Aircraft turbine engine equipped with an electrical machine

An aircraft turbine engine comprising:

• a gas generator;
• a fan arranged upstream from the gas generator and configured to generate a main gas flow, one part of which flows into a duct of the gas generator to form a primary flow, and another part of which flows in a duct around the gas generator to form a secondary flow, the gas generator comprising a low-pressure body that comprises a main shaft for driving the fan via a mechanical reduction gear;
• said low pressure body further comprising a low pressure compressor having wheels provided with discs which are attached to a trunnion which is connected to an intermediate shaft connected to the main shaft,
• an electrical machine mounted coaxially downstream of the reduction gear and upstream of an intermediate casing, the electrical machine including a rotor connected to the intermediate shaft, and a stator, having an upstream end and a downstream end, extending around the rotor of the electrical machine;
• a first annular shroud, which is surrounded by a second annular shroud, the first and second shrouds delimiting between them a portion of said duct of the primary flow, wherein the first annular shroud is mounted around the electrical machine and extends directly around the stator of the electrical machine, and wherein, between the upstream end and the downstream end, the stator abuts a radially inner surface of the first annular shroud, so that the first annular shroud has its radially outer surface swept by the primary flow of gases so as to cool said stator with aid of the primary flow.