Elastodynamic Modeling and Analysis for an Exechon Parallel Kinematic Machine

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Jun Zhang ◽  
Yan Q. Zhao ◽  
Yan Jin
Keyword(s):  
Differential Equations ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Structural Features ◽  
Parallel Kinematic Machine ◽  
Dynamic Behaviors ◽  
Elastodynamic Modeling ◽  
Parallel Kinematic ◽  
Moving Platform

As a newly invented parallel kinematic machine (PKM), Exechon has attracted intensive attention from both academic and industrial fields due to its conceptual high performance. Nevertheless, the dynamic behaviors of Exechon PKM have not been thoroughly investigated because of its structural and kinematic complexities. To identify the dynamic characteristics of Exechon PKM, an elastodynamic model is proposed with the substructure synthesis technique in this paper. The Exechon PKM is divided into a moving platform subsystem, a fixed base subsystem and three limb subsystems according to its structural features. Differential equations of motion for the limb subsystem are derived through finite element (FE) formulations by modeling the complex limb structure as a spatial beam with corresponding geometric cross sections. Meanwhile, revolute, universal, and spherical joints are simplified into virtual lumped springs associated with equivalent stiffnesses and mass at their geometric centers. Differential equations of motion for the moving platform are derived with Newton's second law after treating the platform as a rigid body due to its comparatively high rigidity. After introducing the deformation compatibility conditions between the platform and the limbs, governing differential equations of motion for Exechon PKM are derived. The solution to characteristic equations leads to natural frequencies and corresponding modal shapes of the PKM at any typical configuration. In order to predict the dynamic behaviors in a quick manner, an algorithm is proposed to numerically compute the distributions of natural frequencies throughout the workspace. Simulation results reveal that the lower natural frequencies are strongly position-dependent and distributed axial-symmetrically due to the structure symmetry of the limbs. At the last stage, a parametric analysis is carried out to identify the effects of structural, dimensional, and stiffness parameters on the system's dynamic characteristics with the purpose of providing useful information for optimal design and performance improvement of the Exechon PKM. The elastodynamic modeling methodology and dynamic analysis procedure can be well extended to other overconstrained PKMs with minor modifications.

Characteristic Equation-Based Dynamic Analysis of a Three-Revolute Prismatic Spherical Parallel Kinematic Machine

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Jun Zhang ◽  
Jian S. Dai ◽  
Tian Huang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Eigenvalue Decomposition ◽  
Mode Shapes ◽  
Design Parameters ◽  
Parallel Kinematic Machine ◽  
Characteristic Equations ◽  
Parallel Kinematic ◽  
Compliance Model

A three-revolute prismatic spherical (3-RPS) parallel kinematic machine (PKM) module is proposed as an alternative solution for high-speed machining (HSM) tool. Considering the PKM as a typical compliant parallel device, whose three limb assemblages have bending, extending, and torsional deflections, this paper applies screw theory to establish an analytical compliance model for the device. The developed compliance model is then combined with the energy method to deduce a comprehensive dynamic model of the 3-RPS module. The solution for the characteristic equations of the dynamic model leads to the modal properties of the PKM module. Based on the eigenvalue decomposition of the characteristic equations, a modal analysis is conducted. The natural frequencies and corresponding mode shapes at typical and nontypical configurations are analyzed and compared with finite element analysis (FEA) results. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of natural frequencies throughout the workspace are predicted to reveal a strong dependency of dynamic characteristics on mechanism's configurations. At the last stage, the effects of some design parameters on system dynamic characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement for the PKM.

scholarly journals Rapid Evaluation for Position-Dependent Dynamics of a 3-DOF PKM Module

2014 ◽  
Vol 6 ◽  
pp. 238928 ◽  
Author(s):  
Hai-wei Luo ◽  
Hui Wang ◽  
Jun Zhang ◽  
Qi Li
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Parallel Kinematic Machine ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Reduction Techniques ◽  
Modal Reduction ◽  
Governing Differential Equation ◽  
Parallel Kinematic ◽  
Analytical System

Based on the substructure synthesis and modal reduction technique, a computationally efficient elastodynamic model for a fully flexible 3-RPS parallel kinematic machine (PKM) tool is proposed, in which the frequency response function (FRF) at the end of the tool can be obtained at any given position throughout its workspace. In the proposed elastodynamic model, the whole system is divided into a moving platform subsystem and three identical RPS limb subsystems, in which all joint compliances are included. The spherical joint and the revolute joint are treated as lumped virtual springs with equal stiffness; the platform is treated as a rigid body and the RPS limbs are modelled with modal reduction techniques. With the compatibility conditions at interfaces between the limbs and the platform, an analytical system governing differential equation is derived. Based on the derived model, the position-dependent dynamic characteristics such as natural frequencies, mode shapes, and FRFs of the 3-RPS PKM are simulated. The simulation results indicate that the distributions of natural frequencies throughout the workspace are strongly dependant on mechanism's configurations and demonstrate an axial-symmetric tendency. The following finite element analysis and modal tests both validate the analytical results of natural frequencies, mode shapes, and the FRFs.

Effect of Slenderness Ratio on the Natural Frequencies of Pre-Twisted Cantilever Beams of Uniform Rectangular Cross-Section

1971 ◽  
Vol 13 (1) ◽  
pp. 51-59 ◽  
Author(s):  
B. Dawson ◽  
N. G. Ghosh ◽  
W. Carnegie
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Slenderness Ratio ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Rotary Inertia ◽  
Cantilever Beams

This paper is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform rectangular cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method introduced by Dawson (1)§ for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. The natural frequencies for the first five modes of vibration are obtained for beams of various breadth to depth ratios and lengths ranging from 3 to 20 in and pre-twist angle in the range 0–90°. The results are compared with those obtained by an alternative method (2), where available, and also to experimental results.

Mechanical Behavior of an Electrostatically Actuated Microplate

2003 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Finite Dimension ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Mode Shapes ◽  
Design Parameters ◽  
Electrostatically Actuated ◽  
Linear Eigenvalue Problem ◽  
Electrically Actuated

We present a nonlinear model of electrically actuated microplates. The model accounts for the nonlinearity in the electric forcing as well as mid-plane stretching of the plate. We use a Galerkin approximation to reduce the partial-differential equations of motion to a finite-dimension system of nonlinearly coupled second-order ordinary-differential equations. We find the deflection of the microplate under DC voltage and study the pull-in phenomenon. The natural frequencies and mode shapes are then obtained around the deflected position of the microplate by solving the linear eigenvalue problem. The effect of various design parameters on both the static response and the dynamic characteristics are studied.

Research on Hydro-Pneumatic Balanced Suspension of Multi-Spindled Vehicle

2011 ◽  
Vol 66-68 ◽  
pp. 855-861 ◽  
Author(s):  
Lin Yang ◽  
Jun Wei Zhang ◽  
Si Zhong Chen
Keyword(s):  
Differential Equations ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Structural Features ◽  
Pneumatic Suspension

A hydro-pneumatic balanced suspension is proposed based on the structural features of general hydro-pneumatic suspension and balanced suspension. Two types of suspensions mathematics models are built and differential equations of motion are derived with Lagrange-Equation. Performance of the two suspensions is simulated with the software of MATLAB. The results show that ride performance of vehicles is improved using hydro-pneumatic balanced suspension. Therefore, hydro-pneumatic balanced suspension is more suitable for multi-spindled vehicles.

Dynamic Behavior of Ground-Effect Machines in Motion Over Waves

1963 ◽  
Vol 7 (02) ◽  
pp. 1-10
Author(s):  
J. D. Lin
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Mass Flow ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Ground Effect ◽  
Small Disturbance ◽  
Third Order ◽  
Dynamic Motion ◽  
Theoretical Predictions

Dynamic motion in heaving and pitching of a ground-effect machine traveling over a train of sinusoidal waves is formulated on the basis of the small-disturbance theory. The equations of motion are derived as two third-order ordinary differential equations with coefficients which depend on the characteristics of the machine and the mass flow into or out of the cavity under the machine. The coefficienis are linearized at the equilibrium height; then, the solutions are obtained for the natural frequencies, the damping, and the steady periodic responses to motion over waves. It is found that a ground-effect machine with peripheral and central jet curtains is generally stable for heaving and pitching, but the damping is rather small. The effect of coupling due to the discontinuity of mass-flow coefficients is also shown to be very weak and thus may be neglected in this linearized analysis. A program, prepared for the IBM 1 620 digital computers at Hydronautics, Incorporated, allows study of the dynamic stability of a machine through variation of pertinent parameters, and also investigations of its dynamic response to various wave-encounter conditions. Theoretical predictions for practical machines, which have in model tests experienced dynamic motions over waves, are presented here and compared with experimental results. Satisfactory agreements are indicated in the natural frequency and response both for heaving and pitching.

Dynamic Characteristics of Resonant Beams With Passive Thermal Stress Regulators

2018 ◽  
Author(s):  
Tyler Kellar ◽  
Pezhman Hassanpour
Keyword(s):  
Boundary Condition ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Mode Shapes ◽  
Elastic Boundary ◽  
Special Cases ◽  
Angular Displacements

This paper addresses the dynamic characteristics of a beam with a particular elastic boundary condition. In this elastic boundary condition, the lateral and angular displacements of the beam are coupled through the elastic constraints. The dynamic characteristic, namely natural frequencies and mode shapes of vibrations are frequently encountered in the design and modeling of resonant micro-structures. The governing equations of motion of the beam is derived using Euler-Bernoulli beam theory considering the elastic coupling between the transverse and rotational displacements of the beam’s end. The characteristic equation for the natural frequencies and mode shapes of vibration is derived by applying the method of separation of variables to the governing partial differential equation of motion. The natural frequencies and mode shapes of the system are derived for various combinations of compliance values of the elastic support and are compared with those of several special cases, namely clamped-free, clamped-guided, clamped-pinned and clamped-clamped beams.

Nonlinear Equations of Motion for the Maneuvering Flexible Aircraft Wings

2006 ◽  
Author(s):  
S. Ahmad Fazelzadeh ◽  
Abbas Mazidi
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Body Motion ◽  
Dynamical Equations ◽  
Flexible Wings ◽  
Aircraft Wings ◽  
Angular Velocities ◽  
Nonlinear Equations Of Motion ◽  
Structural Motion

In this paper, the complete dynamical equations for the general maneuvering flexible wings with sweep and dihedral angles are formulated. These equations are valid for an isotropic non-uniform wing; include transverse shear and warping effects. The equations of motion and boundary conditions are derived using Hamilton’s variational principle. Interaction between rigid-body motion caused by the angular velocities of the general maneuver, and elastic deformations of the wing, results in nonlinear terms, form an important contribution to the final equations. For model validation, the simplified partial differential equations of pull-up maneuver are transformed into a set of differential equations through a Galerkin approach and finally the results of numerical simulation are presented. The combination of flexible structural motion and maneuver parameters are very effective on natural frequencies and instability boundaries.

scholarly journals Kinetoelastodynamics Modeling and Analysis of Spatial Parallel Mechanism

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xiulong Chen ◽  
Yunfeng Li ◽  
Yu Deng ◽  
Wenbin Li ◽  
Haibin Wu
Keyword(s):  
Geometric Nonlinearity ◽  
Parallel Mechanism ◽  
Natural Frequencies ◽  
Theoretical Base ◽  
Dynamic Behaviors ◽  
Modeling And Analysis ◽  
Velocity Error ◽  
Spatial Parallel Mechanism ◽  
Elastodynamic Modeling ◽  
Simulation Results

The nonlinear elastodynamic modeling and analysis of the 4-UPS-UPU spatial 5-degree-of-freedom parallel mechanism are investigated. The kinetoelastodynamics theory is used to derive the elastic dynamic equations of 4-UPS-UPU spatial parallel mechanism. In order to grasp the effect of geometric nonlinearity on dynamic behaviors, such as displacement error output, velocity error output, acceleration error output, stress of driving limbs, and natural frequencies, the variations of dynamic behaviors considering geometric nonlinearity and without considering geometric nonlinearity are discussed, respectively. The numerical simulation results show the nonlinear elastodynamic model established can reasonably reflect the dynamic behaviors of 4-UPS-UPU spatial parallel mechanism with flexible driving limbs. And geometric nonlinearity is demonstrated to have significant impact on dynamic response and dynamic characteristics of spatial parallel mechanism. The researches can provide important theoretical base for the optimal design of spatial parallel mechanism.

On Performance Enhancement of Parallel Kinematic Machine

2005 ◽  
Author(s):  
Dan Zhang ◽  
Lihui Wang
Keyword(s):  
Remote Control ◽  
Degrees Of Freedom ◽  
Geometric Model ◽  
Kinematic Model ◽  
Parallel Kinematic Machine ◽  
Web Based ◽  
Remote Manipulation ◽  
Parallel Kinematic ◽  
Moving Platform ◽  
Three Degrees Of Freedom

This paper proposes a spatial three degrees of freedom parallel kinematic machine enhanced by a passive leg and a web-based remote control system. First, the geometric model of the three degrees of freedom parallel kinematic machine is addressed; in the mechanism, a fourth kinematic link — a passive link connecting the base center to the moving platform center — is introduced. This last link is used to constrain the motion of the tool (located in the moving platform) to only three degrees of freedom, as well as to enhance the global stiffness of the structure and distribute the torque from machining. With the kinematic model, a web-based remote control approach is then applied. The concept of the web-based remote manipulation approach is introduced and the principles behind the method are explored in detail. Finally, an example of remote manipulation is demonstrated to the proposed 3-DOF structure using web-based remote control concept before conclusions.

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