Scaling Laws and Regime Transitions of Macroturbulence in Dry Atmospheres

In simulations of a wide range of circulations with an idealized general circulation model, clear scaling laws of dry atmospheric macroturbulence emerge that are consistent with nonlinear eddy–eddy interactions being weak. The simulations span several decades of eddy energies and include Earth-like circulations and circulations with multiple jets and belts of surface westerlies in each hemisphere. In the simulations, the eddy available potential energy and the barotropic and baroclinic eddy kinetic energy scale linearly with each other, with the ratio of the baroclinic eddy kinetic energy to the barotropic eddy kinetic energy and eddy available potential energy decreasing with increasing planetary radius and rotation rate. Mean values of the meridional eddy flux of surface potential temperature and of the vertically integrated convergence of the meridional eddy flux of zonal momentum generally scale with functions of the eddy energies and the energy-containing eddy length scale, with a few exceptions in simulations with statically near-neutral or neutral extratropical thermal stratifications. Eddy energies scale with the mean available potential energy and with a function of the supercriticality, a measure of the near-surface slope of isentropes. Strongly baroclinic circulations form an extended regime in which eddy energies scale linearly with the mean available potential energy. Mean values of the eddy flux of surface potential temperature and of the vertically integrated eddy momentum flux convergence scale similarly with the mean available potential energy and other mean fields. The scaling laws for the dependence of eddy fields on mean fields exhibit a regime transition between a regime in which the extratropical thermal stratification and tropopause height are controlled by radiation and convection and a regime in which baroclinic entropy fluxes modify the extratropical thermal stratification and tropopause height. At the regime transition, for example, the dependence of the eddy flux of surface potential temperature and the dependence of the vertically integrated eddy momentum flux convergence on mean fields changes -— a result with implications for climate stability and for the general circulation of an atmosphere, including its tropical Hadley circulation

Eddy Influences on Hadley Circulations: Simulations with an Idealized GCM

An idealized GCM is used to investigate how the strength and meridional extent of the Hadley circulation depend on the planet radius, rotation rate, and thermal driving. Over wide parameter ranges, the strength and meridional extent of the Hadley circulation display clear scaling relations with regime transitions, which are not predicted by existing theories of axisymmetric Hadley circulations. For example, the scaling of the strength as a function of the radiative-equilibrium equator-to-pole temperature contrast exhibits a regime transition corresponding to a regime transition in scaling laws of baroclinic eddy fluxes. The scaling of the strength of the cross-equatorial Hadley cell as a function of the latitude of maximum radiative-equilibrium temperature exhibits a regime transition from a regime in which eddy momentum fluxes strongly influence the strength to a regime in which the influence of eddy momentum fluxes is weak. Over a wide range of flow parameters, albeit not always, the Hadley circulation strength is directly related to the eddy momentum flux divergence at the latitude of the streamfunction extremum. Simulations with hemispherically symmetric thermal driving span circulations with local Rossby numbers in the horizontal upper branch of the Hadley circulation between 0.1 and 0.8, indicating that neither nonlinear nearly inviscid theories, valid for Ro → 1, nor linear theories, valid for Ro → 0, of axisymmetric Hadley circulations can be expected to be generally adequate. Nonlinear theories of axisymmetric Hadley circulations may account for aspects of the circulation when the maximum radiative-equilibrium temperature is displaced sufficiently far away from the equator, which results in cross-equatorial Hadley cells with nearly angular momentum-conserving upper branches. The dependence of the Hadley circulation on eddy fluxes, which are themselves dependent on extratropical circulation characteristics such as meridional temperature gradients, suggests that tropical circulations depend on the extratropical climate

Self-Organization of Atmospheric Macroturbulence into Critical States of Weak Nonlinear Eddy–Eddy Interactions

It is generally held that atmospheric macroturbulence can be strongly nonlinear. Yet weakly nonlinear models successfully account for scales and structures of baroclinic eddies in Earth's atmosphere. Here a theory and simulations with an idealized GCM are presented that suggest weakly nonlinear models are so successful because atmospheric macroturbulence organizes itself into critical states of weak nonlinear eddy–eddy interactions. By modifying the thermal structure of the extratropical atmosphere such that its supercriticality remains limited, macroturbulence inhibits nonlinear eddy–eddy interactions and the concomitant inverse energy cascade from the length scales of baroclinic instability to larger scales. For small meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are set by radiation and convection, and the supercriticality is less than one; for sufficiently large meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are modified by baroclinic eddies such that the supercriticality does not significantly exceed one. In either case, the scale of the energy-containing eddies is similar to the scale of the linearly most unstable baroclinic waves, and eddy kinetic and available potential energies are equipartitioned. The theory and simulations point to fundamental constraints on the thermal structures and global circulations of the atmospheres of Earth and other planets, for example, by providing limits on the tropopause height and estimates for eddy scales, eddy energies, and jet separation scales

Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear Lattices

We consider the leading order quasicontinuum limits of a one-dimensional granular medium governed by the Hertz contact law under precompression. The approximate model which is derived in this limit is justified by establishing asymptotic bounds for the error with the help of energy estimates. The continuum model predicts the development of shock waves, which are also studied in the full system with the aid of numerical simulations. We also show that existing results concerning the Nonlinear Schrodinger (NLS) and Korteweg de-Vries (KdV) approximation of FPU models apply directly to a precompressed granular medium in the weakly nonlinear regime

Robotic Automation of Turning Machines in Fenceless Production: A Planning Toolset for Economic-based Selection Optimization between Collaborative and Classical Industrial Robots

Ursprünglich wurden Industrieroboter hauptsächlich hinter Schutzzäunen betrieben, um den Sicherheitsanforderungen gerecht zu werden. Mit der Flexibilisierung der Produktion wurden diese scharfen Trennbereiche zunehmend aufgeweicht und externe Sicherheitstechnik, wie Abstandssensoren, genutzt, um Industrieroboter schutzzaunlos zu betreiben. Ausgehend vom Gedanken dieser Koexistenz bzw. Kooperation wurde die Sicherheitssensorik in den Roboter integriert, um eine wirkliche Kollaboration zu ermöglichen. Diese sogenannten kollaborierenden Roboter, oder Cobots, eröffnen neue Applikationsfelder und füllen somit die bestehenden Automatisierungslücken. Doch welche Automatisierungsvariante ist aus wirtschaftlichen Gesichtspunkten die geeignetste? Bisherige Forschung untersucht zum Großteil isoliert eine der beiden Technologien, ohne dabei einen Systemvergleich hinsichtlich technologischer Spezifika und Wirtschaftlichkeit anzustellen. Daher widmet sich diese Dissertation einer Methodik zum wirtschaftlichen Vergleich von kollaborierenden Robotern und Industrierobotern in schutzzaunlosen Maschinenbeladungssystemen. Besonderer Fokus liegt dabei auf dem Herausarbeiten der technischen Faktoren, die die Wirtschaftlichkeit maßgeblich beeinflussen, um ein Systemverständnis der wirtschaftlichen Struktur beider Robotertechnologievarianten zu erhalten. Zur Untersuchung werden die Inhalte eines solchen Planungsvorhabens beschrieben, kategorisiert, systematisiert und modularisiert. Auf wirtschaftlicher Seite wird ein geeignetes Optimierungsmodell vorgestellt, während auf technischer Seite vor allem die Machbarkeit hinsichtlich Greifbarkeit, Layoutplanung, Robotergeschwindigkeiten und Zykluszeitbestimmung untersucht wird. Mit deduktiven, simulativen, empirischen und statistischen Methoden wird das Systemverhalten für die einzelnen Planungsinhalte analysiert, um die Gesamtwirtschaftlichkeit mit einem Minimum an Investment,- Produktions,- und Zykluszeitinformationen a priori vorhersagen zu können. Es wird gezeigt, dass durch einen Reverse Engineering Ansatz die notwendigen Planungsdaten, im Sinne von Layoutkomposition, Robotergeschwindigkeiten und Taktzeiten, mithilfe von Frontloading zu Planungsbeginn zur Verfügung gestellt werden können. Dabei dient der Kapitalwert als wirtschaftliche Bewertungsgrundlage, dessen Abhängigkeit vom Mensch-Roboter-Interaktionsgrad in einem Vorteilhaftigkeitsdiagramm für die einzelnen Technologiealternativen dargestellt werden kann. Wirtschaftlich fundierte Entscheidungen können somit auf quantitiativer Basis getroffen werden.:1. Introduction 25 1.1 Research Domain 25 1.2 Research Niche 26 1.3 Research Structure 28 2. State of the Art and Research 31 2.1 Turning Machines and Machine Tending 31 2.1.1 Tooling Machine Market Trends and Machine Tending Systems 31 2.1.2 Workpiece System 34 2.1.3 Machine System 36 2.1.4 Logistics System 39 2.1.5 Handling System 41 2.2 Robotics 43 2.2.1 Robot Installation Development and Application Fields 43 2.2.2 Fenceless Industrial and Collaborative Robots 48 2.2.3 Robot Grippers 55 2.3 Planning and Evaluation Methods 56 2.3.1 Planning of General and Manual Workstations 56 2.3.2 Cell Planning for Fully Automated and Hybrid Robot Systems 59 2.3.3 Robot Safety Planning 61 2.3.4 Economic Evaluation Methods 70 2.4 Synthesis - State of the Art and Research 71 3. Solution Approach 77 3.1 Need for Research and General Solution Approach 77 3.2 Use Case Delineation and Planning Focus 80 3.3 Economic Module – Solution Approach 86 3.4 Gripper Feasibility Module – Solution Approach 89 3.5 Rough Layout Discretization Model – Solution Approach 94 3.6 Cycle Time Estimation Module – Solution Approach 97 3.7 Collaborative Speed Estimation Module – Solution Approach 103 3.7.1 General Approach 103 3.7.2 Case 1: Quasi-static Contact with Hand 107 3.7.3 Case 2: Transient Contact with Hand 109 3.7.4 Case 3: Transient Contact with Shoulder 111 3.8 Synthesis – Solution Approach 114 4. Module Development 117 4.1 Economic Module – Module Development 117 4.1.1 General Approach 117 4.1.2 Calculation Scheme for Manual Operation 117 4.1.3 Calculation Scheme for Collaborative Robots 118 4.1.4 Calculation Scheme for Industrial Robots 120 4.2 Gripper Feasibility Module – Module Development 121 4.3 Rough Layout Discretization Module – Module Development 122 4.3.1 General Approach 122 4.3.2 Two-Dimensional Layout Pattern 123 4.3.3 Three-Dimensional Layout Pattern 125 4.4 Cycle Time Estimation Module – Module Development 126 4.4.1 General Approach 126 4.4.2 Reachability Study 127 4.4.3 Simulation Results 128 4.5 Collaborative Speed Estimation Module – Module Development 135 4.5.1 General Approach 135 4.5.2 Case 1: Quasi-static Contact with Hand 135 4.5.3 Case 2: Transient Contact with Hand 143 4.5.4 Case 3: Transient Contact with Shoulder 145 4.6 Synthesis – Module Development 149 5. Practical Verification 155 5.1 Use Case Overview 155 5.2 Gripper Feasibility 155 5.3 Layout Discretization 156 5.4 Collaborative Speed Estimation 157 5.5 Cycle Time Estimation 158 5.6 Economic Evaluation 160 5.7 Synthesis – Practical Verification 161 6. Results and Conclusions 165 6.1 Scientific Findings and Results 165 6.2 Critical Appraisal and Outlook 173Initially, industrial robots were mainly operated behind safety fences to account for the safety requirements. With production flexibilization, these sharp separation areas have been increasingly softened by utilizing external safety devices, such as distance sensors, to operate industrial robots fenceless. Based on this idea of coexistence or cooperation, safety technology has been integrated into the robot to enable true collaboration. These collaborative robots, or cobots, open up new application fields and fill the existing automation gap. But which automation variant is most suitable from an economic perspective? Present research dealt primarily isolated with one technology without comparing these systems regarding technological and economic specifics. Therefore, this doctoral thesis pursues a methodology to economically compare collaborative and industrial robots in fenceless machine tending systems. A particular focus lies on distilling the technical factors that mainly influence the profitability to receive a system understanding of the economic structure of both robot technology variants. For examination, the contents of such a planning scheme are described, categorized, systematized, and modularized. A suitable optimization model is presented on the economic side, while the feasibility regarding gripping, layout planning, robot velocities, and cycle time determination is assessed on the technical side. With deductive, simulative, empirical, and statistical methods, the system behavior of the single planning entities is analyzed to predict the overall profitability a priori with a minimum of investment,- production,- and cycle time information. It is demonstrated that the necessary planning data, in terms of layout composition, robot velocities, and cycle times, can be frontloaded to the project’s beginning with a reverse engineering approach. The net present value serves as the target figure, whose dependency on the human-robot interaction grade can be illustrated in an advantageousness diagram for the individual technical alternatives. Consequently, sound economic decisions can be made on a quantitative basis.:1. Introduction 25 1.1 Research Domain 25 1.2 Research Niche 26 1.3 Research Structure 28 2. State of the Art and Research 31 2.1 Turning Machines and Machine Tending 31 2.1.1 Tooling Machine Market Trends and Machine Tending Systems 31 2.1.2 Workpiece System 34 2.1.3 Machine System 36 2.1.4 Logistics System 39 2.1.5 Handling System 41 2.2 Robotics 43 2.2.1 Robot Installation Development and Application Fields 43 2.2.2 Fenceless Industrial and Collaborative Robots 48 2.2.3 Robot Grippers 55 2.3 Planning and Evaluation Methods 56 2.3.1 Planning of General and Manual Workstations 56 2.3.2 Cell Planning for Fully Automated and Hybrid Robot Systems 59 2.3.3 Robot Safety Planning 61 2.3.4 Economic Evaluation Methods 70 2.4 Synthesis - State of the Art and Research 71 3. Solution Approach 77 3.1 Need for Research and General Solution Approach 77 3.2 Use Case Delineation and Planning Focus 80 3.3 Economic Module – Solution Approach 86 3.4 Gripper Feasibility Module – Solution Approach 89 3.5 Rough Layout Discretization Model – Solution Approach 94 3.6 Cycle Time Estimation Module – Solution Approach 97 3.7 Collaborative Speed Estimation Module – Solution Approach 103 3.7.1 General Approach 103 3.7.2 Case 1: Quasi-static Contact with Hand 107 3.7.3 Case 2: Transient Contact with Hand 109 3.7.4 Case 3: Transient Contact with Shoulder 111 3.8 Synthesis – Solution Approach 114 4. Module Development 117 4.1 Economic Module – Module Development 117 4.1.1 General Approach 117 4.1.2 Calculation Scheme for Manual Operation 117 4.1.3 Calculation Scheme for Collaborative Robots 118 4.1.4 Calculation Scheme for Industrial Robots 120 4.2 Gripper Feasibility Module – Module Development 121 4.3 Rough Layout Discretization Module – Module Development 122 4.3.1 General Approach 122 4.3.2 Two-Dimensional Layout Pattern 123 4.3.3 Three-Dimensional Layout Pattern 125 4.4 Cycle Time Estimation Module – Module Development 126 4.4.1 General Approach 126 4.4.2 Reachability Study 127 4.4.3 Simulation Results 128 4.5 Collaborative Speed Estimation Module – Module Development 135 4.5.1 General Approach 135 4.5.2 Case 1: Quasi-static Contact with Hand 135 4.5.3 Case 2: Transient Contact with Hand 143 4.5.4 Case 3: Transient Contact with Shoulder 145 4.6 Synthesis – Module Development 149 5. Practical Verification 155 5.1 Use Case Overview 155 5.2 Gripper Feasibility 155 5.3 Layout Discretization 156 5.4 Collaborative Speed Estimation 157 5.5 Cycle Time Estimation 158 5.6 Economic Evaluation 160 5.7 Synthesis – Practical Verification 161 6. Results and Conclusions 165 6.1 Scientific Findings and Results 165 6.2 Critical Appraisal and Outlook 17

A Climatology of Tropospheric Zonal-Mean Water Vapor Fields and Fluxes in Isentropic Coordinates

Based on reanalysis data for the years 1980–2001 from the European Centre for Medium-Range Weather Forecasts (ERA-40 data), a climatology of tropospheric zonal-mean water vapor fields and fluxes in isentropic coordinates is presented. In the extratropical free troposphere, eddy fluxes dominate the meridional flux of specific humidity along isentropes. At all levels, isentropic eddy fluxes transport water vapor from the deep Tropics through the subtropics into the extratropics. Isentropic eddy fluxes of specific humidity diverge near the surface and in the tropical and subtropical free troposphere; they converge in the extratropical free troposphere. Isentropic mean advective fluxes of specific humidity play a secondary role in the meridional water vapor transport in the free troposphere; however, they dominate the meridional flux of specific humidity near the surface, where they transport water vapor equatorward and, in the solstice seasons, across the equator. Cross-isentropic mean advective fluxes of specific humidity are especially important in the Hadley circulation, in whose ascending branches they moisten and in whose descending branches they dry the free troposphere. Near the minima of zonal-mean relative humidity in the subtropical free troposphere, the divergence of the cross-isentropic mean advective flux of specific humidity in the descending branches of the Hadley circulation is the dominant divergence in the mean specific humidity balance; it is primarily balanced by convergence of cross-isentropic turbulent fluxes that transport water vapor from the surface upward. Although there are significant isentropic eddy fluxes of specific humidity through the region of the subtropical relative humidity minima, their divergence near the minima is generally small compared with the divergence of cross-isentropic mean advective fluxes, implying that moistening by eddy transport from the Tropics into the region of the minima approximately balances drying by eddy transport into the extratropics. That drying by cross-isentropic mean subsidence near the subtropical relative humidity minima is primarily balanced by moistening by upward turbulent fluxes of specific humidity, likely in convective clouds, suggests cloud dynamics may play a central role in controlling the relative humidity of the subtropical free troposphere