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Advanced Harmonic Analysis in Roundness Metrology

What is Harmonic Analysis in Roundness Metrology?

A harmonic on a circular profile can be considered as a uniform waveform ( a sine wave) which is superimposed on the surface of a component and all-rounders profiles consist of a series of sine waves which when ‘added together’, produce the complete profile.

Where is This Harmonic Analysis Used?

For harmonic analysis we have several examples of where it's vital to the production process and to the design process. Particularly of bearings - inner and outer races and some ball bearings, large bearing, and a ball screw where we can measure the spiral harmonics. Below we can see a vacuum chuck holding a small a miniature bearing and a typical instrument with active anti-vibration a very high precision spindle able to measure all these parts.

Applications of Harmonic Analysis

What are Harmonics?

Harmonics are undulations and they are usually produced by the manufacturing process; any roundness profile can be broken down into its constituent parts which consist of undulations around the profile.

Harmonics Analysis

The word UPR means undulations per revolution, it is the same thing as the Harmonic, so when we're talking about the 60th harmonic, we could be talking. We would be talking about 60 undulations per revolution, or 60 UPR, and you will see that used throughout this process.

The word UPR means undulations per revolution. It is the same thing as the Harmonic, so when we are talking about the 60th harmonic, we could be talking about 60 undulations per revolution, or 60 UPR.

Typically, a roundness profile will consist of many different harmonics of varying amplitudes. If we look at the first harmonic that is known as the eccentricity and again it means, it is got one peak and one Valley.

The second harmonic is ovality and we can see 2 two peaks to valleys, the 5th Harmonic, 5 peaks 5 valleys. So, all roundness profiles consist of these pure sine waves when they have different amplitudes. When we add them all together, we get the complete profile. So harmonic analysis is doing the opposite, it is breaking down that profile into these parts because we can see these and identify the causes of problems in our manufacturing more easily.

So, what harmonic analysis does is it breaks this down using a Fourier transform Fourier analysis and it breaks it down into these pure sine waves of different amplitude. So, we can see which is the most significant characteristic on a roundness profile.

Watch Video on Advanced Harmonics Analysis with examples


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Spiral Harmonics on Things Like Ball Screws and Ball Nuts

Before you can measure something that is a spiral, such as a worm gear or a bull screw or a ball nut,we must make sure that we have aligned it properly. So we need to be able to measure the bull screws and bold nuts very precisely, to do that the measuring instrument must have a low noise capability, otherwise we won't be able to distinguish between the noise of the instrument and the noise of the parts themselves.

One way of verifying that is to use a Taylor Hobson harmonic standard. This harmonic standard though allows you to measure up to very high UPR and it will verify what we are seeing on spirals as well as on plain bearings.

We measure the thread harmonics around the helical shape, keeping on track at a certain point around the ball screw. This is the contact point of the ball bearings that sit in here. There's one on the upper surface as well. If we measure them separately, we can better define where the errors are coming from and so from this, we can then look at the waviness or the harmonics around the surface.

Spiral Harmonics on Ball Screws and Ball Nuts

Harmonic Analysis Software

Taylor Hobson’s advanced harmonic software enables bearings manufacturers to extract harmonic information from any rotational measurement. Results can be viewed as a full harmonic histogram with tolerance bands and pass/fail warning messages. The software allows analysis up to 5000 upr and provides a ranking system according to wave depth or harmonic amplitude. Results can be compared to CSV or GKD files.

Harmonic Analysis Software


Advanced Harmonic Standard

Taylor Hobson has developed a traceable harmonic standard for use in the bearings industry. This standard is used on Talyrond® systems, providing complete confidence in your harmonic results.

Advanced Harmonic Standard Taylor Hobson - Talyrond 500hs

•    Provides confidence in your results

•    Traceable to international standards

•    The only standard to provide 1500 upr

•    A precision machined standard with the following undulations in 360 degrees: 15 upr, 50 upr, 150 upr, 500 upr, 1500 upr


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