SUMMARYA non-iterative, ÿnite element-based inverse method for estimating surface heat ux histories on thermally conducting bodies is developed. The technique, which accommodates both linear and non-linear problems, and which sequentially minimizes the least squares error norm between corresponding sets of measured and computed temperatures, takes advantage of the linearity between computed temperatures and the instantaneous surface heat ux distribution. Explicit minimization of the instantaneous error norm thus leads to a linear system, i.e. a matrix normal equation, in the current set of nodal surface uxes. The technique is ÿrst validated against a simple analytical quenching model. Simulated low-noise measurements, generated using the analytical model, lead to heat transfer coe cient estimates that are within 1% of actual values. Simulated high-noise measurements lead to h estimates that oscillate about the low-noise solution. Extensions of the present method, designed to smooth oscillatory solutions, and based on future time steps or regularization, are brie y described. The method's ability to resolve highly transient, early-time heat transfer is also examined; it is found that time resolution decreases linearly with distance to the nearest subsurface measurement site. Once validated, the technique is used to investigate surface heat transfer during experimental quenching of cylinders. Comparison with an earlier inverse analysis of a similar experiment shows that the present method provides solutions that are fully consistent with the earlier results. Although the technique is illustrated using a simple one-dimensional example, the method can be readily extended to multidimensional problems.

It is well known that isotropic, nondispersive continuous hyperbolic problems become dispersive and anisotropic upon discretization. The purpose of this paper is to conduct a dispersion analysis of the nondissipative numerical approximations to plane wave motions in isotropic elastic solids. The discrete formulations considered are: an explicit, second-order accurate ®nite difference scheme, a consistent mass matrix formulation with linear quadrilateral elements and the corresponding lumped mass matrix formulation. Dispersion relation is derived for each of these formulations. In the context of the ®nite difference scheme, expressions for group velocity for both the shear and longitudinal waves are derived and the effect of using meshes of unequal size in x and y directions is studied. Results from numerical experiments con®rming the predictions of analysis are also presented. IntroductionDispersion relation is the relation between the frequency and wavenumber. The ratio of the frequency and wavenumber is the phase speed whereas the gradient of the frequency with respect to the wavenumber is the group speed. For a nondispersive problem, the group speed does not depend on the frequency and is identical to the phase speed. For a dispersive problem on the other hand, the group speed depends on the frequency and in general is different from the phase speed.It is well known that when a nondispersive continuous problem is discretized, the discrete model becomes dispersive. In the case of one-dimensional problems, dispersion leads to waves of different lengths propagating at different speeds. In the case of two and three dimensions, not only do different wavelengths travel at different speeds but they also travel in wrong directions. That is, the discrete models become anisotropic even if the continuous problem is isotropic.A survey of the literature shows that a large body of work has been done on analyzing the dispersion errors induced due to numerical approximations. Much of the work related to one-dimensional and two-dimensional scalar wave equations can be found in the monograph by Vichnevetsky [10]. Dispersion analysis of a three-dimensional scalar wave equation was conducted by Abboud and Pinsky [1]. The excellent review article by Trefethen [9] surveys the role of group velocity in ®nite difference approximations to one-dimensional and two-dimensional scalar wave equations. Recently, Monk and Parrott [8] studied the dispersion errors introduced in various ®nite element approximations to Maxwell's equations.However, surprisingly, there appears to be very little work done on the dispersion analysis of numerical approximations to the wave propagation problems in isotropic, elastic solids in two and three dimensions. Only the one-dimensional elastic wave propagation problem appears to have received the attention of several researchers previously (see [3,7] and the references cited therein). In addition, most of this work appears to consider only one type of wave propagating through the body.In the case of two and th...

Machining processes, including turning, are a critical capability for discrete part production. One limitation to high material removal rates and reduced cost in these processes is chatter, or unstable spindle speed-chip width combinations that exhibit a self-excited vibration. In this paper, an artificial neural network (ANN)—a data learning model—is applied to model turning stability. The novel approach is to use a physics-based process model—the analytical stability limit—to generate a (synthetic) data set that trains the ANN. This enables the process physics to be combined with data learning in a hybrid approach. As anticipated, it is observed that the number and distribution of training points influences the ability of the ANN model to capture the smaller, more closely spaced lobes that occur at lower spindle speeds. Overall, the ANN is successful (>90% accuracy) at predicting the stability behavior after appropriate training.

In this work, the operating sensitivity of the hydrostatic thrust bearing with respect to pressure-induced deformations will be studied in a stationary setting. Using the classical lubrication equations for low Reynold’s number flow, closed-form expressions are generated for describing the pressure distribution, the flow rate, and the load carrying capacity of the bearing. These expressions are developed to consider deformations of the bearing that result in either concave or convex shapes relative to a flat thrust surface. The impact of both shapes is compared, and the sensitivity of the flow rate and the load carrying capacity of the bearing with respect to the magnitude of the deformation is discussed. In summary, it is shown that all deformations increase the flow rate of the bearing and that concave deformations increase the load carrying capacity while convex deformations decrease this same quantity relative to a non-deformed bearing condition.

R ecent studies have shown that many semiconductor and ceramic materials can be machined in ductile fashion under high pressures and at low depths of cut. In a previous study, the authors reported results from numerical simulations of the orthogonal machining of silicon nitride using a pressure independent material model with the von M ises yield criterion. In the present work, the mechanical behaviour of silicon nitride is treated using the D rucker-Prager yield criterion implemented in the commercial machining software AdvantEdge. N umerical simulations are carried out for depths of cut ranging from 1 to 40 mm and at cutting speeds ranging from 25 to 300 m/min. R esults from the simulations are presented, and modelling issues are discussed.