Aiming at the fatigue crack fracture problem of a speed-increasing gear of a wind turbine,based on the M integral method,the law of the growth of the speed-increasing gear with initial three-dimensional cracks was explored.According to the analysis and calculation of fracture mechanics principle and finite element principle,the change laws of stress intensity factor and the number of fatigue expansion cycles were obtained.The 3D crack model was created after determining the maximum force on the tooth root of the speed-increasing gea;by changing the longitudinal position of the 3D crack on the edge of the tooth root,the stress intensity factor and fatigue life change of the 3D crack during the growth process were explored.The results show that with the number of crack expansion steps increases,the stress strength factor KI of 3 groups of cracks increases,and the stress strength factor of root crack 1 remains the maximum;the fatigue life of the crack on the edge of spur gear decreases as it gets closer to the tooth root.