Stress Analysis of a Chicago Electric 4½ Angle Grinder
By
Khalid Zouhri
A Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
In Partial Fulfillment of the
Requirements for the degree of
MASTER OF MECHANICAL ENGINEERING
Approved:
_________________________________________
Dr.Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
March, 2010
(For Graduation August 2010)
1
© Copyright 2010
by
Khalid Zouhri
All Rights Reserved
2
Table of Contents
Abstract………………………………………………………….……………………………......6
1. Introduction …………………………………………………….…………….…….…….……7
2. Data ...........................................................................................................................................12
3. Force Analysis ..........................................................................................................................16
4. Stress Analysis……………………………………………………….…………….……….....22
5. Finite Element Analysis ……..........................................................................................................31
6. Conclusion………………………………………………………….….….…………………..34
References……………………………………………………………..….….…………………..34
3
List of Figures
Figure 1: Chicago Electric Angle Grinder ......................................................................................7
Figure 2: Spiral bevel gear (large) and a spiral bevel pinion gear (small)…………….……….... 8
Figure 3: Complete Component Assembly ....................................................................................8
Figure 4: Shaft with Bevel Pinion Gear..........................................................................................9
Figure 5: Shaft with Bevel Pinion Gear Removed .........................................................................9
Figure 6: Spiral bevel pinion gear .................................................................................................10
Figure 7: SolidWorks Model Assembly .......................................................................................10
Figure 8: SolidWorks Assembly Exploded...................................................................................11
Figure 9: Exploded view of components analyzed…....................................................................11
Figure 10: ME-2 Rockwell Hardness Testing System ..................................................................13
Figure 11: Pinion Close-up with Reference Lines ........................................................................15
Figure 12: Schematic Drawing .....................................................................................................16
Figure 13: Free Body Diagram of Shaft .......................................................................................16
Figure 14: Pinion- Bevel Schematic .............................................................................................17
Figure 15: Force Analysis 2-D Planes ..........................................................................................19
Figure 16: Load, Shear Force, and Bending Moment Diagrams ..................................................21
Figure 17: Restraints at Bearing D ..................................................................................................... 31
Figure 18: Restraints at Bearing C ......................................................................................................31
Figure 19: Shaft with Constraints and Loads and Study Run .............................................................32
Figure 20: Probe Value of Maximum Stress .......................................................................................32
List of Tables
Table 1: Manufacturing Specifications ......................................................................................12
Table 2: Hardness Testing Results .............................................................................................13
Table 3: Hardness Conversion Chart. ........................................................................................14
Table 4: Data of the gear and Shaft............................................................................................15
4
List of Symbols
Symbol Definition
b
Tooth width (mm) or (in)
davg
Avg. diameter of pinion (mm) or (in)
dout
Outside diameter of pinion (mm) or (in)
FS
Factor of Safety
Fa
Axial (thrust-bearing) load (N) or lbf
Fr
Radial (separating) load (N) or (lbf)
Ft
Tangential (torque-producing) load (N) or (lbf)
Kv
Velocity Factor
np
Rotating speed of pinion (rpm)
Ng
Number of teeth on ring (driven) gear
Np
Number of teeth on pinion (driver) gear
J
Geometry factor for bending strength
P
Diametral pitch: large end of tooth (mm)
T
Torque
Vav
Avg. velocity (m/s.)
Km
Load distribution factor
Ko
Overload factor
Kv
Velocity Factor
Φ
Pressure angle (°)
Φn
Pressure angle in the plane normal to the tooth (°)
ψ
Helix angle (°)
γ
Pitch cone angle (°)
5
Abstract
The Electromechanical device Chicago 4.5 inch angle grinder used in many different
applications. The device uses two gears, a bevel pinion gear and spiral pinion gear, the spiral
bevel gear is attached to the shaft and to two other bearings. The components are driven by an
electrical motor. The purpose of this project is to investigate the state of stress in the bevel pinion
gear and in the shaft using standard hand calculations and finite element analysis (FEA) with the
COSMOS software.
6
1. Introduction
The purpose of this Engineering Project is to perform stress analysis of the electromechanical device
Chicago 4.5 inch angle grinder ITEM 91223-1VGA [Fig 1]. The grinder utilizes two spiral gears, a
bevel gear and spiral bevel gear [Fig 2] with output angular velocity (ω) 11,000 rpm. The pinion gear
is directly coupled to the rotor shaft of the electric motor and supplies torque to the other bevel gear
which is closed coupled to the output shaft. The pinion gear is held onto the end of the rotor shaft by
a nut which forces the pinion against one of the two shaft bearings .The pinion gear will be the first
component to be analyzed, the second component will be the rotor shaft of the electric motor.
Figure 1: Chicago Electric Angle Grinder
7
Figure 2: Spiral bevel gear (large) and a spiral bevel pinion gear (small)
Figure 3 shows the complete component assembly of the grinder. The motor is on the left,
surrounding the rotor shaft. The gearing system is enclosed inside the gear box on the right.
Figure 3: Complete Component Assembly
8
Figure 4 shows the spiral bevel pinion gear attached to the end rotor shaft by a nut.
Figure 4: Shaft with Bevel Pinion Gear
Figure 5 shows the two bearings attached to the end of the shaft (while the pinion gear has been
removed for hardness testing – Fig 6).
Figure 5: Shaft with Bevel Pinion Gear Removed
9
Figure 6: Spiral bevel pinion gear
Figure 7 shows the Solid Works representation of the assembly (bevel pinion gear, pinion shaft,
bevel shaft, bearings, bevel gear, bevel casting, chuck washer, washer), Figure 8 shows an
exploded view and Figure 9 shows a detailed view of the two components that will be analyzed ,
the bevel pinion gear and the shaft.
Figure 7: SolidWorks Model Assembly
10
Figure 8: SolidWorks Assembly Exploded
Figure 9: Exploded view of components analyzed
11
2 Data
Table 1 shows the given manufacturing specifications of the machine.
Table 1 Manufacturing Specifications
Angular Velocity
11,000 rev/min
Voltage
110 Volts
Frequency (AC)
60 Hz single phase
Power
570 watts
Amperage
4.5 amps
For single phase armature motors one hp is generated by 720 watts. Assuming that the most
efficiency expected out of a single phase motor is approximately 60% the motor power is calculated as
hp 
570 w 3
 hp
720 w 4
For proper analysis, additional data must be collected. The material used in the angle grinder was
unknown, therefore it was necessary to perform hardness testing to obtain material data. A
Rockwell Hardness Testing Machine was used to measure the hardness of the shaft and bevel
pinion gear. The bevel gear was completely isolated from its main subassembly. This ensured no
cutting of material or extended surface hardening from clamping and pulling. The shaft was
permanently fixed to its immediate subassembly. Luckily the shaft was just long enough to get
true readings.
Figure 10 shows the hardness test machine use d in this work. Before the hardness test, proper
surface preparation was needed to ensure proper results. Three readings were done on the shaft as
well as on the bevel in different locations to obtain an average hardness number. The location of
testing on the material was also changed to get a variety of readings and to avoid tainted results from
nearby surface hardening created by testing. It is imperative to note that the material will be much
harder on the tooth of the gear rather than in the makeup material. There was no way to test the
hardness of the material directly on the tooth without risking safety for the holder. The reading,
however, was done as close as possible to the side of the tooth without risking the ball sliding
down the face of the tooth. The results are shown in table 2.
12
Figure 10: ME-2 Rockwell Hardness Testing System
Table 2: Hardness Testing Result
Using a hardness conversion chart [2] and the information from Shigley’s Mechanical
Engineering Design in Table 5 [3], material grade and tensile strength can be determined and the
result for the shaft is shown highlighted in table 3.
13
Table 3: Hardness Conversion Chart
For the gear, the following AGMA formula was use to calculate the tensile strength :
S t  77.3H b  12,800 psi
S tpiniom  77 .3 * 294  12,800 psi
S tpiniom  35 .526 kpsi
Additional geometrical data were also required for the analysis .The following calculations are
based on the presentation given in Example 13.8 from Shigley’s Mechanical Engineering Design
(8th edition).
As shown in figure 11 the outside diameter of the bevel pinion gear is d=20.0mm, therefore the
diametrical pitch is given by
Pt 
N
d

13
teeth / mm  0.65teeth / mm
20
where N =13 Teeth
14
The helical angle needed to be determined. In the illustration below, lines were added
and a protractor was used to measure it.
Figure 11: Pinion Close-up with Reference Lines
By using the reference lines the helical angle was measured to be 40 degrees.
The normal diametrical pitch is calculated with the following formula
Pn 
Pn 
Pt
cos 
0.65
teeth / mm  0.8485teeth / mm
cos 40 
and the formula below is used to calculate the Pitch diameter
dp 
N
13teeth

 15.32mm
Pn 0.8485teeth / mm
The obtained data are summarized in table 4.
Table 4: Data of the gear and shaft
15
3. Force Analysis
In this section I perform force analysis using the methods described in Example 13:10 from
Shigley’s Mechanical Engineering Design 8th edition
Figure 12 shows the schematic drawing for the shaft with the bevel pinion gear.
Figure 12: Schematic Drawing
Figure 13 show the free body diagram for all the forces that apply to the shaft and bevel pinion gear
and bevel gear. For each force we have tangential and axial and radial force
Figure 13: Free Body Diagram of System
16
Gear Force Calculation
Figure 14 show the pinion bevel schematic .When gears are used to transmit motion between
intersecting shafts, some form of bevel gear is required. A bevel gearset is shown in
Fig.14.Although bevel gears are usually made for a shaft angle of 90, they may be produced for
almost any angle. The teeth may be cast, milled, or generated. Only the generated teeth may be
classed as accurate.
The pitch of bevel gears is measured at the large end of the tooth, and both the circular pitch and
the pitch diameter are calculated in the same manner as for spur gears. It should be noted that the
clearance is uniform. The pitch angles are defined by the pitch cones meeting at the apex, as
shown in the figure. They are related to the tooth numbers as follows:
tan y = N/Ng
tan T = Ng/N
Where the subscripts P and G refer to the pinion and gear, respectively, and where y and T are,
respectively, the pitch angles of the pinion and gear.
Figure 14 also shows that the shape of the teeth, when projected on the back cone, is the same
as in a spur gear having a radius equal to the back-cone distance “rb”. This is called Tredgold's
approximation. The number of teeth in this imaginary gear is
N' = 2 rb/p
Where N' is the virtual number of teeth and p is the circular pitch measured at the large end of
the teeth. Standard straight-tooth bevel gears are cut by using a 20 pressure angle, unequal
addenda and dedenda, and full-depth teeth. This increases the contact ratio, avoids undercut, and
increases the strength of the pinion.
Figure 14: Pinion- Bevel Schematic
17
To get the angle T we have to use formula below to get the “y” angle and from there we get “T “.
  tan 1 (
PinionTeet h
)  22.1
Bevelteeth
  90  22.1  67.9
We use the formula below to get the distance t2 from the end of the bevel pinion gear to the pitch
point.Same way to get the ‘y ‘axis distance from the end of the bevel pinion gear to the pitch
point.
t 3  3.25mm  sin( 22.1 )  1.222mm
t 2  3.25mm  cos(22.1 )  3.011mm
These thicknesses represent the location of the pitch point and are illustrated above in Figure 14.
The distance from bearing D to the horizontal pitch point location P is:
 9.5 mm is from outside of bevel pinion to far side of bearing
 Bearing is 7 mm wide so half of bearing is 3.50 mm
DP( x)  19.5  (3.011mm  3.50mm)  13mm
The distance from bearing D to the horizontal pitch point location P is:
DP( y ) 
20 mm
 1.222 mm  8.78mm
2
d p  8.78mm  2  17.56mm( pitchdiameter)
We use the formula below to calculate the axial and Tangential and radial force that apply from the bevel
gear into the bevel pinion gear.
t
WBP
60,000  hp

 *d *n
r
t
WBP
 WBP
 tan()  cos( )
r
WBP
 74.2N  tan 20  cos22.1  25.02N
t
WBP
3
60,000  hp
4

 74 .2 N
 *17 .56 mm *11,000 rpm
a
t
WBP
 WBP
 tan()  sin( )
a
WBP
 74.2N  tan 20  sin 22.1  10.16N
18

W  10 .16 i  25 .02 j  74 .2k N
W  ABS(W )  78.96N
Shaft Force Calculations:
Figure 15 shows the free body diagram for the shaft, with all the forces applied by the bearings and
the bevel gear.
Taking the moment around D:
Figure 15: Force Analysais 2-D Planes
(x-y) plane:
So we take the moment at the point D to get the one equation with one unknown, and from there we solve
for the force Fcy
 M D   Fcy  136 .5mm  10.16 N  8.78mm  25.02 N .13mm  0
Fcy  1.73N (change  direction )  1.73N 
The total force in X direction equal to zero (static condition), to calculate the force FDx

 Fx  W a  FDX
0
FDx  10.16N 
19
The total force in y direction is equal to zero (static condition), to calculate the force FDy .

 Fy  W r  FDy  Fcy  0
.
FDy  26.75N 
(x-z) Plane:
Now we take the moment at the point D to get one equation with one unknown and from there we solve
for the force Fcz

Fcz  7.07N (change  direction )  7.07N 
M D  W t  13 mm  Fcz .136 .5mm  0
The total force in the z direction equal to zero (static condition), so the force FDz is then

 Fz  W t  FDZ  FCZ  0
FDZ  81.27N 
FC  ABS ( FC )  7.28 N

 1.73 j  7.07 K N 
F
c
F D  {10 .16i  26 .75 j  81 .3K}N
FD  ABS ( FD )  86 .2 N
Figure 16 shows the calculated and shear force and bending moment diagram.
20
Figure 16 : Load, Shear Force, and Bending Moment Diagrams
21
4. Stress Analysis
Bending Stress and Bending Factor of Safety
We use the formula below to calculate the Dynamic Factor (Kv).
Kv  (
A  200 .V B
)
A
The dynamic factor Kv accounts for internally generated gear tooth loads which are induced by
non-uniform meshing action (transmission error) of gear teeth. A quality number value of 6 is
assumed. The transmission accuracy level number (Qv) could be taken as the quality number Qv = 6.
The American gear manufacturing association has defined a set of quality control numbers which can
be taken as equal to the transmission accuracy level number Qv, to quantify these parameters
(AGMA 390.01). Classes 3< Qv<7 include must commercial quality gears and are generally suitable
for any applications.
Kv  (
A  200 .V B
)
A
A  50  56(1  B)  ifB  0.25(12  Qv )
B  0.25 * (12  6)
2
3
V
m
sec
 *d p *np
60
 *17.56 mm *11,000 rev / min
Kv  (
3
A  50  56(1  0.8254)  59.77
 0.8254
We use the formula below to calculate the velocity in
V
2
60
 10,113 .8 mm sec  10.114 m sec
59 .77  200 10 .114 m / sec .8254
)
 1.59
59 .77
22
The overload Factor (Ko), assuming uniform loading is Ko = 1.
The Size Factor Ks is calculated using table 14-2 [5] in Shigley’s Mechanical Engineering Design. 8th
Ed. (s, Yp (13T)and value is 0.261 .
The width 6.5 mm →6.5 mm/25.4 mm/in= 0.2559 in hence
P = 0.8485 Teeth/mm = 21.552 Teeth/inch
Ks 
1
F Y 0.0535
 1.192  (
)
kb
P
This is for standard units
Ks 
1
F Y 0.0535
0.2559 in * 0.261 0.0535
 1.192  (
)
 1.192 * (
)
 0.907
kb
P
21.552 T / in
K H  Cmf  1  Cmc * (C pf *C pm  Cma*Ce )
Assuming uncrowned so (load correction factor) Cmc=1
F  10.00
C pf 
In (Pinion Proportion factor) Cpf;
F
6.5mm
 0.025 
 0.025  0.0120
10 * d
10 *17.56 mm
Cpm (pinion proportion modifier) =1.0
Cma(Mesh alignment factor)
Cma  A  BF  CF 2
Using the table 14.9 [6], Value for A, B, C are as follows:
A=0.127
B=0.0158
C  .930 10 4
Cma  0.127  0.0158 0.2559  .930104 *.25592  .1310
Ce(Mesh alignment correction factor )1
23
K H  Cmf  1  1* (0.0120*1  0.1310*1)  1.143
The rim thickness factor Kb=1 due to consistent thickness of gear.
Speed Ration mG;
mG 
N G 32T

 2.46
13T
NP
Load Cycle factor (Yn) using 13T for pinion and life cycle 10
YN ( P)  1.3558* N p 0.0178  1.3558* (108 ) 0.0178  0.977
From Table 14-10 [7] and a reliability of 0.90, KR (YZ) = 0.85;
From Figure 14-6 [8], The YJ(P) = 0.21
KT (Temperature Factor) Temperature is less than 250 °F so K T = 1
St (Allowable Bending Stress for Hardened Steels) for 294 Brinell.
Grade 1:
St  (0.533 H B  88.3)MPa  (0.533 * 294 * 88.3)  245 MPa
Sc (Contact fatigue strength) for Brinell and grade 1.
S c  (2.22 H B  200 )Mpa  (2.22 * 2.94  200 )  852 .7Mpa
The pinion tooth bending stress is
 p  W t K0 Kv ks *
P KH KB
*
F
Yj
 p  16.7ibf *1*1.59 * .907 *
21.552 T / in 1.143 *1
*
 11040 psi  76.1Mpa
0.2559 in
.21
We use the formula below to calculate the bending fatigue factor of safety for the pinion
24

S t * YN
S F ( P)  
  p  KT  K R

 245 MPA * .977 
  3.7
S F ( P )  
76
.
1
Mpa
*
1
*
.
85






 p  76.1MPa
S F ( P)  3.7
Wear Stress and Bending Factor of Safety
Surface Condition Factor Cf=Zr=1(No surface defects specified)
We use the formula below to show the stress and bending factor of safety Z
2 2
Z  [(rp  a) 2  r 2 bp ] 2  [(rG  a) 2  rbg
]  (rp  rg ) sin t
1
1
Where;
rp  8.78mm
rG  18 .74 mm
rbG,bp  r cost , rbg  16.93mm
a
rbP  7.93mm
1
1

 1.17855
pn 0.8485
t  tan
1
tan  n tan 20 

 25 .41

cos
cos 40
Z  4.71mm
n  20
pn  pn cos  n 
mN 

pn
cosn 

0.8485 mm
pN
3.479 mm

 .778
0.95 Z .95 * 4.71mm
I  Z1 
mG
cos 20  sin 20 
*
2 * mN
mG  1
25
cos 20   3.479 mm
I  Z1 
cos * sin 
2.46
*
 0.147
2 * 0.778
2.46  1
From the table 14-8 [9] from Shigley’s we calculate the value of Ze (Elastic coefficients factor);
C p  Z E  191 MPa  2300 psi
We use the formula Stress cycle factors for pinion;
 0.023  1.4488* (108 ) 0.023  .948
Z N ( P)  1.4488* N p
Finally we use the formula below to calculate the contact stress:
 c  C p W t K0 Kv K s
Cf
KH
*
d ( p) * F
I
  2300 psi 16 .7ibf *1*1.59 * .907 *
1.1385
1
*
 74 .7ksi  515 MPa
.69134 in * .2559 .147
and use the formula below to calculate the wear Factor of safety:
[
S H ( P) 
sC * z N
]
KT * K R
C
852 .7 MAP * .948
]
1
*
.
85

 1.85
515 MPa
[
  515 MPa
S H ( P)  1.85
Stress Analysis of Output Shaft using the vector cross product
We use the formula below to get the absolute value for W
W  {10 .16i  25 .02 j  74 .2k}N
W  ABS (W )  78 .96 N
26
RDP  {13i  8.78 j}mm
RDC  {136 .5i}mm
From both equations above we use the values to calculate the torque T
t
T  8.78 mm *WBp
 8.78 mm * 74 .2 N  651 N .mm
T  651 .5iN.mm
Taking the moment around D to calculate the force FZC :
 M D  RDP *W  RDC * FC  T  0
 M D  {13i  8.78 j}mm *{10.16i  25.02 j  74.2k}N  {136 .4i}mm *{Fyc j  Fzc k}N  {Ti}  0
FZC 
964 .6 N .mm
 7.07 KN
136 .5mm
FYC 
236 .1N .mm
 1.73 j..N
 136 .5mm
F C  {1.73 j  7.07 k}N
Fc  ABS ( FC )  7.28 N
To get Fd, we use the equation below (sum the forces equal to zero, static condition).
Fd  FC  W  0
Since the sum of the force equal to zero (static condition)
27
 F  {Fxd i  FyD  FZD }lbf  {0i  1.73 j  7.07}N  {10.16i  25.02 j  74.2}N  0
Fxd  10.16i.N
Fyd  26 .75 . j.N
Fzd  81.3K.N
F  {10 .16i  26.75 j  81 .3k}N
The absolute value for Fd is calculated below.
FD  ABS ( F D )  86 .2 N
The safety factor of the shaft.
We use the formula below to calculate the moment on the shaft at point D of the bearing.
M max  (965 N .mm) 2  (236 .2 N .mm) 2  993 .5N .mm
M max  993 .5N .mm
Tmax  651 .5N .mm
D / d  10.10 mm / 8mm  1.26
Assume r=2.54 mm (0.1in)
r / d  2.54 mm / 8mm  .3175
K t  1.4[12]
K ts  1.2[13]
Notch sensitivity (q) =0.95[14]
Shear notch sensitivity (qshear)=1 [15]
K f  1  q( Kt  1)  1  0.95(1.4  1)  1.38
28
K fs  1  q s ( K ts  1)  1  1(1.2  1)  1.2
 a"  K f
32 .M max
 .d
 1.38
3
16 .Tmax
 m"  3.[ K fs
 m"  3.[1.2
 .d
3
32 * 993 .5 N .mm
 .(8mm ) 3
 27 .28 MPa
]2
16 . * 651 .5 N .mm
 .(8mm )
3
]2  13 .47 MPa
Assume Sy=0.775Sut
Sut=106Ksi = 730.8MPa
So the safety factor of the shaft is calculated using the formula below.
n yield 
Sy
n yield 
 m'   a'
0.775 * 730 .8MPa
 13.9
13.47 MPa  27.28 MPa
Fatigue Factor of Safety Calculations
Analysis based on Modified Goodman Design Theory
Se'  0.5 * Sut
Se'  0.5 * 730.8MPa  365.4MPa
Using the table 6-2[5] from Shigley’s and assuming a surface finishes of mechanized or cold
drawn:
a=4.51
b=-0.265
Surface Factor Ka;
K a  a * Sut b  4.51 * 730 .8MPa 0.265  0.786
29
Combined Loading so Kc=1
Room Temperature operation so kd=1
From table 6-5[4] from Shigley’s and also assuming 90% reliability ke=0.897
Se  K a Kb K c K d K e Se'  .786 *.993*1*1*.897 * 365.4MPa  255.82MPa
1
n fatigue

n fatigue 
 a'
Se

 m'
S ut
 n fatigue 
S e * S ut
S ut *  a'  S e . ' m
255 .82 MPa * 730 .8MPa
8
730 .8Mpa * 27 .28 MPa  255 .82 MPa  13 .47 MPa
Comparing N yield and N fatigue
n yield  13.9  n fatigue  8
This shows that the shaft will fail by fatigue.
30
5. Finite Element Analysis
Figures 17 and 18 show the load and restraint setup on Cosmos software. The green arrows in
the pictures represented the mechanical constrain impose by bearings D and C on the shaft.
At bearing D, radial and axial restraints were set. Restraints were applied to a 2 mm cylindrical face
placed at the midpoint of the bearing location. The bearing restraint at C was set for only a rotational
restraint. This was to ensure that over-constraining the shaft was avoided. This restraint was also
applied to a 2 mm cylindrical face placed at the midpoint of the bearing location.
Figure 17: Restraints at Bearing D
Figure 23: Restraints at Bearing C
Figure 18: Loads at Pitch Point Applied Using Remote Load
31
Figure 19 shows the shaft with constraints and loads and the computed values of the von Mises stress
are also shown. The maximum stress (=28.12 MPa ) appears on the bearing area.An expanded view
of the most highly stressed area is shown in figure 20.
Figure 19: Shaft with Constraints and Loads and Study Run
'
m
ax
Figure 20: Probe Value of Maximum Stress
32
'
Using Von Misses to get an analytical value for  max
'
 max
  m2   m *  a   a2  3. m2
'
 max
 (1.38 *
32 * 965 N .mm 2
16 * 236 .2 N .mm 2
)  3.(1.2
)  26 .9MPa
 * (8mm )
 .(8mm ) 3
% Difference :
x1  x2
*100
x1  x2
2
26 .9MPa  28 .12 MPa
% Difference 
*100  4.43 %diffrence
26 .9MPa  28 .12 MPa
2
% Difference 
Using COSMOS, the maximum value found was 28.12 MPa. There is a difference of 4.43 % from a
calculated value of 26.9MPa. This could be attributed to model building techniques in SolidWorks.
There could also be variations in part measurements which could skew calculations slightly. Changes
in restraint locations and “bearing” restraints types may bring different results. Better understanding
and practice of COSMOS could also produce improved results. Overall the stress analysis attributed
by COSMOS is an excellent representation of the type of stress the part may succumb to.
33
6. Conclusion
The project exemplified real world tasks that definitely sharpened my skills a young engineer. The
hands-on experience gained by using the laboratory equipment and software tools was invaluable.
The experience of using specific tools, acquiring data, and using this data in calculations was a
particularly useful experience. It provided some relevance of the knowledge learned from work
experience and my other engineering courses.
Also COSMOS in particular was beneficial not only because I was able to use it as a comparison tool
but also because of the practical experience gained which will be useful in the a ‘real-world’
application. This tool gives a visual representation of the types of stresses and possible deformations
that may occur in design. This quick reference will give the design engineer an approximation of
what to expect under certain loads or applications. This brief exposure to COSMOS will certainly be
invaluable.
Reference
[1] Manufacturing Specifications link,
http://www.harborfreight.com/cpi/ctaf/displayitem.taf?Itemnumber=43471
p/english/gear/myset/spiral.html
[2] Hardness conversion chart,
http://www.carbidedepot.com/formulas-hardness.htm
[3] AGMA Strength Graph for Hardened Steels,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. pp 727
[4] Reliability Assumption,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Table 6-5, pp 285
[5] Parameters for Marin Surface Modification Factors,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Table 6-2, pp 280
[6] Lewis Form Factor,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Table 14-2, pp 718
[7] Empirical Constants for Load Distribution Factor
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
34
York NY, 2008. Table 14-9, pp 740
[8] Reliability Factor KR
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Table 14-10, pp 744
[9] Geometry Factor,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Figure 14-6, pp 727
[10] For Elastic Coefficient,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Table 14-8, pp 737
[12] For Stress Concentration Value Kt,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Appendix Figure 15-6, pp 1007
[13] For Stress Concentration Value Kts.
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Appendix Figure 15-8, pp 1008 32
[14] Notch Sensitivity q,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Figure 6-20, pp 287
[15] Shear Notch Sensitivity q,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Figure 6-21, pp 288
[16] pitch diameter p,
Budynas, R., Nisbett, K., Shigley’s Mechanical Engineering Design. 8th Ed. McGraw Hill, New
York NY, 2008. Example 13:15, pp 245
35