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Defining these terms permits discussion from a common frame of reference. What Is Accuracy? Most of us have, at one time or another, shot a gun or bow, or thrown a dart. This same analogy applies to machine tools. But the machine sometimes has different ideas. An accuracy spec quantifies how well we hit the target. Each linear positioning standard defines a method for determining accuracy and other specifications on a consistent basis. Machine tool builders talk about three kinds of accuracy: unidirectional forward, unidirectional reverse and bidirectional.
The accuracy while walking toward the target would be unidirectional forward accuracy and that walking away from the target is unidirectional reverse.
Each of these are scored individually. You can also score the overall accuracy forward and reverse. This is called bidirectional accuracy because it takes both directions into account. Machine tool builders can describe accuracy with terms like error-band, accuracy, positional deviation, position uncertainty and mean-to-mean accuracy.
Each of these terms is calculated differently. What Is Repeatability? If we look again at Figure 1, the distance between each hit illustrates repeatability. This pattern is repeatability. Machine tool slides also vary about the target point. Figure 2 shows a very tight pattern. Therefore, the repeatability is very good. The result is poor accuracy. We can enter the same contest of shooting at a target while walking toward it and away from it.
Walking toward the target we get a pattern of holes perhaps like Figure 3. This represents forward repeatability. Walking away from the target we may get a pattern like Figure 4. This illustrates reverse repeatability.
Repeatability is tested as the total range, so if the bottom bullet hole and the top bullet hole are 0. There is also a bidirectional repeatability which takes into account both Figures 3 and 4, and as a value would be the distance from the bottom bullet hole on Figure 4 to the top hole on Figure 3.
Transferring this comparison to a machine tool, we have six targets for each machine slide. We position to these targets from both directions seven times and from this information we derive repeatability. Repeatability may be described by terms such as forward repeatability, reverse repeatability, bidirectional repeatability, and positional scatter.
If you look closely at Figures 3 and 4 you will notice our marksman has lost motion. In Figure 3, all the bullets are left of center, and in Figure 4 they are right of center.
The difference between them is lost motion. Other lost motion terms are reversal error, and mean reversal error. Now assume we have six targets, and position to each target seven times. If we position to six targets, turn around and position to the same six targets on our way back to zero, save all the errors at each target point, then repeat this seven times, we have 84 pieces of data.
Figure 5 will give you the general idea of the normal collection process for these data. From this data accuracy, repeatability, and lost motion specifications are calculated. Sigma But before we calculate any of these values, we must talk about sigma.
Sigma is also known as Standard Deviation. Standard deviation is normally shown using a bell shaped curve as shown in Figure 6 at right. On each side of center x is 3s, which is three times one sigma. If we position to our six targets seven times each, calculate the standard deviation, and multiply it by six, then times out of 1,, we would hit our six targets within that value. The same raw data was used for all six comparisons. This data is in the inch system of measurement and all values are in microinches millionths of an inch.
So, for example a measurement of as indicated on the chart would be 0. This may render the appearance of a lower number. NMTBA is the only standard that statistically calculates using bidirectional data. The other statistical standards generate their bidirectional data from the individual forward and reverse information only.
ASME B5. However, each standard has its place depending on your taste for either statistical data or actual raw data. However, we must be aware that one standard can allow the machine to appear to be more accurate than it will be when evaluated using another standard. Comparison Overview As can be seen from the numerical comparison table at the bottom of this page , values represented by the various standards can vary dramatically given the same raw data.
Because this standard has been the reigning monarch of American machining centers for several decades, we will use it as the standard for comparison of all others. ISO calculates forward, reverse, and bidirectional repeatability. This is because ISO uses the largest of six sigma forward and reverse or the sum of three sigma forward plus three sigma reverse plus the absolute value of lost motion, whereas NMTBA statistically calculates the bidirectional repeatability.
NMTBA calculates accuracy forward, reverse, and bidirectionally; all statistically. ISO uses only forward and reverse data. Positioning uncertainty P is related to bidirectional accuracy but is calculated using averages and averages of averages. This procedure reduces the actual numbers to about 40 percent of the NMTBA value in this example compare and Positional deviation Pa is mean-to-mean accuracy.
It is the average of the forward runs less the average of the reverse runs; then the average of these is taken. Positional scatter Ps is related to bidirectional repeatability. VDI averages sigma from forward and reverse, gets the absolute value, then multiplies the value by six and keeps the largest value. NMTBA statistically calculates the bidirectional sigma value, multiplies it by three, and uses this 3 value as bidirectional repeatability.
On the chart, lost motion or reversal error is U. JIS B treats accuracy and repeatability differently than most other standards. Accuracy is measured by positioning to equal increments covering almost the entire travel of the slide, once in each direction. The accuracy is then the largest error range of either the plus or minus direction. For repeatability, the standard requires positioning to a point at one end of travel seven times.
This procedure is then repeated at the center of travel and again at the opposite end of travel. The largest error at any of the three points is saved. The process is repeated in the opposite direction. Lost motion is calculated by positioning to a reference point, continuing in the same direction by a known increment, then reversing by the same increment.
This procedure is repeated at both ends and the center of travel. At each location, data are collected seven times, averaged, and the largest of the three averages is called lost motion. The standard specifies three round trips.
Since the data used for this discussion is seven round trips, the numbers will be of a wider range than normal. An additional linear performance attribute is also obtained from the averages. The B5. However, most manufacturers and most laser software calculate the repeatability directly from the accuracy runs. This provides more data which is spread over all target points compared to the ten bidirectional hits at two locations that the current standard calls for.
Thus a request is under consideration to change this part of the standard.
VDI/DGQ 3441:1977-03 (R2014)
How Accurate Is Your Machining Center?