Compound stiffness modelling of an integrated open-die forging centre with serial–parallel heavy-duty manipulators

Abstract This paper presents a method for modelling the compound stiffness of an integrated open-die forging centre that consists of a forging press as well as a manipulator that handles the workpiece. Open-die forging has considerable differences to general machining processes due to the complex plastic deformation effects created by consecutive forging strikes. The manipulator must comply with the movement of the workpiece during forging. The stiffness of the integrated system mainly comes from two sources: the compliance of the manipulator and the elastic deformation of the workpiece during forging. First, the stiffness matrix of the workpiece is derived using the theory of mechanics of materials. Then, the complete Cartesian stiffness matrix of the manipulator is developed by using the conservative congruence transformation method. Finally, the compound stiffness model is constructed by combining these two stiffness matrices. A numerical algorithm is developed that is able to simulate the compliance motion of a programmed open-die forging process. Two numerical examples are presented to validate the proposed modelling method and numerical algorithm.