Hunting stability is a critical factor affecting high-speed locomotives dynamic performance, inherently connected to wheel-rail contact geometry. Tread wear typically increases the nonlinearities in the contact geometry, causing stability disparities. Previous studies on stability have often overlooked these nonlinear aspects, which can be captured by the equivalent conicity function. In this study, the equivalent conicity functions of worn wheel treads are systematically categorized into six distinct classes. This classification allows for a comprehensive evaluation of their respective influence on hunting stability failure, enabling the analysis of stability characteristics of typical worn wheel treads. The limited research available on three-axle bogies motivate the selection of a locomotive equipped with such bogies as the basis for framework, aiming to bridge the gap in existing literature. Based on different stability evaluation methods, theoretical, small-amplitude hunting, and engineering critical speeds have been determined. The observed differences in different critical speeds from the perspective of equivalent conicity function are elucidated. The results show that a high equivalent conicity at small displacement can significantly reduce the theoretical critical speed, and therefore, the engineering critical speed is recommended as a criterion for stability assessment and optimization. Moreover, the Driving Energy Loss Ratio (DELR), a metric assessing both primary and secondary hunting stability, is developed to evaluate the stability of self-excited vibrations. This research provides guidance for the evaluation and optimization of railway vehicle stability.