GD&T

Geometric Dimensioning and Tolerancing - Symbols, Datums, and Tolerance Zones

Controlling and tracking engineering design changes has become more important as the design and manufacturing line becomes more agile and separated between design firms, contractors, subcontractors, specialized manufacturing and testing firms, etc. As design becomes agile, engineering drawings and communications are touched by more hands, introducing more variables and points of failure within a design and manufacturing line.

Geometric dimensioning and tolerancing (GD&T) can guarantee an engineering drawing is interpreted in the same manner by everyone who is involved in the pipeline. Completely tolerancing a drawing will not only reduce variables and points of failure, but will also protect the designers against cost liability. When all features and components on an individual part and on an assembly are controlled for form, location, and orientation per the ISO and ANSI/ASME standards, cost liability due to manufacturing will be limited to design changes and manufacturing capability.

# Symbols

Maximum Material Requirement (Condition)

Least Material Requirement (Condition)

Projected Tolerance Zone

Free State

Regardless of Feature Size

Tangent Method

Unsymmetrical Tolerance Zone

Line Profile

Straightness

Roundness

Surface Profile

Flatness

Cylindricity

Angularity

Parallelism

Perpendicularity

[True] Position

Coaxiality

Symmetry

Circular Run-Out

Total Run-Out

# Datums

The datum is a reference point, surface, or axis on a part that controls the geometric feature measurements are made from. Dimensions and geometric tolerances can reference datums, indicating that the measurement is with respect to that reference frame. Each part or feature is controlled by a coordinate system that introduces degrees of freedom onto the feature. The primary, secondary, and tertiary reference datums control the feature by fully defining the location and orientation.

**Primary Datum** – Datum feature oriented with respect to the location of the form tolerance zone (or the surface where the feature is controlled) and relative to the surface making up the geometric feature the datum is taking form of, such as a plane.

**Secondary Datum** – Oriented perpendicular to the primary datum with similar location controls.

**Tertiary Datum** – Oriented perpendicular to both the primary and secondary datum and located on a surface relative by translation to the location of the form tolerance zone.

# Definition of Geometric Tolerances

Each geometric tolerance is defined by a geometric element, and therefore, each part or component feature can be broken up into geometric elements.

- Planes
- Cylinders
- Cones
- Spheres
- Etc.

The geometric elements are relative to the degrees of freedom determined by the datums and are considered the nominal, or theoretical exact, form of the feature. Geometric tolerances and standard tolerances allow for controlled deviation from the nominal values, creating a design and manufacturing buffer zone where the part will continue to work properly.

### Form Tolerance

The permitted maximum value of form deviation on a line or a surface. Form deviation can be measured on a 2d or a 3d geometric feature, and is controlled by the reference datum.

### Orientation Tolerance

The permitted maximum value of orientation deviation including angularity, parallelism, and perpendicularity with respect to a reference datum.

### Location Tolerance

The permitted maximum value of location deviation including position, coaxiality, and symmetry with respect to a feature or a reference datum. The difference between the theoretical location and actual location cannot exceed half of the location tolerance.

### Run-Out Tolerances

The permitted tolerance zone is between two geometric elements, such as a plane, that are parallel or concentric and equidistant apart from the nominal location. The spacing of the geometric elements is the run-out tolerance value.

### Line Profile Tolerances

The line profile is a 2d representation of a 3d feature. The deviation of the cross-section is can be controlled by the line profile tolerance, which imposes an upper and lower limit to the deviation, equidistant from the nominal line profile. The upper and lower limits are equal in profile to the nominal profile. The space between the equidistant line profile tolerance limits is considered the tolerance zone.

### Straightness Tolerance

The maximum deviation of line straightness, where the nominal line profile is a straight line and the limits are composed of parallel and equidistant lines with respect to the nominal location/orientation.

### Roundness (Circularity) Tolerance

Each cross-section of a circular profile must fit between two concentric circles.

### Surface Profile Tolerance

The whole surface profile deviation is permitted to be between two surface profiles of equal properties to and with parallel tangent lines to the nominal surface profile. The area between the two profiles is the tolerance zone. The surface profile is the 3d representation of the line profile cross-section.

### Cylindricity Tolerance

The surface deviation is contained between two coaxial cylindrical geometric features.

### Flatness Tolerance

The surface deviation is contained between two parallel planer geometric features.

### Angular Tolerance

The deviation is permitted between two parallel planes angled equally with respect to the nominal geometric element, based on the called out datum. The angular tolerance controls for the angle over the entire feature length, but does not control for flatness or straightness within the angular tolerance zone.

### Perpendicularity Tolerance

The deviation is permitted between two parallel planes perpendicular to the called out datum.

### Parallelism Tolerance

The deviation is permitted between two parallel planes parallel to the called out datum.

### Positional Tolerances

The deviation from the nominal position is contained within a cylinder whose axis is on the nominal positional location. The geometric tolerance is with respect to one or multiple datums.

For example, designing a positional tolerance zone for a through-hole that will contain a bolt or a dowel pin is controlled by the minimum size of the hole and the maximum size of the bolt or pin. In this example, the location tolerance for the threaded hole and the clearance hole will be equal (in many cases, the tolerance will be disproportional and the clearance hole will be given a larger tolerance zone) and the tolerance can be calculated by the following:

For more information on this type of example, read this newsletter: http://ttc-cogorno.com/Newsletters/130315FixedFasteners.pdf

Standard values for clearance holes with respect to a thread diameter can be found in the ISO 273 document. (http://www.metricmcc.com/catalog/ch10/10-1040.pdf) Similar calculations for fit and interference clearance on other types of features can be used while designing for positional tolerance. Non-standard shapes should be controlled by other geometric tolerances in parallel with positional tolerances to limit the maximum material conditions if interference on a fit is possible.

### Coaxial Tolerance

The deviation of the axis of a feature is contained within a cylinder, limiting variance by translation, angle, and straightness. Coaxial tolerance is considered concentricity tolerance if the feature is on a thin sheet or a measurement of an engraving.

### Symmetry Tolerance

The surface deviation is contained between two parallel planes symmetrically disposed about a surface datum plane located on the nominal surface.

### Run out tolerance

Each cross-section, coaxial section or conical section with respect to the called out datum can deviate between two concentric or parallel 2d geometric features.

### Total run out tolerance

The surface is contained between two concentric, parallel, or coaxial 3d geometric features with respect to the called out datum.

# Tolerance Zone

The tolerance zone of a geometric tolerance constraint is the maximum allowed deviation in all directions for a dimensioned feature on a part. For example, the tolerance zone of a feature constrained with a roundness tolerance will be in the shape of the space between 2 concentric circles because the edges of the allowed deviation take the same shape as the nominal.

The tolerance zone can be considered 2d or 3d and is formed using geometric elements at the edge cases of the geometric tolerance at the maximum material condition or the minimum material condition. Example shapes of the tolerance zone are:

- Circle
- 2 concentric circles
- 2 equidistant lines or parallel lines
- Sphere
- Cylinder
- 2 coaxial cylinders
- 2 equidistant faces or parallel planes
- Parallelepiped – 3 dimensional figure formed by 6 parallelograms

Another example: Let’s say we have a slot with different geometric positional tolerance constraints in each direction and the tolerances are with respect to different datums. Each tolerance case will be looked at separately and will have individually associated tolerance zones. At the maximum condition of the slot (found using standard tolerances associated with the slot dimensions), the tolerance zone is determined to be made up of two parallel lines or planes in a direction with respect to datum A and two parallel lines or planed in a direction with respect to datum B, forming a rectangular tolerance zone encompassing the feature and all geometric tolerancing associated with the feature.

## Projected tolerance zones

Tolerance zones that dictate the fit across multiple features or components can involve compounding geometric tolerances that can cause interference. Projected tolerance zones are a form of interference analysis that limit the center axial translation and orientation to allow the design to work under the worst manufacturing conditions.

For example, the axial tolerance zone on a through-hole between two mating parts will restrict the angle and translation of the bolt or dowel pin used in this assembly.

### Maximum Material Requirement

The maximum material requirement is the instruction used when the worst case manufacturing conditions based on the feature tolerances and geometric tolerances will still allow the part to work as intended.

The maximum material condition (MMC) is the maximum edge condition of a feature where the maximum material exists. For example, the maximum material condition for a hole will be the smallest hole allowable, controlled by the feature tolerances. The most common GD&T symbol that MMC is applied to is the positional tolerance (or true position).

Using the MMC is useful if the possibility of interference of fit needs to be reduced or eliminated. A design with MMC on an opening and MMC on a feature that fits into the opening will (in most cases) guarantee the assembly works as intended in the worst manufacturing conditions.

The maximum material virtual size (MMVS) is the MMC and the maximum geometric tolerance applied. An inspection gauge can be created by determining the MMVS of a feature and using the limits to create a mating part with respect to the GD&T datums.

### “Bonus” Tolerance

If the feature is made to the MMC, “bonus” geometric tolerance is created because the allowed deviation is not being used fully. If a hole is near the edge of the geometric tolerance zone, the hole size can be increased to relieve the tolerance limits. If a pin is near the edge of the geometric tolerance zone, it can be reduced in size to relieve the tolerance limits.

The bonus tolerance is the difference between the MMC and the actual manufactured condition.

## Accumulation of tolerances (Compounding tolerances)

The accumulation of tolerances, or compounding of tolerances, between multiple part features or assembly features can cause interference of fit and cause the part or assembly to not work as intended. An interference analysis of the minimum and maximum tolerance conditions will shed light on how the accumulation of tolerances is affecting the conditions of the assembly.

Stacking individual tolerances can cause overall dimensions to become unattainable, therefore controlling dimensions for the limits of tolerances is recommended. Part-wide and assembly-wide tolerances limit the maximum tolerance deviation and can be used in conjunction with localized feature tolerances and geometric tolerances.

Controlling for tolerance limits can dramatically increase the cost of a part to procure. Limiting the tight tolerance zones in the interference analysis where necessary will reduce the overall headache. The statistical analysis of the manufacturing process and determining a bell curve limit for all compounding tolerances and dimensions will allow the design engineer to determine a reasonable risk factor and additional rework costs involved.

*Jarrett Linowes**Mechanical Engineeromniamfg@gmail.com*

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