Abstract:The exhaustion of natural resources has increased petroleum prices and the environmental impact of oil has stimulated the search for an alternative source of energy such as biodiesel. Waste cooking oil is a potential replacement for vegetable oils in the production of biodiesel. Biodiesel is synthesized by direct transesterification of vegetable oils, which is controlled by several inputs or process variables, including the dosage of catalyst, process temperature, mixing speed, mixing time, humidity and impurities of waste cooking oil that was studied in this case. Yield, turbidity, density, viscosity and higher heating value are considered as outputs. This paper used multi-response surface methodology (MRS) with desirability functions to find the best combination of input variables used in the transesterification reactions to improve the production of biodiesel. In this case, several biodiesel optimization scenarios have been proposed. They are based on a desire to improve the biodiesel yield and the higher heating value, while decreasing the viscosity, density and turbidity. The results demonstrated that, although waste cooking oil was collected from various sources, the dosage of catalyst is one of the most important variables in the yield of biodiesel production, whereas the viscosity obtained was similar in all samples of the biodiesel that was studied.

The experimental stress-strain curves from the standardized tests of Tensile, Plane Stress, Compression, Volumetric Compression, and Shear, are normally used to obtain the invariant λi and constants of material Ci that will define the behavior elastomers. Obtaining these experimental curves requires the use of expensive and complex experimental equipment. For years, a direct method called model updating, which is based on the combination of parameterized finite element (FE) models and experimental force-displacement curves, which are simpler and more economical than stress-strain curves, has been used to obtain the Ci constants. Model updating has the disadvantage of requiring a high computational cost when it is used without the support of any known optimization method or when the number of standardized tests and required Ci constants is high. This paper proposes a methodology that combines the model updating method, the mentioned standardized tests and the multi-response surface method (MRS) with desirability functions to automatically determine the most appropriate Ci constants for modeling the behavior of a group of elastomers. For each standardized test, quadratic regression models were generated for modeling the error functions (ER), which represent the distance between the force-displacement curves that were obtained experimentally and those that were obtained by means of the parameterized FE models. The process of adjusting each Ci constant was carried out with desirability functions, considering the same value of importance for all of the standardized tests. As a practical example, the proposed methodology was validated with the following elastomers: nitrile butadiene rubber (NBR), ethylene-vinyl acetate (EVA), styrene butadiene rubber (SBR) and polyurethane (PUR). Mooney–Rivlin, Ogden, Arruda–Boyce and Gent were considered as the hyper-elastic models for modeling the mechanical behavior of the mentioned elastomers. The validation results, after the Ci parameters were adjusted, showed that the Mooney–Rivlin model was the hyper-elastic model that has the least error of all materials studied (MAEnorm = 0.054 for NBR, MAEnorm = 0.127 for NBR, MAEnorm = 0.116 for EVA and MAEnorm = 0.061 for NBR). The small error obtained in the adjustment of the Ci constants, as well as the computational cost of new materials, suggests that the methodology that this paper proposes could be a simpler and more economical alternative to use to obtain the optimal Ci constants of any type of elastomer than other more sophisticated methods.

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

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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