Gramian-constrained optimization process for the stiffness model identification of industrial manipulators

This work deals with the elastostatic identification of industrial manipulators. By reviewing the basics of the physical elastic properties of both links and joints in the framework of the lumped stiffness modeling techniques, the Gramian nature of the stiffness matrices has been found out adequate to do so. Then, a novel optimization method has been developed, which incorporates the Gramian matrix formulation along a non-linear optimization process, acting as an intrinsic constraint for the conservativeness of the elastostatic modeling. Numerical and experimental analyses evince the effectiveness of the proposed method, as the elastostatic models obtained by means of the proposed technique predict more than 93.7% of the compliance deviations of a real industrial robot. The proposed method is simple enough to be jointly applicable to the most recent elastostatic model reduction techniques.

An algorithm to calibrate analytical models of multi-story buildings from vibration records

The common approach to develop analytical models of multi-story buildings from their vibration records is to match the modal properties identified from the records. However, the models developed by matching only the modal properties do not necessarily represent the real structure. In other words, more than one model can match the recorded motions. Moreover, modal properties do not give information on the distribution of stiffness and damping along the height of the building. In this study, an algorithm is developed to identify the dynamic characteristics of each story of multi-story buildings using the transfer-matrix formulation of the response. The building is considered as the superposition of 1-story structures, put one on top of the other. Starting from the top story and going downward, each story’s natural frequency and damping ratio are identified as it were a 1-story building. A key requirement for this approach is to have vibration records from every story. Since this is not typically the case, we utilize the so-called Mode Shape-Based Estimation (MSBE) method to estimate the vibration time histories at non-instrumented floors. Once vibration records are available at every floor, and starting from the top story, we can calculate the individual frequency and damping ratio of each story (i.e. as if it were a 1-story building) by minimizing the error between the recorded and estimated Fourier amplitude spectra (FAS) of the vibration records in that story. The analytical models calibrated in this way are more accurate, and the system identified is unique. Numerical examples are provided to show the application of the methodology.

Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme

Various combinatorially non-local field theories are known to be renormalizable. Still, explicit calculations of amplitudes are very rare and restricted to matrix field theory. In this contribution I want to demonstrate how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra applies to any combinatorially non-local field theory which is renormalizable. This algebraic method improves the understanding of known results in noncommutative field theory in its matrix formulation. Furthermore, I use it to provide new explicit perturbative calculations of amplitudes in tensorial field theories of rank r>2.

Analytical Compliance Equations of Generalized Elliptical-Arc-Beam Spherical Flexure Hinges for 3D Elliptical Vibration-Assisted Cutting Mechanisms

Elliptical vibration-assisted cutting technology has been widely applied in complicated functional micro-structured surface texturing. Elliptical-arc-beam spherical flexure hinges have promising applications in the design of 3D elliptical vibration-assisted cutting mechanisms due to their high motion accuracy and large motion ranges. Analytical compliance matrix formulation of flexure hinges is the basis for achieving high-precision positioning performance of these mechanisms, but few studies focus on this topic. In this paper, analytical compliance equations of spatial elliptic-arc-beam spherical flexure hinges are derived, offering a convenient tool for analysis at early stages of mechanism design. The mechanical model of a generalized flexure hinge is firstly established based on Castigliano's Second Theorem. By introducing the eccentric angle as the integral variable, the compliance matrix of the elliptical-arc-beam spherical flexure hinge is formulated. Finite element analysis is carried out to verify the accuracy of the derived analytical compliance matrix. The compliance factors calculated by the analytical equations agree well with those solved in the finite element analysis for the maximum error; average relative error and relative standard deviation are 8.25%, 1.83% and 1.78%, respectively. This work lays the foundations for the design and modeling of 3D elliptical vibration-assisted cutting mechanisms based on elliptical-arc-beam spherical flexure hinges.

A General Framework for Crankshaft Balancing and Counterweight Design

In the automotive field, the requirements in terms of carbon emissions and improved efficiency are shifting the focus of designers towards reduced engine size. As a result, the dynamic balancing of an engine with strict limitations on the number of cylinders, the weight and the available space becomes a challenging task. The present contribution aims at providing the designer with a tool capable of selecting fundamental parameters needed to correctly balance an internal combustion engine, including the masses and geometry of the elements to be added directly onto the crankshaft and onto the balancing shafts. The relevant elements that distinguish the tool from others already proposed are two. The first is the comprehensive matrix formulation which makes the tool fit for a wide variety of engine configurations. The second is an optimisation procedure that selects not only the position of the mass and centre of gravity of the counterweight but also its complete geometric configuration, thus instantaneously identifying the overall dimensions and weight of the crankshaft.

MATRIX STUDY OF THE EQUATION OF SOLID RIGID MOTIONS

In this article, we described the equations of motion of a rigid solid by a matrix formulation. The matrices contained in our movement description are homogeneous to the same unit. Inertial characteristics are met in a 4x4 positive definite symmetric matrix called "tensor generalized Poinsot." This matrix consists of 3x3 positive definite symmetric matrix called "inertia tensor Poinsot", the coordinates of the center of mass multiplied by the total body mass and the total mass of the rigid body. The equations of motion are formulated as a gender skew 4x4 matrices. They summarize the "principle of fundamental dynamics". The Poinsot generalized tensor appears linearly in this equality as required by the linear dependence of the equations of motion with the ten characteristics inertia of the rigid solid.

A Novel Graphene Modelling: Bottom up Approach - Band Gap Studies to Transport in Python

In this work we develop a computational, quantum level monolayer graphene nanoribbon (GNR) MOSFET of channel length of 10 and 20 nm, with a width of 2 nm and contacts of 2nm width is attached. To develop the MOSFET channel, a bottom up approach is adopted by developing the material model. First the material models of graphene nanoribbon is developed using pybinding module tool in python. The material models of monolayer, bilayer graphene nanoribbon are built on the principles of tight binding module. The methodology developed is based on the Hamiltonian matrix formulation that has been used to determine the E-k plots and LDOS plots of graphene monolayer, bilayer graphene nano ribbon. The GNR MOSFET that is structurally built in python is used to simulate graphene as a switch. Its band gap characteristics is presented as its performance as a switch and is verified with relevant work. Then GNR MOSFET is modelled using quantum principles of NEGF and greens function to determine the transmission characteristics and the I-V characteristics for channel lengths of 10 nm and 20 nm.

Multi-Energy Flow Calculation Considering the Convexification Network Constraints for the Integrated Energy System

To alleviate environmental pollution and improve the energy efficiency of end-user utilization, the integrated energy systems (IESs) have become an important direction of energy structure adjustment over the world. The widespread application of the coupling units, such as gas-fired generators, gas-fired boilers, and combined heat and power (CHP), increases the connection among electrical, natural gas, and heating systems in IESs. This study proposes a mixed-integer nonlinear programming (MINLP) model combining electrical, natural gas, and heating systems, as well as the coupling components, such as CHP and gas-fired generators. The proposed model is applicable for either the radial multi-energy network or the meshed multi-energy network. Since the proposed MINLP model is difficult to be solved, the second-order cone and linearized techniques are used to transform the non-convex fundamental matrix formulation of multi-energy network equations to a mixed-integer convex multi-energy flow model, which can improve the computational efficiency significantly. Moreover, the potential convergence problem of the original model can also be avoided. A simulation of IEEE 14-node electrical system, 6-node natural gas system, and 23-node heating system are studied to verify the accuracy and computational rapidity of the proposed method.

Full Wave Modeling of Electromagnetic Scattering by an Object buried between two Rough Surfaces: Application to GPR

<pre>In this paper, we present an efficient numerical method to calculate the frequency and time responses of the field scattered by an object buried between two random rough surfaces. This method is called Generalized PILE (GPILE) method because it extends the PILE method which considers only two surfaces or an object buried under a surface. The GPILE method solves rigourously the Maxwell equations by using a simple matrix formulation. The obtained results have a straightforward physical interpretation and allow us to investigate the influence of the object buried between the two rough surfaces. We distinguish the primary echo of the upper surface, the multiple echoes coming from the lower surface and those arising from the object. The GPILE method is applied to simulate the Ground Penetrating Radar (GPR) signal at nadir. The resulting time response helps the user to detect the presence of the object buried between the two random rough surfaces.</pre>

Full Wave Modeling of Electromagnetic Scattering by an Object buried between two Rough Surfaces: Application to GPR

<pre>In this paper, we present an efficient numerical method to calculate the frequency and time responses of the field scattered by an object buried between two random rough surfaces. This method is called Generalized PILE (GPILE) method because it extends the PILE method which considers only two surfaces or an object buried under a surface. The GPILE method solves rigourously the Maxwell equations by using a simple matrix formulation. The obtained results have a straightforward physical interpretation and allow us to investigate the influence of the object buried between the two rough surfaces. We distinguish the primary echo of the upper surface, the multiple echoes coming from the lower surface and those arising from the object. The GPILE method is applied to simulate the Ground Penetrating Radar (GPR) signal at nadir. The resulting time response helps the user to detect the presence of the object buried between the two random rough surfaces.</pre>