crankshaft report
TRANSCRIPT
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/>.