Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

All manufactured products have geometrical variations which may impact their functional behavior. Tolerance analysis aims at analyzing the influence of these variations on product behavior, the goal being to evaluate the quality level of the product during its design stage. Analysis methods must verify whether specified tolerances enable the assembly and functional requirements. This paper first focuses on a literature overview of tolerance analysis methods which need to deal with a linearized model of the mechanical behavior. Secondly, the paper shows that the linearization impacts the computed quality level and thus may mislead the conclusion about the analysis. Different linearization strategies are considered, it is shown on an over-constrained mechanism in 3D that the strategy must be carefully chosen in order to not over-estimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level

Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods

One of the aims of statistical tolerance analysis is to evaluate a predicted quality level at the design stage. One method consists of computing the defect probability PD expressed in parts per million (ppm). It represents the probability that a functional requirement will not be satisfied in mass production. This paper focuses on the statistical tolerance analysis of over-constrained mechanisms containing gaps. In this case, the values of the functional characteristics depend on the gap situations and are not explicitly formulated with respect to part deviations. To compute PD, an innovative methodology using system reliability methods is presented. This new approach is compared with an existing one based on an optimization algorithm and Monte Carlo simulations. The whole approach is illustrated using two industrial mechanisms: one inspired by a producer of coaxial connectors and one prismatic pair. Its major advantage is to considerably reduce computation time

An iterative statistical tolerance analysis procedure to deal with linearized behavior models

Tolerance analysis consists of analyzing the impact of variations on the mechanism behavior due to the manufacturing process. The goal is to predict its quality level at the design stage. The technique involves computing probabilities of failure of the mechanism in a mass production process. The various analysis methods have to consider the component’s variations as random variables and the worst configuration of gaps for over-constrained systems. This consideration varies in function by the type of mechanism behavior and is realized by an optimization scheme combined with a Monte Carlo simulation. To simplify the optimization step, it is necessary to linearize the mechanism behavior into several parts. This study aims at analyzing the impact of the linearization strategy on the probability of failure estimation; a highly over-constrained mechanism with two pins and five cotters is used as an illustration for this study. The purpose is to strike a balance among model error caused by the linearization, computing time, and result accuracy. In addition, an iterative procedure is proposed for the assembly requirement to provide accurate results without using the entire Monte Carlo simulation

A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.Comment: 31 pages, 17 figure

On the Interplay between the Evolvability and Network Robustness in an Evolutionary Biological Network: A Systems Biology Approach

In the evolutionary process, the random transmission and mutation of genes provide biological diversities for natural selection. In order to preserve functional phenotypes between generations, gene networks need to evolve robustly under the influence of random perturbations. Therefore, the robustness of the phenotype, in the evolutionary process, exerts a selection force on gene networks to keep network functions. However, gene networks need to adjust, by variations in genetic content, to generate phenotypes for new challenges in the network’s evolution, ie, the evolvability. Hence, there should be some interplay between the evolvability and network robustness in evolutionary gene networks. In this study, the interplay between the evolvability and network robustness of a gene network and a biochemical network is discussed from a nonlinear stochastic system point of view. It was found that if the genetic robustness plus environmental robustness is less than the network robustness, the phenotype of the biological network is robust in evolution. The tradeoff between the genetic robustness and environmental robustness in evolution is discussed from the stochastic stability robustness and sensitivity of the nonlinear stochastic biological network, which may be relevant to the statistical tradeoff between bias and variance, the so-called bias/variance dilemma. Further, the tradeoff could be considered as an antagonistic pleiotropic action of a gene network and discussed from the systems biology perspective

T-Cell activation: a queuing theory analysis at low agonist density

We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation—for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface

A Contribution to the Design of Highly Redundant Compliant Aerial Manipulation Systems

Es ist vorhersehbar, dass die Luftmanipulatoren in den nächsten Jahrzehnten für viele Aufgaben eingesetzt werden, die entweder zu gefährlich oder zu teuer sind, um sie mit herkömmlichen Methoden zu bewältigen. In dieser Arbeit wird eine neuartige Lösung für die Gesamtsteuerung von hochredundanten Luftmanipulationssystemen vorgestellt. Die Ergebnisse werden auf eine Referenzkonfiguration angewendet, die als universelle Plattform für die Durchführung verschiedener Luftmanipulationsaufgaben etabliert wird. Diese Plattform besteht aus einer omnidirektionalen Drohne und einem seriellen Manipulator. Um den modularen Regelungsentwurf zu gewährleisten, werden zwei rechnerisch effiziente Algorithmen untersucht, um den virtuellen Eingang den Aktuatorbefehlen zuzuordnen. Durch die Integration eines auf einem künstlichen neuronalen Netz basierenden Diagnosemoduls und der rekonfigurierbaren Steuerungszuordnung in den Regelkreis, wird die Fehlertoleranz für die Drohne erzielt. Außerdem wird die Motorsättigung durch Rekonfiguration der Geschwindigkeits- und Beschleunigungsprofile behandelt. Für die Beobachtung der externen Kräfte und Drehmomente werden zwei Filter vorgestellt. Dies ist notwendig, um ein nachgiebiges Verhalten des Endeffektors durch die achsenselektive Impedanzregelung zu erreichen. Unter Ausnutzung der Redundanz des vorgestellten Luftmanipulators wird ein Regler entworfen, der nicht nur die Referenz der Endeffektor-Bewegung verfolgt, sondern auch priorisierte sekundäre Aufgaben ausführt. Die Wirksamkeit der vorgestellten Lösungen wird durch umfangreiche Tests überprüft, und das vorgestellte Steuerungssystem wird als sehr vielseitig und effektiv bewertet.:1 Introduction 2 Fundamentals 3 System Design and Modeling 4 Reconfigurable Control Allocation 5 Fault Diagnostics For Free Flight 6 Force and Torque Observer 7 Trajectory Generation 8 Hybrid Task Priority Control 9 System Integration and Performance Evaluation 10 ConclusionIn the following decades, aerial manipulators are expected to be deployed in scenarios that are either too dangerous for human beings or too expensive to be accomplished by traditional methods. This thesis presents a novel solution for the overall control of highly redundant aerial manipulation systems. The results are applied to a reference configuration established as a universal platform for performing various aerial manipulation tasks. The platform consists of an omnidirectional multirotor UAV and a serial manipulator. To ensure modular control design, two computationally efficient algorithms are studied to allocate the virtual input to actuator commands. Fault tolerance of the aerial vehicle is achieved by integrating a diagnostic module based on an artificial neural network and the reconfigurable control allocation into the control loop. Besides, the risk of input saturation of individual rotors is minimized by predicting and reconfiguring the speed and acceleration responses. Two filter-based observers are presented to provide the knowledge of external forces and torques, which is necessary to achieve compliant behavior of the end-effector through an axis-selective impedance control in the outer loop. Exploiting the redundancy of the proposed aerial manipulator, the author has designed a control law to achieve the desired end-effector motion and execute secondary tasks in order of priority. The effectiveness of the proposed designs is verified with extensive tests generated by following Monte Carlo method, and the presented control scheme is proved to be versatile and effective.:1 Introduction 2 Fundamentals 3 System Design and Modeling 4 Reconfigurable Control Allocation 5 Fault Diagnostics For Free Flight 6 Force and Torque Observer 7 Trajectory Generation 8 Hybrid Task Priority Control 9 System Integration and Performance Evaluation 10 Conclusio

The particle finite element method (PFEM) in thermo‐mechanical problems

The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo‐mechanical problems. In particular, the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes, and thermal effects. The framework of the numerical scheme is based on the particle finite element method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (α − shape method), in this work, the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function. The description of the thermo‐mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u‐p mixed formulation, with a stabilization of the pressure term via the polynomial pressure projection, is proposed. One of the novelties of this work is the use of a combination between the isothermal split and the so‐called IMPL‐EX hybrid integration technique to enhance the robustness and reduce the typical iteration number of the fully implicit Newton–Raphson solution algorithm. The new set of numerical tools implemented in the PFEM algorithm, including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo‐mechanical problems. Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking‐free element type and different time integration schemes for thermo‐mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

The statistical tolerance analysis has become a key element used in the design stage to reduce the manufacturing cost, the rejection rate and to have high quality products. One of the frequently used methods is the Monte Carlo simulation, employed to compute the non-conformity rate due to its efficiency in handling the tolerance analysis of over-constrained mechanical systems. However, this simulation technique requires excessive numerical efforts. The goal of this paper is to improve this method by proposing a probabilistic model of gaps in fixed and sliding contacts and involved in the tolerance analysis of an assembly. The probabilistic model is carried out on the clearance components of the sliding and fixed contacts for their assembly feasibility considering all the imperfections on the surfaces. The kernel density estimation method is used to deal with the probabilistic model. The proposed method is applied to an over-constrained mechanical system and compared to the classical method regarding their computation time

A spectral deferred correction strategy for low Mach number reacting flows subject to electric fields

We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction (MISDC) algorithm designed to advance the conservation equations in time at scales associated with advective transport. The fast and nontrivial interactions of electrons with the electric field are treated implicitly using a Jacobian-Free Newton Krylov approach for which a preconditioning strategy is developed. Within the MISDC framework, this enables a close and stable coupling of diffusion, reactions and dielectric relaxation terms with advective transport and is shown to exhibit second-order convergence in space and time. The algorithm is then applied to a series of steady and unsteady problems to demonstrate its capability and stability. Although developed in a one-dimensional case, the algorithmic ingredients are carefully designed to be amenable to multidimensional applications