There is a blank in the domestic and foreign literatures on the research on the calculation formula of the friction torque of the steel wire flexible shaft. In order to obtain the calculation formula of the friction moment of the wire flexible shaft under different bending states

the theoretical derivation to obtain the required formula is firstly used. Through experimental analysis

the important parameters in the formula are calculated

and then combining with the simulated annealing optimization algorithm

the parameters in the formula are optimized. The parameters in the formula are modified by using the simulated annealing algorithm

and the optimized friction torque formula corresponding to the wire flexible shaft at different angles is obtained. Using the optimized formula for calculation

the overall error is 2.831%

which is 4.312% lower than the original overall error of 7.143%. At the same time

the calculation results show that the optimized formula is also applicable to the bending rotational friction moment generated by flexible shafts with different shaft diameters under a certain angle.