Infuence of the Friction Force, the Tooth Correction Coefficient and the Normal Force Radial Component in the Form Factor and the Stress in the Feet of Spur Gear’s Teeth

Abstract

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