May 3, 2023

Crankshaft Design and Analysis

Stephen BiboSan Diego State University

Mechanical Engineering Department

Jason CastanedaSan Diego State University

Mechanical Engineering Department

Christopher GouletSan Diego State University

Mechanical Engineering Department

EXECUTIVE SUMMARY

We were tasked to reverse engineer a crankshaft for a vehicle of our choice. We modeled the kinematics, forces, moment, and bending and shear stresses on the crankshaft. We were to analyze the crankshaft under dynamic loading (internal fatigue) and to determine the hydrodynamic journal bearing parameters and the minimum RPM for full-film lubrication. The crankshaft we chose came out of an early 1990’s Volkswagen four cylinder engine. We concluded that for the given crankshaft specifications and calculated data from our analysis that the crankshaft shaft would serviceable for at least 200000 miles with a minimum factor of safety of 1.74. We determined that full-film lubrication begins immediately upon ignition provided the pump can provide the oil pressure.

1. REQUIREMENTS

Design the automobile, truck, or motorcycle crankshaft associated with the camshaft designed in Project #2. This project requires consideration of both dynamic loading (fatigue) due to shear and bending stresses exerted on the crankshaft as well as the design of the main and offset (or throw) hydrodynamic journal bearings.

2. BACKGROUND INFORMATION

The crankshaft is the part of an engine that translates reciprocating linear piston motion into rotation. It typically connects to a flywheel, used to start the engine via geared teeth and also to reduce the pulsation characteristic of the four-stroke cycle. The opposite end sometimes has a torsional or vibrational damper to reduce the torsion vibrations often caused along the length of the crankshaft by the cylinders farthest from the output end. The crankshaft was invented by the inventor Al-Jazari in the 12th century.

The crankshaft has a linear axis about which it rotates, typically with several bearing journals riding on replaceable bearings held in the engine block. As the crankshaft undergoes a great deal of loading from each cylinder in a multicylinder engine, and must be supported by several such bearings. The crankshaft also has a sequence of rod journals offset from the main centers. The amount of offset the rod journal has in relation to the main journals is ½ the length of the stroke.

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

3. CRANKSHAFT INFORMATION

We chose a 1990 Volkswagen 4-cylinder 1.9L engine single overhead cam with two valves per cylinder.

Volkswagen 1788CC, SOHC, 4 Cylindercylinder firing order 1-3-4-2

maximum RPM 6000compression ratio 8.0:1

bore diameter (Bore) 82.5 mmstroke (Stroke) 86.4 mm

rod length center to center (b) 136 mmrod journal diameter 48 mmrod journal length 25 mm

distance from journal to rod center of mass 41 mm

distance from piston to rod center of mass 95 mm

main journal diameter 58 mmmain journal length 25 mm

distance from main bearing to throw center of mass 12.7 mm

1050 AISI Steel normalizedTensile Yield Strength (Sy) 427 MPa

Ultimate Tensile Strength (Sut) 745 MPaBrinell Hardness (-HB) 217

R. Norton, Machine Design, An Integrated Approach, Third Edition, Prentice Hall (2006)

Component Massescomponent mass (grams)

connecting rod 588

piston and pin 300

throw 500

4. PROJECT ASSUMPTIONS

1. At the intake stroke, the intake manifold pressure is NOT equal to atmospheric pressure rather it is under vacuum created by the piston downstroke pulling air into the chamber.

2. The maximum temperature of the engine is on 90% of the adiabatic flame temperature of gasoline .

3. The rotational speed of the crankshaft is constant.4. Air-fuel mixture is considered as an ideal gas.5. Intake, compression, power and exhaust processes can be considered

isentropic except for combustion.6. Polytropic exponent is 1.3 for IC engine.

4. FORCE ANALYSIS

We used the following equations to create an excel sheet to model the kinematics, forces, moments, and bending and shear stresses on the crankshaft. The data is represented in the graphs following the equations.

Piston Forces

crankshaft anglethrow offsetrod length

average engine speed

Polytropic equations

Piston displacement

Piston area

Total cylinder volume

Cylinder volume

Intake volume

Intake pressure

Intake temperature

Pressure during compression

Temperature during compression

Combustion temperature

The adiabatic flame temperature of gasoline (octane) is 2262 K. The engine max temperature is based on 90% of the adiabatic flame temperature of gasoline.

Pre-combustion pressure

Pre-combustion temperature

Combustion pressure

Temperature during power stroke

Pressure after combustion

Cylinder Pressure, P(θ)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

crankshaft angle, θ (degrees)

cylin

der p

ress

ure,

p(θ

) (kP

a)

Gas force

Gas Force, Fgas(θ)

-2000.00

0.00

2000.00

4000.00

6000.00

8000.00

10000.00

12000.00

14000.00

0 100 200 300 400 500 600 700 800

crankshaft angle, θ (degrees)

gas

forc

e, F

gas(

θ) (N

)

Piston displacement

Piston velocity

Piston acceleration

Piston body force

Force on crankshaft due to gas and piston body forces

Torque on crankshaft due to gas and piston body forces

Connecting Rod Forces

Rod x-position

Rod x-velocity

Rod x-acceleration

Rod y-position

Rod y-velocity

Rod y-acceleration

Rod equivalent mass

Body x-force

Body y-force

Torque on crankshaft due to rod body forces

Force on crankshaft due to rod body forces

Throw Forces

Centripetal force

Total Forces

Torque

Body force on main shaft

Force of one cylinder

Force of One Cylinder, Fcyl(θ)

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 25 50 75 100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

525

550

575

600

625

650

675

700

crankshaft angle, θ (degrees)

forc

e (N

)

cylinder force, Fcyl(θ) body force, Fbody(θ) gas force Fgas(θ)

5. STRESS ANALYSIS

bearing diameter

Area

Polar moment of inertia

Moment of inertia

Torsion

Bearing reaction forces

Shear force

Transverse shear stress

Total shear stress

Bending moment

Stress Concentration

Total Shear Stress on Output Bearing, τ(θ) and Bending Moment, M(θ)

-6

-4

-2

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

crankshaft angle, θ (degrees)

tota

l she

ar s

tres

s, τ

(θ) (

MPa

)

-1,500

-1,000

-500

0

500

1,000

1,500

2,000

bedn

ing

mom

ent,

M(θ

) (N

m)

shear stress, τ(θ) bending moment, M(θ)

Bending stress

Total Shear Stress, τ(θ) and Bending Stress, σbend(θ)

-60

-40

-20

0

20

40

60

80

100

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

520

540

560

580

600

620

640

660

680

700

720

crankshaft angle, θ (degrees)

stre

ss (M

Pa)

shear stress, τ(θ) bending stress, σbend(θ)

Expected fatigue life

We assume that the crankshaft will be expected to last for around 200000 miles at an average speed of 60 miles per hour at an average of 3000 revolutions per minute.

Bending stressFrom our spreadsheet data

Stress Concentration

fillet radius r = 1.5875 mm, d = 58 mm, D = 76 mm, ,

From Figure E-2 (all tables and figures from Norton’s Machine Design: An Integrated Approach)A = 0.960, b = -0.231

Static stress concentration factor

From Table 6.6 for

Notch sensitivity

Fatigue stress concentration factor

Since

Shear stress concentration factorSince

Von Mises stress

6. INTERNAL FATIGUE ANALYSIS

Since the crankshaft is expected to last over a million cycles, we assume infinite life for fatigue analysis.

Uncorrected endurance limit for steel,

Correction factors for primarily bending

For a rotating solid shaft

From Figure 6.26 for polished

For

Factor of safety

Assuming that = constant

7. HYDORDYNAMIC JOURNAL BEARING ANALYSIS

Main Bearing

Crankshaft roughness

Bearing roughness for cadmium base bearing material

Total roughness

Ocvirk number

Eccentricity ratio from Figure 10-10

Maximum force on main bearing from spreadsheet data

Average oil pressure

Oil viscosityOil viscosity for SAE 30W engine oil @

Specific film thickness for full-film lubrication

Minimum RPM for full-film lubrication

Rod Bearing

Maximum force on rod bearing from spreadsheet data

Average oil pressure

Oil viscosityOil viscosity for SAE 30W engine oil @

Minimum RPM for full-film lubrication

The minimum RPM is far below idle speed of around 900 RPM.

8. CONCLUSION

The crankshaft can withstand the forces applied with a minimum factor of safety of 1.74. Full film lubrication is maintained in the bearings from 1.89 RPM through redline. The full-film lubrication is accomplished only when the pump can provide adequate pressure.

Realistically, the pump cannot provide sufficient pressure until approximately idle speed. Therefore, full-film lubrication likely occurs at around idle speed.

9. REFERENCES"Engine Formula." 4-Stroke. Engineers Edge. 9 Dec. 2005 <http://www.engineersedge.com/engine_formula_automotive.htm>.

Norton, Robert L. Machine Design, an Integrated Approach. 3rd ed. : Worcester Polutechnic Institute, 2005.

Rollins, Mike. "What is the Speed of a Piston with an offset crankshaft?." 13 May. 2006. <http://www.wfu.edu/~rollins/piston/offset/>.