# Ball Size Measuring Compatibility

The main problem that we face in achieving customer compatibility on ball size measurement is educating those customers who have unrealistic expectations as to their ball measuring capability. As cold as this may sound, measuring precision balls presents some totally unique problems.

The first and a very important step in any metrology situation is to develop a realistic error budget for the entire gauging system. Just because a gage reads out in increments of ten micro inches. (.25 micrometers), does not mean that you can accurately measure ten micro inches. (.25 micrometers) with it. Our every day shop gages read out in increments of two micro inches. (50 nanometers) and our laboratory master gages read out to two tenths of a micro inch (5 nanometers). With the large number of factors that are involved, however we are only absolutely sure of our commercial ball diameter measurement to ten micro inches. (.25 micrometers).

In the old days, there was the ten to one rule for gages, which basically states that the gage must be ten times more accurate than the measurement you expect to make with them. As tolerances have shrunk over the years this ten to one rule has been relaxed, so today we have the three to one, or the four to one rule, but whatever the realistic ratio, it is never one to one.

A list of customer measuring problems starts with the number one problem, which is not properly correcting for the Hertzian elastic deformations due to the gauging force. When the contact forces of the gauging members are applied to the two surfaces of the ball, the spherical shape of the ball will penetrate the measuring surfaces of the gage to some degree. At the same time the ball is penetrating the measuring surfaces, these surfaces will cause both surfaces of the ball to flatten. The resultant amounts of these four elastic compressions are substantial, and it is very complex to calculate the corrections for these deformations.

The next most common problem is geometry errors of the measuring surfaces. Flat, parallel measuring surfaces are the best possible geometry for measuring balls, but getting these surfaces truly flat and parallel is no simple task. The flat parallel conditions can be evaluated by measuring the diameter of an ultra precise, small diameter, tungsten carbide ball. Measure the ball in the front, at the back, at the top, on the bottom and in the center. To simplify this task the ball is mounted on a long stem like handle.

This problem is followed by the inaccurate mastering of comparator gages. The best master for a comparator gage is a ball of the same size and material as the ball to be measured. The problem here is to get a really round ball with a good surface finish that has been accurately calibrated. At the present time N.I.S.T. is the only reliable U.S. source for this calibration. The alternative is to use gage blocks to master the comparator gage. This approach opens another bucket of worms. A new set of elastic deformations are involved. There is also the problem of selecting and wringing the gage blocks as well as their original calibration. (See our paper on "Handling Gage Blocks".)

Still in the top standing of problems is temperature variation from the international standard. The ball the gage and the environment must all be at exactly 68 degrees Fahrenheit i.e. 20 degree Centigrade or complex corrections of questionable accuracy must be made.

Why temperature and what temperature? All know but few really understand the effect of temperature. The ball to be measured may be small in diameter but the gage and the stand are not. All elements of the gauging system and the subjects must be held stable and at the standard metrology temperature.

Many years ago the international measuring community established 68 degrees Fahrenheit or 20 degrees Celsius as the common measuring temperature. Every material changes dimensional size with variations in temperature. There are some wonderful materials such as Invar and Zerodur ® that have thermal coefficients of almost zero and carbon, which actually has a negative expansion when heated, but most engineering materials change size considerably with temperature.

The next factor is that a gage must have excellent repeatability to even be considered for measuring ball diameter. The fact that a gage will repeat to a given level of accuracy does not however mean that it is accurate to that level.

In most cases there is not a single cause of measuring error but a combination of these different factors that can often add up to be a huge overall error budget.

Adding the errors in quadrature or taking the square root of the sum of the squares of the maximum individual errors is a simple quick and painless way of quantifying the overall effect of the individual errors on the uncertainty of the measurement. This may be an over simplification of the problem but it will give a close estimation that can then be multiplied by some safety factor for practical use.

At an international measuring conference, one of the national laboratories presented a paper on measuring thread wires.

They built four state of the art measuring machines. All four machines were based on the very best fundamentals of physics. Each machine had nanometer resolving capability but each machine used slightly different basic design features and methods of resolving the end point. All four machines were used to measure the same artifact. The resultant readings were all plotted on a single chart. Each one of the machines had a measurement distribution or error cloud that amounted to only a very few nanometers. The problem was that the error clouds for all four machines were distributed across several micro inches. Which machine measured the true diameter? Who is to say?

Should the readings be averaged? If four more machines were built would they have the same characteristics as the originals?

If the original machines were shipped to a new lab 1000 miles away how would they read? No matter how deterministic you may be or rather your system may be, no two gages will read the same subject to exactly the same value. Even two identical gages may not read the same subject to the same value. Now take two different gages into two different locations in two different environments with two different technicians; and try and imagine how much the two measurements will differ even under the best of circumstances. I have seen the results of international round robins that have been conducted among prominent metrology institutions. In some cases you would think that they had to have been measuring different subjects, because the spread of their readings were so great.

To add another dimension to the problem, where does the surface texture of the subject end and the actual body of the part begin? If our subject ball has a pretty decent one- micro inch (25 nanometers) Ra surface finish, it will have a peak to valley of at least three micro inches. (75 nanometers) and may be as much as five micro inches. (125 nanometers). The Ra surface finish on a high grade commercial ball is one and one half micro inches. (37.5 nanometers), so now we are talking about four and one half (112.5 nanometers) to seven and one half micro inches. (175 nanometers) on both sides of the ball when it is being measured. If this isn't bad enough, what about the surface texture of the measuring surfaces of the gage?

How do we factor in the sphericity errors of the ball? Why not take a lot of measurements and average them. What we find is that time is a very serious enemy to high quality metrology. Gage drift during the time it takes to make a lot of measurements will probably be your undoing. Unless you have a fully robotic setup, which totally excludes the technician from the gage environment, making many measurements will introduce more error than you can live with. To further complicate this matter the common geometry errors imparted to balls by the ball making process are almost always in an odd number of lobes, most often three. No amount of measuring with a two-point gage will even detect these errors.

When we at Bal-tec are making serious measurements, we use a measuring machine that is constructed entirely of Invar. The laser scale on this instrument reads out directly in two tenths of a micro inch increments and the machine is semi robotic. The only problem is that this machine costs over \$50,000.00 to construct; and it will only measure a moderate size range of balls.

As you may have read in other of our papers, we feel that you should make three exactly orthogonal measurements and arithmetically average them. The point here is that all balls are somewhat out of round at best and how the variations caused by this condition are factored into the final size measurement can substantially skew the ball diameter reported.

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