Improved Stiffness Modeling for An Exechon‑Like Parallel Kinematic Machine(PKM)and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.

Generalized stiffness and effective mass coefficients for power-law Euler-Bernoulli beams

We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials.We provide the generalized stiffness and effective mass coefficients for the power-law Euler-Bernoulli beams under standard geometric and load conditions.In particular,our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law.Since there are no known solutions to the dynamic power-law beam equations,solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.

Effect of the Wall Thickness of the Vessel on FFRCT of Carotid Artery Stenosis

Fractional flow reserve(FFR)computed from computed tomography angiography(CTA),i.e.,FFRCT has been used in the clinic as a noninvasive parameter for functional assessment of coronary artery stenosis.It has also been suggested to be used in the assessment of carotid artery stenosis.The wall thickness of the vessel is an important parameter when establishing a fluid-structure coupling model of carotid stenosis.This work studies the effect of the vessel wall thickness on hemodynamic parameters such as FFRCT in carotid stenosis.Models of carotid stenosis are established based on CTA image data using computer-aided design software.It is assumed that the vessel wall is a linear elastic and isotropic material,and the blood an incompressible Newtonian fluid.Under the pulsating flow condition,ANSYS Transient Structural and CFX are used to simulate the blood flow of fluid-structure coupling in the carotid stenosis model in order to obtain hemodynamic parameters and the corresponding FFRCT.The results show that when the elastic modulus of the vessel wall is fixed,FFRCT will decrease with the increase of the wall thickness.Similarly,FFRCT will decrease with the increase of the elastic modulus when the wall thickness is fixed.The difference in hemodynamic parameters such as FFRCT,however,is relatively small if the stiffness of the two models are close.The results demonstrate that the effect of the vessel wall thickness,especially for a model with small elastic modulus,should be taken into account in using FFRCT for functional assessment of carotid stenosis.Moreover,under the linear elasticity and isotropic material assumptions,the stiffness coefficient may replace the elastic modulus and wall thickness as a parameter reflecting material property of the vessel wall in the carotid stenosis model.

Energetic Nature of Rigidity

The work is to present the energetic nature of the rigidity. It starts with the definition by introducing the notion of sensual magnitudes with the pyramidal structure of all surrounding magnitudes known by a human being. Next the selection of the subject is provided in view of a smooth categorization of magnitudes describing the reality. The adequate description of the considered mechanical phenomenon is presented by formulating general stiffness characteristics. There are several characteristics analyzed, both functional and parametric. An essential, quite a new one is the characteristic of stiffness energy measure which is the stiffness potential. The proper and gained stiffness potentials situated on stable and unstable potential fields have been analyzed. An example of using of this theory to practice is given. It has been referred to a cylindrical grinder case. The presented theory allowed describing the entire stiffness characteristics, including its initial very essential course which has been usually, though inequitably, extrapolated by a straight line segment coming out of zero point with zero coordinates.