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.
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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,
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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.
0
25 -0.5
0.2
E
E
0
12 -0.2
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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
25
0.2
E
12
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-0.5
E
0
-0.2
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Verifying Concentricity
25
0
-0.5
0.2
E
12
E
At every measuring
location of diametrically
opposed elements, a
median point must be
established.
0
-0.2
25
0.2
E
12
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0
-0.5
E
0
-0.2
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Verifying Concentricity
25
0
-0.5
0.2
E
12
E
At every measuring
location of diametrically
opposed elements, a
median point must be
established.
0
-0.2
25
0.2
E
12
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0
-0.5
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
-0.2
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SYMMETRY OF SIZE FEATURES
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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.
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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
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Symmetry of Size Features
A
8.8
8.2
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
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TOLERANCES OF POSITION
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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.
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COORDINATE TOLERANCING
COMPARED TO POSITION
TOLERANCING
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COORDINATE LOCATION
TOLERANCING
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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).
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Coordinate tolerancing
of a hole location
.750
.005
24.000
.005
Each of the tolerances on the coordinate dimensions is  .005, or .010 inches.
First, add the tolerance limits on the horizontal dimension.
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Coordinate tolerancing
of a hole location
.755 (.750 + .005)
.750
.005
.745 (.750 - .005)
24.000
.005
Next add to the drawing the plus and minus value to the vertical dimension.
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Coordinate tolerancing
of a hole location
.755 (.750 + .005)
.750
.005
.745 (.750 - .005)
24.005
24.000
.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.
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Coordinate tolerancing
of a hole location
.755 (.750 + .005)
.750
.005
.745 (.750 - .005)
24.005
24.000
.014
.005
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.
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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).
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POSITION LOCATION TOLERANCING
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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.
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Coordinate Location Tolerance
.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.
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Coordinate Location Tolerance
.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%!
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Coordinate Location Tolerance
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.
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TRUE POSITION GEOMETRIC
TOLERANCING
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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.
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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.
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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.
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Basic Dimensions on Drawings
In the past, basic dimensions were labeled BASIC or BSC following or below the
dimension (see MIL STD 8C; ANSI Y14.5-1973; ANSI Y14.5–1982). This
practice is no longer recommended.
3.438 BASIC
3.000 BSC
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Basic Dimensions on Drawings
In the past, basic dimensions were labeled BASIC or BSC following or below the
dimension (see MIL STD 8C; ANSI Y14.5-1973; ANSI Y14.5–1982). This
practice is no longer recommended.
3.438 BASIC
3.000 BSC
Basic dimensions are (and were) also identified in a special symbol –an enclosing
rectangle:* 24.6
* Current recommended practice ASME Y14.5M-1994
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Basic Dimensions on Drawings
In the past, basic dimensions were labeled BASIC or BSC following or below the
dimension (see MIL STD 8C; ANSI Y14.5 1973; ANSI Y14.5–1982). This
practice is no longer recommended.
3.438 BASIC
3.000 BSC
Basic dimensions are (and were) also identified in a special symbol –an enclosing
rectangle:* 24.6
They were also called out in special notes.*
UNLESS OTHERWISE SPECIFIED, ALL UNTOLERANCED DIMENSIONS ARE BASIC
* Current recommended practice ASME Y14.5M-1994
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MMC BOUNDARY THEORY
(INTERNAL FEATURES—HOLES)
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Boundary Theory
(Internal Features—Holes)
Two center planes are necessary to
identify the location of a hole.
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Boundary Theory
(Internal Features—Holes)
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).
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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(Virtual ConditionHole at MMC – GTOL Tolerance)
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Boundary Theory
(Internal Features—Holes)
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 (bluegreen circle).
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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Boundary Theory
(Internal Features—Holes)
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.
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MMC BOUNDARY THEORY
(EXTERNAL FEATURES—SHAFTS)
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
The true position is located For an external feature.
True Position
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
A cylindrical tolerance zone is established in the feature control frame.
True Position
Cylindrical
Tolerance
Zone
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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Shaft at MMC + GTOL Tolerance)
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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MMC Boundary Theory
(External Features—Studs, Posts, Etc.)
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.
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TOLERANCE OF POSITION
REQUIREMENTS
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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.
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DATUM REFERENCES AND POSITION
TOLERANCES
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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.
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TOLERANCE OF POSITION AT
REGARDLESS OF FEATURE SIZE
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Slide 65
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Tolerance of Position -- RFS
.490 - .500
A
.014
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).”
B
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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.
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Slide 66
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Tolerance of Position -- RFS
The exact location of the hole is established with basic dimensions.
True Position
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Slide 67
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Tolerance of Position -- RFS
The cylindrical tolerance zone is established in the feature control frame –( .014).
True Position
.014
A
B C
Location Tolerance
Zone –RFS
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Slide 68
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Tolerance of Position -- RFS
True Position
For the worst possible condition,
the hole axis is located at the
extreme limit of the cylindrical
tolerance zone.
.014
A
B C
Location Tolerance
Zone –RFS
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Slide 69
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Tolerance of Position -- 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
.014
MMC Diameter
A
B C
Location Tolerance
Zone –RFS
(Always the Same)
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Slide 70
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Tolerance of Position -- RFS
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
.014
MMC Diameter
GD&T Location Table of Contents
B C
Location Tolerance
Zone –RFS
(Always the Same)
LMC Diameter
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A
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Slide 71
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 72
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Tolerance of Position -- RFS
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
.014
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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A
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Slide 73
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 74
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 75
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 76
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 77
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 78
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 79
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 80
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Tolerance of Position -- RFS
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
.014
A
B C
MMC Boundary
(VC Functional Gauge)
MMC Diameter
Location Tolerance
Zone –RFS
LMC Diameter
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Slide 81
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TOLERANCE OF POSITION AT
MAXIMUM MATERIAL CONDITION
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Slide 82
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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.
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Slide 83
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Tolerance of Position -- MMC
.490 - .500
A
.014 M
A
B C
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.”
B
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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.
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Slide 84
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Tolerance of Position -- MMC
True Position
The exact location of the hole is
established by basic dimensions.
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Slide 85
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Tolerance of Position -- MMC
The maximum material condition
diameter of .490 is shown at its
maximum offset from true
position—one-half the specified
location tolerance.
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MMC Diameter (Axis
at Maximum Offset)
True Position
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Slide 86
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Tolerance of Position -- MMC
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.
MMC Diameter
True Position
Location Tolerance
Zone at LMC
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Slide 87
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Tolerance of Position -- MMC
The additional tolerance for
the hole axis location (which is
equal to the amount of
departure from MMC), is
called “bonus tolerance.”
MMC Diameter
True Position
LMC
Diameter
Bonus Tolerance
Location Tolerance
Zone at LMC
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Slide 88
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Tolerance of Position -- MMC
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.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
Location Tolerance
Zone at LMC
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Slide 89
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Tolerance of Position -- MMC
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.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
LMC Boundary
Location Tolerance
Zone at LMC
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Slide 90
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Tolerance of Position -- MMC
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.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
Zone at LMC
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Slide 91
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 92
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 93
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 94
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 95
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 96
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 97
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 98
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Tolerance of Position -- MMC
Axis location variance
possibilities when position
tolerance is modified to
MMC.
MMC Diameter
True Position
LMC
Diameter
MMC Boundary
(VC=MMC-Tol)
LMC Boundary
Location Tolerance
at MMC
Location Tolerance at LMC
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Slide 99
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ZERO POSITION TOLERANCE AT MMC
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Slide 100
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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.
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Slide 101
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Zero Position Tolerance at MMC
(Min Hole=Max Fastener Fit)
A
0 M A B C
When the holes are at MMC,
the hole positions must be
exact. As the hole size moves
towards LMC, the location
tolerance increases
proportionately.
B
C
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Slide 102
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POSITION TOLERANCES CONTROLLING
PLANAR APPLICATIONS
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Slide 103
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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
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A B C
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Slide 104
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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
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Slide 105
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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
(20.0-20.5mm), 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
0.4
R N
20.5
20.0
R
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Slide 106
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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
0.4
R N
20.5
20.0
Mating Envelope
R
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Slide 107
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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 20.0-20.5 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.
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Slide 108
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Symmetrical Features Controlled
With Position Tolerancing at MMC
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.
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Slide 109
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8.8
8.4
K
0.2 M J
Symmetrical Features Controlled
With Position Tolerancing at MMC
K M
20.5
20.0
J
GROOVE FEATURE SIZE
DATUM K
FEATURE
SIZE
MMC
8.4
8.5
8.6
8.7
8.8
20.5
0.2
0.3
0.4
0.5
0.6
20.4
0.3
0.4
0.5
0.6
0.7
20.3
0.4
0.5
0.6
0.7
0.8
20.2
0.5
0.6
0.7
0.8
0.9
20.1
0.6
0.7
0.8
0.9
1.0
20.0
0.7
0.8
0.9
1.0
1.1
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.
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Width of
Tolerance
Zone
LMC
Slide 110
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POSITIONING MULTIPLE
SYMMETRICAL FEATURES AT MMC
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Slide 111
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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.
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Slide 112
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Locating Symmetrical Features
8X 45º
40
0.4
0
52
25
0
0.6
0
0.4
8X 6.0 - 6.2
Dimension locations and relationships between features, and specify the number
of instances followed by the size specification.
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Slide 113
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Locating Symmetrical Features
8X 45º
40
D
0.4
0
52
0
0.6
E
25
0
0.4
8X 6.0 - 6.2
Identify and label related datums
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Slide 114
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Locating Symmetrical Features
8X 45º
40
D
0.4
0
52
0
0.6
E
25
0
0.4
8X 6.0 - 6.2
0.5 M D E M
Complete the specification with the position tolerance, including appropriate
references to the related datums, in the feature control frame.
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Slide 115
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NONPARALLEL FEATURES
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Slide 116
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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.
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Slide 117
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Angled and Nonparallel Features
8X
A
A
8X 45º
4X
B
+ 0.2
0
0.2 M A B M
8
+ 0.2
0
0.4 M A B M
10
75.2
75.0
SECTION A–A
20
4X 45º
12
A
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Slide 118
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POSITION TOLERANCES AT LMC
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Slide 119
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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.
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Slide 120
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Position Tolerances at LMC
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.
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Slide 121
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Position Tolerances at LMC
Tolerance zone at LMC
True position
True position is determined by basic dimensions, and the tolerance is depicted at
the maximum diameter limit—(LMC).
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Slide 122
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Position Tolerances at 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
Hole size at maximum diameter (LMC)
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Slide 123
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Position Tolerances at 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
Hole size at maximum diameter (LMC)
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Slide 124
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Position Tolerances at 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
Hole size at maximum diameter (LMC)
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Slide 125
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Position Tolerances at 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.
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Slide 126
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Calculating Least Material Condition
A
25.4 - 25.6
54.0 - 54.2
0.4 L A
L
12.0 - 12.2
This is a hollow step shaft. A minimum wall thickness of 6.0 mm must be assured.
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Slide 127
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Calculating Least Material Condition
A
25.4 - 25.6
54.0 - 54.2
0.4 L A
L
12.0 - 12.2
Expanding pin or mandrel establishes datum axis A
25.4 LMC
Datum A is first established using a variable gage.
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Slide 128
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Calculating Least Material Condition
A
25.4 - 25.6
54.0 - 54.2
0.4 L A
L
12.0 - 12.2
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.
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Slide 129
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Calculating Least Material Condition
A
25.4 - 25.6
54.0 - 54.2
0.4 L A
L
Expanding mandrel establishes datum axis A
12.0 - 12.2
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.
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Slide 130
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Calculating Least Material Condition
A
25.4 - 25.6
54.0 - 54.2
0.4 L A
L
Expanding mandrel establishes datum axis A
0.4 (Cylindrical) Zone
6.4 Minimum wall
12.0 - 12.2
25.0 Theoretical
Boundary
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).
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Slide 131
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Calculating Least Material Condition
54.0 - 54.2
0.4 L A
L
Expanding mandrel establishes datum axis A
0.4 (Cylindrical) Zone
6.4 Minimum wall
25.4
- .4
= 25.0
- 12.2
12.8
2
= 6.4
A
25.4 - 25.6
12.0 - 12.2
LMC
Tol Zone
(VC)
LMC of ‘A’
Rad. Factor
Min Wall
25.0 Theoretical
Boundary
25.4 LMC
Go through the process again. Make sure you understand what is being done in
this calculation.
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Slide 132
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COMPOSITE POSITION TOLERANCING
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Slide 133
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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
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0.4
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M
X Y Z
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Slide 134
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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.
A Feature-relating Tolerance Zone Framework (FRTZF) establishes the
interrelationships between features.
PLTZF
FRTZF
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0.4
M
X Y Z
0.15
M
X
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Slide 135
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Composite Position Tolerancing
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.
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Slide 136
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Composite Position Tolerancing
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
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M
X Y Z
Glossary
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Slide 137
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Composite Position Tolerancing
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.
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Slide 138
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Composite Position Tolerancing
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.
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0.4
M
X Y Z
0.15
M
X
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Slide 139
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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 singleline 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
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0.4
M
X Y Z
0.1
M
X Y Z
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Slide 140
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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
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0.4
M
X Y Z
0.1
M
X Y Z
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Slide 141
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Composite Feature Control Frames
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.
0.4
M X Y Z
0.15 M X
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Slide 142
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Composite Feature Control Frames
The theoretically exact hole pattern location is positioned with basic dimensions
with reference to datums X, Y, and Z.
0.4
M X Y Z
0.15 M X
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Slide 143
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Composite Feature Control Frames
The cylindrical tolerance zones (shown in yellow) for the pattern locating
tolerance zone is located at the pattern’s true position.
0.4
M X Y Z
0.15 M X
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0.4 tolerance zone
(PLTZF)
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Slide 144
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Composite Feature Control Frames
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.
0.4
M X Y Z
0.15 M X
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0.4 tolerance zone
(PLTZF)
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Slide 145
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Composite Feature Control Frames
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.
0.4
M X Y Z
0.15 M X
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0.4 tolerance zone
(PLTZF)
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Slide 146
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Composite Feature Control Frames
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
0.15 M X
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0.4 tolerance zone
(PLTZF)
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Slide 147
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Composite Feature Control Frames
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
0.15 M X
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0.4 tolerance zone
(PLTZF)
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Slide 148
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Composite Feature Control Frames
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.
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Slide 149
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ALIGNMENT OF COAXIAL FEATURES
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Slide 150
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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).
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Slide 151
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Linear Coaxial Feature Alignment
Datum Reference in the PLTZF
3X
6
+ 0.2
0
0.4 M
A B
0.1 M
A B
A
B
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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.
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Slide 152
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Linear Coaxial Feature Alignment
Datum Reference in the FRTZF
3X
6
+ 0.2
0
0.4 M
A B
0.1 M
A B
A
B
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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.
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Slide 153
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Linear Coaxial Feature Alignment
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.
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0.4 M
A B
0.1 M
A B
Glossary
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Slide 154
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Linear Coaxial Feature Alignment
3X
6
+ 0.2
0
0.4 M
A B
0.1 M
A B
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.
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0.4 M
A B
0.1 M
A B
Glossary
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Slide 155
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Linear Coaxial Feature Alignment
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.
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0.4 M
A B
0.1 M
A B
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Slide 156
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Linear Coaxial Feature Alignment
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.
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0.4 M
A B
0.1 M
A B
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Slide 157
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Linear Coaxial Feature Alignment
At MMC, the hinge pin will still slide through the three holes without interference.
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0.4 M
A B
0.1 M
A B
Glossary
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Slide 158
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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.
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Slide 159
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Linear Coaxial Feature Alignment
3X
6
+ 0.2
0
0.4 M
A B
0.1 M
A
B
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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.
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Slide 160
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Linear Coaxial Feature Alignment
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.
3X
6
+ 0.2
0
0.4 M
A B
0.1 M
A
B
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Slide 161
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Linear Coaxial Feature Alignment
No Datum Reference in the FRTZF
3X
6
+ 0.2
0
0.4 M
A B
0.1 M
A
B
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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.
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Slide 162
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Linear Coaxial Feature Alignment
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
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Slide 163
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Linear Coaxial Feature Alignment
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
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Slide 164
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Linear Coaxial Feature Alignment
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
A B
0.1 M
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Slide 165
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Linear Coaxial Feature Alignment
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
A B
0.1 M
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Slide 166
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Linear Coaxial Feature Alignment
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.
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Slide 167
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Coaxial Feature Alignment
Different Size Holes
0.6 M
A B
0.3 M
TWO COAXIAL HOLES
5.0 - 5.2
10.0 - 10.2
A
B
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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.
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Slide 168
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COUNTERBORED HOLES
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Slide 169
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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.
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Slide 170
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Counterbored Holes
In this example, both the clearance hole and the counterbore specification are
controlled with a single geometric tolerance for position.
4X
B
5.4 - 5.6
8.4 - 8.6
5.0 - 5.5
0.2 M A B C
C
A
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Slide 171
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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
Datum Plane A
0.2 cylindrical tolerance zone --for
both the hole and the counterbore
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Slide 172
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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
5.4 - 5.6
0.2 M A B C
8.4 - 8.6
5.0 - 5.5
0.5 M A B C
C
A
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Slide 173
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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
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Slide 174
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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
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Slide 175
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FLOATING AND FIXED FASTENERS
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Slide 176
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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
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Slide 177
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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)
Bolt Diameter (MMC)
Position Tolerance
.390
.375
.015
.015
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Slide 178
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Floating Fasteners
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
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Slide 179
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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)
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Slide 180
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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
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Slide 181
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PROJECTED TOLERANCE ZONES USING
POSITION TOLERANCES
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Slide 182
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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.
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Slide 183
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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.
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Slide 184
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Projected Tolerance Zones
This is an example of tapped holes located with true position but without a
projected tolerance zone
C
E
D
2X .500 13 UNC – 2B
.010 M
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Slide 185
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No Projected Tolerance Zone
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 .500 13 UNC – 2B
.010 M
C
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Slide 186
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No Projected Tolerance Zone
2X .500 13 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.
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Slide 187
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No Projected Tolerance Zone
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.
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2X .500 13 UNC – 2B
.010 M
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Slide 188
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No Projected Tolerance Zone
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.
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2X .500 13 UNC – 2B
.010 M
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Slide 189
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No Projected Tolerance Zone
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 .500 13 UNC – 2B
.010 M
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Slide 190
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No Projected Tolerance Zone
Because no projected tolerance zone
was specified, there is a reasonable
possibility that interference will
result when attempting to assemble
the fastener at MMC.
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Slide 191
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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.
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Slide 192
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Projected Tolerance Zone
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 .500 13 UNC – 2B
.010
M
P
1.25 C D E
C
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Slide 193
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Projected Tolerance Zone
.010 inch positional tolerance
zone at MMC
2X .500 13 UNC – 2B
.010
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P
1.25 C D E
Slide 194
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Projected Tolerance Zone
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
2X .500 13 UNC – 2B
.010
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1.25 C D E
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Slide 195
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Projected Tolerance Zone
.010 inch positional tolerance
zone at MMC
Worst case mating part simulated
at assembly.
2X .500 13 UNC – 2B
.010
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1.25 C D E
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Slide 196
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Projected Tolerance Zone
Hardware assembly
without interference.
2X .500 13 UNC – 2B
.010
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1.25 C D E
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Slide 197
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SPHERICAL FEATURE CONTROL
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Slide 198
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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.
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Slide 199
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Spherical Feature Control
The spherical object in this illustration is controlled in its relationship to the flat
planar surface.
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Slide 200
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Spherical Feature Control
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
48.0 - 48.5
S
0.6 A B
B
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Slide 201
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Spherical Feature Control
Datum plane A
True Position
S
A
48.0 - 48.5
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
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Slide 202
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ADVANTAGES OF
POSITION TOLERANCES
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Slide 203
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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.
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Slide 204
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