Vibration & The 3-Axis Of Acceleration

Recently, we’ve been measuring vibration in wheels and building on the complexity of the measurements we are gathering to further our understanding of the role that vibration plays in determining impedance break point. Our original work used a uni-directional accelerometer, which measures accelerations in one plane and simplifies the output. This uni-directional sensor was mounted to a skewer and measured the vibration in the y-axis, or up and down—like the up and down of a bike going over bumps.

Last week, we discussed adding a 3-axis accelerometer to the fork and to the wheel. This week, we’re breaking down the the three axes and how they align. Below is an image of the accelerometer and the alignment of the axis:

For the fork mount, the concept is simple since the accelerometer is stationary. Below, we highlight the direction of each acceleration and what causes each one:

• X-Axis: acceleration up and down caused by bumps and imperfections in the road, popping wheelies, or hitting sweet jumps.
• Y-Axis: acceleration forwards and backwards caused by going faster or slower
• Z-Axis: acceleration side to side caused by rocking the bike left to right.

While the image below shows a sensor mounted to the fork at an angle, the concept stays the same.

A wheel spins, so here things get a little more complicated. Let’s talk through the acceleration of each axis and its cause.

• X-Axis: acceleration in rotation in the direction of rotation; caused by spinning the wheel.
• Y-Axis: called centripetal acceleration in the direction of the hub; caused by spinning the wheel.
• Z-Axis: acceleration side to side caused by rocking the bike.

The image below shows the sensor mounted to the rim of a wheel:

The only axis that is predictable is the z-axis. While the wheel is rotating, the side to side motion is relatively unaffected. Now, if you are sprinting and really rocking the bike, of course the motion would be affected more, but in a regular riding situation, things stay fairly consistent. Let’s talk about the x-axis and y-axis.

• X-Axis: The x-axis is acceleration that follows the direction of the rotating wheel. Below highlights the different key positions.
  • 12 o’clock Position: The sensor is at the top of the wheel, and the acceleration is forward with the direction of travel.
  • 3 o’clock Position (front of wheel): The sensor is in front of the wheel, and the acceleration is down.
  • 6 o’clock Position: The sensor is at the bottom of the wheel, and the acceleration is actually zero, since when in contact with the road, the velocity at that point is 0.
  • 9 o’clock Position (back of wheel): The sensor is in the back of the wheel, and the acceleration is up.

At first glance this may seem simple, however you still have to factor gravity into the equation. At 12 and 6 there is no gravitational acceleration since the orientation of the x-axis is perpendicular to gravity, but at 3 and 9 you are either working with (moving down) or against (moving up) gravity. This complicates your output, and the position is tough to determine.

• Y-Axis: A good way to visualize the y-axis is to imagine the feeling of being in a car and going around a sharp corner at high speed. That acceleration you feel is the same acceleration felt by the y-axis in the wheel. The faster the wheel goes, the higher the acceleration. Gravity is opposite of the x-axis, and comes into play at 12 and 6.

Below is the output from for the x-axis, y-axis, and z-axis on both the fork and wheel at 120 psi. You can see the differences in each. Note the graph below is a Fast Fourier Transform (FFT) plot of the acceleration felt which looks at frequency excluding time.

Finally, we can look at the resultant vectors. This means we are looking at a combination of the x, y, and z axis results.

Wheels definitely make things more complex. However, we are interested in looking at the data from the wheel since it is the closest thing to the tire we can measure. Next week we will discuss sensor data from rollers to understand what happens in a more controlled environment.