In this paper, a theoretical research is made on the influence of the friction force, the correction coefficient of the tooth and the radial component of the normal force in the Form Factor applicable to the stress on spur gears’ teeth. The Industrial Standards AGMA, ISO and DIN use the Lewis factor as the Form Factor but it doesn’t consider the above mentioned effects. The Standard GOST uses a Form Factor that considers the effect of the correction coefficient of the tooth and the radial component of the normal strength, but it doesn’t include the effect of the friction force. In this paper, a Mathematical Model is developed that incorporates all those effects. The obtained values of the form factors were represented graphically in function of the number of teeth, the correction coefficient and the friction coefficient. A graph is drawn for the driver gear and the driven gear, in which a remarkable influence of the simultaneous action of friction and correction coefficients is appreciated. In this new approach, it is found that the correction coefficients needed to optimize the resistance to the stress fracture of the teeth, in dependence of the values of the friction coefficient, should be greater that those used in the traditional approach. On the other hand, it has always been considered that gears with small number of teeth are the weakest with respect to stress fracture; however, in multiplying transmissions it is possible for driver gears with high number of teeth to be the weakest gear, given the favourable effect of the friction force on Form Factor in the driven gear and unfavourable in the driver gear. For the validation of the obtained results the Program of Finite Elements Analysis COSMOS Design Start 4.0 was used, obtaining very good results. Using FEA and Multiple Lineal Regression, a new expression for the calculation of the stress concentration coefficient in the feet of the tooth, in function of the number of teeth and of the correction coefficient, was found: kσMEF=1.497+0.126−0.003933Z
In this paper, a new scheme of analysis is used for the stress calculation in the throat area of the weld in lap joints with fillet welds transversely and longitudinally loaded. New calculation expressions are obtained that belong together better than the classic expressions with relationship to the values obtained by the Finite Elements Analysis.
A computer-aided methodology that applies the Finite Element Method (FEM) to gear design is presented in this work. The analysis takes into account the real tooth profile created by the involute flank of the tooth and the trochoidal fillet at the bottom of the tooth. The method enables gears with modified addendum and with any number of teeth to be modeled, so it can be used in CAD systems that require accurate models. Finally, the design process uses finite element modeling as an analysis tool to study the behaviour of components or products before they physically exist, thereby eliminating the need to create physical prototypes and providing a clean engineering design process.
The fillet welds are conventionally calculated to shear stress in the weakest section: the throat area of the weld. This consideration is a simplification for any fillet weld. Nevertheless, this procedure is internationally accepted as a justified procedure, mainly, for the simplification that makes the calculation of the welded joints of an engineering construction an easy procedure. This premise has motivated that different authors try to obtain calculation expressions for different cases that are presented in the practice, looking to facilitate the work of the industry technicians and engineers in charge of carrying out the calculation of these unions, however, in this pawn they don’t always use the most appropriate methods settled down by the Mechanics of the Materials introducing inaccuracies in these expressions. The Fracture Mechanics has outlined a new necessity: the development of methods of predicting defects that could exist in the welding cords. In order to do that, it is required to determine the stresses that arise in the welding with a superior accuracy. In this paper, the Theory of the Torsion of Thin Walls Profiles is applied to the calculation of the torsion shear stresses of the fillet weld joints. New calculation expressions are obtained that belong together better than the classic expressions with relationship to the values obtained by the Finite Elements Method.
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