Position at Maximum Material Condition (MMC) Applied to Internal Threads
R. Dean Odell
This article explains what the options are if a drawing indicates position at MMC on an internal thread. It is not a prescription to not use position at MMC. Many manufacturers and inspectors do not have the option to change drawings, and have to deal with what they have. This article is meant to address those needs.
Unified threads have tolerances given by ASME B1.1-2003 Unified Inch Screw Threads.(Other thread forms like ACME have their own standards) If the position of an internal thread is modified at regardless of feature size (RFS), the actual size of the thread is normally verified by a GO/NOGO gage, see figure 2. A thread location gage can be used to extract the axis of the pitch cylinder of the thread,
see figure 1.
The thread location gage is necessary to find the axis of the pitch cylinder. This is a requirement as quoted below.
From ASME Y14.5-2018 Section 5.10 “Screw Threads”
“UOS, each tolerance of orientation or position and each datum reference specified for a screw thread applies to the pitch cylinder axis. When an exception to this practice is necessary, the specific feature of the screw thread (such as “MAJOR DIA” or “MINOR DIA”) shall be stated beneath or adjacent to the datum feature symbol, as applicable.”
If the thread is modified at maximum material condition (MMC), the tolerances of the thread must be known to calculate additional (bonus) tolerance. This is not to say that this is a functional relationship. The axis of the pitch cylinder will not necessarily shift if it is made to a larger size (within the specified thread tolerances).
Any additional (bonus) tolerance gained will not result in an appreciably looser fit between the thread and fastener as long as the thread is within the size tolerance given by ASME B1.1-2003.
Before discussing the implications of the MMC modifier, keep in mind that the location of the thread can be measured the same as if it was modified at RFS. Axis interpretation, see quote below.
*From ASME Y14.5-2018 5.9.4.2 “Explanation of the Axis Method”
When an orientation or position tolerance is applied on an MMC basis, the feature’s axis, centerplane or centerpoint shall not violate the tolerance zone. The tolerance available is the specified value if the unrelated actual mating envelope is at the MMC limit of size. When the size of the unrelated actual mating envelope departs from MMC, the tolerance zone increases. The increase in the tolerance zone is equal to the difference between the specified MMC limit of size and the unrelated actual mating envelope size. The resulting tolerance is equal to the stated geometric tolerance plus the additional tolerance.
Surface interpretation of position is not feasible in any case with a thread. A thread location gage will reveal the X and Y deviations from the true position. It is only if the location is not within tolerance that the bonus tolerance will need to be considered. These gages technically find the axis in the projected tolerance zone. This must be accounted for when interpreting the data collected during inspection, whether at the surface plate or on a CMM.
The bonus tolerance for an internal thread is calculated as actual pitch cylinder diameter minus the MMC pitch cylinder diameter.34
Measuring the actual pitch cylinder of an internal thread is difficult (compared to a GO/NOGO check), but not impossible. One option is to make a rubber casting of the feature and measure that casting, see figure 3. Another option is an internal thread comparator, see figure 4.
Figure 4 Internal Thread Comparator
Some commercial options available:
https://www.reprorubber.com/index.php
*There is no relationship between the author and these companies or products*
Here are the tolerances for a .500-13 UNC-2B internal thread given by
ASME B1.1-2003:
Pitch Cylinder ⌀.4565-.4500
Minor Diameter ⌀.434-.417
Major Diameter ⌀.5000 MIN
Keep in mind that the total tolerance on the pitch cylinder of, for example, a .500-13 UNC-2B thread is ⌀.0065”. The measurement uncertainty of the inspection method must be considered to make this worthwhile (it may not be).
Here is an example:
Figure 5 Incomplete Drawing Showing a Threaded Hole with Position at MMC
An internal threaded feature has a position tolerance of ⌀.007” at MMC, see figure 5. The axis is measured and reported to be .005 off in the X direction and 0 off in the Y direction, see figure 6.This would result in an actual tolerance diameter tolerance zone of ⌀.010”. The axis of the feature is out by .0015”. At this point, the pitch cylinder can be measured, and if it is larger than the MMC size by ⌀.003”, then the bonus can be added to the specified ⌀.007” and the feature can be accepted. Keep in mind that the threaded feature is still within tolerance, so there should not be any functional difference in “fit” between the internal threaded feature and the mating fastener.
Figure 6 Axis Relative to True Position (Not to Scale)
Here is an example:
Figure 7 Incomplete Drawing Showing a Threaded Hole with Position at MMC, applied to the minor diameter.
An internal threaded feature has a position tolerance of ⌀.007” at MMC, referring to the minor diameter, see figure 7. The axis is measured and reported to be .010” off in the X direction and 0 off in the Y direction, see figure 8. This would result in an actual tolerance diameter tolerance zone of ⌀.020”. The axis of the feature is out by .0065”. At this point, the minor diameter can be measured, and if it is larger than the MMC size by ⌀.013”, then the bonus can be added to the specified ⌀.007” and the feature can be accepted.
If the position of the thread is specified to apply to the MINOR DIA, the inspection is greatly simplified. The minor diameter axis can be simulated with a cylindrical gage pin. This gage pin can be used for determining the location of the axis of the unrelated actual mating envelope of the minor diameter, and the actual size of the minor diameter.
For a .500-13 UNC-2B thread, the total tolerance on the minor diameter is ⌀.017”. This allows significantly more error than the pitch cylinder tolerance.
Figure 8 Axis Relative to True Position (Not to Scale)
Keep in mind that the axis of the pitch cylinder is not necessarily affected by the minor diameter, so when something is threaded into this feature, it will likely be located at the .010” away from the true position, even with the extra size allotted to the minor diameter.
Here is an example with zero at MMC:
Figure 9 Incomplete Drawing Showing a Threaded Hole with Position at MMC
If a thread position has zero tolerance at MMC as shown in figure 9, the inspection must ascertain the diameter of the actual pitch cylinder to determine how much position tolerance is available, unless the axis of the pitch cylinder is determined to be exactly coincident with the true position. In the author’s opinion, this specification should be avoided, but is not necessarily wrong.
Can these issues be resolved with a coordinate measuring machine (CMM)?
In the context of tactile CMM measurement, finding the diameter of the pitch cylinder of an internal thread is typically not achievable. The stylus probe, whether spherical or cylindrical, is only capable of reaching the minor diameter. Thus, only the axis of the unrelated actual mating envelope of the minor diameter can be found. Likewise, only the diameter of the minor diameter is able to be measured. Thread location gages can be used with CMM machines to find the axis of the pitch cylinder.
Should I apply MMC to the Position of Threaded Holes?
The functional utility of applying MMC to the position of threads is not clear to the author, but the drawing requirement is not wrong, and should be respected unless some arrangement has been made to modify the drawing requirement. From a design perspective, applying MMC to a threaded hole will not do the same thing as applying MMC to a plain hole. A plain hole can be made larger, which will allow more room for a mating part while maintaining a virtual condition. Threaded holes can not be verified with the surface method, so a virtual condition does not exist in any practical sense. The location of the axis of the pitch cylinder will not necessarily change if the pitch cylinder is made larger.
What about projected tolerance zones?
In the author’s opinion, because the axis of an internal thread can only be reasonably found using the axis (resolved geometry) method, the addition of a projected tolerance zone is not appreciably distinct. If the position tolerance applies to the pitch cylinder, a thread location gage should be used to simulate the axis, depending on the length of the projected tolerance zone, a special length pin may be required on the thread location gage.
Tolerance Stack Implications
Because threads are self centering, the boundaries for a thread feature should be calculated at RFS, even if MMC is applied. As mentioned above, increasing the diameter of the pitch cylinder or minor diameter of an internal thread will not necessarily change the location of the axis. This is in contrast to a plain hole, where an increase in size will result in potential shift.
Some definitions that may be helpful:
From ASME B1.7-2006 “Screw Threads: Nomenclature , Definitions and Letter Symbols”
Page 13 “Pitch Cylinder”
An imaginary cylinder of such diameter and location of its axis that its surface would pass through a straight thread in such a manner as to make the widths of the thread ridge and the thread groove equal. Therefore, it is located equidistant between the sharp major and minor cylinders of a given thread form. On a theoretically perfect thread, these widths are equal to half of the pitch.
Page 12 “Minor Cylinder”
An imaginary cylinder that would bound the root of an external straight thread or the crest of an internal straight thread
Page 13 “Minor Diameter”
On a straight thread, the minor diameter is that of the minor cylinder.