누적공차 해석 software 개발을 위한
선행연구
2012 December 20
Prof. Hyun Chung
Marine Design & Production Systems Lab.
Ocean Systems Engineering
KAIST
Contents
• Background
• Tolerance
– Tolerance definition
• Tolerance analysis methodologies
– Methods for tolerance analysis
• Assembly models
• System diagram for tolerance analysis software
• Conclusions
Background
• Preliminary research on the tolerance analysis
software development project
– Review of existing tolerance analysis methodologies
– Plans for the main project
Product Quality
Product Quality
Product Quality
Tolerance!?
• The Permissible limit or limits of variation in
– A physical dimension
– A measured value of physical property of a material, manufactured
object, system, or service
– Other measured values (such as temperature, humidity, etc.).
– …..
– The space between a bolt and a nut of a hole, etc.
Tolerance!?
• Why?
– Nothing is perfect!
– Large variation may affect the functionality of the part
– Small variation will effect the cost of the part
• Requires precise manufacturing
• Requires inspection and the rejection of parts
• When it becomes important?
– Assemblies:
• May not fit together
• Variations stack-up
– Interchangeability:
• Replacement parts
– Tolerance in relation to money
Tolerance Stack Up
•
•
•
•
Failure to assemble
Interference between parts
Failure of parts to engage
Failure to function as intended
3.00±0.01
7.00±0.01
4.00±0.02
How are Tolerance specified?
• Size
– Limits specifying the allowed variation in each dimension
– Length, width, height, diameter, etc.
• Geometry
– Geometric tolerancing
• Allows for specification of tolerance for the geometry of a part separate from its size
• GD&T (Geometric Dimensioning and Tolerancing) uses special symbols to control differen
t geometric features of a part
How are Tolerance specified?
How are Tolerance specified?
How are Tolerance specified?
How are Tolerance specified?
How are Tolerance specified?
Datum and Modifiers
• Datum
– Reference frame where the measurement is taken
• Modifiers
– MMC: maximum material condition
– LMC: least material condition
– RFS: regardless of features size
• This indicates that the tolerance must be maintained, regardless of variations in this size
of the object
– Projected tolerance zone
• A tolerance zone can be extended beyond a surface.
Tolerance analysis
• How the part variation affects the assembly variation?
• And then, how to control the tolerances?
How the tolerance of parts
propagate?
Tolerance analysis
Response of the assembly (a measurabl
e feature such as gap, etc.)
Values of some characteristics
(ex. Dimensions) of individual part
• Linear vs. Nonlinear propagation
– Linear propagation:
• Easy to analyze mean and standard variation of the assembly
• Easy to accurately calculate the sensitivity
– Nonlinear propagation
• Most practical problem falls into this category
• Approximation methods such as Taylor expansion can be used
• Numerical simulation such as Monte Carlo Simulation can be used.
Tolerance analysis
• Linear tolerance
– Linearity between measure and tolerance
Measure direction
20±0.2
Measure = Dimension + Tolerance
Tolerance analysis
• Nonlinear tolerance
– Non-Linearity between measure and tolerance
• True distance measure
• Angle measure
• Measure which includes logics
– Conditional, iterative, etc..
• Dual, triple tolerance
• Hole-pin floating or bonus tolerance
Measure = L x sin(arctan(T/L))
Tolerance Analysis Big picture
Assembly models
Tolerance analysis
methods
Tolerance synthesis
methods
Relational models
Worst case
Iterative approach based
on analysis methods
Hierarchical models
Linearization (RSS)
Mathematical
programming
Datum flow chain
Extended Taylor series
approximation
Heuristic optimization
Object oriented
models
Six sigma
Design of experiments
Monte Carlo
simulation
Tolerance analysis
Model
Worst
Case
Statistical
(RSS)
Six Sigma
Measure
d
Data
Stack Formula
Predicts
Application
Extreme limits of variation Critical system
No rejects permitted
Most costly
Probable variation
Percent rejects
Reasonable estimate
Some rejects allowed
Less costly
Long-term variation
Percent rejects
Drift in mean over
time is expected
High quality levels are
desired
Variation using existing
part measurements
Percent rejects
After parts are made
What-if? studies
Tolerance Analysis Approaches
• Manual/Automation Tolerance Charts
– Most common approach
– Suitable for 1-D tolerance analysis
• Monte Carlo Simulation
– Numerical simulation for statistical tolerance model
– Can be applied to general problems regardless of statistical distribution and the
tolerance propagation of target system
– Computationally expensive
• Vector Loop(or Kinematic) method
– Represents the relationships among the parts with vector and matrix based on
Assembly flow
– Analyzes the tolerance propagation with individual vector loop and datum loop
• Tolerance maps (T-maps)
– Represents the tolerance as zone and combine the part tolerances as the
combination of zones
– Optimize the tolerances by shape optimization of tolerance zone
Vector Loop
Dim
Nominal
Tolerance
a
10.00m
±0.3mm
b
30.00
±0.3
c
31.90
±0.3
d
15.00
±0.3
e
55.00
±0.3
f
75.00
±0.5
g
10.00
±0
r
10.00
±0.1
R
40.00
±0.3
θ
17.0 deg
±1.0 deg
Vector Loop
• Step 1 – create an assembly graph
Vector Loop
• Step 2 – Locate the datum reference frame for each part
Vector Loop
• Step 3 – Locate kinematic joints and create datum path
Vector Loop
• Step 4 – Create vector loops
Assembly loop 1 and 2
Vector Loop
• Step 5 – Generate assembly equations from vector loops
𝑛
𝑖
𝑖=1
𝑛
𝑗=1
𝑖
𝑖=1
𝑛
𝑗=1
𝑖
𝑖=1
𝑗=1
𝐻𝑋 = � 𝐿𝑖 𝑐𝑐𝑐 � 𝛼𝑗
=0
𝐻𝑌 = � 𝐿𝑖 𝑐𝑐𝑐 � 𝛽𝑗
=0
𝐻𝑍 = � 𝐿𝑖 𝑐𝑐𝑐 � 𝛾𝑗
=0
𝑛
𝐻𝛼 = � 𝛼𝑖 = 0° 𝑜𝑜 360°
𝑖=1
𝑛
𝐻𝛽 = � 𝛽𝑖 = 0° 𝑜𝑜 360°
𝑖=1
𝑛
𝐻𝛾 = � 𝛾𝑖 = 0° 𝑜𝑜 360°
𝑖=1
Vector Loop
• Step 5 – Generate assembly equations from vector loops
Vector Loop
•
•
•
•
•
Step 6 – Calculate derivative and form matrix equation
Step 7 – Solve for assembly tolerance sensitivity
Step 8 – Form worst case and RSS expression
Step 9 – evaluation and design iteration
Step 10 – Percent contribution chart
Datum Flow Chart (DFC)
• Assembly flow
– Explains the relationship between individual parts in the assembly
– Main assembly flow, sub-assembly flow
– Vector loop and datum flow
• Datum flow chain
– Includes Key Characteristics (KC) of individual parts
– Represents the relationships between individual parts
– Includes the flow of KCs in the assembly
– Vector loops
Datum Flow Chart (DFC)
• Procedure
Feature
Liaison Diagram(assembly flow diagram)
Key Characteristics diagram
Datum Flow Chains
• Basic DFC diagram
– Arrows: datum flow
X, θz
– Label: constrains of DOF (degree of freedom)
A
– Double lines: Key Characteristics A
D
D
B
C
Liaison diagram
(6)
(6)
B
Y, Z
θx , θy
C
Datum flow chain
Datum Flow Chart (DFC)
• Assembly Flow Chain
– Main assembly
– Sub-assembly: battery, torque limiter, transmission, motor assembly
Datum Flow Chart (DFC)
• Assembly Flow Chain
Datum Flow Chart (DFC)
• DFC for transmission
Datum Flow Chart (DFC)
• DFC for transmission
4& 6: Torque Limiter & Power Generator
8.3: PG1 Internal Gears
KC#1
20
18
17 26
19
KC#2
8.1: Planetary Gear 1 Washer
8.10:Hi/Lo Lever
25
21
24
8.2: PG3 Pinion Gears
16
8.4: PG1 Carrier/PG2 Sun Gear
14
8.8: PG2 Coupling Gear
13
Alternative
8.9:PG2 Locking Gear
12
15
8.7: PG2 Washer
8.6: PG2 Pinion Gears
23
22
9
Alternative
8.13:PG2 Carrier/PG3 Sun Gear
11
10
8.14:PG3 Washer
8.15:PG3 Internal Gear
7.2: Bit Holder Housing
4
7
6
2
8
5
8.2: PG3 Pinion Gears
3
1
8.16 & 7.1:PG3 Carrier & Bit Holder
System diagram for tolerance analysis software
• 3DCS (for CATIA)
Model Viewing
Point 및 공차에 의한 변형 및 GD&T show/hide
Feature Information, Preference 및 MTM Setting
Assembly 관계 확인 및 해석 기능
Feature Points 생성
<기능분석>
System diagram for tolerance analysis software
• CETOL (for Pro/E)
<Flow chart of joint-creation process>
<general flow of a CETOL analysis>
<Flow chart of overlay part dimensioning scheme>
System diagram for tolerance analysis software
Assembly
Model 구성도
• Assembly
시스템
Information
Vector Format
for Analysis
Mating
Information
Feature
Input
Tolerance
Input
UG 모듈 (C++, VB)
Random Number
Generator
Statistics Analysis
System
Matrix Calculation
Module
공차해석모듈
Generate Report
Conclusion
• Tolerance analysis
– Overall review of tolerance and tolerance analysis
– Tolerance analysis methods and Assembly models
– DFC approach and MCS are recommended for robustness and
expandability
• Future Works
– Tolerance analysis engine development
• Selection of GD&T feature to be included
– Detailed Software system diagram
•
•
•
•
•
•
Assembly 구성 정보 추출 및 재구성 작업
부품에 대하 mating 관계 정의
공차 feature 정의를 위한 input UI 구성
UI 단순화
공차해석 part로 넘기기 위한 input format 정의
Measure 정의
Thank you for your attention!!