Today our definition of terms will focus on “actual local size.” This term refers to a group of values that can be assessed and applied to any feature of size, values that establish the small and sometimes minute irregularities about a feature’s geometry. To understand what this means we first need to go back to a cornerstone of our convention: perfect world / real world. We must acknowledge that GD&T has the job of connecting perfect ideas to real world situations.

A definition of geometry can have its basis in perfection, such as a cylinder. A cylinder in the perfect world has perfectly straight line elements on its surface, parallel to the cylinder’s axis and at any cross section perpendicular to the cylinder’s axis the resultant section must be perfectly circular. That combination of geometry results in a cylinder.  Now while we can have a definition of geometry in the perfect world, we cannot make that definition happen in the real world. That can only be accomplished in the real world using tolerance. Tolerance makes the manifestation of ideas possible in the real world. Without tolerance these things cannot happen. GD&T provides a language that allows engineers to state the conditions of geometry they require, to any degree of accuracy they need, except to a perfect degree. No one has ever released a drawing that said make this feature cylindrical to a tolerance of zero (0.) And they haven’t because it’s impossible. Staying within the confines of our manufacturing rules makes any definition of form, fit and function changeable under the influence of the laws of physics. Hence we need tolerance to provide the wiggle room to accomplish our jobs. Our perfect cylinder in real life actually looks like the graphic below. The closer we look the more imperfections are revealed.

Having said this we can now talk about what “actual local size” means. Let’s imagine a machinist is given a drawing. The part on this drawing shows a cylinder 10.00” long, 1.25” in diameter and its material is specified as low carbon steel. The title block on the drawing identifies the 2 place decimal tolerance to be +/-.03”. So since we don’t see any feature control frames or characteristic symbols on our drawing can we say it’s actually a GD&T drawing? By virtue of the ASME Y14.5 standard note, even without geometric identifiers it is controlled by the fundamental rules of our system. Our machinist appreciates the value of his time so he figures the shortest path to make this part to print is using A36, hot rolled steel bar. He knows this bar will meet the specs for size and finish without needing to turn the OD on his lathe, so he knows he can saw the piece off and face the ends to length and put the finished part and work order on the parts bench and move on to the next job. He might saw his blank from a bar like this:

Let’s imagine what this part looks like under close scrutiny. Anyone who is familiar with mass produced steel bar can tell you that hot rolled stock is fairly rough and although diameter tolerances vary by manufacturer, a published tolerance for this 1.25” bar was found to be +/-.011”. As we can see our machinist made a good choice for this job but let’s take a closer look. GD&T applies a complete set of rules to the parts and features it controls. The rules are thorough so that parts will conform to any circumstance of tolerance. We can look at this hot rolled cylinder specifically to see what the “actual local size” criteria impose on its geometry. Actual local size refers to the condition of a part or feature where all of its high and low surface points have been assessed. In the case of our cylinder, if we used a point or blade micrometer and measured our hot rolled bar in hundreds of places around and along its surface we would find a set of numbers that reflected all the high and low points of its rough and relatively imprecise surface. This set of numbers represents the real value of the cylinder’s actual local size range.    

I’ve had students comment, “isn’t this taking things to an extreme?” when studying this and similar aspects of GD&T. My response usually sounds something like, “how right does our mechanical world need to be?” GD&T is meant to describe a very precise set of conditions. Parts that find their way into Boeing 787 landing gear assemblies deserve this degree of scrutiny. The engineers that design and detail these pieces of hardware are tasked with the job of making sure their parts will fit and function under extreme conditions. So if we look at those parts in this extreme light we can see that they are exactly what they need to be and we can prove it. The consequence of this level of scrutiny is a guarantee that the millions of lives ferried to their destinations aboard our 787 will arrive as they were intended, thanks in part to actual local size.  

In the world of engineering and manufacturing, we say that GD&T gives us the ability to explicitly describe both nominal geometry and its allowable departure or tolerance from that nominal value. One side of the convention allows for the definition of the geometry and the other allows for the definition of tolerance.

Accomplishing the definitions of both the geometry and tolerancing requires a fairly complex set of rules and procedures which include the very fundamentally indispensable use of datums. Datums provide engineers and countless manufacturing technicians a starting point or reference, fixed on a feature or features of a part, that is used to create and orient the 3-dimensional space in which that part exists. Datums, as we’ve seen with some of our other terms, have different definitions in the perfect world and real world. Datums in the perfect world are defined as perfect things. A datum reference frame is composed of three mutually perpendicular planes, both perfectly perpendicular with each other and each perfectly planar. However when that frame is adapted to a real-world part the story changes. All feature definitions must have applied tolerances and those tolerances always manifest as imperfect features. In the case where a feature is used as a datum, it is called a datum feature. Like some other things we’ve looked at an actual part feature has uniqueness. That uniqueness makes each part, as the term implies, different. I’ll borrow a comparison to say actual part features are like snowflakes, no two are alike. This statement can be argued with because practicality sometimes rules but the truth is that the closer we look, the closer we inspect a real-world feature, the more differences we’ll find. For this reason when a datum is defined by the design or drawing it is one thing and when it becomes a feature on a real-world part it is something else. To prove this point our Y14.5 standard describes the 3, 2, 1 rule. That rule assumes that any real-world part will first need to be landed or fixed in a datum reference frame arrangement in order to measure how that part’s features conform to their requirements. To get an idea of how this is accomplished we need to have a part that gives us a taste of what a real-world part looks like when it’s adapted to a perfect world datum reference frame. So let’s imagine a brick. This first image shows a drawing of the brick and because it’s presently an idea we can call it perfect. The second image is the real world version of the brick, one that’s made from clay in a crude mold and fired in an oven to make it hard. Now if we want to determine if the real world brick is true to what the engineer wants we have to measure the real world item in a perfect world frame of reference. That means we have to apply the 3, 2, 1 rule to it. First, we take the brick and set it in our datum reference frame and position it so it conforms to the engineer’s needs. See the image below to see a reference frame with a rectangular cube arranged in it. The brick’s bottom will be the primary datum A, so we set the brick on the DRF’s perfect A plane and because the brick is really imperfect we learn the brick only comes to a rest on the A plane when it sits on 3 protrusions or points, on its bottom. That’s great because that’s the 3 in our 3, 2, 1 rule. Now, if we look at the picture of our brick we can easily see that it doesn’t form an accurate rectangular cube. The sides on not real planar and they are not square and parallel to each other. So the next thing that needs to happen is the brick needs to scoot on its bottom until it runs into the B plane. Again, because the brick is fairly crude we will only be able to contact that B plane touching two points on the brick’s side, the two high points. Now our brick is sitting in the DRF flat on the A plane and also flat against the B plane, as well as can be accomplished because of the high points on this object. Now our third side of the brick (its end,) needs to lay against the C datum as is then established by scooting the part on its primary datum plane and along its contact with the B datum until it touches the C reference datum plane with what will inevitably be 1 high point of contact. When this has been accomplished the datum features are now said to be located in our datum reference frame. That means we can measure any features on the part as they adhere to the datum reference frame and all the part’s features can be confirmed as to whether they conform to the drawing’s requirements. I think the thing that may be difficult to understand is just how different the real world parts may be from the datum reference frame.   Understanding this procedure helps us to establish a methodology for dealing with datum features (real-world features) as the engineer intended those features to be manufactured and measured. Let’s take this one step further and imagine our brick is a part of an assembly with bearing bores and fluid passages and such. We will now be able to take our part, snuggled into its datum reference frame and measure any of its features to whatever tolerance they need to conform to while the part is adapted to the instruments and devices in the measuring lab through the datum reference frame’s perspective.

Today our featured GD&T term is “features,” which includes “features of size.” But before we jump into this we need to talk about a basic term or thing or maybe we’ll call it a concept, which is the term part. In GD&T a part needs to be thought of as an item, or two or more items joined together, such that their disassembly would cause the impairment or destruction of that thing’s designed use. I think this is important because we in the manufacturing environment labor, discuss and sometimes argue over drawings that have parts on them and those parts are what our GD&T tolerances get applied to. They are the basic unit of our focus and attention. A part is a part.

Now parts come in a wide variety of sizes and complexities. But whether they are complex or simple they can be thought of as being composed of things that fit into the above definition of “disassembly causes destruction” which are called features, and from that we get features of size, which are features with distinctions. We can take more steps to break down these features into their more complex constituents, and we will in future posts, but for now we’ll stay here. A feature is defined as being a physical portion of a part such as a surface, hole, boss or slot. A feature of size is defined in the 2009 Y14.5 standard as “one cylindrical or spherical surface (or circular element,) or two opposed parallel elements (or parallel surfaces,) associated with a directly toleranced dimension.” That’s a mouthful but let’s see if we can translate it. Now the first important thing that pops out is “two opposed parallel elements or surfaces.” A cylinder, whether internal or external, fills that bill. The opposing elements on its surface are parallel and they have an associated dimension, which the engineer is required to put on the drawing; so they qualify. Features which are cylinders can be through holes, blind holes, shafts and bosses. A part can have any number of features on it. A planar part has, as the words imply, planes that make up its “wholeness.” A cube is something we easily recognize as a planar part. A typical cube has 6 planar sides. This simple sketch of a cube shows us those planes. For our purposes here we assume it’s solid. This sketch also shows us how complex things can get in a hurry. Assuming we can see all the features on this part (in other words the sides we can’t see don’t have any other features on them. The features here are 3 holes, to be more precise the holes are blind; they don’t go through the part. So how many features does our cube have now? Did you guess 9? That would be wrong. There are now 12 features that make up our part. 6 planar sides, three cylindrical holes and 3 planar features at the bottom of our 3 holes. Now let’s look at the next sketch. It’s a dice, allowing that in English die is one of a pair of dice but dice is a proper word for both a pair and one dice. Let’s look at our sketch. The part pictured is a cube with rounded corners and it has 3 sides evident with a number of indentations representing the numbers 1, 2 and 4. Let’s assume this dice only has the marks representing numbers on the 3 sides we see. But we can assume that the cube itself is complete as we see it on all the other 6 sides. So it has 6 planar sides and 7 spherical indentations (those representing the 3 numbers we looked at. So how many features does our dice have? 6 planes and 7 cylinders with 7 bottoms like our first example? No, it has 33 features.   No kidding. It has 6 planar sides, it has 7 spherical indentations, it has 12 radiuses joining all of the planar sides at their corners and it has all 8 spherical corners that meet at the joints of the 3 lines that converge where 3 planar sides meet at 90 degrees, for a total of 33.  So we have our definition of features and parts. In GD&T tolerances apply to features as those features relate to parts. GD&T tolerancing controls the shape of features and their orientation to other features. Tolerances control the position and symmetry of features and the relationship of surfaces to the rotational axes of features and parts. And finally, in our digital world, we have controls that tolerance complex surfaces, some of which can only be specified in a computer dataset. This last type makes up what we call tolerances of profile. An airplane wing is an example of a complex surface. There’s one more level that we want to talk about while we’re talking about features. There’s a rule in GD&T that says a tolerance applies to the full width, depth and height of a feature. What does that mean? Let’s look at the dice one more time. We could talk about one of the planar sides and if we applied an orientation tolerance like parallelism to it, as it relates to a plane opposite to it, we could have a viable tolerance responsibility. We’d have to make that cube with two of its sides parallel to a given number expressed in our control. Now for this the tolerance would apply to the full width and height of the plane but not the depth, simply because by definition a plane has no geometric depth. It is a plane. But if we applied that parallelism tolerance to one of the radii that exist at the joint of two of the 6 planar outside surfaces then our definition of the full width, depth and height of our feature can be seen to be valid. The point is that a feature has definition. Features exist where they are defined, in 2 or 3 dimensions and because engineering drawings must have complete definitions for all the things on them then whether our feature is a 2 dimensional plane or a 3 dimensional cylinder, it’s defined size or any tolerance that applies to it must apply to its full width, depth and height.  

In GD&T basic dimensions used to be a fairly simple thing to define. However, today, among other things, “Basic dimensions” are numbers on an engineering drawing that represent values of size in whatever the measurement system being used on the drawing is. Those values are used to describe the theoretically exact size, profile, orientation or location of a feature or datum target. Those values can be recognized as “basic dimensions” because they are identified by the fact that they’re contained in a box drawn with a thin solid line.

Basic dimensions, identified by the engineer, locate tolerance zones. Because that’s true, basic dimensions identify tolerance information located in feature control frames that state geometric tolerances. When an engineer makes a statement of tolerance, that statement is made in the form of a feature control frame. Feature control frames have an defined format in the ASME Y14.5 standards, which can be found elsewhere in this glossary. It can be said that Basic dimensions were identified by the engineer to eliminate possible confusion resulting from which dimensions would or should be used to establish the tolerance contained in the feature control frame. We can see in the illustration below that there is an angularity tolerance stated to control the angled surface that the feature control frame points to. It states a tolerance of .030 units to datum A. We can also see that the toleranced surface and the datum A surface have extension lines leading to a value listed inside a box stated as 60 degrees. So we see in this very simple drawing all the ingredients for our tolerance. We have a tolerance type, a tolerance value and when we look for our basic dimension we see the identified 60 degree value inside the box, which is our basic dimension.

However, today, due to the advent of CAD based models that control part geometry the industry is seeing some new wrinkles. It’s becoming common, usually with the addition of a note on the drawing, to find that it (the note,) says that for undimensioned features refer to 3D data-file. All dimensions from the file are considered basic and shall be controlled by the tolerance (meaning the applicable geometric tolerance) indicated on the drawing. Drawings with this verbiage, in our experience, contain increasingly less dimensioning on the face of the 2D drawing in keeping with what is known as PDD (partially defined drawing.) This, in our minds, does a good job of defeating the purpose of basic dimensions. GD&T was constructed and developed around the concept that coordinate tolerancing lacked the ability to adequately specify both the geometry and tolerancing of our mechanical world. GD&T gives us those capabilities. But PDDs may be causing problems with GD&T’s ability to be precisely specific. I’m looking at a customer’s drawing. That customer is a government prime contractor. The drawing I’m looking at portrays a part that serves as a mounting plate, with more than 50 various size holes that are tapped in a number of sizes, or reamed for hardware installation etc. The part also has a number of cutouts that may be lightening features and some that likely serve to mount specialty assemblies or hardware. There are 14 GD&T feature control frames on the drawing. There are a total of 5 coordinate tolerances on the drawing, and two reference dimensions. Except for the written notes that’s it. Not one dimension inside our defined boxes. The note I mentioned earlier, about undimensioned features is meant to absolve the company and its engineers from giving us the data that our ASME standard promised. I’m sure there are arguments to justify why companies are doing this but in our mind those arguments only support a value to the originator of the drawings. It saves time and makes their drawings more concise, which are good things for them. But that note doesn’t do away with why the standards defined and implemented basic dimensions in the first place. They define the exact size, profile, orientation and location of features.

Today we’re going to look at the concentricity control. This control is used a lot in a variety of situations that involve coaxial relationships. The definition states that concentricity controls ‘all’ diametrically opposed elements of a figure of revolution.

 

Breaking Down the Basics

Let’s break that down and look at a few rules for this tolerance. First we have the term ‘diametrically opposed.’ In geometry this means exactly opposite on a diameter.  Next we have the word elements. This refers to an entity that satisfies all the conditions of being in a set. In our case this set contains all the lines that intersect both the diameter and the axis of the cylinder in question, when those elements are normal or square to that axis. Each element is a line that passes through the opposite sides of a cylinder and through and perpendicular to the axis of the cylinder.  On an imperfect cylinder, which includes all the cylinders in our manufacturing world these elements run from one side of the cylinder to the other and because the inside (or outside, because each is simply a surface,) of our cylinder is imperfect each element will touch imperfections on both sides of that surface so when the axis of the cylinder divides the element in two, the two parts will be unequal.

Using Elements To Divide An Imperfect Cylinder

 If we can imagine inscribing even a moderate number of these elements inside our cylinder it’s not too difficult to imagine a bunch of dividing points on our line elements and because they are each located at a different place inside our imperfect cylinder the points that divide them will definitely not be lined up, in fact they will appear to be what is described as a cloud of points. Our cloud of points is made up of the bisections of all those diametral elements. And when our cloud is associated to a concentricity tolerance, such as we’re working to define, that cloud must lie inside a cylinder equal to the value of the tolerance in the FCF.  I’ve seen this cloud referred to as a derived median line but it’s really a derived solid, imperfect cylinder.

Foundational Knowledge of Concentricity

Concentricity is also allowed where we have two or more radially disposed features about a datum axis such as hex features and other like geometry. Concentricity must reference a datum to be a valid control. That datum is always the axis or point of rotation of the datum feature. It is also OK to reference two datums, one primary and one as the datum axis, in cases where a flange or hub feature attaches to a rotating member and the hub face must be acceptably perpendicular to the datum axis as well as coaxial.  Concentricity is always to be taken at RFS. No material condition modifiers or datum feature modifiers such MMC or MMB are used with this control. The tolerance zone is always cylindrical and coaxial to the datum axis or spherical and coaxial to the datum center point. Controlled features are usually cylindrical but can be spherical and I’ve seen conical features included in the definition but that may be OK because a cone can be looked at as an extremely imperfect cylinder.      So here we have a concentricity callout in our FCF. It states that the feature in question must be concentric to datum A to a tolerance of .001”. That’s pretty much a typical callout. I took it right off of a drawing I quoted last week.  Now we can step back and assess what we’ve described. For the most part we have a feature of size that’s been chosen to have a close relationship to some other feature’s datum axis. To make an assessment of whether the part conforms to our concentricity callout we must make a representative check of the surface of our controlled cylinder as it compares, by our definition, to the datum axis.  To accomplish the task we must make a considerably large number of measurements. We would need to determine if our bisected, diametrically opposed elements, describe a cloud of points that all fall within our tolerance zone cylinder. Not only is that a mouthful but it’s a sizable measuring job.

Justifying The Use Of Concentricity

Here we get to a place where there are a number of opinions flying about our GD&T user world. “To use or not to use concentricity, that is the question.”  My cut at it is, “Don’t, unless you need to.” Coaxiality can be achieved in GD&T using several methods. Position accomplishes it and so does runout. So why might we not use concentricity could be explained with the above definition of the complexity of the tolerance. Why we would use it should probably boil down to if we really need it.  There’s a consensus of expert opinion that the possible real need for concentricity would be in cases where there is a high speed rotating mass or perhaps a need for extreme balance in a coaxial relationship. Concentricity does provide a close distribution of coaxial mass, which would lend a needed quality of balanced mass and inertia.      So in cases where these qualities are needed, the onerous task of proving concentricity would be justified. However, for the task of achieving simple coaxiality, position or runout can be used where the axes of the datum and toleranced feature can be measured by finding the actual mating envelope of the feature or simply putting an indicator on a rotating assembly.    I think the long history of using concentricity to achieve coaxiality is no longer needed. It’s interesting that concentricity has been used on coordinate toleranced drawings for a long time, long before the prevalent use of GD&T, and maybe that’s the reason why we still see it used as much as we do.