OPTIMAL DESIGN OF CYLINDRICAL GEARS WITH CONVEX-CONCAVE CONTACT: OBJECTIVE FUNCTION AND VARIABLES PLANNING

Reducing the mass and dimensions of gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with a convex-concave contact of the teeth. Therefore, the study is devoted to the development of methods for the optimal design of cylindrical gears with convex-concave contact of the working surfaces. Optimality criteria: minimum contact stresses and (or) minimum relative sliding velocities, taking into account design, geometrical and technological constraints. C-C gearing was chosen as the object of research. It was proposed by the Slovak scientists M. Boshanski and M. Veresh. An objective function is constructed for the case of minimizing contact stresses. The optimality criterion is formulated as follows: contact stresses σH in the mesh must take the minimum possible value when all constraints are met. An objective function is also constructed for the case of minimizing the relative sliding velocities of profiles. The optimality criterion is formulated as follows: the relative sliding s velocities of profiles λ at the extreme points of mesh must take the minimum possible value when all the constraints are met. Variables planning are defined. These are pressure angle at the pole αС, the curvature radius at the upper part of contact path rkh, and the curvature radius at the lower part of contact path rkd. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned to form a system of constraints on variables planning, to develop methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results. Keywords: gear, convex-concave contact, optimal design, objective function, variables planning

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Solving the problem of optimal design for a two-stage reducer by using a modified evolutionary algorithm

MATEC Web of Conferences ◽

10.1051/matecconf/202031701004 ◽

2020 ◽

Vol 317 ◽

pp. 01004

Author(s):

Oleksandr Ustynenko ◽

Oleksiy Bondarenko ◽

Volodymyr Serykov

Keyword(s):

Optimal Design ◽

Evolutionary Algorithm ◽

Specific Problem ◽

Functional Limitations ◽

Evolutionary Process ◽

Design Parameters ◽

Initial Population ◽

Objective Functions ◽

Two Stage ◽

Test Points

The work is devoted to solving the problem of selecting optimal geometric parameters of gears of a two-stage cylindrical reducer using a modified evolutionary algorithm (EA). The statement of the problem is considered, design parameters, objective functions, limitations on design parameters are determined. This allowed us to propose a modification of EA. To generate the initial test points, it was proposed to use the LP-τ sequence, this allowed us to reduce the initial population of test points and bring EA closer to a truly “random” process. The scheme of the proposed algorithm is considered, which gives an idea of the sequence of operations that are carried out with populations of test points at each stage of the evolutionary process. The solution of the specific problem of selecting optimal parameters for a serial reducer is given. The input data, numerical and functional limitations are determined, the objective functions are formed. The results of the solution are shown in several presentation formats: tabular and graphical, which allows to qualitatively interpret and analyze the results. Conclusions are made about testing the proposed algorithm for solving a specific problem of optimal design. Further ways of improving this methodology are proposed.

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Modeling and Assessment of a Biomass Gasification Integrated System for Multigeneration Purpose

International Journal of Chemical Engineering ◽

10.1155/2016/2639241 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11 ◽

Cited By ~ 16

Author(s):

Shoaib Khanmohammadi ◽

Kazem Atashkari ◽

Ramin Kouhikamali

Keyword(s):

Optimal Design ◽

Objective Function ◽

Electrical Power ◽

Clean Energy ◽

Biomass Gasification ◽

Integrated System ◽

Design Parameters ◽

Base Case ◽

Cost Rate ◽

Gasification Process

The use of biomass due to the reduction in greenhouse gas emissions and environmental impacts has attracted many researchers’ attention in the recent years. Access to an energy conversion system which is able to have the optimum performance for applying valuable low heating value fuels has been considered by many practitioners and scholars. This paper focuses on the accurate modeling of biomass gasification process and the optimal design of a multigeneration system (heating, cooling, electrical power, and hydrogen as energy carrier) to take the advantage of this clean energy. In the process of gasification modeling, a thermodynamic equilibrium model based on Gibbs energy minimization is used. Also, in the present study, a detailed parametric analysis of multigeneration system for undersigning the behavior of objective functions with changing design parameters and obtaining the optimal design parameters of the system is done as well. The results show that with exergy efficiency as an objective function this parameter can increase from 19.6% in base case to 21.89% in the optimized case. Also, for the total cost rate of system as an objective function it can decrease from 154.4 $/h to 145.1 $/h.

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Simulation-based search for optimal designs of accelerated life tests through response surface methodology

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-11-2020-0384 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Daniel Ayasse ◽

Kangwon Seo

Keyword(s):

Response Surface Methodology ◽

Optimal Design ◽

Objective Function ◽

Response Surface ◽

Failure Time ◽

Simulated Data ◽

Accelerated Life Test ◽

Design Parameters ◽

Content Type ◽

Accelerated Life

PurposePlanning an accelerated life test (ALT) for a product is an important task for reliability practitioners. Traditional methods to create an optimal design of an ALT are often computationally burdensome and numerically difficult. In this paper, the authors introduce a practical method to find an optimal design of experiments for ALTs by using simulation and empirical model building.Design/methodology/approachInstead of developing the Fisher information matrix-based objective function and analytic optimization, the authors suggest “experiments for experiments” approach to create optimal planning. The authors generate simulated data to evaluate the quantity of interest, e.g. 10th percentile of failure time and apply the response surface methodology (RSM) to find an optimal solution with respect to the design parameters, e.g. test conditions and test unit allocations. The authors illustrate their approach applied to the thermal ALT with right censoring and lognormal failure time distribution.FindingsThe design found by the proposed approach shows substantially improved statistical performance in terms of the standard error of estimates of 10th percentile of failure time. In addition, the approach provides useful insights about the sensitivity of each decision variable to the objective function.Research limitations/implicationsMore comprehensive experiments might be needed to test its scalability of the method.Practical implicationsThis method is practically useful to find a reasonably efficient optimal ALT design. It can be applied to any quantities of interest and objective functions as long as those quantities can be computed from a set of simulated datasets.Originality/valueThis is a novel approach to create an optimal ALT design by using RSM and simulated data.

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Single Spur Gear Reducer Optimization Design Mathematical Modeling

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.273.198 ◽

2013 ◽

Vol 273 ◽

pp. 198-202

Author(s):

Yu Xia Wang

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Optimal Design ◽

Objective Function ◽

Optimization Design ◽

Spur Gear ◽

Design Parameters ◽

Constraint Function ◽

Design Variables ◽

The Mathematical Model

In a given power P, number of teeth than u, input speed and other technical conditions and requirements, find out a set of used a economic and technical indexes reach the optimal design parameters, realize the optimization design of the reducer, This paper determined unipolar standard spur gear reducer design optimization of the design variables, and then determine the objective function, determining constraint function, so as to establish the mathematical model.

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Optimal Design of Disk Springs

Journal of Mechanisms Transmissions and Automation in Design ◽

10.1115/1.3260748 ◽

1985 ◽

Vol 107 (4) ◽

pp. 477-481

Author(s):

S. M. Metwalli ◽

G. S. A. Shawki ◽

A. A. Elzoghby

Keyword(s):

Optimal Design ◽

Objective Function ◽

Design Parameters ◽

Disk Spring ◽

Maximum Utilization

In this paper the optimal disk spring is defined. Spring resilience is used as an objective function in order to attain maximum utilization of material. Various constraints on stress and/or deflection are considered. Results indicate that the radially tapered section represents the optimal realistic disk spring which maximizes the objective function and satisfies stipulated constraints. Optimal design parameters for radially tapered disk springs are thus considered and compared with those for uniform-section disk springs.

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Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v12i430292 ◽

2021 ◽

pp. 15-28

Author(s):

Samson W. Wanyonyi ◽

Ayubu A. Okango ◽

Julius K. Koech

Keyword(s):

Optimal Design ◽

Literature Review ◽

Optimality Criterion ◽

Process Variable ◽

Optimality Criteria ◽

Mixture Modeling ◽

Process Variables ◽

Combination Model ◽

Design Optimality ◽

Plot Design

A design optimality criterion, such as D-, A-, I-, and G- optimality criteria, is often used to analyze, evaluate and compare different designs options in mixture modeling test. A mixture test is an experiment where the descriptive variable and response rely only on the mixture's relative ratio in the mix but not its composition. The study geared toward exploring D-, A-, I-, and G- optimality criteria and their efficiency in determining an optimal split-plot design in mixture modeling within the presences of process variables. We evaluated and discussed in detail D-, A-, I-, and G- optimality criteria based on literature review. We also explored and examine why I- and D-optimal criteria are often involved within the formulation of an optimal design in the context of mixture process variable settings. We recommend that optimality criterion must always be used when assessing the various styles of designs so as to search out a desirable design that matches a combination model.

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Optimal Design of Conventional In-Line Fuel Injection Equipment

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1243/pime_proc_1995_209_194_02 ◽

1995 ◽

Vol 209 (2) ◽

pp. 135-141 ◽

Cited By ~ 12

Author(s):

B Kegl

Keyword(s):

High Pressure ◽

Optimal Design ◽

Objective Function ◽

Fuel Injection ◽

Design Procedure ◽

Injection Rate ◽

Design Parameters ◽

Special Treatment ◽

Mathematical Programming Problem ◽

Injection Equipment

The paper describes an application of optimal design procedure employed on conventional in-line fuel injection equipment for a diesel engine. The procedure is applied to a set of design parameters concerning the design of the cam, high-pressure pump, delivery valve, snubber valve, high-pressure tube and injector respectively. The values of these design parameters are optimized simultaneously within specified maximum and minimum values in order to approach a target injection rate history. The proposed optimal design procedure is defined as a solution process of a non-linear mathematical programming problem defined by the objective and constraint functions. The objective function measures the difference between the target and actual injection rate histories while the constraints concern the response of the system as well as several technological limitations. The form of the objective function is such that it requires special treatment similar to those employed in optimal design of dynamic multi-body systems. However, the complexity of the fuel injection equipment causes specific numerical difficulties when the ideas employed for dynamic systems are adopted. The paper describes how to modify the usual approach in order to circumvent these difficulties. The theory is illustrated with a numerical example comparing the usual versus the modified approach.

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Optimal Design of the Dynamic Gear Flowmeter

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.502.426 ◽

2012 ◽

Vol 502 ◽

pp. 426-430 ◽

Cited By ~ 3

Author(s):

Zhang Jun ◽

Cheng Zhang ◽

Zhang Teng ◽

Tao Juan ◽

Zhang Bin

Keyword(s):

Optimal Design ◽

Objective Function ◽

Computer Software ◽

Design Parameters ◽

Multi Objective Optimization ◽

Flow Pulsation ◽

Software Optimization ◽

Optimization Function ◽

And Performance ◽

Performance Constraint

Multi-objective optimization of the dynamic gear flowmeter was established by using computer software optimization toolbox. We established the objective function with flow pulsation coefficient minimum and smallest volume of the meter as optimized object, by establishing boundary constraint conditions and performance constraint conditions, choosing proper parameters and initial values, and then we can optimize the design parameters by the help of computer software using optimization function. The optimizing methods can greatly improved the design and optimizing efficiency, which can help us to get the optimal design in the shortest time.

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Justification of design parameters of the fractional reaping conveyor and its devices for removal of beveled stems from under the wheels of the vehicle

Agricultural Technologies ◽

10.35599/agritech/01.03.01 ◽

2019 ◽

Vol 1 (3) ◽

pp. 1-10

Author(s):

Mikhail M. Konstantinov ◽

Ivan N. Glushkov ◽

Sergey S. Pashinin ◽

Igor I. Ognev ◽

Tatyana V. Bedych

Keyword(s):

Optimal Design ◽

Technological Process ◽

Design Parameters ◽

Theoretical Studies ◽

Optimal Parameters ◽

Belt Conveyor ◽

Grain Crops ◽

Mode Of Operation ◽

Optimal Values ◽

Main Component

In this paper we consider the structural and technological process of the combine used in the process of separate harvesting of grain crops, as well as a number of its parameters. Among the main units of the combine, we allocate a conveyor and devices for removing beveled stems from under the wheels of the vehicle. The principle of operation of the conveyor at different phases of the Reaper and especially the removal of cut stems from under the wheels of the vehicle during operation of the Reaper. The results of theoretical studies on the establishment of the optimal design of the parameters of the belt conveyor are presented, the ranges of their optimal values are considered and determined. Studies on the establishment of optimal parameters of the screw divider in the Reaper, which is the main component of the device for removal of beveled stems, are presented. Taking into account the optimal design and mode of operation of the screw divider, the correct work is provided to remove the cut stems from under the wheels of the harvester.

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