Non-redundant identification of geometric errors in multilateration of rotary axis

Abstract

The multilateration measurement acquires sufficient data for the identification of the position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of the rotary axis. However, because of redundancy in the used intermediate parameters, existing identification methods suffer from a loss of accuracy and precision caused by the relatively lower stability to the influences of random errors. Meanwhile, this may result in a more complicated process if additional constraints are added to reinforce stability. This paper proposes a non-redundant method for identifying both the PIGEs and PDGEs of the rotary axis. Firstly, the identification model, in which the rotating component pose errors are fully and non-redundantly described by the twists, is established to identify the pose errors caused by geometric errors. Then, by deriving the relationship between the pose error twists and the PIGE & PDGE parameters, the sequential decoupling algorithm applying the least squares condition, together with identification models, for both the PIGEs and PDGEs is developed. Comparative simulations and experiments are carried out. With no redundancy, the proposed method exhibits smaller discrepancies between the identified and preset test lengths in the cone path test simulation, yielding an average improvement of 15.73% and 56.97% in two identification modes, respectively. Furthermore, the method demonstrates smaller discrepancies between the predicted and measured test data in the cross-validation experiment with an average improvement of 80.21% and 86.87% in the two modes, respectively. These results jointly verify the improvement in accuracy for identifying the PIGE and PDGE parameters. In addition, an overall reduction of the PIGE and PDGE uncertainties is observed in the Monte-Carlo simulations, which verifies the precision improvement.