Introducing: The Thrust/Torque Test Stand!

A good autonomous quadrotor needs to be able to measure, in real units such as kilograms and seconds, important aspects about itself such as orientation, motor thrust, acceleration, and so on. It's fairly easy to make a remote controlled quadrotor platform since the human in the loop can intuitively correct for many small errors, and our eyes are very good at collecting the necessary raw information. An autonomous quadrotor does not have this luxury, and must explictly define each kinematic and dynamic equation. Most of the fundamental equations that a quadrotor must use will have some sort of general constant in them. This constant is meant to account for small errors in the system, differences between almost identical parts, and so on. Some of the most important constants and most difficult to measure are the motor torque and thrust constants. This post will cover details about our motor thrust/torque test stand.

I posted the equations last week, but here they are again:

[If your browser is like mine and is messing up the equations, then the first is K_T = T / (rho*n^2*D^4) and the second is K_Q = Q / (rho*n^2*D^5) ]

Don't be intimadated by equations. Most of the quadrotor mathematics look very difficult and impossible to understand, but it's my belief that understanding is not too difficult. I'm writing a paper to address the subject in great detail, and I'll be covering each equation from first principles to implementation.

Above, we have the two equations that define how our motors affect our quadrotor system. The form that they are in now makes it convienient for us to measure the constants K_T and K_Q: if we can somehow measure the terms on the right hand side then we can figure out what the constants are.

But first, we need to cover some notation details. When a term is written with a subscript it will be denoted in this text with an underscore (e.g. K_T is K with subscript T), and exponents are denoted with a chevron ( ^ ).  Greek letters such as rho (the sideways 'p') will be spelled out with the standard English letters. Other notation follows standard mathematical practice. The terms used are:

K_T - Thrust constant

K_Q - Torque constant

T - Thrust

Q - Torque

rho - air density

n - motor shaft rotation rate

D - propeller diameter

From these equations, it is clear that we need to measure thrust, torque, air density, rotation speed, and the propeller diameter. Ideally, we would build a machine that for any given motor and propeller combination will automatically test and produce the constants, along with information about how the motor operates and it's efficiency. Measuring rotor diameter, motor speed and air density are all fairly easy to do, and so we won't cover it here. The real challenge comes from measuring motor thrust and torque.

Most of the people who measure motor thrust seem to be RC airplane people. They measure the motor thrust in order to properly size a motor for their airplanes. Most motor thrust test stands are simple: a motor is mounted at the end of a lever arm with the opposite end fixed in place, and an L bend that presses on a scale (similar to a sensitive bathroom scale). From there the hobbyist powers the motor and and reads the force directly off of the scale and ends up with a thrust measurement. Easy.

Calculating torque is a bit more complicated: the motor body needs to be mounted on a rotating axis that is directly in line with the motor shaft, and the torque along this axis needs to be measured. In my research I found only a few examples of a motor torque test stand. This is likely because on an airplane the torque that a motor produces can be considered negligable since the motor is so proportionally small. Unfortunately, this is not the case on a quadrotor. In fact we rely on the torque to yaw the quadrotor vehicle.

To measure torque, most test stands had the motor mounted to a rod, which then had a lever arm attached that pressed on a scale. In a same way as thrust the force pressing on the scale can be read, and with the length of the lever arm torque can be calculated.

We want our test stand to be different: we want to measure both thrust and torque simultaniously, and we want to do all the testing automatically. To do this means that we will need a method to measure force (or pressure) without relying on scale, since a scale would be difficult to connect a microcontroller to. We have decided to try using the Flexiforce pressure sensors. These sensors vary the resistance based on the amount of pressure, and resistance is very easy to measure with a microcontroller.

For motor speed we will be using a Eagle Tree brushless RPM sensors, and we will use an contactless IR thermometer from Parallax. Our main control board will simply be the quadpower board that we have developed for our quadrotor. This has the advantage of being identical to what we will be flying, it will have the motor current and voltage sensing built in, and we'll be able to test the functionality of the board.

At this point, the motor test stand is almost completely built, and we are almost done with the hardware. The hardware is particularly complex because each joint needs ball bearings to make friction negligible, and there are some odd mechanical linkages that we need to account for.

I'll post more later this week when we (hopefully!) have a test stand up and running.