A variational model for data fitting on manifolds by minimizing the acceleration of a B\'ezier curve

We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closed-form, numerically stable and efficient algorithm to compute the gradient of a B\'ezier curve on manifolds with respect to its control points, expressed as a concatenation of so-called adjoint Jacobi fields. Several examples illustrate the capabilites and validity of this approach both for interpolation and approximation. The examples also illustrate that the approach outperforms previous works tackling this problem

Investigation of a quantified sound probe for stud weld quality measurement with numerical simulation data

Drawn arc stud welding with ceramic ferrules is a widely used joining process for joining sheet metal to studs, which can be threaded or sheared. During the welding process, various irregularities can occur which adversely affect the resulting mechanical properties. Arc blowing is one of the most common process defects. Arc blowing can result in an asymmetric weld bead which can increase the failure rate of the stud. An approach to stud testing is given in DIN ISO EN 14555. A sound probe carried out by an experienced welder provides qualitative information about the weld bead. The sound probe causes the stud to vibrate at its natural frequencies. If the eigenfrequencies can be calculated for each weld bead shape, the sound probe can be quantified. To this end, a new simulation approach is presented which allows the rapid calculation of the eigenfrequencies of the stud with different weld bead shapes. A data set is also generated and analyzed

Effect of reduced ambient pressure and atmospheric composition on material removal mechanisms of steel and aluminum by means of high-speed laser processing

Balancing processes require highly precise mass corrections especially in case of high-speed turning rotors. Material removal by means of cw-mode laser radiation represents a novel approach for industrial balancing applications in order to achieve sufficient removal rates. Thereby, spatter formation was identified as primary removal mechanism. In this study, the effect of reduced ambient pressures and atmospheres with varying concentrations of argon, nitrogen and oxygen on spatter formation and loss of mass were investigated for AISI304 (1.4301, X5CrNi18-10) and EN AW-2618 (DIN 3.1924) under the use of a 400W single mode-fiber laser

Local Shielding Gas Supply in Remote Laser Beam Welding

The use of shielding gases in laser beam welding is of particular interest for materials interacting with ambient oxygen, e.g., copper, titanium or high-alloy steels. These materials are often processed by remote laser beam welding where short welds (e.g., up to 40 mm seam length) are commonly used. Such setups prevent gas nozzles from being carried along on the optics due to the scanner application and a small area needs to be served locally with inert gas. The article provides systematic investigations into the interaction of laser beam processes and parameters of inert gas supply based on a modular flat jet nozzle. Based on the characterization of the developed nozzle by means of high-speed Schlieren imaging and constant temperature anemometry, investigations with heat conduction welding and deep penetration welding were performed. Bead-on-plate welds were carried out on stainless steel AISI 304 for this purpose using a disc laser and a remote welding system. Argon was used as shielding gas. The interaction between Reynolds number, geometrical parameters and welding/flow direction was considered. The findings were proved by transferring the results to a complex weld seam geometry (C-shape)

Systematic adjustment of the joining time in pulsed laser beam welding of aluminum-copper joints by means of a closed-loop control

Electric mobility has become increasingly important in recent years. For this purpose, the use of copper is essential due to its electrical properties. In order to save weight and costs, copper is replaced by aluminum in many electrical conductors.In this paper, the required joining time for pulsed laser beam welding of aluminum-copper joints is investigated to minimize the mixing of both materials. By using an external controller and photodiodes, it was possible to develop a real-time pulse control laser welding process based on process emissions. The spectral emission was used to detect when the lower joining partner is reached during the deep welding process. The control enables the adjustment of different joining times, on the one hand by a signal drop of the spectral emission, on the other hand by a specific time. The laser pulse was terminated between 500 - 800 [my]s after reaching this event. This led to differences in process conditions, resulting in significant changes in mechanical properties. In this way, a decisive influence was exerted on the resulting joining zone. The interaction duration and the work piece transition are of primary interest. By comparing the results with high-speed recordings in the half-section set-up, the resulting mechanisms can be identified. It could be shown that the breakup time have an high impact for the shear tensile force and the welding depth. A Change in the breakup time of 40 [my]s could lead to high changes in the tensile shear force

Influence of different Ni coatings on the long-term behavior of ultrasonic welded EN AW 1370 cable/EN CW 004A arrestor dissimilar joints

The increasing demand for energy-efficient vehicles requires suitable methods for cost and weight reduction. This can be achieved by the replacement of copper by aluminum, in particular for the on-board power systems. However, the complete substitution is restricted by the mechanical and physical material properties of aluminum as well as challenges in the aluminum copper interface. The challenges concern the corrosion vulnerability and the occurrence of brittle intermetallic compounds (IMC) which can negatively influence the mechanical properties and the electrical conductivity. Therefore, current investigations focus on the one hand on the realization of dissimilar aluminum copper joints by suitable joining technologies, like ultrasonic welding, and on the other hand on the assurance of a sufficient prevention against harmful corrosion effects. In cases where the joint cannot be protected against corrosion by sealing, nickel coatings can be used to protect the joint. In the present study, the influence of electroless, electroplated, and sulfamate nickel coatings was investigated regarding the long-term stability. The joints were performed as industry-related arrester connections, consisting of EN AW 1370 cables and EN CW 004A terminals. The samples were exposed to corrosive as well as electrical, thermal, and mechanical stress tests according to current standards and regulations

Intensity of Coulomb Interaction between quasiparticles in diffusive metallic wires

The energy dependence and intensity of Coulomb interaction between quasiparticles in metallic wires is obtained from two different methods: determination of the temperature dependence of the phase coherence time from the magnetoresistance, and measurements of the energy distribution function in out-of-equilibrium situations. In both types of experiment, the energy dependence of the Coulomb interaction is found to be in excellent agreement with theoretical predictions. In contrast, the intensity of the interaction agrees closely with theory only with the first method, whereas an important discrepancy is found using the second one. Different explanations are proposed, and results of a test experiment are presented.Comment: Submitted to Solid States Communication

Electron coherence at low temperatures: The role of magnetic impurities

We review recent experimental progress on the saturation problem in metallic quantum wires. In particular, we address the influence of magnetic impurities on the electron phase coherence time. We also present new measurements of the phase coherence time in ultra-clean gold and silver wires and analyse the saturation of \tauphi in these samples, cognizant of the role of magnetic scattering. For the cleanest samples, Kondo temperatures below 1 mK and extremely-small magnetic-impurity concentration levels of less than 0.08 ppm have to be assumed to attribute the observed saturation to the presence of magnetic impurities.Comment: review article, 14 pages, 11 figures. Physica E (in press

Influence of microstructure and microgeometry of the probe on friction stir welding of AA 6060 T66

Increasing demands on joining technology in terms of lightweight construction and component complexity require the further development of technologically suitable welding processes. Friction stir welding is a promising alternative to conventional fusion welding processes. The central element of this technology is a tool consisting of a shoulder and a probe, which generates a friction-induced heat input through rotation and pressure. The process is used in automotive, shipbuilding and aerospace applications due to its excellent mechanical material properties, which are similar to those of the base material. However, FSW is subject to process-specific challenges, including comparatively high process forces, high clamping requirements and tribological stresses during welding, as the process involves constant contact between the tool and the workpiece. As the welding process progresses, the tribochemical stresses cause the tool shape and material to change. The result is premature tool failure and reduced process reliability. While previous investigations have focused on increasing wear resistance by selecting a suitable coating system and varying tool geometries, the aim of this study is to adapt the surface of the welding probe by changing the microgeometry and microstructure. Based on the current state of the art, the present work investigates the influence of the welding probe by adapting the microgeometry and microstructure and shows the extent to which tool wear, weld seam quality and behaviour in the welding process can be influenced. By analogy with machining, individual welding probes will be prepared by drag finishing and the effect on tool geometry and wear will be demonstrated. In addition, a feasibility study will be carried out on the thread rolling of welding probes with metric threads. This process, which is used to adjust the microstructure, will show whether production by rolling is feasible and to what extent the surface finish of the rolled welding probes differs from that of conventionally produced ones. The investigations were carried out using a force-controlled robotic welding setup to weld 5 mm thick AA 6060 T66 sheets. A Kistler multicomponent dynamometer type 9139AA was used to measure the cartesian forces in the x-, y- and z-directions. The weld seam properties of the initial and the optimized tool designs were determined by visual and metallographic inspection and tensile tests to DIN EN ISO 25239-5

Process control by real-time pulse shaping in laser beam welding of different material combinations

Joining of metallic material combinations with limited solubility is a challenging task. Because of low solubility, such material combinations lead to the formation of intermetallic compounds (IMC) during common weld bath. IMC then lead to increased hardness and brittleness. Generally, these properties are undesirable and the aim is to reduce intermetallics to a minimum. In this contribution, a process control by real-time pulse shaping is realized, whereby the power is adjusted in each individual pulse. The material-specific emissions are continuously detected by photodiodes and used as control variable. By equipping the photodiodes with band-pass filters, the wavelength can be selected in a material-dependent manner. The control loop including data processing and pulse shaping as well as the connection to the power supply of the laser beam source is realized by a novel system in less than 10 µs. This enables laser welding of different metals with a nearly constant penetration depth at the boundary layer and, therefore, the limitation of IMC