Motor starter calibration requires long-distance rotation of a setting cam to locate current graduation points, generating substantial non-value-added mechanical travel time on production lines. This paper proposes a cam pre-adjustment angle prediction method that integrates a phenomenological gray-box bimetallic model with a hierarchical combinatorial algorithm framework. A generalized lumped-parameter model incorporating heat dissipation correction and mechanical gap compensation is constructed to describe the electrothermal–mechanical coupling of the bimetallic strip. An improved fuzzy C-means (IFCM) algorithm addresses the cold-start problem for new material batches, and an adaptive particle swarm optimization (APSO) algorithm performs online parameter identification. To handle the process asymmetry arising from the unidirectional cam rotation mechanism, an optimized gray wolf optimizer with one-sided error control (GWO-OSE) based on an asymmetric loss function is employed to inversely determine the optimal pre-adjustment angle while actively suppressing over-prediction. Validation on 1200 production line samples across three material batches demonstrates an over-prediction rate of only 2.8%, a mean absolute angle prediction error of 23.9°, a reduction in single-product calibration time of approximately 12 s, and an improvement in overall production line efficiency of 24.5%. This efficiency gain results from the process-level redesign facilitated by the pre-adjustment strategy rather than from minimizing absolute prediction error, and the proposed method provides an engineering-applicable optimization strategy for reducing non-value-added calibration time in motor starter production lines.
Ru et al. (2026) studied this question.