Motor Controller Cooling

Design:

The motor controller will be screwed (M4) onto an aluminum heat sink which will be enclosed by a multi print 3-D printed (cracks sealed with JB weld) ASA enclosure with splash proof connectors and lid. The heat sink will need to be cut and drilled. An intake duct may need to be attached to provide air from the wheel well. This enclosure will be mounted behind the back right wheel (wheel with motor) and onto tabs from the frame.

https://pdm.getbild.com/0d9d31f0-3579-4fcd-82a8-b5347c436243/branch/main?tab=project_files&dir=f10bac09-82af-4c70-a506-89a20340b9d5

Motor Controller Datasheet:

Cooling - Prohelion Documentation

Dimensions

Heat Sink Selected:

https://www.digikey.com/en/products/detail/advanced-thermal-solutions-inc/ATS-EXL6-254-R0/5848412

Datasheet

Fans Selected:

Coolerguys 80mm (80x80x25mm) 12 VDC 3Pin High Speed IP67 Fan CG8025H12-IP67

Datasheet

Enclosure Connector:

ePower-Lite

Calculations: (no ducts)

P_loss = R_eqI_o² + (αI_o + β)V_bus + C𝑓_eqV_bus² (from datasheet)

Req= 1.0800E-2, 𝛼= 3.3450E-3, β= 1.8153E-2, C𝑓eq= 1.5625E-4

V_bus = 134.4V (battery 100% SOC), I_o = 60/sqrt(2) A (rms value)

P_loss = 43.7757W (heat generated)

We can assume that all of the power loss will be converted to heat, therefore the heat generated will be considered 43.78W. For the sake of simplicity, we are also assuming all of this heat is being transferred to the heat sink attached to the motor controller and that the airflow is distributed evenly across the heat sink.

Q = hA_total(T_object−T_ambient) (Newton’s Law of Cooling)

A_total = (((2 ⋅ fin height ⋅ length) ⋅ number of fins) + (length ⋅ width) (0.592m²)

P_r = 0.71 (Prandtl number for air at ambient temp 100F)

R_e = ρvL/μ (Reynold’s number)

v = 4.16m/s (Air velocity caused by fans, I used an online calculator)

ρ is the air density (typically 1.2 kg/m³ at room temperature).
v is the airflow velocity (m/s), which can be estimated from the fan's specifications.
L is a characteristic length (0.250m)
μ is the dynamic viscosity of air (1.918E-5 kg/ms, at ambient temp 100F)

We can calculate Nusselt’s number (N_u) with the Dittus-Boelter Equation which is used for turbulent flow through a smooth pipe. Although our enclosed fins are more akin to a rectangular prism.

N_u = 0.023 ⋅ R_e^0.8⋅ P_r^0.33

N_u = hL/k (Nusselt’s number equation relating to h)

h: is the heat transfer coefficient
L: is the characteristic length (0.250m)
k: is the thermal conductivity air (0.026 W/mk, at ambient temp 100F)

h = (0.023 ⋅ R_e^0.8⋅ P_r^0.33 ⋅ k)/L

Q = ((0.023 ⋅ R_e^0.8⋅ P_r^0.33 ⋅ k)/L)A_total(T_object−T_ambient)

Q = ((0.023 ⋅ ρvL/μ^0.8⋅ P_r^0.33 ⋅ k)/L)A_total(T_object−T_ambient) (heat transferred)

Q = 27.2885 ⋅ ΔT

Q = 8.9679 ⋅ ΔT

We can conclude that with the given cooling system, the temperature difference between the surface of the motor controller and the ambient temperature will need to be >5C to transfer the heat generated at peak power usage. Basically, it only cools the heat plate if we’re not just blowing hot air over hot metal.

However, given our ideal assumptions that heat and airflow is evenly distributed throughout the heat sink, velocity is constant and not accounting for humidity and that the motor controller is inside an enclosure, we can assume that the temperature difference needed for effective heat transfer is considerably greater than 5C.

Assuming the highest temperature conditions of 100F, we can estimate that the ambient temperature within the aeroshell will be able to reach at least 120-130F given that it’s outside in the sun all day and the battery, motor controller, MPPT’s, and other electronics are producing heat that’s not entirely expelled outside the aeroshell. The MPPT shutoff temperature is 70C (158F). With our effective ΔT value, the motor controller will hover dangerously close to it’s max temperature given bad weather conditions and continuous high current draw, which is dangerous and affects performance.

Conclusion: The cooling efficiency without ducts is questionable, but should be adequate if we add ducts leading from the wheel well to provide cooler air for convection.

Sources:

Air - Prandtl Number

Viscosity of Air, Dynamic and Kinematic

Nusselt number and the factors influencing it for perforated fin array of different shapes

Dittus-Boelter Equation | Correlation & Calculation | nuclear-power.com

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