Optimization Model of Process Parameters for Full-Plate Long-Roll Straightening considering Equipment Bounce

Roll straightening is an important process link in sheet production. Due to the step change of the straightening force during the straightening bite and the tail flick, the whole-plate length straightening and pressing process changes will affect the straightening effect. Based on the solution of the curvature integral straightening process, this paper introduces the stiffness coefficient of the straightening equipment. Through C language programming, the iterative solution has been realized, and the process parameters of the dynamic change of the straightening reduction have been obtained. The enumeration method was used to establish a calculation method to optimize the entire board-length straightening process. The laboratory comparison of the 11-roll straightening machine proves that the straightening process optimization model meets the application requirements.

Connecting the Wilson depression to the magnetic field of sunspots

Context. In sunspots, the geometric height of continuum optical depth unity is depressed compared to the quiet Sun. This so-called Wilson depression is caused by the Lorentz force of the strong magnetic field inside the spots. However, it is not understood in detail yet how the Wilson depression is related to the strength and geometry of the magnetic field or to other properties of the sunspot. Aims. We aim to study the dependence of the Wilson depression on the properties of the magnetic field of the sunspots and how exactly the magnetic field contributes to balancing the Wilson depression with respect to the gas pressure of the surroundings of the spots. Methods. Our study is based on 24 spectropolarimetric scans of 12 individual sunspots performed with Hinode. We derived the Wilson depression for each spot using both a recently developed method that is based on minimizing the divergence of the magnetic field and an approach that was developed earlier, which enforces an equilibrium between the gas pressure and the magnetic pressure inside the spot and the gas pressure in the quiet Sun, thus neglecting the influence of the curvature force. We then performed a statistical analysis by comparing the Wilson depression resulting from the two techniques with each other and by relating them to various parameters of the sunspots, such as their size or the strength of the magnetic field. Results. We find that the Wilson depression becomes larger for spots with a stronger magnetic field, but not as much as one would expect from the increased magnetic pressure. This suggests that the curvature integral provides an important contribution to the Wilson depression, particularly for spots with a weak magnetic field. Our results indicate that the geometry of the magnetic field in the penumbra is different between spots with different strengths of the average umbral magnetic field.

Matter Dynamics in a Unitary Relativistic Quantum Theory

We describe the matter dynamics as a positively defined density and show that, according to the general theory of relativity, such a distribution can be conceive only as of a fragment of matter with a finite mass equal to a mass , as a characteristic of the matter dynamics, – the matter quantization. The group velocities of the Fourier conjugate representations in the coordinate and momentum spaces describe the dynamics of a quantum particle in agreement with the Hamiltonian equations. Under the action of an external (non-gravitational) field, the acceleration of the quantum matter has two components: 1) A component perpendicular to the velocity, given by the relativistic mechanical component of the time dependent phase, and 2) A component given by the additional field terms of this phase. A free quantum particle is described by a non-dispersing wave function , contrary to the solution of the Schrödinger equation. A coherent electromagnetic field, in resonance with a system of active quantum particles in a Fabry-Perot cavity, has a wave vector approximately proportional to the metric elements, as the resonance frequency is approximately constant – a gravitational wave can be detected by the transmission characteristics of an active Fabry-Perot cavity. In a constant gravitational field, a quantum particle undertakes a velocity and an acceleration, which, at the boundary of a black hole are null – absorption and evaporation processes at the boundary of a black hole arise only by gravitational perturbations. Generally, a quantum particle is described by a time-space volume, called graviton, with a spin 2, and a distribution of a specific matter in this volume, with a half-integer spin for Fermions and an integer spin for Bosons. A graviton Lagrangian is obtained as a curvature integral on a graviton volume, and a Hamiltonian tensor is obtained for the gravitational coordinates and velocities.

Cartan ribbonization and a topological inspection

We develop the concept of Cartan ribbons together with a rolling-based method to ribbonize and approximate any given surface in space by intrinsically flat ribbons. The rolling requires that the geodesic curvature along the contact curve on the surface agrees with the geodesic curvature of the corresponding Cartan development curve. Essentially, this follows from the orientational alignment of the two co-moving Darboux frames during rolling. Using closed contact centre curves, we obtain closed approximating Cartan ribbons that contribute zero to the total curvature integral of the ribbonization. This paves the way for a particularly simple topological inspection—it is reduced to the question of how the ribbons organize their edges relative to each other. The Gauss–Bonnet theorem leads to this topological inspection of the vertices. Finally, we display two examples of ribbonizations of surfaces, namely of a torus using two ribbons and of an ellipsoid using closed curvature lines as centre curves for the ribbons.

A novel control strategy for the multi-step straightening process of long/extra-long linear guideways

The straightening process for a linear guideway with particular cross-section shape is normally conducted by the three-point pressure bending method. However, the single-step straightening process (SSSP) of a long/extra-long linear guideway may make the workpiece from a single-curvature curve into a more complex shape. Due to these limitations of SSSP, a quantitative control strategy for the multi-step straightening process (MSSP) of a long/extra-long linear guideway is proposed in this paper based on the straightening principle of SSSP. Firstly, the predictive models for straightening stroke and helix angle after unloading with respect to SSSP are developed based on the elasto-plastic theory and curvature integral model. Depending on the established analytical model for SSSP, the MSSP is then mathematically modelled to obtain corresponding straightening parameters considering feeding process, clamping process and straightening process. Besides, the finite element method has been applied to validate the developed mathematical model for the MSSP. Taking the approach of a linear guideway as an example, the experimental results have also shown that the proposed control strategy is appropriate for the MSSP of a long/extra-long linear guideway.

Application of Stereological Relations for the Characterization of Porous Materials via Microscopic Image Analysis

In this work we demonstrate the application of stereology-based image analysis for the characterization of highly porous cellular ceramics (alumina foams) prepared by biological foaming with yeast and subsequent drying (80-105 °C) and firing (1570 °C). It is shown that the ceramics prepared usually have total porosities in the range 78-84 % and that the porosities made up by large pores (volume fraction of foam bubbles) are usually in the range 58-75 %. Further it is shown that the mean chord length and the Jeffries size, i.e. pore size measures related to the interface density and the mean curvature integral density, respectively, are relatively close to each other (usually 0.8-1.4 and 0.8-1.2 mm) with a ratio close to unity (0.9-1.3) and that the mean surface-to-surface distance of pores gives a realistic picture of the average pore wall thickness (usually 0.46-0.69 mm). Using a special processing variant (excess ethanol addition) it is possible to obtain microstructures with lower porosity (total porosity 68-70 %, foam bubble volume fractions 50-56 %) and smaller pore size (approx. 0.5 mm). Absolute errors are calculated using normalized deviations corresponding to 95 % reliability in the Student distribution and the standard errors for the quantities in question (both observed and estimated). Relative errors are found to be below 12 % when the number of measurements is of order 400-1000.