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CHAPTER 1 INTRODUCTION 1.1 INTRODUCTION TO ROCKER ARM The rocker arm is used to actuate the inlet and exhaust valves motion as directed by the cam and follower. It may be made of cast iron, cast steel, or malleable iron. In order to reduce inertia of the rocker arm, an I-section is used for the high speed engines and it may be rectangular section for low speed engines. In four stroke engines, the rocker arms for the exhaust valve are the most heavily loaded. Though the force required to operate the inlet valve is relatively small, yet it is usual practice to make the rocker arm for the inlet valve of the same dimensions as that for exhaust valve.
Fig.1.1 Rocker Arm A typical rocker arm for operating the exhaust valve is shown in Fig.1.1 The lever ratio a / b is generally decided by considering the space available for rocker arm. For moderate and low speed engines, a / b is equal to one. For high speed engines, the ratio a / b is taken as 1/ 1.3.
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The various forces acting on the rocker arm of exhaust valve are the gas load, spring force and force due to valve acceleration. 1.2 APPLICATION OF ROCKER ARM 1.2.1 Valve Gear Mechanism The valve gear mechanism of an I.C. engine consists of those parts which actuate the inlet and exhaust valves at the required time with respect to the position of piston and crankshaft. Fig. 1.2 (a) shows the valve gear arrangement for vertical engines. The main components of the mechanism are valves, rocker arm, valve springs, push rod, cam and camshaft.
Fig.1.2 Valve gear mechanism The fuel is admitted to the engine by the inlet valve and the burnt gases are escaped through the exhaust valve. In vertical engines, the cam moving on the rotating camshaft pushes the cam follower and push rod upwards, thereby transmitting the cam action to rocker arm. The camshaft is rotated by the toothed belt from the crankshaft. The rocker arm is pivoted at its centre by a fulcrum pin.
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When one end of the rocker arm is pushed up by the push rod, the other end moves downward. This pushes down the valve stem causing the valve to move down, thereby opening the port. When the cam follower moves over the circular portion of cam, the pushing action of the rocker arm on the valve is released and the valve returns to its seat and closes it by the action of the valve spring. In some of the modern engines, the camshaft is located at cylinder head level. In such cases, the push rod is eliminated and the roller type cam follower is made part of the rocker arm. Such an arrangement for the horizontal engines is shown in Fig.1.2 (b)
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CHAPTER 2 LITERATURE SURVEY N. Lenin Rakesh [1] has been done the project to find out the stress analysis of rocker arm and the hand crank by using finite element analysis software ANSYS. The structure of the hand crank and rocker arm model was performed using pro-E 4.0 version. Then finite element analysis are performed using ANSYS. The tensile stress of rocker arm and torsional stress of hand crank is calculated manually and is being compared with the experimentally obtained results. Siraj Sheikh [2] has been Rocker arm of Tata Sumo victa that was designed and analyzed to find the critical regions. CAD models of Rocker Arm was created using Pro/E and ANSYS V11software was used for analysis of rocker arm. The CAD model was inputted in ANSYS Workbench and Equivalent Stress and Maximum Shear Stress was found. The obtained results provided by ANSYS Workbench are compared to the results obtained by manual calculation. Syed Mujahid Husain [3] has been optimized in rocker arm design and material for better performance. This project present what rocker arm is, where it is used and why it is used, History related to rocker arm and it working is described. Various types of rocker arm used in vehicles and different materials used for making rocker arm are studied in this project. Reasons for Failure of rocker arm are also discussed in this project. Mohd Hafiz Bin Ghazalli [4] has been project used the cam, rocker arms, valve lifter, exhaust valve and accessories used in 4G13 engine in type. Solidworks, Cosmosmotion and Algor software are used for determination of stress concentration on the components.
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CHAPTER 3 ANALYTICAL DESIGN OF ROCKER ARM 3.1SPECIFICATIONS OF VALVE We are going to design a rocker arm using analytical method of calculation for that taking some standard specification are given on following Table 3.1 Table 3.1 Specification of valve Parameters
Value
Diameter of the valve head
80 mm
Lift of the valve
25 mm
Mass of associated parts
0.4 kg
Angle of action of camshaft
110°
Speed of the crankshaft
1500
Pressure on exhaust valves
0.4 N/mm2
Suction pressure
0.02 N/mm2
Angle between the two arms
135°
3.2 DESIGN CALCULATION First of all, the various forces acting on the rocker arm of the exhaust valve shown in Fig. 3.2 Gas load on the valve, P1 = (π/4) × dv2 × pc = (π/4) × 802 × 0.4 = 2011 N
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Weight of associated parts with the valve, w =m·g = 0.4 × 9.8 = 3.92 N
Fig. 3.1 Layout of Rocker Arm Total load on the valve, P = P1 + w = 2011 + 3.92 = 2014.92 N
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Initial spring force considering weight of the valve, Fs = (π/4) × dv2 × ps – w = (π/4) × 802 × 0.2 – 3.92 = 96.6 N The force due to valve acceleration (Fa) may be obtained as follows Speed of camshaft = N/2 = 1500/2 = 750 rpm Angle turned by the camshaft per second = (750/60) × 360 = 4500 deg/s Time taken for the valve to open and close, t = (Angle of action of cam/Angle turned by camshaft) = 110/4500 = 0.024 s Maximum acceleration of the valve a = ω2 × r = (2π/t) 2 × r = (2π/0.021) 2 × 0.0125 = 857 m/s2
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Force due to valve acceleration, considering the weight of the valve, Fa = m × a + w = 0.4 × 857 + 3.92 = 346.72 N Maximum load on the rocker arm for exhaust valve, Fe = P + Fs + Fa = 2014.92 + 96.6 + 346.72 = 2458.24
2460 N
Since the length of the two arms of the rocker are equal, therefore, the load at the two ends of the arm are equal, i.e. Fe = Fc = 2460 N. We know that reaction at the fulcrum pin F, RF = √ =√ = 4545 N 3.2.1 Design of fulcrum pin Let
d1 = Diameter of the fulcrum pin, and l1 = Length of the fulcrum pin = 1.25 d1
Consider the bearing of fulcrum pin. Load on the fulcrum pin (RF), 4545 = d1 × l1 × pb
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= d1 × 1.25 d1 × 5
(pb = 5 N/mm2)
= 6.25 (d1)2 (d1)2 = 4545 / 6.25 = 727 d1 = 26.97
30 mm
l1 = 1.25 d1 = 1.25 × 30 = 37.5 mm Check the average shear stress induced in the pin. Since the pin is in double shear, therefore, load on the fulcrum pin (RF) 4545 = 2 × (π/4) × d12 × τ = 2 × (π/4) × 302 × τ = 1414 τ τ = 4545/1414 = 3.2 N/mm2 This induced shear stress is quite safe, External diameter of the boss, D1 = 2d1 = 2 × 30 = 60 mm
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Assuming a phosphor bronze bush of 3 mm thick, the internal diameter of the hole in the lever, dh = d1 + 2 × 3 = 30 + 6 = 36 mm Check the induced bending stress for the section of the boss at the fulcrum which is shown in Fig. 3.2
Fig. 3.2 Sectional view of Boss at fulcrum Bending moment at this section, M = Fe × l = 2460 × 180 = 443 × 103 N-mm Section modulus, Z = [(1/12) × 37.5 × (603 – 363)] ÷ (60/2) = 17640 mm3
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Induced bending stress, σb = M/Z = 443 × 103/17640 = 25.1 N/mm2 The induced bending stress is quite safe. 3.1.2 Design for fork end Let
d2 = Diameter of the roller pin, and l2 = Length of the roller pin = 1.25 d2
Consider bearing of the roller pin. Load on the roller pin (Fc), 2460 = d2 × l2 × pb = d2 × 1.25 d2 × 7 = 8.75 (d2)2 (d2)2 = 2460 / 8.75 = 281 d2 = 16.76 18 mm l2 = 1.25 d2 = 1.25 × 18 = 22.5
24 mm
(pb = 7 N / mm2)
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Check the roller pin for induced shearing stress. Since the pin is in double shear, therefore, load on the roller pin (Fc), 2460 = 2 × (π/4) × d22 × τ = 2 × (π/4) × 182 × τ = 509 τ τ = 2460/509 = 4.83 N/mm2 This induced shear stress is quite safe. The roller pin is fixed in the eye and thickness of each eye is taken as one-half the length of the roller pin. Thickness of each eye, t2 = l2/2 =24/2 = 12 mm Check the induced bending stress in the roller pin. The pin is neither simply supported in fork nor rigidly fixed at the end. Therefore, the common practice is to assume the load distribution as shown in Fig. 3.3. The maximum bending moment will occur at Y–Y. Neglecting the effect of clearance, we have Maximum bending moment at Y – Y, M = (Fc/2) × [(lc/2) + (t2/3)] – [(Fc/2) × (lc/4)] = (2460/2) × [(24/2) + (12/3)] – [(2460/2) × (24/4)]
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= 12300 N-mm
Fig. 3.3 Sectional view of Roller End Section modulus of the pin, Z = (π/32) × d23 = (π/32) × 183 = 573 mm3 Bending stress induced in the pin = M/Z = 12300/573 = 21.5 N/mm2 This bending stress induced in the pin is within permissible limits.
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Since the radial thickness of eye (t3) is taken as d2 / 2, therefore, overall diameter of the eye, D2 = 2d2 = 2 × 18 = 36 mm The outer diameter of the roller is taken slightly larger (atleast 3 mm more) than the outer diameter of the eye. In the present case, 42 mm outer diameter of the roller will be sufficient. Providing a clearance of 1.5 mm between the roller and the fork on either side of the roller, we have l3 = l2 + 2 × (t2/2) + 2 × 1.5 = 24 + 2 × (12/2) + 3 = 39 mm 3.1.3 Design for tappet screw The adjustable tappet screw carries a compressive load of Fe = 2460 N. Assuming the screw is made of mild steel for which the compressive stress (σ c) may be taken as 50 MPa. Let
d2 = Core diameter of the taper screw
The load on the tappet screw (Fe) 2460 = (π/4) × dc2 × σc = (π/4) × dc2 × 50 = 39.3 × dc2
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dc2 = 2460 / 39.3 = 62.6 or dc = 7.9 8 mm Outer or nominal diameter of the screw, d = dc/0.84 = 8/0.84 = 9.52
10 mm
We shall use 10 mm stud and it is provided with a lock nut. The diameter of the circular end of the arm (D3) and its depth (t4) is taken as twice the diameter of stud. D3 = 2 × 10 = 20 mm t4 = 2 × 10 = 20 mm
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CHAPTER 4 FEM ANALYSIS OF ROCKER ARM The data from the analytical calculation is used for modeling the rocker arm, the CAD modeling is done on CREO Parametric 2.0 as shown in Fig. 4.1
Fig. 4.1 Rocker Arm modeled using Creo parametric Then the model is imported to FEM Software, the FEM package used for is ANSYS 14.0 4.1 ANALYSIS OF ROCKER ARM There are four analysis are carried out in a Rocker arm 1. Total deformation 2. Equivalent strain 3. Equivalent stress 4. Shear stress
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4.2 MATERIAL PROPERTIES The material used for selected rocker arm is structural steel and the properties of the material are presented in the Table 4.1 Table 4.1 Material Properties of Structural steel Parameters
Value
Density
7850 kg m-3
Young’s modulus
2E+5 MPa
Poisson’s Ratio
0.3
Bulk Modulus
1.6667E+5 MPa
Shear Modulus
7.6923E+4 MPa
Tensile yield strength
2.5E+02 MPa
Compressive yield strength
2.5E+02 MPa
Tensile ultimate strength
4.6E+02 MPa
4.3 DIMENSION OF ROCKER ARM The Dimensions are obtained from the Analytical calculations done in Chapter – 3 and arranged in Table 4.2 Table 4.2 Dimensions of Rocker Arm Parameters Diameter of the fulcrum pin Length of the fulcrum pin
Value 30 mm 37.5 mm
External diameter of the boss
60 mm
Diameter of the roller pin
18 mm
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Length of the roller pin
24 mm
Thickness of each eye
12 mm
Overall diameter of the eye
36 mm
Core diameter of the tappet screw
8 mm
Diameter of circular end of arm
20 mm
Depth circular end of arm
20 mm
4.4 MESHING The mesh is done by default mesh element of ANSYS 14.0 using fine mesh settings. The meshing must be very fine for obtain the highly accurate analysis answer as shown in Fig. 4.2.
Fig. 4.2 Meshed model 4.5 LOADS AND BOUNDARY CONDITIONS As shown in the Fig. 4.3 the loads and boundary conditions are assigned, the analysis are carried out in without gravity settings.
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Fig. 4.3 Boundary condition applied model 4.6 RESULTS Following four results are produced using ANSYS 1. Total deformation 2. Equivalent strain 3. Equivalent stress 4. Shear stress 4.6.1 TOTAL DEFORMATION The total deformation is obtained as shown in Fig. 4.4
Fig. 4.4 Total deformation
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4.6.2 EQUIVALENT STRAIN The Equivalent Strain is obtained as shown in Fig. 4.5
Fig. 4.5 Equivalent strain 4.6.3 EQUIVALENT STRESS The Equivalent Stress is obtained as shown in Fig. 4.6
Fig. 4.6 Equivalent stress
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4.6.4 SHEAR STRESS The Shear Stress is obtained as shown in Fig. 4.7
Fig. 4.7 Shear stress
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CHAPTER 5 CONCLUSION The analytical design calculation has been calculated and then 3D modeling of the Rocker arm is done by using Creo parametric 2.0 software. The modeling was done using Creo by the help of the calculated parameters and the values. The stress analysis of the Rocker arm was found out manually by using formula and data taken from the Design data book, and then the specified stress concentration was analyzed by using ANSYS. The result found was compared with the values found out manually. The compared result was found satisfactory. From this project, it was found that the analytical calculations of new section are more effective than that of older section.
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REFERENCES 1. N. Lenin Rakesh, A. Thirugnanam and Jitesh Mishra “Stress Analysis of Hand Crank and Rocker ARM” Middle-East Journal of Scientific Research 12 (12): 1687-1689, 2012, ISSN 1990-9233 2. Syed Mujahid Husain, Prof.Siraj Sheikh “Rocker Arm: - A Review” International Journal of Innovative Research in Science, Engineering and Technology Vol. 2, Issue 4, April 2013, ISSN: 2319-8753 3. Syed Mujahid Husain, Siraj Sheikh “Design and Analysis of Rocker Arm” International Journal of Mechanical Engineering and Robotics Research. Vol. 2, No. 3, July 2013, ISSN 2278 – 0149.
4. Mohd
Hafiz Bin Ghazalli “Finite Element Analysis Of Cam And Its
Follower Contact Stress Mechanism”.
5. Khurmi R S and Gupta J K (2011), “I.C Engine Parts”, Machine Design, pp. 584-589 and 1192-1195.
6. Dong-Woo
Lee, Soo-Jin Lee, Seok-Swoo Cho and Won-Sik Joo (2005),
“Failure of Rocker Arm Shaft for 4-Cylinder SOHC Engine”, Engineering Failure Analysis,Vol. 12, No. 3, pp. 405-412.
