This paper analyzes the impact of manufacturing tolerances on the cogging torque of a 24-slot 28-pole tooth-coil-winding permanent magnet synchronous machine with a modular stator core (TCW-MPMSM). Dimensional tolerances and asymmetries associated with the modular topology are studied by means of finite element simulations in order to identify key parameters that increase the cogging torque above the expected values of a faultless machine. Among five selected dimensional parameters, it was found that angular displacement, radial displacement, and tooth–tip width deviations of the stator segments have the most significant impact on the cogging torque. Considering these three key parameters, a full-range tolerance analysis is carried out by means of a proposed superposition-based approach, evaluating all possible combinations of typical deviation values. It is concluded that the cogging torque increment, generated by tolerances, is relatively independent of the faultless tooth–tip width of the stator segments and the arc-to-pole ratio. Robustness of the TCW-MPMSM, regarding cogging torque generation, depends on both the tightness of the tolerances handled in the manufacturing process and the rated cogging torque: the lower the cogging torque of the ideal machine, the less robust is the machine and, therefore, manufacturing imperfections will be required to be tightened.