# Configuring BLDC motor for low-speed application

Given: I need to the simulate sinusoidal forces on a wind-tunnel model using a bench-top setup. I've designed a rig where I spin a load at high speeds to generate centrifugal centripetal forces, and those forces--which will periodically align completely in the X, Y, or Z directions--will serve as my sinusoidal forces.

I will mount the rig on top of a six-axis load cell, and I will measure the periodic forces via the load cell.

At this point, my load consist of a TBD-length aluminum or steel rod. I've derived the following expression for my loading given the rod's mass/unit length ($\rho^{l}$), desired centripetal force ($F_c$), the length of the rod ($L$), and the distance from the end of rod to installation bolt hole ($d$):

$$F_c = \rho^{l} (\frac{L^2}{2} - Ld)\omega^2$$

or, when re-arranged to solve for $\omega$:

$$\omega = \sqrt{\frac{F_{c}}{\rho^{l} (\frac{L^2}{2} - Ld)}}$$

Problem: For safety, I'm trying to keep the forces and speeds low. To generate a 2 lb. (8.90 N) load and a 20 lb. (89.0 N) load (one load needs to be 10X greater than the other) with a 4 inch (0.0762 m) long, 0.5 in (0.0127 m) diameter steel rod, I require spinning my rods at 467 RPM (48.9 rad/s or 7.8 Hz) and 1478 RPM (154.7 rad/s or 24.6 Hz) respectively.

Originally, I just bought 2 hobby BLDC motors and figured I'd command "slow" speeds via the ESC, but now I realize that they operate way too fast for my 2 lb load without some sort of reduction. A quick test of the Viking motors at 2 cells and a "slow" PWM command (1 ms/20 ms pulse) yielded average speeds around 1200 RPM.

My questions:

1. Given that I only have 2 weeks to run my experiment, will a brushed DC motor like this work for the 2 lb. load, or is the motor going to wear out? More abstractly, what is the usable continuous-operation lifespan of micro brushed DC motors?
2. How strong are the ball bearings in small, hobby BLDC motors? Could my Viking motors withstand a 20 lb. radial force? More abstractly, what is the radial force limit on small, hobby BLDC motors?
3. Would you recommend some other motor system for this low-speed application? Stepper? BLDC with smaller $K_v$? BLDC + speed reducer?

Many thanks, and please let me know how I can improve my question.

UPDATES: Your comments/answers and further research on my end are pushing me towards buying some sort of speed reducer for both motors/loads. I will operate my motors at 4000 and 6500 RPM, and I will use 11.73:1 and 4.5:1 speed reducers + external ball bearings to safely reduce 4,000 RPM and 6,500 RPM to near 467 RPM and 1477 RPM respectively.

Thanks to @John Birckhead for making me think about this: My steel rods have mass of 0.098 kg, length of 0.102 m. When the rod is perfectly parallel to the ground, rotating the rod will require torque (T) of 0.053 Nm | T = mgL/2 = 0.053 Nm. If $K_\tau = \frac{1}{K_V}$, then my motor has a Kt of 0.0023 Nm/A, and generating 0.053 Nm of torque will require 22.8 A (!). This is greater than the max current rating of the motor (16.7 A). I understand momentary current spikes from a motor are OK, but can a motor sustain momentary current spikes for many cycles? This gravitational torque will fight my motor for a fraction of every cycle.

• Go metric, man. Go metric! (1) This is an international site. (2) The calculations are so much simpler and intuitive. – Transistor Jul 20 '17 at 19:02
• SOunds more like a mechanical engineering question to me – Trevor_G Jul 20 '17 at 19:10
• @Transistor edited question with metric units. I was already calculating with metric, but I was still in imperial mode because I've been working with our fab shop to build this. Sorry! – techSultan Jul 20 '17 at 19:15
• @Trevor: Yeah, but I figured EE.SE would know more about BDC lifespan and operations than Engineering.SE, though I wouldn't mind a migration by the mods. – techSultan Jul 20 '17 at 19:16
• It depends on motor quality. Have seen small brushed DC motors running for 15 yrs on industrial machines. In any case you need a speed reducer head. Perhaps you get cheaper hobby BLDC with planetary gearhead. – Marko Buršič Jul 20 '17 at 19:29