Physics-guided ultrasonic guided-wave sensing for gear meshing force measurement using multipath contact-modulated fusion

Accurate in situ measurement of gear meshing force is essential for gear dynamics analysis, condition monitoring, and reliability evaluation, yet it remains challenging because of moving tooth contact, restricted sensing accessibility, and rotating-environment constraints. This article proposes a physics-guided ultrasonic guided-wave sensing method for quantitative gear meshing state measurement based on multipath contact-modulated fusion. The meshing interface is treated as a force- and position-dependent acoustic modulation boundary: variations in gear meshing force change the effective contact window and interfacial coupling, whereas meshing-position migration changes the spatial relationship between this modulation boundary and the guided-wave propagation paths. To capture these contact-induced modulations, a flexible in situ piezoelectric sensing network with one actuator and six receivers is integrated on the gear end face, and multipath guided-wave responses are acquired under controlled meshing loads and angular positions. A multipath contact-modulated guided-wave fusion network, termed MP-CMGFNet, is developed to encode local wave-packet features, temporal dependencies captured by bidirectional long short-term memory, and interpath complementary information. Two task-specific calibration instances are constructed for gear meshing force and meshing position estimation, respectively. Experiments verify that both force and position variations induce measurable energy, amplitude, and waveform changes in the guided-wave responses. On an independent test set containing unseen angular positions and an unseen intermediate load of 669 N, MP-CMGFNet achieved a gear meshing force mean absolute error (MAE) of 16.03 N and root mean square error (RMSE) of 20.25 N, together with a meshing-position MAE of 4.59° and RMSE of 6.35°. Ablation studies and benchmark comparisons show that the proposed architecture outperforms representative temporal and deep feature extraction models. These results indicate that multipath contact-modulated guided waves can serve as an effective nonintrusive sensing carrier for quantitative gear meshing state measurement.