Project AS01 2015 Final Report

Mechanical Engineering 4M06
Final Project Report
AS01 - Preferred CAD/CAM GD&T Specification and Measurement Methods
Project Supervisor: Dr. Allan Spence, McMaster University
Due date: April 7, 2015
Daniel Brown Shaun Chiasson
1059065 1070043

Table of Contents
Table of Figures .............................................................................................................................. 3
1.0 How A Coordinate Measuring Machine (CMM) Works.......................................................... 4
1.1 CMM Introduction................................................................................................................ 4
1.2 Defining a Meter................................................................................................................... 5
1.3 Functions of a CMM............................................................................................................. 6
1.3.1 Structural Components................................................................................................... 7
1.3.2 Bearings ......................................................................................................................... 8
1.3.3 Drive Systems ................................................................................................................ 9
1.3.4 Displacement Transducers........................................................................................... 10
1.3.5 Probing......................................................................................................................... 11
1.3.5.1 The Process of Probing............................................................................................. 11
1.4 CMM Summary .................................................................................................................. 13
2.0 Geometric Dimensioning & Tolerancing (GD&T): ............................................................... 14
2.1 GD&T Introduction: ........................................................................................................... 14
2.2 Definitions and Terminology:............................................................................................. 15
2.3 Interpreting Tolerance Call-outs:........................................................................................ 18
2.4 Design and Manufacturing Considerations:........................................................................ 23
2.5 GD&T Summary:................................................................................................................ 24
3.0 How to Fasten Part During Inspection (Fixturing) ................................................................. 25
3.1 Design of the Fixturing:...................................................................................................... 25
3.1.2 Stand Off Post Design:................................................................................................. 29
3.2 Part Positioning Repeatability Testing: .............................................................................. 31
3.3 Final Fixture Design: .......................................................................................................... 35
3.4 Part Inspection Analysis: .................................................................................................... 38
4.0 Conclusion: ............................................................................................................................. 41

Appendix 1:List of Acronyms ...................................................................................................... 43
Appendix 2: Stand Off Post Test Results ..................................................................................... 44
Appendix 3: Suction Cup Testing Results.................................................................................... 46
Appendix 4: CMM results from the part firmly fixed in place..................................................... 48
Appendix 5: CMM results from suction cup testing..................................................................... 51
Appendix 6: Initial CMM results for part..................................................................................... 54
Bibliography ................................................................................................................................. 57

Table of Figures
Figure 1: Basic components of a laser interferometer.[1]............................................................... 6
Figure 2:Teeth meshing of a rack and pinion drive system.[1] ...................................................... 9
Figure 3: Belt drive system.[1] ....................................................................................................... 9
Figure 4: Schematic of a friction drive system.[1] ......................................................................... 9
Figure 5: Schematic of a transmission scale.[1] ........................................................................... 10
Figure 6: Schematic of a reflection scale.[1] ................................................................................ 10
Figure 7: Components of a touch trigger probe.[1] ...................................................................... 11
Figure 8: Traditional X-Y method and Mr. Parkers modified GD&T positioning method.[2].... 14
Figure 9: A part constrained to remove all degrees of freedom by three planes A,B and C.[4]... 17
Figure 10: Project part with basic dimensions, tolerances call-outs, modifiers, and datum
definitions. .................................................................................................................................... 18
Figure 11: Part views with datum definitions showing tolerances one and three......................... 19
Figure 12: Detail view of an acceptable profile variation for tolerance one when datum D is at
MMB............................................................................................................................................. 21
Figure 13: Showing the geometric considerations for a shift on tolerance one............................ 22
Figure 14: Initial three stand off and one spring clip fixture design for the part.......................... 25
Figure 15: Second fixture design with part raised for use with indexing probe head. ................. 26
Figure 16: Five sided star probe head for use in part inspection. ................................................. 27
Figure 17: Raised fixture design with two spring clips, a) without part, b) with part. ................. 27
Figure 18: Proposed fixture design with folding stand off posts, a) unfolded, b) folded. ............ 29
Figure 19: Initial design content, a) design #1, b) design #2........................................................ 30
Figure 20: Second iteration for a) design #1 and b) design #2..................................................... 30
Figure 21: Final design iteration for a) design #1 and b) design #2 ............................................. 31
Figure 22: Example of point output from Calypso CMM operating software. ............................ 32
Figure 23: Fixture set up for the stand off post testing................................................................. 33
Figure 24: Schematic of the suction cup system to be tested. ...................................................... 36

1.0 How A Coordinate Measuring Machine (CMM) Works
1.1 CMM Introduction
Technology in this day and age has become so sophisticated that that just about anything
can be made. With increasing technologies and more complicated machinery components need
to be made to high accuracies and tolerances.
In the late 1800's a need for accurate parts to make guns became paramount as no one
part was the same size which led to countries having to buy new guns instead of being able to
replace parts. This prompted engineers to begin designing measuring instruments so that parts
could be the right size. Many different measuring instruments have been made which can
measure features on the scale of micrometers but with increasing complexities of parts it quickly
became expensive and time consuming to measure all of the important features by hand. To
measure features by hand was prone to human error and some of these instruments could only be
used properly by skilled engineers so something had to change.
Early forms of measurement began with gage blocks and in the 1950's engineers began to
develop a machine called Coordinate Measuring Machines or CMM for short. CMM's are
machines that have a moving arm with a probe tip that measures the coordinates of various
points on the surface of a part to ensure they fall within the dimensions and tolerances specified
by the drawing. There is a lot of interest in this field because it allows companies to measure
manufactured parts and ensure that they are supplying high quality products to their clients
which keeps the customers happy and the manufacturers continue making money. By analyzing
the coordinates measured changes in the process of how the parts get made can be applied to
increase the number of highly accurate parts.

Though most people never realize it the advancement in technology is related to the
advancement in measuring techniques. As engineers are able to ensure that parts are made to a
desirable tolerance they are able to design components with more and more complexities. This
report will focus on the components that comprise a CMM, where the uncertainties in
measurement come from and how a CMM works.
1.2 Defining a Meter
Before anybody could go out and start making a CMM machine there needed to be a
global consensus on the exact length of a meter. Large companies that develop machinery like
aircraft or cars require a lot of components to be made and they often contract out the work to
various manufacturing firms who are expected to deliver parts that are within the specified
tolerances. These manufacturing firms are not always in the same country but all of the
components need to fit together in the end which means that everybody's definition of a meter
needs to be the same.
A meter is defined as "...the length of a path traveled by light in a vacuum a time interval
of 1/299,792,458 of a second..." [1] or 1/c where c is the agreed upon speed of light in a vacuum.
The uncertainty in the measurement of length is the measure of time since l=cxt. Currently the
best time measurement uncertainty is 5 parts in 1016
which serves the purposes of engineering
quite well since it amounts to an uncertainty 4.9906 x10-7
nm in one meter.
There is a common technique known as Laser Displacement Interferometry which is used
to measure components or to calibrate measuring equipment. Currently high resolution
interferometers can measure increments in length as small as 0.1 nm which is much smaller than
most tolerances used in manufacturing. The interferometer works by splitting a laser beam into a
reference beam and one that creates interference with the reference beam. By moving the

movable mirror it changes the phase when the two beams come back together at the detector.
The phase changes create fringes which are then counted and used to determine the displacement
of the movable mirror, see Figure 1.
Figure 1: Basic components of a laser interferometer.[1]
1.3 Functions of a CMM
A CMM's purpose is to provide the user with the actual shape of the measured part and
compare it to the desired geometry specified by the Geometric Dimensioning & Tolerancing
standards (GD&T) associated with the part. The size, form, orientation and location of the part is
generated by probing several points on each surface and processing the information using
computer algorithms.
When a manufacturer buys a CMM they expect it to increase the speed at which parts can
be measured and either be accepted or rejected. The faster they can get parts through the machine
the more money they can make or the more time they can save. Speed is very important in this
process because there may be many points that need to be measured. What this means is that the
driving systems need to move quickly and the dynamic properties of all the components need to
be maximized to allow quick and accurate movements.

A CMM is a rigid frame that is designed to move in three axes. It has a computer to
process data, a control unit and a series of driving systems, sensors, displacement transducers
and mechanical components. CMM utilizes Cartesian coordinates to track the orientation and
position (Xw,Yw,Zw) of the part/workpiece relative to the machines coordinate system
(Xm,Ym,Zm). A set of commands is sent to the machine to touch the probe tip to the surface of the
part. Once it has probed all of the necessary points the geometric parameters are evaluated and
then reported so that the operator can assess whether or not the part is acceptable according to
the GD&T specified.
For the purpose of this report the only CMM configuration considered is the moving
bridge configuration which is the most widely used. This configuration has advantages over
others like the cantilever because the two supporting columns reduce the potential for bending
and increase the natural frequency which is a good thing since rotary motion can excite
components if brought to the right frequency.
1.3.1 Structural Components
The materials chosen to make a CMM are crucial because changes in temperature cause
materials to expand which contributes to the uncertainty of measurements. The operators can
take measures to keep the environment at a steady temperature but the reality is that sometimes it
cannot always be controlled. Sensors embed in the CMM can send information to the computer
to make adjustments in the values reported. Aluminum is a common material used in the design
of the frame because of its high thermal conductivity. Aluminum is chosen for its ability to
quickly reach thermal stability when subjected to fluctuations in temperature even though it has a
high coefficient of thermal expansion because the computer can adjust the values. Granite is
often used as the table of the CMM as it will not deform nearly as much as Aluminum will if a

heavy part is measured. As the CMM moves around the elastic deformation may be significant
enough to employ an algorithm that corrects for the deformation as the CMM moves into various
positions.
To improve the speed at which parts can be measured it is key to have a high stiffness-to-
weight ratio with good damping properties. The motors used to move the three axes generate
acceleration in the structure which leads to deformation of components. A well designed
structure has high stiffness and low weight to reduce the deformation and improve the dynamic
performance. A common practice is to use hollow tubing as structural components because it has
very high stiffness compared to other beam or column designs with similar weight. Hollow
tubing could also protect wiring, sensors and motors from being potentially damaged by outside
factors.
1.3.2 Bearings
Bearings are an important consideration in CMM's because they directly contribute to the
dynamic properties of the entire system and the uncertainty of measurement. There are two types
of bearings used in CMM's, they are air bearings and contact hard bearings. Air bearings support
components on a very thin cushion of air which means that the two components theoretically
never come into contact. Air bearings may prove to be more reliable in the long run because
there is no contact and the only maintenance required is to keep the surface clear of debris. A
source of uncertainty might arise due to the cushion of air acting as a spring when there are
changes in acceleration in the Z direction. Contact hard bearings are similar to ones found in a
bicycle wheels and are more suitable to CMM's dealing with higher loads. The issue with contact
hard bearings is that they need to be lubricated regularly and each individual ball bearing has its
own uncertainty in diameter which will contribute to the overall uncertainty.

1.3.3 Drive Systems
Rack and pinion drives are the simplest
way to translate rotational motion into linear
displacement. These are used in cost-effective
designs due to gears not connecting properly
when the direction of motion is changed, this
effect is known as backlash. See Figure 2.
Belt drives are quiet and do not transmit high
frequency vibrations though the belt into the structure. The
belt drives can operate at high accelerations and speeds but
tend to have a lot of error associated with them due to the
elasticity of the belt. See Figure 3.
Friction drives are highly accurate and have a small
region were the drive roller slips along the drive bar. The
downside to friction drives is the lack of friction to
withstand the torques required for quick movements.
See Figure 4.
Each of the three drive systems above are valid for CMM's but choosing which to use
depends on the application of the CMM. If a manufacturer is willing to sacrifice some speed of
operation for higher accuracy a friction drive might be more appropriate where as a belt drive
could be used if speed is desired and the manufacturers are willing to sacrifice some accuracy.
Figure 2:Teeth meshing of a rack and pinion drive
system.[1]
Figure 3: Belt drive system.[1]
Figure 4: Schematic of a friction drive
system.[1]

1.3.4 Displacement Transducers
Displacement transducers are the instruments used to count very small increments of
length, a computer then multiplies the number of increments by the spacing of the increments to
get a displacement value.
Transmission scales work by shinning an LED
light source through a scanning reticle with very thin
slits, the photocells then activate and add an increment
to the count when the light happens to pass through the
scale which has slits. The number of increments is then
multiplied by the distance between the slits on the scale.
Reflection scales are similar to transmission
scales except after passing through the index grating the
light reflects off the metallic scale onto the photocells.
An interferential scale is similar to a reflection
scale except photoelectric heads are used to measure
interference fringes.
Transmission and reflection scales end up having a resolution of about 0.1-10
micrometers whereas interferential scales and laser displacement interferometers have a
resolution on the order of 1 nanometer. The errors associated with measuring interferential scales
and laser displacement interferometers is limited to atmospheric air conditions when measuring
wavelengths of laser beams. Errors associated reflection and transmission scales are temperature,
thermal expansion and the accuracy to which the grating slits were made to. Choosing the right
Figure 5: Schematic of a transmission
scale.[1]
Figure 6: Schematic of a reflection scale.[1]

transducer depends on how tight the tolerances need to be. As a general rule the uncertainty of
each of these scales should be less than a quarter of the tolerance desired.
1.3.5 Probing
For the purposes of this report only single touch-trigger probes will be discussed. The art
of contact probing is a crucial part of the process and there are a number of important
considerations when picking a probe tip.
1.3.5.1 The Process of Probing
When the part is ready to be measured the probe tip must be brought close to the part
without colliding with it, a collision would result in possible plastic deformation of the stylus or
the part. See Figure 7 for a diagram of the probe. When the probe touches the surface of the part
it causes the probe tip and hence the stylus to move away from the part but the spring element
generates a reaction force so that the probe tip will not move. It is important that the reaction
forces from the spring be consistent with each measurement so that results are repeatable. After
contact is initiated a signal is sent out to stop the movement of the CMM where the position of
the probe tip is recorded relative to the coordinate system of the CMM.
To get the best possible position of the point of contact the length of the stylus and
diameter of the probe tip must be known to a high degree of accuracy. It is very important that
Figure 7: Components of a touch trigger probe.[1]

the probe tip does not experience much force or pre-travel at all because it causes elastic
deformation of the stylus and probe tip and it also creates high stresses in the probe tip due to its
small diameter. Algorithms can be implemented to account for the elastic deformation but it is
better to just keep the contact force to a minimum to increase the life of the probe. Every time a
probe needs to be replaced the CMM must be recalibrated to ensure that the new probe is going
to provide accurate results.
Once the machine has recorded the point the probe tip moves away and approaches the
next location to be measured and the process repeats until all of the necessary measurements
have been taken. A method called scanning can be used which essentially drags the probe tip
across the surface to generate an infinite number of points along that line but this method wears
the probe tip and the is higher uncertainty due to the dynamic effects of the CMM. The
algorithms that analyze the points create geometric approximations using a least squares fit of all
the points on a surface. For example, if a hole is being measured and it is not actually round the
algorithm will generate a circle that best fits the points and determine the center from that.
1.3.5.2 Size and Material Considerations
Isotropic materials are desired for both the probe tip and stylus because no matter the
direction of approach the process of probing requires similar deformation in all directions. Ruby
is a typical material used for the probe tip, it is useful because it is very hard and resistant to
wear. The size of the probe tip is determined by the smallest interior feature size of the part.
When the CMM records a value it is using the effective diameter of the probe tip. What this
means is when a force is applied to the probe tip by the part causes the probe tip to flatten out at
the point of contact. The distance from the center of the probe tip to the deformed surface of the
probe tip represents the effective diameter. To get this effective diameter the probe is put through

qualification which tests it against a control sphere which is very hard. The importance of having
repeatable pre-travel shows up again because if the pre-travel changes significantly the effective
diameter of the probe tip changes and that is a quantity that needs to be qualified, a process that
is not done while measuring a part.
The material of the stylus is important as well because just like the frame it needs to be
strong but also nearly massless. The reason for it to be massless is the dynamic characteristics of
the CMM become worse when weight is added at the farthest point from the frame.
1.4 CMM Summary
CMM's are a very useful piece of machinery able to measure parts to incredible
accuracies. Continuing development of CMM machines and the all of the processes associated
with it ensure that measurement accuracy and repeatability will only get better with time. CMM's
have revolutionized the way parts are inspected by considering more and more sources of error
and uncertainty and by removing the need for engineers to measure parts by hand or using
specific machines to measure one dimension. The very fact that these machines exist means that
manufacturers are able to pump out more parts every because they are able to measure more
parts in a day. With continued research into materials science new materials may be developed
that can lighter and stronger which better suit the applications of CMM's. The downside to using
CMM's is that they are very expensive but it definitely pays off by allowing manufacturers to
increase their production output.

2.0 Geometric Dimensioning & Tolerancing (GD&T):
2.1 GD&T Introduction:
In the past parts were dimensioned using an X-Y-Z coordinate system. Each dimension
would have an allowable range of sizes that were deemed acceptable because it is nearly
impossible to manufacture parts exactly. Looking at a simple two axis system composed of X
and Y dimensions it can be seen that this method of dimensioning forms a square tolerance zone
that defines whether a feature is acceptable. It was during world war two while constructing
torpedoes in Great Britain that a man named Stanley Parker realized that this system was causing
good parts to be rejected [2]. It was then he defined a new system to measure the position of a
hole that was more true to the function of the part. His idea was that the maximum allowable
distance from the desired position of the hole could form a diameter that would describe a larger
zone of acceptable positions for the center point. This new method illustrated in Figure 8 results
in far less parts being rejected and no loss to the functionality of the part.
Figure 8: Traditional X-Y method and Mr. Parkers modified GD&T positioning method.[2]
The military quickly caught onto the value of this new methodology and adapted it in
their manufacturing. From this new position tolerance other tolerances were conceived and
around 1950 these concepts caught on in civilian manufacturing industries as well. The
introduction of these new methods of measuring and defining allowable variation in part sizes

and features came with a new set of problems all their own. In the past X-Y system there was a
lot of misinterpretation of the tolerances and allowable sizes. People were confused about how
to interpret and check the different sizes and information provided in the specifications. The new
system that was emerging would have to address these issues as well.
2.2 Definitions and Terminology:
Since the creation of the first known position tolerance many more have evolved to
control different types of features sizes, shapes, and allowable variations. A standard of
communicating these tolerances need to be created in order to eliminate confusion over their
particular meanings and applications. The different types of tolerances fall into separate
categories such as form, orientation, position/location, profile, and runout. These tolerances are
communicated on the part drawings using symbols as listed in Table 1.
Table 1: Standard tolerance call-out symbols and modifiers with definitions.[3]

The scope of this project is limited to the tolerances included in Table 1 so examination
of other more complex tolerances will not be explored. In addition to these tolerance call-outs
there are modifiers (Table 1) that are used in geometric dimensioning and tolerancing (GD&T).
These modifiers refer to conditions that may arise with respect to the specific part geometries to
which they are applied, and can have a dramatic influence on the overall allowable tolerance
limits. Within this project the modifier that will be applied is maximum material condition
(MMC). This modifier is defined as the condition where a feature has the most possible material
remaining. For example a hole is at MMC when at its smallest size, and a shaft is at MMC when
it’s at its largest size.
Datums are the way in which part inspection criteria is defined. A datum can be a plane
defined by a part surface or even a feature of size (FOS). When a datum is a plane it also defines
a direction as the normal vector to that plane. A feature of size could be a hole for example, it
has a specific size that can vary but it can also serve as a datum reference. Datums are described
by sequential letters usually starting from A and working through the alphabet. The first of the
defined datum planes is the primary, next the secondary, and third the tertiary. The primary
plane is usually defined by the most important mating plane and the others are defined in the
order of significance at assembly. Usually three datums can remove all the parts degrees of
freedom during inspection as shown in Figure 9, and more datums are used if feature tolerances
are important relative to a feature of size. A degree of freedom (DOF) is the parts ability to
move in space. A part can rotate in three directions, and it can translate in three directions so
there are a total of six degrees of freedom for an unconstrained part. Together the three planes
can remove all of these degrees of freedom to fully constrain the part in space. They are
identified by specific call-outs much like tolerances. The datum identifiers can be attached to a
particular feature or to a tolerance call-out. The goal of the datums is to remove all degrees of

freedom from the part during inspection and to provide important reference points that apply to
the limitations of other part geometries. Using and interpreting datums appropriately means that
important geometric relations are defined and that the inspection will be carried out properly no
matter whom is doing the inspection.
Figure 9: A part constrained to remove all degrees of freedom by three planes A,B and C.[4]
Tolerance limits can be described in two ways. For a position tolerance the limits are
expressed in terms of a diameter as described in Figure 8. Other tolerance limits are described
by an envelope of a specific range that encompasses the nominal dimension symmetrically
unless otherwise specified (UOS). A nominal dimension is the size target for a particular
feature. A hole specified with a diameter of ten millimeters with an allowable tolerance is said to
have a nominal dimension or basic dimension of ten millimeters. Other examples of basic
dimensions are the X-Y coordinates that define the ideal center for the hole, commonly known as
true position. In the past, methods of dimensioning used in a drawing such as baseline or chain
dimensioning played a big role in the allowable tolerance zones. Chain dimensioning starts a
new dimension from the end of a previous one which can cause tolerances to accumulate.
Tolerance accumulation is when the tolerance of the first dimension effectively adds to the
tolerance of the second chained dimension potentially causing the tolerance zone to increase to
more than its intended size. Baseline dimensioning takes all the dimensions for a specific

direction to start from the same place, usually a datum. Baseline dimensioning in the past had
the advantage of not causing tolerance accumulation. Today’s world of GD&T can produce the
exact same tolerance zone sizes and locations for any dimensioning method used. In Figure 10
the part for inspection during the project is shown with the tolerances that will be inspected, as
well as the prescribed tolerance types, zones, modifiers, and datums.
Figure 10: Project part with basic dimensions, tolerances call-outs, modifiers, and datum definitions.
2.3 Interpreting Tolerance Call-outs:
Two tolerances from Figure 10 have been selected for examples of how to read and
interpret tolerance call-outs. The two that will be examined demonstrate two different types of
tolerances, form and position. In addition to this they also use the MMC modifier but in two
distinctly different manners that can sometimes be a source of confusion at the inspection stage.
Recently in the year 2009, the American Society of Mechanical Engineers (ASME) who creates
the standards for GD&T introduced a new concept to help clarify the different uses of the MMC
modifier. The previous definition of MMC still holds true, however when a MMC modifier is
used on a datum in the call-out where the datum itself is a FOS, then it is now referred to as the

maximum material boundary (MMB). Sometimes the MMC is describing the same information
as the MMB but this is a special case. In the majority of cases they will not be describing the
same information. The special case will be explored while looking into the meaning and
interpretation of tolerance one. The use of the MMC modifier will be explored in its traditional
sense in the interpretation of tolerance 3. In Figure 11 tolerances one and three are displayed
with the respective geometry to which they apply to.
Figure 11: Part views with datum definitions showing tolerances one and three.
First looking at tolerance three and reading it from left to right and from top to bottom.
The diameter tolerance is given in a bilateral form with the basic dimension of 30 millimeters
(mm) as the target size with a plus or minus 0.2 mm. This defines the minimum acceptable size
as 29.8 mm (the features MMC) and the acceptable maximum size as 30.2 mm. In the next line
down the tolerance type is defined as a position tolerance with a diameter of 0 mm when the
feature is at MMC. It is important to note that in this case the MMC modifier is applied directly
to the tolerance size by having it placed next to the value of the diameter for the position zone.
Following this are three datum definitions A,B, and C. This indicates that the part is to be
constrained by these datum planes during the inspection of this feature. In this instance these
three datums will remove all possible DOF from the part during inspection. Lastly there is a

datum tag attached to the tolerance, this is identifying this particular hole as datum D. Since the
MMC modifier is applied directly to the size of the position tolerance zone size it will have the
effect of providing a bonus tolerance the further the actual size of the hole departs from its size at
MMC. The bonus tolerance is then added to the initial tolerance to find the actual tolerance
dimension. With an initial tolerance diameter of 0 mm the effect of this bonus tolerance will be
clear in the calculated tolerance values in Table 2.
Table 2: Calculating the allowable tolerance zone diameter considering the bonus tolerance from MMC
modifier.
Hole Size
(mm) Position Ø (mm)
Hole Size - MMC
(mm)
Actual Tolerance Ø
(mm)
MMC 29.8 0.0 0.0 0.0
- 29.9 0.0 0.1 0.1
- 30.0 0.0 0.2 0.2
- 30.1 0.0 0.3 0.3
LMC 30.2 0.0 0.4 0.4
It can be seen that the actual tolerance zone grows in size the larger the hole becomes so
from a manufacturers point of view it would be easier to satisfy this tolerance condition for the
hole when it’s larger rather than smaller. A tight tolerance of 0 mm at MMC indicates that this
particular hole is a mating feature with another part, and that when the hole is smallest there is no
room for any error from the true position.
Now taking a look at tolerance one the difference between a MMC modifier applied to a
tolerance size and MMB applied to a datum will be demonstrated. Tolerance one specifies a
bilateral profile tolerance envelope of 0.2 mm when constrained by datum A, D at MMB, and B.
This tolerance applies from point a, to point b on the profile as noted below the tolerance call-
out. In order to better understand how this tolerance works the first case that will be examined is
when datum D is at MMB. When datum D is at MMB then the allowable tolerance envelope is

0.2 mm from the true profile curve which in this case is a radius of 100 mm. Figure 12 shows
the relationship between the actual part profile, the true profile, and the tolerance envelope when
datum D is at MMB.
Figure 12: Detail view of an acceptable profile variation for tolerance one when datum D is at MMB.
In this example datum D is at MMB when the hole itself is at MMC because there is no
allowable position tolerance for the MMC of datum D, this is a special case as previously
mentioned. If there was an allowable position tolerance then the MMB for datum D would have
a smaller diameter than the diameter that occurs at MMC. The smallest perfect diameter that
would fit though the hole when at its worst possible condition would be the size of the MMB and
would be the size of the pin that would be affixed to the gage for inspection. Careful
consideration of the specified datums for this tolerance indicates that the part is not fully
constrained when the feature size of datum D is not at MMB. The part is not allowed to rotate at
all but it would in fact be able to translate in a direction parallel to datum plane B. This
allowable translation leads to what is called a tolerance shift. In a sense it’s a bonus tolerance,

when the profile is within the specified 0.2 mm bilateral envelope of a 100 mm radius but the
mid-plane of the part radius is not coincident with the mid-plane of the gage then it is acceptable
to move the part in the direction parallel to datum plane B to see if the tolerance can be satisfied.
Assuming that the profile tolerance envelope about a radius of 100 mm is satisfied, and the hole
has a center line perpendicular to datum plane A, but the mid-planes are not aligned, Figure 13
illustrates how the tolerance shift can be applied.
Figure 13: Showing the geometric considerations for a shift on tolerance one.
As long as the profile falls within a bilateral envelope of 0.2 mm and the mid-plane gap is
less than or equal to the diameter gap in the direction of the shift, then the part is accepted. The
possible values for these gaps can be calculated from the given tolerance information and the
allowable shift is determined by the diameter gap, not the mid-plane gap.
Tolerance shifts and the MMC modifier can’t be applied to every tolerance type.
Sometimes they can be applied to the same tolerance, but it is important to know which
tolerances are allowed to make use of these bonus allowances. There is plenty of information
available regarding tolerancing; the American Society of Mechanical Engineers (ASME) offers a
certification course for those who require an intimate knowledge of GD&T [4].

2.4 Design and Manufacturing Considerations:
It is the job of the designer to determine the allowable variation in part sizes and features
and communicate this to manufacturing on the part drawing. The overall concept involves
figuring out the maximum allowable deviation from the nominal dimensions. Determining the
allowable tolerance is accomplished by looking at the virtual condition (worst case geometry) of
two mating parts. A simple two dimensional example of a hole and a shaft mating with no
position tolerance, the virtual condition can be described as the largest size of the shaft mating
with the smallest size of the hole. If the parts will mate under this virtual condition then the
variation on the nominal dimensions are acceptable, if no interference between the parts is
desired. If the hole and shaft are dimensioned relative to a feature or plane on their respective
parts then it becomes necessary to establish the allowable position tolerance that should be
assigned such that the parts will mate under the virtual condition. Any clearance between the
shaft and hole at the virtual condition will provide the basis for the position tolerance.
Manufacturers have the responsibility of creating the parts within the specified
tolerances. This requires them to have an intimate knowledge of their process capabilities, how
accurately they can produce features, as well as the repeatability of the process. If tolerances are
very tight then precision manufacturing processes may need to be employed to meet the
specifications. The more complex the manufacturing process used, the more the part will cost.
This is why part designers aim to have the tolerances are large as possible without compromising
the three F’s, form, fit, and function of the part. In today’s world of engineering design and
manufacturing concurrent engineering is very common. This is when the designers and
manufactures employ a feedback loop so that during the processes of design and manufacturing
there is cooperation between the two groups. This cooperation helps ensure that the part is made

to a reasonable specification in the cheapest easiest ways, and that it will still perform as desired
when assembled.
A designer may wish to select the datums based on the mating surfaces or features of a
part. This may not always be the best way of doing it because there are other considerations to
make when selecting datums. Datums should be chosen usually with the primary datum as a
mating surface or feature, the other datums may be selected as planes or features that are easily
accessible on the part, and of a significant enough size to allow for easy constraint of the part at
the inspection stage. It should be easy to relate the various dimensions of the part from the
datums selected so that inspection of the part will be relatively easy and not require a
sophisticated gage to be produced. Having a simple gage design will help reduce the overall cost
of the part as well as ensure that the results from inspection are reproducible and reliable. Often
times more than one of the same parts will need to be inspected to do some quality control
statistical analysis of the parts to see if the batch of parts is acceptable. The gage design should
also include features that make it easy for the inspector to insert and remove parts quickly if this
is the case.
2.5 GD&T Summary:
It is necessary to know what the different tolerance symbols mean and which type of
geometries they can be applied to. Understanding the uses of the different modifiers, their
meanings and interpretations will be critical when figuring out how to tolerance and inspect parts
properly. Well defined datums will help improve production, the inspection process, and make
gage design much simpler and cheaper. Concurrent engineering is a method which the
manufacturers and designers can use to help each other ensure that the parts are made correctly

and work correctly without overinflating the costs. The implications of GD&T are far reaching
in society and the world, far beyond that of simply having a rejected part.
3.0 How to Fasten Part During Inspection (Fixturing)
3.1 Design of the Fixturing:
One of the most important aspects of inspecting a part is how to fix the part on the CMM
machine. There are many considerations to be made when designing a fixture, first and foremost
is that the part is secure in place and cannot move. The features of the part that need to be
measured should be easily accessible by the touch probe on the CMM machine and the supports
should be set up in a way to make collision avoidance between the probe and fixture as easy as
possible. It is ideal if the entire part can be measured in one set up; having to remove the part
and replace it on the machine is time consuming and would require an additional program to be
generated. Several designs for the fixture were conceived and evaluated against these criteria,
the first of which is presented in Figure 14.
Figure 14: Initial three stand off and one spring clip fixture design for the part.

This design is limiting because the part cannot be measured on all sides with one setup
and the stand off posts make it difficult to avoid collision when the inspection program is being
written. The only aspect of the design that passes is that the part will not move when the CMM is
running the inspection program.
In the second iteration of the fixture design the part is raised so that an indexing probe
head can measure the underside of the part without having to run a second inspection program.
The part sits on three posts on datum A, and rests against three posts on datums B and C with
three spring clips to hold the part down, see Figure 15.
Figure 15: Second fixture design with part raised for use with indexing probe head.
While the entire part can be measured there is an increased chance of probe collision
because there are two more spring clips and three stand off posts under the part in the design that
get in the way during measurement. This iteration of the design theoretically solves the problem
of not being able to measure all sides of the part without writing another inspection program but
there was no access to an indexing probe head so the next best probe head will be used, a five
sided star probe head as seen in Figure 16.

Figure 16: Five sided star probe head for use in part inspection.
The five sided star probe head in Figure 16 will allow the part to be measured on all
sides because there are probe heads that point in every direction but the part will have to raised
even more so that the probe head pointing downwards does not collide with the base plate. With
the addition of the extra probe heads this made it more difficult to avoid collision overall because
while measuring with one probe head the others could collide with the fixturing.
For the third iteration it was necessary to raise the part further and remove one of the
spring clips to reduce likelihood of collision and provide more access to datum surface A.
Figure 17 shows the fixture with and without the part.
Figure 17: Raised fixture design with two spring clips, a) without part, b) with part.

The fixture design in Figure 17 allows the probe to measure all of the surfaces and keeps
the part in place but limits the amount of surface area available for measurement. Ideally the
entire surface area of the part should be measured but since there is fore knowledge of the
production process it can be assumed that by measuring part of a surface the entire surface
conforms to those measurements. However, this is an assumption and there could be a defect
behind one of the stand off posts that would cause the part to be rejected so it is still preferable to
be able to measure the maximum surface area possible. Looking at the datum surface B, it can
be seen that the stand off posts occupy a significant portion of the surface area thus limiting the
area that can be inspected.
More than 30% of the area of datum surface B has been lost to the fixturing, the total area
lost due to fixturing would include the area lost on datum surface C as well as the area lost on
datum surface A. The loss of 31.67% is a conservative estimate because the diameter of the
probe head must avoid the stand of posts and spring clips resulting in an additional loss. Moving
forward it was clear that the stand off posts resting against datum surfaces B and C need to be
eliminated.
In the fourth iteration of the fixture design a method must be devised that allows the part
to be located in the proper location but allow for more surface area to be measured and have the
part stay in place while the CMM is running the inspection program. Commercially available
components that satisfy the criteria above were sought after to simplify the design process but
they do not exist and therefore it became necessary to design something from scratch. Several

ideas were conceptualized like unscrewing the stand off posts from the base plate, having a quick
release for the stand off posts to be removed but with these methods the locations of the stand off
posts would need to be tracked and there would be the possibility of misplacing one of the posts.
In the end it was more practical to implement a stand off that can fold which is fixed to the base
plate. Figure 18 illustrates the concepts of the design that was to be developed.
Figure 18: Proposed fixture design with folding stand off posts, a) unfolded, b) folded.
The major problem with this concept is that there is nothing holding the part in place and
this is something that needed to be addressed in a final fixture design. Before addressing that
problem in the fixture design it was required that testing be done on the potential folding stand
off posts to assess their validity for use in industry.
3.1.2 Stand Off Post Design:
Through the process of concept generation many ideas were tabled and eliminated. Two
of the best designs that met the criteria for ease of use by single hand operation, minimum of
ninety degree fold angle, positioning in the unfolded state should be repeatable within reason.
With these criteria as metrics the final two design concepts were selected and developed as
follows.

Figure 19: Initial design content, a) design #1, b) design #2
In Figure 19 design #1 locks in the upright position using a clip that would be held in
place via a torsion spring which blocks the upper part of the stand off post from rotating, this
design folds in both directions. Design #2 uses an internal keyway to lock the upper part in the
upright position, this design only folds in one direction.
Figure 20: Second iteration for a) design #1 and b) design #2
In Figure 20 design #1 is very similar to the first iteration in Figure 19 but there is
proper spacing so that the parts can rotate without interference and some edges rounded off.
Design #2 in Figure 20 has an external keyway that locks in the upright position when the gray
shaft is pushed to the right, this design only rotates in one direction.

Figure 21: Final design iteration for a) design #1 and b) design #2
In Figure 21 design #1 has a ball plunger which has a spring pushing against a ball
embedded in the green component, when the green component is rotated into the upright position
the ball is pressed into the ball seat in the gray component. Design #2 in Figure 21 is similar to
iteration 2 except the stand off can rotate in both directions and there are three locking angles;
45, 60 and 90 degrees relative to the horizontal.
Based on the small dimensions of these parts it would be ideal to use investment casting
for mass production. Investment casting is capable of produce parts with good tolerances so any
machining that would need to be done is minimal. Aluminum would be ideal for this type of
casting because of its flow characteristics and it would be more than strong enough for the
application.
3.2 Part Positioning Repeatability Testing:
For the testing of the part placement repeatability it was deemed only necessary to test in
a singular direction. Datum surface C was chosen since it requires a stand off post to position
the part initially and also there was only one post used for that surface. This allowed one
variable to be altered which was the use of the folding stand off, and one variable to be tested for

any resulting change. By selecting five random points on datum surface C which is normal to
the x direction on the CMM, and measuring the position of these points over several tests where
the part is placed and removed it is possible to get a measurement of the repeatability of the part
placement when using the folding stand off designs. Both of folding stand off designs were
tested using the exact same five points on the part as to not introduce any additional sources of
error or variables.
The part was placed by hand in position on the CMM, then the stand off was folded out
of they way ensuring that the post did not rub onto the part itself. Five points were then
measured for the x co-ordinate and recorded for later comparison and analysis. The data output
form each point is illustrated in Figure 22, noting that the actual co-ordinate is the one of
interest. Figure 23 shows the folding stand off post design #2 in action for the folding stand off
testing done in the MMRI.
Figure 22: Example of point output from Calypso CMM operating software.

Figure 23: Fixture set up for the stand off post testing
The actual values from each test outputted from Calypso were compared against each
other for each point individually. The difference between the actual values for the five tests are
calculated generating ten comparative results, the maximum of the ten difference values was then
taken and this is the error used for determining the repeatability as shown in Table 3.
Table 3: Taking difference of actual values between tests 1 through 5 and displaying the maximum difference
for Point #1 on the part.
Test # Nominal Actual Test A - Test B delta X value Test # Nominal Actual Test A - Test B delta X value
1 120 119.3089 1-2 0.1096 1 120 119.9941 1-2 0.0798
2 120 119.4185 1-3 0.1975 2 120 119.9143 1-3 0.2724
3 120 119.1114 1-4 0.5997 3 120 119.7217 1-4 0.0753
4 120 119.9086 1-5 0.192 4 120 119.9188 1-5 0.1287
5 120 119.1169 2-3 0.3071 5 120 119.8654 2-3 0.1926
2-4 0.4901 2-4 0.0045
2-5 0.3016 2-5 0.0489
3-4 0.7972 3-4 0.1971
3-5 0.0055 3-5 0.1437
4-5 0.7917 4-5 0.0534
Max delta 0.7972 Max delta 0.2724
Folding Stand Off Post Design #1 Folding Stand Off Post Design #2
For a complete set of the results for the stand off post tests see Appendix 2.
Once the maximum difference value for each for each point was found the largest
maximum difference value among the five points was used as the error for each stand off design
as shown in Table 4.

Table 4: Largest maximum difference values among Point 1 through 5 for both stand off designs.
Maximum Difference among Points 1 through 5
Design #1 0.7972
Design #2 0.2803
Built into the inspection program the CMM has a search distance set by the programmer
where the probe slows down as it expects to touch the part. A typical search zone is about 3 mm
and the part generally needs to be placed within maximum of 0.5 mm from the expected location
though it is ideal if the part is located within 0.25 mm. What this means is that the CMM
operator can use the same inspection program over and over since the part is being located in the
same spot every time without the need to redefine the location of the datum planes for each part.
The operator can also adapt these folding stand off posts while not having to change their
standard programming practices regarding search criteria. It can be seen in Table 4 that the rapid
prototyped Design #1 does not locate the part within the maximum allowable zone of 0.5 mm,
therefore it would not be considered as a valid design. The maximum value of 0.2803 mm for
Design #2 falls very close the ideal search zone criteria of 0.25 mm and would be considered a
valid design. If Design #2 were to be manufactured from some metal alloy it would be much
more rigid and the maximum difference value would be reduced because of less potential
deflection when the part is loaded.
Considering the fact that datum surface B has two stand off posts positioning it, it was
reasonable to conclude that the repeatability of the part placement in the y direction would have
been less than or equal to that of the x direction if folding stand offs were used on datum surface
B. A conservative estimate of the xy repeatability of the folding stand off design would then be
represented by the following equation.

The value obtained from the estimate of xy repeatability still places the part within the
allowable search zone criteria of 0.5 mm.
3.3 Final Fixture Design:
Once the validity of the folding stand off design had been checked and verified it was
then necessary to address the previously mentioned problem of how to hold the part in place with
no spring clips. After investigating commercially available products it was determined that the
best possible solution to this problem was to employ the use of a suction cup system that could
hold the part down adequately in the z direction. If the part had been ferrous, magnets could
have been used to hold it in place, but in this particular case the part is made of Aluminum which
is nonferrous so the suction cup system is required. The system consists of a venturi pump that
is connected to a manifold that directs the suction to the suction cups through a suction line. It
was required to attach a throttle valve with a pressure gauge in order to be able to make
adjustments to the operating pressure that is experienced by the venturi pump. The maximum
allowable pressure for the venturi is 58 psi and the air supply line in the laboratory was providing
slightly more than 80 psi. Once the system had been assembled as shown in Figure 24, it was
determined that the suction cup system would allow for some degrees of freedom in the xy plane
of the part under adequate force. It became apparent that a test needed to be developed in order
to determine whether or not the part itself would move when exposed to the forces associated
with a normal inspection run on a part. If movement were to occur the validity of the inspection
results could be called into question, and this could possibly cause good parts to be rejected.

Figure 24: Schematic of the suction cup system to be tested.
In order to test if there was any movement of the part during an inspection process the
decision was made to run an inspection of the center hole which is datum D prior to testing
another random five points for their respective locations. The same five points were used for
each test in each direction. Using the diameter of datum D allowed for the normal force from the
probe touch to act in all possible directions in the xy plane. A standard inspection speed of
15mm/s was used in order to simulate a real world inspection run on the part. Each direction
was tested individually; five tests were run on the x direction then another five tests were done
separately for the y direction. The best possible result from these tests would be that the amount
of movement measured during the tests would be comparable to the level of uncertainty that the
CMM has on its own. If that were the case then it would have been reasonable to say that there
was no movement of the part and any resulting change in measurements is simply a result of the
machines inherent uncertainty. The part was initially located by hand using fixed stand off posts,

the posts were then gently removed to avoid affecting the part placement. A few inspections
were run on the diameter of datum D to help the part settle in place and remove any forces that
may have remained due to the initial part placement, as well as the initiation of the suction
system.
Table 5: Results for point 1 of 5 in each direction for five tests each direction.
Test # Actual Value (mm) Test A - Test B Difference (mm) Test # Actual Value (mm) Test A - Test B Difference (mm)
1 -0.5703 1-2 0.1261 1 -0.0237 1-2 0.0003
2 -0.4442 2-3 0.1349 2 -0.024 2-3 1E-04
3 -0.5791 3-4 0.0002 3 -0.0241 3-4 0.0002
4 -0.5789 4-5 0 4 -0.0243 4-5 0.0002
5 -0.5789 5 -0.0245
X-Direction Y-Direction
For a complete list of results for the suction cups test see Appendix 3.
Once the largest change in position was found for each of the five points in each direction the
largest value among the five points was used to determine the maximum error in each direction
as seen in Table 6.
Table 6: Largest maximum difference values among Point 1 through 5 for X and Y direction
X-Direction max 0.1566
Y-Direction max 0.2274
In order for the suction system to be a valid option to use in a manufacturing setting the
maximum error in Table 6 should be on the same order of the uncertainty of the CMM. Typical
CMM's have an uncertainty of about 4-10 µm which is about ten times smaller than the smallest
value of 0.1566 mm or 156.6 µm although the Zeiss CMM in the MMRI has an uncertainty
closer to ±2 µm. The suction cup system was intended to limit translation in the xy plane by
generating a friction force between the part and the suction cups only using the downward force
of the part against the suction cups. For the purposes of getting accurate measurements of the

part the system failed because the part moved more than the uncertainty of the CMM. To further
decrease the translation it was proposed that O-rings be stretched over the suction cups in such a
way that when suction is activated the part would be pressing against the O-rings which would
have a higher coefficient of friction than the suction cups. The amount of force the probe head
exerts on the part is so small but it caused the part to move still but the extra friction against the
O-rings should be enough to keep the movement within the uncertainty range of the CMM.
3.4 Part Inspection Analysis:
The results of the part inspection revealed that fourteen of the thirty two tolerances on the
part were not to specification as shown in the inspection results Appendix 4. Of these fourteen
out of specification tolerances twelve of them are related to the four counterbore holes. For all
four holes the diameters of the top and bottom holes are far too small and the depth of the
counterbore is far too shallow. The fact that the depth of the counter bore is too shallow is very
interesting because the tolerance for the depth is ±1mm which is a generous allowance. This is
an indication that the length of the tool used was not calibrated correctly on the CNC to account
for the difference in the length of the tool used when compared to the length of the tool used in
the programming of the CNC code. The incorrect diameter of the two portions of the holes
appears to be due to the use of imperial tools in place of metric tools. The result shows that the
actual diameters correspond to values consistent with imperial sizes. The top portion of the holes
have a diameter of 14.41mm which converts to 0.567in, and the closest tool size in imperial is
9/16in which is 0.5625in. The bottom portion of the holes have a diameter of 8.01mm which
converts to 0.315in, and the closest tool size in imperial is 5/16 which is 0.3125in. The use of
imperial tools in place of metric tools accounts for the deviation in the diameters and could also
account for the incorrect depth of the counterbore. Conversion of tool lengths and sizes seems to
be a factor in the fact that the holes did not come out to specification. If in fact metric tools were

used it would seem that incorrect sizes were used and the tools were not zeroed properly on the
CNC machine. These problems in production are not difficult to fix and never should have
occurred in the first place.
The position tolerance on the hole corresponding to datum D is also not to specification.
The location of the hole exceeds the tolerance allowed by the MMC modifier and also exceeds
the maximum allowable tolerance when the hole is at LMC. After examining the features that
are used in locating datum D, it can be seen that there is one possible way to rework the part so
that the position is within specification. If the overall width of the part is decreased by 0.3mm
from removing material on datum C, then the position of datum D will be within specification
and not interfere with any other tolerances. The tolerance for datum D is very tight to begin
with, allowing a 0mm zone when the hole is at MMC. To avoid rework and rejected parts it may
be necessary for the designer of the part to make changes to the dimensions of the hole to allow
for a larger tolerance at MMC. In order to ensure that the largest bonus tolerance is available on
the position of this hole, the hole target diameter could be adjusted to 31mm. Having the target
dimension close to that of LMC will allow for a larger tolerance zone on datum D and all other
related features that are toleranced from datum D. The process capability of the CNC machine
used in the manufacture of this part should have been able to meet the specification for the
position of datum D. The fact that the position was not within specification is an indication that
potentially too many set ups were used in the creation of this part. It would be worthwhile to
investigate the number of set ups used and the means by which this number can be reduced.
The final tolerance that was not to specification is the perpendicularity of datum surface
C with respect to datums A, and B. Again this is likely due to having too many different set ups
used in the creation of the part. It is likely that datum surface C was not cut in the same set up as
datum surface B which has led to nonconformance issues. A problem that can occur with

multiple set ups is that there could be a chip or small fragment of material or debris that is in the
fixture which would affect the alignment of the part during the machining process. It is also a
possibility that the tool used was too long and the cutting forces caused excessive deflection thus
resulting in non-perpendicularity of the surface.
For this particular part the minimum number of set ups that is required is two. If a small
amount of thickness was added to the stock material for clamping in a vice with machined groves
then all the features but datum surface A could be machined in a single set up. This would
reduce the number of rejected parts because the process capability of a properly calibrated and
programmed CNC should easily be able to meet the specifications of this part. Once all the
features were machined, the part could then be flipped upside down in order to complete the
facing of datum surface A. This proposal would require additional material costs for each part
initially, but the possible savings from a minimal amount of rejected parts would offset this
additional initial cost. The chips from the machining process should also be recycled which will
allow for the recuperation of a substantial amount of the cost for the additional material used.
It is important to note that the results presented in Appendix 4 made use of the diameter
found in the initial inspection results found in Appendix 6. The diameter for datum D 29.97mm,
found in the initial result was used to calculate the bonus tolerances for related specifications
used in the inspection done in Appendix 6, the bonus tolerance was found to be 0.1738mm when
the uncertainty of the CMM was ignored. The bonus tolerance used was conservative because
the results in Appendix 6 gave a diameter that was slightly larger than the initial value. This
bonus was then applied to all relevant tolerances for the inspection results found in Appendix 4
so that the results presented there are considered to be correct. This was necessary because it
was not possible to apply the MMC modifier where required within Calypso, the operating
software for the CMM. Results from the inspections were truncated to the second decimal place

due to the uncertainty of the Zeiss CMM, which is applicable to the micrometer scale. When the
part inspection results from the suction cup tests shown in Appendix 5 are compared to the other
results from testing done with a fixed part it can be seen that the amount of movement
experienced by the part when held by only the suction cups had a significant effect. When the
part was tested with only suction cups a total of nineteen tolerances were found to be out of
specification which is five more than the previous tests. This is further evidence that there was
indeed excessive movement of the part that is not acceptable and more improvements need to be
done on the suction cup system to be applicable to industry when used in conjunction with the
folding stand off design.
It is evident that the part inspected can be carefully reworked to satisfy all of the
tolerances if in fact there is a ±0.5mm tolerance on the basic dimensions of the part, namely the
width of the part. This is only possible because the features in question have an excess of
material remaining which can be removed. Interpretation of the results provides a great deal of
information on how to adjust the manufacturing process so that the majority of the parts
produced are acceptable, except for any unexpected events such as tool failure during the
machining process or improper placement of the part in the fixtures.
4.0 Conclusion:
In conclusion, fixturing is a crucial and problematic area in engineering when dealing
with CMM’s. After rapid prototyping and testing the two designs for folding stand off posts it
was determined that only design #2 was suitable for further development keeping in mind that
the results for the folding stand off posts are conservative and would perform even better if they
were made out of Aluminum. The suction cup system for holding down the part allows for a

larger surface area of the part to be measured but the suction cups are not rigid enough to keep
the part in place so that it is not a significant source of error. The proposed solution is to have O-
rings fitted around the suction cups or another means to create more friction between the suction
cup so that the part is resting against a surface with a higher static coefficient of friction allowing
it to stay in place. Through the inspection results it was determined that the part was out of
tolerance but could be reworked to be acceptable. The analysis also provided information that
could be used to make suggestions to the manufacturer to avoid rejected parts in the future.

Appendix 1:List of Acronyms
GD&T: Geometric Dimensioning and Tolerancing
MMC: Maximum Material Condition
MMB: Maximum Material Boundary
LMC: Least Material Condition
FOS: Feature of Size
DOF: Degree of Freedom
UOS: Unless Otherwise Specified
ASME: American Society of Mechanical Engineers
CNC: Computer Numerical Control
CMM: Coordinate Measuring Machines

Appendix 2: Stand Off Post Test Results
Point #1:
Test # Nominal (mm) Actual Value (mm) Test A - Test B Difference (mm) Test # Nominal (mm) Actual Value (mm) Test A - Test B Difference (mm)
1 120 119.3089 1-2 0.1096 1 120 119.9941 1-2 0.0798
2 120 119.4185 1-3 0.1975 2 120 119.9143 1-3 0.2724
3 120 119.1114 1-4 0.5997 3 120 119.7217 1-4 0.0753
4 120 119.9086 1-5 0.192 4 120 119.9188 1-5 0.1287
5 120 119.1169 2-3 0.3071 5 120 119.8654 2-3 0.1926
2-4 0.4901 2-4 0.0045
2-5 0.3016 2-5 0.0489
3-4 0.7972 3-4 0.1971
3-5 0.0055 3-5 0.1437
4-5 0.7917 4-5 0.0534
Design #1 Design #2
Point #2:
1 120 119.1976 1-2 0.1682 1 120 119.9348 1-2 0.0887
2 120 119.3658 1-3 0.1479 2 120 119.8461 1-3 0.2759
3 120 119.0497 1-4 0.3533 3 120 119.6589 1-4 0.079
4 120 118.8443 1-5 0.1436 4 120 119.8558 1-5 0.1363
5 120 119.054 2-3 0.3161 5 120 119.7985 2-3 0.1872
2-4 0.5215 2-4 0.0097
2-5 0.3118 2-5 0.0476
3-4 0.2054 3-4 0.1969
3-5 0.0043 3-5 0.1396
4-5 0.2097 4-5 0.0573
Design #1 Design #2
Point #3:
1 120 119.2365 1-2 0.2054 1 120 120.0082 1-2 0.0942
2 120 119.4419 1-3 0.1163 2 120 119.914 1-3 0.2782
3 120 119.1202 1-4 0.3238 3 120 119.73 1-4 0.0823
4 120 118.9127 1-5 0.1127 4 120 119.9259 1-5 0.1415
5 120 119.1238 2-3 0.3217 5 120 119.8667 2-3 0.184
2-4 0.5292 2-4 0.0119
2-5 0.3181 2-5 0.0473
3-4 0.2075 3-4 0.1959
3-5 0.0036 3-5 0.1367
4-5 0.2111 4-5 0.0592
Design #1 Design #2

Point #4:
1 120 119.0944 1-2 0.2284 1 120 119.8869 1-2 0.0987
2 120 119.3228 1-3 0.0969 2 120 119.7882 1-3 0.2791
3 120 118.9975 1-4 0.3057 3 120 119.6078 1-4 0.0842
4 120 118.7887 1-5 0.0935 4 120 119.8027 1-5 0.1465
5 120 119.0009 2-3 0.3253 5 120 119.7404 2-3 0.1804
2-4 0.5341 2-4 0.0145
2-5 0.3219 2-5 0.0478
3-4 0.2088 3-4 0.1949
3-5 0.0034 3-5 0.1326
4-5 0.2122 4-5 0.0623
Design #1 Design #2
Point #5:
1 120 119.2203 1-2 0.2558 1 120 120.0375 1-2 0.1003
2 120 119.4761 1-3 0.0731 2 120 119.9372 1-3 0.2803
3 120 119.1472 1-4 0.2828 3 120 119.7572 1-4 0.0849
4 120 118.9375 1-5 0.0695 4 120 119.9526 1-5 0.1493
5 120 119.1508 2-3 0.3289 5 120 119.8882 2-3 0.18
2-4 0.5386 2-4 0.0154
2-5 0.3253 2-5 0.049
3-4 0.2097 3-4 0.1954
3-5 0.0036 3-5 0.131
4-5 0.2133 4-5 0.0644
Design #1 Design #2
Results:
Design #1 0.7972
Design #2 0.2803

Appendix 3: Suction Cup Testing Results
Point #1:
1 -0.5703 1-2 0.1261 1 -0.0237 1-2 0.0003
2 -0.4442 2-3 0.1349 2 -0.024 2-3 1E-04
3 -0.5791 3-4 0.0002 3 -0.0241 3-4 0.0002
4 -0.5789 4-5 0 4 -0.0243 4-5 0.0002
5 -0.5789 5 -0.0245
Point #2:
1 -0.5142 1-2 0.0022 1 0.2565 1-2 0.0003
2 -0.5164 2-3 0.0007 2 0.2562 2-3 0.0002
3 -0.5157 3-4 0.0001 3 0.256 3-4 0
4 -0.5156 4-5 0.0003 4 0.256 4-5 0.0002
5 -0.5153 5 0.2558
Point #3:
1 -0.3635 1-2 0.0035 1 0.0295 1-2 0.2267
2 -0.36 2-3 0.1557 2 0.2562 2-3 0.2274
3 -0.5157 3-4 0.1566 3 0.0288 3-4 1E-04
4 -0.3591 4-5 0 4 0.0287 4-5 0.0002
5 -0.3591 5 0.0285
Point #4:
1 -0.3798 1-2 0.0044 1 0.1793 1-2 0.0002
2 -0.3842 2-3 0.0007 2 0.1791 2-3 0.0001
3 -0.3835 3-4 0.0002 3 0.179 3-4 0.1147
4 -0.3833 4-5 0.0003 4 0.0643 4-5 0.1143
5 -0.3836 5 0.1786
Point #5:
1 -0.4442 1-2 0.0112 1 0.0649 1-2 0.0003
2 -0.4554 2-3 0.0011 2 0.0646 2-3 0.0001
3 -0.4543 3-4 1E-04 3 0.0645 3-4 0.0001
4 -0.4542 4-5 0 4 0.0644 4-5 0.0003
5 -0.4542 5 0.0641

Results:
X-Direction max 0.1566
Y-Direction max 0.2274

Appendix 4: CMM results from the part firmly fixed in place

Appendix 5: CMM results from suction cup testing

Appendix 6: Initial CMM results for part

Bibliography
[1] R .J. Hocken, P .H. Pereira. Coordinate Measuring Machines and Systems, 2nd ed., CRC Press,
2011
[2] History of GD&T., Geometric Learning Systems, [online] 2008,
http://gdtseminars.com/2008/03/25/history-of-gdt/ (Accessed October 11, 2014).
[3] File:GD&T.png., Wikipedia The Free Encyclopedia, [online] 2006,
http://upload.wikimedia.org/wikipedia/en/2/25/Gd%26t.png (Accessed October 11, 2014).
[4] Geometric Tolerancing., CETOL Tolerance Analysis, [online] 2010,
http://www.roymech.co.uk/Useful_Tables/Drawing/draw_geom_notes.html
(Accessed October 18, 2014)
[5] GD&T (Y14.5) – Geometric Dimensioning and Tolerancing Professional Certification.,
ASME, [online] 2009, https://www.asme.org/shop/certification-accreditation/personnel-
certification/gdtp-y14-5-geometric-dimensioning-and-tolerancing (Accessed October 18, 2014)

Project AS01 2015 Final Report

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