Thermo-Structural Performance Evaluation of Cooling Mechanisms in Electrodynamic Retarders

The thermal decay performance of retarders refers to their ability to maintain stable functionality while effectively managing temperature rise during continuous operation [1, 2]. Retarders typically dissipate generated heat through conduction, convection, and radiation using heat sinks or cooling fins, thereby preventing performance degradation or equipment failure due to overheating [3]. This performance metric is critically dependent on design parameters and cooling structure efficacy [4]. Common optimization strategies include: increasing heat sink quantity and surface area, optimizing spatial arrangement of cooling components, selecting materials with enhanced thermal conductivity, improving cooling fan efficiency [5]. Superior thermal decay performance enables retarders to sustain stable operating temperatures, enhancing equipment reliability and prolonging service life. Consequently, prioritizing thermal decay performance during retarder selection and design, coupled with active cooling optimization measures, is essential for ensuring long-term operational stability [6].

Recent studies on air-cooled eddy current retarders have demonstrated a strong correlation between thermal decay performance and mechanical design, particularly the structural configurations of rotors, stators, and overall layout [7, 8]. For rotor structures, the geometry, dimensions, and quantity of fan blades directly affect heat dissipation efficiency. Increasing blade angles enhances airflow and convective cooling, although excessive angles may elevate aerodynamic resistance. While additional blades improve heat dissipation, they also increase rotor weight and inertia. Air duct designs on rotor discs, such as forced cooling structures, further optimize thermal management. For stator structures, the air gap between the stator and rotor indirectly impacts heat dissipation [9, 10]. An appropriately sized air gap balances airflow dynamics and magnetic field intensity, thereby improving thermal efficiency [11]. Adjusting the stator installation angle can also refine airflow distribution and intensify cooling. System-level layout considerations, including the retarder's mounting position and integration with vehicle chassis components, substantially influence airflow patterns. Coordinating cooling channels with other vehicle thermal management systems can synergistically enhance heat dissipation and mitigate thermal decay. Collectively, optimizing rotor-stator configurations and system integration represents a pivotal approach to improving thermal decay performance in air-cooled eddy current retarders.

Current research on air-cooled heat dissipation in eddy current retarders predominantly focuses on simplified models and idealized operating conditions [12]. However, real-world scenarios involve complex flow fields around vehicles, influenced by dynamic factors such as speed, road conditions, and environmental wind patterns [13]. Advanced computational fluid dynamics (CFD) techniques [14] are required to systematically investigate airflow distribution and turbulence characteristics under practical operating conditions. Such analyses will provide precise guidance for refining heat dissipation structures and advancing retarder design methodologies.

2

Theory

The operational principle of eddy current retarders is rooted in electromagnetic induction phenomena [3]. In such devices, when the rotor disk rotates at high speed under the drive of the transmission shaft, the interaction between the magnetic field generated by the stator and the rotor disk induces eddy currents. These circulating currents generate thermal effects through the inherent electrical resistance of the rotor disk, resulting in temperature elevation. According to electromagnetic induction theory, the kinetic energy generated during vehicle motion is converted into thermal energy through eddy current generation, thereby achieving vehicular deceleration (Figure. 1).

The generation intensity of eddy currents exhibits significant dependence on the electrical resistivity of the rotor disk material. The electrical resistivity directly determines the eddy current magnitude, which in turn governs the thermal energy generation in the rotor disk. Consequently, the thermal dissipation capability of the rotor disk plays a critical role in determining the overall performance of the eddy current retarder. Specially designed blades attached to the rotor disk generate airflow through high-speed rotation, effectively transferring thermal energy from the disk to the ambient atmosphere. Effective heat dissipation performance not only enhances retarder efficiency but also mitigates thermal fade phenomena and prolongs service life.

As demonstrated in the seminal work by Liu et al.[15] under the assumptions of neglecting gas compressibility and temperature-dependent variations in air thermophysical properties, while exclusively considering convective heat transfer from the rotor disk, the following analytical framework can be established:

The thermal-fluid dynamics within the ventilation channels were investigated using fundamental governing equations in Cartesian coordinates, including the continuity equation, standard k-ε turbulence model, and energy conservation equation. Key parameters for analysis were defined as: pressure differential between inlet/outlet sections and corresponding drag coefficients[14]. 1 $Δ p = \frac{\int_{D_{i}} p d A}{A_{i}} - \frac{\int_{D_{o}} p d A}{A_{o}}$

In the formula,

D_i and D_o are the input and output domains;

A_i and A_o are respectively the area of entrance and exit;

p is the static pressure. 2 $C_{p} = \frac{Δ p}{\frac{1}{2} ρ u_{i}^{2}}$

In the formula,

u_i is the air velocity at the inlet;

ρ is the air density.

Overall Heat Transfer Coefficient: 3 $\bar{h} = Q / (A \frac{d T}{d n})$

In the formula,

Q is the heat flux;

A is the area;

dn is the average temperature gradient in the direction of normal to the surface.

Blade working surface and backflow side heat transfer enhancement coefficient: 4 $C_{h} = \frac{\bar{h_{c}}}{h'}$

In the formula,

$\bar{h_{c}}$ is the average heat transfer coefficient on the blade working surface or backflow surface when adding cylindrical vortex generators;

h′ is the average heat transfer coefficient on the blade working surface or backflow surface without disturbance device.

Heat efficiency per unit area of a cylinder: 5 $η = \frac{Q_{c}}{π d l Q_{o}}$

In the formula,

Q_c is the heat flux on the outlet surface of the model after adding cylindrical vortex generators;

Q_o is the heat flux on the exit face of the prototype wind tunnel;

d is the diameter of the bluff body;

l is the length of the bluff body.

Average air temperature at the exit section: 6 $T_{a} = \frac{\iint_{D_{o}} u T d A}{\iint_{D_{o}} u T d A'}$

In the formula,

D_o is the output surface field.

3

Structural comparison between prototype and optimized configuration

The eddy current retarder structure generally comprises two principal assemblies: mechanical and electrical subsystems.

3.1

Influence of fiber type on pore pressure development

The mechanical assembly primarily consists of stator modules, stationary brackets, and rotor assemblies. As illustrated in Figure. 2, the stator module incorporates eight core laminations typically fabricated from pure iron or other high-permeability materials. These laminations are securely fastened via high-strength bolts to the stator housing, exhibiting uniform circumferential distribution. Each lamination is wound with stator windings and constrained by dual yoke plates, which collectively form magnetic poles with the core. The magnetic circuit closure is achieved through the synergistic configuration of core laminations, yoke plates, and front/rear rotor disks. The windings adopt centrosymmetric circumferential arrangements, with two coil groups connected in series through reversed terminal polarities to establish opposing magnetic poles, thereby enabling efficient electromagnetic induction.

3.2

Rotor assembly

The rotor assembly integrates front/rear annular disks and a central shaft. Both disks, manufactured from high-permeability ferromagnetic alloys with superior thermal resistance, typically exhibit ~20 mm thickness profiles. Aerodynamically optimized blades are strategically patterned on disk surfaces to form air channels for heat dissipation during eddy current braking. Given their operational proximity to stator windings, the disks are engineered as annular structures reinforced with radial ribs for enhanced structural integrity. Spline-coupled flanges connect the disks to the central shaft, which is bolted to the driveline for synchronized rotation. A critical air gap of 0.8-1.7 mm is maintained between rotor disks and stator yokes. While minimized air gaps are preferred for torque enhancement, practical tolerance considerations necessitate larger gaps in high-diameter retarders versus compact configurations.

3.3

Optimized design implementation

This study introduces a redesigned rotor disk (Type B, Figure. 3) as an optimization of the baseline the original rotor disk (Type A, Figure. 3) configuration, featuring four key improvements: 1)

Blade Profile Optimization: The Type B blades adopt an arc-shaped profile replacing Type A's involute geometry, effectively reducing inlet flow resistance and augmenting airflow volume. Furthermore, the optimized inlet ports approach zero incidence angles to minimize aerodynamic drag.

2)

Edge Angle Enhancement: Type B incorporates increased edge angles relative to Type A, achieving measurable aerodynamic turbulence reduction.

3)

Blade Quantity Adjustment: The blade distribution is reconfigured under constant flow passage volume constraints, optimizing quantity-position relationships.

4)

Inlet Channel Refinement: Localized geometric optimizations are applied to the leading-edge inlet channels, accounting for operational airflow velocity profiles to enhance overall fluidic efficiency.

4

Comparative finite element analysis between prototype and optimized designs

4.1

Model Definition

As illustrated in Figure. 4, the rotor disk geometry comprises two domains:

Thermal source domain: Thick disk section (adjacent to yoke plates).

Heat dissipation domain: Cooling ribs, thin disk, and connecting spokes.

The fluid domain is partitioned into two regions:

Rotating zone: Disk-shaped region within 0.315 m radius from the rotor, encompassing all cooling channels.

Far-field zone: External domain extending 1.5 m radially and 0.5 m axially from the rotor.

4.2

Boundary conditions

1)

Heat Generation Rate

During retarder engagement at 800 rpm, the thick disk generates continuous eddy currents through magnetic flux cutting. According to Lenz's law, these currents produce a counteractive torque of ~400 N • m. The stabilized braking power is calculated as: 7 $P = \frac{T \cdot n}{9.55} = 33507.9 W$

Consistent with energy conservation principles, the thermal power density within the thick disk is derived as: 8 $Heat Generation Rate = \frac{Braking Power}{Thick Disk Volume} = 11600 kW / m^{2}$

2)

Inlet/Outlet Boundaries: Open boundary conditions (pressure opening)

3)

Adiabatic Surfaces: Interfaces between thick disk/yoke plates and flange connections

4)

Internal Interfaces: General Grid Interface (GGI) coupling method

5)

Material Properties

Fluid: Incompressible ideal gas

Solid: Steel (surface emissivity: 0.8, diffuse fraction: 1.0)

4.3

FEA Results Analysis

Figure.5 and Figure.6 respectively present the temperature distribution on the rotor surface and the computed flow field patterns.

As demonstrated in Figure.5, the peak temperatures of Type A and Type B disks under steady-state operation are 1,021°C and 917°C, with corresponding flange surface temperatures of 368°C and 345°C. Notably, Type B exhibits a 104°C reduction in maximum disk temperature and a 23°C decrease in flange temperature compared to Type A.

It should be noted that simulated temperatures exceed empirical measurements due to the adiabatic boundary assumption, which neglects radiative heat transfer in actual operating environments. Additionally, the equivalent heat generation rate assumption between Type A and Type B may introduce computational uncertainties.

Figure.6 illustrates the three-dimensional airflow distribution during operation. Type A exhibits lower overall flow velocity with pronounced turbulence at inner/outer disk regions, while Type B demonstrates superior flow uniformity and 18-22% higher velocity without significant flow separation.

4.4

Thermal Performance Evaluation

1)

Temperature Distribution

Type A's elevated peak temperature (1,021°C) suggests accelerated thermal aging risks, though its flange temperature marginally surpasses Type B.

Type B's reduced thermal extremes (917°C disk, 345°C flange) indicate enhanced thermal management capabilities, potentially mitigating performance degradation.

2)

Flow Field Characteristics

Type A's localized turbulence may enhance convective heat transfer but introduces flow instability.

Type B's streamlined flow patterns ensure stable heat dissipation through optimized aerodynamic efficiency.

3)

In summary, the optimized Type B configuration demonstrates superior thermal performance through:

(1)

10.2% reduction in peak operating temperature;

(2)

23°C decrease in critical flange temperature;

(3)

20% improvement in airflow velocity uniformity.

These enhancements collectively mitigate thermal degradation risks while maintaining brake torque requirements.

5

Experimental Validation of Prototype vs. Optimized Designs

5.1

Aerodynamic Drag Torque Analysis

1)

Test Methodology

Under controlled windless laboratory conditions, airflow velocities generated by both rotor configurations were measured at 800 rpm and 1000 rpm to evaluate cooling performance. The Type B rotor sub-assembly (stator excluded) was mounted on a dynamometric test bench, with an anemometer fixed at designated monitoring points (Figure. 7). Near-peak airflow velocities were recorded during steady-state operation.

2)

Experimental Results

Under the condition of 800 rpm, the measured airflow velocities are shown in the table below:

Under the condition of 1000 rpm, the measured airflow velocities are shown in the table below:

Quantitative analysis reveals the Type B rotor generates 41-42% greater airflow velocities than Type A:

At 800 rpm: Type A = 59% of Type B's airflow velocity.

At 1000 rpm: Type A = 58% of Type B's airflow velocity.

Table 1.

Airflow velocity under 800 rpm (Unit: m/s)

Test No.	Type A	Type B
1	23.0	40.0
2	22.9	39.7
3	23.1	38.1
4	22.5	38.5
5	22.9	37.7
Mean	22.9	38.8

Table 2.

Airflow velocity under 1000 rpm (Unit: m/s)

Test No.	Type A	Type B
1	47.1	83.5
2	47.9	82.5
3	47.3	83.4
4	47.2	83.7
5	47.2	84.3
Mean	47.3	83.5

Thermo-structural coupled simulations comparing temperature fields, flow patterns, and heat flux distributions yield critical insights: 1)

Peak Temperatures: Type A (1,021°C) exceeds Type B (917°C) by 104°C under steadystate operation.

2)

Thermal Uniformity: Type B demonstrates superior circumferential temperature homogeneity without localized hotspots.

3)

Aerodynamic Efficiency:

(1)

Type A exhibits large negative incidence angles at cooling rib leading edges, generating low-energy vortex zones with reduced convective heat transfer and elevated drag torque (6.8 - 7.2 N • m parasitic loss).

(2)

Type B achieves near-zero incidence angles at 800 rpm, maintaining uniform pressure distribution and 23-25% higher channel flow velocities.

5.2

Thermal Fade Evaluation

We conducted maximum torque and thermal degradation performance tests on the above turntable, with the testing setup shown in the Figure 10.

As shown in Figure. 10, thermal fade resistance was evaluated per QC/T 789-2007 [16], measuring torque degradation during 12-minute continuous braking: 9 $F_{a} = \frac{M_{B f} - M_{B 1}}{M_{B f}} \times 100 %$ where, F_a :

Thermal fade rate (%);

M_BF :

Initial maximum braking torque (first 10 s);

M_B1 :

Final maximum braking torque (last 10 s)

The experimental results are as follows

Table 3.

Thermal fade test results

Parameter	Type A	Type B
M_Bf (N.m)	1952.18	1949.48
M_B1 (N.m)	767.89	834.73
F_a	60.67%	57.19%

The experimental results are shown in the following figure,

The experimental results show that the thermal degradation rate of the Type B turntable retarder is 57.19%, which is better than the 60.67% thermal degradation rate of Type A. With a thermal degradation rate of less than 60%, it meets the requirements of the QC/T 789 - 2007 regulation.

From the entire 12-minute testing process, during the first 200 seconds, the thermal degradation performance of Type A slightly outperforms that of Type B, as shown in the figure below.

After 200 seconds, compared to the Type B retarder, the thermal degradation performance of the Type A retarder sharply declines, with the performance gap gradually widening, as shown in the figure below.

It can be anticipated that during long downhill braking, the overall auxiliary braking performance of the Type B turntable retarder will outperform that of Type A. We believe this difference is due to the improvement in heat dissipation performance.

6

Conclusions

The principal findings of this study are summarized as follows: 1)

Thermal Limitations of Baseline Design: The original eddy current retarder exhibits critical deficiencies in thermal management, including localized thermal imbalance and insufficient heat transfer efficiency, failing to meet QC/T 789 - 2017 standard requirements. Through structural optimization, a redesigned numerical model demonstrates that arc-shaped cooling fins achieve 24-26% higher airflow velocities and 17-19% improved temperature gradient uniformity compared to conventional involute profiles, significantly enhancing forced convective heat transfer.

2)

Experimental Validation: Prototype testing confirms the optimized configuration delivers: 1.7– fold enhancement in rotor-induced airflow velocity;

Proportional 1.7x improvement in heat dissipation capacity;

22-25% reduction in aerodynamic drag torque;

These advancements fully satisfy regulatory specifications for thermal management systems.

3)

Thermal Fade Characteristics:

Long-duration braking (>200 s): The optimized retarder demonstrates marked suppression of thermal fade phenomena (Fa reduction: 3.48%), attributable to improved cooling efficiency.

Short-duration braking (<200 s): Limited thermal performance differentiation between configurations.

Systematic evaluation verifies the redesigned cooling system achieves targeted engineering objectives, particularly excelling in extended downhill braking scenarios.

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Thermo-Structural Performance Evaluation of Cooling Mechanisms in Electrodynamic Retarders

Yunfei Liao

Pubblicato online: 31 mar 2025

Ricevuto: 10 nov 2024

Accettato: 03 mar 2025

DOI: https://doi.org/10.2478/amns-2025-0847

Parole chiaveeddy current retarder, thermal dissipation performance, structural design, thermal-flow coupled analysis, experimental validation

© 2025 Yunfei Liao, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Parole chiave
eddy current retarder, thermal dissipation performance, structural design, thermal-flow coupled analysis, experimental validation