What Is Roundness and How to Measure It?

In the manufacturing industry, it has been estimated that there are more circular workpieces than flat workpieces, ranging from screws, nuts, gaskets, to cylinders and bearings.

The application of circular workpieces is indeed very high.

Today, I’d like to talk about the topic of “roundness” in the field of measurement (reference standards: ISO/DIS 1101:2017, ISO 5459).

Roundness

“Roundness”

In JIS B0621-1984, definition and expression of form and position deviation, roundness is defined as “the size that deviates from the geometric circle of a circular body“.

The representation method is recorded as “when the roundness is 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 with (f), and the roundness is expressed as mm or μm.

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For rotating components, the problem that needs to be urgently solved is usually how to evaluate their true circular “shape”.

This is about to start 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 following figure, the extracted circumference should be limited within the tolerance zone between two coplanar concentric circles with a radius difference of t.

Roundness tolerance zone

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

  • Poor roundness and cylindricity caused by vibration of processing machinery;
  • Poor roundness and cylindricity caused by the deterioration of the rotating part of the processing machine;
  • Poor roundness and cylindricity caused by poor shape of central hole;
  • When grinding with centerless grinder, the roundness and cylindricity are poor due to the deformation of previous processing;
  • Distortion of the workpiece caused by improper holding fixture or holding method of the annular parts;
  • Poor roundness caused by wear, poor installation and vibration of cutting tools;
  • Deformation caused by heat treatment after finishing.

How to measure and evaluate roundness? What are the methods?

Evaluation of roundness

There are many roundness evaluation methods, each of which has its own characteristics and advantages.

Usually, we will choose according to the needs of the workpiece.

Simple measurement methods

Such as:

Diameter method

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Read the diameter of roundness directly through micrometer and other measuring tools.

This simple measurement method is very simple and easy to operate.

However, when evaluating triangle and pentagonal equal diameter strain circles, it is easy to be incorrectly measured as a positive circle if it is not a positive circle.

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Three point method

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

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However, the tangent line at the support point selected in the three-point method is different, and it may not be measured correctly.

The center of the benchmark cannot be determined, and the up and down movement with the rotation of the measured object will produce errors.

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Measurement methods based on relevant standards

Such as:

Radius method

The radius method uses the difference between the maximum radius and the minimum radius obtained by rotating the workpiece for one cycle to evaluate the roundness.

As shown in the following figure, the measurement results are also easily affected by the horizontal operation of the workpiece.

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

Central method

Compared with the central method, it 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 lead to different central positions of the reference circle, so it will affect the axial position of the measured circular feature.

  • Least square circle LSC

By fitting a circle to the measured contour, the sum of squares of the deviation of the contour data from the circle is minimized, and 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

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  • Minimum area circle MZC

Two concentric circles are positioned to surround the measured contour to minimize the radial difference.

The roundness value is defined as the radial interval between the two circles.

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

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  • Minimum circumscribed circle MCC

Create the smallest circle that surrounds the measured profile.

Then the roundness value is defined as the maximum deviation between the contour and the circle.

It is often used in the evaluation of shafts, rods, etc.

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

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  • Maximum inscribed circle MIC

Create the largest circle that can surround 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.

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In the process of evaluating roundness, in order to reduce or eliminate the influence of unnecessary noise, the obtained contour is usually filtered.

Influence of filter on measured contour

According to different measurement requirements, the filtering methods are also different, and the set filtering cut-off values are also different. (upr: fluctuation per revolution), as shown in the figure below, we can see that the influence of filter setting on the measured contour is different.

No filter:

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Low pass filter:

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Bandpass filter:

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As evaluators, what can these figures tell us?

Analysis of measurement chart

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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.

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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.

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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.

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5~15 UPR component

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

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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.

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Main parameters for evaluating roundness

ParameterMeaning
RONtThe measured value of roundness represents the difference between the maximum value of positive roundness curve and the minimum value of negative roundness curve or the sum of absolute values.
RONpThe measured peak height of roundness curve represents the maximum value of positive roundness curve.
RONVThe measured value of roundness represents the absolute value of the minimum value of the negative roundness curve.
RONqThe double root mean square roundness measurement represents the double root mean square of the roundness curve.
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Finally, let’s take a look at what tools and instruments are available to measure roundness?

Common tools / instruments for evaluating roundness

Micrometer:

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Roundness measuring instrument:

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Coordinate measuring machine:

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

Conclusion

After reading this article, I believe you must have a deep understanding of roundness. If you have any other questions, please leave a message in the comment area.

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