Method of bending and bending machine for the execution of a method of bending

Method of bending a tubular metal article for obtaining a bent tubular article comprising at least the steps of:

• a) determining a bending sequence of the tubular metal article by means of a calculating unit;
• and
• b) bending the tubular metal article according to the bending sequence determined during the execution of the step a);
• wherein during the step a) at least the following sub-steps are executed by the calculating unit:
• a1) defining an initial configuration and a final configuration of the tubular metal article which differs from the initial configuration by a number N of bends;
• a2) determining one or more explorative bending sequences as a function of the initial configuration and the final configuration, each explorative bending sequence having a cost (F) which is a function of the bending costs in terms of energy and/or time;
• and
• a3) proposing at least one or more explorative bending sequences having minimal costs as the determined bending sequence;
• wherein during the step a2) one or more paths from the initial configuration to the final configuration are defined;
• wherein each path presents a plurality of intermediate configurations of the tubular metal article;
• wherein each intermediate configuration is connected to a subsequent intermediate configuration by means of a bend;
• wherein the respective associated cost for each one of the one or more paths is determined, the associated cost being dependent on the cost of the respective bends;
• wherein the respective bends of the one or more paths corresponding to the minimum associated costs, define the one or more explorative bending sequences to be proposed during the step a3);
• wherein during the step a2) one or more paths are explored by means of the execution of the following sub-steps:
• a2i) setting the initial configuration as a start configuration;
• a2ii) determining the cost (F) from the start configuration to a subsequent intermediate configuration in proportion to the sum (G) of the bending cost from the initial configuration to the subsequent intermediate configuration and in function of an estimate of the bending cost (H) of the remaining path from the subsequent intermediate configuration to the final configuration;
• a2iii) repeating the sub-step a2ii) for one or more of the other subsequent intermediate configurations;
• a2iv) choosing the one or more subsequent intermediate configurations with the minimal cost;
• a2v) for each chosen subsequent intermediate configuration setting the subsequent intermediate configuration as the new start configuration and repeating the sub-steps a2ii) to a2v) until arriving at the subsequent intermediate configuration defined by the final configuration.