Changes In Design Variables Research Articles

Modification of natural frequencies of an automotive belt drive system based on eigen-sensitivity analysis of its configuration parameters

Abstract A methodology is presented to simultaneously modify natural frequencies of an automotive belt drive system via configuration modification to match natural frequencies of the system with its working conditions. In this methodology, the configuration modification is regarded as an inverse eigenvalue problem in which necessary changes of a set of configuration parameters are determined for achieving a desired natural frequency variation relative to the original design value. Natural frequencies and mode shapes of the system are obtained by solving an eigenvalue problem that is directly derived from established governing equations of motion of a typical automotive belt drive system. Explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters are derived by differentiating the eigenvalue equation. Several configuration parameters are selected as design variables and their corresponding modification regions and directions are given based on frequency sensitivity analysis. In the inverse eigenvalue problem, variations of natural frequencies caused by changes of multiple design variables are approximated using the first and second order Taylor series expansions, which are based on explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters. By solving the inverse eigenvalue problem, necessary changes of design variables are determined and the desired natural frequencies are achieved so that resonance conditions are successfully avoided.

Pareto optimal design of swirl cooling chambers with tangential injection using CFD, GMDH-type of ANN and NSGA-II algorithm

In this research, with regards to the considered geometrical parameters, a multi-objective optimization has been performed with the goal of achieving maximum heat transfer and minimum pressure loss in a swirl chamber. This objective has been accomplished by using the Computational Fluid Dynamics (CFD) technique, GMDH type Neural Network and the NSGA-II multi-objective optimization algorithm. The design variables include the ratio of inlet slot width to swirl chamber diameter, ratio of inlet slot height to swirl chamber diameter and the inlet slot angle. These variables are just related to geometrical parameters; and the Reynolds number, tangential jet temperature and the wall temperature are considered as constant. The objective functions include the averaged Nusselt number over swirl chamber wall and the pressure loss coefficient. CFD technique is used to analyze the flow and heat transfer and to compute the values of objective functions. The polynomials that relate the objective functions to input variables are obtained by means of GMDH algorithm. The obtained models are used to predict the values of objective functions as inputs for NSGA-II multi-objective optimization. Considering the range of changes of design variables, Pareto optimal points are obtained for the objective functions, and the Pareto points with special characteristics are introduced and discussed.

Design of Dynamic Systems Using Surrogate Models of Derivative Functions

Optimization of dynamic systems often requires system simulation. Several important classes of dynamic system models have computationally expensive time derivative functions, resulting in simulations that are significantly slower than real time. This makes design optimization based on these models impractical. An efficient two-loop method, based on surrogate modeling, is presented here for solving dynamic system design problems with computationally expensive derivative functions. A surrogate model is constructed for only the derivative function instead of the simulation response. Simulation is performed based on the computationally inexpensive surrogate derivative function; this strategy preserves the nature of the dynamic system, and improves computational efficiency and accuracy compared to conventional surrogate modeling. The inner-loop optimization problem is solved for a given derivative function surrogate model (DFSM), and the outer loop updates the surrogate model based on optimization results. One unique challenge of this strategy is to ensure surrogate model accuracy in two regions: near the optimal point in the design space, and near the state trajectory in the state space corresponding to the optimal design. The initial evidence of method effectiveness is demonstrated first using two simple design examples, followed by a more detailed wind turbine codesign problem that accounts for aeroelastic effects and simultaneously optimizes physical and control system design. In the last example, a linear state-dependent model is used that requires computationally expensive matrix updates when either state or design variables change. Results indicate an order-of-magnitude reduction in function evaluations when compared to conventional surrogate modeling. The DFSM method is expected to be beneficial only for problems where derivative function evaluation expense, and not large problem dimension, is the primary contributor to solution expense (a restricted but important problem class). The initial studies presented here revealed opportunities for potential further method improvement and deeper investigation.

A modified stochastic perturbation algorithm for closely-spaced eigenvalues problems based on surrogate model

Aiming at uncertainty propagation and dynamic reanalysis of closely-spaced eigenvalues, with consideration of uncertainties in design variables, a modified stochastic perturbation method is proposed. Concerning quasi-symmetric or partial-symmetric structures that frequently appear, one of their primary features is closely-distributed natural frequencies. For structure with closely-spaced eigenvalues, due to its instability and sensitivity to the changes of design variables and its excessively concentrated adjacent eigenvalues, conventional uncertainty analysis or dynamic reanalysis methods for distinct eigenvalue are no longer available. Initially, the spectral decompositions of stiffness and mass matrices are provided; by transfer technique, the eigen-problem of closely-spaced eigenvalues is converted to that of repeated eigenvalues with two perturbation parts appended; then the perturbed closely-spaced eigenvalue is rewritten as the sum of original closely-spaced eigenvalues’ mean value and surrogate model which approximates the first-order perturbation term by polynomial chaos expansions. According to this method, statistical quantities of perturbed closely-spaced eigenvalues are calculated directly and accurately, which contributes to its uncertainty analysis and dynamic reanalysis. Furthermore, the capability of proposed method in dealing with relatively large uncertainties and complex engineering structure is demonstrated. The accuracy and efficiency of proposed method have been verified sufficiently by numerical examples.

Continuous direct compression as manufacturing platform for sustained release tablets

This study presents a framework for process and product development on a continuous direct compression manufacturing platform. A challenging sustained release formulation with high content of a poorly flowing low density drug was selected. Two HPMC grades were evaluated as matrix former: standard Methocel CR and directly compressible Methocel DC2. The feeding behavior of each formulation component was investigated by deriving feed factor profiles. The maximum feed factor was used to estimate the drive command and depended strongly upon the density of the material. Furthermore, the shape of the feed factor profile allowed definition of a customized refill regime for each material. Inline NIRs was used to estimate the residence time distribution (RTD) in the mixer and monitor blend uniformity. Tablet content and weight variability were determined as additional measures of mixing performance. For Methocel CR, the best axial mixing (i.e. feeder fluctuation dampening) was achieved when an impeller with high number of radial mixing blades operated at low speed. However, the variability in tablet weight and content uniformity deteriorated under this condition. One can therefore conclude that balancing axial mixing with tablet quality is critical for Methocel CR. However, reformulating with the direct compressible Methocel DC2 as matrix former improved tablet quality vastly. Furthermore, both process and product were significantly more robust to changes in process and design variables. This observation underpins the importance of flowability during continuous blending and die-filling. At the compaction stage, blends with Methocel CR showed better tabletability driven by a higher compressibility as the smaller CR particles have a higher bonding area. However, tablets of similar strength were achieved using Methocel DC2 by targeting equal porosity. Compaction pressure impacted tablet properties and dissolution. Hence controlling thickness during continuous manufacturing of sustained release tablets was crucial to ensure reproducible dissolution.

A liquid metal-based structurally embedded vascular antenna: II. Multiobjective and parameterized design exploration

Research on the structurally embedded vascular antenna concept leverages past efforts on liquid metal (LM) reconfigurable electronics, microvascular composites, and structurally integrated and reconfigurable antennas. Such a concept has potential for reducing system weight or volume while simultaneously allowing in situ adjustment of resonant frequencies and/or changes in antenna directivity. This work considers a microvascular pattern embedded in a laminated composite and filled with LM. The conductive liquid provides radio frequency (RF) functionality while also allowing self-cooling. Models describing RF propagation and heat transfer, in addition to the structural effects of both the inclusion of channels and changes in temperature, were described in part 1 of this two-part work. In this part 2, the engineering models developed and demonstrated in part 1 toward the initial exploration of design trends are implemented into multiple optimization frameworks for more detailed design studies, one of which being novel and particularly applicable to this class of problem. The computational expense associated with the coupled multiphysical analysis of the structurally embedded LM transmitting antenna motivates the consideration of surrogate-based optimization methods. Both static and adaptive approaches are explored; it is shown that iteratively correcting the surrogate leads to more accurate optimized design predictions. The expected strong dependence of antenna performance on thermal environment motivates the consideration of a novel ‘parameterized’ optimization approach that simultaneously calculates whole families of optimal designs based on changes in design or operational variables generally beyond the control of the designer. The change in Pareto-optimal response with evolution in operating conditions is clearly demonstrated.

Variable impact analysis of linear generator by using response surface method

Energy harvesting is the process which gathers and converts external energies such as light, vibration, movements of people and heat which are disposed into reusable electrical energy and uses such electrical energy. Harvesting using vibration energy is a technology which converts mechanical vibrations into electrical energy, and the methods using electrostatic, electromagnetic and piezoelectric effects are available. The method using electrostatic is advantageous for miniaturization but its energy conversion efficiency is low, and harvesting using piezoelectric uses piezoelectric ceramic so that stress cracking occurs easily so that the performance cannot be maintained. However, the harvesting system using electromagnetic has advantages that its production cost is relatively low in comparison to the methods using electrostatic and piezoelectric and electric power generated through harvesting has a high efficiency. In this study, the analysis of effect on the generation quantity according to a change in design variables of linear electromagnetic generator which could harvest vibration energy effectively. The number and shape of permanent magnets and number of coil turns were set as design variables, and the generation quantity analysis was carried out using MAXWELL, a commercial electromagnetic finite-element analysis program, and the effect of variables on the generation quantity was analyzed statistically through the response surface analysis method.

Two-stage local optimization of lattice type support structures for offshore wind turbines

Offshore wind turbines are exposed to stochastic dynamic loading that includes non-linear aerodynamic effects. Hence, time domain simulations are needed for the analysis of support structures, resulting in a time consuming and computationally demanding optimization process. Here, the structural optimization was performed assuming that changing dimensions of a structural member does not affect other members of the structure, a heuristic based on the principle of domain decomposition. This allows for a simple sizing algorithm, which optimizes area and stress concentration factors element-wise using a meta-model for the structural performance. In order to further speed up the algorithm, designs were evaluated based on performance data from earlier analyses, while searching for the most suitable changes in design variables. This was found to be very efficient, resulting in a nearly full utilization of fatigue resistance and a saving of analysis time of roughly 40%. Randomly chosen initial designs initiated sequences that converged to the same minimum weight using fewer than seven structural analyses. Fatigue damage was the design driver in this analysis, while ultimate and buckling performance were controlled within the given constraints.

Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method

This paper presents a new sensitivity reanalysis of static displacement for arbitrary changes of design variables. The current displacement of modified sensitivity equations is approximately calculated by using Taylor series expansion and then the direct sensitivity equations are solved by combined approximate method. Two types of numerical examples, including size sensitivity and shape sensitivity, are used to verify the accuracy and efficiency of the proposed method, which is more efficient than the existed methods. Although the Kirsch and Papalambros reanalysis method is more accurate, the proposed method can also acquire the accurate solution for the case of large modification. Therefore, this new method will have great potential application in the gradient-based structural optimization.

Design Sensitivity Method for Sampling-Based RBDO With Varying Standard Deviation

Conventional reliability-based design optimization (RBDO) uses the mean of input random variable as its design variable; and the standard deviation (STD) of the random variable is a fixed constant. However, the constant STD may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is present as a percentage of the mean value. For this kind of design problem, the STD of the input random variable should vary as the corresponding design variable changes. In this paper, a method to calculate the design sensitivity of the probability of failure for RBDO with varying STD is developed. For sampling-based RBDO, which uses Monte Carlo simulation (MCS) for reliability analysis, the design sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STD in addition to the change in the mean. As copulas are used for the design sensitivity, correlated input random variables also can be used for RBDO with varying STD. Moreover, the design sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed design sensitivity method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate design sensitivity in the optimization process.

연료분사펌프의 윤활 특성 개선: 제2부 - 그루브의 적용

This study evaluates the effect of grooves on the stem part of a plunger on the lubrication characteristics of a fuel injection pump (FIP) by using hydrodynamic lubrication analysis. The current study uses the two-dimensional Reynolds equation to evaluate the changes in lubrication characteristics with variations in clearance, viscosity, and grooves for a laminar, incompressible, and unsteady state flow. This study investigates the lubrication characteristics by comparing the dimensionless minimum film thickness or the film parameter, which is the ratio of the minimum film thickness to surface roughness. The analysis method for the groove section differs depending on the depth of the groove. For instance, in the case of a shallow groove, the film thickness equation considers the depth of the groove, while in the case of a deep grove, it considers the flow continuity. The lubrication characteristics of the FIP are more sensitive to changes in the groove width than to changes in other design variables. Moreover, the application of a groove is more effective under low viscosity conditions. The smaller the distance from the edge of the stem part to the first groove in the case of shallow grooves, the better are the lubrication characteristics of the FIP. In contrast, in the case of deep grooves, the lubrication characteristics of the FIP improve as the distance increases. The application of shallow grooves is more effective for improving the lubrication characteristics than the application of deep grooves.

Structural Dynamics Optimization of Rotor Systems for a Small-Size Turboprop Engine

This paper presents the results of the rotordynamic analysis and design optimization performed for a turboprop engine-rotor system consisting of a free-power turbine and a gas generator. Predictions of static stresses, natural frequencies, and amplitudes are obtained by the in-house finite-element code. A detailed analysis of the finite-element method model (various beam formulations, three-dimensional axisymmetric model, point masses, and one-dimensional rigid disk elements) is provided. A sizing optimization problem of total shaft mass minimization is considered. Design variables are inner radii and wall thicknesses of shaft sections. Constraints are imposed on static stresses, natural frequencies, and amplitudes of the unbalance response. Changes in design variables are constrained to avoid contacts between the shafts of the twin-spool configuration. An in-house implementation of the sequential quadratic programming method is coupled with hybrid, analytical and numerical, sensitivity analysis. Results of the optimization show that a significant mass reduction in comparison with the baseline configuration can be achieved with all constraints being simultaneously satisfied. The optimal designs, however, must be finalized to meet other requirements not considered during the optimization. The Campbell diagram of the free-power turbine rotor system is significantly affected by the optimization.

Avaliação da influência da mudança de variáveis de projeto de barragens sobre as alterações hidrológicas e componentes do regime de vazão natural

Dams provide benefits to the society through hydro power generation and when they supply cities with water, for example. However they also have negative impacts, such as hydrological changes in the long, medium and short term. Once the hydrological impacts can be predictors of changes in aquatic biota, is extremely important that studies of such changes caused by dams are made still in the design phase. This paper presents an assessment of how the change in dam design variables influence the hydrological changes and the five components of the natural flow regime (magnitude, frequency, duration, time of occurrence and rate of change).For this, changes imposed by dams on a perennial river were simulated. In possession of the modeling data these changes were evaluated and classified with the Indicators of Hydrological Alteration (IHA) and the Hydrological Regime Alteration Dundee Method (DHRAM).And then a sensitivity analysis was performed using statistical concepts of Factorial Design. The hydrological changes affected in different ways and with different degrees each group of hydrological parameters of the IHA. The classification of DHRAM indicated that the storage capacity directly influenced the impact of hydrologic alteration. The sensitivity analysis suggests that the demand and the remaining flow affect the hydrological changes and the natural flow of components. The obtained results indicate that the study of hydrological changes can be made even in the design phase to select a project alternative that takes into account, among other issues involved (eg, technical and economic factors), also the least impact on the hydrological regime of a river

Probabilistic sensitivity analysis for novel second-order reliability method (SORM) using generalized chi-squared distribution

Reliability-based design optimization (RBDO) requires evaluation of sensitivities of probabilistic constraints. To develop RBDO utilizing the recently proposed novel second-order reliability method (SORM) that improves conventional SORM approaches in terms of accuracy, the sensitivities of the probabilistic constraints at the most probable point (MPP) are required. Thus, this study presents sensitivity analysis of the novel SORM at MPP for more accurate RBDO. During analytic derivation in this study, it is assumed that the Hessian matrix does not change due to the small change of design variables. The calculation of the sensitivity based on the analytic derivation requires evaluation of probability density function (PDF) of a linear combination of non-central chi-square variables, which is obtained by utilizing general chi-squared distribution. In terms of accuracy, the proposed probabilistic sensitivity analysis is compared with the finite difference method (FDM) using the Monte Carlo simulation (MCS) through numerical examples. The numerical examples demonstrate that the analytic sensitivity of the novel SORM agrees very well with the sensitivity obtained by FDM using MCS when a performance function is quadratic in U-space and input variables are normally distributed. It is further shown that the proposed sensitivity is accurate enough compared with FDM results even for a higher order performance function.

Effect of small variations in rocket design parameters on its performance

The effects of small changes in the design variables of a rocket on its flight performance- all-burnt velocity and height at all-burnt are deduced. Also the effects on all-burnt height when all-burnt velocity is kept constant by changing either (i) payload weight or (ii) propellant weight or (iii) thrust separately have been found with changes in other design parameters.

횡방향 모드추적을 고려한 코일스프링의 신뢰성기반 최적설계

When the values of design variables change, mode switching can often occur. If the mode of interest is not tracked, the frequencies and modes for design optimization may be miscalculated owing to modes that differ from the intended ones. Thus, mode tracking must be employed to identify the frequencies and modes of interest whenever the values of design variables change during optimization. Furthermore, reliability-based design optimization (RBDO) must be performed for design problems with design variables containing uncertainty. In this research, we perform RBDO considering the mode tracking of a compressive coil spring, i.e., a component of the joint spring that supports a compressor, with design variables containing uncertainty by using only kriging metamodels based on multiple responses approach (MRA) without existing mode tracking methods. The reliability analyses for RBDO are employed using kriging metamodel-based Monte Carlo simulation.

Sensitivity Analysis for Coupled Atomistic and Continuum Simulations Using Bridging Scale Decomposition

This paper presents sensitivity analysis methods for coupled atomistic and continuum problems. Many bridging methods, which couple atomistic simulations to continuum simulations, have been proposed. They offers the ability to examine atomistic-scale dynamics in great detail, and yet keep the computation affordable by only using molecular dynamics (MD) in localized regions and a continuum simulation method everywhere else. Among the many excellent methods developed, the bridging scale decomposition is, in our opinion, the most advanced and is inherently geared for dynamic problems. We are investigating the impact of design changes at the macrolevel; including material, sizing, and shape, to the responses at the atomistic level. This paper focuses on sensitivity analysis for one-dimensional (1D) problems, where responses of atomistic motion to the changes in design variables are formulated analytically. These formulations are then implemented numerically in Matlab. Accuracy of the sensitivity coefficients are verified using overall finite difference method. The major contributions of this paper are: first, it demonstrates the feasibility of the sensitivity analysis for the bridging scale; second, the paper proposes a method that overcomes the issue of discontinuity in shape design due to the discrete nature of the MD simulations; and third, the paper provides a basis for future extension to 2D and 3D problems that support structural design.

Multistate Design Approach to Analysis of Twin-Engine Aircraft Performance Robustness

DOI: 10.2514/1.C031338 This article introduces an integrated approach for the early-stage multistate design and analysis of aircraft requiringrobustperformanceacrossarangeofoff-nominalsystemstates.Itisappliedtothecasestudyofanexisting twin-engineaircraft,enabledbythedevelopmentofamultimodalperformancemodelcalibratedwith flight-testdata collected at Edwards Air Force Base Flight Test Center. The methodology includes elements for determining responsesinaircraftexpectedperformanceandavailabilitytochangesinstaticdesignvariables(geometry),dynamic design variables (control gains), and component failure rates, which are the three driving input categories affecting performance robustness. This is accomplished using Markov chain analysis within the design loop to stochastically modelstatetransitionsbasedonfailureratesaswellasgainoptimizationthroughsimulationtoensurecontrollability at each design point. Results showed unsafe performance in 15% of the King Air geometry-state responses under investigation.Althoughmanyoccurredinthefullyfailedstateandwereexpected, fiveoccurredinpartiallydegraded states where the majority of geometries were able to meet performance requirements. Furthermore, this behavior clearly exhibited itself in the resulting design sensitivities, confirming that such an approach allows designers to identifyelementsthatmightdrivesystemlossthroughanalysisofperformancechangesacrosssystemstatesandtheir respective response to changes in design variables.

Application of Value-Driven Design to Commercial AeroEngine Systems

Value-Driven Design provides a framework to enhance the systems engineering processes for the design of large systems. By employing economics in decision making, Value-Driven Design enables rational decision making in terms of the optimum business and technical solution at every level of engineering design. This paper explains the application of ValueDriven Design to the aero-engine system through two case studies, which were conducted through workshops under the Rolls-Royce plc Advanced Cost Modeling Methodologies project. The Surplus Value Theory was utilized to provide a metric that can trade-off component designs with changes in continuous and discrete design variables. Illustrative results are presented to demonstrate how the methodology and modeling approach can be used to evaluate designs and select the value-enhancing solution.

New Standard for Evaluating Casing Connections for Thermal-Well Applications

Summary Casing connections in thermal wells experience extreme loads owing to exposure to high temperatures ranging as high as 200 to 350°C, stresses exceeding the elastic limit, and cyclic plastic deformation. To date, no standard procedure has been adopted by the industry to qualify casing connections for such conditions. In particular, the existing evaluation standard published jointly by the International Organization for Standardization (ISO) and American Petroleum Institute (API) ISO 13679/API 5C5 (ISO 2002) does not apply to tubular loads beyond pipe body yield and temperatures above 180°C. Proprietary procedures have been used to qualify connections for individual thermal operations, but none of those has been accepted as an industry standard. This paper introduces a new protocol for evaluating casing connections for thermal applications: Thermal Well Casing Connection Evaluation Protocol (TWCCEP). While founded on longstanding work in the thermal-well arena, TWCCEP was developed through a multiclient project sponsored by several major operators and connection manufacturers. Following project completion, TWCCEP was released to the public domain and submitted to ISO for adoption as an international standard. TWCCEP uses both analytical and experimental procedures to assess performance of a candidate connection under conditions typical of service in thermally stimulated wells. The objective of the analytical component is to assess sensitivities of the candidate connection to selected design variables, and identify worst-case combinations of those variables for configuration of specimens for physical testing. The purpose of the physical testing is to verify performance of the connection specimens under assembly-and- loading conditions simulating thermal-well service. In addition to an overview of TWCCEP, this paper illustrates how engineering analysis, numerical simulation, and reduced-scale physical testing were used to examine the impacts of various design and loading variables on connection strength and sealability, and subsequently to formulate the analysis-and-test matrix prescribed in the TWCCEP evaluation procedure. Adoption and consistent use of TWCCEP is expected to increase operational reliability and decrease failure potential of casing strings in thermal wells. Learnings from the protocol development process will also help in the formulation of guidelines for connection requalification for thermal applications, in cases when one or more of the design variables change.