Cyclic-Torque-Ripple Propagation in Student-Built Gearbox Test Rigs for Engineering Education: A Strain-Rosette Calibration Linking Tooth-Mesh Misalignment to Fatigue-Life Prediction Bounds

Student-built gearbox test rigs are widely used in engineering education to connect kinematic theory with measurable mechanical behaviour, yet the transmission of cyclic torque ripple from a misaligned tooth mesh to the strain-rosette signals that students interpret is rarely modelled explicitly. The framework combines a kinematic transmission-error model, a strain-rosette decomposition of the local stress state, and a Basquin-type fatigue-life bound derived from the calibrated stress amplitude. A design-based evaluation of the before-after-control-impact estimator was conducted under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64) across 2000 replications per design cell, with cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The evaluation indicated that 56 clusters are required to detect a 5-percentage-point effect at 80% power. The framework provides a defensible route from rig geometry and rosette placement to a bounded fatigue-life estimate, and it clarifies the conditions under which student-collected strain data can support quantitative design judgements rather than illustrative demonstration alone.