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In order to improve the electromagnetic performance and ease the manufacture process, particularly stator winding, it is often preferable to employ a modular stator, e.g., individual stator tooth/back-iron segments, or separate stator tooth segments and back-iron segments. However, due to manufacture limits, there always exhibit additional air gaps between the stator teeth and back-iron segments. In practice, such gaps are likely to be nonuniform due to manufacture tolerances. This paper investigates the influence of uniform and nonuniform additional gaps on the cogging torque of permanent-magnet machines having either unskewed or step-skewed rotors. It is found that the presence of these gaps increases the cogging torque magnitude due to increased flux leakage through the tooth tips, while the uneven gaps can cause a significant increase in both the peak and periodicity of cogging torque waveform, which causes the skew method ineffective, as confirmed by both finite-element analyses and experiments.