A method for robust design using response surface method and tolerance model to consider the variation of the influencing factors of the rotor system was proposed. According to this method

response surface methodology was used to obtain the functional relationship between multi-parameters and multi-objectives

while the multi-order critical speed distribution was taken as the constraint condition

and the sensitivity of the critical speed to minimize the variation of the support stiffness was formulated for the design goal. This proposed method was applied to the critical speed distribution design of low-pressure rotor system of a small bypass ratio turbofan engine. In consideration of the variation of each support stiffness

the critical speed distribution of the flexible rotor system meets the given standards. Meanwhile

the sensitivity of the critical speed to the variation of the support stiffness is lowest

proving that this method is feasible and effective.