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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To ensure realistic results when modeling welded joints using the finite element method (FEM), it is essential to appropriately characterize the thermo-mechanical behavior of the elastic-plastic Finite Element (FE) models. This task is complex. Any small differences between the actual welded joints and the welded joints based on FEM can be amplified enormously in the presence of nonlinearities. Due to the intense concentration of heat on a small area to create such joints, the regions near the weld line undergo severe thermal cycles. These generate significant angular distortion due mainly to the residual stresses. This paper proposes a method to determine the parameters that are most appropriate for modeling the Butt joint single V-groove welded joint FE models' thermo-mechanical behavior that were created by the one-pass Gas Metal Arc Welding (GMAW). The method is based on experimental data, as well as genetic algorithms (GA) with multi-objective functions. As a practical example, the proposed methodology is validated with three different welded joints specimens that are manufactured by different voltages and currents (26 volts and 140 amps, 28 volts and 210 amps, and 35 volts and 260 amps). The electrode orientation, shielding gas flow rate, distance between nozzle and plate, and welding speed were considered to be constant for all of the specimens that were studied, and their values were 80 • , 20.0 L/min, 4.0 mm, and 6 mm/s, respectively. The base material was EN 235JR low carbon steel, whereas the weld bead was ER70S-6 for the three specimens that were welded. An agreement between the temperature field and the angular distortion that was obtained by the adjusted FE models and those that were obtained experimentally demonstrates that the proposed methodology may be valid for automatically determining the most appropriate parameters.

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