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.

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.

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.

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 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 Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

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