Design of spur gearbox shafts for fatigue Fatigue Design of Spur Gearbox Shafts

Spur gearboxes are used in machine drives to transfer torque from the engine to the machine’s working element: the driving wheel of the car, the rotor of the helicopter or the drum of the conveyor. Spur gears and bearings are mounted on the shafts of the gearbox. Under the action of torque and forces in the gearing of the wheels, tangential and normal stresses occur in the cross section of the shaft. Normal stress varies in a symmetrical cycle and leads to material fatigue. In view of this, a mathematical model is proposed to improve the accuracy of calculating the overall safety factor for shaft fatigue resistance. Based on the von Mises deformation theory, equivalent stress parameters (amplitude and the mean) are determined. To assess the safety margin of the shaft, Soderberg, Goodman, Gerber, and ASME criteria are used. The stress amplitude margin is calculated depending on the endurance limit of the shaft material, refined according to the specified conditions. The average stress margin is determined relative to the yield strength of the material or the ultimate strength. Formulae for calculating the overall safety factor of amplitude and average stress are obtained. With a known safety factor and load, it is possible to determine the shaft diameter at the preliminary design stage of the gearbox according to the fatigue resistance condition.

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