This research work has been triggered by an industrial project aimed at modelling and manufacturing a small-scale very high speed motor. Very high speed electrical motors offer the main advantage of reducing the size of a system. Indeed, at constant output mechanical power, increasing the rotational speed enables to decrease the electromagnetic torque, hence the size of the motor. When a system already possesses very high speed devices, it becomes attractive to combine them with an electrical machine. Combined with very high speed, the miniaturisation of motors benefits limited weight and space applications. Used as hand tools, they provide solutions for otorhinolaryngology or dental surgery.

Because they can be freely arranged in the airgap, slotless windings represent a substantial capacity for enhancement. Thanks to new manufacturing technologies, the design of windings can be rethought. Different shapes and topologies can be embraced leading to improved performances for electrical motors.

The aim of this thesis is consequently twofold: to give multiphysics models enabling the design and the optimisation of small scale very high speed permanent magnet synchronous motors, and to propose an innovative solution for a new type of slotless winding topology entailing the performances of electrical motors.

By essence, very high speed motors are pushed to their limits: they experience high mechanical stresses in the materials of the rotor and the bearings, are subject to critical speeds, operate sometimes at high temperature and harsh environments and, due to high electrical frequencies, produce significant iron and winding losses. As a result, robust and reliable multiphysics models have to be established. In this thesis, a very complete set of both mechanical and electromagnetic analytical models is presented. Analytical models are preferred to numerical models as they bring more insight in understanding physical phenomena occurring in the motors and require less computational effort for optimisation.

All the aforementioned analytical models are used in the context of the design and the optimisation of small scale very high speed slotless permanent magnet motors with ball bearings. With an appropriate optimisation algorithm, fixed constraints on the maximal size and the operating point, optimal designs are obtained for several rotational speeds. In particular, an original contribution comes from the comparison of Litz-wire and rectangular wires as well as hollow and solid magnet rotors used in small-scale very high speed slotless motors.

In order to experimentally validate the models, a 400 krpm 12.7 mm diameter prototype is manufactured and tested up to 475 krpm. In addition, it demonstrates the feasibility of miniaturised very high speed motors. An astute experimental method is implemented in order to separate the losses components related to the rotation of the rotor. Therefore, every model can be obtained and/or validated independently.

Finally, the research work emphasis on the modelling and the optimisation of a novel slotless winding topology. By challenging the traditional way of manufacturing windings, the use of nonconstant wire sections and an optimised shape enables the performances of the winding, and thereby the motor, to be significantly improved. A prototype of the new winding topology is manufactured and leads to the validation of the theoretical model.