Thermal Analysis of an Air-Cooled NEMA23 Stepper Motor

Edit 07/09/2024: The values calculated in this post seem a little suspect. If anyone with thermo experience can spot any errors that would be greatly appreciated.

This analysis was conducted as part of my PrintNC-Derivative CNC Router project. The machine uses four NEMA23 open-loop stepper motors for the X,Y, and Z axes, with DM542T and DM556T stepper drivers for control.

Each of the drivers has the capacity to push over 100W per motor, an amount which cannot be practically dissipated by natural convection only. For this reason, to enable the full torque capacity, a blower and shroud will be fitted to each motor.

I will be using Sunon VF60381B1-Q000-S99 60mm server fans, which I managed to score a half-dozen of at near scrap value (They are ~$54NZD ea. new!). These are serious beasts, rated for 70,000 hours at 18300 RPM.

Heat Load

80mm NEMA23 steppers with DM542T drivers (3A RMS) are used on the Y and Z axes. The X axis uses a 113mm stepper with a DM556T driver (4A RMS). All stepper run on 36V, making for maximum continuous powers of 106.9W and 142.6W respectively.

Natural Convection Analysis

Analytical Solution

A crude estimate of natural convection heat transfer can be made by approximating the rectangular motor profile as a cylindrical one (and assuming it has infinite length). The correlations and fluid parameters are taken from Fundamentals of Thermal-Fluid Sciences (Yunus A. Çengel, John M. Cimbala etc.). Some fluid properties are taken at ambient, rather than the film temperature, for convenience, however the difference is negligible compared to other assumptions.

It is difficult to say whether the assumption of a circular profile would over or underestimate the overall heat transfer without additional knowledge of the flow behavior. On one hand the sharp 90-degree corners might impede flow, however they could also act to create turbulence, disrupting the boundary layer and increasing heat transfer.

Regardless, convective loss is only half of the picture, and at 100 degrees Celsius, radiation loss is already over the predicted convective loss (12.3W vs 10.2W, assuming 100% emissivity).

CFD Solution

A very simple two-dimensional CFD analysis was conducted in Ansys Fluent to validate against the analytical solution. The solver setup uses a fixed power density for the motor, calculated as below:

The results differed significantly from the analytical results, which could have been from a combination of reasons:

• A square geometry was used instead of circular (the CFD was intended to validate the hand calcs, but in typical fashion I forgot that the correlation was for a circular, not square profile.
• The fluid domain may have been too small (too short primarily) to fully represent the convective plume.
• Convergence was poor, with velocity residuals not falling below ~1E^-4. The solver setup or mesh may have been responsible for this – not checked due to time constraints.

Forced Convection Analysis

Two approaches were taken to estimate heat transfer by forced convection: Parallel flow over a flat plate, and a square profile in crossflow.

Parallel Flow over a Plate:

To simplify the problem, an equivalent 10mm deep by 160mm wide (twice the 80mm motor length) flow channel is assumed. Due to the much higher expected heat transfer coefficient compared to natural convection, the use of air properties evaluated at the ambient temperature is more appropriate.

The blower flow rate of 25.53 liters per second, and the assumed channel dimensions, create a flow velocity of 15.96 m/s. This results in a Reynolds number of 1E^5 < 5E^5, indicating laminar flow. Due to the effects of the blower however the flow would almost certainly be turbulent from the start.

This leads to a specific heat rate of 1.4W/K under turbulent flow, approximately double the 0.78W/K under laminar flow.

Rectangular Profile in Crossflow:

The problem can also be very roughly be approximated as a square profile in a uniform crossflow.

For this it was was assumed that the blower flow was spread evenly across a 60mm x 60mm square area, resulting in a flow velocity of 7.09m/s, and a Reynolds Number of 26,383. Like with the flat plate assumption however, turbulence from the blower would make for a higher effective value. This would increase heat transfer by disrupting the boundary layer, and possibly delaying the flow separation angle.

Using Re=26,383, and the correlation for a square profile in crossflow, a specific heat rate of 0.657W/K is found, around half of that calculated for the flat plate interpretation.

Calculated Heat Transfers Compared

Under forced convection, the motor reaches estimated surface equilibrium temperatures of between 89C and 144C, representing a heat transfer effectiveness (ϵ) is only 2.5-5%. This low effectiveness is as a result of the small heat transfer area relative to the flow rate, with air taking an estimated time of only ~7ms to exit the duct.

In practice however, lower temperatures are expected due to the extreme degree of turbulence and mixing caused by the blower.