Mathematical Optimal Sequence Model Development to Process Planes and Other Interconnected Surfaces of Complex Body Parts

Experience in application of multi-operational machines CNC (MOM CNC) shows that they are efficient only in case of significantly increasing productivity and dramatically reducing time-to-market cycle of new products. Most full technological MOM capabilities are revealed when processing the complex body parts. The more complex is a part design and the more is its number of machined surfaces, the more tools are necessary for its processing and positioning, the more is an efficiency of their application. At the same time, the case history of using these machines in industry shows that MOM CNC are, virtually, used mostly for technological processes of universal equipment, which is absolutely unacceptable. One way to improve the processing performance on MOM CNC is to reduce nonproductive machine time through reducing the mutual idle movements of the working machine. This problem is solved using dynamic programming methods, one of which is the solution of the traveling salesman problem (Bellman's method). With a known plan for treatment of all elementary surfaces of the body part, i.e. the known number of performed transitions, each transition is represented as a vertex of some graph, while technological links between the vertices are its edges. A mathematical model is developed on the Bellman principle, which is adapted to technological tasks to minimize the idle time of mutual idle movements of the working machine to perform all transitions in the optimal sequence. The initial data to fill matrix of time expenditures are time consumed by the hardware after executing the i-th transition, and necessary to complete the j-transition. The programmer fills in matrix cells according to known routing body part taking into account the time for part and table positioning, tool exchange, spindle and table approach to the working zone, and the time of table rotation, etc. The mathematical model was tested when machining the body part with 36 transitions on the MOM model MS 12-250 of horizontal spindle configuration. Due to optimization, up to 25% reduction of nonproductive machine time has been reached