# Accurately Measuring the Ball Center to Ball Center Length of a Ball Bar

## Temperature Stability- of the Measuring Machine

It will take a full 48 hours for the large volume of the Pratt and Whitney measuring machine, to “equilibrate” ( thermally stabilize ). At first this may seem like a fault, but it actually contributes dramatically to the accuracy of the measurement, because it effectively averages all of the short term perturbations of the room temperature. The air conditioner must be set at 68°F and left on for a full two days before any attempt is made to measure.

## Compensation

This Cast Iron measuring machine will change size 6.4 millionths of an inch per inch per degree Fahrenheit. After a two day soaking period, the actual temperature of the measuring machine frame is measured. If for instance the temperature of the frame is plus 1°F and you are measuring a 10 inch long ball bar, you multiply the expansion and contraction rate of 6.4 micro inches by 10 to get the correction.

Assuming a Plus temperature, the correction that you would apply to the measuring machine will be 64 microinches. It is plus so you would subtract 64 microinches from the measured length of an Invar Ball Bar. If you are measuring a steel Ball Bar which has the same 6.4 microinches, per inch per degree Fahrenheit, thermal coefficient of expansion that the cast iron does, the Ball Bar is at the same temperature as the measuring machine; and there is no compensation required.

## Correcting Elastic Deformation

One of the most significant problems in making an accurate calibration of a Ball Bar is to compensate for all of the Hertzian elastic deformations involved due to the measuring force being applied to the balls. Each side of the ball will be somewhat flattened and each one of the flat measuring surfaces will be somewhat dimpled by this measuring force. This very complicated situation will go away entirely, by simply setting the machine to zero, while measuring one of the actual Ball Bar Balls. What you effectively do is to subtract two ball radii, along with all four of the elastic deformations from the overall measurement.

As a question that is often asked is, “how much shorter will the Ball Bar measure due to the effect of the measuring force squeezing the long length of the Ball Bar?” The answer is that there will be no measurable change.

## The International Inch

In the 1960’s they rounded off the International Inch, making it equivalent to 25.4 mm exactly. What this did in effect was to shorten the “New International Inch” by 2 millionths of an inch per inch. If you use old measuring equipment to measure with, you must subtract 2 micro inches from each inch of length measured. If a Ball Bar measures 10 inches exactly, you would subtract 20 micro inches from the reading, so the actual corrected length of the Ball Bar would be 9.99998.”

## Mechanical Alignment of the Ball Bar

It is imperative that the axis defined by the centerline between the two balls, be coincident with the linear axis of the measuring machine. To do this, one end of the Ball Bar, must be raised and lowered to find the longest distance. Then it must be moved forward and back to find the longest distance in that direction. To put it another way, you must find the high point up and down and in and out.

When doing this exercise, it is good practice to lubricate the end of the ball. You are basically measuring the high point of a long arc, so the movements are not that critical. You are moving the Ball Bar thousandths of an inch to change the reading millionths of an inch.