# Design of a Rotary Transformer for Installations on Large Shafts
## 1 Introduction  
Transformers are electrical machines that allow us to transfer power between two different parts of a circuit. Their more common application is in the field of power systems and electrical transmission and distribution, since they can ensure galvanic insulation between the windings and they allow us to change voltage and current levels between the two sides of the circuit. In the last decades, new applications arose due to the spread of power electronics. In particular, the possibility to push the operational frequency up to hundreds or thousands Hz allowed the exploitation of magnetic cores which are far smaller than the corresponding counterparts working at 50 or 60 Hz (see [1]) as well as enable their exploitation on electronics systems and printed circuit boards. Among these new applications, rotary transformers [2; 3], allow power flow between parts of the systems which are in relative rotation. Since this energy transfer is obtained by splitting the core in two by inserting an air gap, no brushes or sliprings are required. Therefore, such systems allow the so-called wireless power transfer, which can be achieved also using a capacitive coupling as shown in [4]. There are some examples of application of wireless power transfer based on inductive coupling in rotating electrical machines. Indeed, sliprings can be substituted by rotary transformers in wound rotor induction machines (see [5; 6; 7]) as well as in synchronous ones (see [8]). In particular, this paper focuses on the design of a rotary transformer suited for installations on large shafts, which are typical of automotive [9], railway [10], naval, aerospace [11; 12], or some industrial applications. The goal of this work is to provide some guidelines for the design of efficient rotary transformers working in such environments. Therefore, the main focus of the steps proposed here in the following is to reduce the weight of the device and to keep its radial size (with respect to shaft diameter) as small as possible. Indeed, an excess of inertia may jeopardize the performance of the system in which the transformer operates (e.g., an electrical machine, a train, an aircraft, etc.). To this aim, two multi-objective optimizations (similar to [13]) were performed. The first is based on a brute-force grid search algorithm, which is needed to start approaching the optimal result by exploring the available solutions. Then, this search was refined using a genetic optimization [14], which is a generalization of the single-objective procedureproposed in [5]. The goal is to obtain a compact, efficient and light device that allows a power transfer of about 4 kW from primary to secondary according to the application presented in [11; 12]. After that, a further weight reduction was obtained by slicing the magnetic core, similar to what is reported in [15]. This operation is a consequence of the higher fragility of bulk cores with respect to split cores, in particular if ferrite or sintered materials are adopted. Since this procedure may seem quite odd and, apparently, might compromise the coupling between the primary and secondary, an experimental validation performed on a reduced-scale prototype is presented. This small-size device was realized following the same steps reported in this paper, allowing us to keep the realization costs limited. However, these tests were aimed at verifying that both the design approach and the developed models allow us to predict the resulting performances of the device in an accurate way. These two points are of paramount importance in view of tailoring this proposed design to a specific application. Therefore, the paper is organized as follows: Starting from a general overview of the device and its equivalent circuits, the study goes on with an analytical investigation of the input impedance of the rotary transformer, which is of paramount importance if some reactive power compensation strategies should be included in the system to improve both the active power transfer and system efficiency (see Section 2).