The coefficient of friction (COF), defined as the maximum of the adhesion coefficient for a given contact condition, fluctuates rapidly due to environmental and operational factors. This paper introduces a torque modulation-based method for COF estimation. A simplified analytical model of the Manchester benchmark bogie operating under dry adhesion conditions is used to evaluate this method. The study presents an analytical equation that confirms earlier simulation-based findings showing a phase difference between applied torque modulation and resulting motor angular velocity. This phase relationship is shown to reflect the shape of the adhesion-slip curve. Notably, when the phase difference approaches 90°, the locomotive operates near the point of maximum adhesion, corresponding to the COF. Furthermore, the sensitivity of this approach to key system parameters, including normal load, wheel rolling radius, and modulation frequency, is examined. The findings provide valuable insights into the robustness and applicability of torque modulation-based COF estimation techniques in real-time traction control systems. The estimated COF can be further leveraged for adhesion management, driver advisory systems, and autonomous train operation.