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William Tandler


Tolerance Zone “Size” and “Mobility” Modifiers

Smart GD&T workshop No. 4

Published: Wednesday, January 9, 2008 - 23:00

Back in the 1940, when Stanley Parker, Mr. GD&T, decided it was time to create a set of tolerancing tools that realistically dealt with reality, two objectives were near the top of his list.

The first was to find a way to encode the fact that as bores get larger they may become ever more offset from their nominal locations and still accommodate a mating shaft. His idea was that stating that on the drawing made it possible for manufacturing to take advantage of this gift of Mother Nature, and for quality assurance to base evaluation on real function rather than mere numbers. His second objective was to find a way to encode the play, or slop, which is often present between mating parts at the beginning of an assembly process, and which allows shifting one slightly relative to the other to accommodate minor location errors in related mating features. The objective again, was to make it possible to accept parts based on their functionality and avoid rejecting them based on criteria that fail to take reality into account.

The tools he ultimately invented have always been called “material condition modifiers” and are represented by the symbols (M) for the maximum material condition (MMC) modifier, (L) for the least material condition (LMC) modifier, and (S) for the regardless of feature size (RFS) modifier. As important as they are, their effect and use are frequently misunderstood. We hope that some precise definitions and appropriate new names can reduce the missunderstanding. As we all know, these modifiers can be associated with the tolerance value and with the datum feature labels in a feature control frame, and in both cases are understood to lead to “bonuses.” The two main problems associated with these modifiers are firstly, when to use which one for exactly what purpose, and secondly how to assign numerical values to the “bonuses” they supposedly produce, when in fact, under some conditions, what might be a bonus could actually turn into a detriment.

Figure 1.  A feature control frame with material condition modifiers

We’ll start our analysis by setting forth the new naming conventions coupled with some brief explanations, and finish with a little demonstration to underpin the applicability and usefulness of the new names. In particular, as detailed in Figure 2., the second compartment of a feature control frame, located on the western side of what we’ll call the “great divide,” is dedicated to specifying the shape and size of a tolerance zone and, with the help of a “tolerance zone size” modifier, the functional effect on it of any changes in the size of the controlled feature. The third compartment, on the other hand, located on the eastern side of the “great divide,” is dedicated to defining the process for establishing the coordinate system (datum reference frame) relative to which the tolerance zone is to be oriented and located. This includes instructions encoded by “tolerance zone mobility” modifiers, as to the exact effect each datum feature is to have on the process. 

In particular, the material condition modifiers associated with tolerance values affect the size of the tolerance zone, whereby (M) leads to (M)ore tolerance, (L) to (L)ots more tolerance, and (S) to a tolerance that is (S)tuck at the indicated value. On the other hand, the material condition modifiers associated with datum feature labels, affect the (M)obility, (L)ability (instability) or (S)tability of the datum reference frame—and therefore also of the associated tolerance zone—relative to each datum feature.

Figure 2. TZS and TZM modifiers—The great divide

Exceptions: Although not explained here, these functions are inverted in the case of non-DRF origin overlapping, non-enveloping, pitch, yaw, and roll constraining datum features.

Tolerance zone size modifiers
In the drawing below, the tolerance zone size modifier (M) in the encircled feature control frame requires the diameter of the position tolerance zone for the lower right hand bore to be fixed at 0.5 mm as long as the bore is at its MMC diameter of 11.5, but to expand by the difference between the actual mating size of the bore and its MMC diameter as the bore gets larger. Thus, the larger the bore, the more offset it may be and still clear a mating shaft.

Figure 3. A GD&T encoded drawing

As a result, we can say that the tolerance zone size (TZS) modifier (M) encodes the clearance function of a bore, and produces a numerical “bonus,” which must be added to the specified tolerance to produce a total tolerance, calculated using the following formula:

Total position tolerance = (nominal position tolerance) + [(actual mating size) – (MMC size)]

If the bore is a cast feature, and the mating feature is a boring tool intended to produce a clean machined surface, then, only as the bore gets smaller may it be more offset. This “interference” function is properly encoded with the TZS modifier (L). Finally, if the bore serves an “aiming” function, as in the case of a threaded feature, changes in size result in no functional benefit. As a result, the aiming function is encoded with the TZM modifier (S) which provides no bonus for a change in size.

Tolerance zone mobility modifiers
Turning now to the functional intent of tolerance zone mobility (TZM) modifiers, we start by reiterating the fact that the alphabet soup pot consisting of datum feature labels and TZM modifiers found in the last compartment of a feature control frame, is really a set of instructions for establishing a datum reference frame. The process includes the visualization, and occasional physical construction, of a set of datum feature simulators referred to in the Y14.5 standard as “true geometric counterparts” from which we extract the associated datums, establish the datum reference frame, and with which we transfer the datum reference frame to the actual part. In the current case, the process results in the datum reference frame indicated by the DRF component labels X[A,B,C], Y[A,B,C] and Z[A,B,C], found in Figures 3 and 4. As shown in Figure 4, the appropriate simulators for the illustrated case consist of an upward pointing planar surface for datum feature A, an expanding shaft for datum feature B, and a “tombstone” fixed at the virtual MMC size, in the case of datum feature C.

Figure 4. A datum feature simulator set

Why must the simulator for B expand? The TZM modifier (S) encodes the fact that datum feature B is expected to mate (S)tably with its mating datum feature, regardless of its size, i.e. without slop or play. To achieve stability relative to datum feature B, the simulator must obviously expand to consume all the available space inside datum feature B. A functional example would be a flathead screw consuming all the space inside a counter sink.

Next, why must the simulator for datum feature C be fixed in size? The TZM modifier (M) encodes the expected play or slop between datum feature C, a slot, and its mating datum feature, a tab. Fixing the simulator for C at the virtual MMC size of the slot, namely 16 mm, will obviously allow the simulator to roll back and forth inside the slot as the slot departs from its virtual MMC size, simulating the residual (M)obility we expect during the assembly process. Because the datum reference frame, relative to which the position tolerance zone is oriented and located, is free to roll about datum B, so is the tolerance zone, which could therefore shift to accommodate a potentially roll displaced bore, as illustrated in Figure 5.

Figure 5.  TZS & TZM modifier effects

The potentially expanding, and residually rolling, cylindrical tolerance zone defined by the encircled feature control frame demonstrates the appropriateness of the new material condition modifier names. It also makes clear that a tolerance zone size (TZS) modifier creates a bonus with a numerical value which can be added to a specified tolerance, but that a tolerance zone mobility (TZM) modifier creates a potential bonus that cannot be captured in simple numerical form and cannot be added to a tolerance value.

Tolerance zone mobility consequences—the rule of simultaneous requirements
Whenever two mating parts experience mutual play, all the features in one part are free to move slightly as a group relative to all the features in the mating part. Therefore, if certain features only mate at one extreme, and others only at another extreme of the mutual play, the part as a whole is nonfunctional. This state of affairs is captured in the extremely important “rule of simultaneous requirements,” which, in its simplest form, requires all features referenced to a common, mobile datum reference frame to meet their requirements simultaneously. Furthermore, if available play is eliminated early in an assembly process by tightening fasteners before the play can be taken advantage of, an otherwise functional part will appear to be nonfunctional. Tolerance zone mobility can therefore occasionally be beneficial, occasionally detrimental, and therefore doesn’t always provide a “bonus.”

Future articles
In our next workshop we’ll look more deeply into the world of datum features, datum targets, datum feature and datum target simulators (true geometric counterparts), datums and datum reference frames we’ve touched on here. In the follow-on article we will detail the datum reference frame establishment process itself, namely the process defined by the list of datum features and tolerance zone mobility modifiers in a feature control frame.

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About The Author

William Tandler’s picture

William Tandler

William Tandler’s professional experience includes three years at the Hewlett Packard R&D laboratory in Palo Alto, CA, where he helped develop a quadruple mass spectrometer; five years with the laser manufacturer Coherent Inc. as international marketing manager; followed in 1975 by the founding of Multi Metrics Inc.

Tandler is currently a member of the ASME Y14.5.1 Mathematization Committee; a subject matter expert for Working Group 4 of the ASME Y14.5 standard focused on datums; and has been a contributor to ISO TC213 in the realm of datum reference frame construction.