Reconfigurable model clusters for scalable modelling of feed drive dynamics

Abstract

This paper presents a novel approach to modeling feed drive dynamics in machine tools. Instead of building and calibrating separate models for each machine, this approach leverages a cluster of pre-calibrated models to represent a fleet of similar machines or a single machine under varying conditions. Bayesian model selection assimilates the internal controller signals into the model cluster, selecting an optimal combination of the models to represent individual machines accurately. This approach facilitates the large-scale development of machine tool digital twins and shadows without additional modeling or experimental calibration. The effectiveness of the proposed approach is demonstrated through numerical simulations with known ground truths. The results highlight the concept's potential to simplify and scale feed drive modeling. Additionally, they outline the key technical and operational considerations necessary for its broader application.

Keywords: Bayesian model updating; Feed drives; Machine tool dynamics.

Fig. 1

RMC modeling framework: (a) Physical system with main components of: 1-positioning controller, 2-power electronics and amplifier, 3-servo motor, 4-ballscrew drive, (b) Model library of the components, (c) Model assembly to build cluster members , , ..., (d) Probabilistic model updating and selection for tailoring an optimal model from the cluster for each physical system.

Fig. 2

(a) 8-DOF feed drive mechanical model used in Simulink model, (b) Simulink model used for numerical experiments.

Fig. 3

Model library. stands for Z-transform, and and are the actual and typical values of the model parameters , respectively.

Fig. 4

Case study I, rigid-body motion. (a) Marginal prior and posterior distributions of model parameters. The bar on the right shows the log of evidence for each cluster member, (b) cluster member reference and output signals versus Simulink data: (1) reference current , (2) output current I, (3) output velocity of table v, (4) output angular velocity of rotor shaft .

Fig. 5

Case study II, motion including one vibration mode. (a) Prior and posterior distributions of model parameters. The bar on the right shows the log of evidence of the corresponding cluster member. (b) Table velocity v and current I outputs of (1,2): , (3,4): , (5,6): , (7,8): .

Fig. 6

Case study II, motion including one vibration mode. Joint prior and posterior distributions of parameters.

Fig. 7

Case study III, library including models with identical structures. Prior and posterior distributions of model parameters. The bar on the right shows the log of model evidence.