Experimental Investigation of Torque and Vibration Characteristics of Rotating Shafts Under Controlled Misalignment

Accurate torque measurement and vibration monitoring are essential for assessing the performance and condition of rotating machinery; however, conventional torque sensors are often intrusive, costly, and difficult to integrate into existing systems. This study presents an integrated experimental and data-driven framework for investigating the relationship between transmitted torque and vibration characteristics of rotating shafts under aligned and controlled angular misalignment conditions. A customized experimental test rig incorporating interchangeable steel shafts, non-contact optical encoders, accelerometers, and a magnetic powder brake dynamometer was developed. Experiments were conducted over a torque range of 20–100 Nm using shaft diameters of 10–14 mm, shaft lengths of 0.5–0.7 m, and angular misalignment levels from 0° to 2°. Torque was estimated from the encoder-measured angular twist using classical torsion theory, while synchronized vibration signals were analysed using statistical and entropy-based features, including root mean square (RMS), standard deviation, skewness, kurtosis, Shannon entropy, and spectral entropy. Supervised machine-learning models were subsequently employed to investigate vibration-based indirect torque estimation, with performance assessed using R², RMSE, and MAE. The experimental results demonstrate a strong relationship between transmitted torque and vibration characteristics and confirm that angular misalignment significantly alters this relationship by increasing vibration amplitude, variability, and signal complexity. At 2° misalignment, RMS vibration increased from 0.00870 g under aligned conditions to 0.02930 g, representing an increase of approximately 237%, while Shannon entropy and spectral entropy increased by approximately 26% and 24%, respectively. Among the investigated feature combinations, RMS together with Shannon entropy and spectral entropy provided the best torque-prediction performance, demonstrating the importance of combining vibration energy and signal-complexity information. The findings establish that controlled shaft misalignment must be explicitly considered in vibration-based torque estimation and demonstrate the potential of integrating non-contact torque sensing, vibration analysis, and machine learning for intelligent condition monitoring and predictive maintenance of rotating machinery.