(See related pages)
Geometric dimensioning and tolerancing (GDT) was developed over the last forty years as a tool to define parts and features more efficiently. GDT takes the function of the part into consideration, as well as its fit with related parts. This allows the designer to define the parts features more accurately, without increasing the tolerances.
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OVERVIEW |
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| 16.1 Within the last 15 years there has been considerable interest in GDT, in part because of the increased popularity of statistical process control. This control process, when combined with GDT, helps reduce or eliminate inspection of features on the manufactured object. The flip side is that the part must be toleranced very efficiently; this is where GDT comes in. Another reason for the increased popularity of GDT is the rise of worldwide standards, such as ISO 9000, which require universally understood and accepted methods of documentation. |
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GDT SYMBOLS |
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| 16.2 At the heart of GDT is a rectangular box, called the feature control frame, in which the tolerancing information is placed. Figure 16.3 shows an example of one. |
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INDIVIDUAL FEATURE OF SIZE |
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| 16.3 This rule covers the individual feature size and states: Where only a tolerance of size is specified, the limits of size of an individual feature prescribe the extent to which variations in its geometric form, as well as size, are allowed. The critical point is that GDT is concerned with both the shape and position of features. |
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MAXIMUM MATERIAL CONDITION |
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| 16.4 Maximum material condition (MMC) is the condition in which: An external feature, like a shaft, is its largest allowable size. An internal feature, like a hole, is its smallest allowable size. Taken together, it means the part will weigh its maximum. |
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| 16.4.1 Three symbols pertaining to material conditions are: M - Maximum material condition L - Least material condition. This is the opposite of MMC (the part will weigh its minimum) S - Regardless of material size. This indicates the material condition is not to be considered. |
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| 16.4.2 Departure from MMC refers to how much less material a part has than its MMC. For a hole, this would mean how much larger it is from MMC. Departure from LMC would be the opposite. |
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| 16.4.3 The envelope principle describes an idealized MMC of a part. Since any departure from MMC means less material, all parts should fit within an envelope described by MMC. |
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| 16.4.4 One of the keys to is that it allows separation of size from form. This added flexibility means that part can be manufactured at the highest allowable tolerance (and thus lowest cost) and still work. This two variables can be manipulated to meet the particular demands of the part functionality. |
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INSPECTION TOOLS |
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| 16.5 Some of the more important inspection tools used in are: Surface plate Height Gage Caliper Micrometer Precision spindle Centers Dial indicator Coordinate measuring machine (CMM) |
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DATUMS AND DATUM FEATURES |
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| 16.6 A datum is a starting point for a dimension. Datums are theoretically ideal locations in space such as a plane, centerline, or point. A datum may be represented either directly or indirectly by an inspection device. The surface of the object which is placed on the inspection device representing the datum is called the datum feature. These datum features are clearly marked in the drawings to indicate which are the reference surfaces to make measurements from. |
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| 16.6.1 Once a datum is established, the measurements can be taken from it rather than features on the object. That is to say, the object feature representing the datum is aligned/placed on the inspection device and the measurement is taken. The datum establishes the method of locating other features on the object relative to each other. |
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| 16.6.2 Datums are not only used internal to a part but, more importantly, in relation to mating parts in an assembly. |
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| 16.6.3 Datum features should be selected carefully based on their size, stability, accessibility, functionality, etc. (See section 16.6.5) |
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| 16.6.4 Datums are the locators and the datum reference frame is the six degrees of freedom of movement from the datum. The six degrees of freedom are the plus and minus directions along the three Cartesian coordinate axes. Another way of looking at the frame is as three orthogonal planes. |
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| 16.6.5 At a minimum, a part will have a primary datum. This datum will be chosen based on a number of criteria: Stability. This is the most important feature. Often dictating that the largest, flattest surface is chosen. Functional relationship. How does the feature mate/interact with other features? Accessibility. Can the part be mounted and measured on the inspection device via this feature? Repeatability. Variations in the datum feature due to manufacturing should be predictable so they can be accounted for. |
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| 16.6.6 Secondary and tertiary datums, if needed, should be located mutually perpendicular to each other and to the primary datum. |
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| 16.6.7 The primary, secondary, and tertiary datums are identified with the letters A, B, and C, respectively. |
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GEOMETRIC CONTROLS |
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| 16.7 Geometric controls fall into three major categories: Form Orientation Position |
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| 16.7.1 A gaging tolerance establishes when a part is 'perfect'. For example, an inspection instrument is considered perfect if it is ten times more accurate than the part being measured. |
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| 16.7.2 Refer to tolerance zones in the section on Tolerances in Chapter 15. |
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| 16.7.3 The virtual condition is the combined effect of the largest allowable size (MMC) and the largest amount of geometric distortion. It is, in effect, the worst allowable condition of the part. |
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| 16.7.4 There are a number of ways parts are inspected: Functional gaging. They are hand built inspection devices made to simplify the inspection of a large number of parts. Open gaging. The inspection of parts without any dedicated fixtures. Examples would be inspection with calipers or surface plates. Feature of size. A feature that is directly measurable. |
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| 16.7.5 Form controls are a comparison of an actual feature to a theoretically perfect one. Refer to the text for the methods of inspection (i.e. the type of gaging) and the basis for rejecting/accepting a part. The controls include: Straightness. All form controls are variations and combinations of straightness. Straightness itself is based on a line element. Straightness has two distinct variations: Line element straightness. This compares a line on the part to a perfectly straight line. If the line is on a flat surface, the direction must be identified. Axis straightness. This compares the axis of a cylindrical feature to a perfectly straight line. The axis can also define other symmetric forms such as a square tube. Roundness. This compares a circular element on a feature to a perfect circle. Roundness could be considered straightness bent into a circle. Note that the circle is being measured for form only (i.e. no MMC is applied). Flatness. Evaluates the highest and lowest point on a surface. That is, the surface is compared to a perfect plane (straightness applied in all directions). Cylindricity. In comparing a feature to a perfect cylinder, three factors are being considered: straightness of all line elements, roundness of all circular elements, and taper (comparison of circular elements to each other). This is probably the most expensive control due to its difficulty in measuring. |
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| 16.7.6 Orientation controls include: Parallelism. This could be considered flatness at a distance or straightness of an axis at a distance. Perpendicularity. This could be considered flatness or straightness of an axis 90 degrees to a datum. Angularity. This could be considered flatness or straightness of an axis at some angle to a datum. Line profile. This takes a cross-sectional slice or slices of a feature and compares it to an ideal shape. The control shape is usually some contiguous collection of mathematically defined line elements (e.g. straight lines, circular arcs, elliptical curves, etc.). Surface profile. This profile is constructed by stacking line profiles into a 3-D surface. |
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| 16.7.7 Position controls include: Concentricity. The condition in which all cross sectional elements share the same datum axis. This control is important for spinning parts where dynamic balance is important. Though concentricity is a control of position, it is also concerned with shape since the shape can affect the location of the axis. Runout. There are two types of runout: single element and total. This control is best described by its method of measurement. Single element runout places a gage on the rotating part and measures the amount of fluctuation. With a perfectly centered cylinder, the gage would not fluctuate. Total runout has the gage move up and down along the central axis to measure all possible cross sections. Position. This is the more flexible and versatile control. A few of the things this control can do is: Locate holes or a pattern of holes. Locate the center of a feature. Keep holes or other features perpendicular or parallel to other features. Keep features straight and round. Allow loose tolerances on the sizes of features while maintaining close control on their locations. Hole location from edges. This is used so that multiple holes are located accurately enough that mating parts with the same number of matching pins will assemble properly. A functional gage designed for this use would have perfect cylinders placed at the exact basic dimension from the surfaces representing the datum(s) and from each other. This positional tolerance would not have any meaning without taking MMC into account. Hole location from hole. The key to this control is that holes are located relative to another hole, not the edge of the part. Coaxial datum and feature. This control ensures that a smaller, internal diameter is centered on a larger, external diameter. Symmetry. This control ensures that the feature is centered on the datum. |
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TOLERANCE CALCULATIONS |
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| 16.8.1 Floating fastener tolerancing is used to confirm that loose bolts, screws or other fasteners have the standard clearance in their holes. |
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| 16.8.2 Fixed fastener tolerancing is measured the same as with floating fasteners except that the fastener is already fixed/located on one of the mating parts and the tolerance is now divided between the parts. |
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| 16.8.3 Hole diameter tolerancing is used to calculate the MMC of the hole. |
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DESIGN APPLICATIONS |
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| 16.9.1 There is a five-step process for applying principles to the design process. They are: Isolate and define the functions of the features/part. Prioritize the functions. Identify the datum reference frame based on functional priorities. Select the proper control(s). |
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| 16.9.2 This section goes into a practical example. It is worth both stepping through this example and then applying the five steps to other simple parts with your students. Often there is not one 'right' answer, but it allows them to think critically about the placement of the reference frame and the selection of controls. |
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STATISTICAL PROCESS CONTROL |
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| 16.10 The goal of statistical process control (SPC) is to use the science of statistics and the predictive capability it gives to minimize the number parts which need to be inspected while still keeping quality at the desired level. Careful evaluation of a selected sample of a produced part will allow the engineer to describe the likely makeup of the rest of the copies of this part coming off the production line. Knowing of and taking into account all of the variables which will affect part quality (e.g. tools wear, raw material quality, worker motivation, etc.) is critical to this process. These variables must be balanced in order to have a representative sample of the parts in order to make this prediction. For example, taking samples just after tooling is changed may give a unrealistic representation as to how much material is being removed from the part. |
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| 16.10.1 GDT interacts well with SPC because it gives uniform, quantifiable data for use in developing a representative description of the statistical sample. |
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| 16.10.2 Tolerancing analysis demands that a tolerance is based on the design requirements of the feature, rather than on the manufacturing method used to create a feature. Following this rule, specifying dimensions on a drawing based on a manufacturing operation (e.g. 12 DRILL) is discouraged in favor of specifying the functional requirements of the feature. The functional requirements may have a tolerance which is greatly divergent from the tolerance of the manufacturing operation specified. |
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SUMMARY |
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Geometric dimensioning and tolerancing (GDT) is essential to the modern manufacturing environment. The first rule of GDT is that size control of a feature (as is given in a dimension) inherently includes controls of form. The goal of GDT is to carefully evaluate the functionality of a part and its features and only control the geometry of those features necessary for the proper functioning of the part. Also related to this goal is to remember that usually involves the loosening, not tightening, of tolerances because its robust specificity allows for trade-offs between size and form. Together, these qualities of GDT, when combined with statistical process control, should help minimize manufacturing costs. This process leads to controlling the fewest number of features, at the largest allowable tolerance, and is confirmed through checking the fewest number of parts; all of this while still keeping quality within a quantifiable goal. |