Optimization of a 2DOF Positioning Stage Using Corrugated Flexure Units Under Stress Constraints

2019 ◽  
Author(s):  
Nianfeng Wang ◽  
Fan Yue ◽  
Canran Li ◽  
Xianmin Zhang
Keyword(s):  
Stress State ◽  
Design Optimization ◽  
Natural Frequency ◽  
Stiffness Matrix ◽  
Stress Constraints ◽  
Axial Stiffness ◽  
Stiffness Ratio ◽  
Maximum Displacement ◽  
Positioning Stage

Abstract The paper introduces the design optimization for micro-positioning stage using corrugated flexure (CF) units under stress constraints. The stress state is solved and the maximum displacement under stress constraints is deduced. The natural frequency formula of the micro-positioning stage is further derived from the results of the stiffness matrix. Finally, the stage configurations corresponding to the maximum displacement are optimized by restricting the off-axis/axial stiffness ratio and natural frequency of the stage.

Optimization of Translational Flexure Joints Using Corrugated Units Under Stress Constraints

2021 ◽  
pp. 1-12
Author(s):  
Canran Li ◽  
Nianfeng Wang ◽  
Fan Yue ◽  
Xianmin Zhang
Keyword(s):  
Natural Frequency ◽  
Stiffness Matrix ◽  
Maximum Stress ◽  
Stress Constraints ◽  
Axial Stiffness ◽  
Stiffness Ratio ◽  
Maximum Displacement ◽  
Element Analysis ◽  
Different Types ◽  
Flexure Joints

Abstract When optimizing 2-DOF corrugated flexure stages, most approaches for calculating the maximum stress on the corrugated flexure (CF) beam depend on finite element analysis (FEA). The current paper introduces the design optimization for stages using CF units under stress constraints. The stress state is solved; then, based on that, the maximum displacement under stress constraints is deduced. The natural frequency formula of the micropositioning stage is further derived from the results of the stiffness matrix. The stage configurations corresponding to the maximum displacement are optimized by restricting the off-axis/axial stiffness ratio and natural frequency of the stage. The optimal results of different types are validated by FEA and experiments.

Design of a Micro-Positioning Stage Using Corrugated Flexure Beam With Cubic Bézier Curve Segments

2018 ◽  
Author(s):  
Nianfeng Wang ◽  
Zhiyuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Axial Stiffness ◽  
Control Points ◽  
Stiffness Ratio ◽  
Element Analysis ◽  
Positioning Stage ◽  
Cubic Bezier Curve

The paper introduces an analytical stiffness matrix method to model a new type of corrugated flexure (CF) beam with cubic Bézier curve segments. In order to satisfy particular design specifications, shape variation for limited geometric envelopes are often employed to alter the elastic properties of flexure hinges. In this paper, cubic Bézier curves are introduced to replace the axis of CF unit to rebuild the CF beam and the micro-positioning stage. Mohr’s integral method is applied to derive the stiffness matrix of the cubic Bézier curve segment. Modeling of the CF unit and the CF beam with cubic Bézier curve segments are further carried out through stiffness matrix method, which are confirmed by finite element analysis (FEA). Discussions about the two control points of the cubic Bézier curve segments are then conducted through search optimization, which highlights the off-axis/axial stiffness ratio and the axial compliance on the position of the two control points, to enable the micro-positioning stage both achieving high off-axis/axial stiffness ratio and large axial compliance. The derived analytical model provides a new option for the design of the CF beam.

Analytical Solution of the Vibration of Delaminated Bimaterial Beams Fully or Partially Supported by Elastic Foundation

2013 ◽  
Vol 394 ◽  
pp. 75-79 ◽  
Author(s):  
Yang Liu ◽  
Dong Wei Shu
Keyword(s):  
Analytical Solution ◽  
Natural Frequency ◽  
Elastic Foundation ◽  
Numerical Solutions ◽  
Vibration Characteristics ◽  
Axial Stiffness ◽  
Stiffness Ratio ◽  
Empirical Estimation ◽  
Beam On Elastic Foundation ◽  
Free Mode

Delaminations in structures may significantly reduce the stiffness and strength of the structure and may affect their vibration characteristics. In the present study, an analytical solution is developed to study the vibration of delaminated bimaterial beams fully or partially supported by elastic foundation. The free mode and constrained mode assumptions in delamination vibration are adopted. This is the first study on the vibration of delaminated bimaterial beam on elastic foundation. Results show that the effect of delamination on reducing natural frequency is aggravated by an increasing stiffness of elastic foundation. An empirical estimation of such effects is provided for engineers. The effects of elastic foundation on the variation of natural frequency against axial stiffness ratio and bending stiffness ratio of beams are thoroughly investigated. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.

Performance evaluation of a special 6-PUS type parallel manipulator

Robotica ◽  
2021 ◽  
pp. 1-15
Author(s):  
Xiaochu Liu ◽  
Yunfei Cai ◽  
Weitian Liu ◽  
Linlong Zhang ◽  
Chengxin Hu
Keyword(s):  
Performance Evaluation ◽  
Natural Frequency ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Shaking Table ◽  
Axial Stiffness ◽  
Neutral Position ◽  
Dynamics Model ◽  
Force Transmissibility ◽  
Kane Method

Abstract In this paper, a special 6-PUS parallel manipulator (PM) is utilized as a shaking table. Unlike the existing results about 6-PUS PMs, we make the actuator direction collinear with the linkage direction at neutral position. With respect to the application background, a further analysis of the special PM is carried out from the perspective of motion/force transmissibility, natural frequency and acceleration capability. Specially, the complete dynamics model is established based on the Kane method. Then, generalized transmission indices based on the screw theory are utilized to reflect its motion ability, and a model of natural frequency is proposed with the axial stiffness of linkages considered. Finally, the effect of the angle between the actuator direction and the linkage direction α on various performances is analyzed, and other results are included to illustrate its feasibility and usability.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

Finite Element Synthesis for Design Optimization

2012 ◽  
Author(s):  
Mahmoud R. Saad ◽  
Sayed M. Metwalli
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Design Optimization ◽  
Linear Relation ◽  
Stiffness Matrix ◽  
Allowable Stress ◽  
Uniform Stress ◽  
Mechanical Structure ◽  
Finite Element Methodology

The present work introduces a new Finite Element methodology that can be used directly in calculating and optimizing the thickness of a mechanical structure. This method depends on the constant strain triangle model after assuming different thicknesses at the elements nodes. A linear relation between the nodes thicknesses is assumed and a new stiffness matrix is created. Nodes thicknesses are optimized using the developed HGP method to reach uniform stress among the structure to satisfy the constrained allowable stress designated by the designer. Examples and sample applications are employed for comparisons and their results culminate in removing unnecessary elements and increasing the thickness, which is subjected to high stresses. Results indicate marked improvements and potential for topology optimization.

Influence of Axial Boundary Conditions on Free Spanning Pipeline Natural Frequencies

2013 ◽  
Author(s):  
Gareth L. Forbes ◽  
Ahmed M. Reda
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Theoretical Calculation ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Axial Stiffness ◽  
Simple Boundary ◽  
Complex Boundary

The effect of axial restraint (boundary conditions) on the natural frequency of a free spanning pipeline is examined in this paper. Theoretical calculation of the natural frequency of a straight pipeline with simple boundary conditions is a trivial task with exact solutions being available. A pipeline lying on the seabed however is neither completely straight and the interaction with the soil at the span shoulders create more complex boundary conditions. DNV-RP-F105 provides guidance on the calculation of free span boundary conditions with these increased complexities. The DNV recommended practice does not however take into account the effect of the axial restraint on the natural frequency. Results are presented in this paper for a range of axial stiffness combined with span out of straightness for a free spanning pipeline. The results presented show that the effect of axial restraint for moderately out of straight free spans can cause significant deviation in the calculation of the span natural frequency.

Sensitivity Study of Pseudodynamic Algorithm with Structure-Dependent Quadrature Equations

2015 ◽  
Vol 15 (05) ◽  
pp. 1450069
Author(s):  
Shuenn-Yih Chang
Keyword(s):  
Bifurcation Point ◽  
Stiffness Matrix ◽  
Stability Problem ◽  
Error Propagation ◽  
Sensitivity Study ◽  
Unconditional Stability ◽  
Conditional Stability ◽  
Stiffness Ratio ◽  
Initial Stiffness ◽  
Propagation Properties

An estimated initial stiffness matrix is generally needed to determine the coefficient matrices of quadrature equations for a structure-dependent pseudodynamic algorithm. It is shown herein that an experimentally determined initial stiffness matrix is, in general, close to the true initial stiffness matrix if an imposed displacement is small enough. This case is often encountered in practice. The case where an estimated initial stiffness is different from a true initial stiffness for employing a structure-dependent pseudodynamic algorithm is also explored. The numerical properties and error propagation properties are evaluated as a function of the initial stiffness ratio, which is the ratio of an estimated initial stiffness over a true initial stiffness. In general, accuracy and error propagation properties are insensitive to the initial stiffness ratio. It seems that the change of bifurcation point between unconditional stability and conditional stability is of worth noting. In order to avoid this stability problem, guidelines are recommended if a structure-dependent pseudodynamic algorithm is used.

Postbuckling and Free Vibrations of Composite Beams

2007 ◽  
Author(s):  
Samir A. Emam ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Axial Load ◽  
Closed Form Solution ◽  
Composite Beams ◽  
Free Vibrations ◽  
Form Solution ◽  
Mode Shapes ◽  
Axial Stiffness ◽  
Fundamental Natural Frequency ◽  
Transverse Vibrations

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse vibrations of a composite laminated beam accounting for the midplane stretching are presented. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single equation governing the transverse vibrations. This equation is a nonlinear fourth-order partial-integral differential equation. We find that the governing equation for the postbuckling of a symmetric or antisymmetric composite beam has the same form as that of a metallic beam. A closed-form solution for the postbuckling configurations due to a given axial load beyond the critical buckling load is obtained. We followed Nayfeh, Anderson, and Kreider and exactly solved the linear vibration problem around the first buckled configuration to obtain the fundamental natural frequencies and their corresponding mode shapes using different fiber orientations. Characteristic curves showing variations of the maximum static deflection and the fundamental natural frequency of postbuckling vibrations with the applied axial load for a variety of fiber orientations are presented. We find out that the line-up orientation of the laminate strongly affects the static buckled configuration and the fundamental natural frequency. The ratio of the axial stiffness to the bending stiffness is a crucial parameter in the analysis. This parameter can be used to help design and optimize the composite beams behavior in the postbuckling domain.

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