A B S T R A C T A computational model for determination of the service life of gears with regard to bending fatigue at gear tooth root is presented. In conventional fatigue models of the gear tooth root, it is usual to approximate actual gear load with a pulsating force acting at the highest point of the single tooth contact. However, in actual gear operation, the magnitude as well as the position of the force changes as the gear rotates. A study to determine the effect of moving gear tooth load on the gear service life is performed. The fatigue process leading to tooth breakage is divided into crack-initiation and crack-propagation period.The critical plane damage model has been used to determine the number of stress cycles required for the fatigue crack initiation. The finite-element method and linear elastic fracture mechanics theories are then used for the further simulation of the fatigue crack growth. a = crack size a 2 = crack-initiation size b 0i = shear fatigue strength exponent b i = axial fatigue strength exponent C = material parameter of Paris equation c 0i = shear fatigue ductility exponent c i = axial fatigue ductility exponent C sur = surface finish correction factor d s = shear damage parameter d t = tensile damage parameter E = elastic modulus FP = final contact point F j = force acting on the gear for jth load case G = shear modulus g = transition function HPSTC = highest point of the single tooth contact i = gear ratio IP = initial contact point K = cyclic strength coefficient k = empirical material constant K c = stress intensity factor critical value K cl = stress intensity factor when closure occurs K I = mode I stress intensity factor
A computational model for determination of crack growth in a gear tooth root is presented. Two loading conditions are taken into account: (i) normal pulsating force acting at the highest point of the single tooth contact and (ii) the moving load along the tooth flank. In numerical analysis it is assumed that the crack is initiated at the point of the largest stresses in a gear tooth root. The simple Paris equation is then used for a further simulation of the fatigue crack growth. The functional relationship between the the stress intensity factor and crack length K = f(a), which is needed for determining the required number of loading cycles N for a crack propagation from the initial to the critical length, is obtained using a displacement correlation method in the framework of the FEM-method considering the effect of crack closure. The model is used for determining fatigue crack growth in a real gear made from case carburised and ground steel 14CiNiMo13-4, where the required material parameters were determined previously by appropriate test specimens. The results of the numerical analysis show that the prediction of crack propagation live and crack path in a gear tooth root are significantly different for both loading conditions considered.
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