Ijmet 06 10_013

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 6, Issue 10, Oct 2015, pp. 115-123, Article ID: IJMET_06_10_013
Available online at
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=10
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
REDUCTION OF STRESS
CONCENTRATION BETWEEN PLATE CAM
AND ROLLER FOLLOWER BY ROUNDING
THE EDGES
Aniket Raje
SIES Graduate School of Technology, Mumbai University, India
ABSTRACT
This paper focuses on reduction of the stress concentration between a cam
and follower by rounding the edges. A cam and its follower are designed for
carrying out a simple harmonic motion. A CAD model of the flat edged cam is
made with dimensions obtained from design calculations, followed by finite
element analysis. Similarly, another CAD model of similar cam with rounded
edges is made with the same dimensions, followed by finite element analysis. It
can be found that the equivalent stress concentration is less at the rounded
edges of the second model than the flat edges of the first model.
Key words: Cam, Cam and Follower, Stress concentration.
Cite this Article: Aniket Raje, Reduction of Stress Concentration Between
Plate Cam and Roller Follower by Rounding The Edges, International Journal
of Mechanical Engineering and Technology, 6(10), 2015, pp. 115-123.
http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=6&IType=10
1. INTRODUCTION
Cam and follower are commonly used machine components and a plate cam with a
roller follower is most commonly used. Cam is a rotating piece which contacts with a
follower to cause linear motion in the follower. It is often mounted on a shaft which is
rotated by other machine components. The cam profile is designed according to
requirement of linear motion of the cam follower. There are two types of cams, viz.
Axial (cylindrical) cams and Radial (plate) cams. Motions are generally classified as
Uniform acceleration & retardation, Uniform motion, Simple harmonic motion and
Cycloidal motion. Different combinations of these motions can be used in a single
cam.
Stress concentration can be reduced in many ways, such as rounding corners,
providing holes near cavities, etc. [1]
In this paper, a cam with roller follower is designed. This cam provides simple
harmonic motion to the follower. By using the dimensions calculated, a two CAD
models are designed, one with flat rolling surface on cam and flat roller follower,

Reduction of Stress Concentration Between Plate Cam and Roller Follower by Rounding The
Edges
while other with curved edges of the cam and roller follower. Finite element analysis
is done to find the stress concentration between the cam and roller. It is then found
that the stress concentration is reduced when the edges are rounded.
2. DESIGN OF CAM AND FOLLOWER
For this study, we will consider a rotary cam with central translatory roller follower. It
contains the following motions
 Forward stroke of 20mm in 100o
of cam rotation with simple harmonic motion.
 Dwell for 40o
of cam rotation.
 Return stroke of 120o
of cam rotation with simple harmonic motion.
 Dwell for 100o
of cam rotation.
Mass of the follower (m) = 1 kilogram.
Cam shaft speed = 500rpm
External force during forward stroke = 500N.
External force during return stroke = 200N.
2.1. Motion analysis of the follower
2.1.1. Displacement analysis
For simple harmonic motion for forward and return stroke, displacement at an angle
is given by
[2]
Where, h = stroke length
= angle turned in the stroke
2.1.2. Velocity Analysis
For simple harmonic motion for forward and return stroke, velocity at an angle is
given by
… [2]
Figure 1 Displacement, velocity and acceleration graphs of the motion

Aniket Raje
From Figure 1 it is observed that at points 1, 3, 4, 6, velocity is zero.
For forward stroke,
At , v = vmaximum
vmaximum = 0.94248 m/s
For return stroke,
At , v = vmaximum
vmaximum = 0.78892 m/s
2.1.3. Acceleration analysis
For simple harmonic motion for forward and return stroke, acceleration at an angle
is given by
… [2]
From Figure 1 it is observed that at points 3 and 5 acceleration is zero.
For forward stroke,
At point 1, , a = amaximum
amaximum = 88.826m/s2
amaximum = -88.826m/s2
For return stroke,
amaximum = 61.6853m/s2
amaximum = -61.6853m/s2
2.2. Calculation of Rp, rp, ,
For forward stroke,
tan = …[2]
=
…[2]
= 0.01m
Let the maximum pressure angle be 25o
tan 25o
= …[2]

Edges
Selecting Rp with the higher value to avoid interference and undercutting of cam
Roller radius = Rr = Rp /5 = 5.8mm
d = 11.6mm
Base circle radius,
rp = Rp – Rr = 23.2mm
For Simple harmonic motion,
tan
Pitch point angle = 41.93o
= 7.4913m
Pitch circle radius = Rp + …[2]
= 36.49mm
= 29.496mm
Radius of Cam profile
= - Rr
2.3. Force analysis
Resultant force acting on cam is given by
FR = mg + m + Fexternal … [3]
Therefore, resultant forces at points 1, 2, 3, 4, 5, 6 are,
Table 1 Force table
Points Force (N)
1 598.64
2 509.81
3 420.98
4 48.12
5 109.81
6 171.49

Aniket Raje
From Table (1)
At point 1,
Fmaximum = 598.64 N
Also, at point 4,
Fminimum = 48.12 N
As minimum force Fminimum 30 N, Spring is not required. … [2]
Now,
Normal force acting on cam surface is given by,
Pn = … [3]
= 660.52 N
Width of the cam can be determined by the following relation
… [2]
Consider roller material as hardened steel and cam material as C20
… [2]
For Steel E1 = E2 = 2.1e05 N/mm2
b = 20.778 mm
Rounding off to next even value.
b 22 mm
3. ANALYSIS
3.1. CAD model
A CAD model was constructed in Solidworks 2015[4] with the dimensions obtained
from the above calculations.
Considering the point of contact to be one with maximum resultant force, i.e.
point 1. (From Figure 1)
3.1.1. Cam and follower without rounded edges
Figure 2 Cam and follower without rounded edges

Edges
3.1.2. Cam and follower with rounded edges
Fillet of radius 2.5mm was provided to the cam and roller edge.
Figure 3 Cam and follower with rounded edges
3.2. Meshing
Meshing was carried out in Ansys Workbench [5]
Statistics
Nodes 111128
Elements 27612
Figure 4 Meshing of Cam and follower without rounded edges
Statistics
Nodes 139634
Elements 33853

Aniket Raje
Figure 5 Meshing of Cam and follower without rounded edges
3.3. Boundary Conditions
A load of 598.64 N is applied on the follower as it is the maximum force at point
1(From figure 1).
3.4. Results
Equivalent (Von misses) stress between cam and roller
Figure 6 Stress distribution between Cam and follower without rounded edges
The maximum equivalent (Von misses) stress is found to be 4.1684e8 Pa in the
cam and follower without rounded edges

Edges
Figure 7 Stress distributions between Cam and follower with rounded edges
The maximum equivalent (Von misses) stress is found to be 1.8839e8 Pa in the
cam and follower with rounded edges
Therefore, it is found that stress is reduced between cam and roller when the edges
are rounded.
4. CONCLUSION
The results clearly show that rounding off the edges of the cam and roller of the
follower reduces the stress between them. This method may not be the only method of
reducing stress concentration between cam and roller follower. Future work can be
carried out on other ways to reduce stress concentration between them. Full
optimization is beyond the scope of this paper.

Aniket Raje
5. GLOSSARY
The terms and abbreviations used in the calculations are as follows,
Term Meaning Unit
h Length of Stroke m
m Mass of follower kg
N Number of revolutions RPM
Angle of turn Degrees
y Distance travelled m
Angle of stroke Degrees
v Velocity of stroke m/s
Angular velocity Rad/s
a Acceleration of stroke m/s2
Pressure angle Degrees
Rp Prime circle radius m
Rr Roller radius m
Pitch Point angle Degrees
Pitch point follower displacement m
Ra Pitch circle radius m
Radius m
FR Resultant force N
g Acceleration due to m/s2
PN Normal force acting on cam surface N
E Young’s modulus N/mm2
b Width of cam m
REFERENCES
[1] V.B. Bhandari, Machine Design, (McGraw Hill Education, India, 2013)
[2] PSG College of Technology, Design Data Book, (Kalaikathir Achchagam, India:
Coimbatore, 2014)
[3] R S Khurmi, J K Gupta, Theory of Machines, (S Chand, India, 2014)
[4] Luxology, LLC, Solidworks 2015
[5] SAS IP, Inc, ANSYS® Workbench™ 15.0.7
[6] Raghavendra Nilugal and Dr. M. S. Hebbal, A Closed-Form Solution For Stress
Concentration Around A Circular Hole In A Linearly Varying Stress Field,
International Journal of Mechanical Engineering and Technology, 4(5), 2013,
pp. 37 – 48.
[7] Aniket Raje, Bikramjeet Singh, Ronak Churai and Pranav Borwankar, A Review
of Tesla Turbine, International Journal of Mechanical Engineering and
Technology, 6(10), 2015, pp. 28 - 31.

Ijmet 06 10_013

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