# Length Calibrated Ball Bars — Calibrated Length Ball Bars

There are three things that are more or less secrets to accurately calibrating and using a Ball Bar as a length standard for C.M.M. evaluation. I am guilty of not disseminating this information until now, because I have worries about its misuse. There are three issues involved in this calibration and use equation.

1. The first is the monumental problem of compensating for all of the Hertzine elastic deformations involved in calibrating a ball bar. The elastic deformation uncertainties involved in measuring the absolute diameters of the two balls and then compensation for all four of the hertzine elastic deformations caused by the force applied by the length measuring machine itself affects the results from using conventional methods of measuring the length of a Ball Bar, making the measurement very uncertain.

After fifteen years of trying to cope with all of the problems involved in measuring the absolute length of a Ball Bar, I woke up one morning with the realization of how all of these uncertainties could be eliminated in toto. The two balls used on the Ball Bar are manufactured round and absolutely the same diameter. The two balls are simply manufactured in the same machine at the same time.

The new measuring technique starts out with the same conventional length measuring machine, and with whatever force the machine happens to apply. How much measuring force is used or even knowing what the actual measuring force is, is no longer of any importance.

Using this new technique, the length measuring machine is set to “zero,” while actually measuring either one of the two balls on the Ball Bar. Now the machine is simply moved out or opened up to measure the full length of the Ball Bar. All of the Hertzine elastic deformations (whatever they are) are automatically factored out because exactly the same deformations occur when the entire Ball Bar is measured as when the original measurement was made on one of the balls alone. One exact ball diameter is automatically subtracted from the overall measurement, so the measured length is the exact ball center to ball center dimension.

This methodology will give accurate length measurements of the Ball Bar that is only limited by the accuracy of the measuring machine itself and the temperature of the measuring environment. Someone is bound to pose the question of how much the length of the Ball Bar itself will be foreshortened by the force that is applied by the measuring machine. Doing the calculations based on an applied load of 14 grams will show that a one meter (39.37 inches) long Ball Bar will only compress two tenths of one micro inch, (0.0000002”) [5 nanometers], so there is obviously no practical effect on the measured length of the Ball Bar.

2. The second factor in using the Ball Bar as a length standard, for C.M.M., calibration, is the lack of perfect macro geometry of Ball Bar frame, (usually a cylindrical tube). There have been reams, recently published, on the “Camber Effect,” and its actual effect on the length of the Ball Bar. This problem is based on the fact that if the slight bend or camber of a long Ball Bar is pointing up when the measurement is made, the absolute length of the Ball Bar will increase in length when the Ball Bar is moved from vertical to horizontal. This is obviously due to the force of gravity.

If this same cambered Ball Bar is measured with the bow or camber pointing down, when it is moved from vertical to horizontal the length of the Ball Bar will actually shrink. See Figure Number 1. The “Camber Effect” is only a measureable problem when the Ball Bar is long or very long. The answer for correcting this problem is not to build gigantic more rigid structures, but to simply “key” the Ball Bar, to eliminate its ability to rotate. This is done by simply mounting a small diameter cylinder, sticking out of the Ball Bar at right angles to its axis and positioning it against another small cylinder held at right angles to it. This point contact between the two cylinders forms a kinematic couple that will repeat to micro inch accuracy. See Plate A.

3. The third issue is the elasticity of the frame of the Ball Bar. A little thought will reveal that this bending issue is also part of the “Camber Effect” that was explored as part of issue number two. To cope with this problem, we have to change or at least modify our entire concept of kinematic support. Lord Kelvin stated in an 1871 paper, that there are only six degrees of freedom for any “rigid body.” The very concept of the existence of a rigid body is the sticking point that we must modify, our concept of. This can be done if we look at elasticity as a seventh degree of freedom. We can eliminate this entire problem by providing one or more preloaded supports to the lower surface of the Ball Bar. This extra support will dramatically reduce or entirely eliminate any change in length between the two balls of the “keyed” Ball Bar when it is moved from vertical to horizontal.

To fully appreciate how small these length changes are, all you need to do is remind yourself that the balls are on the neutral bending plane of the Ball Bar. Any change in length due to bending of the bar is a second order, cosine function, not a first order error. Supporting long Ball Bars in a manner that substantially “prevents” sag when the Ball Bar goes from Vertical to Horizontal, is a prerequisite to using a long Ball Bar as a length standard for C.M.M. evaluation or for that matter for volumetric tests. See Plate B.

We have built an elaborate measuring machine with micro inch resolution which empirically proves all of the theory involved in both the camber effect and the effects of elastic sag. See Plate C. A Ball Bar can be the ultimate length standard for C.M.M. evaluation, but only if their limitations are understood and corrected for.

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