Introduction

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More than one way to skin a cat

The number of ways to measure acceleration has become staggering.  We accelerometers to measure things that people do like walking, running and aerobic activities.  They are used in building construction from demolition and excavation to driving piles into the ground to form a good building foundation.  They are used on bridges, in automobiles, aircraft and in missiles. They provide the sensor input for football helmets and in physical therapy devices.  They are used to monitor earthquakes and volcanos.  They allow for image stabilization in cameras and orientation of displays.
So how do we actually measure acceleration?  It all starts with a proof mass.  A proof mass is a mass of known quantity that is used along with a spring or other compliant device to measure movement. A very simple accelerometer can be constructed of a spring, a mass and a ruler.  Hang the mass from a spring. Mount the ruler next to the mass and spring with an indicator pointing at the ruler.  If you take this device into an elevator, you will see the effects of the acceleration and deceleration.  The accelerometers that are used in actuality are more sophisticated, more reliable and more repeatable, but they are based on the same simple principles as the mass spring device.

Newtons Second Law

It was late in the 17th century when Isaac Newton wrote his now famous Mathematical Principles of Natural Philosophy.  In those pages, he explained the relationship between force, mass and acceleration and called it his second law.  It simply states that the force on an object is equal to the change in momentum of that object. Momentum is the mass of an object times its velocity (m*v) and the change in momentum is the mass times the change in velocity which is also called acceleration (m*a).  So, force equals mass times acceleration (F=ma).

If it looks like a duck…

Servo Force Balance
One type of accelerometer involves a pengulus mass (mass on the end of a stick) suspended so that the stick is perpendicular to the direction of acceleration.  The stick has a mass much lower than that of the proof mass and it is compliant, which allows it to bend or flex.  There is a servo of some sort (electromagnets are very popular) that pushes in the opposite direction as the acceleration.  You will need something to measure the position of mass.  These are called pickoffs and can be made to vary in capacitance, resistance or optical intensity with the movement of the proof mass.  Now you ‘simply’ make a control system.  Apply enough force with your servo to exactly balance the acceleration at all times.  If you know how much force you are applying with the servo you know the acceleration.

Gyroscopic Acceleration

One of my favorite accelerometers involves the use of gyroscopic force.  This force is at right angles to the axis of spin of a gyro.  This is the force that makes it possible to ride a bicycle.  I remember a demo of a gyro made of a very heavy wheel.  They spun it up and then balanced it on the axle on the top of a post; one axle on the post the other in free air.  It looked like magic.  Then they took a young girl in a chair and placed it on the axle protruding out the other side of the gyro and she sat there slowly tuning in a circle with apparently nothing supporting her.
To use this property in an accelerometer we need a gyro that has a mass attached to one side.  Imagine the axis of the gyro horizontal to the floor.  Gravity will place a force on the mass and try to move it down until the axis of the gyro is pointed at the floor.  If we rotate this device around in a circle (think about sitting on a record player turn table – an archaic device used to play music before the invention of the CD) we will apply a force on the mass that will oppose the force of gravity.  We can balance the two forces by changing the speed of the turn table.  Increasing the speed puts more force on the mass while decreasing the speed decreases the force opposing the force of gravity.  Of course, you must turn the table in the correct direction switching directions will switch the direction of the applied force.
To make this work you need a pickoff to sense the position of the mass and a control system to turn the servo motor at the correct speed to keep the pickoff at the null position.  They use these types of gyros in ballistic missiles.  Accelerometers of this type are the most accurate man has ever made.  Unfortunately, they cost more than most hobbyist can afford, about $100k each.

Piezoelectric Force Sensor

Another type of accelerometer uses a mass and a piezoelectric device to measure how much force the mass is putting on the crystal.  The output is charge which is proportional to the force on the piezo device. These come in both shear and compressive configurations.

Strain Gauge

Made with a beam with a mass on it and a strain gauge attached to the beam.  The strain gauge is often place in a bridge arrangement.

Silicon MEMS

In modern accels, a proof mass is etched into a silicon wafer and suspended by small beams.  The response to an acceleration is a deflection.  There are usually two ways to sense the magnitude of the deflection, capacitive and piezoelectric effects.
There are many more varieties and features available in the measurement of acceleration, but this is becoming a long newsletter.  The chip accelerometer has become the most common device used.  For 2 bits (50 cents) you can buy an accelerometer that will measure +/- 2, 4, 8 or 16g’s and tell you the result in a variety of ways (I2C, SPI, UART, analog – current or voltage).  Did I mention this is for a three-axis device?
While the silicon devices are cheap and small, they will never come close to the accuracy of the iron wheel devices used in navigation systems.  Choosing the right type of sensor for the job is key to success.

Final thoughts

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