Estimation Of The Cutting Force After the output torque of the AC spindle motor is calculated, the estimation procedure to obtain the cutting force is identical to the previous method [4] Because the detailed description of the procedure is given in Huh et [4], a brief explanation is shown here for reader's A model of the AC spindle-drive is composed of the mechanical parts (the spindle drive) and the electrical parts (the AC Induction motor) The rotational equation of motion for the The above equation is discretized with the zero-order-hold sampler and can be expressed in the following form to obtain the estimation of the total external where h is the sampling period (= 05 second) and b is the model parameter () The equivalent damping coefficient is known to be sensitive to temperature changes, thus updated automatically right before the tool contacts the workpiece [4] The estimated total external torque includes not only the cutting torque applied to the workpiece, but also the nonlinear friction torque occurred in the spindle Coulombic friction torque b1 at idling can be determined from a family of steady-state power test with no In order to extract the normal cutting torque from the estimated total external torque, detailed information of the nonlinear friction torque increase is Under the assumption that there is no dynamic relation between b7, and, T the nonlinear friction torque is modeled wherefto) and g(WM) are the functions of the motor speed and depends on a batch of The estimated cutting force using the relations in Eq (I) through Eq (8) is illustrated in F I Contrary to the previous method [4], the estimated cutting force shows little time lag at the transient but very oscillatory at the steady-3Synthesized Cutting Force Monitor The previous method [4] needs to measure only two signals (output power and motor speed) from the motor driver in order to estimate the cutting force, but its performance has a critical time lag at the transient
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