The direct-on-line start-up of a synchronous motor results in alternating torques which can excite the lowest torsional natural frequency of compressor trains used in the oil & gas industry. Considering a slip-dependent variation of the rotor parameters, an integrated electrical and mechanical simulation model is developed, providing an accurate estimation of the air-gap torque. The proposed approach is validated by an accurate testing campaign carried out during moto-compressor field test activities.