cages. The compressive preload and the strengths of the cancellous bone were set as noise factors. From the results of the FEA and the Taguchi method, we suggest that the optimal cage positioning has a wide anterior placement, and a diverging angle between the two cages. The results show that the optimum cage position simultaneously contributes to a stronger support of the anterior column and lowers the risk of TFPS loosening.

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