Improving electrical discharging machining efficiency by using a Kalman filter for estimating gap voltages

- State space model built between white noise and gap voltages by Yule-Walker method.
- Composite measurement and process noise used in deriving auto-covariance matrix.
- Steady-state gain derived from measured voltage to estimated voltage for scaling.
- Machining time decreased by a Kalman filter as compared with a moving average filter.

Gap voltage can be used as an indicator on the direction of the electrode movement along a desired tool path in electrical discharging machining (EDM) processes. However, due to the noise induced by electrical discharges, the estimation of gap voltages is difficult due to the lack of an appropriate state space model. In this paper, gap voltage signals are considered to be generated as a summation of colored noise through a linear filter and measurement noise. Obtained by the Yule-Walker auto-covariance method, the transfer function of the linear filter can be converted into a state space model. The composite process noise and the composite measurement noise are defined to derive the composite noise covariance matrices. A Kalman filter can thus be designed based on the state space model and the noise covariance matrices. Experimental results showed that, as compared with the traditional 10-point moving average filter, the Kalman filter can decrease the average machining time as well as improve the discharging gap status.