Final Analysis Report
MIE 313 � Design of Mechanical Components
Juliana Amado
Charlene Nestor Peter Walsh
i
Table of Contents Abstract: ......................................................................................................................................... iii
Introduction:.................................................................................................................................... 4
Procedure: ....................................................................................................................................... 5
Results:............................................................................................................................................ 6
Reliability:....................................................................................................................................... 8
Redesign:......................................................................................................................................... 8
Conclusion: ..................................................................................................................................... 9
Table of Figures Figure 1: Table saw Fence Assembly ............................................................................................. 4
Figure 2: Clamp Block Assembly................................................................................................... 4
Figure 3: Critical Stress Locations.................................................................................................. 6
Figure 4: Stress Intensity for fast fracture....................................................................................... 7
Figure 5: Existing Clamp Block ..................................................................................................... 8
Figure 6: Redesigned Clamp Block ................................................................................................ 8
Tables
Table 1: Stress Analysis Results ..................................................................................................... 6
Table 2: Critical Stress Redesign vs. Original ................................................................................ 9
ii
Appendices Appendix A: Energy Analysis of Input Force .......................................................................... I
Appendix B: Force Model & Hand Calculations................................................................... III
Clamp Block: Simplified Stress Calculations ........................................................................... IV
Lifter: Simplified Hand Calculations .......................................................................................VII
Dog: Simplified Hand Calculations.........................................................................................VIII
Appendix C: FEA Loads and Constraints............................................................................... X
Clamp Block .............................................................................................................................. XI
Lifter .........................................................................................................................................XII
Dog ..........................................................................................................................................XIII
Appendix D: FEA (Existing Design) ....................................................................................... XIV
Appendix E: FEA (Redesign) ................................................................................................XVIII
Appendix F: Reliability Calculations ........................................................................................XX
Existing Clamp Block............................................................................................................. XXI
Redesigned Clamp Block ....................................................................................................... XXI
Appendix G: Engineering Drawings ......................................................................................XXIII
Clamp Block ........................................................................................................................ XXIV
Lifter ......................................................................................................................................XXV
Dog ..........................................................................................................................................XIII
iii
Abstract: The part being analyzed is the Clamp Block component of the clamping mechanism of a
table saw fence assembly. The clamping system acts as a spring and applies normal force to the
fence rails. This normal force results in friction forces that prevent the fence from sliding
horizontally along the fence rails. The Clamp Block has failed by fast fracture near an abrupt
change in geometry.
The overall objective of this project is to analyze the mode of failure of the Clamp Block
and redesign it accordingly. Finite element analysis was used in conjunction with hand
calculations to determine the cause of failure of the Clamp Block. Three critical locations were
identified in the area of fracture. The most highly stressed was at an inside corner on a horizontal
web that spans between the two sides of the Clamp Block. The magnitude of stress was not
above the yield of the material at this location, but statistical analysis shows that the failure rate
was approximately 5%. The concentration of stress at this critical point may have caused cracks
to propagate causing fast fracture on subsequent loading cycles.
To improve the reliability, changes were made in the geometry of the Clamp Block near
the critically stressed area. These included increasing the thickness of the web from 4mm to
5mm, and adding a 3mm radius at an inside corner. These changes did not interfere with the
other components in the system, and increased the reliability to a level of 99%.
4
Introduction:
The focus of this analysis and redesign project is the clamp block component of the
clamping mechanism of a table saw fence assembly. The in use operational purpose of the fence
is to set the cutting width of the saw. It moves on two pipe rails that are perpendicular to the
fence and saw blade. The user sets the cutting width, then clamps the fence to the rails by
applying force to the hand lever. Once the user has rotated the hand lever to the locked position
the system acts as a spring, storing the applied energy. This spring energy is what maintains the normal force on the rails that is necessary to keep the fence from sliding sideways.
Figure 1: Table saw Fence Assembly
The component in this system that has failed is the clamp block. It has fractured as
shown below in Figure 2.
Figure 2: Clamp Block Assembly
5
Objectives:
The objective of this project is to analyze the mode of failure of the Clamp Block and
redesign it accordingly. Issues that will be addressed are: static loading, dynamic loading,
fatigue, and reliability. To reach this end, the previously developed solid and force models will
be the basis for finite element analysis using the Pro-Mechanica software package. The FEA will
be verified using simplified hand calculations, and the results of both techniques of stress
analysis will be used as a foundation for decisions about the redesign. FEA analysis will also be
run on the Lifter, and Dog components that are in direct contact with the Clamp Block in order to
see if they are being stressed close to the limits of their capacities.
Procedure: Design Analysis:
1. Solid model representations of critical components.
• Simplify solid models if necessary.
• Develop force model based on solid geometry and conditions of use.
2. FEA critical components
• Model loads using information developed in the solid and force models.
• Constrain components against motion in a manner that simulates the actual boundary
conditions.
• Plot graphical results of the FEA.
• Validate FEA results using simplified hand calculations.
• Determine the critical locations and magnitudes of stresses in the Clamp Block
Redesign:
• Assess significance of static versus dynamic loading as factors contributing to failure.
• Assess significance of fatigue as a factor contributing to failure.
• Assess reliability of existing part using FEA and hand calculation results.
• Determine desired reliability of the redesigned part.
• Redesign to meet desired reliability parameters.
6
Results: The results of the FEA and hand calculations agree closely, and indicate that there are
three critical locations in the area of the fracture.
Figure 3: Critical Stress Locations
The most highly stressed was point C on a horizontal web that spans between the two
sides of the clamp block. This is the result of the 773 N load causing compressive stress, σyy,
along the web. The change in section of the web at point C causes a significant stress
concentration. An examination of the broken part showed small cracks originating from corners
at point C, and extending towards the area of point B. The part was broken cleanly along the red
line indicated between points A and B.
FEA σσσσe (Mpa) Hand σσσσe (Mpa) Sy (Mpa)
Clamp Block: A
(Grey Cast Iron)
0.183 � 41.7
41.6
152
Clamp Block: B 0.183 � 41.7 31.8 152
Clamp Block: C 83.4 � 125 145 152
Lifter (HR Steel) 736-883 795 910
Dog (HR Steel) 842-947 844 910
Table 1: Stress Analysis Results
7
One explanation for the failure is that the cracks originating at point C reached the area of
point B and caused fast fracture to occur along the line A-B. Using the relationships for stress
intensity factors ki and kic, the plausibility of fast fracture as a failure mode can be assessed.
Figure 4: Stress Intensity for fast fracture
Although ki is not greater that kic,, it is close enough that fast fracture is clearly possible
given that the material properties of the casting will vary from sample to sample. This issue of
reliability will be explored in the next section of this analysis.
Fatigue due to cyclic loading was considered as a possible cause of failure, but, because
this is a hand operated system, and is used relatively infrequently, it is unlikely that the Clamp
block component experienced 106 loading cycles More likely on the order of 103 cycles.
Likewise, because the input energy is applied to the system rather slowly by a human hand
dynamic loading was also dismissed as a possible cause of failure.
The stress analysis results listed in Table (1) indicate that the Dog and Lifter are also
being stressed close to their limits. These components may also need redesign in order to achieve
an adequate level of reliability for the system as a whole, but since the analysis was primarily on
the Clamp Block, the redesign of the Lifter and the Dog were not addressed in this report.
gi ck σ⋅⋅= 8.1 and yic ck σ⋅⋅= 0.2 (Juvinall-Marshek eq. 6.1 & 6.2 pg 209)
where kI is stress intensity factor and kic is the fracture toughness of the material.
When kI ≥ kic fast fracture will occur.
Assuming a maximum crack length of 7 mm, σg = max stress on section = 125Mpa, and σy =
yield strength of grey cast iron = 152 Mpa.
23
19125007.08.1−
−=⋅⋅= mNki 23
5.25152007.02−
−=⋅⋅= mNkic
8
Reliability:
Reliability is a concept closely related with the factor of safety. In industrial production,
reliability factor plays an important role; the goal is to obtain a product with a high reliability
avoiding failure.
The clamp block of the table saw was subjected to a load of 125 MPA. The yield strength
of the ASTM 20 Grey Cast Iron is 152 MPA. This means that failure will not always occur under
these loading conditions.
The interference theory of reliability prediction was used to approximate the failure
percentage that would be expected from the original design. The clamp block was found to be
95% reliable and with a factor of safety equal to 1.22. (See Appendix F: Reliability Calculations)
Redesign:
To improve its reliability the Clamp Block was redesigned. Geometric changes were
made in the area of point C as follows: The thickness of the web was increased from 4mm to
5mm, and a 3mm radius replaced the sharp inside corner at point C. The results of an FEA on the
redesigned part, and reliability analysis showed that the stress in the critical locations was
reduced, and that the component as redesigned is 99% reliable with a factor of safety of 1.4.
(See Appendix F: Reliability Calculations)
Figure 5: Existing Clamp Block Figure 6: Redesigned Clamp Block
9
Conclusion:
The results of this analysis indicate that the most critically stressed location on the Clamp
block is in the area of points C and B. An inspection of the failed part showed small cracks
emanating from point C toward the area of point B. This observation, coupled with FEA and
hand calculations, led to the conclusion that the Clamp block cracked under load near point C,
and that these cracks caused fast fracture of the section along a line from point B to A on
subsequent loadings. (See Figure 3: Critical Stress Locations)
While the levels of stress intensity at the critical locations do not exceed the yield
strength of grey cast iron, an analysis of the reliability of the Clamp block using the interference
theory of reliability prediction showed that as originally designed and under the assumed loading
conditions, the Clamp block had a failure rate of approximately 5%. This is a relatively high rate
of failure � the component was redesigned to reduce the stress at critical locations and give a
failure rate of 1%.
The stress at point C is primarily due to direct compressive stress on the web between the
two sides of the Clamp block. At point C there is a sharp corner that causes a significant stress
concentration. This group�s recommendation for redesign is that the thickness of the web be
increased from 4mm to 5mm, and that the sharp corner at point C be replaced with a 3mm radius.
These changes in geometry should not cause any interference with the other components in the
system, and an FEA run on the modified part indicates that the stress at the critical location has
been reduced enough that the 99% reliability target has been reached. Graphical plots of the
redesigned FEA are in Appendix E.
Original Design FEA σσσσe (Mpa) Sy (Mpa) %Fail S.F Clamp Block: C 83.4 � 125 152 5% 1.22
Redesign
Clamp Block: C 75.7-113 152 1% 1.40
Table 2: Critical Stress Redesign vs. Original
I
Appendix A: Energy Analysis of Input Force
II
Work Analysis of Applied Force The force being applied to the hand lever results in forces acting on the Clamp Block,
Lifter, and Dog. In order to find these forces and develop FBD�s for the Clamp Block, Lifter, and
Dog, the tension in linking rod must be established.
Figure 3. Work Analysis
At the beginning of the hand lever rotation the entire system is at rest- there is no elastic
energy stored in the system and so the initial applied force is zero. As the hand lever is rotated
the components of the system are stretched and the required input force increases until it reaches
a maximum at the locked position. Using Data from Human Factors Design Handbook, an
applied force of F=80 N has been established as the upper range of force that an average person
can easily apply when pushing down on a lever from a standing position. Assuming the force
varies linearly from 0 N to 80 N over the displacement then Fav=40 N. Using the principle of
conservation of energy, the work applied at the hand lever equals the work done on the linking
rod. Wlever = Wrod Sf θf π/4
⌠ ⌠ ⌠ ⌡F ds = T ds = ⌡ Fav cos θ r dθ ⇒ Trod (.003m) = ⌡(-40 N) (0.100m) cos θ dθ Si θi 0 ⇒ 4 sin (π/4) = Trod (0.003m) ⇒ Trod = 943 N
45°
III
Appendix B: Force Model & Hand Calculations
Clamp Block
Lifter
Dog
IV
Clamp Block: Simplified Stress Calculations
Stress at (A): Bending stress σzz at extreme fiber.
)1530(1230)1526(12301073)1035(773 −⋅−−⋅+⋅++⋅−=AM
mmNM A −= 31975
+⋅+
−+⋅⋅= 2
32
3
1312
5.320)1519(12
385.32AI
4322816mmI A =
Kt≅2.8 (From Juvinall-Marshek Figure 4.39, pg 133)
8.232281
1531975 ⋅⋅=zzσ
Mpaezz 6.41== σσ
V
Stress at (B): Combined bending stress σzz at extreme fiber and axial compressive stress σyy from 773 N contact force.
σσσσzz:
1912303773)335(773 ⋅−⋅+−⋅=BM
mmNM B −= 3685
⋅−
⋅=12
61312
1420 33
BI
44105mmI B = C=-7mm
4105)7(3685 −⋅=zzσ
Mpazz 31.6=σ
σσσσyy:
tyy k⋅⋅
=144
773σ
5.2≈tk (From Juvinall-Marshek Figure 4.41, pg. 135)
5.2144
773 ⋅⋅
=yyσ
Mpayy 5.34=σ
σσσσe:
[ ]21
22 5.3431.65.3431.6 ⋅−+=eσ
Mpae 8.31=σ
VI
Stress at (C): Combined bending stress σzz, axial compressive stress σyy.
σσσσzz:
19123035773 ⋅−⋅=CM
mmNM C −= 3790
44105mmIC = mmc 8=
410483790 −⋅=zzσ
Mpazz 7.3−=σ
σσσσyy:
tyy k⋅⋅
=144
773σ
10≈tk (From Juvinall-Marshek Figure 4.41, pg. 135)
1064
773 ⋅⋅
=yyσ
Mpayy 147=σ
σσσσe:
[ ]21
22 1477.31477.3 ⋅−+=eσ
Mpae 145=σ
VII
Lifter: Simplified Hand Calculations
Mx=My at the element is 53 N-m
σσσσ1: IcM x
x == σσ1 433
45712)14(2
12 mmbhI === mmc 7=
2
3434457
)7(103.28mm
Nxx ==σ
σσσσ2: IcM y
y == σσ 2 433
28812)12(2
12 mmbhI === mmc 6=
2
3590288
)6(103.28mm
Nxy ==σ
yx σσ ≠ , but both are positive so there is no need to use a Mohr circle to find combined stress,
instead will use σx and σy to calculate Von Mises stress.
VIII
Simplified Hand Calculations, Lifter contd.
σσσσe: 2122 )( yxyxe σσσσσ −+=
22
122 530)]590(434590434[mm
Ne =−+=σ
This calculation of Von Mises stress does not take into account the stress concentration due to
the bore for the pin. Using the tabulated data for stress concentration factor kt, and the geometry
of the lifter kt≈2.3
36.06.166 ==b
d From Juninall/Marshek figure 4.40-a pg 134: kt≈1.5
So, the σe taking stress concentration into account is approximately:
2max 795)5.1(530mm
Nktee === σσ
Dog: Simplified Hand Calculations
IX
4
336412
)4(1212 mm
NbhI === mmc 2=
2
384464
)2(102721mm
NxI
Mc ==== σσ
( ) ( ) ( ) ( )( )[ ] 22
12221
212
22
1 844844844844844mm
Ne =−+=−+= σσσσσ
σe max = 844 N/mm2
X
Appendix C: FEA Loads and Constraints
Clamp Block
Lifter
Dog
XI
Clamp Block
Figure 10. Loads and Constraints Applied to Clamp Block
The Clamp Block has symmetry about the Y-Z plane so a half model was used as the
basis for the FEA. Using a half model requires that the cutting plane through the part be
constrained against translation along the X, and Y axes, but free to translate along the Z axis. It is
free to rotate about the X, Y, and Z-axes. The top face of the Clamp Block is bolted to the fence
extrusion, so in the FEA model it will be constrained against motion along all axes.
There are four loads on the Clamp Block. The force magnitudes from the force model
must be halved because this is a half model. The 1230-N load in the positive Z direction has been
modeled as a line load along the points of contact with the fence rail. The 773-N force couple is
modeled as line loads along points of contact with the Dog. The load at the pin is modeled as a
distributed load over the surface of the pin bore.
XII
Lifter
Figure 11. Loads and Constraints Applied to Lifter
The lifter was modeled as a solid. Although it is symmetrical about the Y-X plane, it was
deemed to be simple enough in shape that using a half model was unnecessary. The bore of the
pin is constrained against translation along the X, Y, and Z-axes, and against rotation about the
X, Y, and Z axes.
The lifter has three loads acting on it, a distributed load on the surface of the pin bore of
1550 N, and two line loads. The force in the �Y direction is a result of the contact with the dog.
They meet at a line; therefore, the force of 1230 N is distributed along this line of contact. The
last force is 943 N in the � X direction applied as a line load along the line of contact with the
linking rod.
XIII
Dog
Figure 12. Loads and Constraints Applied to Dog
The Dog is modeled as a solid, and is constrained against translation along the X, Y, and
Z-axes, and rotation about the X, Y, and Z-axes. The constraints are applied along two lines at
points of contact with the Clamp Block.
The dog has four loads acting on it, and all of them are line loads at points of contact with
the clamp block, lifter, and fence rail. There are two force couples; one 1230-N couple in the y-
direction and 773-N couple in the x-direction.
XIV
Appendix D: FEA (Existing Design)
Clamp Block
Lifter
Dog
XV
XVI
XVII
XVIII
Appendix E: FEA (Redesign)
Clamp Block
XIX
XX
Appendix F: Reliability Calculations
Existing Clamp Block
Clamp Block Redesigned
XXI
Clamp Block Reliability: Interference theory of reliability prediction
Figure 7, Reliability Calculations: Original Design Data: µ x = 152 MPA (Yield strength) σ x = 12.2 MPA (Standard deviation) µ y = 125 MPA (Load) σ y = 10 MPA (Standard deviation) The variance is 8 % of the mean. This is an assumed variance and more accurate variance can be obtained in a Material�s Manual.
Using: σ z = (σ y ² + σ y ²) ½ σ z = [(12.2)² + (10)²] ½ = 15.8 MPA Knowing: µ z = µ x - µ y µ z = 152 MPA � 125 MPA = 27 MPA Then: µ z - k σ z = 0 k = - 1.71 The Figure 6.20 from Juvinall on page 228 has a table which relate the failure of k (number of standard deviation) and % of reliability and % of failure.
For k = -1.71 95 % of reliability or 5 % failure.
XXII
µ y = 114 MPA
Factor of safety = Significant strength of the material = SF Corresponding significant stress
SF = 152 MPA = 1.22 125 MPA For the redesign the goal is to make a product, which is 99% reliable. Calculations: To achieve 99 % reliability the k factor should be equal to (-2.4). µ Y = ? σ z = 15.8 MPA µ z - k σ z = 0 µ z = (2.4) x (15.8) = 38 MPA µ z = µ x - µ y 38 MPA = 152 MPA - µ y
This is the maximum acceptable magnitude of stress for 99% reliability.
The geometric changes made during the redesign stage meet its required stress intensity. And the
component is 99% reliable. We tested our results by running a Finite Element Analysis of the
component.
Factor of safety = Significant strength of the material = SF Corresponding significant stress
SF = 152 MPA = 1.4 114 MPA
XXIII
Appendix G: Engineering Drawings
Clamp Block
Lifter
Dog
XXIV
XXV
XXVI