Loaded tooth contact analysis is an important technique for analyzing the meshing performances under load.The known algorithms can't be concerned with the tooth surface design directly because of a great deal of calculation

iteration or equations.A new simplified formulation was thus proposed based on application of the time varying stiffness.The transmission errors under loads were calculated by the developed formulation and finite element method

respectively.The results for the two methods were compared with respect to the magnitude

shape and 1st component of frequency spectrum of loaded transmission errors

and showed good agreement.The developed formulation was used to study the relationship of real contact ratio and load

the law of the loaded transmission errors versus real contact ratio

and the effect of contact pattern

transmission errors on loaded transmission errors.The analysis results provide the theoretical bases for the optimization strategy to tooth surface design of spiral bevel gear.The calculation of the loaded transmission errors is embedded to constitute the design route in the courses of the optimization.The design variables include contact path orientation and magnitude of transmission error;the objective of optimization is that the magnitude of the loaded transmission error fluctuates less under wide load ranges.