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The machining of shaped surfaces of parts with circular cross-sections is carried out on CNC machines using the control program. These control programs can be designed in the CAM-system in the form of G-codes, received from the postprocessor and loaded into the rack of a CNC lathe. Most CAM-systems model the stock removal process using canned cycles. The G71 cycle caters for the removal of the rough allowance by longitudinal cuts, the G72 cycle accounts for cross cuts, and the G73 cycle controls tool movement along paths equidistant to the workpiece contour [1, 2, 3]. In this case, the technologist-programmer, based on their working experience, chooses the appropriate cycle for machining a specific part.

When using any of the roughing cycles, you must specify the depth of cut, which determines the distance between passes. This essential cutting parameter, as well as the feed and spindle speed, is also intuitively chosen by the programmer.

Furthermore, the shape of the allowance that remains for the finishing pass also depends on the cutting cycle of the rough allowance. The unevenness of the allowance leads to errors along the contour, which are caused by elastic deformations, even in the contour sections that are portrayed by one geometric element. It should also be noted that these patterns are made known through the practice of contour machining on CNC machines. This is why, after roughing passes, an additional pass is usually required to even out the finishing allowance. This, of course, reduces the work cutting error, but owing to the variable nature of the transmission functions of the elastic system of machine, it does not completely solve the problem, but rather leads to a decrease in productivity.

In addition, during the finishing pass, changes in the cutting conditions along the contour of the part necessitate the regulation of cutting modes to stabilize the force parameters involved in the process. A correct solution of all the listed problems is only achievable through the results of preliminary simulating of the machining, using a priori information about the machine, workpiece, and tool with the determination of the main characteristic of the cutting process – the material removal rate (MRR) – along the machined contour.

Thus, the task of optimizing the turning of shaped surfaces of parts with circular cross-sections should be solved in two stages. First, it is necessary to select a cycle for removing the roughing allowance, which, with even cutting conditions, ensures a minimum cycle time. In this case, it is necessary to evaluate the allowance that remains for finishing. Next, it is necessary to solve the classic single-criterion optimization problem: assign components of the cutting mode (depth, feed and speed) that lead to a minimum cycle time while fulfilling all requirements for accuracy and quality.

The solution of such a problem is further complicated by the fact that during machining, the cutting conditions change, which means that there is no alternative to solving the optimization problem than to rely on the results of simulating using digital technologies.

Conclusions
To optimize the turning of shaped surfaces of parts with circular cross-sections, the cycle selected according to the minimum time criterion must carry out a simulation to determine the cutting mode, which will ensure maximum productivity while fulfilling all the requirements of accuracy and surface quality.

Optimization of contour turning, criteria for selecting a cycle, simulation of the machining of allowance removal