Induction-Motor Slip Estimation Bias in Student-Built Engineering Education Load Banks: A Stroboscopic Speed Benchmark Linking Tachometer Quantization to Torque-Speed Curve Reliability

Student-built load banks used in undergraduate electrical machines laboratories typically derive rotor speed from a slotted-disc tachometer whose pulse train is quantised by a fixed sampling clock, and the resulting slip estimate feeds directly into the torque-speed curve that students report. the present analysis treats the slip estimator as a formal object and derives its sampling distribution under a declared measurement model in which the tachometer quantisation interval is the dominant error source. The slip estimator is biased, that the bias is a function of the ratio of quantisation interval to synchronous period, and that the bias propagates into the torque-speed curve as a systematic displacement of the pull-out region rather than as random scatter. A replication-based evaluation was conducted: 600 data sets of N = 500 were drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2), and the ordinary least squares estimator was characterised under the stated process. The estimated bias for the intercept was -0.02315 and for the exposure coefficient 0.00064; the root mean squared errors were 0.88484 and 0.01581 respectively; empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The results indicate that the estimator is essentially unbiased for the slope but that the intercept carries a small negative displacement, and that the quantisation mechanism identified analytically is consistent with the direction and magnitude of the observed intercept bias. The stroboscopic benchmark should be reported alongside the torque-speed curve so that the slip bias is visible to the student and to the assessor.