scholarly journals Optimization of two support spindle shaft on nonlinear elastic supports by rigidity characteristics

2021 ◽  
pp. 61-68
Author(s):  
Sergij Yurijovich Pogorilov ◽  
Valerij Lvovich Khavin ◽  
Inna Petrovna Khavina
Keyword(s):  
Metal Cutting ◽  
Optimization Problems ◽  
Spindle Assembly ◽  
Graphical Form ◽  
Design Parameters ◽  
Variable Parameters ◽  
Elastic Supports ◽  
Spindle Shaft ◽  
Cantilever Length ◽  
Nonlinear Elastic

One of the main structural elements of metalworking machines is the spindle assembly (spindle), which is used to hold cutting tools or workpieces. The rigidity of the spindle assembly plays a decisive role in ensuring the accuracy and efficiency of the machine as a whole. The assessment of the spindle shaft stiffness is carried out on the basis of the analysis of the static bending of the spindle shaft, which made it possible to formulate and solve the problems of optimizing the spindle shaft according to the stiffness characteristics for two supporting structures on nonlinear elastic supports. To determine the stiffness of roller bearings, the work uses the dependence obtained on the basis of solving the problem of contact interaction of an elastic steel cylinder with curvilinear elastic steel half-spaces. For the considered design scheme, the optimization goals were chosen for the conditions of the smallest displacement of the end section of the spindle shaft console, the achievement of the minimum angle of rotation in this section or the minimum of their normalized superposition, which ensures maximum rigidity in the processing zone. Consideration has also been given to minimizing the swing angle at the front support to maximize bearing life. Mathematically, the problem is presented in the form of minimizing one of the 4 proposed objective functions by changing the variable parameters - the length of the cantilever and the value of the inter-support distance, represented as dimensionless quantities - the cantilever coefficient and the inter-support distance coefficient. Minimum and maximum values ​​of the cantilever length and shaft span were considered as constraints on the variable parameters. Varying the console coefficients and the inter-support distance was carried out by the method of sequential enumeration within the specified constraints, the solution of optimization problems is presented in a graphical form. The solution to the problem of shaft bending was carried out on the basis of the equation of the bent axis of the beam in the framework of the Euler - Bernoulli hypotheses and presented in an analytical form together with analytical dependencies for calculating the radial stiffness of a roller bearing as a function of the supporting force acting on it. The algorithm for solving optimization problems is implemented in the MatLAB package. Optimal solutions have shown that the minimum of the combined functions, consisting of the sum of the relative deflection values ​​at the end of the console and the angles of rotation at the end of the console and on the front support, is achieved at the same variable parameters as the minima of the angles of rotation at the end of the console and on the front support. The proposed approach to the design of the shafts of spindle units of metal-cutting machines, which are optimal in terms of rigidity characteristics, forms a tool for a reasonable choice of bearings and design parameters of spindle shafts.

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

A New Integration Framework for Modeling and Optimizing Systems in Preliminary Design Phase

2012 ◽  
Author(s):  
Jad Matar ◽  
Raphael Chenouard ◽  
Alain Bernard
Keyword(s):  
Optimization Problems ◽  
Constraint Satisfaction Problem ◽  
System Engineering ◽  
Design Parameters ◽  
Integration Framework ◽  
Domain Specific ◽  
Variability Modeling ◽  
Wide Range ◽  
Architecture Description ◽  
Description Languages

In this paper we propose a new integration framework model for simplifying the feasible space exploration and product optimization in early design phases. Hence, modeling and optimizing tasks are core activities in this framework. Currently, system engineering problems are modeled and optimized using a wide range of domain-specific languages. One should not duplicate these languages by creating a new system engineering language capable of modeling and optimizing every aspect of a system. Thus we combine the UML2 language and the formalism of Constraint Optimization Problems (COPs). UML2 is a visual modeling language, which provides a set of diagrams and constructs for modeling the major aspects of a product. In order to optimize design parameters, we reformulate some of this modeling knowledge into a COP. A COP may be defined as a regular constraint satisfaction problem (CSP) augmented with a set of objective functions. Thus the optimization problem to be solved is stated declaratively with acausal constraints. Then, COP solvers are based on generic solving algorithms computing a set of optimal solutions. In this paper, generic concepts integrating variability modeling concepts and based on architecture description languages are introduced. We also briefly describe transformation strategy using ATL language to perform a bidirectional mapping between UML2 constructs and the corresponding COP models.

Application of Particle Swarm Optimization Based on Support Vector Machine in Multi-Objective Structure Optimization

2012 ◽  
Vol 201-202 ◽  
pp. 283-286
Author(s):  
Chen Yang Chang ◽  
Jing Mei Zhai ◽  
Qin Xiang Xia ◽  
Bin Cai
Keyword(s):  
Support Vector Machine ◽  
Particle Swarm Optimization ◽  
Optimization Design ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Structure Optimization ◽  
Design Parameters ◽  
Support Vector ◽  
Swarm Optimization ◽  
Multi Objective

Aiming at addressing optimization problems of complex mathematical model with large amount of calculation, a method based on support vector machine and particle swarm optimization for structure optimization design was proposed. Support Vector Machine (SVM) is a powerful computational tool for problems with nonlinearity and could establish approximate structures model. Grey relational analysis was utilized to calculate the coefficient between target parameters in order to change the multi-objective optimization problem into a single objective one. The reconstructed models were solved by Particle Swam Optimization (PSO) algorithm. A slip cover at medical treatment was adopted as an example to illustrate this methodology. Appropriate design parameters were selected through the orthogonal experiment combined with ANSYS. The results show this methodology is accurate and feasible, which provides an effective strategy to solve complex optimization problems.

Evolving Particle Swarm Optimization Implemented by a Genetic Algorithm

2008 ◽  
Vol 12 (3) ◽  
pp. 284-289 ◽  
Author(s):  
Jenn-Long Liu ◽  
Keyword(s):  
Genetic Algorithm ◽  
Particle Swarm Optimization ◽  
Social Learning ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Search Space ◽  
Design Parameters ◽  
Search Process ◽  
Swarm Optimization ◽  
Learning Rates

Particle swarm optimization (PSO) is a promising evolutionary approach related to a particle moves over the search space with velocity, which is adjusted according to the flying experiences of the particle and its neighbors, and flies towards the better and better search area over the course of search process. Although the PSO is effective in solving the global optimization problems, there are some crucial user-input parameters, such as cognitive and social learning rates, affect the performance of algorithm since the search process of a PSO algorithm is nonlinear and complex. Consequently, a PSO with well-selected parameter settings may result in good performance. This work develops an evolving PSO based on the Clerc’s PSO to evaluate the fitness of objective function and a genetic algorithm (GA) to evolve the optimal design parameters to provide the usage of PSO. The crucial design parameters studied herein include the cognitive and social learning rates as well as constriction factor for the Clerc’s PSO. Several benchmarking cases are experimented to generalize a set of optimal parameters via the evolving PSO. Furthermore, the better parameters are applied to the engineering optimization of a pressure vessel design.

Detuning the Natural Frequencies of a Compressor Impeller Blade Through the Design Optimization

2015 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Alexander V. Sheremetyev ◽  
Viktor V. Tykhomirov ◽  
Alexey V. Petrov
Keyword(s):  
Natural Frequency ◽  
Centrifugal Compressor ◽  
Natural Frequencies ◽  
Optimization Problems ◽  
Detailed Comparison ◽  
Element Model ◽  
Optimization Method ◽  
Design Parameters ◽  
Impeller Blade ◽  
Compressor Impeller

This paper describes a theoretical approach to shift individual natural frequencies of centrifugal compressor impeller blades. The approach applies sizing optimization of blade’s geometry using a gradient-based optimization method. Calculation of gradients is carried out by the finite-difference method. A new centrifugal compressor blade profile generator incorporating a blade parametrization procedure is developed. The blade’s geometry is parametrized using intuitive geometric parameters. Five design parameters related to the length of the sectional profile generator line, profile thicknesses and rotation angles at hub and shroud are defined for each of the blade sectional profiles. In addition, two global design parameters are defined to control rigid rotation of the blade hub and shroud sections in circumferential direction. Four nonlinear optimization problems containing multiple frequency constraints and constraints on the static equivalent stresses are considered. The optimization aims are either shifting a particular natural frequency of a blade or minimization of blade’s mass. For instance, one of the considered optimization problems is to decrease the 1st natural frequency of an impeller blade by 5%, while the 2nd and the 3rd natural frequencies must be simultaneously increased by 5%. The analysis is applied to the centrifugal compressor of a small-size turboprop engine. A three-dimensional finite element model of the impeller blade is developed in ANSYS Mechanical software package to perform static and modal analyses. The results of the optimization show that the code can meet defined objectives and constraints with reasonable accuracy. A detailed comparison of optimized profiles with the baseline geometry is provided.

scholarly journals Optimal Design of a Dragonfly-Inspired Compliant Joint for Camera Positioning System of Nanoindentation Tester Based on a Hybrid Integration of Jaya-ANFIS

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Ngoc Le Chau ◽  
Thanh-Phong Dao ◽  
Van Thanh Tien Nguyen
Keyword(s):  
Taguchi Method ◽  
Mean Squared Error ◽  
Optimization Problems ◽  
Hybrid Approach ◽  
Design Parameters ◽  
Positioning System ◽  
Jaya Algorithm ◽  
Inference System ◽  
Computing Technique ◽  
Compliant Joint

Camera positioning system is a critical member of a nanoindentation tester characterizing the mechanical properties such as hardness, creep, surface roughness, or elastic modulus of a material sample. This paper presents a design optimization for a dragonfly-inspired compliant joint. This joint is used to drive the camera positioning system. A new hybrid approach of Taguchi method, adaptive neuro-fuzzy inference system (ANFIS), and Jaya algorithm is developed to solve the multi-objective optimization problem. The Taguchi method is used to build the numerical data and to find the best membership functions for the ANFIS structure by minimizing the root mean squared error. Then, the weight factor of each objective function is determined by established equations well. Subsequently, a structure of ANFIS is developed to map the design parameters and responses. Sensitivity analysis of each controllable parameter is analyzed by the statistical method. Finally, Jaya algorithm is initialized to find the optimal solution. The results found that the optimal displacement, frequency, and stress are about 12581.11 μm, 67.76 Hz, and 333.68 MPa, respectively. The proposed hybrid optimization algorithm is a robust and effective optimizer and considered as soft computing technique for engineering optimization problems.

scholarly journals Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Debiao Meng ◽  
Xiaoling Zhang ◽  
Hong-Zhong Huang ◽  
Zhonglai Wang ◽  
Huanwei Xu
Keyword(s):  
Interaction Design ◽  
Large Scale ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
System Level ◽  
Design Parameters ◽  
Large Scale Systems ◽  
Interaction Prediction ◽  
Design Variables ◽  
Subsystem Level

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.

Geometric displacement optimization of external helical gear pumps

2009 ◽  
Vol 223 (9) ◽  
pp. 2191-2199 ◽  
Author(s):  
K J Huang ◽  
C C Chen ◽  
Y Y Chang
Keyword(s):  
Optimization Problems ◽  
Influence Factors ◽  
Flow Characteristics ◽  
Flow Property ◽  
Helical Gear ◽  
Design Parameters ◽  
Face Width ◽  
Design Variables ◽  
Gear Pumps ◽  
Tooth Number

An approach to geometric displacement optimization of external helical gear pumps is presented. In addition, relations of pump flow property and its influence factors are also investigated. During that, only the pumps with transverse contact ratios of not less than one are discussed. First, using the involute property, an analytic representation for flowrates is deduced, by which displacements and fluctuation coefficients of helical gear pumps can be calculated accurately and efficiently. Then, by incorporating several design considerations, optimization problems for maximum geometric displacement are formulated and solved integrally by an optimization code, Multifunctional Optimization System Tool, with which various types of design variables including real, integer, and discrete can be simultaneously dealt with. Finally, the desired pumps with optimal displacement can be obtained. The proposed approach facilitates the design optimization of helical gear pumps. Moreover, influences of design parameters on the displacement and flow characteristics of the optimal pumps by assigning individual parameters are investigated. The result also concludes that the pump with a larger module, larger face width, or smaller tooth number has bigger displacement but may cause more severe flowrate fluctuation.

scholarly journals THE RESULTS OF STUDIES OF THE DEPENDENCE OF THE PERFORMANCE OF THE VIBRATING TWO-SHAFT CENTRIFUGAL MODULE ON THE MODE AND DESIGN PARAMETERS

2019 ◽  
pp. 5-10
Author(s):  
Vladimir Naduty ◽  
Anastasia Loginova ◽  
Vitaliy Sukharev
Keyword(s):  
Rock Mass ◽  
Vibration Amplitude ◽  
Experimental Studies ◽  
Design Parameters ◽  
Crushed Rock ◽  
Experimental Sample ◽  
Elastic Supports ◽  
Loaded Rock ◽  
The Given

The article presents a new design of a vibrating twin-shaft centrifugal module designed for grinding and classification of rock mass. In this design, in addition to grinding, the operation of classification or screening of the crushed mass was added, which does not allow its regrinding and increases the productivity of the device. This is achieved by installing in the bottom of the chamber grinding mesh with cells in accordance with the required class size. At the same time, the classification process is intensified by the presence of vibration from vibration exciters fixed on the camera body and the installation of the camera on elastic supports. The reciprocating horizontal vibrations of the chamber with a given amplitude and frequency contribute to the segregation of the crushed rock mass in the bed by size, which positively affects the efficiency of classification and grinding. The presence of vibration helps to unload the oversize product from the grinding chamber. Also, the article considers experimental studies performed on a vibrational two-shaft centrifugal module to determine the dependence of the performance of a given design on five variable factors: rotor shaft revolutions (n, rpm), size of the loaded rock mass (Δ, mm), rock mass strength (σ, kg/mm2), camera vibration frequency (ω, rpm) and its vibration amplitude (A, mm). Studies have shown the efficiency and increased productivity of the new design in relation to a centrifugal disintegrator without a classification grid and vibration. The results of the work allow us to recommend the design under study for the manufacture of an experimental sample according to the given initial requirements, and the established dependences (Q = f (n, Δ, σ, ω, A) make it possible to develop a mathematical model of the grinding process in this setup to calculate the required parameters.

scholarly journals Refreshment topics II: Design of distillation columns

2006 ◽  
Vol 60 (3-4) ◽  
pp. 92-102
Author(s):  
Svetomir Milojevic ◽  
Dejan Skala
Keyword(s):  
Production Process ◽  
Distillation Column ◽  
Separation Process ◽  
Normal Operation ◽  
Distillation Unit ◽  
Design Parameters ◽  
Specific System ◽  
Variable Parameters ◽  
Distillation Columns ◽  
The Right

For distillation column design it is necessary to define all the variable parameters such as component concentrations in different streams temperatures, pressures, mass and energy flow, which are used to represent the separation process of some specific system. They are related to each other according to specific laws, and if the number of such parameters exceeds the number of their relationships, in order to solve a problem some of them must be specified in advance or some constraints assumed for the mass balance, the balance of energy, phase equilibria or chemical equilibria. Knowledge of specific elements which are the constituents of a distillation unit must be known to define the number of design parameters as well as some additional apparati also necessary to realize the distilation. Each separate apparatus might be designed and constructed only if all the necessary and variable parameters for such a unit are defined. This is the right route to solve a distilation unit in many different cases. The construction of some distillation unit requires very good knowledge of mass, heat and momentum transfer phenomena. Moreover, the designer needs to know which kind of apparatus will be used in the distillation unit to realize a specific production process. The most complicated apparatus in a rectification unit is the distillation column. Depending on the complexity of the separation process one, two or more columns are often used. Additional equipment are heat exchangers (reboilers, condensers, cooling systems, heaters), separators, tanks for reflux distribution, tanks and pumps for feed transportation, etc. Such equipment is connected by pipes and valves, and for the normal operation of a distillation unit other instruments for measuring the flow rate, temperature and pressure are also required. Problems which might arise during the determination and selection of such apparati and their number requires knowledge of the specific systems which must be separated. The experience of the designer and his creativity for proposing a solution for an industrial unit which enables optimal process operation accompanied with minimal energy consumption, as well as a small number of apparati, and minimal total length of pipes and number of instruments is always a valuable additional effect for minimal investment costs and an optimal production process.

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