Conformities to law of changeability of the tool geometrical parameters, parameters of сut section, parameter of the chip formation, cutting forces, cutting temperature and machining surface roughness at machining of the shaped surfaces are set.
There is researched character of change of the working edge angle, cutting face edge angle, width and thickness of cut section, cutting speed on position of blade top on the convex and concave shaped surface.
The analytical dependences of the chip contraction coefficient, cutting forces, cutting temperature and machining surface roughness on the cutting speed and feed are certain. The method of determination of the cutting forces, thermal streams and cutting temperature at turning of the shaped surfaces is created taking into account changeability of the geometrical parameters and parameters of сut section. There are set coefficients, which allow expecting these parameters in any point of the convex and concave shaped surfaces.
The method of account of the cutting process parameters changeability at optimization of the cutting regimes at turning of the shaped surfaces on the criterion of maximum productivity is developed. With the use of method of the linear programming analytical dependences of the optimum-cutting regime from the turning parameters taking into account variable limitations on cutting forces, cutting temperature and machining surface roughness are definite.