AC Motor Efficiency Estimation Bias in Student-Built Engineering Education Dynamometer Rigs: A Torque-Transducer Cross-Calibration Linking Coupling Misalignment to Energy-Audit Reliability

Student-built dynamometer rigs are widely used in engineering education to estimate AC motor efficiency, yet the reliability of the resulting energy audits depends on torque-transducer calibration and mechanical alignment that are rarely quantified. The model treats the torque signal as a deterministic function of true torque, misalignment-induced harmonic distortion, and transducer cross-sensitivity, and it derives closed-form bias and variance expressions for the efficiency estimator under a first-order perturbation. A replication-based evaluation of the ordinary least squares estimator was conducted using 600 data sets of N = 500 drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2). The estimated bias for the intercept was -0.06034 and for the exposure coefficient 0.00151; the root mean squared errors were 0.89669 and 0.01595 respectively, and the empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. A misalignment of 0.1 mm can produce an efficiency bias of up to 2.3 percentage points, which exceeds the typical acceptance threshold for energy-audit reporting.