A Review and Gap Analysis of Exploiting Aerodynamic Forces as a Means to Control Satellite Formation Flight

Using several small, unconnected satellites flying in formation rather than a single monolithic satellite has many advantages. As an example, separate optical systems can be combined to function as a single larger (synthetic) aperture. When the aperture is synthesized, the independent optical systems are phased to form a common image field with its resolution determined by the maximum dimension of the array. Hence, a formation is capable of much finer resolution than it could be accomplished by any single element. In order for the formation to maintain its intended design despite present perturbations (formation keeping), to perform rendezvous maneuvers or to change the formation design (reconfiguration) control forces need to be generated. To this day, using chemical and/or electric thrusters are the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. In the mid-eighties, Caroline Lee Leonard published her pioneering work [1] proving the potential of using differential drag as a means of propellant-less source of control for satellite formation flight. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Since its control authority is limited to the in-plane motion, Horsley [2] proposed to use differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researches around the world have enhanced Leonard’s work over past decades which results in a multitude of available literature. Besides giving an introduction into the method the major contributions of this paper is twofold: first, an extensive literature review of the major contributions which led to the current state-of-the-art of different lift and drag based satellite formation control is presented. Second, based on these insights key knowledge gaps that need to be addressed in order to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain and advanced satellite surface materials as well as the necessity of robust control methods able to cope with the occurring uncertainties is assessed.Peer ReviewedPostprint (published version

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed.Peer ReviewedPostprint (author's final draft

The Mechanism of Abrupt Transition between Theta and Hyper-Excitable Spiking Activity in Medial Entorhinal Cortex Layer II Stellate Cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. ‘In vitro’ experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current

Experimental and Numerical Determination of the Required Initial Sheet Width in Die Bending

So far, determining the necessary precut dimensions of metal sheets prior to bending has been an unsolved question. During the last decades numerous calculation methods have been suggested. However, comparing these different methods indicates that different calculation methods suggest diverging precut dimensions. Especially in roll-forming, where multiple bend operations occur within the same bend part, these differences between several calculation methods can add up to some millimetres. The accuracy of presently available methods can hardly be compared. Thus an optimized method is needed. One possibility to determine the initial sheet width is identifying the position of the unlengthened layer in the bend zone. This study compares the position of the unlengthened layer determined in experiments and numerical simulations for different bend geometries and materials. The results indicate that even state of the art measuring technique is not accurate enough to determine the position of the unlengthened layer properly. Due to high measurement uncertainties, numerical simulations are required to assess the influence of geometry or material parameters on the position of the unlengthened layer. However, combining numerical and experimental results shows that the geometry of the bend part influences the position of the unlengthened layer and thus the required precut dimension. In contrast, a significant influence of material strength on the position of the unlegthened layer was not found

Optimierte Berechnung der abgewickelten Länge beim Biegen von Blech zu Kaltprofilen und Rohren

Für die Berechnung der abgewickelten Länge beim Biegen von Blech bietet der Stand der Technik verschiedene Ansätze, die bei gleicher Aufgabenstellung zu un-terschiedlichen Ergebnissen kommen. In der Regel finden dabei weder die Materi-aleigenschaften noch Einflüsse aus dem Biegeverfahren Berücksichtigung. Die Prozessauslegung verlangt so vom Prozessplaner ein hohes Maß an Erfahrung, wenn aufwändige Korrekturschleifen in der Produktion vermieden werden sollen. In diesem Forschungsprojekt werden zunächst die Grundlagen der aktuellen Berechnungsmethoden analysiert. Die Erarbeitung einer experimentellen Methode zur Bestimmung der Position der ungelängten Faser schafft die Voraussetzung für experimentelle Untersuchungen zur Bestimmung der abgewickelten Länge. Durch diesen experimentellen Ansatz können anschließend Gesenkbiege-, Schwenkbiege- und Walzprofilierprozesse analysiert werden. In einen Abgleich der experimentellen Ergebnisse mit numerischen Simulationen werden die wesentlichen Einflussgrößen auf die abgewickelte Länge bestimmt. Gleichzeitig können durch einen Vergleich experimenteller und numerischer Ergebnisse Empfehlungen für geeignete Modellierungsparameter für Biegeprozesse in der numerischen Simulation abgeleitet werden, die die Bestimmung der abgewickelten Länge ermöglichen. Abschließend wird durch eine Interpolation der Versuchsergebnisse eine verbesserte Berechnungsempfehlung erstellt. Als Haupteinflussgröße auf die abgewickelte Länge hat sich das Verhältnis von Biegeradius zu Blechdicke herausgestellt. Insbesondere beim Walzprofilieren nach dem Fertigradienverfahren beeinflusst ferner die Festigkeit des genutzten Stahls die Position der ungelängten Faser und somit die abgewickelte Länge. Bei der Abbildung von Biegeprozessen in numerischen Simulationen empfiehlt sich die Verwendung von Elementen mit quadratischen Ansatzfunktionen. Um die Position der ungelängten Faser in der numerischen Simulation auswerten zu können, ist eine Diskretisierung von acht Elementen in Blechdickenrichtung bei einem Biegeverhältnis von 2,5 notwendig. Die durch Interpolation der Versuchsergebnisse erstellten Berechnungsvorschriften zur verbesserten Bestimmung der abgewickelten Länge konnten in ersten Referenzversuchen bestätigt werden. Das Ziel des Forschungsvorhabens wurde somit erreicht

Experimental and Numerical Determination of the Required Initial Sheet Width in Die Bending

So far, determining the necessary precut dimensions of metal sheets prior to bending has been an unsolved question. During the last decades numerous calculation methods have been suggested. However, comparing these different methods indicates that different calculation methods suggest diverging precut dimensions. Especially in roll-forming, where multiple bend operations occur within the same bend part, these differences between several calculation methods can add up to some millimetres. The accuracy of presently available methods can hardly be compared. Thus an optimized method is needed. One possibility to determine the initial sheet width is identifying the position of the unlengthened layer in the bend zone. This study compares the position of the unlengthened layer determined in experiments and numerical simulations for different bend geometries and materials. The results indicate that even state of the art measuring technique is not accurate enough to determine the position of the unlengthened layer properly. Due to high measurement uncertainties, numerical simulations are required to assess the influence of geometry or material parameters on the position of the unlengthened layer. However, combining numerical and experimental results shows that the geometry of the bend part influences the position of the unlengthened layer and thus the required precut dimension. In contrast, a significant influence of material strength on the position of the unlegthened layer was not found

Energy efficient roll forming processes through numerical simulations

Due to ongoing efforts to mitigate climate change especially large scale manufacturing methods such as roll forming have to be optimized with respect to energy consumption. The required amount of drive power in roll forming is strongly affected by the rotational velocity of the tools. Due to the contoured shape of the rolls resulting in varying circumferential speed, the relative speed between tool and blank sheet can be positive, negative or zero. In consequence, neighboring sections of the same forming roll can accelerate or decelerate the blank sheet. Inappropriate speed ratios between different shafts cause some shafts to decelerate the blank sheet while other shafts have to compensate this deceleration and waste energy. Presently, the rotational speed of the shafts is mainly chosen based on the operator’s experience leading to a high risk of an energy inefficient process setup. This paper demonstrates how numerical simulations can optimize the energy demand in roll forming and validates the results experimentally. The drive power for each individual shaft is minimized by balancing accelerating and decelerating tool sections. Thus, the optimal rotational velocity for each shaft is derived. The numerical simulation predicts an energy saving potential of 50 . However, due to limited control accuracy only 14 could be realized in experiments to date

Five Ways to Determine the Initial Sheet Width in Bending

Different bending methods are applied in manufacturing sheet metal parts. Research on sheet metal bending has identified several distinct ways of determining the initial sheet width (e.g. by Oehler 1, by Mäkelt 2, and by DIN 6935 3), also termed unfolded length, but has been unable to resolve the question which of these methods is most advisable in general. Especially in roll-forming, where multiple bend operations occur within the same bend part, these different calculation methods lead to differing recommendations for the initial sheet width. One approach to resolving this discrepancy is the experimental investigation of the position of the unlengthened fibre in bending. This study compared five different experimental approaches to determining the position of the unlengthened fibre in order to identify the most advisable approach - a prerequisite for improving the calculation of the unfolded length