An XFEM-Based Approach to Fatigue Crack Growth in Press-Fit Spur Gears

Gears mounted on a shaft via interference fit are the subject of an internal pressure which is essential for power transmission between gear and shaft. The pressure between shaft and gear is responsible for additional stresses occurring both in shaft and gear. This study examines the effect of stresses arising due to the interference on the crack growth that exists at the root of the gear tooth. The numerical analyses were conducted on models having different rim thicknesses by using the extended finite element method that allows mesh-independent crack modeling and does not need re-meshing. The results showed that internal pressure yields additional stresses in the tangential direction. The increment in tangential stress changed the location and intensity of the maximal 1st principal stress and accelerated crack growth. As the tightness of the fit increased, the crack turned towards the rim rather than towards the tooth. As the crack growth through the rim may cause a catastrophic failure of gear, the increment in tangential stress due to internal pressure is crucial for the fatigue life of the gear.

Análise de estruturas de suporte para sinalizações viárias

El cálculo de las estructuras de soporte para señalizaciones viales se realiza mediante la norma AASHTO con la cual se realiza fundamentalmente el chequeo a Fatiga, pero con ella no se llegan a conocer las tensiones von Mises, las tensiones tangenciales ni los desplazamientos en cualquier punto de la estructura. En el presente trabajo se determinan las cargas actuantes, así como sus combinaciones más críticas para el análisis. Se realiza el cálculo analítico a través de los métodos y las normas establecidas para ello y se confecciona un modelo de elementos finitos cuya simulación numérica complementa los resultados obtenidos por las normas. The calculation of the support structures for highway signs is carried out by means of the AASHTO standard, with which the Fatigue check is fundamentally carried out, but with it the von Mises stress, the tangential stress and the displacements at any point of the structure are not known. In the present work, the acting loads are determined, as well as their most critical combinations for the analysis. The analytical calculation is performed through the methods and standards established for it and a finite element model is created whose numerical simulation complements the results obtained by the standards.

Determination of Reynolds shear stress from the turbulent mean velocity profile and spectral characteristics of Orr-Sommerfeld -Squire equations

Theoretically, based on a waveguide model, the expression of the tangential stress is formulated for steady, two-dimensional incompressible fluid flow over a flat plate in turbulent boundary layer. It is dependent on some factors, one of them, the behaviour of the last damping mode eigenvalues, and eigenfunctions, that are deduced from solution Orr-Sommerfeld equation by spectral Chebyshev collocation Method. Verification of the latter method is investigated by comparison the deduced formula of turbulent tangential stress with experimental data. In addition to, weight factors in this expression are connected to define the condition of dynamical system solution for multiple 3-wave resonance. This system is solved numerically, and the dynamic invariant is normalized to obtain the time average of the square modulus harmonic, and sub harmonics amplitudes by theorem Birkhoff-Khinchin. Comparison is made between the time-averaged and the phase average for the square modulus of harmonic, and sub harmonic amplitudes that defined on the unit sphere, in the state of multiple 3-wave resonance.

Geometry Effects on Mode I Brittle Fracture in VO-Notched PMMA Specimens

This paper gathers experimental and theoretical investigations about both the geometry-dependent fracture initiation angle and the fracture strength in VO-notched polymethyl methacrylate (PMMA) specimens under mode I loading conditions. The numerical analyses revealed that despite the application of pure mode I loading on the geometrically symmetric VO-notched samples, the maximum tangential stress occurs at two points symmetrically placed on either side of the notch bisector line. The experimental tests performed on some specimens showed that a crack does not necessarily propagate along the notch bisector line. Stress-based theoretical studies were then carried out to justify the experimental findings. The conventional maximum tangential stress (MTS) criterion gave weak predictions of the fracture. Therefore, the predictions were checked with the generalized MTS (GMTS) criterion by taking into consideration the higher-order stress terms. It was demonstrated that the GMTS criterion predictions have satisfactory consistency with the experimental results of the crack initiation angle and the fracture strength.

Determination of Thermal Material Properties for the Numerical Simulation of Cutting Processes

Thermal properties of work materials, which depend significantly on the change in cutting temperature, have a considerable effect on thermal machining characteristics. Therefore, the thermal properties used for the numerical simulation of the cutting process should be determined depending on the cutting temperature. To determine the thermal properties of the work materials, a methodology and a software-implemented algorithm were developed for their calculation. This methodology is based on analytical models for the determination of tangential stress in the primary cutting zone. Based on this stress and experimentally or analytically determined cutting temperatures, thermal properties of the work material were calculated, namely the coefficient of the heat capacity as well as the coefficient of thermal conductivity. Three variants were provided for determining the tangential stress: based on the normal stress calculated using the Johnson-Cook constitutive equation, based on the experimentally determined cutting and thrust forces as well as by directly calculating the tangential stress. The thermal properties were determined using the example of three different materials: AISI 1045 and AISI 4140 steel as well as Ti10V2Fe3Al titanium alloy (Ti-1023). With the developed FE cutting model, the deviation between experimental and simulated temperature values ranged from approx. 7.5–14.4%.

A New Unified Solution for Deep Tunnels in Water-Rich Areas considering Pore Water Pressure

Pore water pressure has an important influence on the stresses and deformation of the surrounding rock of deep tunnels in water-rich areas. In this study, a mechanical model for deep tunnels subjected to a nonuniform stress field in water-rich areas is developed. Considering the pore water pressure, a new unified solution for the stresses, postpeak zone radii, and surface displacement is derived based on a strain-softening model and the Mogi-Coulomb criterion. Through a case study, the effects of pore water pressure, intermediate principal stress, and residual cohesion on the stress distribution, postpeak zone radii, and surface displacement are also discussed. Results show that the tangential stresses are always larger than the radial stress. The radial stress presents a gradually increasing trend, while the tangential stress presents a trend of first increasing and then decreasing, and the maximum tangential stress appears at the interface between the elastic and plastic zones. As the pore water pressure increases, the postpeak zone radii and surface displacement increase. Because of the neglect of the intermediate principal stress in the Mohr-Coulomb criterion, the postpeak zone radii, surface displacement, and maximum tangential stress solved by the Mohr-Coulomb criterion are all larger than those solved by the Mogi-Coulomb criterion. Tunnels surrounded by rock masses with a higher residual cohesion experience lower postpeak zone radii and surface displacement. Data presented in this study provide an important theoretical basis for supporting the tunnels in water-rich areas.

Field investigation and analysis of rockburst and spalling in a deep hard-rock mine

In order to investigate the ground pressure disasters in deep hard-rock mines, field investigation and theoretical analysis were carried out in a deep hard-rock mine. It is found that the degree and number of ground pressure disasters in the mine have increased significantly with depth. When the maximum tangential stress between 0.4-0.6 times the uniaxial compressive strength of surrounding rock, surrounding rock is prone to local spalling. When maximum tangential stress is greater than 0.6 times uniaxial compressive strength, serious failure is easy to occur, such as rockbursts and large-area collapses. After excavation, the rebound strain and displacement of surrounding rock increases linearly with buried depth, and the strain energy released of surrounding rock increases rapidly with the second power of buried depth. The rapidly increasing strain energy is main reason why deep ground pressure disasters in the mine are becoming more and more serious. In terms of surrounding rock support, energy-absorbing materials such as energy-absorbing bolts can well absorb strain energy released by surrounding rock. The energy-absorbing bolts are used for design of roadway support in the mine.