Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring

A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost complete overview of residual stress states in the component during each production step. To reduce the measurement time in the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process. Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well.     

Residual stress field and reduction of stress intensity factors in cold-worked holes

Closed-form and semi-analytical solutions are obtained for the residual stress distributions in a plate caused by pressure acting on a central circular hole, representing the cold-work process. The material is elastic–perfectly plastic. Both Tresca and von Mises yield criteria are used and the corresponding residual stress distributions are compared. The relation between the dimension of the plastic zone and the value of internal pressure is presented. The relation between the magnitude of the residual stresses and the remote uniform tensile stress required to open symmetrical radial cracks is also presented. The reduction of the stress intensity factors of cracked open and riveted holes as a function of the internal pressure applied (or mandrel radial displacement) is investigated using numerical models for both an elastic–perfectly plastic material and for an Al 2024-T3 Alclad aluminum alloy.     

Symmetric differentiation on time scales

We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can be symmetric differentiable.     

Lie point symmetries of the Lane-Emden systems

It is shown that a Lie point symmetry of the Lane-Emden system is a Noether symmetry if and only if its parameters belong to the critical hyperbola.     

GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

We propose a GRASP using an hybrid heuristic-subproblem optimization approach for the Multi-Level Capacitated Minimum Spanning Tree (MLCMST) problem. The motivation behind such approach is that to evaluate moves rearranging the configuration of a subset of nodes may require to solve a smaller-sized MLCMST instance. We thus use heuristic rules to define, in both the construction and the local search phases, subproblems which are in turn solved exactly by employing an integer programming model. We report numerical results obtained on benchmark instances from the literature, showing the approach to be competitive in terms of solution quality. The proposed GRASP have in fact improved the best known upper bounds for almost all of the considered instances.     

Regularity of maps between Sobolev spaces

In this paper, we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-\(\mathrm {Spin}(9)\) structures. We also construct almost complex structures on the twistor space for parallel even Clifford structures and check their integrability. Moreover, we prove that in some cases one can give Kähler and nearly Kähler metrics to these spaces.     

The number of faces of the tridiagonal Birkhoff polytope

Counting basic objects as the vertices of polyhedra is a demanding problem in general, even for the most basic structured polytope. In this paper, we determine the number of q-faces for some q ≥ 1 of the polytope of tridiagonal doubly stochastic matrices.