# Multiphysics Design of an Automotive Regenerative Eddy Current Damper

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}.

## 2. Multi-Physics Model of the REC Damper

#### 2.1. Definition of the System

_{1,}and corresponds to a blow-off pressure at 0.2 m/s piston velocity. The slope decreases for an increasing piston velocity (${C}_{2}=\frac{\u25b3{F}_{d2}}{\u25b3{v}_{2}}$). The damping coefficient is rather small in the third quadrant (${C}_{3}=0.15{C}_{1}$). The proposed REC damper is not designed to bear such loads as those encountered for double wishbone front suspension. The upper bound for the outer diameter, ${D}_{o},$ of the damper is 84 mm.

#### 2.2. Electromagnetic Model

_{emf}, for each coil can be expressed in terms of the Faraday—Lenz law as:

_{L}= 0) of an ${A}_{w}$ cross section area can be determined as:

_{r}, its effect can be maximised, even for a small increase. A similar benefit also results from ${v}_{z}$ in Equation (3). Dimensionless quantities are preferred for damping coefficient C* = C/C

_{max}, damping force F* = F

_{d}/F

_{max}, and power P* = P/P

_{max}for easy comparison purposes.

#### 2.3. Quarter Car Dynamic Model

_{s}and unsprung mass m

_{us}. The suspension spring stiffness k

_{s}, damping coefficient c

_{s}, tire stiffness k

_{t}and damping c

_{t}are set as linear coefficients.

#### 2.4. Mesh Sensitivity

## 3. Results

#### 3.1. REC Damper FE Optimisation

_{p}, in Figure 1). Its maximum value was attained for a ratio of the pitch size-to-the height of the piston (ζ) equal to 0.18. This ratio determined the pitch size that maximised the damping coefficient. The damping coefficient should then be maximised with respect to the IP height-to-pole pitch size ratio, as we previously demonstrated in [24]. The maximum value of the proposed REC device was attained at 0.27 of the aforementioned ratio, which was within the previously found range of 0.21–0.29 [24]. The linear damping condition found here for the REC could be compared with the reference hydraulic damper shown in Figure 7b. As can be noted, the two damping conditions were only comparable for high piston speed conditions, which meant that the suspension handling requirements could not be satisfied. Therefore, a much larger damping capacity was still necessary for the REC damper. However, we were able to take the predicted REC damping coefficient (Figure 7b) as a reference (C

_{ref}), and further tune it over the remaining free parameters (stator optimisation) to obtain the damping coefficient of the hydraulic damper.

_{new}, while keeping the thickness of the conductor and that of the back steel constant. According to Figure 1, the change in the PM radii affects the outer radius of the tube, and the latter, in turn, affects the mass of the piston. Thus, these two components should be changed accordingly. The resulting tuning procedure of C

_{new}(starting from C

_{ref}) is shown versus the normalised outer radius of the damper tube (r

_{new/}r

_{ref}) in Figure 8a (left axis). The corresponding CM

_{new/}CM

_{ref}ratio of the specific damping coefficients (CM is the damping coefficient divided by the mass of the piston) is shown in the same figure (dotted curve) on the right axis.

_{ext}= 0).

_{2}damping at a lower resistance, which now operated in the higher power output range, as shown in Figure 10b by the leftward shift of the vertical green line from 33 to 21 Ω. Thus, SAE 4340 steel was selected to manufacture the external tube (1.6 mm thick), because of its outstanding bearing properties, whereas Armco iron was selected for the back iron, because of its superior ferromagnetic properties. However, Armco pure iron was avoided for the manufacturing of the outer external tube, as its low strength would induce on-service straining in the outer tube as well as in the inner (back iron) tube. The latter, in turn, would gradually and irreversibly deteriorate its magnetic hysteresis properties [30,31,32].

_{1}′ = 0.853 C

_{1}damping in the short circuit condition, while C

_{2}′ damping operated at 21 Ω, and C

_{3}′ = 6.7 C

_{3}in the open circuit condition.

#### 3.2. Ride Comfort and Handling

#### 3.3. Thermal Behaviour of the REC Damper

_{1}), even for piston speeds faster than 0.2 m/s, to account for any failure in the power electronics.

## 4. Discussion

_{1}) decrease and a bump damping (C

_{3}) increase, resulting from the effects of back iron, influence the dynamics of a vehicle. The comfort performance of a vehicle equipped with an REC damper experiences minimal changes on both class roads, whereas the road holding index is slightly deteriorated on B class roads. The latter performance index is more sensitive to damping changes. Figure 12 shows the RMS piston velocity range for the analysed cruise velocities of the vehicle. Maximum RMS values were found at 0.135 and 0.31 m/s for B class and C class roads, respectively. The low piston speed damping coefficient (C

_{1}) is predominant within such piston speed ranges for B class road. Consequently, the road holding index is affected more, thereby confirming our analysis results shown in Figure 11a,b.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Piecewise linearisation of the nonlinear, normalised maximum force (${F}^{*}$) vs. piston speed characteristics of the reference hydraulic shock absorber (of a typical B-class passenger-vehicle) used in this work for the design and optimisation of the REC damper.

**Figure 5.**Mesh sensitivity with an increasing overall number of finite elements (curve parameter): (

**a**) normalised damping force vs. piston speed; (

**b**) normalised harvested power vs. piston speed.

**Figure 6.**Mesh sensitivity of the thermal and CFD fields for the analysed time period; the legend indicates the overall number of finite elements in the mesh.

**Figure 7.**REC damper optimisation starting from the dimensions of the existing hydraulic damper and using the design model developed in [24]: (

**a**) normalised damping coefficient during piston optimisation as a function of the pitch size-to-the total piston length ratio; (

**b**) comparison of the damping force of the optimised REC (linear) and the reference hydraulic damper shown in Figure 2 (line colours follow explanations of Figure 2).

**Figure 8.**Optimisation strategy of the RCE damper versus the normalised outer radius of r

_{new/}r

_{ref}of the damper tube: (

**a**) damping increase as a ratio of the damping in Figure 7b—Left axis, normalised damping coefficient (true damping coefficient divided by the piston mass)—Right axis; (

**b**) Optimised damping with equal IP and MP heights (cyan dashed line) and optimised as in Figure 4a (red dash-dot line) compared with the reference hydraulic damper (blue line).

**Figure 10.**Damping and electric power performances of the REC damper: (

**a**) the SAE 4340 steel and Armco pure iron hysteresis loops considered in the FE design and optimisation process; (

**b**) the normalised damping coefficient curve versus load resistance (left axis) for the back iron material models and periodic cycle-averaged power output of the REC damper versus load resistance (right axis); curves in the legend: the initial magnetisation curve of the Armco iron (dashed), the magnetic hysteresis loop of the Armco pure iron (continuous), and the magnetic hysteresis loop of the SAE 4340 steel (dash—dotted).

**Figure 11.**Comparison of the performance indices for the hydraulic reference and REC dampers: (

**a**) ride comfort and (

**b**) road holding safety on ISO B-class and C-class roads for variations of the vehicle cruise speed.

**Figure 12.**Piston RMS speed on B-class and C-class roads for variations of the vehicle cruise velocity.

**Figure 14.**Thermal performance analysis: (

**a**) temperature field; (

**b**) average temperature evolution at the stator mid-stroke location.

**Figure 15.**Frequency response transfer function of the road disturbance and sprung mass with a damping coefficient as a curve parameter. The arrows point to increased damping.

Symbol | Value |
---|---|

${m}_{s}$ | 333.54 kg |

${m}_{us}$ | 41.46 |

${k}_{s}$ | 21.6 kN/m |

${k}_{t}$ | 194.4 kN/m |

**Table 2.**Details of the discretized geometry in the region near the sliding piston and relative overall number of computed finite elements for the magnetic field.

Number of elements | (857) | (1852) | (9134) |

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**MDPI and ACS Style**

Jamolov, U.; Peccini, F.; Maizza, G.
Multiphysics Design of an Automotive Regenerative Eddy Current Damper. *Energies* **2022**, *15*, 5044.
https://doi.org/10.3390/en15145044

**AMA Style**

Jamolov U, Peccini F, Maizza G.
Multiphysics Design of an Automotive Regenerative Eddy Current Damper. *Energies*. 2022; 15(14):5044.
https://doi.org/10.3390/en15145044

**Chicago/Turabian Style**

Jamolov, Umid, Francesco Peccini, and Giovanni Maizza.
2022. "Multiphysics Design of an Automotive Regenerative Eddy Current Damper" *Energies* 15, no. 14: 5044.
https://doi.org/10.3390/en15145044