May 27, 2011

Camshaft Design and Analysis

Stephen Bibo San Diego State University

Mechanical Engineering Department

Jason Castaneda

San Diego State University Mechanical Engineering Department

Christopher Goulet

San Diego State University Mechanical Engineering Department

1. REQUIREMENTS

Choose an automobile, truck, or motorcycle camshaft. This project requires consideration of

both internal fatigue due to the bending stresses exerted on the camshaft and surface fatigue due

to the sliding contact between the cam lobes and the valve lifters.

2. BACKGROUND INFORMATION

Fundamentals of Four Stroke Engine

A camshaft is an apparatus used in piston engines to operate the valves. It consists of a

cylindrical rod running the length of the cylinder head with one oblong lobe or cam protruding

per valve. The cams force the valves open as they rotate depressing the lifter, spring, and valve

assembly.

The four stroke engine was first demonstrated by Nikolaus Otto in 1876. Four strokes engines

consist of four cycles: intake, compression, power and exhaust. Every stroke of the piston

corresponds to 180 crank degrees. Therefore, four cycles corresponds to 720 degrees of the

crankshaft. The camshaft is designed to rotate half as fast as the crankshaft. The camshaft’s

main function is to have the piston, intake, and exhaust valves operate in sequence throughout

the four stroke cycle.

Piston Direction

Intake Port

Exhaust Port

Crankshaft Degrees

Camshaft Degrees

Power Down, TDC to BDC

Closed Closed 0 to 180 0 to 90

Exhaust Up, BDC to TDC

Closed Open 180 to 360 90 to 180

Intake Down, TDC to BDC

Open Closed 360 to 540 180 to 270

Compression Up, BDC to TDC

Closed Closed 540 to 720 270 to 360

Intake, Stroke 1 (FIGURE 1): During the intake stroke, the piston moves downward, drawing a

fresh charge of vaporized fuel/air mixture. Figure 1 shows the intake valve opening to allow the

fuel mixture to be sucked into the cylinder. The exhaust valve is held shut by a spring.

Compression, Stroke 2 (FIGURE 2): As the piston rises the valve is forced shut by the valve

spring according to the camshaft angle. The crankshaft drives the piston upward, compressing

the fuel/air mixture. Compression allows for a more powerful explosion.

FIGURE 2

STROKE

STROKE

FIGURE 1

Power, Stroke 3 (FIGURE 3): At the top of the compression stroke the spark plug fires,

igniting the compressed fuel. As the fuel burns, it expands, driving the piston downward.

FIGURE 3

Exhaust, Stroke 4 (FIGURE 4): At the bottom of the power stroke, the exhaust valve is opened

by the cam/lifter mechanism. The upward stroke of the piston drives the exhaust out of the

cylinder.

FIGURE 4

STROKE

STROKE

4. CAMSHAFT INFORMATION

We chose a 1990 Volkswagen 4-cylinder 1.8L engine single overhead cam with two valves per

cylinder. The single camshaft operates both intake and exhaust valves; each lobe handles one

intake or exhaust valve.

The engine’s valves are actuated by flat-faced lifters riding on the lobes. The lifter depresses the

spring allowing the valve to open. The valve opens with the rise of cam profile and reaches

maximum lift when the lifter is positioned on the nose of the lobe. The valve closes wit the fall

of the cam profile until it is completely closed at the heel or base radius of the lobe. The valve

stays closed with a minimal spring force along the base radius of the circle until the cam profile

begins to rise.

Camshaft Timing .101 mm

Valve Opens Closes Duration

Intake 27 BTDC 65 ABDC 272º

Exhaust 67 BBDC 25 ATDC 272º

Volkswagen 1788CC, SOHC, 4 Cylinder

Cylinder Firing Order 1-3-4-2

Minimum RPM 3000

Maximum RPM 6000

Lobe Separation 110º

Maximum Lift 11.68 mm

Valve Spring Specifications

Closed Load 85 lbs @ 33.3mm

Open Load 233 lbs @ 22.1mm

Valve Train Components

Component Mass (g)

Spring Seat 18.8

Spring (inner and outer) 13.3 + 33.3

Hydraulic Lifter 46

Valve 24

Total 135.4

5. PROJECT ASSUMPTIONS

1. The cam profile can be modeled by a 4-5-6-7 polynomial.

2. The camshaft material is ductile iron 80-55-06 annealed.

3. The lifter follower material is alloy tool steel HRC 60-62.

4. The weight of the camshaft is negligible in the moment calculation because the

eccentric weight is small.

Ductile Iron 80-55-06 camshaft

Ultimate Tensile Strength (Sut) 365 MPa (53 kpsi)

Tensile Yield Strength (Sy) 565 MPa (82 kpsi)

Modulus of Elasticity (E) 168.9 GPa (24.5 Mpsi)

Poisson’s Ratio

( )

0.30

Alloy Tool Steel HRC 60-62 follower

Modulus of Elasticity (E) 206.8 GPa (30.0 Mpsi)

Poisson’s Ratio

( )

0.28

5. The camshaft is most susceptible to failure at the fillets between the shaft and

lobes.

6. The valve spring can be considered as a linear spring.

7. Since the contact between the lobe and follower is lubricated, the contact can be

approximated as rolling with 9% sliding.

6. FORCE ANALYSIS

We used the following equations to create an excel sheet to model the kinematics, forces,

moments, and bending stress on the camshaft. The data is represented in the graphs

following the equations.

camshaft angle

maximum lift

Camshaft angular displacement to maximum lift

Camshaft angular velocity

Linear displacement

Linear velocity

Linear acceleration

Jerk

Body force

Spring force

Using the open load value given in the valve spring specifications as a reference and

assuming a linear spring

Total force

Reaction forces

IF

1R

EF

2R

Moment calculated at assumed

point of failure

Maximum moment at point x

Moment of inertia for a solid circular shaft

Bending stress

6. STRESS ANALYSIS

We assume that the camshaft will be expected to last for around 200000 miles at an

average speed of 40 miles per hour at an average of 4500 crank revolutions per minute.

Bending stress

From our spreadsheet data

Concentration factor

fillet radius r = 0.0625 in., d = 0.953 in., D = 1.33 in., ,

From Figure E-2 (all tables and figures from Norton’s Machine Design: An Integrated

Approach)

A = 0.950, b = -0.244

Static stress concentration factor

From Table 6.6 for

Notch sensitivity

Fatigue stress concentration factor

Since

Von Mises stress

We neglect transverse shear stress.

7. INTERNAL FATIGUE ANALYSIS

Since the camshaft is expected to last over a million cycles, we assume infinite life for

fatigue analysis.

Uncorrected endurance limit

for iron,

Correction factors

for bending

For a rotating solid shaft

From Table 6.3 for machined, A = 4.51, b = -0.265

For

Factor of safety

Assuming that = constant

8. SURFACE FATIGUE ANALYSIS

From our spreadsheet data

Cylindrical contact

For a flat-faced follower

From Table C.1 for alloy steel follower

for ductile iron lobe

From Table 7.7 for rolling with 9% sliding and HRC 60-62 tool-steel follower on nodular

iron, Gr. 100-70-03, h-t HB 240-260 lobe

Desired life for this camshaft is cycles, as solved earlier,

9. CONCLUSION

Our analysis indicated an internal fatigue safety factor of 6.31 and a surface fatigue safety

factor of 26.6. Although the camshaft may appear to be overdesigned, other factors in the

design of the engine may affect the design of the camshaft. This analysis suggests that

the camshaft is probably one of the components that is least susceptible to failure in

automobile engines.

10. REFERENCES

Websites:

http://www.cranecams.com

http://www.howstuffworks.com

Books:

Robert L. Norton. Machine Design: An Integrated Approach. Third Edition.

New Jersey: Prentice Hall, 2006.

Dr. Robert L. Norton. Design Machinery. Third Edition. New Jersey: Prentice

Hall, 2006.

J. Angeles and C.S. Lopez-Cajun. Optimization of Cam Mechanisms. The

Netherlands: Kluwer Academic Publishers, 1991.