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This study aims to finding out the calculation formula of friction resistance of steel wire's flexible shaft in bending push-pull state. The operation principle is based on the adhesive friction theory and Newton's classical friction formula. The friction force f is measured by experiment under the conditions of same length L, different diameter D and different curvature K, and the curve trajectory equation is obtained by curve fitting with mathematical tools. Then, according to the experimental data, the greater the curvature of flexible shaft is (that's, the smaller the bending radius is), the greater the positive pressure between shaft core and the sheath will be. The positive pressure N between the shaft core and the sheath is equal to the curvature K direct ratio. Therefore, it can be concluded that the positive pressure N of the shaft core and sheath is proportional to the curvature K, and the proportional coefficient β is introduced. The experimental results show that the functional relationship between the friction force F and the curvature K of the flexible shaft can be derived, the diameter D and curvature K of the mandrel have a great influence on the friction resistance of the flexible shaft, that is, the empirical friction resistance formula. In order to reduce the relative error and improve the accuracy of the formula. By combining elite retention strategy with roulette method and replacing the current worst genetic algorithm with historical optimum, the parameter β in the formula is optimized. After optimization, the calculation formula of friction resistance of four flexible shafts of steel wire under bending push-pull state is obtained. The author's pioneer work has contributed to the calculation of friction resistance under bending push-pull, and the average calculation error is 5%, which meets the requirements of calculation accuracy.

Study on the friction resistance calculation method of a flexible shaft of wire rope based on genetic algorithm