# 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. Jul 20, 2017 at 19:02
• SOunds more like a mechanical engineering question to me Jul 20, 2017 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! Jul 20, 2017 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. Jul 20, 2017 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. Jul 20, 2017 at 19:29

## 1 Answer

Side loading is probably an issue with a motor this small, but here is the real problem: if the rod "weighs" .96 N, and the center of gravity is .102/2 or .051 meters from the shaft, you have a torque load of .049 N-m on the way up. Even if you find a motor large enough to provide this torque, it won't run at a constant speed because you will have this torque opposing you on the way up and aiding you on the way down, so you won't get a sinusoid with any small bare motor without feedback. You could go with a stepper or possibly a brushless or brush motor with a gearbox and hall feedback, or if sensorless, very good speed control. By the time you get to a motor or gearbox capable of providing the torque, you will likely have bearings that can handle some side loading.

• Hey John, thanks for the input. The torque on the upswing has been on my mind, but I just have to live with it because I am required to have one of the "centrifuges" mounted parallel to the Z-vector. I forgot to mention that the entire setup (including the load cell) will be mounted atop a shaker. The obj of my experiment is to see if we can still get reliable readings of the sinusoid under "shake", so it's fine if the sinusoids aren't perfect. Jul 20, 2017 at 20:39
• Also, I think you're off on your calcs. The steel rod has mass of 0.098 kg, length of 0.102 m. At most, rotating the rod will require torque (T) of 0.053 Nm | T = mgL/2 = 0.053 Nm. If Kt = 1/Kv, 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), but is that ok if the motor only needs 23 A for part of the revolution? Jul 20, 2017 at 21:06
• You are right! I missed the mass of steel and the length in meters, so I corrected as above. I need to stick to imperial units. Anyway, you are also right that your motor can briefly run at higher currents. If your motor has a stall torque spec, this is all you will get. Also, watch out for current flowing back into your power source on the other side. Jul 20, 2017 at 21:28
• Further question, can the motor sustain momentary unrated currents for many cycles? That gravitational torque isn't going away after the first revolution! And what do you mean about current flow back into the PSU? Jul 21, 2017 at 13:41
• So in answer to your question, you probably won't have a problem if your motor is drawing current all the time, but if the controller is braking, you will be pouring power into the motor on the upstroke and pouring that same power into the controller on the downstroke and your average motor power will be high. Jul 21, 2017 at 18:55