Cutting Force Estimation in Sensor-Equipped Metal Cutting Tools Using Strain-Force Transfer Function 91 500 1000 1500 2000 2500 0 0.5 1 1.5 2 2.5 3 3.5 4 Fig. 7 comparison of the strain FRFs from the analytical model after model updating Hϵ ana, the measurement Hϵ mea, and the minimum phase transformationHϵ min. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 0.5 1 1.5 2 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 -3 -2 -1 0 Fig. 8 Illustration of the combined strain FRF, Hϵ com, by the strain FRF of analytical model, Hϵ ana, multiplying the strain FRF of inverse minimum-phase filter, (Hϵ min)−1. response of the transfer function corresponds to a delay in the time domain. The time delay can be calculated based on the linear phase response by equation 15 [17]. In Figure 8, the time delay is approximately0.126 ms. D(ω) ≜− d dω Θ(ω) (15) The results of estimated and measured impact forces are shown in Figure 9. The test result shows good agreement between the measured and predicted impact forces, highlighting the capability of the proposed method for estimating forces acting on the tool tip based on measured strain response data.
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