Inertia Constraints Research Articles

Wire twisting stiffness modelling with application in wire race ball bearings. Derivation of analytical formula and finite element validation

Since Erich Franke produced the first wire race bearings in 1934, they have not been used profusely until these last years in applications such as computerized tomography, X-ray machines, wheels with direct drive… where low weight and inertia constraints are important. Accounting for the structural behaviour of the bearing, there exist a key phenomenon not present in other kind of more known bearings, which is the wire twisting under load; this wire twisting steers the force transmission among the bearing rings and the rolling elements. In this sense, for design and selection purposes, if a complete structural model of the bearing is to be done in an efficient way to assess bearing stiffness and load distribution over the rolling elements, the twisting stiffness of the wire has to be modelled properly. This work develops a simple analytical expression of that stiffness to be used in structural models, derived from an evidence-based deformation assumption at differential level for the section of the wire.

A user-driven feedback approach for 2D direct current resistivity inversion based on particle swarm optimization

We have developed an inversion approach based on particle swarm optimization (PSO) for 2D direct current resistivity data. Once the PSO algorithm is implemented, cost-function changes on constraints and misfit criteria can be easily performed and an approximate invariance of the Lagrange multipliers is obtained if each term of the cost function is properly normalized. More importantly, the interpreter can divide the mesh into partitions and apply a different constraint or combination of constraints in each partition. We explore several restrictions on the log-resistivity variation, either in single or in joint versions, including spatial continuity constraints in the [Formula: see text]-and [Formula: see text]-norms, total variation, sparsity constraints using the discrete cosine transform and Daubechies bases, and minimum moment of inertia constraints to impose concentration of resistive or conductive materials along target axes. In the latter case, the earth surface might be used also as a target axis. In addition, the final state of the PSO algorithm, once a stopping condition has been reached, contains not only the best solution but also a cluster of good suboptimal solutions that can be used for uncertainty analysis. As a result, the interpreter has the flexibility to perform an interpretation process based on a feedback trial-and-error inversion approach, in a similar manner that he/she has when using a friendly forward modeling software. The interpreter can then drive the tentative solutions obtained along the inversion process to incorporate their conceptions about the geologic environment, besides appraising misfit and stability of the solutions. We evaluate synthetic and field data examples. In the first case, we determine how the interpreter can drive the inversion process in a karst environment to image dissolution features. In the second case, we explore a similar situation aiming to optimize borehole locations in fracture zones in crystalline rocks.

A Framework for Assessing Renewable Integration Limits With Respect to Frequency Performance

The increasing penetration of nonsynchronous renewable energy sources (NS-RES) and demand side-technologies alter the dynamic characteristics, and particularly, the frequency behavior of a power system. Given this, we propose a framework for assessing renewable integration limits concerning power system frequency performance using a time-series scenario based approach. By considering a large number of future scenarios and their sensitivities with respect to different parameters, we can identify maximum nonsynchronous instantaneous penetration limits for a wide range of possible scenarios. Further, we derive a dynamic inertia constraint and incorporate it into the market dispatch model to reduce the detrimental impacts of high NS-RES penetration on the frequency performance. The results using the Australian future grid as a test case show that such an explicit inertia constraint ensures power system frequency stability for all credible contingencies. To improve the frequency performance, we assess and quantify the contribution of a wide range of technologies, including synchronous condensers, synthetic inertia from wind farms and a governor-like response from de-loaded wind farms. The results show that the last option is the most effective one.

Power System Enterprise Control With Inertial Response Procurement

As the power system evolves to better address environmental and reliability concerns, its overall dynamics changes and consequently challenges the adequacy of established operating procedures. This evolution brings a significant increase in the number of integrated renewable energy sources (RES) and HVDC connections. RES are normally connected to the grid through power electronic converters, which reduces or completely eliminates their electrical coupling to the power grid. As a result, such units are unable to contribute to the inertia of the system, posing a potential threat to the grid's physical security. More specifically, postfault frequency characteristics, such as rate of change of frequency (RoCoF), frequency nadir, and quasi-steady-state frequency, depend on the system inertia and their respective limits may potentially be violated. One way to address this problem is adding constraints to the unit commitment formulation so that operations maintain their frequency characteristics within acceptable limits. This paper studies how such changes affect the system frequency deviation from its rated value. The power system is modeled as an enterprise control that combines multiple layers of control operations into one package. Such integration allows capturing how the effects of wind integration and the addition of unit commitment inertia constraints propagate through control layers to impact the system frequency.

Running accuracy analysis of a 3-RRR parallel kinematic machine considering the deformations of the links

Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields. However, high precision is still one of the challenges when they are used for advanced machine tools. One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations, especially at high speeds and under heavy loads. A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process. Based on the dynamic model constructed by the Newton-Euler method, all the inertia loads and constraint forces of the links are computed and their deformations are derived. Then the kinematic errors of the machine are derived with the consideration of the deformations of the links. Through further derivation, the accuracy of the machine is given in a simple explicit expression, which will be helpful to increase the calculating speed. The accuracy of this machine when following a selected circle path is simulated. The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated. The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine. The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.

Crop Productivity and the Global Livestock Sector: Implications for Land Use Change and Greenhouse Gas Emissions

The livestock sector accounts for 30% of global land area and is a major driver of land use change. The price reductions generated by crop yield increases should, ceteris paribus, encourage farmers to replace some of the grass in ruminant rations with crops. This would lead to land sparing and related carbon dioxide emission reductions in regions where the feed productivity per unit of area is higher for cropland than for grassland. Six land cover types are distinguished in GLOBIOM: cropland, grassland, short rotation tree plantations, managed forest, unmanaged forest and other natural vegetation. Depending on the relative profitability of the individual activities, and on the inertia constraints, the model can switch from one land cover type to another. Comprehensive greenhouse gas accounting for agriculture and land use change is implemented in the model. Crop yield development will play a critical role in future land use dynamics. Indeed, it will determine the requirements for additional cropland, and also have a strong impact on grassland expansion.

Optimal Packing Configuration Design with Finite-Circle Method

The Finite-circle Method (FCM) is further developed to solve 2D and 3D packing optimization problems with system compactness and moment of inertia constraints here. Instead of using the real geometrical shape as in existing solutions, we approximate the components and the design domain with circles of variant radii. Such approximation makes it possible to transform the original problem into a basic packing problem of FCM approximated components. Meanwhile, the overlapping between different components can be easily avoided by limiting the distance between corresponding circles in terms of their radii. With this formulation, the FCM provides a general and systematic approach and makes gradient-based optimization algorithms applicable. Furthermore, FCM has been extended to 3D packing problems by simply replacing circles with spheres in this paper. Several examples designing the compactness and moment of inertia of the component systems are presented to show the effect of FCM.

Ockham’s razor: Deriving cyclic evolutions from viability and inertia constraints

This article deals with a theme to which Claude Lobry has been interested for a long time: what is the nature of mathematics motivated by biological sciences? It starts by presenting the subjective opinions of its author, illustrated by the simplest application one can think of: demonstrating that it is possible to produce cyclic evolutions on the simple basis of viability and inertia constraints, without using periodic differential equations. It is not impossible that this approach is foreign to an explanation of biological clocks (or economic cycles) in another field. Cet article traite d’un thème auquel Claude Lobry s’est longtemps intéressé : quelle est la nature des mathématiques motivées par les sciences biologiques ? Il commence par exposer les opinions subjectives de l’auteur, illustrées pas une application des plus simples démontrant qu’il est possible de produire des évolutions cycliques à partir de simples hypothèses (contraintes de viabilité et d’inertie) pour produire des évolutions cycliques, sans faire appel aux équations différentielles périodiques. Il n’est pas impossible que ce point de vue soit étranger à une explication du fonctionnement des horloges biologiques (ou des cycles économiques dans un autre domaine).

Carbon dioxide sequestration: how much and when?

Carbon dioxide (CO2) sequestration has been proposed as a key component in technological portfolios for managing anthropogenic climate change, since it may provide a faster and cheaper route to significant reductions in atmospheric CO2 concentrations than abating CO2 production. However, CO2 sequestration is not a perfect substitute for CO2 abatement because CO2 may leak back into the atmosphere (thus imposing future climate change impacts) and because CO2 sequestration requires energy (thus producing more CO2 and depleting fossil fuel resources earlier). Here we use analytical and numerical models to assess the economic efficiency of CO2 sequestration and analyze the optimal timing and extent of CO2 sequestration. The economic efficiency factor of CO2 sequestration can be expressed as the ratio of the marginal net benefits of sequestering CO2 and avoiding CO2 emissions. We derive an analytical solution for this efficiency factor for a simplified case in which we account for CO2 leakage, discounting, the additional fossil fuel requirement of CO2 sequestration, and the growth rate of carbon taxes. In this analytical model, the economic efficiency of CO2 sequestration decreases as the CO2 tax growth rate, leakage rates and energy requirements for CO2 sequestration increase. Increasing discount rates increases the economic efficiency factor. In this simple model, short-term sequestration methods, such as afforestation, can even have negative economic efficiencies. We use a more realistic integrated-assessment model to additionally account for potentially important effects such as learning-by-doing and socio-economic inertia on optimal strategies. We measure the economic efficiency of CO2 sequestration by the ratio of the marginal costs of CO2 sequestration and CO2 abatement along optimal trajectories. We show that the positive impacts of investments in CO2 sequestration through the reduction of future marginal CO2 sequestration costs and the alleviation of future inertia constraints can initially exceed the marginal sequestration costs. As a result, the economic efficiencies of CO2 sequestration can exceed 100% and an optimal strategy will subsidize CO2 sequestration that is initially more expensive than CO2 abatement. The potential economic value of a feasible and acceptable CO2 sequestration technology is equivalent – in the adopted utilitarian model – to a one-time investment of several percent of present gross world product. It is optimal in the chosen economic framework to sequester substantial CO2 quantities into reservoirs with small or zero leakage, given published estimates of marginal costs and climate change impacts. The optimal CO2 trajectories in the case of sequestration from air can approach the pre-industrial level, constituting geoengineering. Our analysis is silent on important questions (e.g., the effects of model and parametric uncertainty, the potential learning about these uncertainties, or ethical dimension of such geoengineering strategies), which need to be addressed before our findings can be translated into policy-relevant recommendations.

Mass and moment of inertia constraints on the lunar crustal thickness: Relations between crustal density, mantle density, and the reference radius of the crust-mantle boundary

Abstract The gravity inversion for the lunar crustal thickness needs three parameters: the crustal density, mantle density, and the reference radius of the crust-mantle boundary. The assumption of crust and mantle densities is found to significantly affect on the resultant crustal thickness variations. Moreover, the recent seismic analyses suggest the possibility of thinner crustal thickness around the Apollo 12 site than that proposed in the Apollo-era, on which the previous gravity inversions relied upon. Therefore the validity of the assumption used in previous gravity-inversion studies must be re-examined in detail. By using a simple three-layered mass model of the Moon including a uniform crust, mantle, and core, we determine possible combinations of the three parameters, satisfying the mass and moment of inertia constraints. The results show that the set of the parameters used in Neumann et al. (1996) can be consistent with mass and moment of inertia constraints, while those in Wieczorek and Phillips (1998) does not satisfy the constraints.

Geochemical constraints on the seismic properties of the lunar mantle

Abstract Thermodynamic modeling of phase relations and physical properties in the Na2O–TiO2–CaO–FeO–MgO–Al2O3–SiO2–Fe–FeS system and a Monte-Carlo inversion procedure have been used to calculate the density and velocity distribution in the mantle, and core radii of the Moon from the mass and moment of inertia constraints from recent Lunar Prospector gravity measurements. For the computation of the phase diagram for a given chemical composition, we have used a method of minimization of the total Gibbs free energy and self-consistent thermodynamic data for minerals and solid solutions. For the crustal thickness and density of 60 km and 3.0 g cm−3, the largest core radii are estimated to be 530 km for an FeS (troilite)-core (4.1% of total mass), 490 km for a eutectic Fe–FeS-core (3.4%), 445 km for an Fe–10 wt.% S-core (2.9%), and 350 km for an Fe-core (2%). The existence of an Fe–FeS-core of intermediate radius of 250–400 km is compatible with recent lunar core information and lend support to a chemically stratified lunar mantle. The sensitivity of density and seismic velocities to temperature, pressure and composition variations is examined. The modeling results indicate that we can determine the permissible density and velocity ranges in the zoned lunar mantle with confidence. The maximum and minimum density changes at depths of the lunar mantle, consistent with geochemical constraints and mass and moment of inertia requirements, are found to be: 3.22 g cm −3 ≤ρ≤3.44 g cm−3 at depths of 60–500 km and 3.34 g cm −3 ≤ρ≤3.52 g cm−3 at depths between 500 km and the core mantle boundary. Core-free models of the Moon are possible only if the lower mantle densities are between 3.49 and 3.52 g cm−3 ( 20 wt .% FeO wt.%). The calculated field of seismic velocities in the zoned lunar mantle shows that over a broad range of mantle compositions, temperatures, and densities the maximum variations are as follows: 4.23 km s −1 ≤V S ≤4.69 km s−1 and 7.41 km s −1 ≤V P ≤8.24 km s−1 at depths of 60–500 km, and 4.24 km s −1 ≤V S ≤4.64 km s−1 and 7.63 km s −1 ≤V P ≤8.39 km s−1 at depths between 500 km and the core mantle boundary. These petrologically and geophysically admissible ranges of velocities and densities may constitute a significant constraint for the analysis of internal structure of the Moon using the Apollo seismic data.

Identifying Shifts in Policy Regimes

One of the mainstays of political sociology and political science for generationshas been debate about the conditions under which onepolicy regime—that is, a distinct mix of public policies—is replaced by another. For instance, a vast literature seeks to identify the factors that caused the shift from orthodox to Keynesian policy regimes in the United States and Europe after the Second World War, as well as the shift during the 1980s to more conservative neoliberal policy regimes (e.g., Campbell 1998; Gourevitch 1986; Hall 1989, 1992;Weir and Skocpol 1985). Similarly, scholars have argued about whether the process through which regime shifts occur is a slow and incremental one, driven by bureaucratic inertia, muddling through, and path-dependent constraints, or a rapid and abrupt one, sparked by cataclysmic events like war that trigger sharp breaks with past policies (e.g., Baumgartner and Jones 1993; Hall 1993; Krasner 1984; Lindblom 1959; Pierson 1993, 1994). Regime shifts have also captured the imagination of historical sociologists who have recognized that history is marked by critical turning points that differentiate among relatively stable time periods and that this requires scholars to carefully identify historically specific patterns among variables (Abbott 1988, 1992, 1997; Isaac 1997).

IQC synthesis based on inertia constraints

Abstract Integral quadratic constraints (IQCs) can be used for proving stability of systems with uncertainties and nonlinearities. Similarly, IQCs can also be used for controller synthesis. Necessary and sufficient conditions for the existence of such a controller is derived. These conditions include linear matrix inequalities (LMIs) and matrix inertia specifying the number of negative eigenvalues of a matrix. In general, these conditions are non-convex. Connections to bilinear matrix inequalities and LMIs with rank constraints are also given.

Decision making under uncertainty and inertia constraints: sectoral implications of the when flexibility

Current debates on climate mitigation emphasize the role of the inertia of the economic system. Our aim in this paper is to study in more depth how sectorally differentiated inertia impacts on optimal CO 2-emission abatement policies. Using the STARTS model, we show that optimal abatement levels and costs differ sensibly among sectors. Differential inertia is the critical determinant of this trade-off, especially in the case of a 20-year delay in the action, or in an underestimation of the growth of the transportation sector. In particular, the burden of any additional abatement effort falls on the most flexible sector, i.e. the industry. Debates on mitigation emphasize the role of inertia of the economic system. This paper aims at studying more in depth how sectorally differentiated inertia should influence optimal CO 2 emission abatement policies. Using a two-sector version of STARTS, we show that under perfect expectations, optimal abatement profiles and associated costs differ sensibly between a flexible and a rigid sector (transportation). In a second step, we scrutinize the role of the uncertainty by testing the case of a 20-year delay of action and an underestimated growth of the transportation sector. We do this for three concentration ceilings and we point out the magnitude of the burden which falls on the flexible sector. We derive some policy implications for the ranking of public policies and for incentive instruments to be set up at international level.

Dynamics of suspension-slider-air-bearing systems: experimental study

Experimental techniques are proposed to evaluate the dynamic properties of suspension-slider-air-bearing systems. The bump responses of the sliders and gimbal structures are measured. The modal parameters, such as frequencies, damping ratios, and mode shapes of the systems are obtained by using the proposed procedure. The techniques are applied to investigate the dynamic properties of three systems. It is found that they have quite different properties, and the suspensions (gimbal) significantly affect the dynamic properties of the air bearings. Some gimbal designs generate additional modes in the frequency band of the air-bearing resonance, or introduce additional stiffness and/or inertia constraints to the slider-air bearings. The results also show that the proposed techniques are robust for experimentally evaluating the dynamic properties of the suspension-slider-air-bearing systems.

Darwinism, Process Structuralism, and Natural Kinds

Darwinists classify biological traits either by their ancestry (homology) or by their adaptive role. Only the latter can provide traditional natural kinds, but only the former is practicable. Process structuralists exploit this embarrassment to argue for non-Darwinian classifications in terms of underlying developmental mechanisms. This new taxonomy will also explain phylogenetic inertia and developmental constraint. I argue that Darwinian homologies are natural kinds despite having historical essences and being spatio-temporally restricted. Furthermore, process structuralist explanations of biological form require an unwarranted assumption about the space of developmental possibility.

No-regret potentials and technical innovation: A viability approach to integrated assessment of climate policies

This paper aims to demonstrate the advantages of a sequential approach to decision making in climate policies. This sequential approach is necessary because of the uncertainties regarding both the avoided costs of climate change and the costs of GHG emission abatement. This assessment focuses on the minimization of learning time, the reduction of technical and institutional inertia, and the possible unexpected non-linearities in abatement curves. A stylized representation of so-called ‘no-regret’ short-term potentials, of long-term innovation trends and of backstop technologies is used. We show that if we do take care of the inertia constraints in the decision process, both policies (namely the no-regret and the innovation process exploitation) becomes crucial in terms of minimization of the learning time.

Optimization of composite rotor blades with advanced structural and aerodynamic modeling

This paper addresses the first significant step in the ongoing research towards the overall goal of developing an integrated dynamic, aerodynamic, and structural optimization methodology for helicopter rotor blades made of composite materials. It investigates the feasibility and the utility of the structural-dynamic phase of the optimization task with realistic blade cross-sections. As opposed to the often used, simplified cross-sections, the lift generating part of the rotor blade has a realistic airfoil shape in the present shape optimization task. A set of ‘primitive’ design variables form the representative design space in the present task of minimizing blade weight under several frequency, autorotational inertia, and airfoil mass-center related constraints. The investigation pertains to the hingeless rotors with frequency constraints for obtaining soft in-plane blades. The composite construction of the blade sections is analyzed via a two-dimensional finite element code, which establishes the beam constitutive law. The subsequent beam analysis is based on an hp-type displacement-finite-element strategy that incorporates all the geometric nonlinearities of the beam equations. The results indicate extreme sensitivity of the optimization process on the formulation of frequency constraints and starting designs. Autorotational inertia constraint also has a significant impact on the final design. The study shows the effectiveness of simpler and more numerous frequency constraints over the complicated and less numerous frequency constraints when trying to achieve an identical goal. The enhanced role of structural couplings (e.g., tension-bending, bending-torsion) was also observed under constraints on high modal frequencies. The work has highlighted the feasibility (and also the associated complexities) of including realistic blade details in a design optimization study. Research is progressing towards the overall objective of an integrated optimization study.

Application of optimization methods to helicopter rotor blade design

The minimum weight design of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies is studied in this paper. A constraint is also imposed on the minimum value of the autorotational inertia of the blade to ensure sufficient autorotational inertia to autorotate in case of an engine failure. A stress constraint is used to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of the nonstructural weights. The program CAMRAD is used for the blade modal analysis and the program CONMIN for the optimization. In addition, a linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function, the autorotational inertia constraint and the stress constraints. A central finite difference scheme is used for the derivatives of the frequency constraints. Optimum designs are obtained for both rectangular and tapered blades. The paper also discusses the effect of adding constraints on higher frequencies and stresses on the optimum designs.

Technical Notes: Minimum Weight Design of Helicopter Rotor Blades with Frequency Constraints

The minimum weight design of helicopter rotor blades subject to constraints on fundamental coupled flap-lag natural frequencies has been studied in this paper. A constraint has also been imposed on the minimum value of the blade autorotational inertia to ensure that the blade has sufficient inertia to autorotate in case of an engine failure. The program CAMRAD has been used for the blade modal analysis and the program CONMIN has been used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for blades in vacuum with both rectangular and tapered box beam structures. Design variables include taper ratio, nonstructural segment weights and box beam dimensions. The paper shows that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for blades with rectangular and tapered box beams.