Vibration-Based Measurement of Steel Wire Rope Fundamental Frequency Using an Optical Sensor: Mitigation of Mass-Loading Artifacts

Non-destructive testing and tension estimation of static steel wire ropes using vibration analysis are conventionally distorted by deterministic mass-loading and local bending stiffness alterations introduced by rigidly clamped contact accelerometers, which artificially shift the system’s dynamic baseline. To address this measurement error, a minimally invasive optical methodology utilizing a 25,600 DPI optical flow sensor architecture is proposed. The method’s metrological validity was verified against a theoretical beam-string model—incorporating the effective rope modulus (Eeff) and structural geometric factor (Gm)—and contact accelerometer measurements across ten independent 6×37 FC steel rope specimens tensioned up to 64 kN. By eliminating the 191 g mass-loading and clamping-stiffness artifacts of traditional accelerometers (validated on a 0 g bare rope surface) and utilizing a lightweight 28 g reflective target plate during degradation tests to mitigate helical surface artifacts without altering local bending stiffness, the measurement chain achieved a combined standard uncertainty of uc=0.0106 Hz (expanded uncertainty U=0.0212 Hz). To establish the laboratory sensitivity limit of the optical chain, progressive structural degradation was artificially induced across all ten specimens by severing 3 to 35 wires at mid-span under constant tension. The system reliably detected initial damage at 3 broken wires (1.35% loss of metallic cross-section, causing a 0.1 Hz shift at 16 kN) and resolved incremental frequency shifts down to Δf=0.036 Hz (between 3 and 5 broken wires, exceeding the 3uc=0.0318 Hz significance threshold). While these artificial wire cuts represent a laboratory metrological sensitivity limit rather than a universal field NDT calibration, the linear correlation at 64 kN (R2=0.9419) confirms that localized axial stiffness loss dominates the dynamic response. The proposed optical approach provides a reliable framework for laboratory baseline verification and tension assessment under controlled conditions.