Synthesis of Gear-Linkage Mechanisms by Topology Optimization

2018 ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Synthesis Method ◽  
Variable Stiffness ◽  
Optimization Methods ◽  
Optimization Method ◽  
Planar Mechanisms ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based

This work is concerned with a new mechanism synthesis method for the simultaneous determination of the type, number and dimension of mechanisms by topology optimization. Earlier topology optimization methods can synthesize linkage mechanisms that consist only of links and joints. The proposed synthesis method is a gradient-based topology optimization method useful for the synthesis of planar mechanisms consisting of linkages and gears. To formulate the topology optimization based method, we propose two superposed design spaces as a ground structure: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks while the linkage design space by rigid blocks. The zero-length springs with variable stiffness are used to control the connectivity of blocks, which in turns determines the configuration of the synthesized mechanism. After the proposed topology-optimization-based synthesis formulation is presented, its effectiveness and validity are checked with various synthesis examples.

Topology Optimization of Planar Gear-Linkage Mechanisms

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Neung Hwan Yim ◽  
Seok Won Kang ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Mechanism Synthesis ◽  
Gear Design ◽  
Linkage Design ◽  
Gradient Based ◽  
Mechanical Elements ◽  
Topology Optimization Method

Topology optimization for mechanism synthesis has been developed for the simultaneous determination of the number and dimension of mechanisms. However, these methods can be used to synthesize linkage mechanisms that consist only of links and joints because other types of mechanical elements such as gears cannot be simultaneously synthesized. In this study, we aim to develop a gradient-based topology optimization method which can be used to synthesize mechanisms consisting of both linkages and gears. For the synthesis, we propose a new ground model defined by two superposed design spaces: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks, each of which is assumed to rotate as an output gear, while the linkage design space is discretized by zero-length-spring-connected rigid blocks. Another set of zero-length springs is introduced to connect gear blocks to rigid blocks, and their stiffness values are varied to determine the existence of gears when they are necessary to produce the desired path. After the proposed topology-optimization-based synthesis formulation and its numerical implementation are presented, its effectiveness and validity are checked with various synthesis examples involving gear-linkage and linkage-only mechanisms.

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

scholarly journals An explicit topology optimization method using moving polygonal morphable voids (MPMVs)

2020 ◽  
Vol 23 (2) ◽  
pp. 536-540 ◽  
Author(s):  
Hoang Van-Nam
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Method ◽  
Density Field ◽  
Optimization Approach ◽  
Design Variables ◽  
Mesh Independence ◽  
Gradient Based ◽  
Element Density ◽  
Optimization Solvers

Introduction: Conventional topology optimization approaches are implemented in an implicit manner with a very large number of design variables, requiring large storage and computation costs. In this study, an explicit topology optimization approach is proposed by movonal morphable voids whose geometry parameters are considered as design variables. Methods: Each polygonal void plays as an empty-material zone that can move, change its shapes, and overlap with its neighbors in a design space. The geometry eters of MPMVs consisting of the coordinates of polygonal vertices are utilized to render the structure in the design domain in an element density field. The density function of the elements located inside polygonal voids is described by a smooth exponential function that allows utilizing gradient-based optimization solvers. Results & Conclusion: Compared with conventional topology optimization approaches, the MPMV approach uses fewer design variables, ensure mesh-independence solution without filtering techniques or perimeter constraints. Several numerical examples are solved to validate the efficiency of the MPMV approach.

scholarly journals Robust Topology Optimization Under Load and Geometry Uncertainties by Using New Sparse Grid Collocation Method

2019 ◽  
Author(s):  
Seyyed Ali Latifi Rostami ◽  
Ali Ghoddosian
Keyword(s):  
Topology Optimization ◽  
Applied Load ◽  
Grid Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Monte Carlo Sampling ◽  
Sparse Grid ◽  
Benchmark Problems ◽  
Robust Topology Optimization ◽  
Cheap Alternative

In this paper, a robust topology optimization method presents that insensitive to the uncertainty in geometry and applied load. Geometric uncertainty can be introduced in the manufacturing variability. Applied load uncertainty is occurring in magnitude and angle of force. These uncertainties can be modeled as a random field. A memory-less transformation of random fields used to random variation modeling. The Adaptive Sparse Grid Collocation (ASGC) method combined with the uncertainty models provides robust designs by utilizing already developed deterministic solvers. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using the adaptive sparse grid method. Numerical examples, such as a 2D simply supported beam and cantilever beam as benchmark problems, are used to show the effectiveness and superiority of the ASGC method.

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yi Lin
Keyword(s):  
Synthesis Method ◽  
Optimization Method ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Planar Mechanisms ◽  
Two Phase ◽  
Phase Synthesis ◽  
Optimum Synthesis ◽  
Centroid Distance ◽  
The One

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

scholarly journals Variable stiffness identification and configuration optimization of industrial robots for machining tasks

2020 ◽  
Author(s):  
Jiachen Jiao ◽  
Wei Tian ◽  
Lin Zhang ◽  
Bo Li ◽  
Junshan Hu ◽  
...  
Keyword(s):  
Variable Stiffness ◽  
Optimization Methods ◽  
Optimization Method ◽  
Industrial Robots ◽  
Axial Stiffness ◽  
Configuration Optimization ◽  
Positional Accuracy ◽  
Stiffness Identification ◽  
Robot Stiffness ◽  
High Flexibility

Abstract Industrial robots are increasingly used in machining tasks because of their high flexibility and intelligence. However, the low structural stiffness of the robot seriously affects the positional accuracy and machining quality of robot operation equipment. Studying robot stiffness characteristics and optimization methods is an effective way to improve robot stiffness performance. Accordingly, aiming at the poor accuracy of stiffness modeling caused by approximating stiffness of each joint as constant, a variable stiffness identification method is proposed based on space gridding. Then, a task-oriented axial stiffness evaluation index is proposed to realize quantitative assessment of the stiffness performance in the machining direction. Besides, by analyzing the redundant kinematic characteristics of the robot machining system, a configuration optimization method is further come up with to maximize the index. For a large number of points or trajectory processing tasks, a configuration smoothing strategy is proposed to achieve fast acquisition of optimized configurations. Finally, experiments on a KR500 robot are conducted to verify the feasibility and validity of proposed stiffness identification and configuration optimization methods.

scholarly journals Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

2021 ◽  
Author(s):  
Atul Kumar Sharma ◽  
Gal Shmuel ◽  
Oded Amir
Keyword(s):  
Topology Optimization ◽  
Electric Fields ◽  
Computational Cost ◽  
Optimization Method ◽  
Phononic Crystals ◽  
Frequency Bands ◽  
Design Variables ◽  
Gradient Based ◽  
Soft Dielectrics ◽  
Design Freedom

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable. To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider than those obtained from the previous metaheuristics-based method, while the computational cost to identify them is reduced by orders of magnitude.

Topology optimization of linkage mechanisms simultaneously considering both kinematic and compliance characteristics

2020 ◽  
pp. 1-51
Author(s):  
Sang Min Han ◽  
Yoon Young Kim
Keyword(s):  
Topology Optimization ◽  
Kinematic Chain ◽  
Variable Stiffness ◽  
Optimization Method ◽  
Vehicle Suspension ◽  
Linkage Mechanism ◽  
Mechanism Synthesis ◽  
Kinematic Characteristics ◽  
Mechanism Kinematic ◽  
Topology Optimization Method

Abstract Studies on the topology optimization of linkage mechanisms have thus far focused mainly on mechanism synthesis considering only kinematic characteristics describing a desired path or motion. Here, we propose a new topology optimization method that synthesizes a linkage mechanism considering not only kinematic but also compliance (K&C) characteristics simultaneously, as compliance characteristics can also significantly affect the linkage mechanism performance; compliance characteristics dictate how elastic components, such as bushings in a vehicle suspension, are deformed by external forces. To achieve our objective, we use the spring-connected rigid block model (SBM) developed earlier for mechanism synthesis considering only kinematic characteristics, but we make it suitable for the simultaneous consideration of K&C characteristics during mechanism synthesis by making its zero-length springs multifunctional. Variable-stiffness springs were used to identify the mechanism kinematic configuration only, but now in the proposed approach, they serve to determine not only the mechanism kinematic configuration but also the compliance element distribution. In particular, the ground-anchoring springs used to anchor a linkage mechanism to the ground are functionalized to simulate actual bushings as well as to identify the desired linkage kinematic chain. After the proposed formulation and numerical implementation are presented, case studies are considered. In particular, the effectiveness of the proposed method is demonstrated with a simplified two-dimensional vehicle suspension design problem. This study is expected to pave the way to advance the topology optimization method for general linkage mechanisms whenever K&C characteristics must be simultaneously considered for mechanism synthesis.

scholarly journals Fast Yaw Optimization for Wind Plant Wake Steering Using Boolean Yaw Angles

2021 ◽  
Author(s):  
Andrew P. J. Stanley ◽  
Christopher Bay ◽  
Rafael Mudafort ◽  
Paul Fleming
Keyword(s):  
Greedy Algorithm ◽  
Traditional Method ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
New Method ◽  
Computationally Efficient ◽  
Gradient Based ◽  
Boolean Optimization ◽  
Plant Power

Abstract. In wind plants, turbines can be yawed into the wind to steer their wakes away from downstream turbines and achieve an overall increase in plant power. Mathematical optimization is typically used to determine the best yaw angles at which to operate the turbines in a plant. In this paper, we present a new method to rapidly determine the yaw angles in a wind plant. In this method, we define the turbine yaw angles as Boolean—either yawed at a predefined angle or nonyawed—as opposed to the typical methods of formulating yaw angles as continuous or with fine discretizations. We then optimize which turbines should be yawed with a greedy algorithm that sweeps through the turbines from the most upstream to the most downstream. We demonstrate that our new Boolean optimization method can find turbine yaw angles that perform well compared to a traditionally used gradient-based optimizer where the yaw angles are defined as continuous. There is less than 0.6 % difference in the optimized power between the two optimization methods for randomly placed turbine layouts. Additionally, we show that our new method is much more computationally efficient than the traditional method. For plants with nonzero optimal yaw angles, our new method is generally able to solve for the turbine yaw angles 50–150 times faster, and in some extreme cases up to 500 times faster, than the traditional method.

Metamodel-Based Optimum Design Examples of Structures

2014 ◽  
pp. 667-676
Author(s):  
Kwon-Hee Lee ◽  
Ji-In Heo
Keyword(s):  
Weight Reduction ◽  
Performance Enhancement ◽  
Fuel Efficiency ◽  
Optimization Methods ◽  
Optimization Method ◽  
The Other ◽  
True Response ◽  
Design Variables ◽  
Weight One ◽  
Gradient Based

In order to achieve greater fuel efficiency and energy conservation, the reduction of weight and enhancement of the performance of structures has been sought. In general, there are two approaches to reducing structural weight. One of which is to use materials that are lighter than steel and the other is to redesign the structure. However, conventional structural optimization methods using gradient-based algorithm directly have difficulties in defining complex shape design variables and preventing mesh distortions. To overcome these difficulties a metamodel-based optimization method is introduced in order to replace the true response by an approximate one. This research presents four case studies of structural design using a metamodel-based approximation model for weight reduction or performance enhancement.

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