There are two generally accepted reasons why manufacturers measure roundness of components. The first is to sort nonconforming parts based on a customer-supplied blueprint before shipment to the customer; the second is to control the process tool with immediate feedback.

Controlling the process tool has become the obvious method of manufacturing in the 21st century, given tight tolerances, thin profits and greater implications if a defect makes its way into a final assembly. The roundness of a component could have an effect on oil retention, oil disbursement, fuel leakage, excessive vibration, friction, as well as many other critical functions of the final assembly.

Most parts measured for roundness are produced on grinding machines. Whether using a center-less or a center-based grinding machine, there are multiple variables that require continuous monitoring. A perfect example of a constantly changing machining process is center-less grinding. A roundness result will point directly to several machine tool variables that require constant adjustment. Some examples include wheel breakdown, the angle of the regulating wheel, wheel shape, wheel composition, inbound guides and outbound guides.

Other conditions detected from a roundness measurement include harmonics, or undulations per revolution (UPR). This characteristic could indicate incorrect balancing of the grinding wheel or an incorrect feed rate.

Another common problem occurs when the steady rest, a part support located between the grinding wheel and the regulating wheel, is set too low. This has a direct impact on the tri-lobing of the part. Moreover, input chutes not perfectly aligned with the grinding path will create a barrel-shaped part.

Each of these factors has a direct effect on the final component shape as well as on the function of the component in its assembly. Using a roundness measurement machine allows one to gain an insight into the setup of the grinder by evaluating the final product.

Understanding the results of the roundness machine is critical to controlling the form of the final component.

## Basics of Measuring Roundness

**Diameter is Not Roundness**

Many incorrectly believe that it is sufficient to measure the diameter of a workpiece in several places, with the difference in readings assumed to represent out-of-roundness of the component.

**Vee-Block Method**

As with the component manufacturing process, it is the level of precision required that determines the measuring method and equipment to be used. In cases where roundness is not very critical, a simple technique is to place the part in a vee-block and rotate it in contact with a dial gage. If the part is perfectly round, the pointer of the gage will not move. The three-point method is greatly influenced by the spacing and phase of profile irregularities as well as the angle of the vee. Thus, the results obtained may not accurately reflect how the component will function, nor will they provide information useful for correction of the machine tool that produced the component.

**Measuring Roundness with a Rotational Datum**

The most accurate method for determining roundness of a component is to measure the variation of radius from an accurate rotational datum using a scanning probe. The probe must be one that remains in contact with the surface and collects a high density of data points. A circle can then be fitted to this data and the roundness calculated from knowledge of the component center.

There are many dedicated instruments made for the measurement of roundness. The most common configuration is a system that contains a rotating table onto which the component is mounted. A gage is mounted on a radial arm, which can be adjusted to bring the gage into contact with the component. The arm itself is mounted on a column that permits the height of the measurement plane to be adjusted.

The linear axes of such instruments are often motorized and of high form accuracy, enabling the instrument to be used to measure other parameters such as flatness, straightness and cylindricity.

**A Picture of the Results is Not Enough**

It is convenient to represent the radial variations output from the gage as a polar profile or graph. Roundness deviation can be determined by placing a template over the graph and visually centralizing the profile. Then the highest peak and deepest valley are identified and the distance between the two is measured. This method is dependent on operator skill and prone to errors.

**Modern Instruments**

First, the old template has been replaced with a computer-generated reference, or “perfect,” circle. Because this circle is derived from the actual measured data, it is possible to mathematically calculate departure of the measured profile from its reference circle. In this way one can numerically and reliably describe an out-of-round condition.

**RONt, RONp and RONv**

The roundness total (RONt) parameter is the most commonly used parameter. It is the maximum deviation inside and outside the reference circle, and is the sum of the roundness peak (RONp) and the roundness valley (RONv), which are companion parameters. All roundness parameters are based on deviations from reference circles and the results will vary depending on the reference circle chosen.

**Why are Reference Circles Important?**

When measuring roundness there are some settings to be aware of. The data collected will obviously be used to make changes to the manufacturing process and as such the filters as well as the reference circle will need to be set to output the data with relevance to the process.

## Reference Circles

Roundness compares measured data with a computer-generated reference circle. Roundness systems have four methods for comparing the measured data to a reference circle for evaluation. It is important to note the reference circle used should be related to the function of the finished component. The final numeric roundness result will be different with the different reference circles applied, so make sure the blueprint accurately reflects the desired result.**Least squares reference circle (LSCI)**is the most commonly used reference circle. A line or figure is fitted to any data such that the sum of the squares of the departure of the data from that line or figure is a minimum. This also is the line that divides the profile into equal minimum areas. Out-of-roundness is then expressed in terms of the maximum departure of the profile from the LSCI, the highest peak to the lowest valley.

**Minimum circumscribed circle (MCCI)**is defined as the circle of minimum radius that will enclose the profile data. The out-of-roundness is then given as the maximum departure of the profile from this circle. MCCI is sometimes referred to as the ring gage reference circle.

**Minimum zone reference circles (MZCI)**is defined as two concentric circles positioned to enclose the measured profile such that their radial departure is a minimum. The out-of-roundness value is then given as the radial separation of the two circles.

**The maximum inscribed circle (MICI)**is defined as the circle of maximum radius that will be enclosed by the profile data. The out-of-roundness is then given as the maximum departure of the profile from this circle. MICI is sometimes referred to as the plug gage reference circle.

## Roundness Parameters

**Eccentricity (ECC)**is the term used to describe the position of the center of a profile relative to some datum point. It is a vector quantity in that it has magnitude and direction. The magnitude of the eccentricity is expressed simply as the distance between the profile center (defined as the center of the fitted reference circle) and the datum point. The direction is expressed as an angle from the datum point.

**Concentricity (CONC)**is similar to eccentricity but has only a magnitude and no direction. The concentricity is defined as the diameter of the circle described by the profile center when rotated about the datum point. It can be seen that the concentricity value is twice the magnitude of the eccentricity.

**Runout (Runout)**is defined as the radial difference between two concentric circles centered on the datum point and drawn such that one coincides with the nearest and the other coincides with the farthest point on the profile. Runout is a useful parameter in that it combines the effect of form error and concentricity to give a predicted performance when rotated about a datum. Runout is sometimes referred to as total indicated reading (TIR).

## Introduction to Harmonic Analysis

A basic understanding of harmonic content is essential in choosing the optimum analysis conditions, particularly in relation to the choice of filters. A fundamental understanding also is invaluable in terms of identifying the root cause of certain shapes in either the manufacture or the measurement of a workpiece. Harmonic analysis is, however, an advanced topic and will be discussed only at a qualitative level in this article.**Frequency = Lobing = Undulations per Revolution (UPR)**

Looking at real-life roundness graphs it is clear that information exists in the data at different frequencies. A classic example is ovality, which indicates an irregularity that occurs two times in one complete revolution. The workpiece would be said to have two lobes or two UPR. An even or an odd number of lobes may be present on a component, with either condition contributing to problems of fit with mating components. High-order lobing, often caused by chatter, vibration and processing marks, is generally more important to function than to fit of a component.

**Methods of Measurement and Analysis**

Rotational methods of measurement are effective for both odd and even lobing conditions as well as low and high UPR. Modern instruments can detect frequencies from 1 UPR to more than 1,000 UPR. Roundness data is particularly suited to harmonic analysis because it is repetitive.

Starting with low UPR and moving to higher UPR enables many factors of out-of-roundness to be investigated. For example, instrument setup, workpiece setup, machine tool effects, process effects and material effects can be evaluated.

**The Effects of Filters**

Roundness measurements always contain imperfections at a number of different UPR. Filters are used to isolate frequencies or ranges of UPR to enable detailed examination of individual effects of machining defects and component function. Filters can be arranged to remove all information above or below a certain frequency. Lowering the number of UPR will filter the data more heavily. The choice of filter will depend on a variety of factors but many components will call for one to 50 UPR. Internationally accepted filter cut-offs are 15, 50, 150, 500 and 1,500 UPR.

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