Virtual sensor using model order reduction for real-time estimation of tool edge temperature

Abstract

Virtual sensor, which is one of the applications of the digital twin, is effective for estimating physical quantities that are difficult to measure. This paper deals with estimation of real-time tool edge temperature by virtual sensor. The tool edge temperature is estimated by inputting the temperature data of the endmill shank obtained from the pyrometer installed in the machine tool to the simulation model created in cyber space. The simulation performed in cyberspace is an unsteady heat transfer analysis, and a state space model with a reduced order of the finite element model using Krylov subspace method is adopted as the simulation model in order to allow real-time simulation. In addition, unknown heat input to the cutting edge was calculated by state feedback control using the temperature data obtained from the pyrometer and the simulation model. The tool edge temperature during cutting was estimated in real time using the developed virtual sensor with the heat transfer analysis block and the input estimation block. The estimated tool edge temperature changed significantly in response to changes such as chipping of the tool edge. The estimated temperature and the measured temperature by the thermocouple method generally matched.

Keywords

• virtual sensor
• digital twin
• model order reduction
• inverse problem
• input estimation
• tool edge temperature
• state space model
• state feedback control
• finite element method