On the Identification of Machine Settings for Gear Surface Topography Corrections

In this paper we set out to investigate the performances of some algorithms proposed in the gear literature for identifying the machine-tool settings required to obtain predesigned gear tooth surface topographies, or needed to compensate for flank form deviations of real teeth. For ease of comparison, the problem is formulated as a nonlinear least squares problem, and the most widely employed algorithms are derived as special cases. The algorithms included in the analysis are: (i) one-step methods, (ii) iterative methods, (iii) iterative methods with step control. The performance index is devised in their ability of returning practical solutions in the presence of: (i) strong model nonlinearities, (ii) ill-conditioning of the sensitivity matrix, (iii) demanding topographic shapes. Instrumental here is an original classification of topographic modifications as either “simple” or “complex”, based on the SVD analysis of the sensitivity matrix. Some selected numerical examples demonstrate that iterative techniques with step control are the most convenient in terms of reliability and robustness of the obtained solutions. The generation process considered here is face-milling of hypoid gears, although the methodology is general enough to cope with any gear cutting/grinding method

A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems

Long-range and long-term interferometric tracking by static and dynamic force-clamp optical tweezers.

Optical tweezers are recognized single-molecule technique to resolve forces and motion on the molecular scale. Complex biological phenomena, such as cell differentiation and locomotion, require long range tracking capabilities with nanometer resolution over an extended period, to resolve molecular processes on the cellular scale. Here we introduce a real-time control of the microscope stage position to perform long-term tracking, with sub-millisecond resolution, of a bead attached to a neuron, preserving sub-nanometer sensitivity on a spatial range of centimeters, seven orders of magnitude larger. Moreover, the suitability of the system is tested by time- modulating the force-clamp condition to study the role of statically and dynamically applied forces in neuronal differentiation

HYPERSINGULAR BOUNDARY INTEGRAL-EQUATIONS HAVE AN ADDITIONAL FREE TERM

In this paper it is shown that hypersingular boundary integral equations may have an additional free term which has been erroneously omitted in former analyses

The science of vehicle dynamics: handling, braking, and ride of road and race cars

Vehicle dynamics is often perceived as a quite intuitive subject. As a matter of fact, lots of people are able to drive a car. Nevertheless, without a rigorous mathematical formulation it is very difficult to truly understand the physical phenomena involved in the motion of a road vehicle. In this book, mathematical models of vehicles are developed, always paying attention to state the relevant assumptions and to provide explanations for each step. This approach allows for a deep, yet simple, analysis of the dynamics of vehicles, without having to resort to foggy concepts. The reader will soon achieve a clear understanding of the subject, which will be of great help both in dealing with the challenges of designing and testing new vehicles and in tackling new research topics. The book covers handling and performance of both road and race cars. A new approach, called MAP (Map of Achievable Performance), is presented and thoroughly discussed. It provides a global and intuitive picture of the handling features of a vehicle. Moreover, the book also deals with several relevant topics in vehicle dynamics that have never been discussed before. Massimo Guiggiani is professor of Applied Mechanics at the Università di Pisa, where he also teaches Vehicle Dynamics in the MS degree program in Vehicle Engineering

COMPUTING PRINCIPAL-VALUE INTEGRALS IN 3-D BEM FOR TIME-HARMONIC ELASTODYNAMICS - A DIRECT APPROACH

Current methods to deal with Cauchy principal-value (CPV) integrals in advanced boundary-element implementations have been almost entirely based on indirect approaches (such as the rigid-body motion in elastostatics). The present paper illustrates an alternative direct approach for the rigorous treatment and numerical evaluation of general CPV integrals in three-dimensional problems. The method has general validity. It can be applied in any field of applied mechanics and with curved boundary elements of any order and type. As expected, the mesh pattern around the pole does not affect the numerical results

The science of vehicle dynamics

Vehicle dynamics is a fascinating subject, but it can also be very frustrating without the tools to truly understand it. We can try to rely on experience, but an objective knowledge needs a scientific approach. Something grounded on significant mathematical models, that is models complex enough to catch the essence of the phenomena under investigation, yet simple enough to be understood by a (well trained) human being. This is the essence of science, and vehicle dynamics is no exception. But the really important point is in the mental attitude we should have in approaching a problem. We must be skeptical. We must be critical. We must be creative. Even if something is commonly accepted as obviously true, or if it looks very reasonable, it may be wrong, either totally or partially wrong. There might be room for some sort of improvement, for a fresh point of view, for something valuable. Vehicle dynamics can be set as a truly scientific subject, it actually needs to be set as such to achieve a deep comprehension of what is going on when, e.g., a race car negotiates a bend. When approached with open mind, several classical concepts of vehicle dynamics, like, e.g., the roll axis, the understeer gradient, even the wheelbase, turn out to be very weak concepts indeed. Concepts often misunderstood, and hence misused. Concepts that need to be revisited and redefined, and reformulated to achieve an objective knowledge of vehicle dynamics. Therefore, even experienced people will probably be surprised by how some topics are addressed and discussed here. To formulate vehicle dynamics on sound concepts we must rely on clear definitions and model formulations, and then on a rigorous mathematical analysis. We must, indeed, “formulate” the problem at hand by means of mathematical formulæ [4]. There is no way out. Nothing is more practical than a good theory. However, although we will not refrain from using formulæ, at the same time we will keep the analysis as simple as possible, trying to explain what each formula tells us. To help the reader, the Index of almost all mathematical symbols is provided at the end of this book. We believe an Index is more useful than a Glossary because it shows in which context each symbol is defined