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In order to realize the digital closed loop manufacturing,the tooth surface should be discretized and the spatial coordinates and the normal vectors of the discrete points on the tooth surface should be calculated. Based on the machining principle of spiral bevel gears and according to the relative position and relative motion relationship between the gear blank and the cutting tool,considering the cutter tilt modification and roll ratio modification motion,and using the method of vector operation,the mathematical model of working tooth surface and the fillet is established. Based on the mathematical model of the whole tooth surface,a method for calculating the spatial coordinates and the normal vector of the discrete points of the tooth surface is established and verified.