Mr.V.H.Waghmare et al. Int. Journal of Engineering Research and Applications www.ijera.
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Vol. 3, Issue 5, Sep-Oct 2013, pp.288-290
RESEARCH ARTICLE OPEN ACCESS
Stress Analysis Of Rocker Arm Of Internal Combustion Engine
Mr.V.H.Waghmare1, Prof. Y.L. Yenarkar 2
1 Student, IV Semester M.Tech (CAD/CAM) Mechanical Engineering Department, Rajiv Gandhi College of
Engg. Research & Technology, Chandrapur-442 401 (Maharashtra) (India)
2
Associate Professor, Mechanical Engineering Department, Rajiv Gandhi College of Engg. Research &
Technology,Chandrapur-442 401 (Maharashtra) (India)
ABSTRACT
The effect of total force i.e. gas pressure, inertia force and initial spring force acting on the existing rocker arm
is evaluated. It is found that the maximum stress is occurred at the push rod side end. For optimization the
various models of rocker arm are developed, keeping its weight constant. The effect of total force on this
various models are evaluated. The model showing less stress is found suitable as compared to other models.
Geometric models are developed in software Pro-E and for analysis software ANSYS 11 is used.
Keywords: Gas pressure, Inertia force, Initial spring force, Analysis.
I. INTRODUCTION (iii) The initial spring force (Pi) to hold the valve on
A rocker arm is a reciprocating lever used in its seat against suction or negative pressure inside the
an internal combustion engine to actuate the inlet and cylinder during the suction stroke.
exhaust valves motion as directed by the cam and Calculation for gas pressure, Pg
follower. The rocker arm of the exhaust valve is the The gas load Pg is given by,
most heavily loaded. On the other hand the force Pg = area of valve × gas pressure when the exhaust
required to operate the inlet valve is comparatively valve opens
less. However, it is usual practice to make rocker πd 2
Pg = ( 4v )Pc
arms for inlet and exhaust valves identical. This
result in ease of manufacturing. The main objective Where,
of the rocker arm as a „lever‟ is to change the dv = diameter of valve head (mm)
direction of force and not the multiplication of the Pc = cylinder pressure or back pressure when the
effort. exhaust valve opens (MPa)
While operating, the internal combustion Cylinder pressure, Pc calculation
Horse Power(H. P. )
engine valve produces the various forces which are Indicated Power(I. P. ) =
acting on the rocker arm. For absorbing this forces, Mechanical Efficiency
the rocker arm model must be properly designed. Mechanical Efficiency = 80% from engine
There is always possibility of optimizing the specification
215
designed rocker model by means of stress analysis, so I. P. = H.P. = 215 (maximum horse power
0.8
that stresses induced in the rocker should be assumed)
minimized. I.P. = 268.75 H.P.
I.P. = 200487.5 watt.
NOTATION MEP × L × A × N
ω Angular Velocity I. P. = × No. of cylinders
60
E Modulus of Elasticity Where,
σ bending stress MEP = Mean Effective Pressure
Pc Cylinder pressure L = stroke = 4.02 inch = 0.12 m (assumed)
Pg Force equivalent to gas pressure π𝐷 2
Pa Inertia force A = area = 4𝑏 (Db = bore diameter is 0.102m
Pi Spring force assumed)
N = 2500 rpm
II. NUMERICAL RESULTS No. of cylinder = 6
The various forces acting on the rocker arm π 0.102 2 2500
MEP × 0.12 × 4 × 2
of exhaust valve are ;- IP = ×6
(i) The gas pressure (Pg) on the valve when it opens. 60
(ii) The inertia force (Pa) when the valve moves up.
𝑀𝐸𝑃 × 0.12 × 0.0081 × 1250
200487.5 = ×6
60
200487.5 = 0.122 × MEP
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Mr.V.H.Waghmare et al. Int. Journal of Engineering Research and Applications www.ijera.com
Vol. 3, Issue 5, Sep-Oct 2013, pp.288-290
Cylinder pressure, Pc = MEP = 1636537.8 N/m2 Unloaded valve spring length = 53.6mm
Cylinder pressure, Pc = 1.64 N/mm2 Valve spring length installed condition (valve fully
Gas pressure, closed) = 42.5 mm
π × dv 2 Axial spring force at the axial deflection of the spring
𝑃𝑔 = × 𝑃𝑐 (53.6 - 42.5 = 11.1 mm) = 22.6 kg
4
π ×36 2 = 22.6 × 9.8
𝑃𝑔 = 4
× 1.64 (valve dia., dv = 36 mm = 221.48 N
assumed) So initial spring force Pi = 221.48 N
Gas pressure, Pg = 1669.32 N Total Force on the Rocker Arm :-
Calculation for Inertia force, Pa Total force (Pe) on the rocker arm of the exhaust
As the valve moves down, the inertia force acts valve is given by,
opposite to the direction of motion. The upward Pe = Pg +Pa + Pi
inertia force Pa is given by, = 1669.32 + 72.796 + 221.48
Pa = mα Pe = 1963.593 N
Where, m = mass of valve (kg) By taking the moment the force on the push
α = acceleration of valve (m/s2) rod end is calculated i.e. of 3057.45N
m = 0.121 kg ( asumed) Above calculated force of 1963.593N is applied to
Calculation for acceleration, α the valve end and the force of 3057.456N is applied
Engine speed is 2500rpm, this gives a cam shaft to pushrod end. From the ANSYS result obtained it is
rotation of 1250 rpm (in a four stroke engine the cam found that expected maximum stresses near the
turns at half the cam shaft speed ). So the time taken bearing bore as shown in fig.1 where the moments
for one revolution of the cam shaft is 0.048 seconds. are highest. Though the moments on either side of the
Total crankshaft angle when the valve is open, boring bore are same, the bending stresses on the
58+180+50 = 2880 (assumed) push rod side are higher because of the curvatures
Total angle of cam action for four stroke engine, and stress concentration. The deflections and stresses
Angle of camshaft = ½ × angle of camshaft. are in close agreement with the theoretical
Angle of camshaft = ½ × 2880 = 1440 calculation.
Cam is open and close the valve for 1440 of its Since the bending stresses and equivalent
rotation. Hence the complete valve cycle is 2/5 of stresses obtained by ANSYS are much lesser than the
camshaft rotation or 0.019 seconds. permissible stress values. There is a scope for certain
The equation describing simple harmonic motion optimization in shape which would equally
is, distributed stresses as against the current results
x = a × cos(𝜔𝑡) which show stress concentration in a particular zone.
Where, x=displacement Hence it was decided to optimize the shape without
a = amplitude altering the mass. Following section described the
t = time alternate model of rocker arm.
𝜔 = angular velocity in radian per second
= 2 × π = 2 × 3.142 (time taken for one cycle) 2.1 ALTERATION OF ROCKER ARM
So the 𝜔 value here is, For decreasing the stresses, the model of
2×3.142 rocker arm is modified. The sharp edges of outer
= 330.737 rad/sec.
0.019 circle is removed by increasing the radius of edge.
Differentiating the equation for expression for Also the material in the outer side of the push rod
displacement gives , circle is increased. While doing this emphasis been
v = - 𝜔 × amplitude × sin(𝜔𝑡), where v = velocity given to the fact that the weight of the rocker arm
Then differentiating again, should not been increased.
a = - 𝜔2 × a cos(𝜔𝑡) Changes in the existing model is given
The maximum acceleration occurs when the term below:
cos(𝜔𝑡) has the maximum value of 1, this occurs at Models-I: In this model the edge of the rib is
the extreme of the motion. changed from radius of 0.2mm to 0.4mm.to remove
Cam has the lift of 11 mm. (measured value of the the sharp contour
cam shaft of 5.9 liter Cummins B-series engine) Modal-II: In this model the outer radius of push rod
The amplitude of the motion is 5.5mm = 0.0055m. end outer circle is taken as 0.5mm. while the radius
So the maximum acceleration is given by, of the outer surface with the rib is taken as 4.5 mm.
acceleration max , = (330.737)2 × (0.0055) = 601.63 Model-III: In this model the outer edge of push rod
m/s2 end outer surface is taken as 1mm. while the outer
Inertia force, Pa = m surface radius with the rib is taken to be 4.5 mm.
= 0.121 × 601.23 Model-IV : In this model the outer edge radius of
= 72.596 N push rod end outer circle is taken as 1.5 mm. while
Calculation for initial spring force, Pi the radius of outer surface to the rib is taken to be 5
Following is the valve spring data assumed:- mm. All the alternate models were further analyzed.
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Mr.V.H.Waghmare et al. Int. Journal of Engineering Research and Applications www.ijera.com
Vol. 3, Issue 5, Sep-Oct 2013, pp.288-290
The result obtained are discussed in following
chapter.
III. RESULTS IN ANSYS
“Fig. 1” shows the stress distribution of rocker arm in
which the maximum stress of 560Mpa is observed
near the push rod end. Fig. 5: Model-IV stress result.
IV. CONCLUSION
The particular section near the top face of
bearing bore towards push rod side in the current
rocker arm shows high stress concentration zone. In
respect of current design of rocker arm it may be
Fig. 1: The equivalent stress distribution of rocker. concluded that the stresses in the rocker arm are not
uniformly distributed and there is a scope for
“Fig. 2” shows the ANSYS result of Model-I, in modifying the contour on the said face so as to
which the maximum equivalent stress of existing reduce the stress concentration.
The curvature in the original design push
rocker arm value is reduced to 380Mpa.
rod hole with the main body of rocker arm is too
sharp its radius was varied from 0.5mm to 1.5mm for
a four different values at the same time the region
beneath this curve is filled with material to strengthen
the region. This resulted in strengthening as analysis
showed significant decrease in equivalent stresses in
subsequent alternate models. The best result were
obtained for Model-IV having the maximum stress of
Fig. 2: Model-I stress result. 302MPa and the wt. of body is 5.3262×10- 002kg is
Model-II result shows that there is further reduction find suitable as compared to previous three models.
in maximum equivalent stress of Model-I value of Further it may also be concluded that though
380MPa to 325Mpa. The stress analysis result of the current rocker arm is in having the maximum
Model-II is shown in the “Fig. 3” equivalent stress much less than the ultimate values
and the rocker arm is serving satisfactorily, there is
scope for modification in respect of shape The
modification proposed are a few and there could be
number of ways, the variation could be made.
However it does not mean that there is an immediate
need to have any alternate design.
Fig. 3: Model-II stress result
REFERENCES
The “Fig. 4” result shows the maximum equivalent [1] Kun cheng, College of Manufcturing
stress of Model-III which is lesser than the maximum Science and Engineering,Southwest
equivalent stress value of Model-II. University of Science and Technology,
Mianyang China “Finite Element Analysis
for Rocker Arms of verticall Roller Mill on
the ANSYS Workbench”.
[2] Chin-Sung Chung, Ho-Kyung Kin,,
Department of Automobile Engineering,
Seoul national University of Technology,
republic of Korea, “Safety Evaluation of the
Fig. 4: Model-III stress result. Rocker Arm of a diesel engine”.
[3] Z.W. Yu, X. L. Xu , Institute of Metal and
The result of Model-IV shows the maximum Technology, Dalian Maritime university,
equivalent stress obtained is of 302MPa which is less chin, “Failure Analysis of Diesel Engine
than the maximum equivalent stress of Model-III. Rocker Arm”.
The model-IV result is shown in “Fig. 5”. [4] J.W. David and Yimin Wei, North Carolina
State University and J.A. Covey, General
Motors, “Optimal Rocker Arm Design in
High Speed Internal Combustion Engine”.
[5] N. B. Bhandari, Design of Machine Element
(Tata McGraw-Hill).
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