MEGR 6181

ENGINEERING METROLOGY

MEASUREMENTS OF ROUNDNESS

RAJESH PATEL

1.INTRODUCTION: Probably one of the biggest challenges a mythologist can encounter is measuring roundness. Unlike measurement of length, width and height, roundness measurement requires a much thorough knowledge of dimensions, features and their relations to the measuring instruments in all three dimensions. While in many of today’s instrument sue of computer technology to automate much of the roundness measurement process, not everyone has access to a computerized instrument. Whether the instrument you use is the latest computerized instrument or an older conventional machine, a thorough understanding of roundness and roundness measurements is essential to obtaining accurate and repeatable results. Roundness measurement needs can range from quick and dirty to extremely high precision. At the quick and dirty end of the spectrum, one can use basic measuring tools to roughly approximate the out of roundness of the specimen. The easiest way to do this is by measuring the diameter with caliper, micrometer or bore gauge. The highly precision measurement of object requires high precision spindles, precise inductive gauges and computerized data processing systems. Depending upon the technique used to measure the roundness, roundness measuring methods can be categorized as (A) Intrinsic Datum Method and (B) Extrinsic Datum Method. The main difference between these two methods is the datum surface from which the measurement is made. 2. METHODS OF ROUNDNESS MEASUREMENTS: 2.1. INTRINSIC DATUM METHODS. In this method points on the surface of the object are used as the datum. These methods are widely used in industries to for productive works. Diametrical measurement, V-block method and bench center method are the example of intrinsic datum method. In the selection of these method the lobbing pattern on the surface of the object play an important role. These methods will not supply the information in complete agreement with the standard circularity standards. Intrinsic methods are very convenient for approximation of the true out of roundness value and require law investments. 2.1.1. DIAMETRICAL MEASUREMENTS. This is a two points measurement method. In this method measurements are made in a common cross sectional plane. Measuring minimum and maximum sizes at various locations can approximate the roundness.

Fig.1 Diametrical method Source :Qualitymag.inc.

This method can only determine the out of roundness value when the part is having even number of lobes. Parts having even lobes, surface will produce out of roundness value larger than the true value. For uniform and symmetrically shaped surface the difference between the true value and measures value will be zero. For parts having an odd lobes the measured value will be smaller then the actual value. Calipers, micrometers, bore gauges and air gauges are used for diametrical measurement. 2.1.2. V- BLOCK MEASUREMENTS.

Gage tip V-Block

Fig.2 V-Block method This is a three points measurement method. This method is only suitable for the parts having an odd number of lobes. The part is placed in a v block and indicator gauge is mounted such that the tip of the gauge can make a contact with the surface of the part. The part is rotated slowly. If the part is perfectly circular the pointer of the gauge will not move. But if the part is out of round the irregularities will cause the indicator to move. The indicator will move depending upon the height and angular spacing of the lobes as well as the angle of the V block. The total indicated reading (TIR) represents the difference between maximum and minimum size. A conversion factor is used to measure the out of roundness from the TIR readings. The included angle of the v block can determine by using following equation.

A = 180 – ( 360 / n )

Where, A = included angle of the V block n. = Number of lobes Table 1. gives the conversion factor and included angle for the odd number lobes that are checked with the proper v block.

TABLE 1

NO OF LOBES INCLUDED ANGLE CONVERSION FACTOR 3 60 3.000 5 108 2.236 7 128 .34 2.110 9 140 2.064

2.1.3. BENCH CENTER MEASUREMENT: This method is only suitable for the parts that are manufactured with machine centers. Part is mounted as shown in fig and the indicator is in contact with the surface. The part is rotate slowly and the indicator will give the different reading depending upon the surface condition. The out of roundness can be calculated by applying the conversion factor to the maximum difference in the indicator reading.

Fig.3 Bench center source : Geneva gage.inc

The reliability of this method is depend upon so many factors such as angles, alignment of part, roundness, surface condition of centers and center holes. Anyone parameter or combination of all parameters can cause a high degree of uncertainty in the measured value. 2.2. EXTRINSIC DATUM METHOD. In this method an external member is used as a reference datum. This method is used for very high precision measurement. High precision spindles, high precision probes and computerized data processing system is used to measure the out of roundness. In this method the parts can be

rotate with precision spindle or it can be keep stationary depending upon the size of the part and the instrument used for the measurement. 2.2.1.ROTATING WORK PIECE TYPE PRECISION SPINDLE: This method uses a precision spindle to rotate a work piece and a fixed inductive gage head to monitor circular deviations of the work piece form. (As shown in fig.)

Fig.4 Rotating work-piece type spindle source : Mahr, Corp.

Early machines used a simple chart recorder to plot the graphs. Current machines use dedicated processors or computers to monitor and analyze the gage head signal. Modern electronics have made the inspection process simple and comprehensive but the heart of roundness machine is the precision spindle. Roundness errors in the spindle have the greatest influence on the measurement results. Most of the equipment manufacturers offer roundness machines with spindle deviations less than 0.000003 in or 1.5 min (departure from the nominal least square circle) SPINDLE Spindle can run on either air or mechanical bearing. Air –bearing spindles are typically less expensive than mechanical bearing in the same accuracy range but require connection to an air supply and regular maintenance. Care must be taken to ensure that the air supply is clean, dry, and of constant pressure. Moister and dirt will contaminate the bearing and can lead to failure. Variation in air pressure can cause vibration or friction. Dynamic load capacity is another factor to consider. Mechanical bearing spindles do not require air supply or maintenance program, but are typically more expensive than air bearing spindles. The precision spindle is always concealed in the base of the roundness machine. Attached to the spindle is a rotary table used to stage the part to be measured. This table is also used to align the work piece axis to the spindle axis, a process called center and tilt correction. Consider the

spindle to be theoretically perfect reference datum and work piece is aligned properly, then all circular deviations detected by the gage head will represent out of roundness. Improper alignment with the spindle causes the work piece to rotate on an elliptical or eccentric path. In this case only some measured deviations can be attributed to the part and the out of roundness value may be incorrect. Most low to middle range roundness and formatting machines will have knobs for manually correction center and tilt alignment. Automatic, motor-driven center and tilt correction is available on higher form testing machines. Older machines relied heavily on an operator’s ability to tap a work piece into alignment. New equipment will usually include a computer-aided routine that guides an operator through the alignment process. INDUCTIVE GAUGE The inductive gauge is a simple electromechanical device that measures in two directions. A process unit records the amplitude and frequency of undulations and converts the data into information about the roundness, shape, or form of work piece. For circular measurements the gage head is normally held stationary while the part is rotated. Typically a vertical column with a horizontal arm is used to hold the gage head and to provide a means of adjustment to suit different work piece heights and diameters. On roundness machines the vertical and horizontal axis are the positioning only. Such machines are relatively inexpensive but can be assess only roundness, coaxiality, concentricity, and run out. To evaluate non- circularity or relational form features, a form-testing machine is required. Form testing machines, with a vertical reference axis, can, in addition to roundness features, be used to measure straightness; parallelism, conicity, angularity, and total radial run out. Most of the manufactures offer more than one type of gage head. Be sure to select one that can handle your application. Look for an adjustable gauging force feature if you have thin-walled, soft, or small diameter parts. If the work piece has interrupted surfaces, consider adjustable pre-level to avoid damaging the probe tip or gauge head. Select a gauge with measuring range to handle worst-case alignment problems. 2.2.2. ROTATING –PICKUP TYPE: In this method a work piece is fixed on the table and the inductive gauge head is rotate on the periphery of the work piece to measure the surface profile.This method is useful for the work-pieces having larger diameter and it is difficult to rotate them. ( Fig. 9 ) 2.3. ADVANTAGES OF EXTRINSIC DATUM METHOD: It gives the true image of the geometric condition of the part by selective magnification. Continuous tracing around the entire surface in the selected plane minimize the possibility of disregarding errors that can be missed by point-to-point measurement. The graphical representation is valuable for thorough analysis and serves as a permanent record.

2.4. The polar graph plotted by the extrinsic datum method can be interpreted by the following four methods. 1.MINIMUM RADIAL SEPARATION.

In this method two concentric circles are chosen on the polar trace such that they have the least radial separation and still they contain the profile of circle between them. The radial separation is the measure of out of roundness.

Out of round ness

Fig. 5 Minimum Radial seperation method The proper location and size of inscribed and circumscribed circles are most conveniently determined by printed or engraved circles on transparent templates. This method requires at least two inner and two outer points for one complete profile traverse. 2. LEAST SQUARE CIRCLE METHOD: A least squares fit of points on the trace to a circle define the parameters of non-circularity of the work piece. A diagram of the measurement method is shown below.

Fig. 6 Least Square Circle Method

Source : Engineering Statistics Handbook

Y = the distance from the spindle center to the trace at an angle θ R = Radius of the circle P = Distance from the center of the circle to the trace. Some measurement of roundness does not require a high level of precision. For that part a single trace covering exactly 360° is made of the work piece and measurements, Yi, at anlges, θ i. Of the distance between the center of the spindle and the trace, are made at

θ i. {i. = 1,… N}

equally spaced angles. A least square circle fit to the data gives the following estimates for the parameters R = 1/N ( ∑ Yi. ) a = 2/N ( ∑ Y i.* cos θi. ) b = 2/N ( ∑ Yi. Sin θi. ) The deviation of the trace from the circle at angle, θi., which defines the non-circularity of the work piece, is estimated by: ∆ = Yi. - R-a cos θi. - b sin θi. 3. MAXIMUM INSCRIBED CIRCLE (MIC): In this method the profile center is determined by the largest circle that can fitted inside the profile. This center can be determined by trial and error method with the help of compass or transparent template. The maximum outward departure of the profile from the inscribed circle is taken as the out of roundness. Out of round-ness Out of roundness Fig.7 MIC Method Fig. 8 MCC Method 4. MINIMUM CIRCUMSCRIBED CIRCLE( MCC ): In this method the profile center is determined by the smallest circle that contains the profile. The center can be determined by similar method used for MIC.The maximum inward departure from the circumscribed circle is taken as the out of roundness.

3. ROUNDNESS MEASUREMENT SYSTEMS: 3.1. INDI-RON GT-50

Fig. 9 Indi-Ron Gt 50 source : Precision Devices Inc.

Components of the system include a portable bench top unit, including air spindle, mounted on a 16” x 20” granite surface plate, constant speed motor drive, Type CT8 centering table (2 axis non tilt) The system is versatile 18” height stand permits easy measurements of the part features, and a high quality granite surface provides an accurate datum around 8” centering table. Specifications:

Measure and charts Out of roundness, concentricity,coaxiality,squareness,cylincricity

Measurement datum Air bearing Radial accuracy +/- 2.5 micro inch Departure from Least square +/- 1.5 micro inch Rotational speed 4 RPM Capacity Part swing Part height

100 lbs 20 inch 24 inch

Weight 120 lbs Power 150 V 60 Hz 120 W

* IndiRon 100 and IndiCorder are other popular product for measuring out of roundness.

3.2. NPL ROUNDNESS MEASUREMENT SYSTEM:

Fig. 10 NPL Roundness measurement System source : National Physical Laboratory.Inc

NPL provides a high accuracy service for measuring out of roundness of spheres and hemispheres up to 100 mm in diameter. This service, which is primarily intended for the measurement of glass hemispheres used to calibrate roundness measuring instruments that is specially developed in collaboration between NPL and Taylor Hobson. Principle of operation: The fundamental basis of the instrument’s design is to use a spindle with a highly reproducible rotation and then use a novel error separation technique to reduce significantly the errors associated with the lack of perfection of the spindle geometry. The instrument used to make the measurement is capable of collecting 2000 points per revolution. In operation , the component to be measured is placed on a rotary stage and data collected at several orientation of the stage. The Fourier-series representation of each measured trace is determined. The mathematical model which relates the the Fourier representations of the component errors and the spindle errors to those of the trace is then solved. The resulting Fourier representation of the component error is used to determine the roundness of the component and to provide values of the component error at points around the circumference. Specifications:

• Measurement of roundness profile of spheres and hemispheres up to 100 mm in diameter. • Roundness measurements traceable to the national standard of length

• NPL certificate of calibration stating the departure from roundness and the radial variations at fifty points around the circumference of the component under test.

• Graphical plot of the radial variations. 3.3.PAPER ROLL OUT OF ROUNDNESS MEASURING DEVICE :

Fig. 11 Paper Roll out of roundness measuring system

source : Auramo,Inc. The spider uses micro processing and ultrasonic sound technology to measure the roundness of a paper roll without destroying the integrity of the roll or roll wrapping. Test results can be viewed on a LCD or directed to a DOS system printer or a computer disk foe further analysis. The lightweight, compact unit’s measurement process is extremely easy. Its aluminum frame is placed on the top of the paper roll and secured with three expandable legs without damaging the wrapping. Precise positioning is not critical. Any misalignment between the centerline of the roll and the unit will be automatically compensated by the analysis program. After fitting the unit, a transducer is rotated around the roll. The distance between the transducer and the roll is than measured at four-degree intervals at an average accuracy of 0.004 inches. A stored data as analyzed by the push on one button, and the out of roundness is displayed on the LCD.

4. PARAMETERS INFLUENCING THE ACCURACY OF ROUNDNESS MEASUREMENT : 1.POOR CLAMPING ARRANGEMENTS: How the part is staged on a turntable can have an influence on measurements. The common three-jaw chuck can deform the thin walled parts so they appear to have a three lobed condition when gagged.

2. INATTENTION TO CENTERING AND LEVELING Centering and leveling are critical elements of a gage setup procedure. A round part that is not level will produce oval measurement trace, while one that is significantly off center on a spindle will produce a heart shaped trace. Even if a gage turntable is equipped with a holding fixture for a particular part, an operator should run a centering and leveling program before measuring. 3.DATUM PROBLEM A part print may specify a tolerance for a geometric relationship between features and fail to specify which features should be used to establish a datum. Ideally a part designer should select a datum, but designers are not always aware about the capabilities or limitations of geometry gauging systems. Specifications are then written that are immeasurable in practice. 4.RISKY RELIANCE ON FILTER DEFAULT VALUES Any part measurement exhibits variation resulting from several influences. The part’s true form is influenced by variable in the manufacturing process, including clamping and tool chatter. Added to these are variables introduced by the measuring process itself, including set up accuracy, part clamping on the turntable and environmental influences. Each influences produces a pattern on the trace of the part surface that the gage gnerate. Bad leveling will make a part to have a two lobed condition. The dynamic of center less grinding process typically impose an odd number of undulations per revolutation (UPR) of the part. Bearing vibration of the machine tool spindle might add a larger number of undulations. Geometry gages incorporate electronic filters to simplify the trace by elimination undulations that apper outside certain desired frequency bands. The ANSI B89.3.1 standard establishes 50 UPR as a default value for measurements of out of roundness. When a 50 UPR filter is engaged undulations that occur at frequencies above 50 UPR are filtered out. Use of this filter is appropriate for many but not for all applications. Some rotating parts may produce undesirable noise if higher frequency undulation exceed certain amplitudes, so it may be necessary to filter gauged data for up to 150 or 500 UPR or even to analyze gage data without electronic filtering. A part designer should define the frequency filter to be used, based on the functional need of the applications. 5. USING THE WRONG STYLUS TIP. The stylus tip represent the s a mechanical filter that must be selected according to part diameter and the maximum number of undulations per revolutions relative to the application. If the radius is too large, it will bridge over small irregularities. Larger tips will exert less pressure against a part, which may be a concern when measuring very sensitive surfaces. New ANSI and ISO draft standards specify the stylus tip as a function of both part diameter and number of undulations per revolution that can be measured. 6.Using the wrong reference circle: Out of roundness is measured by comparing profile irregularities to a gage spindle axis of the rotation by means of one of the four reference circle methods discussed as earlier. All four methods are described in ANSI B89.3.1. Results generated by these four methods can differ by as much as 10-15 percent when evaluating the same profile.

Today, PC driven geometry gages offer all four methods. Part designers should specify the method best suited to the application. 7. CONFUSION OVER SCALING EFFECT. The trace of a roundness measurement as shown on a gage’s computer screen or a chart print out, rarely looks “round”. It usually looks like a mass of sharp peaks and valleys. This can distress users who believe that the chart shows terrible part geometry. A gage applies a different level of magnification to the size of part than it applies to a deviation from the ideal geometry being measured. This may involve a low level of magnification for small parts or even a reduction in scale for large parts. Deviation is highly magnified from 1000X to 2000X or more. Geometry gages allow the user to select a magnification level. Even though the computer’s trace does not accurately depict the part’s actual profile, the relations between peak heights and valley depths remains consistent with the level of magnification chosen. Peaks and valleys also retain accurate angular relationships to one another around the circumference. 8. IGNORING THE ADVANCED GAGE FUNCTIONS. Advanced metrology software can tell a user much more than simply wither a part is within tolerence. While simply isolating bad parts may be a worthwhile task in some applications, skilled QA technicians can subject parts to more in depth analysis to find out what is wrong in a production process, to identify ways to correct it, and to predict the performance of a bad part if it is installed. *Slope analysis is an advanced analysis feature in some geometry gauging software. In part geometry, slope is the rate of change of the radius with respect to the angle of rotation. The maximum difference between the longest and the shortest radius on a roundness trace (measured out of roundness) might be “ x “ for a given part. If the longest and shortest radii occur within just a few degrees of rotation of one another, the slope connecting the two points on the circumference will be steep (the other hand, if the longest and shortest radii occur diametrically opposite one another, the slope will be gradual). A given amount of out of roundness might be acceptable in some applications where the slope is gradual but unacceptable if the slope is steep. Harmonic analysis is an advanced feature available in some geometry software that allows analysis of individual, predominant numbers of undulations per revolution. While filtering techniques allows a user to view the effect on out of roundness of several undulations within a relatively broad frequency, harmonic analysis allows a user to focus on a single harmonic or frequency. Yet the vary high degree of sophistication in geometry gages that allows a diminished expertise level of an operator still requires a user’s sound understanding of a gage’s capabilities and limitations to obtain optimum results.