# Natural Frequency: Does It Matter In Cycling?

In last week’s article, we discussed measuring impedance break points by looking at vibration, and revealed that we were able to measure a change in vibration acceleration at the impedance break point. As a recap, below is a FFT plot of vibration at 60 psi and 120 psi. In the 60 psi plot you see smooth section in the 40-60 Hz range. However, the 120 psi plot shows a spike between 40-60 Hz. We knew this was important and conjectured that this was because of the wheel’s natural frequency. So, let’s talk about natural frequency.

# Natural Frequency

All objects vibrate naturally at a certain frequency.  If you think of a tuning fork, the fork vibrates at a specific frequency when tapped. For example, middle C on a piano vibrates at a frequency of 262 Hz. What are hertz (Hz)? Hertz are the number of cycles per second. If a tuning fork is vibrating a 262 Hz for middle C, that means that the arms of the fork move back and forth 262 times per second. You can feel the vibration when the fork is struck and this vibration is the forks natural frequency.

A cycling wheel is no different. If you tap a cycling wheel, it will vibrate at its natural frequency. While the effect on a wheel is not as drastic or long lasting as a tuning fork, the principle is the same.

# Excitation

Excitation refers to when an objects natural frequency starts to vibrate or “gets excited.” For instance, if you’ve ever seen an opera singer shatter a glass by holding a note, the vibration from the note held is exciting the natural frequency of the wine glass. You can shatter a glass with enough power from the voice because the glass gets so excited that the natural frequency vibration causes the glass to break.

Excitation happens in two ways—the first is when you match a natural frequency, the second is if you apply a broad spectrum vibration signal. Broad spectrum is like a shotgun approach. Instead of a single frequency, you apply multiple frequencies in the signal. During our testing we learned that riding a cycling wheel over a road surface produced broad spectrum noise.

# How Does This Relate To Cycling Wheels?

Last week, we theorized that you can detect an impedance break point by measuring an increase in vibration. Since we found that to be true, the next step was to understand the frequency range that we needed to monitor for an increase in vibration at the impedance break point. In other words, we needed to find the natural frequency of the wheel.

# Finding A Cycling Wheels Natural Frequency

My friend and vibration expert, Matt, helped out once again. To find that natural frequency, we used a modal impact hammer and performed a tap test on a wheel and tire combination. Here’s how that worked:

1. We used the same data analyzer that we used last week to measure road vibration data for natural frequency of the wheel and tire combination.
2. The data analyzer had two devices attached—a unidirectional accelerometer, which is placed on the surface of the tire, and a modal impact hammer that is used to tap the wheel.
3. With the accelerometer held in place on the tire surface, we tapped the tire with the hammer. The vibration from the wheel was detected in the accelerometer and the tip of the hammer, and the data analyzer calculated the wheel’s natural frequency.

For the first test, we tested a Continental GP 5000 28mm tire on a FLO 64 AS Disc from 60-120 psi in 5 psi increments. This matched the pressures we used during our on road testing discussed last week.

# What We Found

The modal impact test results are shown below. There are two primary spikes in the data. The  peaks at roughly 40- 60 Hz are a part of the natural frequency profile of the wheel and tire combination. As pressure increased from 60-120 psi, the peak frequencies only shifted by about 2 Hz. This surprised me. If I were a betting man, I would have put my money on a larger shift.

When you compare this to the data discussed last week, you see that at the break point (roughly 85 psi) these same peaks were excited. It’s still early, but what this shows is that the point at which the wheel hits its natural frequency and starts to get excited (vibrate), is the same that we see the impedance break point.  Pretty cool right!?

Next week we will discuss the natural frequencies of different tires, weights, and wheels, and how the position of the wheel—front and rear—impacts the natural frequency of the wheel and tire. This gets kind of interesting.

## 1 comment

Have you done a hammer tests without the tire? Also while not mounted to the fork? I’d be curious to know which component(s) in the system are contributing to the peaks at 40 and 60 Hz in the FRF. Is it the tire, rim, fork, etc? Understanding the mode shapes will be important too.

I’d also expect resonance of the air in the tire cavity to be ~160 Hz, rim cavity to be ~180 Hz. You would be able to hear that, but it probably wouldn’t contribute much to rolling resistance.

A.E.

Armchair Engineer August 11, 2020