On the Use of the Cumulative Distribution Function for Large-Scale Tolerance Analyses Applied to Electric Machine Design

In the field of electrical machine design, excellent performance for multiple objectives, like efficiency or torque density, can be reached by using contemporary optimization techniques. Unfortunately, highly optimized designs are prone to be rather sensitive regarding uncertainties in the design parameters. This paper introduces an approach to rate the sensitivity of designs with a large number of tolerance-affected parameters using cumulative distribution functions (CDFs) based on finite element analysis results. The accuracy of the CDFs is estimated using the Dvoretzky–Kiefer–Wolfowitz inequality, as well as the bootstrapping method. The advantage of the presented technique is that computational time can be kept low, even for complex problems. As a demanding test case, the effect of imperfect permanent magnets on the cogging torque of a Vernier machine with 192 tolerance-affected parameters is investigated. Results reveal that for this problem, a reliable statement about the robustness can already be made with 1000 finite element calculations.

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A Step-by-Step Procedure to Perform Preliminary Designs of Salient-Pole Synchronous Generators

Energies ◽

10.3390/en14164989 ◽

2021 ◽

Vol 14 (16) ◽

pp. 4989

Author(s):

Thiago de Paula Machado Bazzo ◽

Vinicius de Oliveira Moura ◽

Renato Carlson

Keyword(s):

Finite Element ◽

Finite Element Simulation ◽

Machine Design ◽

Synchronous Machines ◽

Design Parameters ◽

Electrical Machine ◽

Synchronous Generators ◽

Salient Pole ◽

Element Simulation ◽

Step Procedure

This paper presents a straightforward step-by-step procedure to design salient-pole synchronous generators, starting with its main specifications and finishing with all necessary data to put it on production. As most of the electricity is generated by synchronous generators, the design of these machines remains an interesting subject, but, although it is important, it is difficult to find a complete step-by-step procedure in the literature. The proposed procedure can be followed by an electrical engineer or student and, distinctively from most papers and books, all steps are presented. Such a procedure is based on analytic calculations, eventually relying on finite element simulation to verify if everything is all right and to adjust some design parameters. All calculations have been chosen to keep the design as simple as possible; otherwise, it would not be possible to present all steps and procedures. Therefore, it can be used for beginners in the art of design-synchronous generators, applied to obtain an initial design, or be adopted by any electrical engineering course, not only aiming to be an introductory electrical machine design course but mainly to enhance the students’ comprehension of synchronous machines. The results have been compared with finite element simulation, presenting very small differences.

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Probabilistic finite element analysis in heat transfer to a nuclear fuel rod bumper support

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406042690425 ◽

2004 ◽

Vol 218 (12) ◽

pp. 1499-1505

Author(s):

Rama Subba Reddy Gorla

Keyword(s):

Heat Transfer ◽

Finite Element ◽

Nuclear Fuel ◽

Cost Effective ◽

Distribution Functions ◽

Cumulative Distribution ◽

Element Analysis ◽

Transfer Rates ◽

Fuel Rod ◽

Design Variables

Heat transfer from a nuclear fuel rod bumper support was computationally simulated by a finite element method and probabilistically evaluated in view of the several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for overall heat transfer rates due to the thermodynamic random variables. These results can be used to identify quickly the most critical design variables in order to optimize the design and to make it cost effective. The analysis leads to the selection of the appropriate measurements to be used in heat transfer and to the identification of both the most critical measurements and the parameters.

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Probabilistic downscaling of precipitation data in a subtropical mountain area: a two-step approach

Nonlinear Processes in Geophysics ◽

10.5194/npg-18-223-2011 ◽

2011 ◽

Vol 18 (2) ◽

pp. 223-234 ◽

Cited By ~ 8

Author(s):

R. Haas ◽

K. Born

Keyword(s):

Complex Terrain ◽

Large Scale ◽

Distribution Functions ◽

Data Availability ◽

Cumulative Distribution ◽

Second Step ◽

Mountain Area ◽

Investigation Area ◽

Distribution Parameters ◽

Mountain Environment

Abstract. In this study, a two-step probabilistic downscaling approach is introduced and evaluated. The method is exemplarily applied on precipitation observations in the subtropical mountain environment of the High Atlas in Morocco. The challenge is to deal with a complex terrain, heavily skewed precipitation distributions and a sparse amount of data, both spatial and temporal. In the first step of the approach, a transfer function between distributions of large-scale predictors and of local observations is derived. The aim is to forecast cumulative distribution functions with parameters from known data. In order to interpolate between sites, the second step applies multiple linear regression on distribution parameters of observed data using local topographic information. By combining both steps, a prediction at every point of the investigation area is achieved. Both steps and their combination are assessed by cross-validation and by splitting the available dataset into a trainings- and a validation-subset. Due to the estimated quantiles and probabilities of zero daily precipitation, this approach is found to be adequate for application even in areas with difficult topographic circumstances and low data availability.

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Efficient Prediction of Contact Behavior in a 6-High Rolling Mill With Continuously Variable Crown Intermediate Rolls

Volume 1: Processes ◽

10.1115/msec2017-3058 ◽

2017 ◽

Author(s):

Feng Zhang ◽

Arif S. Malik

Keyword(s):

Finite Element ◽

Large Scale ◽

Mixed Finite Element ◽

Mixed Finite Element Method ◽

High Strength ◽

Computational Time ◽

Ferrous Alloys ◽

Thickness Profile ◽

Wide Range ◽

Contact Force Distribution

Continuously Variable Crown (CVC) shifting mechanisms represent a control technology with wide range of capability to influence the thickness profile and flatness (shape) of metal strip and sheet in rolling-type manufacturing processes. Further, because of the efficiency and extensive control capability to operate on thin-gauge, high-strength ferrous alloys, the 6-high mill with CVC profiles machined onto the intermediate rolls (IR) represents a popular mill configuration. This is because of the large control range for the strip thickness profile and flatness, which results from lateral shifting of the CVC intermediate rolls. However, together with this efficiency and capability comes very complex contact behaviors between the rolls and strip, including highly non-linear contact force distribution, loss of contact, asymmetric roll wear, unwanted strip wedge profiles, and the need to apply corrective roll tilting. Therefore, for most effective industry use of 6-high mills with intermediate roll CVC shifting, a rapid and accurate mathematical rolling model is needed to predict and account for these complex contact behaviors. This paper introduces an efficient roll-stack computational model capable of simulating such rolling mills under steady-state conditions. The model formulation applies the simplified mixed finite element method (SM-FEM), which is adapted to simulate asymmetric 6-high CVC mill contact behaviors. Results for a specific case study compare favorably to those obtained from a large-scale commercial finite element simulation, yet require a small fraction of the associated computational time and effort.

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A new stochastic analysis method for mechanical components

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212467735 ◽

2012 ◽

Vol 227 (8) ◽

pp. 1818-1829 ◽

Cited By ~ 2

Author(s):

YL Zhang ◽

YM Zhang

Keyword(s):

Finite Element ◽

Dimension Reduction ◽

Probability Density ◽

Maximum Entropy ◽

Maximum Entropy Principle ◽

Distribution Functions ◽

Cumulative Distribution ◽

Entropy Principle ◽

Input Variables ◽

First Four Moments

Univariate dimension-reduction integration, maximum entropy principle, and finite element method are employed to present a computational procedure for estimating probability densities and distributions of stochastic responses of structures. The proposed procedure can be described as follows: 1. Choose input variables and corresponding distributions. 2. Calculate the integration points and perform finite element analysis. 3. Calculate the first four moments of structural responses by univariate dimension-reduction integration. 4. Estimate probability density function and cumulative distribution function of responses by maximum entropy principle. Numerical integration formulas are obtained for non-normal distributions. The non-normal input variables need not to be transformed into equivalent normal ones. Three numerical examples involving explicit performance functions and solid mechanic problems without explicit performance functions are used to illustrate the proposed procedure. Accuracy and efficiency of the proposed procedure are demonstrated by comparisons of the estimated probability density functions and cumulative distribution functions obtained by maximum entropy principle and Monte Carlo simulation.

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Finite-Element Analysis of the Magnetic Field in a Magnetic Gear Mechanism

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.479-480.230 ◽

2013 ◽

Vol 479-480 ◽

pp. 230-233

Author(s):

Yi Chang Wu ◽

Bo Syuan Jian

Keyword(s):

Magnetic Field ◽

Finite Element Analysis ◽

Finite Element ◽

Permanent Magnets ◽

Design Parameters ◽

Element Analysis ◽

Magnetostatic Field ◽

Gear Mechanism ◽

Magnetic Gear ◽

The Magnetic Field

This paper presents finite-element analysis (FEA) of the magnetic field of a magnetic gear mechanism. An external type magnetic gear mechanism, which consists of two identical magnetic gears with sector-shaped permanent magnets, is introduced first. Then, the magnetostatic field distribution and transmitted torque of the magnetic gear mechanism are simulated by a commercial FEA package Ansoft/ Maxwell. Next, the effects of design parameters, including the air-gap length, the number of magnetic pole pairs, and the height of permanent magnets, on the maximum transmitted torque are discussed. The results of this work are beneficial to the design of magnetic gear mechanisms.

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Optimum Design of Tractor Clutch PTO Finger by Using Topology and Shape Optimization

Volume 9: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2015-52008 ◽

2015 ◽

Cited By ~ 1

Author(s):

O. Dogan ◽

F. Karpat ◽

N. Kaya ◽

C. Yuce ◽

M. O. Genc ◽

...

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Topology Optimization ◽

Shape Optimization ◽

Optimization Techniques ◽

Design Parameters ◽

Agricultural Activities ◽

Element Analysis ◽

Design Life ◽

Topology And Shape Optimization

Tractors are one of the most important agricultural machinery in the world. They provide agricultural activities in challenging conditions by using various agricultural machineries which are added on them. Therefore, there has been a rising demand for tractor use for agricultural activities. During the power transmission, tractor clutches are exposed to high static and cyclic loading directly. Thus, most of clutch parts fail before completing their design life which is under 106 cycles. Especially, because of the high stress, there are a number of fractures and breakages are observed around the pin area of the finger mechanisms. Due to these reasons, it is necessary to re-design these fingers by using modern optimization techniques and finite element analysis. This paper presents an approach for analysis and re-designs process of tractor clutch PTO finger. Firstly, the original designs of the PTO fingers are analyzed by using finite element analysis. Static structural analyses are applied on these fingers by using ANSYS static structural module. The boundary conditions are determined according to the data from the axial fatigue test bench. Afterwards, the stress-life based fatigue analyses are performed with respect to Goodman criterion. It is seem that the original design of the PTO finger, failed before the design life. Hence, the PTO finger is completely re-designed by using topology and shape optimization methods. Topology optimization is used to find the optimum material distribution of the PTO fingers. Topology optimization is performed in solidThinking Inspire software. The precise dimensions of the PTO fingers are determined by using shape optimization and response surface methodology. Two different design parameters, which are finger thickness and height, are selected for design of experiment and 15 various cases are analyzed. By using DOE method three different equations are obtained which are maximum stresses, mass, and displacement depending on the selected design parameters. These equations are used in the optimization as objective and constraint equations in MATLAB. The results indicate that the proposed models predict the responses adequately within the limits of the parameters being used. The final dimensions of the fingers are determined after shape optimization. The new designs of the PTO fingers are re-analyzed in terms of static and fatigue analysis. The new design of the PTO finger passed the analysis successfully. As a result of the study, the finger mass is increased 7% but it is quite small. Maximum Equivalent Von-Misses stress reduction of 25.3% is achieved. Fatigue durability of the PTO finger is improved 53.2%. The rigidity is improved up to 27.9% compared to the initial design. The optimal results show that the developed method can be used to design a durable, low manufacturing cost and lightweight clutch parts.

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The Influence of PBL Parameterization on the Practical Predictability of Convection Initiation during the Mesoscale Predictability Experiment (MPEX)

Weather and Forecasting ◽

10.1175/waf-d-16-0174.1 ◽

2017 ◽

Vol 32 (3) ◽

pp. 1161-1183 ◽

Cited By ~ 10

Author(s):

Bryan M. Burlingame ◽

Clark Evans ◽

Paul J. Roebber

Keyword(s):

Large Scale ◽

Distribution Functions ◽

Forecast Skill ◽

Cumulative Distribution ◽

Spatial Error ◽

Error Distributions ◽

Pbl Parameterization ◽

Large Scale Flow ◽

Planetary Boundary Layer Parameterization ◽

Convection Initiation

Abstract This study evaluates the influence of planetary boundary layer parameterization on short-range (0–15 h) convection initiation (CI) forecasts within convection-allowing ensembles that utilize subsynoptic-scale observations collected during the Mesoscale Predictability Experiment. Three cases, 19–20 May, 31 May–1 June, and 8–9 June 2013, are considered, each characterized by a different large-scale flow pattern. An object-based method is used to verify and analyze CI forecasts. Local mixing parameterizations have, relative to nonlocal mixing parameterizations, higher probabilities of detection but also higher false alarm ratios, such that the ensemble mean forecast skill only subtly varied between parameterizations considered. Temporal error distributions associated with matched events are approximately normal around a zero mean, suggesting little systematic timing bias. Spatial error distributions are skewed, with average mean (median) distance errors of approximately 44 km (28 km). Matched event cumulative distribution functions suggest limited forecast skill increases beyond temporal and spatial thresholds of 1 h and 100 km, respectively. Forecast skill variation is greatest between cases with smaller variation between PBL parameterizations or between individual ensemble members for a given case, implying greatest control on CI forecast skill by larger-scale features than PBL parameterization. In agreement with previous studies, local mixing parameterizations tend to produce simulated boundary layers that are too shallow, cool, and moist, while nonlocal mixing parameterizations tend to be deeper, warmer, and drier. Forecasts poorly resolve strong capping inversions across all parameterizations, which is hypothesized to result primarily from implicit numerical diffusion associated with the default finite-differencing formulation for vertical advection used herein.

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Structural Design Optimization of Side/Rear Impact Guards Using a Coupled Genetic Algorithm Finite Element Method

Transportation: Transportation and Environment ◽

10.1115/imece2004-62270 ◽

2004 ◽

Author(s):

De-Shin Liu ◽

Nan-Chun Lin ◽

Chao-Chin Huang ◽

Yin-Lee Meng

Keyword(s):

Genetic Algorithm ◽

Finite Element ◽

Optimal Design ◽

Computational Time ◽

Design Parameters ◽

Fe Model ◽

Passenger Cars ◽

Rear Impact ◽

Structural Design Optimization ◽

Energy Absorbing

Underride protective structure can reduce serious injures when passenger cars collide with the rear end or side of the heavy vehicle. This paper describes the use of Genetic Algorithm (GA) coupled with a dynamic, inelastic and large deformation finite element (FE) code LS-DYNA to search optimal design of the Side/Rear impact guards. In order to verify the accuracy of the FE model, the simulation results were compared with real experiments follow with the regulation ECE R73. The validated FE model then used to study the optimal design base on under running distance and total amount of energy absorbing capacity. The results from this study shown that this newly developed method not only can found multi-objective design parameters but also can reduce computational time significantly.

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