This paper proposes a methodology that combines the Finite Element Method and multiple response surface optimization to search for the optimal operating conditions of a double-row Tapered Roller Bearing (TRB) that has a Preload (P), radial load (F r ), axial load (F a ) and torque (T). Initially, FE models based on a double-row TRB are built and validated in the basis of experimental data and theoretical models. Three of the most important parameters used in the design of TRB were obtained from a simulation of the FE models with a combination of several operating conditions that were previously selected in accordance with a design of experiments. The design parameters are: contact stress radio for both rows of rollers (S 1 and S 2 ), maximum deformation of the outer raceway (a max ), and the difference between the gaps of the inner raceways (Dd) or misalignment. Based on the results of the FE simulations, quadratic regressions models are generated that use the response surface method to predict the design parameters when new operating condition are applied. Then, a multi-response optimization study based on these models and using desirability functions is conducted. It is concluded that the accuracy of the results demonstrates that this methodology may be used to search for the optimal operating condition in a double-row TRB. KeywordsDouble row tapered roller bearing Á Finite element method Á Design of experiments Á Multiple response surface optimization List of symbols l t Rollers' effective length (mm) d m Mean diameter of tapered roller (mm) D max Diameter of tapered roller at large end (mm) D min Diameter of tapered roller at small end (mm) D m Bearing pitch diameter (mm) D i Bore diameter (mm) D o Outer diameter (mm) L Longitude of the bearing (mm) Z Number of rollers b oSemi minor axis of the projected contact ellipse (mm) K n Load deflection factor r

One of the main objectives when designing welded products is to reduce strains and deformations. Strains can cause excessive angular distortion. This results in a welded product that does not meet acceptable tolerances. The geometry of the weld bead (height and width) depends on the input parameters (speed, voltage and current), and provides the welded joint with strength and quality. As welded products become increasingly complex, deformations become more difficult to predict as they depend greatly on the welding sequence. This paper shows how a combination of the Finite Element Method, Genetic Algorithms and Regression Trees may be used to design and optimize complex welded products. Initially, Artificial Neural Networks and Regression Trees that are based on heuristic methods and evolutionary algorithms were used in predicting the weld bead geometry according to the input parameters. Then, thermo-mechanical Finite Element models were created to obtain the temperature field and the angular distortion using the weld bead geometry that the best predictive models generated. Finally, optimization techniques that are based on Genetic Algorithms were used to validate these Finite Element models against experimental results, and to subsequently find the optimal welding sequence to use in the manufacture of complex welded products.

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This paper demonstrates that combining regression trees with the finite element method (FEM) may be a good strategy for modelling highly non-linear mechanical systems. Regression trees make it possible to model FEM-based non-linear maps for fields of stresses, velocities, temperatures, etc., more simply and effectively than other techniques more widely used at present, such as artificial neural networks (ANNs), support vector machines (SVMs), regression techniques, etc. These techniques, taken from Machine Learning, divide the instance space and generate trees formed by submodels, each adjusted to one of the data groups obtained from that division. This local adjustment allows good models to be developed when the data are very heterogeneous, the density is very irregular, and the number of examples is limited. As a practical example, the results obtained by applying these techniques to the analysis of a vehicle axle, which includes a preloaded bearing and a wheel, with multiple contacts between components, are shown. Using the data obtained with FEM simulations, a regression model is generated that makes it possible to predict the contact pressures at any point on the axle and for any condition of load on the wheel, preload on the bearing, or coefficient of friction. The final results are compared with other classical linear and non-linear model techniques.

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