This paper uses the lognormal probability function to modify deterministic design equations into probabilistic design, thereby transforming the traditional safety factor into a reliability factor. The reliability factor is related to the coefficients of variation (covs) of design parameters and a failure probability. An approximation of the reliability factor for initial sizing is defined as probabilistic design factor. The serviceability design model parameters are treated as random variables characterized by mean values and covs. The cov of the design model is obtained by using first order Taylor series expansion. Multiple serviceability criteria such as bending strength, lateral torsional stability, transverse deflection, and fillet weld strength are considered. The results from this study compare favorably with previous ones and sometimes give solutions with lower weight. In the first example, the solution in the present approach deviates on the conservative side from the previous one by 2.6% for 99.9% reliability and 3.8% for 99.997% reliability. These results are practically the same, suggesting that the method presented is reasonable and accurate. In the second example, the beam in the new solution has 23.65% lower volume or weight and the weld bead volume is lower by 8.4%. This suggests possible substantial cost reductions. From the sizes of the beam and weld bead, it can be concluded that the “factor of reliability” approach of this study and the stochastic Monte Carlo simulation method used previously are in good agreement. Due to the very good results from the examples considered, it seems reasonable to say that the “factor of reliability” method presented is a satisfactory model. The approach has the advantage of being much less computationally intensive and requires no specialized software or skills. These features can lead to cost savings in design projects. Design sizes from this method may be used to create solid models which can be optimized using FEM (Finite Element Method). In addition, and from an instructional perspective, the method could be used to introduce undergraduate engineering students to probabilistic design approaches.

Based on the Tredgold geometric approximation, a transparent contact stress capacity model for straight bevel gears is presented. A bevel load factor is defined which provides a kinetic link between the physical bevel gear and virtual spur gear. Three design cases of contact stress computations from different references are carried out and compared with AGMA estimates. Differences in results vary from 2.4% to 23.4% with the new model estimates, generally lower than AGMA values. The design sizing version of the new model is applied in two design cases. Comparison of the service load factor values for design sizing and design verification indicates a difference of 0.76% in case 4 and-1.65% in case 5. While more design cases are necessary for further verification of the design approach presented, it may however, be concluded from the results of our study that the design model presented appears reasonable.

A probabilistic method for determining a design factor is presented based on the lognormal probability density function. Design parameters are characterized by mean values and coefficients of variation (covs)

A revised Lewis bending fatigue stress capacity model for spur gears is presented and used to study the influence of mesh friction on root stress. It took the original Lewis formula and made modifications for dynamic loads, shear stress, and mesh friction in spur gear design. The study reveals that mesh friction may increase bending stress by up to 6% in enclosed cylindrical gear drives when an average mesh friction coefficient of 0.07 is assumed. A possible increase of 15% in root stress may occur in open gear drives when the mesh friction coefficient is taken as 0.15, a value considered to be representative for properly maintained open drives. To account for mesh frictional load and other factors directly influencing mesh friction, a friction load factor of 1.1 is suggested and introduced to gear service load estimation for enclosed gear drives and 1.15 for open gear drives.

Abstract. In combustion computational analysis, reduced mechanisms are often used in place of detailed kinetic chemistry. Since the computational costs of including all the species in the reactor model are always prohibitively high, several reduced mechanisms have been developed for propane and other hydrocarbon oxidation. In this study we employed ANSYS Fluent Computational Fluid Dynamics (CFD) package, (hereinafter referred to as Fluent) to analyze propane oxidation mechanism in a conical reactor.The k - scheme was used to model the effects of turbulence. The reaction kinetics employed in this study is that based on the work of Westbrook and Dryer [14] [20]. The results show that the bulk of the turbulent kinetic energy was produced in the inlet jet. The computed values of * y were found to confirm that the use of the law-of-the-wall functions was valid and also showed that the computational mesh for the present model was appropriate.