# Ball Diameter Errors

We have occasional complaints from customers that our ball size measurements are incorrect. We have collected the last two years of complaints and carefully analyzed each one of them. Here is a list of the most common problems.

The most common problem we encounter is that many customers are using horizontal measuring machines for ball size evaluation. This type of machine has several common problems.

The first and by far the most common is the high measuring force typically applied to the ball by these machines. The higher the measuring force used, the more difficult and the less accurate the corrections for elastic deformation are. The compression of both sides of the ball and the indentation of the contact surfaces of the measuring machine are very large error sources that must be corrected for.

On smaller diameter balls, we find that customers using these machines are frequently exceeding the elastic limits of the ball material and permanently deforming the surfaces of the ball. It takes only 15 grams of force to put permanent flats on a 1/64-inch ( 0.15625", 0.39688 mm ) diameter steel ball, and not many Horizontal-measuring machines will operate at even this force. The formulas for correcting Hertzian elastic deformation are very complex and most of the factors used in this formula are not known with great accuracy.

The second problem is related to the first. Many, if not most, of these machines use a coil spring to apply the measuring force. This system simply is not accurate, and it doesn't repeat to the level necessary for accurate ball evaluation. The measuring force applied to the ball must be evaluated with an accurate dynamometer, as it is a major element in the correction equation. The same dynamometer should be used to carefully check the repeatability of the measuring force.

Next: the materials used for the measuring faces vary from steel with a Young's modulus of elasticity or stiffness of 30,000,000 P.S.I. to tungsten carbide ( T.C. ) that is 98,000,000 PSI. As this is the second most important element, you must know the correct values and they must be applied to the elastic deformation formula. Complaints caused by these problems are the more frequent. These disparities in the measurements are far greater on small diameter balls as these balls are far more compressible and therefore they cause errors of far greater dimensional magnitude.

The measuring surfaces on these machines are frequently worn out of flat through use. This condition can be quickly and simply checked with an optical flat and a monochromatic light. It is common to find anvils on these machines 5 or in extreme cases 10 light bands out of flat. This is 50 to 100 micro inches or (1 to 2 micrometers). The measuring anvils can be seriously out of parallel. This condition should be checked by measuring a high quality small diameter ball (preferably one made of tungsten carbide ) in five places. It should be measured at the top of the anvils, at the bottom, on the left hand side, on the right hand side and in the very center. This problem is so frequent that a special, long handled ball probe is used for checking this condition. It uses a high stiffness, low expansion and very wear resistant tungsten carbide master ball that is spherical to less than 3 micro inches (75 nanometers).

During a visit to a European plant that was building these horizontal measuring machines, their lapping expert said that it took him a full day to lap the flat and parallel measuring anvils of a single machine. This, he said, was the most difficult operation of all in manufacturing the machine.

While the first condition compresses the ball and dimples the measuring surfaces, both of which makes it look smaller than it really is, the out of flat and out of parallel anvil usually causes the ball to measure oversize or larger than it really is.

We have eight horizontal measuring machines in our facilities, so we have some first hand expertise with the problems that afflict them. On larger balls, there can be still another problem with this type machine. Many of these machines are very old, and because they were so well built, they last forever. Many of the older machines were made before the international inch was adopted; and they measure several micro inches per inch longer than the newer 25.4 millimeters of the present international inch

A whole new set of problems is unleashed when comparison gages are used instead of absolute measuring machines to measure the ball diameter. When using this approach the best possible approach is to set the gage with a master ball of the same diameter and of the same material as the unknown exemplar ball. Even this approach, as good as it is, has problems.

The first problem is just who measured the master ball? It must be a direct N.I.S.T. calibration, otherwise, who is to say the measurement is true. Even N.I.S.T. gives an uncertainty of plus or minus ten micro inches ( 250 nanometers ). At the time of this writing, March 2003, there is not a single lab in the United States that is NVLAP accredited to measure the absolute diameter of a ball, to the ISO-17025 specification, so any calibration other than one directly from N.I.S.T. must be questioned.

We have found companies repeatedly using tungsten carbide master balls to set their gage when they are measuring steel balls that have only one third the stiffness of the T. C. ball. Even though a master ball is the best approach for setting a comparison gage, a realistic gage uncertainty must still be assigned to these measurements.

If the comparator gage uses flat parallel gauging surfaces, (a policy that we strongly endorse) the same geometry problems that applied to the Horizontal Measuring machine will apply here. If a flat anvil (table) and a spherical gage tip are used the Hertzian elastic deformation will be dramatically increased. As tungsten carbide or diamond gage tips are most often used, extreme care must be exercised so that the correct Young's modulus, i.e. (stiffness), is used in calculating the Hertzian elastic deformations.

When gage blocks are used to master the comparison gage, a new series of problems arise, (see our paper on using gage blocks). What material are the contact surfaces of the gage blocks made of? It is generally good practice to use tungsten carbide wear blocks on the ends of a steel gage block combination, but chrome carbide and ceramic blocks are widely used today. It is important to take the stiffness and thermal coefficient of these materials into

When using a comparison gage with a spherical tip, it is common practice for the technician to manipulate the ball forward and back and side-to-side to find the highest point by hand or more specifically with their fingers. Transferring our 98.6 degree Fahrenheit body temperature to the ball and placing it in the vicinity of the gauging system will cause such a dramatic and instantaneous change in the zeroing that no serious measurement can possibly be made. The simple solution to this problem is to drill a close fitting hole in a block of plastic. The test ball is placed in this hole and the plastic block is maneuvered to find the high point of the ball, thus eliminating the temperature problems.

An often overlooked factor is the effects of temperature. The international standard temperature for dimensional metrology is the well-known 68 degrees Fahrenheit or 20 degrees Centigrade. Any variation from this temperature will have dramatic effects on the measurement. Devices like the horizontal measuring machine and other absolute measuring equipment are especially vulnerable to variations from the standard temperature. Comparison gages actually have an advantage in this area. If the setting master and the test ball have the same thermal properties, temperature variations will have much less effect on the measurements. With all of these detailed problems, it is important to remember that the inherent repeatability, linearity, and over all accuracy of the fundamental gauging mechanism is also a major consideration. These additional factors are involved in every gauging system and should be evaluated to establish practical error budgets.

If all of these commonly used ball measuring devices have so many problems, how then should balls be measured? We believe that the best answer to serious ball diameter evaluation can be conducted with a laser scale (absolute) instrument using a flat table and a flat parallel gage-measuring tip. This is not an inexpensive approach, but it works; and it is reliable.

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