# What Is Roundness and How to Measure It?

## “Roundness”

In JIS B0621-1984, the definition and expression of form and position deviation, roundness is defined as “the deviation from the geometric circle of a circular body.” The representation method is recorded as “when the roundness of a circular body (C) is sandwiched by two concentric geometric circles, the minimum interval between the two concentric circles is expressed as the radius difference of the two circles (f), and the roundness is expressed in millimeters or micrometers.

For rotating components, the immediate problem to be addressed is how to evaluate their true circular shape, which begins with “roundness tolerance”

## What is “roundness tolerance”?

Roundness tolerance zone refers to the tolerance zone between two concentric circles of the same section. As shown in the figure, the extracted circumference should be limited within the tolerance zone between two coplanar concentric circles with a radius difference of t.

Why does roundness and cylindricity tolerance occur? There are usually these reasons:

• Vibration of processing machinery causing poor roundness and cylindricity;
• Deterioration of the rotating part of the processing machine leading to poor roundness and cylindricity;
• Poor shape of central hole leading to poor roundness and cylindricity;
• Roundness and cylindricity being poor due to the deformation of previous processing when grinding with centerless grinder;
• Improper holding fixture or holding method of the annular parts causing distortion of the workpiece;
• Poor roundness caused by wear, poor installation, and vibration of cutting tools;
• Deformation caused by heat treatment after finishing.

What are the methods for measuring and evaluating roundness?

## Evaluation of roundness

There are several methods for evaluating roundness, each with its own unique features and advantages. The method to use is typically selected based on the specific requirements of the workpiece.

### Simple measurement methods

Such as:

Diameter method

Roundness can be directly measured using tools such as micrometers. This method is simple and easy to perform. However, when evaluating triangle and pentagonal equal-diameter circles, it is easy to measure them as circular if they are not, leading to incorrect results.

Three point method

The three-point method can obtain roundness data through [V-block + micrometer / meter + bench].

However, the three-point method may result in incorrect measurements due to differences in the tangent line at the selected support point and difficulties in determining the center of the reference point. Additionally, errors may occur during measurement due to the up and down movement with the rotation of the object being measured.

### Measurement methods based on relevant standards

Such as:

The radius method evaluates the roundness by using the difference between the maximum and minimum radius obtained after rotating the workpiece for one cycle. As shown in the figure, the measurement results can also be easily impacted by the workpiece’s horizontal operation.

The tolerance zone is between two concentric circles on the same section

Central method

Compared with the central method, the radius method is mostly used for more precise measurement needs. The data of roundness detection depends on the reference circle. Different evaluation methods of the test circle will result in different central positions of the reference circle, thereby affecting the axial position of the measured circular feature.

• Least square circle LSC

To determine roundness, the measured contour is fit to a circle and the sum of squares of the deviation of the contour data from the circle is minimized. Then, the roundness value is defined as the difference between the maximum deviation (the highest peak value to the lowest valley value) of the contour and the circle.

ΔZ=Rmax-Rmin, symbol representing roundness value through LSC

• Minimum area circle MZC

To minimize the radial difference, two concentric circles are placed around the measured contour. The roundness value is defined as the radial interval between the two circles.

ΔZ=Rmax-Rmin , symbol representing roundness value through MZC

• Minimum circumscribed circle MCC

First, create the smallest circle that encloses the measured profile. Then, the roundness value is defined as the maximum deviation between the contour and the circle. This method is commonly used for evaluating shafts, rods, and similar objects.

ΔZ=Rmax-Rmin , the symbol of roundness value through MCC.

• Maximum inscribed circle MIC

Create the largest circle that can enclose the measured profile. Then, the roundness value is defined as the maximum deviation between the contour and the circle.

ΔZ=Rmax-Rmin , the symbol indicating roundness value through MIC.

When evaluating roundness, the obtained contour is typically filtered to reduce or eliminate the influence of unnecessary noise.

## Influence of filter on measured contour

Filtering methods and the set filtering cut-off values (UPR: fluctuations per revolution) can vary depending on the specific measurement requirements. The figure below illustrates the varying effects of filter settings on the measured contour.

No filter:

Low pass filter:

Bandpass filter:

As evaluators, what can these figures tell us?

## Analysis of measurement chart

Figure: chart of measurement results

### 1UPR component

1 UPR: only one wave is retained after filtering:

1UPR component indicates the eccentricity of the workpiece relative to the rotating axis of the measuring instrument.

The amplitude of the waveform depends on the adjustment of its level.

### 2UPR component

2UPR components may indicate:

① Insufficient level adjustment of measuring instruments;

② Circular runout caused by incorrect installation of the workpiece on the machine tool forming its shape;

③ The shape of the workpiece is oval in design, for example, in the piston of IC engine.

### 3~5UPR component

May indicate:

① Deformation caused by too tight retaining chuck on the measuring instrument.

② Relaxation deformation caused by stress release when unloading from the fixed chuck of the processing machine tool.

### 5~15 UPR component

It usually refers to unbalanced factors in the processing method or the process of producing workpieces.

### 15 (more) UPR components

15 (or more) UPR conditions are usually caused by their own causes, such as tool chatter, machine vibration, coolant transfer effect, material inhomogeneity, etc.

## Main parameters for evaluating roundness

Finally, let’s take a look at what tools and instruments are available to measure roundness?

## Common tools / instruments for evaluating roundness

Micrometer:

Roundness measuring instrument:

Coordinate measuring machine:

The space is limited, and you are welcome to leave a message and criticize the matters not covered.