# Design of a Rotary Transformer for Installations on Large Shafts

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Rotary Transformer: Model and Parameters

#### 2.1. Equivalent Circuits

#### 2.2. Compensation Strategy

#### 2.3. Power Electronics

## 3. Finite-Elements Analysis

#### 3.1. Two-Dimensional Analyses

^{®}. Due to the coupling of the two aforementioned softwares, it was possible to estimate the parameters ${L}_{1}$, ${L}_{2}$ and M of the rotary transformer, computing the flux linkage in FEMM for the two windings while supplying them one at a time. Then, the values of the parameter were used in MATLAB

^{®}to solve the equivalent circuit reported in Figure 3 (a supply voltage of ${V}_{\mathrm{DC}}=270\hspace{0.17em}\mathrm{V}$ was assumed, which could be obtained using a rectifier on a monophase system) and inject the computed currents ${I}_{1}$ and ${I}_{2}$ back into each corresponding wire in FEMM in a new simulation to check the saturation of the magnetic core. An example of the output of one of these analyses is reported in Figure 6. The problem was set to be axisymmetric, i.e., the drawn section was considered to be perfectly symmetrical over a rotation of 360° with respect to the shaft.

#### 3.2. Three-Dimensional Analyses

## 4. Design of the Transformer

#### 4.1. Grid-Search Optimization

- the air gap between the two cores was set to $g=1\hspace{0.17em}\mathrm{m}\mathrm{m}$;
- the radius of the shaft was set to ${r}_{\mathrm{s}}=90\hspace{0.17em}\mathrm{m}\mathrm{m}$;
- the height of the core was set to ${h}_{\mathrm{c}}=20\hspace{0.17em}\mathrm{m}\mathrm{m}$.

- $3\hspace{0.17em}\mathrm{m}\mathrm{m}\le {w}_{\mathrm{c}}\le 8\hspace{0.17em}\mathrm{m}\mathrm{m}$, step between consecutive samples equal to $0.2$ $\mathrm{m}$$\mathrm{m}$;
- $100\le {N}_{\mathrm{Litz}}\le 250$, step between consecutive samples equal to 5;
- $6\le N\le 13$, step between consecutive samples equal to 1.

^{®}Core

^{™}i7-8700 processor at 3.20 GHz and with 16 GB RAM.

#### 4.2. Genetic Optimization

^{®}, finding the Pareto front of three fitness functions using the genetic algorithm. These three functions to be minimized were the overall weight of the device, $\left|{P}_{2}-3.6\hspace{0.17em}\mathrm{k}\mathrm{W}\right|$ and $\left|{j}_{1}-10\hspace{0.17em}\mathrm{A}/\mathrm{m}{\mathrm{m}}^{2}\right|$. It is important to note that ${j}_{1}$ was chosen because the primary current is always higher than the secondary. Moreover, in view of a practical realization of a prototype of the device, the two cores were constrained to be equal to simplify their manufacturing process. The size of the flux path in the whole cross section was set constant (as suggested in [2]), that is, ${w}_{\mathrm{c}1}={w}_{\mathrm{c}2}={w}_{\mathrm{c}}$, and the width of the winding slots ${w}_{\mathrm{w}}$ was considered a variable, as well. Therefore, the following ranges of variations were considered:

- $2\hspace{0.17em}\mathrm{m}\mathrm{m}\le {w}_{\mathrm{w}}\le 6\hspace{0.17em}\mathrm{m}\mathrm{m}$;
- $4\hspace{0.17em}\mathrm{m}\mathrm{m}\le {w}_{\mathrm{c}}\le 6\hspace{0.17em}\mathrm{m}\mathrm{m}$
- $5\le {N}_{1}\le 15$
- $5\le {N}_{2}\le 15$

^{®}Core

^{™}i7-8700 processor at 3.20 GHz and with 16 GB RAM.

#### 4.3. Realization of the Core and Further Weight Reduction

## 5. Validation over a Reduced-Scale Prototype

^{™}LaunchPad

^{™}Piccolo F28069M, together with the converter board TI BOOSTXL-DRV8301 BoosterPack, was adopted in practice for running the power transfer test. Figure 13a shows the adopted setup. Results of both simulation and measurement show that both the inductance and power values were close, despite the fact that the materials could not be exactly characterized in the FEM software, the volume of the coils did not match the actual and the real supply voltage was far from being an ideal square wave. This mismatch in the harmonic content of the input voltages explains and partly justifies the big difference between the resulting shape of the voltage and current waveforms. Figure 13a,b show the real test setup adopted for running these tests and a comparison between the measured waveforms, ${v}_{1}\left(t\right)$, ${v}_{2}\left(t\right)$, ${i}_{1}\left(t\right)$ and ${i}_{2}\left(t\right)$, and the simulated waveforms.

^{®}. Namely, ${L}_{1}$, ${L}_{2}$ and M were inserted in a mutual inductor model and the equivalent circuit reported in Figure 3 was built. In this case, the waveform adopted in the real test was acquired and used to supply the Simulink

^{®}scheme through a controlled voltage generator. The results of this virtual test and their comparison with the measurements are reported in Figure 13c, which shows a much better agreement between simulation and test results than before in terms of harmonic content. As a matter of fact, the simulation in Simulink

^{®}allowed us to predict a power transfer equal to $4.20$ $\mathrm{W}$, which means a difference with respect to the measured value equal to 1.67%. Finally, the Simulink

^{®}model could be used to study different working points of the device. As an example, an additional test was carried out at 20 $\mathrm{k}$$\mathrm{Hz}$ (keeping ${V}_{\mathrm{DC}}=8\hspace{0.17em}\mathrm{V}$ and ${R}_{\mathrm{L}}=5\hspace{0.17em}\mathsf{\Omega}$) and compared with simulation, as shown in Figure 14. In order to provide a quantitative mismatch between measured and simulated quantities, Table 3 reports the comparison between the RMS values of ${i}_{1}$, ${i}_{2}$ and ${v}_{2}$. The input voltage ${v}_{1}$ is not reported there because it is imposed to be the same waveform both in real and simulated tests.

## 6. Conclusions

^{®}; in this framework, the identified inductance matrix can be combined with working conditions which can deviate from the nominal conditions, allowing us to predict voltages, currents and transferred power for a wide set of working points, reducing the simulation time (compared to 3D FEM co-simulation runs). Future work can focus on the realization of a prototype able to transfer 3–$4\hspace{0.17em}\mathrm{k}\mathrm{W}$ from primary to secondary tailored for a specific application and on the validation of the prediction on the full-size device.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 4.**Rotary transformer with series compensation of ${X}_{\mathrm{in}}$: (

**a**) single-capacitor compensation and (

**b**) dual-capacitor compensation.

**Figure 5.**Equivalent circuit of the rotary transformer supplied by a full-bridge converter. For the sake of simplicity, no compensation is reported in this picture.

**Figure 6.**Density plot of the absolute value of the induction field $\left|B\right|$ superimposed to the field lines of the real part of the magnetic vector potential $\widehat{A}$ for a realistic geometrical configuration of the rotary transformer.

**Figure 7.**Electromagnetic model of the rotary transformer in ANSYS Maxwell: (

**a**) shows top view and (

**b**) shows front view of a generic slice of the transformer, whereas (

**c**) shows the complete 3D model.

**Figure 9.**Electromagnetic model of the rotary transformer with C-shaped ferrites forming the cores: (

**a**) top and (

**b**) perspective views of the complete 3D model.

**Figure 10.**Geometrical dimensions of each C-ferrite adopted in the reduced-size prototype. Quotes are reported in $\mathrm{m}$$\mathrm{m}$.

**Figure 11.**Reduced-size prototype. Both (

**a**,

**b**) allow us to appreciate some details in the realization of the core and the windings.

**Figure 12.**FEMM model of the small-size prototype realized in ANSYS Maxwell: rotary transformer with supports (

**a**) and cores realized with C-shaped ferrites (

**b**).

**Figure 13.**Experimental setup (

**a**), comparison between the measured and simulated voltages and currents in ANSYS Maxwell (

**b**) and comparison between measured and simulated voltages and currents in Simulink

^{®}(

**c**). In (

**b**,

**c**) the system is working at 5 $\mathrm{k}$$\mathrm{Hz}$. RMS values for ${i}_{1}$, ${i}_{2}$ and ${v}_{2}$ are reported in Table 3.

**Figure 14.**Comparison between the measured and simulated voltages and currents in Simulink

^{®}. In this picture, the device is supplied with a 20 $\mathrm{k}$$\mathrm{Hz}$ waveform. RMS values for ${i}_{1}$, ${i}_{2}$ and ${v}_{2}$ are reported in Table 3.

Parameter | Grid-Search | Genetic Algorithm | C-Ferrites |
---|---|---|---|

${\mathit{w}}_{\mathbf{c}}$ | $4.20$ $\mathrm{m}$$\mathrm{m}$ | $4.04$ $\mathrm{m}$$\mathrm{m}$ | $4.04$ $\mathrm{m}$$\mathrm{m}$ |

${\mathit{w}}_{\mathbf{c}1}$ | $5.40$ $\mathrm{m}$$\mathrm{m}$ | $4.04$ $\mathrm{m}$$\mathrm{m}$ | $4.04$ $\mathrm{m}$$\mathrm{m}$ |

${\mathit{w}}_{\mathbf{c}2}$ | $4.78$ $\mathrm{m}$$\mathrm{m}$ | $4.04$ $\mathrm{m}$$\mathrm{m}$ | $4.04$ $\mathrm{m}$$\mathrm{m}$ |

${\mathit{w}}_{\mathbf{w}}$ | $2.97$ $\mathrm{m}$$\mathrm{m}$ | $2.05$ $\mathrm{m}$$\mathrm{m}$ | $2.05$ $\mathrm{m}$$\mathrm{m}$ |

${\mathit{P}}_{\mathbf{2}}$ | $2.70$ $\mathrm{k}$$\mathrm{W}$ | $3.72$ $\mathrm{k}$$\mathrm{W}$ | $3.76$ $\mathrm{k}$$\mathrm{W}$ |

${\mathit{L}}_{\mathbf{1}}$ | $130.61$ $\mathsf{\mu}$$\mathrm{H}$ | $306.46$ $\mathsf{\mu}$$\mathrm{H}$ | $283.04$ $\mathsf{\mu}$$\mathrm{H}$ |

${\mathit{L}}_{\mathbf{2}}$ | $130.70$ $\mathsf{\mu}$$\mathrm{H}$ | $427.83$ $\mathsf{\mu}$$\mathrm{H}$ | $395.87$ $\mathsf{\mu}$$\mathrm{H}$ |

$\mathit{M}$ | $125.89$ $\mathsf{\mu}$$\mathrm{H}$ | $351.55$ $\mathsf{\mu}$$\mathrm{H}$ | $325.59$ $\mathsf{\mu}$$\mathrm{H}$ |

${\mathit{N}}_{\mathbf{1}}$ | 7 | 11 | 11 |

${\mathit{N}}_{\mathbf{2}}$ | 7 | 13 | 13 |

Weight | $0.91$ $\mathrm{k}$$\mathrm{g}$ | $0.66$ $\mathrm{k}$$\mathrm{g}$ | $0.55$ $\mathrm{k}$$\mathrm{g}$ |

**Table 2.**Measured vs. estimated transformer parameters. Supply frequency $=5\hspace{0.17em}\mathrm{kHz}$.

Parameter | Measured | ANSYS Maxwell^{®} | $\left|\mathbf{\Delta}\right|$ |
---|---|---|---|

${L}_{1}$ | 114 $\mathsf{\mu}$$\mathrm{H}$ | 104 $\mathsf{\mu}$$\mathrm{H}$ | 8.47% |

${L}_{2}$ | 165 $\mathsf{\mu}$$\mathrm{H}$ | 142 $\mathsf{\mu}$$\mathrm{H}$ | 13.9% |

M | 100 $\mathsf{\mu}$$\mathrm{H}$ | 105 $\mathsf{\mu}$$\mathrm{H}$ | 4.96% |

${P}_{2}$ | $4.13\hspace{0.17em}\mathrm{W}$ | $4.06\hspace{0.17em}\mathrm{W}$ | 1.72% |

Frequency | Quantity | Measurement | Simulation | $\left|\mathbf{\Delta}\right|$ |
---|---|---|---|---|

5 $\mathrm{kHz}$ | ${i}_{1}$ RMS | $2.333$ $\mathrm{A}$ | $2.251$ $\mathrm{A}$ | 3.64% |

${i}_{2}$ RMS | $0.909$ $\mathrm{A}$ | $0.945$ $\mathrm{A}$ | 3.83% | |

${v}_{2}$ RMS | $4.543$ $\mathrm{V}$ | $4.724$ $\mathrm{V}$ | 3.83% | |

20 $\mathrm{kHz}$ | ${i}_{1}$ RMS | $0.938$ $\mathrm{A}$ | $0.997$ $\mathrm{A}$ | 5.86% |

${i}_{2}$ RMS | $0.537$ $\mathrm{A}$ | $0.574$ $\mathrm{A}$ | 6.53% | |

${v}_{2}$ RMS | $2.684$ $\mathrm{V}$ | $2.871$ $\mathrm{V}$ | 6.53% |

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**MDPI and ACS Style**

Toscani, N.; Brunetti, M.; Carmeli, M.S.; Castelli Dezza, F.; Mauri, M.
Design of a Rotary Transformer for Installations on Large Shafts. *Appl. Sci.* **2022**, *12*, 2932.
https://doi.org/10.3390/app12062932

**AMA Style**

Toscani N, Brunetti M, Carmeli MS, Castelli Dezza F, Mauri M.
Design of a Rotary Transformer for Installations on Large Shafts. *Applied Sciences*. 2022; 12(6):2932.
https://doi.org/10.3390/app12062932

**Chicago/Turabian Style**

Toscani, Nicola, Massimo Brunetti, Maria Stefania Carmeli, Francesco Castelli Dezza, and Marco Mauri.
2022. "Design of a Rotary Transformer for Installations on Large Shafts" *Applied Sciences* 12, no. 6: 2932.
https://doi.org/10.3390/app12062932