Mechanical-Draft Measurement Error in Student-Operated Extrusion Rigs for Engineering Education: A Torque-Transducer Calibration Method Linking Frame Compliance to Filament-Diameter Tolerance Bounds

Student-operated extrusion rigs used in engineering education commonly report filament diameter from a torque-transducer signal whose calibration ignores the compliance of the machine frame. The method is formalised as a two-stage estimator: a static compliance identification stage using dead-weight loading, and a dynamic compensation stage that corrects the transducer signal for frame deflection during extrusion. A propagation theorem is derived that maps frame-compliance uncertainty into a bound on filament-diameter error, and the bound is shown to be tight under stated regularity conditions. The design is characterised through a replication-based evaluation of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells. The evaluation indicates that 54 clusters are required for 5 percentage-point effects at 80% power. The contribution is a calibration protocol that makes the tolerance bound auditable in the teaching laboratory, together with a formal statement of the conditions under which frame compliance dominates the error budget.