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:
$kσMEF=1.497+0.126−0.003933Z$
1.
Bonori G., Andrisano, A. O., Pellicano F. Stiffness Evaluation and Vibration in Tractor Gear. Proceedings of IMECE 04. 2004.—p. 8–9.
2.
Carroll
R. K.
Optimal Design of Compact Spur Gears Sets
.
Transmissions and Automation Design
106
, (
1
), p.
95
101
,
1984
.
3.
Fuentes, Aznar A., Pedrero, J. I., Bending Stress Analysis of Involute Spur Gears, Doctoral Thesis, U.N.E.D., Madrid, 1996.
4.
Machado, A., Moya, J. y Ferna´ndez, J., Consideraciones acerca del Disen˜o de los engranajes Cili´ndricos de Dientes Rectos, aplicables a su Recuperacio´n. Tesis Doctoral, UCLV, Santa Clara, 2000.
5.
Goytisolo R. y Moya, J. Influencia de la Correccio´n en la Lubricacio´n de las Transmisiones por Engranajes. Tecnologi´a. Serie: Centro Construccio´n de Maquinaria. An˜o 1, No. 1. Enero-Junio, 1976.
6.
Goytisolo R. y Moya, J. Correccio´n de Altura para Ma´xima Resistencia a la Picadura. Tecnologi´a, Serie: Centro Construccio´n de Maquinaria. An˜o 2, No. 2. Julio-Diciembre, 1977.
7.
Goytisolo R. y Moya, J. Correccio´n de Altura para Ma´xima Resistencia al Desgaste. Tecnologi´a, Serie: Centro Construccio´n de Maquinaria. An˜o 3, No. 2. Julio-Diciembre, 1978.
8.
Goytisolo R., Moya, J. y Pe´rez de la Fuente, A. Calculo de la Correccio´n de Altura en Engranajes. Tecnologi´a Meca´nica, No. 1, 1991.
9.
Goytisolo R., Moya, J. y Cabello, J.J. Height Correction to Maximize Gear Resistance to Fatigue. Proceedings 16th Canadian Congreso of Applied Mechanics. CANCAMM’97, Canada, 1997.
10.
Otarov, A. A., Goytisolo, R. y R. Lo´pez, D. Incremento de la Capacidad de Carga en Reductores Helicoidales mediante la Correccio´n. Tecnologi´a, Serie: Ingenieri´a Meca´nica, No. 3. 1974.
This content is only available via PDF.