>> This lecture is for lab number 16
on geometric dimensioning and tolerancing.
Now, we've talked about tolerancing before.
It's the allowance for specific variation in the size
and geometry of a part.
So when you're manufacturing or creating something,
it's expected that it would not be perfect
and therefore would be subject to errors.
However, if we allow errors, we need to be specific
about how much error or what is our tolerance for error
that is acceptable for our part.
The need for tolerancing is because it is impossible
to manufacture a part to an exact size or geometry.
And since variation from the drawing cannot be avoided,
we must specify the acceptable degree of variation
and for our part to still function properly.
Because if you allow too much variation,
the part may not be functional anymore.
However, if you allow too small of a variation,
it may affect the cost of manufacturing the part
because you would require precise manufacturing.
And also, it would result in incorrect rejection
or in quality control of parts
that otherwise would have been functional.
So we need to be careful about being too precise as well.
We have to remember
that tolerance should follow the function.
For assemblies, for instance, parts will not fit together
if their dimensions do not fall
within a certain range of values.
And we don't want that, because you won't be able
to assemble the different parts of the assembly.
And also, for interchangeable parts, if a replacement is used,
it must be a duplicate of the original part.
But of course within certain limits of deviation
because you cannot expect it
to be exactly the same as the original.
The relationship between functionality and size or shape
of an object varies with the part.
So for instance, for automobile transmission, the transmission,
it's very sensitive to the size and shape of the gears.
On the other hand, for bicycles, it's not as sensitive.
Therefore you can allow bigger variation.
There's two forms of physical tolerance.
One is size.
Okay? Which gives limits to the allowed variation
in each dimension, maybe the length, width,
height, diameter, et cetera.
And a second part, which is a little more difficult
to specify is tolerance with respect to geometry,
meaning a cylinder has to be --
say if you have a cross sectional area that's circular.
Of course, you cannot get a perfect circle.
So how would you specify the deviation from a circle
that you would allow, the deviation
from being a perfect circle?
And that's what we deal with in geometric dimensioning,
in tolerancing, or GDT.
Allows for specification of tolerance for the geometry
of the part, not just the size, but the actual geometry,
its deviation from a perfect form or geometry.
Geometric dimensioning tolerance uses special symbols
to control the different geometric features of a part.
And it's an elaborate system.
And it would take more than just one lab
to understand it, to master it.
But I just wanted to have an understanding of how it works.
Now, there's generally three levels of tolerances:
the default tolerance, which is placing the drawing title-block
by the engineering firm.
And it typically conforms to routine tolerance levels.
So it's what applies to tolerances for parts
within your drawing, okay, unless otherwise specified.
Okay, that's the default.
The general one is placing the drawing
by the design engineer as a note, okay?
It applies to the entire drawing.
So there might be a note saying: So-and-so is the tolerance
for all parts, or say, for all circles.
And it supersedes, of course, the default tolerance
because there's an explicit statement in the note
through a note that is a general tolerance.
We also have specific tolerances associated
with a single dimension or geometric feature.
And of course, it supersedes the two previous types
of tolerances.
And there's different ways of specifying a tolerance.
Limit dimensions.
This is called limit dimensioning, okay,
where you give the minimum and the maximum, the upper
and the lower value of the dimension.
So that an acceptable part may be at the upper limit,
lower limit or any value in between.
The advantage of using this is it's easy for fabricators
to just measure the total distance and make sure
that it's really in this limit.
Okay, here's another way
of specifying deviations by limit dimensions.
A plus or minus, it's called unilateral deviation
if only in one direction.
And bilateral if the error is allowable in both directions.
It will be slightly bigger that the idea value,
and it could also be slightly smaller.
Basic size dimensions given with tolerances noted
as a plus or minus range.
So you have a target value and a plus or minus.
Okay? And in terms of bilateral, you can have it equal,
meaning the error in the positive and error
in the negative are exactly the same.
Here an example.
If it's equal or bilateral tolerance is easiest
to fabricate because most errors are random in nature.
And most errors have more or less the same probability
of being too big or too small.
All you have to do is give the target values
and the random error can be added or subtracted depending
on the random case that you have.
Yeah, so the fabricator can simply set the machine
to the target value.
And the error could be plus or minus and it would be acceptable
as long as it's within the limits.
Geometric dimension
and tolerancing stresses tolerance levels not just
for sizes, how big or small it is, but in terms of tolerances ,
in terms of deviations from perfect geometry.
That's why it's called geometric dimension.
It uses standard symbols to indicate tolerances
that are based on the feature's geometry.
It's also called, sometimes called feature-based
dimensioning and tolerancing
or true position dimension and tolerancing.
But everyone knows what GDT means.
It's based on feature control frames to indicate tolerances.
In fact, for your labs most
of it will just be creating these feature control frames
in order to specify the tolerance that is being required
for a particular dimension.
And it's the state of the art in terms of indicating tolerances.
Just a brief history of tolerancing.
In the 1800s many factories used the cut and try,
file and fit approach.
So basically you cut it and try if it fits.
If it doesn't fit you file it until it fits.
But it's sort of a trial and error.
And then a slight improvement of that would be the plus and minus
or coordinate system of tolerancing.
So basically you are just giving tolerances in terms of size.
If it is slightly bigger or slightly smaller.
But in the 1900s, they developed the first GDT geometric
dimension and tolerance standards in order
to improve quality and utility of engineering drawings.
And it evolved quite a bit since then.
In 1966 the united GDT standards were published.
The geometric dimensioning tolerancing is based
on what's called envelope principle,
which establishes an envelope of and acceptable part
that satisfies the functionality of that particular part.
Any deviation in form is acceptable as long
as it's within this envelope.
So, here's an illustration of the envelope principle, okay?
So the red dashed lines represent the lower limit.
This is the smaller one.
The upper limits.
So anything in between them will be an envelope.
So those are the dashed red lines indicate the envelope.
So as long as the actual part is inside that envelope.
As you can see, the geometry, it's not perfect anymore, right?
The cross section is probably not perfectly circular.
And the surface of the cylinder is also crooked.
But as long as it's inside the envelope,
it is acceptable according to the envelope principle.
So, note that the deviation is not just in size.
It deviates from the perfect geometric properties of,
say, a perfect cylinder.
Limits of size indicates a variation in form
that is allowable between the least material condition
and the maximum material condition.
Okay? So the conditions wherein you are using the least amount
of material to make the part.
And the other extreme is using the maximum material
for the part and still be acceptable to do its function.
So here's another illustration of the envelope principle.
Giving the minimum and the maximum.
And anything that's inside the envelope will be acceptable.
So the envelope principle defines the size.
It's not just the size, but also the form,
geometric relationships for the parts.
And as I said earlier, GDT is based
on the feature control frame.
Okay? And here's the simplest illustration of that.
So, they are the basic dimension symbols, for instance.
And we've talked about it before.
Any dimension that doesn't have a tolerance is identified
as basic dimension by putting it inside a rectangular box.
Letter B. All these examples here are samples
of GDT feature control frames.
So for instance, this definition here is a definition
of a datum reference letter.
Okay, a datum is either a surface or an axis or an edge
that can be used to refer geometric properties.
Okay, here is geometric characteristic symbol.
Okay? That is used for, this an example, that's called flatness.
Let's talk about that.
Here is the actual tolerance level.
And we'll understand how it's interpreted.
Here's another example.
We have this position a geometric characteristic symbol.
Here, this symbol is for cylindrical tolerance.
This is the tolerance value.
And this modifier here.
M is for maximum material condition.
Here is a specific example of a feature control saying
that that has a datum reference.
So the interpretation of this particular one here means
that the particular feature
to which you attach this feature control frame should be
perpendicular within a tolerance of .05 with respect to datum,
therefore it's the same.
Okay? So this is other example of feature control frames.
So these feature control frames are based on symbols
that determine form and orientation,
terminal control form and orientation.
And these 14 characteristics may be controlled.
There's three basic types of controls.
Those are based on controlling forms, orientation and location.
So for instance, with respect to controlling form,
we have flatness shown by this symbol.
Straightness, okay.
Circularity, this is self-explanatory.
And cylindricity or the cylindrical center.
So these are measures of form, geometric forms.
On the other hand, and there's no individual --
there's no datum reference needed.
So, if something is flat, it's flat relative to itself
or straight or circular or cylindrical.
On the other hand, we also have orientation controls
such as length profile, surface profile, as shown here.
Perpendicularity, angularity and parallelism.
And of course, these orientation controls would be relative
to a datum.
So for instance when you say this particular feature is
perpendicular to within a certain tolerance.
Perpendicular with respect to what?
It's got to be with respect to some reference or datum.
Cylindrical tolerance zone.
It indicates that the position can vary along a
cylindrical region.
So here's the tolerance cylinder, right here.
And if we say that, say, the position of the center of, say,
this cylindrical hole has a cylindrical tolerance region.
What that means is if you look at the axis of the cylinder,
okay the cylindrical hole,
as long as it's inside the cylindrical tolerance zone,
whether it's off-center
or whether the axis is slightly tilted, okay?
It's okay as long as it's inside this cylindrical tolerance zone.
So cylindrical means that instead
of just varying the position or location in one direction,
or in two directions, it's actually
in a cylindrical zone that you can vary.
Material conditions.
We have something called maximum material condition, okay?
It's the largest acceptable size for external features.
So if it's an external feature, so it's a solid,
the bigger the size is, the more material you're going
to be using.
That's why it corresponds to the largest acceptable size.
It also corresponds to the smallest acceptable size
for internal features, meaning a hole.
So for instance maximum materials condition is achieved
when this outer feature here, the diameter is maximum.
On the other hand, it's achieved by making the hole,
the internal feature, as small as possible.
As a result of using the maximum material,
the object weighs the most under this condition.
On the other hand, least material condition corresponds
to either the smallest acceptable size
for external feature because you'll be using materials the
smaller the object is.
Or the largest acceptable size for internal features.
So the larger this hole is,
the less material you're going to use.
The smaller the outer external dimension is,
the less material you're going to use.
Of course, it corresponds to the least weight of the object.
If the size of the feature doesn't matter,
we have this condition called regardless of feature size.
Indicates that the material condition is not
to be considered.
A datum is a starting point for a dimension.
Datum are theoretically ideal location in space
such as a plane, centerlines.
Not every GDT feature requires a datum.
The form controls don't.
Orientation and location do.
There are different ways of defining a datum reference.
Now, we're going to use these dashes before
and after the letter.
Here is an illustration
on how you're going to do it on AutoCAD.
Again, simply attach it to the -- to an extension line.
Let's understand some of the controls.
Flatness, okay?
You see this symbol here?
Flat to within .25.
What that means is the surface, okay, may be within this limit
of two parallel planes or .25 apart.
Straightness.
Straightness within .02 means that.
For instance it is the -- yeah, this edge here.
Okay? What that means is as long as any point in that edge is
within .02 tolerance zone you're okay.
Here's an illustration of a cylindrical tolerance zone.
So for instance here, for the axis of the cylinder here,
cylindrical tolerance zone of .04 means that as long
as any point in the axis of the object is inside a cylinder
of the cylindrical tolerance zone of .04, you're okay.
Circularity or roundness, okay?
Again, it's an indication of how much you can deviate
from being a perfectly circular cross section,
for instance, okay?
So here's your tolerance zone.
What that means is as long as you are within that zone
of .25 wide, you're okay for circularity.
Cylindricity.
Very similar, okay?
You're inside this tolerance zone of .25
of your cylinder anywhere along the length
of cylinder you'll be okay.
Parallelism.
So, here's the reference.
What that means is this edge here
or this plane here should be parallel
to the plane in the bottom.
This is your reference, 3.12.
So again, there's a tolerance zone of .12 within any point
of your surface could vary and still be parallel
to the datum plane A. Concentricity.
It means having the same center for two circles, okay?
And again, this is an example of a cylindrical tolerance zone,
which means that the location of the center can be anywhere.
The center of the circle cylinder can be anywhere along
that cylindrical tolerance zone.