1. Automating GD&T Schema Synthesis
for Mechanical Assemblies
ASU DAL 1

2. Terminology
Feature (Part Feature): A feature refers to a physical portion of a part, such as a surface, hole or
slot
Feature of Size (FOS): Any three dimensional feature with a size dimension
Assembly Feature: Mating feature pairs on distinct parts in an assembly
ASU DAL 2

3. Terminology
Target Feature: Refers to the to be toleranced feature
Datum Feature: An actual feature of a part that is used to establish a datum.
Datum: A theoretically exact point, axis, or plane derived from the datum feature.
Datum Feature Datum (axis) established by datum feature
ASU DAL 3

4. Terminology
Datum Reference Frame (DRF): Coordinate systems used to locate and orient a part feature. All
measurements for the features, which have geometric tolerances related to the datums will
originates from the established datum reference frame, and not a part. Tolerance zones are
located or oriented to the datum reference frame and no the datum features.
ASU DAL 4

5. Terminology
Degree of Freedom (DOF): Each body in 3D space has tree translational DOFs along and three
rotational DOFs around x, y, z axes.
Tolerance Synthesis: Determination of allowable geometric and dimensional variations to meet
assemblability condition and design function; consists of schema development and tolerance
allocation.
ASU DAL 5

6. Terminology
Auto-Tolerancing: Software to automate tolerance synthesis.
First Order Tolerancing: GD&T based only on geometric conditions for assemblability.
Second Order Tolerancing: GD&T based on both assemblability and design intent/function.
Third Order Tolerancing: GD&T based on all of the above, while optimizing manufacturing cost.
ASU DAL 6

7. Tolerance Background and Its Standards
It is impossible to manufacture a part without imperfections and deviations from the nominal
geometry due to human errors, machine inaccuracies, and environment conditions
Tolerances define the degree to which the nominal design can vary without compromising
functional requirements
Two GD&T standards in use: ASME Y14.5 and equivalent ISO standard
Dimensional
Variations
Geometric
Variations
ASU DAL 7

8. Problem Statement / Motivation
Tolerancing of the design is done typically by the detailers towards the end of the design
process. Application of a good tolerance schema requires in-depth knowledge and years of
experience in the GD&T field
Available computer-aided tolerance software packages (CATS) do not aid tolerance synthesis.
They require the user to input a complete GD&T scheme
This project was proposed as a mean for solving two issues: the lack of GD&T expertise amongst
designers and the GD&T data exchange problems (GD&T information can not be transformed
across different CAD systems)
ASU DAL 8

9. Problem Statement / Motivation
In DAL, we investigated the degree to which tolerance synthesis can be automated
First Order Tolerancing: GD&T based only on geometric conditions for assemblability.
Second Order Tolerancing: GD&T based on both assemblability and design intent/function.
Third Order Tolerancing: GD&T based on all of the above, while optimizing manufacturing cost.
Tolerance synthesis:
1- Tolerance schema development (Scope of this research)
2- Tolerance value allocation and analysis
ASU DAL 9

10. Problem Decomposition
ASU DAL 10
Create automated 1st
order GD&T schema
generation Module
Identify to be
toleranced
features
Define
tolerance types
Create DRFs
Identify the
sequence of control
(Datum Flow Chain)
Represent features,
constraints and
tolerances

11. OVERVIEW OF THE AUTO-TOLERANCING
PROJECT
ASU DAL 11

12. OVERVIEW OF THE AUTO-TOLERANCING
PROJECT (Phase 1-Previous Phase)
ASU DAL 12

13. OVERVIEW OF THE AUTO-TOLERANCING
PROJECT (Phase 2- Current Phase)
ASU DAL 13
ASU GD&T Global Model
Constraint, Tolerance, Feature (CTF) Graph

14. ASU GD&T Global Model (CTF)
ASU DAL 14

15. Objective and Function Requirements of the
Schema Generation Module
ASU DAL 15
Mating FOS
and datums
Size, location,
orientation, and
form
Feature scoring
system
DOF algebra
Assembly Loops Object Oriented
Design
ASU GD&T Global
Model
Create automated 1st
order GD&T schema
generation Module
Identify to be
toleranced
features
Define
tolerance types
Create DRFs
Identify the
sequence of control
(Datum Flow Chain)
Represent features,
constraints and
tolerances

16. Flowchart
ASU DAL 16
Rulesets based on the input from experts in RECON SERVICES
S ruleset: Defines the rules for assigning size tolerance
L ruleset: Defines the rules for assigning location tolerance
D ruleset: Defines the rules for datum selection
X ruleset: Defines the rules for assigning secondary tolerances

17. Enhancing Input Data
Some of the geometric properties that are required for schema generation is not provided
through input files (Preprocessing Modules).
1- Non-mating features
2- Coplanar features
Finding non-mating and coplanar features require extracting Directions of Control (DoC)
ASU DAL 17

18. Directions of Control
In GD&T practices, dimensions and tolerances are controlled in finite number of particular
directions.
ASU DAL 18
-------

19. Modified Directions of Control
Extracting DoCs of the to be toleranced features (Reduces memory consumption)
Original DoC function Modified DoC function
ASU DAL 19

20. Non-Mating Features Recognition
Tab/slot: Two antiparallel faces with same shape and same area
Mating Features
ASU DAL 20

21. Coplanar Features Recognition
In each direction, coplanar faces have zero relative distance with respect to each other.
Using this property helps us finding coplanar features.
Zero
relative
distance
ASU DAL 21

22. Location Tolerance Frame Creation
Creating location tolerance frame starts with finding potential datums and creating DRF
Feature scoring system (utility functions) is the Machine readable interpretation of the D rules
Planar and prismatic features have the same metrics. Different metrics are defined for
cylindrical features
The scoring system is designed and implemented in a way that can be tuned later
ASU DAL 22

23. Feature Scoring System
Scores for planar and prismatic features:
1- Area ratio score:
The area of a plane is the most important characteristic that makes a plane to be selected as a
datum. The area ratio score is defined as the ratio of the feature’s area to the largest area in the
part.
2- Aspect ratio score:
Based on the GD&T good practices, planes with the high aspect ratio are not good candidates to
be selected as datum.
ASU DAL 23
Aspect ratio score
100
Aspect ratio
8

24. Feature Scoring System
3 – Accessibility score:
Planes with low accessibility are not good candidates to be datums. Accessibility is defined by
the ratio of the number of concave edges to the number of convex edges
Scores for cylindrical FOS:
1- Length ratio score:
Cylinders with large lengths establishes an appropriate datums. The length ratio score is defined
as the ratio of the feature’s length to the largest cylinder’s length in the part
2- Aspect ratio score:
Very long cylinders with small diameters are hard to control, hence, not appropriate datums.
The aspect ratio defined as the ratio of feature’s length to its diameter.
ASU DAL 24
Aspect ratio score
100
Aspect ratio
4

25. DOF Algebra
DOF algebra tells us how far the datum selection should go. Based in this concept, datum
selection stops when datums in reference frame constrain all active DOFs (aDOFs) of the target
feature
Geometric primitives have some active and invariant DOFs (do not location and orientation of
the feature)
Line
4 aDOFs 2 iDOFs
2 TDOF (x, y) 1 TDOF (z)
2 RDOF (α, β) 1 RDOF (γ)
Plane
3 aDOFs 3 iDOFs
1 TDOF (z) 2 TDOF (x, y)
2 RDOF (α, β) 1 RDOF (γ)
ASU DAL 25

26. DOF Algebra
Geometric features are special cases of geometric primitives. They only have extra size DOF(s).
A cylindrical pin is a line with radius and height parameter.
A tab is a plane with radius and height parameter.
β
y
Z
Y
Mid-plane
β
Y
Z
ASU DAL 26

27. DOF Algebra
Different number of active DOFs of a target feature is constrained by each datum regarding
target feature’s type, datum’s type and the orientation between them.
T D
CY
CY PL / PR
AR AT CR CT CR CT CR CT CR CT
2 2 1 1 2 2 2 0 1 1
ASU DAL 27
T D
PR
CY PL / PR
AR AT CR CT CR CT CR CT CR CT
2 2 1 0 1 1 1 0 2 1
T = Target feature
D = Datum feature
CY = Cylindrical feature
PL = Planar feature
PR = Prismatic feature
AR = active RDOF
AT = active TDOF
CR = constrained RDOF
CT = constrained TDOF

28. DOF Algebra- An Example
How DOF algebra helps the process of creating DRF
0 A B C
A: 2 aRDOF around x and z
B: 1 aTDOF along z
C: 1 aTDOF along x
ASU DAL 28

29. Size Tolerance Creation
S ruleset defines the criteria for creating size tolerance
S1, S3: FOS is datum flow chains need size tolerance
S4: Appropriate number of size tolerance is required to constrain all size DOFs of the target feature
Feature
Type
CY PR
P
H
T/S
P/H
P
H
TH BH TH BH
Size
DOFs
1 DR
1 HT
1 DR
1 DR
1 DH
1 HT
1 WH
1 WH
1 LH
1 HT
1 WH
1 LH
1 WH
1 LH
1 DH
ASU DAL 29
CY = Cylindrical feature
P/H = Pin/Hole
TH = Trough Hole
BH = Blind Hole
PR = Prismatic feature
T/S = Tab/Slot
DR = Diameter
WH = Width
LH = Length
DH = Depth
HT = Height

30. Secondary Tolerance Frame Creation
Tolerance zones defined by primary tolerances controls the orientation and form tolerances as
well (ASME Y14.5M rule #1). Secondary tolerances are required when no primary tolerance is
assigned or a finer tolerance zone is required.
X ruleset defines the criteria for assigning secondary tolerances
X1,X2,X3,X4: Secondary tolerances are applied to features in datum flow chain
Unrequired orientation and form tolerances will be filtered after tolerance allocation in the
value allocation/verification module
ASU DAL 30

31. Case Study / Software Verification
Cam Follower Assembly
Provided by our industry partner RECON SERVICES
Contains 13 parts including 6 standard bolts
Standard bolts don’t require GD&T
The process of creating GD&T is presented for one
part as an example. Same procedure is applicable
to other parts.
The GD&T recommended by software is compared
with the GD&T applied by an expert
ASU DAL 31
Right Support

32. Case Study / Software Verification
Preprocessing Results
AFR results
PFR results
AFR Results for the assembly:
Total number of 35 part features
and 23 assembly features
PFR Results for the assembly:
Total number of 5 part patterns
ASU DAL 32

33. Case Study / Software Verification
Enhancing Input Data
Extracted active DoCs
Extracted non-mating features
Extracted coplanar features
ASU DAL 33

34. Case Study / Software Verification
Creating Location Tolerance
ASU DAL 34
Type Non-Cylindrical Score
1 The external T-shape FOS 65
2 Mating face where at the left end 52
3 The mating slot 31
4 The external U-shape FOS 27
5 Coplanar faces where two holes seat 24
6 The external square-shape FOS 19
7 Coplanar faces at the right end 17 Rule L4

35. Case Study / Software Verification
Creating Location Tolerance
ASU DAL 35
Type Non-Cylindrical Score
1 The external T-shape FOS 65
2 Mating face where at the left end 52
3 The mating slot 31
4 The external U-shape FOS 27
5 Coplanar faces where two holes seat 24
6 The external square-shape FOS 19
7 Coplanar faces at the right end 17

36. Case Study / Software Verification
Creating Size Tolerance
ASU DAL 36

37. Case Study / Software Verification
Creating Orientation and Form Tolerances
ASU DAL 37

38. Case Study / Software Verification
Full Recommended GD&T
ASU DAL 38

39. Case Study / Software Verification
Comparing GD&T Schemas
GD&T schema created by software GD&T schema created by an expert
ASU DAL 39

40. Case Study / Software Verification
Comparing GD&T Schemas
GD&T schema created by software
GD&T schema created by an expert
ASU DAL 40

41. Conclusion / Future Works
Summary:
Generating the appropriate GD&T scheme needs an in-depth knowledge and years of
experience and in the field of tolerance synthesis and analysis.
This module as a part of Auto-Tolerancing project automates the process of the 1st order
tolerance schema synthesis
Limitations:
1- Second and third order tolerancing haven’t been taken into account
2- Runout and profile tolerances are not used
2- Datum targets are not defined neither in the CTF nor in the data structure of this module
ASU DAL 41

42. Conclusion / Future Work
Future work:
1 – Incorporating the results of the Assembly Analysis module (assembly loops information) in
the schema generation module as complimentary tool for datum selection where a local control
is required
ASU DAL 42

43. Conclusion / Future Work
Future work:
2 - A feedback system from the value allocation/analysis module to the schema generation
module
3 - Incorporating second and third order tolerancing, so the profile and run out tolerances can
be considered
4 - More test cases can be studied to verify the comprehensiveness of the recommended
tolerances schemas and scalability of the module
ASU DAL 43

44. Publications
Hejazi, S. M., Biswas, D., Venkiteswaran, A., Shah, J. J., and Davidson, J. K., 2016, Automated 1st
order tolerancing: Schema generation,” Accepted to IDETC/CIE 2016, ASME, Charlotte, NC, Paper
#DETC2016-60147
Venkiteswaran, A., Hejazi, S. M., Biswas, D., Shah, J. J., and Davidson, J. K., 2016, “Interoperability
of GD&T data through STEP AP242,” Accepted to IDETC/CIE 2016, ASME, Charlotte, NC, Paper
#DETC2016-60133
Biswas, D., Venkiteswaran, A., Hejazi, S. M., Shah, J. J., and Davidson, J. K., 2016, “Automated
Iterative Tolerance Value Allocation and Analysis,” Accepted to IDETC/CIE 2016, ASME, Charlotte,
NC, Paper #DETC2016-60145
ASU DAL 44

45. Acknowledgments
Special thanks to Dr. Jami Shah, Dr. Joseph Davidson and Dr. Dianne Hansford
ASU DAL 45
Grant No. 14-02-05