Ultrasonic-assisted deep drilling (UAD) behaves as a nonlinear, energy-dissipative system driven by high-frequency excitation, where torque fluctuations directly reflect transient mechanical energy within the cutting zone. This study introduces a derivative-based statistical framework that utilizes the first-order torque gradient with respect to drilling depth (Formula: see text) to quantify the instantaneous rate, polarity and fluctuation intensity of energy dissipation. High-resolution torque–depth data were collected for both conventional drilling (CD) and UAD of AISI 304 stainless steel under identical cutting conditions. Eight quantitative metrics — including mean derivative, standard deviation, extreme derivative amplitudes (Formula: see text, Formula: see text), spike frequency (Fₛpike), sign-change frequency (Fₛign), cumulative dissipation activity Formula: see text and composite dynamic-stability index Formula: see text — were extracted to characterize system dynamics. Experimental results indicate that UAD significantly mitigates high-magnitude derivative spikes, with Fₛpike reduced by approximately 65%, and decreases cumulative dissipation activity (A) by 78. 2% compared to CD. Simultaneously, the dynamic-stability index Formula: see text increased by 127%, reflecting a more coherent and energy-efficient cutting regime. Furthermore, UAD decreased the mean derivative Formula: see text by 64% and the standard deviation StDFormula: see text by 47. 8%, while extreme transient energy bursts Formula: see text and Formula: see text increased by 173% and 176%, respectively, illustrating controlled and reversible energy transfer induced by ultrasonic excitation. These findings demonstrate that UAD stabilizes energy flow, reduces stochastic, entropy-generating irregularities at the tool–material interface and promotes a self-regulated oscillatory drilling state. The proposed derivative-based framework provides a novel and physically interpretable methodology for quantifying dynamic stability and energy dissipation in complex nonlinear machining systems.
Chu et al. (Thu,) studied this question.