LOCATION TOLERANCES Concentricity Symmetry Position

LOCATION TOLERANCES Concentricity Symmetry Position
These are the three geometric tolerance controls and their associated symbols, that are available within the family of location tolerances.

Concentricity DEFINITION
Concentricity is normally applied to (Two or more) features that are required to revolve around a datum axis. A time- and resource-intensive verification process—usually involving a complex mathematical analysis—is required. Concentricity is a condition where the median points of all diametrically opposed elements of a feature of revolution around an axis coincide with the axis or center point of a datum feature. Concentricity is always applied to features of size, always applies regardless of feature size, and always requires a datum reference. A concentricity tolerance and its datum reference can only apply regardless of feature size and therefore, cannot be modified to MMC or LMC,

Concentricity Concentricity is most often thought of as a coaxiality control, and because it must be verified from surface elements, it always applies RFS. Concentricity cannot be applied to a feature; it must always be applied to features of size. However, it cannot be modified to take advantage of bonus tolerances, and must always reference a datum axis. In addition, fixed (functional) gages cannot be used in the verification process. Verification must be done with variable gaging—usually resulting in higher costs. 12 -0.2 25 -0.5 E E

Concentricity Regardless of feature size, median points from all opposing two-point measurements on the head of the pin in this example, must be within a cylindrical tolerance zone, 0.2 mm in diameter. A variable gage will be used to secure datum feature E, and determine the datum axis. Apposing point measurements will then be taken to verify median points for all measurements across the diameter of the head of the pin. The clustering of all derived median points must be within the cylindrical tolerance zone centered around datum axis E. -0.5 25 E E -0.2 12

Verifying Concentricity
-0.5 25 E E At every measuring location of diametrically opposed elements, a median point must be established. -0.2 12 -0.5 25 E E -0.2 12

Verifying Concentricity
-0.5 25 E E At every measuring location of diametrically opposed elements, a median point must be established. -0.2 12 -0.5 25 E E Regardless of feature size, all median points of diametrically opposed elements of the feature must lie within the 0.2 diameter cylindrical tolerance zone, which is also centered around the datum axis. -0.2 12

SYMMETRY OF SIZE FEATURES

Symmetry DEFINITION: Symmetry is a condition where the median points of all opposed or correspondingly-located elements of two or more feature surfaces are coincident with the axis or center plane of a datum feature. Symmetry is always applied to features of size, always applies regardless of feature size, and always requires a datum reference. A symmetry tolerance and its datum reference can only apply regardless of feature size. Symmetry cannot be modified to MMC or LMC. Symmetry, like concentricity, requires a time- and resource-intensive verification process. Median points for all opposed elements of the controlled feature, must be verified.

Symmetry of Size Features
The requirement for this object is that the two sides of the groove be symmetrical about the center plane. The center plane is established by the height feature of size dimension, and the symmetry control is called out in the feature control frame. 8.8 8.2 A 0.4 A 20.5 20.0

Symmetry of Size Features
8.8 8.2 A 0.4 A 20.5 20.0 Center plane of datum feature A, ascertained by variable gage. The median points of all opposed elements of the groove (measurements across the opening and perpendicular to the center plane) must lie between two parallel planes 0.4 mm apart, which planes must also be parallel to the center plane. 0.4 wide tolerance zone

TOLERANCES OF POSITION

TOLERANCES OF POSITION
Industry uses tolerances of position because they: control the theoretically exact location of features, simulate mating part (worst case) relationships, may be modified to MMC and LMC, provide flexibility in verification and simulation, may be used to control features in coaxial relationships, provide symmetrical controls of features relative to a center plane, and frequently provide generous margins of cost-savings.

COORDINATE TOLERANCING COMPARED TO POSITION TOLERANCING

COORDINATE LOCATION TOLERANCING

Coordinate tolerancing of a hole location
Using standard dimensions with plus and minus tolerances, locate the intersecting center planes which locate the center line or axis of a feature (in this case, a hole).

Each of the tolerances on the coordinate dimensions is  .005, or .010 inches. First, add the tolerance limits on the horizontal dimension.

.755 ( ) .745 ( ) Next add to the drawing the plus and minus value to the vertical dimension.

.755 ( ) .745 ( ) 24.005 23.995 The tolerance zone (in this case) will now measure exactly ten thousandths on any vertical or horizontal coordinate. However, when measured along any other orientation, the distance increases proportionately.

.755 ( ) .745 ( ) 24.005 .014 23.995 The tolerance zone in this case will now measure exactly ten thousandths on any vertical or horizontal coordinate. However, when measured in any orientation other than vertical or horizontal, the distance increases proportionately, until a maximum is reached at the corners of the tolerance zone.

The Coordinate Tolerance Dilemma
The assignment of coordinate dimensions with their associated tolerance limits (plus/minus or otherwise), creates a set of interesting problems for design personnel. A careful analysis of any design project that has been defined using coordinate plus and minus tolerances, reveals the following circumstances that must be dealt with by the designer or engineer: Coordinate tolerances produce 3-D rectangular tolerance zones--(width, height, and depth). The feature axis can be established and exist anywhere within the limits of the tolerance zone. The 3-D diagonal measurement through a rectangular tolerance zone must be functionally acceptable to the designer. If the diagonal measurement is valid, then generally speaking, shouldn’t the same value be acceptable in all directions? Coordinate dimensions for location of features requires additional evaluation to determine the worst case scenario (diagonal measurements).

POSITION LOCATION TOLERANCING

Coordinate Location Tolerance
.010 .010 .014 Returning to the previous example, let’s examine both the dilemma and a solution. If the designer can live with a tolerance of .007 on the diagonal—in the worst case, then the tolerance of .005 for coordinate locating dimensions could be specified, all of which compounds the tolerance analysis. Instead of using a rectangular coordinate zone, let’s substitute a cylindrical tolerance zone that will allow .007 in all directions from its center.

.010 .010 .014 The tolerance zone for acceptable axis location increases significantly when the tolerance zone is defined as a cylinder. By defining the zone in this way, axis location is permitted to vary from its true position by an equal amount in all directions. In other words, the tolerance zone expands to include areas that were previously unacceptable. In some instances, useable parts have been rejected because the axis location of features was found to be outside the limits of coordinate tolerance boundaries—but would have been within the circular limits.

.010 .010 .014 Geometric (position) tolerancing allows the tolerance zone to be defined as a cylinder, the diameter of which is equal to the diagonal distance across the corners of the coordinate tolerance zone. The previously unusable tolerance area increases the available tolerance by 57%!

The 57% increase in usable tolerance (shaded areas) derived from geometric tolerancing, would not be acceptable in coordinate tolerancing situations. The small red crosses represent a few of the infinite number of possible axis locations that would be unacceptable, using coordinate tolerancing, but which would be acceptable in position tolerancing. Consequently, geometric position tolerancing –in appropriate applications—has provided significant cost savings.

TRUE POSITION GEOMETRIC TOLERANCING

DEFINITION True Position is the exact or perfect location of a point, line or plane—usually the center of a size feature—in relationship to a datum reference frame and/or other features of size.

DEFINITION True Position Tolerance A specified area or zone, within which the center, axis, or center plane of a feature of size is permitted to vary from its theoretically exact or ‘true’ position.

DEFINITION True Position Tolerance A specified area or zone, within which the center, axis, or center plane of a feature of size is permitted to vary from its theoretically exact or ‘true’ position. Note: When features of size are controlled at MMC or LMC, the tolerance is defined by the virtual condition boundary, located at its theoretically exact position, which cannot be violated by surface elements of the controlled feature.

Basic Dimensions on Drawings
In the past, basic dimensions were labeled BASIC or BSC following or below the dimension (see MIL STD 8C; ANSI Y ; ANSI Y14.5–1982). This practice is no longer recommended. 3.438 BASIC 3.000 BSC

In the past, basic dimensions were labeled BASIC or BSC following or below the dimension (see MIL STD 8C; ANSI Y ; ANSI Y14.5–1982). This practice is no longer recommended. Basic dimensions are (and were) also identified in a special symbol –an enclosing rectangle:* 3.438 BASIC 3.000 BSC 24.6 * Current recommended practice ASME Y14.5M-1994

In the past, basic dimensions were labeled BASIC or BSC following or below the dimension (see MIL STD 8C; ANSI Y ; ANSI Y14.5–1982). This practice is no longer recommended. Basic dimensions are (and were) also identified in a special symbol –an enclosing rectangle:* They were also called out in special notes.* 3.438 BASIC 3.000 BSC 24.6 UNLESS OTHERWISE SPECIFIED, ALL UNTOLERANCED DIMENSIONS ARE BASIC * Current recommended practice ASME Y14.5M-1994

MMC BOUNDARY THEORY (INTERNAL FEATURES—HOLES)

Boundary Theory (Internal Features—Holes)
Two center planes are necessary to identify the location of a hole.

True Position Basic dimensions locate the true position of the hole by locating the two required center planes from datum surfaces (or other features of size that are, themselves, located relative to a datum or datums).

Cylindrical Tolerance Zone True Position A feature control frame is associated with the size dimension of the hole, and specifies the tolerance zone (shape and size) for the feature—in this case a cylindrical tolerance zone for the axis of a hole.

Cylindrical Tolerance Zone True Position The theoretical boundary for the hole is determined by subtracting the position tolerance from the maximum material condition of the hole size (this is also the virtual condition or VC of the hole). This boundary is centered on the true position. Theoretical Boundary (Virtual Condition- Hole at MMC – GTOL Tolerance)

Cylindrical Tolerance Zone True Position (Actual Hole Diameter) M The location of the hole axis may vary within its cylindrical tolerance limits (yellow circle), but no element of the hole surface may ever be inside the theoretical boundary (blue-green circle). Theoretical Boundary

Cylindrical Tolerance Zone True Position (Actual Hole Diameter) M The series of slides that follow, show various positions of the axis and resulting hole. Notice that the theoretical boundary is never violated. Theoretical Boundary

Cylindrical Tolerance Zone True Position (Actual Hole Diameter) M Note that for every incremental change of axis location (always located at an extreme position), the actual hole surface is outside the theoretical boundary. Theoretical Boundary

MMC BOUNDARY THEORY (EXTERNAL FEATURES—SHAFTS)

MMC Boundary Theory (External Features—Studs, Posts, Etc.)
The true position is located For an external feature. True Position

A cylindrical tolerance zone is established in the feature control frame. True Position Cylindrical Tolerance Zone

True Position Cylindrical Tolerance Zone The theoretical boundary is established by adding the maximum material condition value of the external feature to the positional tolerance, and centering the resulting boundary circle at the true position. This value is also the virtual condition of the external feature of size. Theoretical Boundary (Virtual Condition – Shaft at MMC + GTOL Tolerance)

True Position Cylindrical Tolerance Zone (Actual External Diameter) M The location of the external feature axis may vary within its cylindrical tolerance limits (yellow circle), but no elements of its surface may be outside the theoretical boundary blue-green circle). Let’s demonstrate that by cycling the pattern through a complete revolution. Theoretical Boundary

True Position Cylindrical Tolerance Zone (Actual External Diameter) M The location of the external feature axis may vary within its cylindrical tolerance limits, but no elements of its surface may be outside the theoretical boundary. Let’s demonstrate that by cycling the pattern through a complete revolution. Theoretical Boundary

TOLERANCE OF POSITION REQUIREMENTS

Position Tolerance Requirements
Wherever position tolerances are used, they must be applied to features of size. Basic dimensions are used to locate and establish the absolute location or true position of size features relative to specific datums and interrelated features. Basic dimensions are not toleranced on the drawing. The absolute locations of features of size are located by basic dimensions. Location tolerances for the size features are called out in feature control frames. In most cases, datum references are required.

DATUM REFERENCES AND POSITION TOLERANCES

Tolerance of Position applied RFS
Some fundamentals of position tolerancing, when applied regardless of feature size, are as follows: The tolerance control is most often established around the feature axis or center plane. No bonus tolerance is available because the stipulated tolerance applies at any increment of size. Part verification requires the use of variable gages –usually at higher cost.

TOLERANCE OF POSITION AT REGARDLESS OF FEATURE SIZE

Tolerance of Position -- RFS
A A B C C The information in the feature control frame would be read as follows: “Regardless of feature size, this feature must be located on true position within a cylindrical tolerance zone of .014 in. on diameter, with reference to datums A (primary), B(secondary), and C (tertiary).” Irrespective of how large or small the actual hole size is—within its size limits—no additional tolerances are available for the location of the feature. I’ll demonstrate in the next few slides. B

The exact location of the hole is established with basic dimensions. True Position

The cylindrical tolerance zone is established in the feature control frame –( .014). True Position A B C Location Tolerance Zone –RFS

For the worst possible condition, the hole axis is located at the extreme limit of the cylindrical tolerance zone. True Position A B C Location Tolerance Zone –RFS

When the axis is located at the extreme limit of the tolerance zone, the MMC hole axis would be offset from the true position by a distance equal to one-half of the position tolerance (.007). True Position A B C MMC Diameter Location Tolerance Zone –RFS (Always the Same)

The actual hole size may vary between MMC (smallest diameter) and LMC (largest diameter), but the axis location cannot violate the boundaries of its location tolerance. True Position A B C MMC Diameter Location Tolerance Zone –RFS (Always the Same) LMC Diameter

The white circle represents the MMC boundary. Its center is located at true position. No element of the hole surface can be inside this boundary. True Position A B C MMC Boundary (VC Functional Gauge) MMC Diameter Location Tolerance Zone –RFS (Always the Same) LMC Diameter

The outer white circle represents the LMC boundary centered on true position. No elements on the surface of the hole can be outside of this boundary. The following series of slides will sequence the progressive position of the center of the hole as it moves around the tolerance zone. LMC Boundary True Position A B C MMC Boundary (VC Functional Gauge) MMC Diameter Location Tolerance Zone –RFS (Always the Same) LMC Diameter

The outer white circle represents the LMC boundary. No elements on the surface of the hole can be outside of this boundary. The following series of slides will sequence the progressive position of the center of the hole as it moves around the tolerance zone. LMC Boundary True Position A B C MMC Boundary (VC Functional Gauge) MMC Diameter Location Tolerance Zone –RFS LMC Diameter

TOLERANCE OF POSITION AT MAXIMUM MATERIAL CONDITION

Tolerance of Position -- MMC
The next example will illustrate the concept of bonus tolerance, in connection with position tolerances. We will use the same drawing example that was used to discuss tolerances of position, when applied regardless of feature size (RFS). One of the significant differences you will see is the advantages of defining the tolerance zone for the axis of a hole as we did before—but this time, we will add the modifier for maximum material condition (MMC) to the tolerance specification in the feature control frame. Notice the changes that occur in location tolerances when modifiers are used, and as departure from MMC occurs.

A A B C M C The information in the feature control frame would be read as follows: “This feature must be located on true position within a cylindrical tolerance zone of .014 on diameter with reference to datums A (primary), B (secondary), and C (tertiary), when the hole is at its smallest size, or MMC.” As the actual hole size increases in size from MMC, additional tolerance (equal to the amount of departure) may be added to the location tolerance for the feature. B

The exact location of the hole is established by basic dimensions. True Position

MMC Diameter (Axis at Maximum Offset) The maximum material condition diameter of .490 is shown at its maximum offset from true position—one-half the specified location tolerance. True Position

MMC Diameter As the size of the hole changes within its tolerance range from MMC—smallest hole size limit, and increases in size towards the LMC, or upper size limit, an equal amount of tolerance can be added to the axis location tolerance. True Position Location Tolerance Zone at LMC

MMC Diameter The additional tolerance for the hole axis location (which is equal to the amount of departure from MMC), is called “bonus tolerance.” True Position LMC Diameter Bonus Tolerance Location Tolerance Zone at LMC

MMC Diameter When the hole size is at its lower limit (MMC), and positioned at the extreme limit of the MMC location tolerance, the MMC boundary is established. When the feature of size is at this limit, no elements of the hole surface may be inside this theoretical boundary. This is the virtual condition of the hole, which also simulates the mating part at its maximum material condition. True Position LMC Diameter MMC Boundary Location Tolerance Zone at LMC

MMC Diameter When the hole size is at its upper limit (LMC), and positioned at the extreme limit of the location tolerance, the LMC boundary is established. No elements of the hole surface can be out-side this boundary. True Position LMC Diameter MMC Boundary LMC Boundary Location Tolerance Zone at LMC

MMC Diameter In this next series of slides, note that while the size and location of the actual hole may vary, the elements on the surface of the holes never violate their boundaries. This series will help you to understand how the hole size changes can affect the location of the center axis—and its orientation. True Position LMC Diameter MMC Boundary (VC=MMC-Tol) LMC Boundary Location Tolerance Zone at LMC

MMC Diameter Axis location variance possibilities when position tolerance is modified to MMC. True Position LMC Diameter MMC Boundary (VC=MMC-Tol) LMC Boundary Location Tolerance at MMC Location Tolerance at LMC Location Tolerance at LMC

ZERO POSITION TOLERANCE AT MMC

Zero Position Tolerance at MMC
Occasionally it may be desirable to increase position tolerances, but maintain specific, albeit acceptable, feature size limits. Such can be achieved by calling out the lower limit of the hole size at the absolute minimum to allow a MMC fastener to be inserted, and specifying a MMC position tolerance of zero.

Zero Position Tolerance at MMC
B C 0 M A B C (Min Hole=Max Fastener Fit) A When the holes are at MMC, the hole positions must be exact. As the hole size moves towards LMC, the location tolerance increases proportionately.

POSITION TOLERANCES CONTROLLING PLANAR APPLICATIONS

Position Tolerances Controlling Planar Features of Size
Tolerance of position principles may also be applied to planar features of size, in which case, the diameter symbol is removed from the feature control frame. 0.6 M A B C

Position Tolerances Controlling Planar Features of Size
Tolerance of position principles may also be applied to planar features of size, in which case, the diameter symbol is removed from the feature control frame. The resulting tolerance zone is established by two parallel planes, separated by a distance equal to the tolerance value. Modifiers, and therefore, bonus tolerances may also be applied under these circumstances. 0.6 M A B C

Symmetrical Features Controlled With Position Tolerancing -- RFS
Let’s consider controlling symmetry of a feature of size, using position tolerancing. The tolerance must be maintained regardless of feature size. A feature of size dimension ( mm), establishes datum centerplane N. Regardless of feature size, the centerplane of the controlled groove must be within two parallel planes, 0.4 mm apart, that is centered on datum plane N and perpendicular to datum plane R. 8.8 8.0 N R N 20.5 20.0 R

Symmetrical Features Controlled With Position Tolerancing -- RFS
In other words, the centerplane of the groove (and its mating envelope) must lie between two parallel planes 0.4 apart. These two planes must be perpendicular to datum plane R and be equally disposed about datum plane N. Two parallel planes, 0.4 mm apart. N R N 20.5 20.0 Mating Envelope R

Symmetrical Features Controlled With Position Tolerancing at MMC
8.8 8.4 K 0.2 M J K M 20.5 20.0 J Datum centerplane K is established by the feature of size dimension mm. The centerplane of the groove on the right side must be within a 0.2 mm tolerance zone, consisting of two parallel planes 0.2 mm apart.

Two parallel planes, 0.2 mm apart. 8.8 8.4 K 0.2 M J K M 20.5 20.0 J When the controlled groove size is at MMC, it must be positioned or located about the centerplane of datum feature K within 0.2 mm,. As departure from the MMC occurs, additional tolerance is available—up to the limits of the groove size tolerance (0.4). The groove centerplane must also be perpendicular to planar datum J within 0.2 mm at MMC. As the datum feature size varies within its tolerance zone, greater flexibility is available.

8.8 8.4 Symmetrical Features Controlled With Position Tolerancing at MMC K 0.2 M J K M 20.5 20.0 J GROOVE FEATURE SIZE MMC 20.5 20.4 20.3 20.2 20.1 20.0 DATUM K FEATURE SIZE Width of Tolerance Zone LMC The chart shows the values of size that would occur as the height of the object, and the groove size depart from MMC towards LMC.

POSITIONING MULTIPLE SYMMETRICAL FEATURES AT MMC

Position Tolerancing, Used to Locate Tabs and/or Slots That Are Symmetrical About Their Center Planes Dimension relationships between features, establish the size specifications and the number of times the features occur in the part. Identify and label all related and controlling datums. Complete the specification with the position tolerance, including appropriate references to the related datums, in the feature control frame.

Locating Symmetrical Features
8X 25 0.4 52 0.6 40 8X 45º Dimension locations and relationships between features, and specify the number of instances followed by the size specification.

D 25 0.4 8X 52 0.6 40 E 8X 45º Identify and label related datums

0.5 M D E M 8X 45º D 25 0.4 8X 52 0.6 40 E Complete the specification with the position tolerance, including appropriate references to the related datums, in the feature control frame.

NONPARALLEL FEATURES

Nonparallel Features Occasionally, holes must be placed at an angle to a surface. There are also instances where the axes of holes may not be parallel to each other --such as a pattern of holes around the outside of a cylinder. Position tolerances may be used in these circumstances to properly locate and position features relative to each other, and to a datum or datums.

Angled and Nonparallel Features
8X 8 + 0.2 A 0.2 M A B M A + 0.2 4X 10 8X 45º B 0.4 M A B M 75.2 75.0 20 SECTION A–A 4X 45º 12 A

POSITION TOLERANCES AT LMC

Position Tolerances at LMC
When a LMC modifier is applied to a tolerance of position, the tolerance applies when the least amount of material is left in the part (largest hole, smallest shaft). Conditions are reversed from the MMC control. There is no bonus tolerance when the feature of size is at LMC, and the full bonus tolerance is available at MMC.

The least material condition modifier is commonly used to Control minimum wall thickness on a part, Maintain a minimum distance from an edge to a feature such as a hole, or Control minimum stock for machining on castings. Variable gaging or open inspection techniques are required for verification.

Tolerance zone at LMC True position True position True position is determined by basic dimensions, and the tolerance is depicted at the maximum diameter limit—(LMC).

Tolerance zone at LMC Locating the LMC diameter of the hole with its axis at the extreme offset from true position, we represent the worst position for wall thickness or distance spacing control from a datum surface. True position True position Hole size at maximum diameter (LMC)

Tolerance zone at LMC The location tolerance zone increases in an amount equal to the departure of the hole size away from LMC (as the hole gets smaller). True position True position Hole size at maximum diameter (LMC)

Tolerance zone at LMC The least material condition (largest hole size) is specified because the minimum wall thickness, or distance from the edge of the hole to the edge of the part must be controlled. As the hole gets smaller, the actual location of the hole becomes less critical. Therefore, bonus tolerance allows for an increase in offset tolerance for the axis of the hole from its true position. True position True position Hole size at maximum diameter (LMC)

This next series of slides present an example problem and solution, dealing with least material condition. There is a minimum of text associate with each slide. Take the time to study the presentation, however, and you will discover that the affects of LMC, in a position context, is calculated just the opposite of the affects of MMC. When minimum edge distance or minimum wall thickness is important, least material condition should likely be considered. It is important to remember that when a position tolerance is modified to apply at least material condition (LMC), all of the principles of MMC are essentially reversed. Bonus tolerances do apply, but they are maximized when the feature of size is at MMC. At least material condition, there is no bonus tolerance.

Calculating Least Material Condition
A 0.4 L A L This is a hollow step shaft. A minimum wall thickness of 6.0 mm must be assured.

A 0.4 L A L Expanding pin or mandrel establishes datum axis A 25.4 LMC Datum A is first established using a variable gage.

A 0.4 L A L Expanding mandrel establishes datum axis A 0.4 (Cylindrical) Zone 25.4 LMC The axis of the internal diameter must be within a cylindrical tolerance zone 0.4 mm in diameter.

A 0.4 L A L Expanding mandrel establishes datum axis A 25.0 Theoretical Boundary 0.4 (Cylindrical) Zone 25.4 LMC The position tolerance is subtracted from the LMC of the internal diameter, resulting in a diameter of 25.0 mm, and producing the critical size limit or boundary-- 25.0 mm.

A 0.4 L A L Expanding mandrel establishes datum axis A 25.0 Theoretical Boundary 0.4 (Cylindrical) Zone 6.4 Minimum wall 25.4 LMC The upper limit of the hole diameter is 12.2 mm. Subtract this amount from the lower limit of the outside diameter (25.0 – 12.2 = 12.8/2 = 6.4 mm minimum wall thickness).

0.4 L A A L 25.4 LMC Tol Zone = (VC) LMC of ‘A’ 12.8 2 Rad. Factor = 6.4 Min Wall Expanding mandrel establishes datum axis A 25.0 Theoretical Boundary 0.4 (Cylindrical) Zone 6.4 Minimum wall 25.4 LMC Go through the process again. Make sure you understand what is being done in this calculation.

COMPOSITE POSITION TOLERANCING

Composite Position Tolerancing
When features such as holes are arranged in a pattern, and the location of the pattern is less significant to the design than the actual relationships between the holes in the pattern (position and orientation), composite position tolerancing should be considered. A Pattern-locating Tolerance Zone Framework (PLTZF) controls the location of the hole pattern. PLTZF 0.4 M X Y Z

When features such as holes are arranged in a pattern, and the location of the pattern is less significant to the design than the actual relationships between the holes in the pattern (position and orientation), composite position tolerancing should be considered. A Pattern-locating Tolerance Zone Framework (PLTZF) controls the location of the hole pattern. A Feature-relating Tolerance Zone Framework (FRTZF) establishes the interrelationships between features. PLTZF FRTZF 0.4 M X Y Z 0.15 M X

The pattern-locating tolerance zone framework (PLTZF) is always located relative to specific datums, using basic dimensions. The PLTZF calls out the larger position tolerance to locate the pattern of features as a group. The PLTZF is always specified in the upper segment of the feature control frame, and establishes the order of precedence for inspection and verification.

The pattern-locating tolerance zone framework (PLTZF) is always located relative to specific datums, using basic dimensions. The PLTZF calls out the larger position tolerance to locate the pattern of features as a group. The PLTZF is always specified in the upper segment of the feature control frame, and establishes the order of precedence for inspection and verification. 0.4 M X Y Z

The feature-relating tolerance zone framework (FRTZF) controls the feature interrelationships within the pattern of features. The FRTZF resides in the lower half of the feature control frame and establishes a smaller position tolerance, controlling the relationships of features to each other, within the located pattern (PLTZF). Basic dimensions used to relate the PLTZF to controlling datums do not apply to the FRTZF. Datum references may be applied, but are not required in the FRTZF. In the example, the orientation (attitude) of the features is controlled with reference to datum X, but with no relationship to datums Y and Z.

The feature-relating tolerance zone framework (FRTZF) controls the feature interrelationships within the pattern of features. The FRTZF resides in the lower half of the feature control frame and establishes a smaller position tolerance, controlling the relationships of features to each other, within the located pattern (PLTZF). Basic dimensions used to relate the PLTZF to controlling datums do not apply to the FRTZF. Datum references may be applied, but are not required in the FRTZF. In the example, the orientation (attitude) of the features is controlled with reference to datum X, but with no relationship to datums Y and Z. 0.4 M X Y Z 0.15 M X

Composite and Single-Segment Feature Control Frames
We will consider the four-hole pattern that is controlled with a composite feature control frame. Note that the three holes near the base of the part are controlled with two single-line feature control frames. This practice is followed when it is necessary to apply the basic dimensions along with the datum references for both the pattern locating and the feature relating tolerances (PLTZF and FRTZF). 0.4 M X Y Z 0.15 M X Y X Z 0.4 M X Y Z 0.1 M X Y Z

Composite Feature Control Frames
Let’s examine the four-hole pattern at the top of the part. An enlarged view may help us evaluate the interaction between the PLTZF and the FRTZF—controls for the location of the hole pattern, and the interrelationships between holes in the pattern. This single, composite feature control frame has a very specific application. 0.4 M X Y Z 0.15 M X Y X Z 0.4 M X Y Z 0.1 M X Y Z

The four-hole pattern must be located as a group from datums X, Y, and Z, with each hole having a cylindrical tolerance zone, 0.4 mm in diameter (PLTZF). The holes must be positioned relative to each other within a cylindrical zone 0.15 mm in diameter (FRTZF), and fully within the larger pattern-locating tolerance zone. The holes will also be perpendicular to datum feature X within 0.15. M X Y Z 0.4 X 0.15 M

The theoretically exact hole pattern location is positioned with basic dimensions with reference to datums X, Y, and Z. M X Y Z 0.4 X 0.15 M

The cylindrical tolerance zones (shown in yellow) for the pattern locating tolerance zone is located at the pattern’s true position. M X Y Z 0.4 X 0.15 M 0.4 tolerance zone (PLTZF)

The cylindrical tolerance zones (shown in yellow) for the pattern locating tolerance zone is located at the pattern’s true position. The small crosses represent a possible displacement of the axes, but still within the tolerance zones. M X Y Z 0.4 X 0.15 M 0.4 tolerance zone (PLTZF)

The misalignment is more obvious with the center planes displayed. Note that the axis location for each hole is within the prescribed location tolerance zone for the pattern of holes. M X Y Z 0.4 X 0.15 M 0.4 tolerance zone (PLTZF)

The feature relating tolerance zone is shown within the larger pattern locating tolerance zone, on the drawing layout. Note that the feature related tolerance zones are mostly within the pattern location tolerance zones. 0.15 tolerance zones (FRTZF) 0.4 M X Y Z 0.4 tolerance zone (PLTZF) 0.15 M X

Feature axes must lie within both tolerance zone cylinders simultaneously. Portions of the feature relating tolerance zones are not available if they extend outside the boundaries of the pattern locating tolerance zones. Parts with hole axes outside the areas included within both circles would be rejected. 0.15 tolerance zones (FRTZF) 0.4 M X Y Z 0.4 tolerance zone (PLTZF) 0.15 M X

The feature axis may be anywhere within the area shared by both inscribing tolerance zones. Any area of the combined tolerance zones that is not included within both circles is sacrificed. In this case, to be accepted, the feature axis could not be within the red portion of the blue circle (FRTZF). It must be in the area shared by both zones, as shown.

ALIGNMENT OF COAXIAL FEATURES

Coaxial Feature Alignment Case Number One
When multiple aligned holes (located as a group) are to be on a controlled linear axis, a composite position tolerance may be used. The pattern locating tolerance zone framework (PLTZF—located on top in the composite feature control frame) is a larger cylindrical tolerance, extending through the part, within which the holes must lie as a group. The smaller cylindrical feature relating tolerance zone framework (FRTZF—the bottom segment in the feature control frame) controls the feature to feature alignment within the pattern locating tolerance boundary (PLTZF).

Linear Coaxial Feature Alignment
Datum Reference in the PLTZF + 0.2 3X 0.4 M A B 0.1 M A B A The three-hole linear pattern on this hinge is to be located on true position with reference to datum features A and B within a cylindrical tolerance of 0.4 mm diameter at MMC. B

Datum Reference in the FRTZF + 0.2 3X 0.4 M A B 0.1 M A B A The features are to be aligned in relation to each other with reference to datum features A and B within a cylindrical tolerance of 0.1 diameter at MMC, which must be within the larger pattern locating tolerance of 0.4 diameter. B

First, let’s examine the affect of the PLTZF. A cylindrical tolerance zone, 0.4 mm in diameter, is specified for the three aligned holes. The axis of all three holes must be within this tolerance zone. 0.4 M 0.1 M A B

+ 0.2 A B 0.4 M 0.1 M A B Notice that in this case, both the PLTZF and the FRTZF have reference to datums A and B. The outcome of this requirement will be considered in the next few slides. 0.4 M 0.1 M A B

The feature relating tolerance is depicted as red cylindrical zone in the drawing. Note that they are centered within the boundaries of the larger pattern locating tolerance zone. The axis of the holes may be anywhere within these boundaries, but must be held, in terms of their position and orientation, with regard to datums A and B. 0.4 M 0.1 M A B

This illustration depicts the worst case for alignment of the axes and the three holes. The hole axes must be within the red tolerance zones which are positioned relative to datums A and B. 0.4 M 0.1 M A B

At MMC, the hinge pin will still slide through the three holes without interference. 0.4 M A B 0.1 M A B

Coaxial Feature Alignment
In this next series of slides, the example will depict a situation where no orientation datum features are identified in the feature relating tolerance zone framework—the lower portion of the composite feature control frame or FRTZF. The refining (FRTZF) tolerance controls the feature to feature alignment within the larger pattern location position tolerance (PLTZF), without regard to the locating datums.

+ 0.2 3X 0.4 M A B 0.1 M A The circumstances in this case are similar to the last example, with one major difference. Notice that the FRTZF (the lower segment of the feature control frame) contains no datum references. The results of this type of control will be illustrated in the next few slides. B

The three-hole linear pattern is to be located on true position with reference to datum features A and B within a cylindrical tolerance of 0.4 diameter at MMC. + 0.2 3X 0.4 M A B 0.1 M A B

No Datum Reference in the FRTZF + 0.2 3X 0.4 M 0.1 M A B A The features are to be aligned in relation to each other without reference to datum features A and B within a cylindrical tolerance of 0.1 diameter at MMC, which must be within the larger pattern locating tolerance of 0.4 diameter. B

The limits of the pattern locating tolerance zone are illustrated below. They position the three holes within the 0.4mm diameter cylindrical tolerance that extends through the part. 0.4 M A B 0.1 M

The feature relating tolerance zone (shown in red) must contain the axes for the three holes. Note that in this case, the feature relating tolerance zone is not centered on the axis of the pattern locating tolerance zone. However, the total feature relating tolerance zone (extended across the part) cannot violate the extents of the pattern locating tolerance zone. 0.4 M A B 0.1 M

The axes and holes are shown in their worst case position and orientation. The pattern locating tolerance zone is maintained with respect to the controlling datums. However, the feature relating tolerance zone has been free to float within the larger locating zone. The hinge pin will still fit into the holes, but it will not be directly linked to datums A and B. 0.4 M 0.1 M A B

In essence, what has been specified, is that the orientation and position of the hinge pin—relative to datums A and B—is less critical to the success of the design, than the position of the linear coaxial pattern of the holes. The part will still function as intended, even though the coaxiality of the feature relationships are not linked directly to the controlling datums. 0.4 M 0.1 M A B

If the holes are different sizes, their diameters must be called out in appropriate views. The feature alignment requirements are identified in the composite feature control frame. Place a note below the feature control frame to indicate the extent of the control. For example: TWO COAXIAL HOLES.

Coaxial Feature Alignment
Different Size Holes 0.6 M 0.3 M A B TWO COAXIAL HOLES A Similar to the last example, the feature relationship is not held relative to the datums, but is controlled relative to the limits of the cylindrical tolerance formed by the pattern location and coaxial requirements. The holes are different sizes, but they must be aligned axially—within both acceptable tolerance zones. B

COUNTERBORED HOLES

Counterbored Holes If the location, datum references, and position tolerance for a counterbore axis is to be the same as the axis of the hole, only one feature control frame is used. If the position tolerance of the counterbore axis is not required to be the same as the hole, then individual callouts may be used –one for the hole, the other for the counterbore.

Counterbored Holes In this example, both the clearance hole and the counterbore specification are controlled with a single geometric tolerance for position. 4X B 0.2 M A B C C A

Counterbored Holes The interpretation of the previous slide indicates that the position of the hole and the counterbore are on the same axis—located on true position relative to the prescribed datums. True Position True Position Datum Plane A Datum Plane A 0.2 cylindrical tolerance zone --for both the hole and the counterbore

Counterbored Holes In this example, the clearance hole and the counterbore specifications are controlled with separate and feature-specific geometric tolerances for location. 4X B 0.2 M A B C 0.5 M A B C C A

Counterbored Holes By interpretation, the axis tolerance for the clearance hole is separate from the axis tolerance for the counterbore. The function of each is the determining factor in this type of decision. True Position Datum Plane A

Counterbored Holes For each of the clearance hole and counterbore, there is a separate tolerance zone specified. If it is necessary to perform these functions separately, this procedure may save costs. If, however, the operations are done simultaneously, tool changes would be required, which may negate any savings due to tolerance advantages. 0.5 cylindrical tolerance zone for counterbore at MMC True Position Datum Plane A 0.2 cylindrical tolerance zone for the hole at MMC

FLOATING AND FIXED FASTENERS

Floating Fasteners When two or more parts are to be joined together using fasteners such as bolts and nuts, and all of the parts have clearance holes, the relationship between the fasteners and the parts being held together is called a ‘floating fastener’ case or relationship. Where the fastener diameters are all the same size, and the clearance holes are the same for all fasteners, the formula for calculating the position tolerance is: T = h - f Where T = Tolerance to be applied to each part h = MMC hole size f = MMC fastener diameter

Calculating Position Tolerances (Floating Fasteners)
The value that is called out in the feature control frame is the difference between the MMC hole diameter and the bolt diameter at MMC. Clearance Hole Diameter (MMC) .390 Bolt Diameter (MMC) Position Tolerance .015

Floating Fasteners T = h - f
Features on mating parts that are to assemble, must be dimensioned on their individual detail drawings, using the same geometric location (position) controls. T = h - f

Fixed Fasteners When parts are being fastened together and one of the parts is threaded, so that the bolt or stud is restrained, the condition is called “fixed fastener case”. If it is desirable to use the same position tolerance for each instance, and the fastener diameters are the same, the following formula is recommended: T = (h - f)/2 Where T = Tolerance (applied on each feature) h = Hole size (MMC) f = Fastener size (MMC)

T = ( h - f )/2 Fixed Fasteners
This is an example of fixed fastener case. On the part that has the tapped holes, the position tolerance would be one-half of the difference between the MMC fastener and the MMC tapped hole. This is the value that would appear in the feature control frame for position tolerance. T = ( h - f )/2

PROJECTED TOLERANCE ZONES USING POSITION TOLERANCES

Projected Tolerance Zones
When threaded fasteners, or press-fit pins or studs are central to functional design and assembly, it may be necessary to control the perpendicularity of the feature axis into the space adjacent to the feature surface. To avoid interference that can occur because of the orientation of a fixed fastener --controlled by the inclination of the hole into which it assembles-- a projected tolerance zone is used.

No Projected Tolerance Zone
Example Number One No Projected Tolerance Zone Parts with holes for press-fit pins, or tapped holes for posts or studs which are located with position tolerances, but without a projected tolerance zone, may encounter interference when assembled with mating parts.

Projected Tolerance Zones
This is an example of tapped holes located with true position but without a projected tolerance zone C E D 2X UNC – 2B .010 M

The thread specification and position tolerance are called out on the drawing. However, there is no projected tolerance zone, and feature control is at MMC. The cylindrical tolerance is .010 inches in diameter, and extends only to the size limits of the part. 2X UNC – 2B .010 M C

2X UNC – 2B .010 M As indicated, the resulting tolerance zone (axis/thread pitch diameter control) ends at the extents of the limits of size of the part.

In this situation, the feature axis orientation may be anywhere within the limits of the cylindrical tolerance zone. The worst possible orientation in the diagonal, is shown for this example. 2X UNC – 2B .010 M

The worst case thread orientation is depicted in this slide. Next, we will depict the mating part with the clearance holes at MMC and maximum offset in the opposite direction. 2X UNC – 2B .010 M

With the mating part at its maximum material condition—the worst possible circumstance permitted by the tolerances on the part, added to the layout, we begin to see the consequences of not specifying the projected tolerance zone. 2X UNC – 2B .010 M

Because no projected tolerance zone was specified, there is a reasonable possibility that interference will result when attempting to assemble the fastener at MMC.

Projected Tolerance Zone
Example Number Two Projected Tolerance Zone Projected tolerance zones extend from the datum feature (surface) away from the part to a minimum distance indicated –either in the feature control frame, or as specified by dimensions on the drawing.

The Projected Tolerance Zone is a .010 inch diameter cylinder extending a minimum of 1.25 inches from the surface indicated, when the feature is at MMC. 2X UNC – 2B .010 M P C D E C

.010 inch positional tolerance zone at MMC 2X UNC – 2B .010 M P C D E

The projected tolerance zone and the threaded (tapped) hole have been adjusted to show the worst-case orientation. .010 inch positional tolerance zone at MMC 1.25 MIN .010 M P C D E 2X UNC – 2B

.010 inch positional tolerance zone at MMC Worst case mating part simulated at assembly. .010 M P C D E 2X UNC – 2B

Hardware assembly without interference. .010 M P C D E 2X UNC – 2B

SPHERICAL FEATURE CONTROL

SPHERICAL FEATURE CONTROL
Spherical features can be located in relation to other features using position tolerancing. When used, the spherical diameter symbol precedes the dimension callout, and is also placed in the tolerance block of the feature control frame.

Spherical Feature Control
The spherical object in this illustration is controlled in its relationship to the flat planar surface.

Datum plane A is the origin from which the spherical diameter is positioned. The tolerance zone is a 0.6 mm sphere which must contain the center point of the spherical surface regardless of any variation in size, within its size limits. The axis upon which it is positioned is the axis of the shaft RFS. S A S 0.6 A B B

Datum plane A True Position S A S 0.6 A B 0.6 diameter spherical tolerance zone B Regardless of feature size, the center of the spherical element must be located on true position within a spherical diameter of 0.6 mm, with reference to datums A and B. Datum Axis B

ADVANTAGES OF POSITION TOLERANCES

Position Tolerance Advantages
Cylindrical tolerance zone -- 57% increase. Controls tolerance accumulation. Utilizes bonus and shift tolerances. Supports design objectives and intent. Specifications verified using “fixed” gages. Reduces production and inspection costs.

LOCATION TOLERANCES Concentricity Symmetry Position

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LOCATION TOLERANCES Concentricity Symmetry Position

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