How to Solve it

T his paper describes the redesign of a heat transfer course in the 2nd year BSc. curriculum in Mechanical Engineering in the faculty of Engineering Technology of the University of Twente. The objective was to improve the engineering ability of students to model and solve practically relevant problems systematically, obtain realistic answers, and obtain better scores at regular exams consisting of such type of problem exercises, as well as achieve a deeper learning. The redesign involves reintroduction of systematic problem analysis , enhancement of student engagement towards active learning, aspects of Student Driven/Student Centered Learning, Students As Partners, Decoding the Discipline, and Threshold Learning Concepts. The redesign has resulted in a new learning experience for students and teacher, reflected in increased participation, and positive evaluation results. The percentage of students passing the exam is improved over previous years which may partly be attributed to the redisign and new learning environment created. These positive results stimulated further development

Amplitude reduction of non-isotropic harmonic patterns in circular EHL contacts, under pure rolling

Surface roughness plays an important role in ElastoHydrodynamically Lubricated contacts, a role which is currently only partially understood. Recent work on waviness in EHL line contacts has shown and quantified the elastic deformation of the waviness inside the contact as a function of a single dimensionless parameter. In the present paper this work is extended to the circular contact problem. First it is shown that the amplitude reduction of an isotropic harmonic pattern can also be described as a function of a single dimensionless parameter. Subsequently, the effects of anisotropy are investigated varying from purely transverse to purely longitudinal. It is shown that one can create a single curve for the case varying from isotropic to longitudinal, and another for the case varying from isotropic to transverse. Both curves can be combined in a single formula

Validation of EHL contact predictions under time varying load

Abstract: In this paper, it is investigated how accurately current models predict the response of an elasto-hydrodynamically lubricated contact to time varying load conditions. For two patterns of time varying load, under conditions of pure rolling, the results obtained experimentally on a ball on disk interferometry apparatus by Sakamoto et al. (Behaviour of point contact EHL films under pulsating loads. Proceedings of the 30th Leeds–Lyon Symposium on Tribology, Elseviers Tribology Series, Vol. 43, pp. 391–399) are compared with the results of numerical simulations using the dynamic contact model of Wijnant (Contact dynamics in the field of elastohydro

Multigrid Solution of the 3D Elastic Subsurface Stress Field for Heterogeneous Materials in Contact Mechanics

The need to increase efficiency, stimulates the development of new materials tailored to specific applications and thermal/mechanical loading conditions, e.g. by controlling the property variations on a local scale: layered, graded, granular, porous and fibre-reinforced. For design and optimization of such materials the response to specific load conditions must be predicted which requires computer simulations. For applications in contact mechanics and lubrication failure criteria need to be developed which require the stress fields inside the (strongly heterogeneous) material induced by surface loading. The geometrical complexity of the subsurface topography and the need of an accurate solution require the use of a very fine discretization with a large number of elements, especially for three-dimensional problems. This requires optimally efficient numerical algorithms. In this paper the authors demonstrate the capability of Multigrid techniques to compute displacement and stress fields with great detail in strongly heterogeneous materials subject to surface loading, and in a contact mechanics application. Results are presented for a ceramic application and a contact problem of material with multiple inclusions. The efficiency of the method will allow extensive parameter studies with limited computational means. Moreover, it can efficiently be used to derive macroscopic stress-strain relations by simulations of microscopic problems. Also the method can be used for computational diagnostics of materials with specific heterogeneitie

Film Thickness Modulations in Starved Elastohydrodynamically Lubricated Contacts Induced by Timne-Varying Lubricant Supply

Many elastohydrodynamically lubricated contacts in practical applications, e.g., in bearings, operate in the starved lubrication regime. As a result their performance is sensitive to variations of the lubricant layers present on the surfaces, which form the supply to the contact. Their shape is often determined by previous overrollings of the track and also by replenishment mechanisms and various migration effects. Variations of the layers induced in the direction of rolling lead to a time-varying lubricant supply to the contact. In this paper, by means of numerical simulations using a starved lubrication model, the film thickness modulations in the center of the contact induced by a harmonically varying inlet supply have been investigated. First, for a given load condition and layer wavelength, the effect of the nominal layer thickness (degree of starvation) and the layer variation amplitude is illustrated. Subsequently, using results for different load conditions, wavelengths, and degrees of starvation, it is shown that the response of the contact to such variations is determined by a nondimensional parameter, which represents the ratio of the entrainment length of the contact to the wavelength of the induced variation, and by the degree of starvation. A simple formula is presented for use in engineering predicting the ratio of the amplitude of the film modulations in the center of the contact to the amplitude of the layer variations in the inlet

Calculation of the potential field in nerve stimulation using a multigrid method

This paper deals with the first step in the modeling of newe stimulation: the calculation of the potential field in a 3D volume conductor model of the nerve. surroundings and electrodes. Because of its time efficiency, a multigrid method was used to calculate the field. Compared to a Gauss-Seidel relaxation (overrelaxation factor = 1.7), a calculation time reduction of a factor 20 was obtaine

Fast Multilevel Panel Method for Wind Turbine Rotor Flow Simulations

A fast multilevel integral transform method has been developed that enables the rapid analysis of unsteady inviscid flows around wind turbines rotors. A low order panel method is used and the new multi-level multi-integration cluster (MLMIC) method reduces the computational complexity for calculating the wake deformation downstream of the wind turbine rotor from O(N^2) for a conventional approach to O(N). The method discretizes the volume surrounding the configuration with cubes. Each cube contains a grid of nodes that are used in the interpolation of the Green’s functions underlying the panel method. The formulation of the panel method is described concisely and verified using exact solutions for a tri-axial ellipsoid in uniform flow and for a rotating ellipsoid in air at rest. For these tests the panel method exhibits an error varying quadratically with panel size. The MLMIC fast multilevel method is described and its accuracy and O(N) computational speed are verified for some model problems. Surface pressure distributions obtained with the fast panel method are compared with results from the MEXICO wind tunnel experiment and with results from a state-of-the-art numerical simulation method based on the Reynolds-averaged Navier-Stokes (RaNS) equations. This work repositions panel methods in the computational landscape as valuable intermediate fidelity computational design method for wind turbine engineering