A new position independent geometric errors identification model of five-axis serial machine tools based on differential motion matrices

• The transformation matrix between PIGEs defined in global and local frames is derived.
• The Jacobian function of PIGEs defined in the global frame is calculated.
• The minimum set of PIGEs can be easily found by referring ISO 230-1:2012.
• Experiments verify the effectiveness of the proposed PIGEs identification algorithm.

Five-axis position independent geometric errors (PIGEs), which are caused by imperfect assembly of machine tools, need to be identified and compensated in order to improve the accuracy of machined parts. In traditional PIGEs identification model based on differential motion matrices (DMM), PIGEs elements are defined in the local frames attached to the previous axis, which is inconvenient to do redundance analysis. In order to fully but un-redundantly identify five-axis PIGEs, this paper proposes a new PIGEs identification model based on DMM in the global coordinate frame. The transfer matrix which realizes the transformation of PIGEs between global and local definitions is derived at first. Then the Jacobian function of the tool center motion errors related to PIGEs defined in the global frame is calculated and adopted for PIGEs identification with the least-square algorithm. For the proposed PIGEs identification model in the global frame, the minimum set of PIGEs can be easily found to make sure full but un-redundant identification, by properly setting up the machine tool coordinate frame using the method of ISO 230-1:2012. The proposed new Jacobian function and PIGEs identification model in the global frame are verified through simulation and experiments with ball-bar tests.