What are datums in gd&t?
All GD&T tolerances are built on top of all these three elements. The understanding of these three elements is essential to thoroughly understand GD&T.
Tolerance zone maybe the most fundamental building block of GD&T. Because, all GD&T conformance and non-conformance decisions are based on verifying features with respect to one or more tolerance zones.
Datum reference provides the origin of coordinates of all GD&T tolerances on a part. All feature positions will be based on this datum reference.
Material condition is a condition to explain how a larger or smaller tolerance values can be obtained when a feature of interest is made smaller or bigger that its nominal size. This material condition concept can be a huge saving in the quality inspection process of parts.
Finally, real examples showing the benefits of using MMC and LMC symbols in feature of size are presented at the end of this post.
Let’s get into them one by one.
Especially for GD&T tolerance with relations (for example orientation, location and run-out) that require datum, a datum system is necessary to be the reference point for all GD&T tolerance verification and comparison.
This datum system is commonly called datum A, B and C (sometimes until D or E depending on tolerance situations and requirements). These datums will intersect each other and the point of all the intersections is called datum reference (datum reference frame). This datum reference is the main reference for all GD&T tolerance on a part or component.
Figure 1 shows a datum system and datum reference/datum reference frame. In figure 1 left below, a datum system containing three datums: datum A, datum B and datum C is shown. A datum can be, for example, a surface or an axis from a symmetrical feature or other geometrical features.
Datum A is the main datum on GD&T tolerances on a part and also the main reference for the other datums (in this case datum B and datum C) on the part. In general, datum A commonly applied to the most stable feature on a part, such as the surface with the largest surface area or as the base of the part.
In figure 7 left above, datum A is applied to the back surface of the part because it has the largest surface area on the part. For datum A, since it is the main and first datum, only un-related GD&T tolerances applied as datum A, such as flatness, roundness and cylindricity.
In addition, the tolerance of datum A should be the tightest among the other datums (in this case datum B and datum C) since datum A is the reference and each small deviation on the manufacturing of datum A will propagate and amplified to the deviation to other features.
The reason datum A should have the tightest tolerance and manufacturing accuracy is because in any manufacturing processes, such as machining and inspection processes, such as by using CMM, the surface of datum A on the part should touch the main table of the machine tool or the CMM.
In figure 7 right, a datum reference frame is shown. Datum reference frame is a point as the result of the intersection of all the datum planes/features represented by datum simulators (see figure 7 right). Datum simulator is a surface that directly touch a datum surface and simulate the datum on a part.
Datum reference frame is the coordinate reference to verify the GD&T tolerances on a part for related tolerances. In real situation, a datum simulator can be the base table of a measuring instrument for datum A and the surface of fixturing for other datum.
A deeper explanation of a datum system with an example is shown in figure 2 above. In figure 2, datum A is the main datum so that an un-related GD&T tolerance is applied, that is flatness.
Note that since datum A is the main and most important datum feature, the feature representing datum A should be accurately manufacture as high as possible. To control this, the tolerance value given on datum A is the tightest among other datums or feature tolerances.
For datum B and C, these datums have related tolerances. Because, there is datum A that can be used as the reference for both datum B and datum C.
Datum B is the second datum on the part (in figure 2 above) so that it has a reference only to datum A. meanwhile, datum C is the third datum on the part (in figure 2 above) so that datum C has two references, to datum B and then datum A.
For the small cylindrical features (in figure 2 above), the axis of the cylinder has a reference to all datum A, B and C.
The explanation is as follow. For datum reference, the reading is from left-to-right. And for inspection or machining, the part positioning sequence should read the datum reference symbol from right-to-left.
For example, a datum symbol shows:
Hence, the reference for the parallelism tolerance (shown in the symbol above) should be read with respect to datum C, datum C with respect to datum B and datum B with respect to datum A.
For the placement of the part (for example in a measuring machine or machine tool base table), the placement sequence should be as follow. The part is placed on the machine base table starting from datum A, then datum B and then datum C.
Tolerance zone is a zone where the surface of a feature of interest lies within this zone. In general, tolerance zone can be in the form of:
Some examples of these tolerance zone are as follows. In figure 3 below, the example of planar tolerance is shown for the perpendicularity tolerance of the axis of a slot feature. The tolerance zone is the distance of two parallel planes (figure 3 right) as far as 0.01 unit distance.
In figure 4, the example of cylindrical tolerance zone is given for the location tolerance of the axis of a hole. The tolerance zone is a hypothetical cylinder with diameter of 0.08 unit distance.
The example of circular tolerance zone is presented for the run-out tolerance of a slider cylinder (figure 5 below). The tolerance zone is the diameter difference between two concentric circles as much as 0.5 unit distance (figure 5 right).
For examples on how to read and interpret GD&T, readers can refer to this post. In this post, many more examples are given from a simple tolerance to complex tolerance on a part.
In GD&T or geometric tolerance, there are two important concepts that need to be understood: material condition and bonus tolerance.
These two concepts have a big role in an assembly process. In an inspection process where there is a bonus tolerance following the material condition requirement from the inspection process measurement, the number of non-conformance part can be reduced. Because, with a bonus tolerance, a component or part still can have more deviations larger than its tolerance limit shown in its technical drawing.
Material condition is a condition where a feature of size is manufactured bigger or smaller than its nominal dimension. For example, a cylinder is made smaller than it should be or a hole is made larger than it should be. Nominal dimension is a value written in its technical drawing.
Material condition is only for feature of size, such as sphere and cylinder. The most common feature to be applied material condition (when the feature is toleranced) is cylinder.
There are two main important types of material conditions:
MMC is when a cylindrical pin or shaft is made at its maximum diameter (the largest pin or shaft) or when a hole is drilled at its smallest diameter (the smallest hole) according to their nominal dimension.
LMC is when a cylindrical pin or shaft is made at its minimum diameter (the smallest pin or shaft) or when a hole is drilled at its largest diameter (the largest hole) according to their nominal dimension.
Figure 6 above shows the examples of MMC and LMC conditions on a pin and hole features. In figure 6 left, for the pin, its MMC is when the diameter is $30 mm$ and its LMC is when the diameter is $29.8 mm$. From figure 6 right, for the hole, its MMC is when the diameter is $19.9 mm$ and its LMC is when the diameter is $20.1 mm$.
The illustration of MMC on a cylindrical pin and the implication of the MMC with regard to the real condition of the cylinder is presented in figure 7 above. In figure 7, it is shown that the cylinder is designed to have a diameter of $100\pm 0.5 mm$. Physically, the representation of the MMC of the cylinder is a hole where the pin is designed to be able to enter the hole to have a specific function, for example, to join two plates together.
With the stated nominal dimension, the MMC of the cylinder is 100+0.5=100.5 mm. In figure 7 (middle), when the cylinder is produced to be smaller than its nominal dimension = 100 mm and is still larger than the minimum tolerable diameter (99.5 mm), hence some shape deformations of the cylinder still can be allowed. These extra allowable shape deformations are called “bonus” (will be explained in a later section).
For example, if the cylinder is produced at diameter of 99.9 mm, hence the cylinder can have a shape deviation as much as 100.5-99.9=0.6 mm. As long as the cylinder (pin) does not have a deviation more than 0.6 mm, then the cylinder (pin) still can be inserted into the hole.
In figure 7 bottom, when the cylinder is produced at its MMC, that is at diameter of 100.5 mm, then the cylinder must have a perfect cylindrical form so that the cylinder can be inserted into the hole. In other words, no allowable deviation on the cylinder shape is permitted.
This “bonus” and MMC as well as LMC concept have a significant economic impact in the manufacturing cost of a component.
Before we discuss “Bonus tolerance”, we need to understand the difference between the meaning of “MMC” and “MMC symbol”. That are:
The same applied for the meaning of “LMC” and “LMC symbol”. That are:
Figure 8 below shows the example of location tolerance of a hole with an MMC symbol. In Figure 8, the hole has a location tolerance as 0.5 mm with MMC symbol (written as “M”) and with respect to datum B and datum A. This MMC symbols means that if the hole is made larger that its minimum diameter (deviated from its MMC value), for example 60 mm (measured value) > 59 mm (its MMC value), then the axis of the hole can move as much as 0.5 mm due to bonus tolerance.
In this case, the bonus tolerance = measured diameter – MMC = 60-59 = 1 mm. Hence, the total tolerance zone size is 0.5 + 1 = 1.5 mm. This larger tolerance zone is because when the hole is made larger than its minimum diameter, if the hole axis shifts more than its allowable value (its location tolerance), then a pin designed to be able to go into the hole still can be fit in due to the larger hole.
In figure 9 below, the example of location tolerance of a hole with an LMC symbol that is 0.5 mm with MMC symbol (written as “L”) and with respect to datum B and datum A. This LMC symbols means that if the hole is made smaller that its maximum diameter (deviated from its LMC value), for example 60 mm (measured value) < 61 mm (its LMC value), then the axis of the hole can move as much as 0.5 mm due to bonus tolerance.
In this case, the bonus tolerance = LMC- measured diameter = 61-60 = 1 mm. Hence, the total tolerance zone size is 0.5 + 1 = 1.5 mm. This larger tolerance zone is because when the hole is made smaller than its maximum diameter, if the hole axis shifts more than its allowable value (its location tolerance), then there will be more material on the hole to be machined, for example, to apply a finishing process to improve the surface quality of the hole.
MMC symbol is used to inform that a hole feature is designed to insert a bolt to join two plates. If the hole is made larger that its minimum allowable diameter, then the probability that a bolt can go into the hole becomes large as well. Because of this reason, there should be a bonus tolerance on the hole.
With the bonus tolerance, the probability of the hole to be rejected becomes small because the tolerance is relaxed during the verification of the hole feature in an inspection process. The reduce of part rejection will reduce scarp or rework cost and will reduce the total production cost of the part.
LMC symbol is used to inform that some materials on a feature after manufacturing the feature should be preserved to allow further machining processes. For example, the excess material on a drilled hole can be finished with a subsequent boring process to improve the surface finish of the hole.
The explanation above show that when a hole is made smaller than its largest diameter. The hole still has some materials that allow further finishing processes applied to the hole. Hence, if the manufactured or drilled hole is deviated from its location tolerance, then the hole still has excess materials for further processing.
It is worth to note that, although bonus tolerance has some benefits, it also has a drawback. Bonus tolerances will increase variation sources on a final assembled product. In 3D tolerance stack-up analysis (including 2D tolerance analysis), bonus tolerances will add more variations to the total variation chain of an assembly.
From the explanation about the GD&T and its element in this post, it can be seen that GD&T symbols (tolerances) have a very deep meaning and explanation. Those GD&T symbols are designed to accommodate the design intention of a mechanical designer to a manufacturing and quality inspection engineer.
The concept of material condition (both MMC and LMC) are presented in detail with examples. These material conditions cause bonus tolerances when verifying the conformance or non-conformance of a geometric tolerance on a part.
A Datum is a plane, axis, or point location that GD&T dimensional tolerances are referenced to. Typically, multiple features will be referenced by each datum, so they’re a very important part of the whole thing. Nearly every GD&T symbol except for form tolerances (straightness, flatness, circularity, and cylindricity) can use datums to help specify the geometric control that is needed on the part.
As we said in the definition, Datums are planes, axes, or point locations, and that’s exactly how they show up on a drawing. Let’s go through each one to see how it looks:
On a Surface (Plane)
Two examples of Datum Sybols on a Surface
We can place the datum symbol either on the surface or on one extension line from the surface. For any surface other than a round cylinder, the datum is strictly on the side where the symbol is shown. However, for a round cylinder, the datum is the entire round surface.
On an Axis
Place the datum symbol on the dimension of a diametric tolerance for Axis control:
A Datum Symbol on an Axis
Remember: this places the Datum on the central axis through the feature, not the surface of the feature. Placing the Datum on an axis is common with GD&T symbols that can have axis control like runout, perpendicularity, or concentricity.
On a Point or Hole’s Axis
To establish a datum axis on a feature such as a hole, there are a number of ways to place the datum symbol:
The “A” Datum can appear in these three different places on a drawing…
Referring to the example above, the “A” Datum can appear in these three different places on a drawing:
– It can be placed directly on the hole, as in the leftmost case. It is of course referring to the axis and not the surface of the hole.
– It can be placed on the leader pointing to the hole as it is in the middle case.
– It can be placed on the Feature Control Frame for the hole.
In addition, the datum symbol could be shown on a side view by denoting the axis.
At this point it is important to talk about the difference between a Datum and a Datum Feature–they are not the same though it is tempting to refer to them as such at first. Datums are abstract geometrical concepts. They correspond to points, lines, and planes. When we refer to the tangible feature on the part that the Datum is associated with, we call it a Datum Feature. The reason they’re not the same is perhaps small, but significant. It is because real features are never perfect abstract geometrical concepts. Surfaces on parts are not perfectly flat planes. Edges on parts are wavy and are not perfect lines.
The standard itself defines a Datum Feature as, “An actual feature of a part that is used to establish a datum.”
You may also come across the term Datum Target, which is defined as, “A specified point, line, or area on a part used to establish a datum.”
This one starts out simple:
A Datum Reference Frame is a coordinate system, and preferably it is a Cartesian coordinate system.
Coordinate systems are valuable because they’re used to locate objects. In GD&T they are used to orient and locate tolerance zones.
Datum Reference Frames and 6 Degrees of Freedom
Every Datum exists within the context of some Datum Reference Frame. In practice, we must eliminate 6 degrees of freedom before we can fully locate and orient a part within a Datum Reference Frame:
Controlling 6 degrees of freedom…
Controlling 6 degrees of freedom means controlling 3 linear distances from Datum planes to establish an X, Y, and Z position and controlling 3 rotary positions to orient the part at that position. We refer to the translational degrees of freedom as X, Y, and Z and the rotational degrees as u, v, and w.
The 3-2-1 rule defines the minimum number of points of contact required for a part datum feature with its primary, secondary, and tertiary datum planes. It only applies when all three plaines are used. The 3-2-1 rule says:
– The primary datum feature has at least 3 points of contact with its datum plane.
– The secondary datum feature has at least 2 points of contact with its datum plane.
– The tertiary datum feature has at least one point of contact with its datum plane.
The 3-2-1 rule only applies to planer datum features.
One may specify a datum feature that is at an angle other than 90 degrees relative to other datum features. These are called Inclined Datum Features.
Datum C corresponds to an Inclined Datum Feature…
Datums are specified in the Feature Control Frame in an Order of Precedence. This Feature Control Frame has 2 Datums specified (A and B):
A Feature Control Frame…
Datum A is the Primary Datum and B is the Secondary Datum. If there had been a third Datum, it would be called the “Tertiary Datum.” It is not necessary to specify the Datums in alphabetical order.
The first step in dimensioning a part is always to select the Datums. When selecting Datums, designers should consider the following characteristics:
– Functional surfaces
– Mating surfaces
– Readily accessible surfaces
– Surfaces of sufficient sizes to allow repeatable measurements
Datums are important and care must be taken when selecting them. They must be easily identifiable on the part. When parts are symmetrical or have identical features that make identification of Datum Features difficult, the Datum Features should be physically identified.
By now you have an idea of how Datums are shown on drawings and how they’re used to establish a coordinate system. You can read them, at least a little bit, but I’ll bet they still don’t feel obvious and you’re wondering how to “write” them (in other words, how to choose Datum Features on your parts).
We’ll have more on exactly how to choose Datum Features shortly. First, we need to talk about Datum Feature Simulators.
GD&T Table of Contents GD&T Symbols
Confusing the terms ‘datum’ and ‘datum feature’ is a common mistake. One must be clear about both to make professional engineering drawings.
A datum feature is a physical, tangible feature of the part that establishes the datum. Since it is a real entity, it is not exact and can have an irregular form.
The datum is a relatively more abstract concept. It is a geometrically exact representation of the datum feature. So, for example, if a rough surface is the datum feature, the datum will be the perfectly smooth plane that best simulates the surface.
The datum reference frame (DRF) is a GD&T term that refers to the coordinate system that locks the part’s degrees of freedom during inspection and measurement. By ‘locking’, it means that it orients and locates the part in space and provides a base system for all tolerance zones. The DRF provides a reference system to measure the part’s features.
Since there are six degrees of freedom for any feature, the DRF should lock all of these. This is typically done with three planes, which are easy to simulate in a physical environment as well.
The figure below presents an example. There are multiple features to measure in the part. First, imagine you want to inspect the part without the blue component. It will be difficult and unreliable as you do not have proper references to measure with. The three blue planes form the DRF that orients and locate the part.
A datum is a plane, a straight line, or a point that is used as a reference when processing a material or measuring the dimensions of a target.
