Multi-phase bearingless machines combine the general advantages of bearingless machines with an increased fault tolerance, lower power ratings per phase and a completely free distribution of the total power between force and torque. As a result, research interest in this topic has increased in recent years, resulting in many publications and also a first proposed winding design procedure, which is based on a linear fundamental model. This paper complements this approach and focuses on the effects of higher order harmonics. Starting from a force/torque formulation based on the airgap field and the Maxwell stress tensor, it is combined with winding function theory to identify critical spatial and time harmonics that cause force/torque couplings or ripple. These results are used to improve the existing design procedure, and considerations are also made to ensure high winding factors. A design example illustrates the benefits of the enhancements.