A Hybrid Contact Implementation Framework for Finite Element Analysis and Topology Optimization of Machine Tools

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Esra Yuksel ◽  
Ahmet Semih Erturk ◽  
Erhan Budak
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Structural Optimization ◽  
Machine Tool ◽  
Machine Tools ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Contact Stiffness ◽  
Contact Forces ◽  
Implementation Framework

Abstract Machine tool contacts must be represented accurately for reliable prediction of machine behavior. In structural optimization problems, contact constraints are represented as an additional minimization problem based on computational contact mechanics theory. An accurate contact constraint representation is challenging for structural optimization problems: (i) “No penetration” rule dictated by Hertz-Signorini-Moreau (HSM) conditions at contacts is satisfied by varying the contact stiffness during a finite element (FE) solution without control of a user which causes increased contact stiffness “erroneously” to avoid penetration of contacting node pairs in an FE solution; and (ii) the reliability of solutions varies according to the chosen computational contact method. This paper is devoted to the topology optimization of machine tools with contact constraints. A hybrid approach is followed that combines the computational contact problem framework and an obtained stable contact stiffness function (analytically or experimentally). According to the proposed method, the existing optimization problem in FE literature is restated in a reliable form for machine tool applications. To avoid the existing computational challenges and reliability problems, contact forces are directly mapped onto an FE model used in the restated topology optimization problem with the help of proposed method. In this study, the existing and the proposed methods for contact are investigated by means of the solid isotropic material with penalization model (SIMP) algorithm for topology optimization. The effectiveness of the proposed method is demonstrated by comparing the experimental measurements on a prototype machine tool manufactured according to the optimization solutions of the proposed method and those of a conventional machine tool.

FE-basierte Optimierung von mehrachsigen Antriebssystemen*/FE-based optimization of multi-axis systems

2018 ◽  
Vol 108 (05) ◽  
pp. 284-288
Author(s):  
W. Herfs ◽  
S. Kehne ◽  
A. Epple
Keyword(s):  
Finite Element ◽  
Machine Tool ◽  
Machine Tools ◽  
Feed Forward ◽  
Finite Elemente

Die Auslegung von Vorschubantrieben in Werkzeugmaschinen ist zu meist ein sehr fehleranfälliger Prozess, da es schwierig ist, abzuschätzen, wie sich die Maschine unter Belastung dynamisch verhält. Diese Veröffentlichung stellt einen Finite-Elemente-basierten Ansatz vor, wie eine Antriebsregelung in eine Mehrkörpersimulation integriert werden kann und wie das Zusammenspiel von zwei Antrieben im Prozess simuliert und optimiert werden kann.   The design of feed forward drives in machine tools is frequently an error-prone process, because it is difficult to estimate how the machine tool acts dynamically during processing. This publication introduces a new finite-element-based approach that integrates axis controllers and is able to simulate and optimize the multi-axis behavior of two axes in a process.

Solving Topology Optimization Problems Using Wavelet Approximations

1998 ◽  
Author(s):  
Giuseppe C. A. DeRose ◽  
Alejandro R. Díaz
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Finite Element Methods ◽  
Condition Number ◽  
Optimization Problems ◽  
Mesh Size ◽  
Elasticity Problem ◽  
New Method ◽  
Galerkin Scheme

Abstract A new method to solve topology optimization problems is discussed. This method is based on the use of a Wavelet-Galerkin scheme to solve the elasticity problem associated with each iteration of the topology optimization sequence. Typically, finite element methods are used for this analysis. However, as the mesh size grows, the computational requirements necessary to solve the finite element equations increase beyond the capacity of current desk top computers. This problem is inherent to finite element methods, as the condition number of finite element matrices increases with mesh size. Wavelet-Galerkin techniques are used to replace standard finite element methods in an attempt to alleviate this problem. Examples demonstrating the performance of the new methodology are presented.

Two-Scale Topology Optimization With Parameterized Cellular Structures

2021 ◽  
Author(s):  
Sina Rastegarzadeh ◽  
Jun Wang ◽  
Jida Huang
Keyword(s):  
Topology Optimization ◽  
High Resolution ◽  
Structural Optimization ◽  
Optimization Problem ◽  
Material Design ◽  
Homogenization Method ◽  
Elasticity Tensor ◽  
Structure Design ◽  
Cellular Structures ◽  
Mapping Technique

Abstract Advances in additive manufacturing enable the fabrication of complex structures with intricate geometric details. It also escalates the potential for high-resolution structure design. However, the increasingly finer design brings computational challenges for structural optimization approaches such as topology optimization (TO) since the number of variables to optimize increases with the resolutions. To address this issue, two-scale TO paves an avenue for high-resolution structural design. The design domain is first discretized to a coarse scale, and the material property distribution is optimized, then using micro-structures to fill each property field. In this paper, instead of finding optimal properties of two scales separately, we reformulate the two-scale TO problem and optimize the design variables concurrently in both scales. By introducing parameterized periodic cellular structures, the minimal surface level-parameter is defined as the material design parameter and is implemented directly in the optimization problem. A numerical homogenization method is employed to calculate the elasticity tensor of the cellular materials. The stiffness matrices of the cellular structures derived as a function of the level parameters, using the homogenization results. An additional constraint on the level parameter is introduced in the structural optimization framework to enhance adjacent cellulars interfaces’ compatibility. Based on the parameterized micro-structure, the optimization problem is solved concurrently with an iterative solver. The reliability of the proposed approach has been validated with different engineering design cases. Numerical results show a noticeable increase in structure stiffness using the level parameter directly in the optimization problem than the state-of-art mapping technique.

Design Optimization of a Beam Structure of Machine Tools

2019 ◽  
Author(s):  
Necmettin Kaya ◽  
M. Onur Genç
Keyword(s):  
Topology Optimization ◽  
Machine Tool ◽  
Machine Tools ◽  
Laser Cutting ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Optimization Technique ◽  
Beam Structure ◽  
Maximum Displacement ◽  
Cutting Machine

Abstract In order to improve the dynamic behavior and cutting accuracy of an industrial laser cutting machine tool, a new beam structure was designed using topology optimization technique. Beams hold the cutting head and laser beam mirrors of laser cutting machine tools. Weight, static and dynamic stiffness of the beam affect the dynamic performance of the machine tool. High weight and low dynamic stiffness in high acceleration and deceleration will result in the vibration of the machine body. In this paper, a new beam is designed using topology optimization to reduce the weight of the beam structure. Static stiffness and natural frequencies were obtained by finite element analyses. The mass reduction obtained was 18%, the maximum displacement is reduced by 13% and the first natural frequency of beam is increased by 29 % in comparison to the original beam. Also the use of aluminum instead of steel was examined and the results are compared.

Comparison Between Structural and Computational Decomposition in Parallel Processing of Design Optimization

1991 ◽  
Author(s):  
Mohamed E. M. El-Sayed ◽  
Ching-Kuo Hsiung
Keyword(s):  
Finite Element ◽  
Parallel Processing ◽  
Structural Optimization ◽  
Parallel Computation ◽  
Optimization Problems ◽  
The Other ◽  
Original Structure ◽  
Element Calculation ◽  
Numerical Examples ◽  
Main Processor

Abstract This paper presents a comparison between two different approaches for parallel computation of structural optimization problems. The first approach decomposes the original structure into several substructures and assigns each substructure to one processor. Each processor handles the finite element calculation of its assigned substructure independently with limited communication between processors. The second approach decomposes the computation of constraint’s gradient evaluation. When a constraint’s gradient evaluation is needed the main processor decomposes it into several computation tasks, then assigns the computation tasks to the other available processors. To compare the speedup of the two approaches some numerical examples on the CRAY X-MP multi-processor system are presented.

Topology Optimization With Multiple Constraints

1995 ◽  
Author(s):  
R. J. Yang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Optimality Criteria ◽  
Topology Design ◽  
Structural Components ◽  
Material Density ◽  
Structural Responses ◽  
Mathematical Programming Method ◽  
General Optimization Problem

Abstract Topology optimization is used for determining the best layout of structural components to achieve predetermined performance goals. The density method which uses material density of each finite element as the design variable is employed. Unlike the most common approach which uses the optimality criteria methods, the topology design problem is formulated as a general optimization problem and is solved by the mathematical programming method. One of the major advantages of this approach is its generality; thus it can solve various problems, e.g. multi-objective and multi-constraint problems. In this study, the structural weight is chosen as the objective function and structural responses such as the compliances, displacements, and the natural frequencies are treated as the constraints. The MSC/NASTRAN finite element code is employed for response analyses. One example with four different optimization formulations was used to demonstrate this approach.

Genetic Optimization for the Design of a Machine Tool Slide Table for Reduced Energy Consumption

2021 ◽  
Vol 143 (10) ◽  
Author(s):  
Matthew J. Triebe ◽  
Fu Zhao ◽  
John W. Sutherland
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Energy Consumption ◽  
Machine Tool ◽  
Machine Tools ◽  
Sandwich Panel ◽  
Sustainable Manufacturing ◽  
Element Model ◽  
Genetic Optimization ◽  
Use Phase

Abstract Reducing the energy consumption of machine tools is important from a sustainable manufacturing perspective. Much of a machine tool’s environmental impact comes from the energy it consumes during its use phase. To move elements of a machine tool requires energy, and if the mass of those elements can be reduced, then the required energy would be reduced. Therefore, this paper proposes a genetic algorithm to design lightweight machine tools to reduce their energy consumption. This is specifically applied to optimize the structure of a machine tool slide table, which moves throughout the use of the machine tool, with the goal of reducing its mass without sacrificing its stiffness. The table is envisioned as a sandwich panel, and the proposed genetic algorithm optimizes the core of the sandwich structure while considering both mass and stiffness. A finite element model is used to assess the strength of the proposed designs. Finite element results indicate that the strength of the lightweight tables is comparable with a traditional table design.

A Two Level Parallel Evolution Strategy for Solving Mixed-Discrete Structural Optimization Problems

1995 ◽  
Author(s):  
Georg Thierauf ◽  
Jianbo Cai
Keyword(s):  
Parallel Computing ◽  
Structural Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Parallel Evolution ◽  
Evolution Strategy ◽  
Parallel Computer ◽  
Computing Architecture ◽  
Design Variables

Abstract A method for the solution of mixed-discrete structural optimization problems based on a two level parallel evolution strategy is presented. On the first level, the optimization problem is divided into two subproblems with discrete and continuous design variables, respectively. The two subproblems are solved simultaneously on a parallel computing architecture. On the second level, each subproblem is further parallelized by means of a parallel sub-evolution-strategy. Periodically, the design variables in the two groups axe exchanged. Examples are included to demonstrate the implementation of this method on a 8 nodes parallel computer.

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