scholarly journals Output decoupling property of planar flexure-based compliant mechanisms with symmetric configuration

2016 ◽  
Vol 7 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Y. S. Du ◽  
T. M. Li ◽  
Y. Jiang ◽  
J. L. Zhang
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Element Analysis ◽  
Modeling Methods ◽  
Stiffness Modeling ◽  
Symmetric Configuration ◽  
Parallel Structures ◽  
The Matrix ◽  
Micro Motion ◽  
Good Agreement

Abstract. This paper presents the output decoupling property of planar flexure-based compliant mechanisms with symmetric configuration. Compliance/stiffness modeling methods for flexure serial structures and flexure parallel structures are first derived according to the matrix method. Analytical model of mechanisms with symmetric configuration is then developed to analyze the output decoupling property. The proposed analytical model shows that mechanisms are output decoupled when they are symmetry about two perpendicular axes or when they are composed of either three or an even number of identical fundamental forms distributed evenly around the center. Finally, output compliances of RRR and 4-RRR compliant micro-motion stages are derived from the analytical model and finite element analysis (FEA). The comparisons indicate that the results obtained from the proposed analytical model are in good agreement with those derived from FEA, which validates the proposed analytical model.

Characterization and Modeling of Elastomeric Joints in Miniature Compliant Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Dana E. Vogtmann ◽  
Satyandra K. Gupta ◽  
Sarah Bergbreiter
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Analytical Models ◽  
Accurate Analysis ◽  
Element Analysis ◽  
Fea Model ◽  
Torsional Spring ◽  
Tension Tests ◽  
In Series ◽  
Efficient Exploration

Accurate analysis models are critical for effectively utilizing elastomeric joints in miniature compliant mechanisms. This paper presents work toward the characterization and modeling of miniature elastomeric hinges. Characterization was carried out in the form of several experimental bending tests and tension tests on representative hinges in five different configurations. The modeling portion is achieved using a planar pseudo rigid body (PRB) analytical model for these hinges. A simplified planar 3-spring PRB analytical model was developed, consisting of a torsional spring, an axial spring, and another torsional spring in series. These analytical models enable the efficient exploration of large design spaces. The analytical model has been verified to within an accuracy of 3% error in pure bending, and 7% in pure tension, when compared to finite element analysis (FEA) models. Using this analytical model, a complete mechanism—a robotic leg consisting of four rigid links and four compliant hinges—has been analyzed and compared to a corresponding FEA model and a fabricated mechanism.

Analytical Model for a Superelastic SMA Beam

2017 ◽  
Author(s):  
N. V. Viet ◽  
Wael Zaki ◽  
Rehan Umer
Keyword(s):  
Analytical Model ◽  
Bending Moment ◽  
Analytical Relation ◽  
Beam Model ◽  
Element Analysis ◽  
Austenitic Phase ◽  
Martensite Variant ◽  
The Moment ◽  
Reversible Phase ◽  
Good Agreement

We propose an analytical model for a superelastic shape memory alloy (SMA) beam. The model considers reversible phase transformation between austenite and a single martensite variant driven by mechanical loading/unloading. In particular, we consider a cantilever beam subjected to a concentrated transverse force acting at the tip. The force is gradually increased from zero to a maximum value sufficient to cause complete transformation of the initially austenitic phase into martensite away from the beam core. The force is then gradually removed, resulting in complete strain recovery. In each stage of the loading/unloading process, an analytical relation is established between bending moment and curvature in terms of position along the axis of the beam. The model is compared to a uniaxial numerical beam model and to finite element analysis (FEA) results for the same beam in 3D, with very good agreement in each case. The moment-curvature relation is then integrated to obtain a nonlinear expression for the deflection and stress distribution in terms of position along the length of the beam. The expression is validated against 3D simulation results.

An Improved Unified Solution for a Vibration Equation of Tension-Stiffening Beam Using Extended Rayleigh Energy Method

2019 ◽  
Author(s):  
Zhijun Yang ◽  
Ruiqi Li ◽  
Youdun Bai
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Energy Method ◽  
Physical Science ◽  
Element Analysis ◽  
Tension Stiffening ◽  
Design And Optimization ◽  
Micro Motion ◽  
Stiffening Effect ◽  
Good Agreement

Abstract The tension-stiffening effect is very important for physical science, which has been widely used in MEMS, sensors and micro-motion stages. The analytical solutions of the tension-stiffening beam are extremely significant, in consideration of the inefficiency of finite element analysis (FEA) for the design and optimization. Commonly, there are three typical types of boundary conditions for tension-stiffening (or stress-induced) beams, i.e., clamped-clamped, clamped-hinged, and hinged-hinged. But only the hinged-hinged beam has an analytical solution. Therefore, a method based on extended Rayleigh energy method is proposed in this paper to deduce the analytical solutions of three boundary conditions. The predictions are verified to be in good agreement with FEA and experiment results.

A Three-Dimensional Analytical Stability Model of Contra-Rotating Compressors Based on Partial Simplification of Euler Equation

2018 ◽  
Author(s):  
Weixiong Chen ◽  
Yangang Wang ◽  
Hao Wang ◽  
Shuanghou Deng ◽  
Haiqi Qin
Keyword(s):  
Euler Equation ◽  
Analytical Model ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Rotating Stall ◽  
Analytical Stability ◽  
Stability Model ◽  
The Matrix ◽  
Unsteady Numerical Simulation ◽  
Good Agreement

The present study developed a three-dimensional compressible analytical model for predicting the rotating stall boundary in turbomachinery. Based on the small perturbation theory and the inviscid Euler equation. Using the perturbation wave dispersion theory and boundary conditions, the problem of stall prediction in turbomachinery can be regarded as the solution of the matrix eigenvalue problem. To validate the feasibility and accuracy of the developed analytical model. After that, the NASA Rotor 67 and NASA Stage 35, which have been disclosed in detail, are selected to validate the 3D analytical model. Results has been successfully verified the accuracy of the developed prediction model. Meanwhile, the advantages of the 3D analytical model, which considers the radial mainstream velocity and disturbance velocity are also demonstrated in comparison with the 2D model developed by Ludwig et al. Finally, the three-dimensional analytical model is used to predict the stall boundary of a contra-rotating compressor test rig. Results show that the downstream rotor encounters rotating stall firstly, and the stall mass flow is about 5.871kg/ s. A good agreement has been also revealed from the unsteady numerical simulation and thus again evidence the ability of the developed three-dimensional analytical model in terms of accuracy and efficiency.

Effect of the Carbon Nanotube Distribution on the Thermal Conductivity of Composite Materials

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Iman Eslami Afrooz ◽  
Andreas Öchsner
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Finite Element Analysis ◽  
Composite Materials ◽  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Fiber Volume ◽  
Element Analysis ◽  
The Matrix ◽  
Good Agreement

Finite element analysis has been employed to investigate the effect of carbon nanotubes (CNTs) distribution on the thermal conductivity of composite materials. Several kinds of representative volume elements (RVEs) employed in this study are made by assuming that unidirectional CNTs are randomly distributed in a polymer matrix. It is also assumed that each set of RVEs contains a constant fiber volume fraction and aspect ratio. Results show that randomness—the way in which fibers are distributed inside the matrix—has a significant effect on the thermal conductivity of CNT composites. Results of this study were compared using the analytical Xue and Nan model and good agreement was observed.

Characterization and Modeling of Elastomeric Joints in Miniature Compliant Mechanisms

2012 ◽  
Author(s):  
Dana E. Vogtmann ◽  
Satyandra K. Gupta ◽  
Sarah Bergbreiter
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Analytical Models ◽  
Accurate Analysis ◽  
Element Analysis ◽  
Torsional Spring ◽  
Tension Tests ◽  
In Series ◽  
Linear Spring ◽  
Analysis Models

Accurate analysis models are critical for effectively utilizing elastomeric joints in miniature compliant mechanisms. This paper presents work toward the characterization and modeling of miniature elastomeric hinges. The modeling portion is achieved using finite element analysis (FEA). Also presented is a 2-dimensional pseudo rigid body (PRB) analytical model for these hinges. Characterization was carried out in the form of several experimental bending tests and tension tests on representative hinges in 5 different configurations. The results of these experiments were then compared to the same tests modeled using FEA. We have represented the experimental results using FEA to within 12% error. This allows the use of FEA to model more complicated mechanisms’ behavior with some assurance of accuracy. Based on these tests and FEA models, a simplified 2-dimensional PRB analytical model was developed, consisting of a torsional spring, a linear spring, and another torsional spring in series. These analytical models enable us explore large design spaces efficiently. The accuracy of this model for geometries without corner effects has been verified to within 3% error when compared to FEA models in bending, and 17% in tension.

scholarly journals Analysis of Local Delamination in A Cracked Composite Laminate Loaded in Tension

1993 ◽  
Vol 2 (6) ◽  
pp. 096369359300200
Author(s):  
J. Zhang ◽  
C. Soutis
Keyword(s):  
Composite Laminate ◽  
Crack Density ◽  
Strain Energy Release ◽  
Matrix Crack ◽  
Total Strain Energy ◽  
Element Analysis ◽  
The Matrix ◽  
Dimensional Finite Element ◽  
Elastic Fracture ◽  
Good Agreement

In the present paper the total strain energy release rate G associated with delaminations that initiate from a matrix crack in a [±θm/90n]s composite laminate is calculated using the potential energy approach in elastic fracture mechanics. The predictions are compared with a two-dimensional finite element analysis. It is found that for delamination lengths greater than two-ply thicknesses the theoretical and numerical results are in good agreement. The new model shows that G is affected by the matrix crack density and residual hygrothermal stresses.

Optimal Structural Design of Micro-Motion Stage with Stiffness Constraints Using Topology and Sizing Optimization Method

2016 ◽  
Vol 679 ◽  
pp. 55-58
Author(s):  
You Dun Bai ◽  
Zhi Jun Yang ◽  
Xin Chen ◽  
Meng Wang
Keyword(s):  
Compliant Mechanisms ◽  
Optimization Methods ◽  
Flexure Hinge ◽  
Leaf Spring ◽  
Element Analysis ◽  
Sizing Optimization ◽  
Flexure Hinges ◽  
Spring Type ◽  
Micro Motion ◽  
Motion Stage

Flexure hinge is widely used in the compliant mechanisms for precision engineering. Generally, compliant mechanisms with flexure hinges are designed using the analytical stiffness formulas, which increases the design complexity. As the development of finite element analysis (FEA) and optimization methods, it is likely to design the flexure hinges directly using the FEA based numerical optimization methods. This paper developed a leaf spring type flexure hinge based micro-motion stage with specific stiffness constraints. Both topology and sizing optimization methods are used in the design of motion stage. The proposed methods is apply to optimal design formed the leaf spring type flexure hinge for a micro motion stage which serves as a guidance mechanism. Further numerical result shows the good stiffness stability of the refined stage.

scholarly journals Development of A New Type of 2-DOF Piezo-Actuated Pseudo-Decoupled Compliant Mechanism for Elliptical Vibration Machining

Micromachines ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 122
Author(s):  
Rongqi Wang ◽  
Xiaoqin Zhou ◽  
Guangwei Meng
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Major Axis ◽  
Response Analysis ◽  
Element Analysis ◽  
Elliptical Vibration ◽  
Compliance Modeling ◽  
The Matrix ◽  
Dynamic Performances ◽  
Harmonic Response Analysis

Currently, the elliptical vibration cutting/coining (EVC2) has been widely employed in fabricating various functional microstructure surfaces applied in many significant engineering fields. Therefore, for this study, a novel type of two-degree-of-freedom (2-DOF) piezoelectrically actuated pseudo-decoupled compliant mechanisms (PDCMs) with non-orthogonal decoupling structures, which can exactly generate the strict ellipse trajectories, was developed for improving the forming accuracies of the EVC2 microstructures. First, the compliance matrices of 2-DOF PDCMs were theoretically modeled using the popular finite beam-based matrix modeling (FBMM) and the matrix-based compliance modeling (MCM) methods, then finite element analysis (FEA) was adopted to verify the effectiveness of the built compliance model for the 2-DOF PDCM with arbitrary structure parameters. Second, the static FEA method was employed to systematically reveal the dependencies of the tracking accuracies of the elliptical trajectories on the decoupling structures of 2-DOF PDCMs. Moreover, their main dynamic performances were also investigated through the FEA-based harmonic response analysis and modal analysis. On these bases, the critical angle of the decoupling structure was optimally set at 102.5° so that the PDCMs had minimum shape distortions of the ellipse trajectories. Thirdly, a series of experiments was conducted on this PDCM system for practically investigating its kinematic and dynamic performances. The actual aspect ratio between the major axis and minor axis of the ellipse trajectory was approximately 1.057, and the first-order and second-order resonant frequencies were 863 Hz and 1893 Hz, respectively. However, the obtained testing results demonstrated well the effectiveness and feasibility of 2-DOF PDCM systems in precisely tracking the ellipse trajectories with different geometric parameters. Several critical conclusions on this study are summarized in detail in the final section of this paper.

Stiffness characteristics of inner–outer ring flexure pivots applied to the ultra-precision instruments

2017 ◽  
Vol 232 (13) ◽  
pp. 2441-2457
Author(s):  
Lang Liu ◽  
Shusheng Bi ◽  
Qizi Yang
Keyword(s):  
Analytical Model ◽  
Strain Energy ◽  
Compliant Mechanisms ◽  
Outer Ring ◽  
Element Analysis ◽  
Qualitative Comparison ◽  
Ultra Precision ◽  
Stiffness Characteristics ◽  
Work First ◽  
Energy Formulation

The inner-outer ring flexure pivot (IORFP), composed of three straight springs that cross each other in space, is studied in this work. First, to emphasize the study value of IORFP, qualitative comparison is applied to IORFP and some of most commonly used flexure pivots. Then an analytical model for the rotational stiffness of IORFP is developed based on the strain energy formulation of a beam flexure, and model applicability is provided as well. Analysis of stiffness, buckling load, and the nonlinear of moment–rotation relation is then carried out. Subsequently, the analytical model is verified by finite element analysis. After that, seven prototypes of IORFP are manufactured, and their rotational stiffnesses are tested. The results show that the analytical model can be used for analysis and designing of compliant mechanisms that contain IORFP. Finally, the study quantitatively compares stiffness characteristics and axis drift of IORFP and the generalized cross-spring pivot, indicating that the former significantly outperforms the latter. IORFP possesses excellent performances and can be widely used to supplant generalized cross-spring pivot in compliant mechanisms and ultra-precision instruments.

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