This paper presents an approach for obtaining an optimized geometry for the flank of atooth by minimizing the equivalent contact stress. The stress calculation method is basedon Hertz theory. As the majority of tooth profiles are involute, the geometric variationof the flank of the tooth is achieved variationally relative to the involute profile. Theoptimum profile is obtained by Monte Carlo simulation. During this optimization, apolynomial expression of the tooth geometry is used. The parameters influencing thesimulation are the four characteristic contact points. The approach presented has beenapplied in a representative case. A study of the geometric sensitivity was conducted onthe optimized tooth profile. Two different approaches were considered: by Monte Carlosimulation and analytical propagation. The robust and linear nature of the behavior of thetooth profile was demonstrated when it was subjected to geometric variations.

A fillet curve is provided at the root of the spur gear tooth, as stresses are high in this portion. The fillet curve may be a trochoid or an arc of suitable size as specified by designer. The fillet stress is influenced by the fillet geometry as well as the number of teeth, modules, and the pressure angle of the gear. Because the relationship is nonlinear and complex, an artificial neural network and a backpropagation algorithm are used in the present work to predict the fillet stresses. Training data are obtained from finite element simulations that are greatly reduced using Taguchi's design of experiments. Each simulation takes around 30 min. The 4-5-1 network and a sigmoid activation function are chosen. TRAINLM function is used for training the network with a learning rate parameter of 0.01 and a momentum constant of 0.8. The neural network is able to predict the fillet stresses in 0.03 s with reasonable accuracy for spur gears having 25–125 teeth, a 1–5 mm module, a 0.05–0.45 mm fillet radius, and a 15°–25° pressure angle.