Chapter3 Form and Position Tolerances形位公差
Terms
术语
Form tolerance
形状公差
Postion tolerance
位置公差
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Form Tolerance: is the variation of the true form of
a single factor to its perfect form make a small shaft
found to be distortion and not cylindrical, or the
section is out of round, or the axes is bended, or
make a plane found to be warp.
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Position Tolerance: is the variation of the actual position of
related factors to its ideal position form. While machining a
stepped shaft, the axial cord of each step may not be the
same, namely, concentricity and coaxality error. Surfaces
expected to be perpendicular are not perpendicular after it
machined.
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Symbols of Form and Position Tolerances
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FORM TOLERANCES
A verification
setup, including a
dial indicator.
This type of setup
is often used in
the process of
verifying form
during the
production of
parts.
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Gages Used To Verify Form
Dial indicators are often used to measure
variation from dimensional limits on form
tolerances. Note the spherical tipped probes of
different size and flexibility.
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Gages Used To Verify Form
V blocks are often used to cradle cylindrical parts in the manufacturing and
inspection processes.
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Gages Used To Verify Form
A surface plate is vital in the processes of manufacturing and inspection. Made
from solid granite, they vary in size and thickness. The surfaces are processed to a
very smooth finish. They are used as datum plane simulators.
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Gages Used To Verify Dimensional Accuracy
Additional tools and fixtures that are used in the inspection process.
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TOLERANCES
OF FORM
FEATURE STRAIGHTNESS
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Straightness Applied To A Feature
In this example, the feature control frame, specifying straightness of line elements, is
applied to the top surface of the part. It is not associated with any dimension, therefore,
it references its own true geometric counterpart—a perfectly straight line. This is the
case with all form tolerances, datums are therefore never referenced in a feature control
frame specifying form control.
0.2
16.0
15.4
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Straightness Applied To A Feature
The shape of the tolerance zone for surface element straightness is two parallel
lines. Notice that the straightness specification is called out in the front view.
Therefore, the control applies in that view only (in the orientation of the front
view, from left to right or right to left). The straightness control from front to back
(as shown in the side view) is equal to the size tolerance (0.6 mm).
0.2
0.2
16.0
15.4
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Straightness Applied To A Feature
Remember, the straightness tolerance control applies only in the orientation depicted in
the view where the straightness tolerance symbol is shown. Straightness in the other
(cross) orientation is controlled by the height (size) dimension tolerance.
Size limit tolerance
0.6 mm (allowed by
General rule #1)
0.2
0.2
16.0
15.4
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Straightness Applied To A Feature
There is an infinite number of surface line elements (in the orientation or direction of the
straightness control) that comprise the surface, and each line element must be verified
independent of all others. Each line is inspected separately (the inspection device is reset
after each segment). Enough passes must be taken to satisfy the inspector that the surface
line elements are within the specified tolerance zone.
0.6
0.2
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Straightness Of Line Elements
0.1
0.05
To further illustrate the principle of orientation, in relationship to straightness
control, consider the drawing above. Two separate geometric tolerances for
straightness have been applied to the same surface, albeit in different orientations;
the front view represents a cross-horizontal orientation—left to right, whereas the
right side view shows a longitudinal-horizontal orientation—front to back.
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Straightness Of Line Elements
0.1
0.05
Each line element on the surface
must lie between two parallel
lines 0.05 apart in the orientation
depicted in the front view, and
0.1 when oriented as shown in the
right-side view of the drawing.
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Straightness Of Line Elements
0.1
0.05
0.1 Tolerance
0.05 Tolerance
The illustration attempts to show the
different tolerance zones that would
result from the two geometric tolerances
called out on the drawing.
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STRAIGHTNESS CONTROLLED
BY DEFAULT—RULE #1
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Rule #1 (Default) Control of Straightness
The dimension between the top and bottom of the object shown below, allows a
size tolerance of 0.5 mm. All line elements, across the entire surface, must be
straight within 0.5 mm.
12.5
12.0
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Rule #1 (Default) Control of Straightness
Straightness of all line elements (in
all directions) must fall within the
0.5 mm tolerance zone defined by
two parallel lines.
12.5
12.0
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STRAIGHTNESS CONTROLLED BY
RULE #1 COMBINED WITH A
GEOMETRIC TOLERANCE
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Straightness Controlled By Rule #1
Combined With A Geometric Tolerance
Rule #1 is never overridden by a straightness control that is applied to surface
elements. The straightness control refines the allowable tolerance straightness
error of the surface.
0.3
10.6
10.0
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Straightness Controlled By Rule #1
Combined With A Geometric Tolerance
The geometric tolerance controlling the straightness of the line elements on the top
surface must be smaller, and be contained within the larger size tolerance.
However, the refining form tolerance may float within the larger size tolerance.
Any line on the top surface (in the specified orientation) must be within 0.3 mm of
perfect straightness. When form tolerances are called out on features, rule #1 is in
effect, and all elements on the surface must be within the limits of size.
Tolerance zone (2 parallel
lines, 0.3 apart) may float
inside Rule #1 limits
0.3
10.6
10.0
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Straightness Controlled By Rule #1
Combined With A Geometric Tolerance
At this checking location. the full range of tolerance for straightness is available,
but remember, every line element is independent of all others.
Tolerance zone (2 parallel
lines, 0.3 apart) may float
inside Rule #1 limits
0.3
10.6
10.0
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Straightness Controlled By Rule #1
Combined With A Geometric Tolerance
At the lower range of the size limits, the full tolerance for straightness is available.
Tolerance zone (2 parallel
lines, 0.3 apart) may float
inside Rule #1 limits
0.3
10.6
10.0
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Straightness Controlled By Rule #1
Combined With A Geometric Tolerance
When departure from MMC is less than the straightness tolerance, as in this case,
some of the tolerance for straightness is compromised, and therefore unavailable,
Tolerance zone (2 parallel lines, 0.3
apart) may float inside Rule #1 limits.
Departure may be less than allowed,
but actual surface elements cannot
violate size limits.
0.3
10.6
10.0
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Straightness of Surface Elements
0.04
14.93 - 15.00
Straightness of a feature is most often used to control the longitudinal surface
elements of a cylinder or cone. An infinite number of longitudinal lines exist on
the surface shown in the illustration above, and the specification implies that all
surface line elements on the pin must be straight within a tolerance of 0.04 mm.
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Straightness Of Surface Elements
0.04
14.93 - 15.00
All longitudinal elements on the surface of the pin must lie between two parallel
lines 0.04 mm apart. The two lines comprising the tolerance zone must also be in
a plane that is common with the axis of the cylindrical pin.
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Straightness Of Surface Elements
There are infinite possibilities for resulting feature form in the drawing displayed,
but in no case can the size limits be violated. Three extreme form possibilities
will be illustrated.
0.04
14.93 - 15.00
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Straightness Of Surface Elements Combined With Rule #1
The first example shows the pin curvature to the extent allowed by the geometric tolerance.
Regardless of how much the diameter size varies, within the 14.93 – 15.00 mm diameter,
the surface line elements must be straight within the specified tolerance. Perfect form is
required at MMC. As departure from MMC occurs, out of straightness is allowed—up to
0.04 mm.
15.00 MMC
0.04
0.04 tolerance zone
14.93 - 15.00
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Straightness Of Surface Elements
“Waisting” can occur on the part, and if so, some of the tolerance may be compromised at
opposite points when at the lower limit of size. If the 0.04 tolerance was maximized all
around the diameter, 0.08 mm would have to be subtracted from the upper limit (15.00 mm),
leaving a total minimum diameter of 14.92 mm. The part would be out of tolerance.
15.00 MMC
0.04
0.04 tolerance zone
15.00 MMC
14.93 - 15.00
0.04 tolerance zone
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Straightness Of Surface Elements
Feature “barreling” could also result. But once again, some of the tolerance could
be compromised at opposite points inasmuch as the full 0.04 mm tolerance could
not be in effect all around the object without violating the overall size tolerance.
15.00 MMC
0.04
0.04 tolerance zone
15.00 MMC
14.93 - 15.00
0.04 tolerance zone
15.00 MMC
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Straightness Of Surface Elements
REMEMBER
In a feature-control application, the straightness tolerance must be less than the size
tolerance.* In the case of barreling or waisting of the surface, the full straightness tolerance
may not be available for opposite elements because the limits of size cannot be violated.
15.00 MMC
0.04
0.04 tolerance zone
15.00 MMC
14.93 - 15.00
*This general rule can be
overridden by a note
specifying that perfect form is
not required at MMC.
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0.04 tolerance zone
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15.00 MMC
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Feature Control Frame Applications
•The application of the feature control frame—whether associated with a feature or a feature
of size—makes a significant difference in the interpretation of the control.
•In the illustration on the left, the control is on a feature; notice the resulting tolerance zone,
controlling the surface line elements.
•The drawing on the right shows the application of the geometric tolerance in conjunction
with the feature of size, thus controlling the median line or axis of the part.
10.6
10.0
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10.8
10.0
0.3
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Rule #1 Default Straightness Control
10.6
10.0
In this example, the maximum possible diameter the pin could be, within its size
limits, is 10.6 mm. At that size (maximum material condition), the cylindrical
form of the pin would have to be perfect, the axis would be perfectly straight, as
would all the longitudinal line elements on the surface. As the pin diameter gets
smaller in size, moving away from maximum material condition towards least
material condition (LMC)—but still within the size tolerance limits—the axis of
the pin is allowed to bow or deform in the same amount.
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Rule #1 Straightness Control
10.6
10.0
Because rule #1 is in
effect, the size envelope
cannot be violated, and
where there is no
geometric tolerance
applied to the dimension,
the virtual condition is
equal to the MMC of the
pin, which in this case, is
10.6 mm. As the pin
diameter decreases in
size, but remains within
the size tolerance, the
straightness of the pin’s
axis may be affected in an
amount equal to the
departure.
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Pin diameter smaller than MMC,
but within size tolerance.
10.6 MMC
Rule #1 Boundary
(Mating Envelope)
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Rule #1 Straightness Control
Shown at the worst case—the
smallest diameter allowed by
the size tolerance or least
material condition—the
tolerance zone for the axis
would be equal to  0.6 mm,
thus permitting the axis to be
out of straightness by the
same amount—the part could
be cylindrical but bowed.
10.6
10.0
Pin Diameter at 10.0
10.6 MMC
Tolerance
Zone Diameter = 0.6
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(Mating Envelope)
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FEATURE OF SIZE
STRAIGHTNESS AT RFS
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Feature Axis Control RFS
12.6
12.0
0.2
In this illustration, the feature control frame is associated with the size dimension—the
diameter of the pin. Thus, the control is on the axis of the part, and applies at any
increment of size within the specified diameter size tolerance. Because the geometric
tolerance is applied to a feature of size, Rule #1 is overridden. The virtual condition, or
mating part envelope of the pin is equal to the MMC of the pin, plus the geometric
tolerance, or 12.8 mm.
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Feature Axis Control RFS
12.6
12.0
0.2
The feature axis
straightness is maintained
regardless of feature size
(RFS). The 0.2 axis
tolerance applies at any
increment of size within the
stated diameter size
tolerance. Rule #1 is
overridden, and the virtual
condition is 12.8 mm.
Pin Diameter--at any cross section, must
be within the limits of size (12.0-12.6 mm).
The smallest true cylinder (an adjustable gage), in contact
with the high points on the surface. The maximum
acceptable diameter would be equal to the virtual condition—
the pin’s MMC plus the geometric tolerance (12.8 mm).
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 0.2 tolerance
zone, regardless of
feature size.
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12.6
12.0
0.2
At any increment of size,
within the size limits, the
tolerance for straightness
of the median line or axis
is constant. Rule #1 is
overridden because the
control is applied to a
feature of size.
Straightness Tolerance Applied to a
Feature of Size RFS
Pin Diameter
12.6
12.4
12.2
12.0
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Straightness Tolerance
Zone Diameter
0.2
0.2
0.2
0.2
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Straightness Tolerance Applied to a Feature of Size MMC
When it is important to modify a straightness control to a condition of MMC, the
tolerance portion of the feature control frame must include the appropriate
material condition modifier.
12.0 - 12.6
0.2
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Straightness Tolerance Applied to a Feature of Size MMC
Pin Diameter, at any cross section, must be
within the limits of size (12.0-12.6).
Virtual
Condition
 12.8
Tolerance
Zone
Pin
12.6
12.0 -12.6
Straightness
Tolerance
0.2
0.2 M
Bonus
Tolerance
Total Diametral
Tolerance Zone
0.0
0.2
This series of visuals illustrate the concept of bonus
tolerance applied as the object departs from MMC.
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Straightness Tolerance Applied to a Feature of Size MMC
Pin Diameter, at any cross section, must be
within the limits of size (12.0-12.6).
Virtual
Condition
 12.8
Tolerance
Zone
Pin
12.4
12.0 -12.6
Straightness
Tolerance
0.2
0.2 M
Bonus
Tolerance
Total Diametral
Tolerance Zone
0.2
0.4
This series of visuals illustrate the concept of bonus
tolerance applied as the object departs from MMC.
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Straightness Tolerance Applied to a Feature of Size MMC
Pin Diameter, at any cross section, must be
within the limits of size (12.0-12.6).
Virtual
Condition
 12.8
Tolerance
Zone
Pin
12.2
12.0 -12.6
Straightness
Tolerance
0.2
0.2 M
Bonus
Tolerance
Total Diametral
Tolerance Zone
0.4
0.6
This series of visuals illustrate the concept of bonus
tolerance applied as the object departs from MMC.
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Straightness Tolerance Applied to a Feature of Size MMC
Pin Diameter, at any cross section, must be
within the limits of size (12.0-12.6).
Virtual
Condition
 12.8
Tolerance
Zone
Pin
12.0
12.0 -12.6
Straightness
Tolerance
0.2
0.2 M
Bonus
Tolerance
Total Diametral
Tolerance Zone
0.6
0.8
This series of visuals illustrate the concept of bonus
tolerance applied as the object departs from MMC.
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Advantages of Straightness Tolerance
Applied to a Feature of Size MMC
Applying straightness to a feature of size—especially if the control is modified to
apply at maximum material condition—allows for additional tolerance as
departure from MMC occurs. This added or bonus tolerance provides greater
flexibility to manufacturing, and can have a positive affect on production costs. In
those instances where the conditions are as described above, fixed gages that
represent the worst case for assembly can also be used for verification, thus
impacting overall costs.
The next series of screens will illustrate this concept. The advantages of MMC
control will be illustrated through the use of sketched parts in various
configurations, in their respective receiver gages.
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Mating Part Boundary Verification
12.8 (VC)
The dimension and control frame are
shown in the lower left corner of the
screen. In the illustration, the part is
shown at the maximum material
condition. It is in the receiver gage is
shown at the mating part boundary
limits or virtual condition. There is
adequate clearance for the parts to
assemble without interference.
(1)
12.6
12.0 -12.6
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0.2 M
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Mating Part Boundary Verification
12.8 (VC)
(1) Pin Diameter at MMC &
perfectly straight.
Gage at Virtual Condition
(1)
12.6
12.0 -12.6
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0.2 M
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Mating Part Boundary Verification
12.8 (VC)
(1) Pin Diameter at MMC &
perfectly straight.
Gage at Virtual Condition
(1)
0.2
12.6
12.8
(2) Pin Diameter at MMC.
Gage will accept with
0.2 variation in
straightness
(2)
12.6
12.0 -12.6
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0.2 M
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Mating Part Boundary Verification
12.8 (VC)
(1) Pin Diameter at MMC &
perfectly straight.
Gage at Virtual Condition
(1)
0.2
12.6
12.8
(2) Pin Diameter at MMC.
Gage will accept with
0.2 variation in
straightness
(2)
0.8
12.6
12.0 -12.6
0.2 M
12.8
(3) Pin Diameter at LMC.
Gage will accept with
0.8 variation in straightness
(3)
12.0
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Mating Part Boundary Verification
Carefully review these concepts.
12.8 (VC)
(1) Pin Diameter at MMC &
perfectly straight.
Gage at Virtual Condition
(1)
0.2
12.6
12.8
(2) Pin Diameter at MMC.
Gage will accept with
0.2 variation in
straightness
(2)
0.8
12.6
12.0 -12.6
0.2 M
12.8
(3) Pin Diameter at LMC.
Gage will accept with
0.8 variation in straightness
(3)
12.0
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TOLERANCES OF FORM
FLATNESS
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TERMS AND DEFINITIONS
•Flatness: A condition where all of the elements of a given surface are in a single
plane.
•Flatness tolerance: The total amount surface elements are permitted to vary from
a true plane.
•Flatness tolerance zone: The distance between two parallel planes within which
all of the elements of the controlled surface must lie.
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Flatness Verification
•Flatness (A 3D tolerance zone) may be determined by a theoretical plane,
established by the high points of the controlled surface in contact with a surface
plate or gage.
•From the theoretical plane, a second plane is offset and parallel by a distance
equal to the tolerance value. All elements of the controlled surface must lie
between the two parallel planes.
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Flatness Verification
Neither the object nor the gage is perfectly flat. They will position themselves on the high
points of contact. Once that is done, the second plane, parallel to the first, is established a
linear distance—equal to the tolerance value—away from the theoretical plane. All of the
elements on the controlled surface must lie between the two planes.
Second Plane
Primary Plane
Flatness
Tolerance Zone
Surface Plate
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Flatness Verification
Flatness may be verified with a dial indicator that extends through a hole in a surface plate.
The indicator is made stationary, and the part is moved around on the surface plate to
ensure that all elements of the controlled surface are checked.
Second Plane
Primary Plane
Flatness
Tolerance Zone
Surface Plate
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Feature Flatness
The flatness tolerance control applies to all elements on the surface to which the
tolerance is applied. The flatness tolerance is allowed to float within the larger
size tolerance. It can be oriented in any location or direction as long as it does not
violate the size tolerance.
Size limit tolerance
0.6mm (allowed by
General rule #1)
0.2
0.2
16.0
15.4
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Feature Flatness
All surface elements must be within the tolerance zone defined by two parallel
planes, 0.2 apart. Enough passes in random directions must be taken to satisfy the
inspector that all of the surface elements are within the specified tolerance zone.
0.2
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TOLERANCES OF FORM
Flatness being verified using a surface plate, a height stand, and a
dial indicator.
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TOLERANCES OF FORM
Inspection/verification setup, comprised of a rotational surface
plate, a height stand, and a digital indicator.
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Default Flatness Controlled By The First Fundamental Rule
Coordinate tolerances combined with the first fundamental rule, when applied to a
feature of size (a distance between two parallel surfaces), provides an automatic
flatness control for both surfaces. At MMC, both surfaces would have to be
perfectly flat. As departure from MMC occurs, however, form variation equal in
amount to that departure is allowed. (Form variation limits are equal to the
difference between the upper and lower size tolerance, and apply equally for both
surfaces). Because rule #1 is in effect, the size limits cannot be violated.
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Flatness Application
0.2
14.0 - 14.6
The feature control frame can be attached to an extension line as shown here. It
may also be attached to a leader, with its arrow touching the surface (as shown on
the next slide). However, it must always be associated with a view where the
surface being controlled for flatness appears as a single line—an edge view.
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Flatness Application
0.2
The top surface is specified to be flat within
a tolerance zone defined by two parallel
planes 0.2 mm apart. The size dimension
allows 0.6 mm of tolerance between the
two surfaces.
14.0 - 14.6
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Flatness Application
0.2
The limits of size are illustrated on the
drawing. Clearly, the part is within the
size tolerance range. But the flatness
tolerance must also be within the size
tolerance, and contain all of the surface
elements.
14.0 - 14.6
14.6 MMC
14.0 LMC
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Flatness Application
0.2
The surface elements are within the size
tolerance but fall outside the prescribed
flatness tolerance.
14.0 - 14.6
0.2 Tolerance Zone
14.6 MMC
14.0 LMC
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Flatness Application
0.2
14.0 - 14.6
As long as the tolerance zone for flatness
is parallel to the theoretical plane
established at the bottom, the elements
will not fit within the tolerance zone.
However, what has been stipulated is
that the top has to be flat. There is no
relationship to the bottom, other than the
size dimension. So. . .
0.2 Tolerance Zone
14.6 MMC
14.0 LMC
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Flatness Application
0.2
14.0 - 14.6
Placing gage blocks under one end of the part
creates an equalizing effect on the object. We
can now verify whether or not, under such
circumstances, the elements of the surface are
within the prescribed tolerance zone. As can
be seen in the illustration, with this
adjustment, all of the elements fall within the
tolerance for size and form.
0.2 Tolerance Zone
14.6 MMC
14.0 LMC
Gage Block
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Flatness Application
0.4
The full range of the tolerance zone for flatness
becomes available only after the departure
from MMC exceeds the width of the tolerance
zone for flatness. This is because the size
limits cannot be violated. When the part is at
the upper limit of the size tolerance, some of
the form tolerance zone must be compromised.
6.0 – 7.2
0.4 Tolerance Zone
7.2 MMC
6.0 LMC
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Flatness Application
This blown up view may help solidify the concept. When nearly at maximum material
condition, there may not be sufficient space to accommodate the entire form tolerance.
The 0.4 tolerance range is compromised in this illustration because its limits extend
beyond the size limits. At MMC the surface would have to be perfectly flat. All surface
elements must be within the size tolerance zone, indicated by yellow phantom lines.
1.2
0.4
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GEOMETRIC TOLERANCES
CIRCULARITY
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DEFINITIONS
•Circularity for a feature other than a sphere is a condition where all points of the
surface intersected by any plane perpendicular to an axis are equidistant from that
axis.
•Circularity for a sphere is a condition where all points of the surface intersected by
any plane passing through a common center are equidistant from that center.
•Circular tolerance: The amount which surface elements of a controlled diameter
may vary from a theoretically perfect circle.
•Circularity tolerance zone: Two concentric circles which are perpendicular to the
diameter axis, or in a plane that passes through the center of a sphere, and separated
by a radial distance equal to the tolerance value, and within which, at any cross
section, each circular element of the surface must lie.
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DEFINITIONS
Circularity for a feature other than a sphere is a condition where all points of the surface
intersected by any plane perpendicular to an axis are equidistant from that axis.
Circularity for a sphere is a condition where all points of the surface intersected by any plane
passing through a common center are equidistant from that center.
Circular tolerance: The amount which surface elements of a controlled diameter may vary from
a theoretically perfect circle.
Circularity tolerance zone: Two concentric circles which are perpendicular to the diameter
axis, or in a plane that passes through the center of a sphere, and separated by a radial
distance equal to the tolerance value, and within which, at any cross section, each circular
element of the surface must lie. (Many cross sections must be inspected)
Note: A circularity tolerance zone—two concentric circles—is conceptually easy to visualize.
However, verification of a circularity form control is complicated enough that a separate ANSI
standard (ANSI B89.3.1) is required to provide an expanded explanation of specification and
inspection requirements. For example, the specification
.005 LSC 150 .010 means that
the roundness of the controlled surface shall be within .005 inches as determined by the least
squares circle method with 150 cycles per revolution, using a .010 radius stylus tip.
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GEOMETRIC TOLERANCES
Circularity being gauged in process of part production.
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Circularity
•Circularity is a (2D tolerance Zone ) surface feature form control. When
circularity is applied to an external feature such as the diameter of a pin or shaft,
the outer boundary (larger tolerance band or circle) is first established by
circumscribing the high points of the surface using a variable gage—one that will
collapse around the external diameter while maintaining its circular shape.
•The inner boundary of the external feature can then be established as radially
smaller than the upper limit of the size tolerance by the amount of the specified
form tolerance. However, the actual feature, at any point of measurement, must be
within the size envelope allowed by rule #1.
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Circularity
•When circularity control is applied to an internal feature, such as a hole, the
inner boundary (smaller tolerance band or circle) is established by gage contact of
the high points of the surface.
•The outer boundary is radially larger than the smaller size tolerance limit by the
amount of the specified form tolerance. In this case also, the feature, at any point
of measurement (perpendicular to the axis), must be within the limits of size.
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Circularity
0.4
The specified circularity requires that within the tolerance limits established by the
size dimension, the form tolerance (all circular cross-sections on the part) must
not vary from true circularity beyond the amount permitted by the circularity
tolerance, which consists of two concentric circles spaced apart by 0.4 mm radial
distance.
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Circularity
Two concentric circles establish the circularity tolerance zone.
0.4
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Circularity
Smallest true circle
that circumscribes
the high points
of the feature
diameter—within
tolerance
0.4
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Circularity
Smallest true circle
that circumscribes
the high points
of the feature
diameter—within
tolerance.
0.4
The outline of the actual part and its cross
section are shown. After a measurement is
taken at a specific location, the part is
rotated slowly approx 30 deg. where another
measurement is taken. This procedure
continues all around the part.
Note that all elements of the circular section
are within the boundaries of the tolerance
limits.
0.4 Offset of
concentric circles
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Circularity
Smallest true circle
that circumscribes
the high points
of the feature
diameter—within
tolerance.
0.4
Measurements are taken at many section
locations along the part.
The gauge is reset between each
measurement.
0.4 Offset of
concentric circles
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Circularity
•Diametrical features such as cylinders, cones, and spheres are the only features
that circularity can appropriately be applied to.
•Circularity cannot be modified to apply at MMC or LMC. It comes under the
control of size tolerances and general rule #1, which stipulates that the form must
be perfect when the part is at MMC. Circularity, therefore, always applies
regardless of feature size, and must be contained within the boundaries of the size
limits.
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Circularity Indirectly Controlled by
Other Geometric Tolerances
If circularity is determined to be a necessary specification, care should be taken
to ascertain the effects of other geometric tolerances that may also influence or
indirectly control circularity. In addition to circularity, geometric tolerances
controlling cylindricity, profile, and runout also influence the circular form of
features.
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FORM CONTROLS
CYLINDRICITY
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FORM CONTROLS
CYLINDRICITY
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Tolerances Of Form—Cylindricity
Definitions of Terms
CYLINDRICITY
Cylindricity: A condition of a surface of revolution in which all points on the surface are
perpendicular and equidistant from a common axis. Cylindricity can control
straightness and circularity
Cylindricity Tolerance: A 3D boundary defined by two theoretically perfect coaxial
cylinders within which all the elements of the specified surface must lie.
Cylindricity (3D) Tolerance Zone: The radial distance between the two coaxial cylinders
defines the tolerance zone and represents the amount that surface elements are allowed
to vary from a perfect cylinder. This numerical value (always less than one-half of the
diametrical tolerance) is specified in the tolerance cell of the feature control frame.
Note: As a surface form control, cylindricity is always considered RFS, and the physical
limits imposed by size dimensions cannot be violated. Datums are neither proper nor
allowed in the feature control frame, and the tolerance cannot be modified to consider
additional tolerance as departure from MMC occurs. A diameter symbol zone
descriptor cannot be used in the feature control frame.
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Tolerances Of Form - Cylindricity
•When cylindricity control is applied to an external feature, the outer boundary
(larger cylinder) is typically established by circumscribing the high points of the
surface. The inner boundary is radially smaller by the amount of the specified
tolerance. The feature, at any point of measurement (a plane, perpendicular to the
axis), must be within the limits of size.
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Tolerances Of Form - Cylindricity
When cylindricity control is applied to an internal feature, the inner boundary (smaller
cylinder) is typically established by gage contact with the high points of the surface.
The outer boundary is radially larger by the amount of the specified tolerance. The
feature, at any point of measurement, must be within the limits of size.
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GEOMETRIC CONTROL
FOR CYLINDRICITY
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Tolerances Of Form - Cylindricity
OVERVIEW
•The geometric control for cylindricity is a feature form tolerance which controls
circular, longitudinal, and parallel elements of the feature surface elements only.
Because it is strictly a surface element control, datums are neither proper nor allowed.
As is the case with all surface controls, cylindricity always applies regardless of feature
size.
•Because cylindricity can only be applied to features and cannot be applied to features
of size, material condition modifiers cannot be used with a cylindricity specification.
•The size envelope imposed by dimensional limits and Rule #1 are never overridden by
a geometric tolerance for cylindricity, and the geometric tolerance becomes the
controlling factor only when departure from MMC exceeds the cylindricity tolerance
value. Therefore, the virtual condition of the controlled feature is not affected.
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Verifying Cylindricity Geometric Tolerance
0.4
OR
0.4
A feature control frame describing cylindricity control may be called out in either
view and is applied by using a leader line, as shown.
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Verifying Cylindricity Geometric Tolerance
0.4
Multiple-section
measurements are
taken just like the
measurements for
Tolerance zone is two
circularity, except the coaxial cylinders
gauge is NOT reset
between sections.
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Verifying Cylindricity Geometric Tolerance
0.4
Smallest true cylinder
that circumscribes
the high points
of the feature
diameter.
Tolerance zone is two
coaxial cylinders
0.4 Radial Distance
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Cylindricity Geometric Tolerance—Always RFS
10.5
9.5
0.2
The size tolerance zone consists of two coaxial
cylinders, 0.5 mm apart. This tolerance defines
the actual local size limits.
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Cylindricity Geometric Tolerance—Always RFS
10.5
9.5
0.2
The size tolerance zone consists of two coaxial
cylinders, 0.5 mm apart. This tolerance defines
the actual local size limits.
The cylindricity tolerance zone consists of two
coaxial cylinders, 0.2 mm apart. This tolerance
can “float” within the larger size tolerance.
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Cylindricity Geometric Tolerance—Always RFS
Feature size tolerance. (While
surface elements are restricted to
the refined tolerance zone, the
actual local [measured] size of
the cylindrical feature may vary
within the larger boundaries.)
Coaxial cylinders establish the
tolerance zone for feature cylindricity.
0.2
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Cylindricity Geometric Tolerance—Always RFS
Feature size tolerance. (While
surface elements are restricted to
the refined tolerance zone, the
actual local [measured] size of
the cylindrical feature may vary
within the larger boundaries.)
At any measuring position, all
surface elements must be within
the cylindricity tolerance zone.
They may vary within the zone,
and the entire zone may expand
or contract within the larger size
tolerance.
Coaxial cylinders establish the
tolerance zone for feature cylindricity
(RFS).
0.2
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Cylindricity Geometric Tolerance—Always RFS
Feature size tolerance. (While
surface elements are restricted to
the refined tolerance zone, the
actual local [measured] size of
the cylindrical feature may vary
within the larger boundaries.)
The cylindricity tolerance zone
may extend beyond the lower
limit of the size tolerance, but
no elements on the surface can
be located outside of those
limits. That part of the tolerance
would be sacrificed.
0.2
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Cylindricity Geometric Tolerance—Always RFS
Feature size tolerance. (While
surface elements are restricted to
the refined tolerance zone, the
actual local [measured] size of
the cylindrical feature may vary
within the larger boundaries.)
The geometric tolerance for
cylindricity becomes the
controlling factor only when
departure from MMC exceeds
the cylindricity tolerance value.
0.2
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