1. No category

ME 452 - Machine Design II
Name of Student:______________________________
Spring Semester 2015
Lecture Division Number:_______________________
Project 2. Stress Analysis and Design of a Crankshaft.
Formal Report: Due in Room ME 3003, before noon, Wednesday, April 1st. Note that the project is to
be completed by each student individually. Any copying or cheating will be grounds for failing, or
expulsion from, the course.
The front and top views of the initial design of a crankshaft for a small, single-cylinder, diesel
engine are shown in Figure 1a and Figure 1b, respectively. The notation is as follows:
The length of the crankshaft is JK.
The crank journal diameters are d1 and d 2 .
The distances from the crank journals to the rectangular plates are s1 and s2 .
The thicknesses of the two rectangular plates are t1 and t 2 .
The widths of the two rectangular plates are w1 and w 2 .
The length of the rod journal is l j.
The rod journal diameter is d j.
The fillet radii at the four plate-journal interfaces are r.
The crank length (or the throw) is h and the corresponding stroke length is S = 2h.
The diameter of the cylindrical piston is d.
The length of the connecting rod is l.
Figure 1a. A front view of the crankshaft. Scale 1cm = 2 cm.
1
Figure 1b. A top view of the crankshaft. Scale: 1cm = 2 cm.
For an initial model of the stresses in the crankshaft, the following data and information can be used:
The distances s1 = s2 = 31.75 mm (refer to Figure 1a).
The widths of the two rectangular plates are w1 = w2 = 25.4 mm (refer to Figure 1b).
The length of the rod journal is l j  38.1 mm.
The crank length is h  50.8 mm, that is, the stroke is S  101.6 mm.
The diameter of the cylindrical piston is d  76.2 mm.
The length of the connecting rod is l  152.4 mm.
The slider-crank is an in-line mechanism, that is, there is no offset (see Figure 4).
The crank has the constant speed N = 2500 rpm.
The weight of the piston is W = 13.35 N. Neglect the weights of the crank and connecting rod.
The following data and information is not specified:
The length of the crankshaft is JK.
The crank journal diameters d1 and d 2 .
The thickness of the two rectangular plates t1 and t 2 .
The rod journal diameter d j.
The fillet radius r at the four plate-journal interfaces.
To validate the initial design you must perform a stress analysis of the crankshaft and modify the
design if necessary. In order to perform the stress analysis you will need to model the motion of the
engine components to determine the loads on the crankshaft, from which you can determine the stresses,
which will fluctuate with time. Combining these fluctuating stresses with the material properties of the
crankshaft will allow you to predict the static and fatigue factors of safety for the crankshaft. You will
also need to specify the material properties and the heat treatment. The key to a successful stress
analysis of the crankshaft is to estimate the stresses in the part at several candidate failure locations. To
do this you will need to know (or be able to predict with reasonable accuracy) the geometry, the loads,
and the material properties of the crankshaft. To begin your study, you can assume that the pressure in
the combustion chamber is as shown in Figure 2. Also assume that the pressure acts uniformly on the
face of the cylindrical piston. Reference: Engineering Fundamentals of the Internal Combustion Engine,
Willard W. Pulkrabek, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 1997.
The final design of the crankshaft will require the final dimensions of the most important
geometrical parameters of the crankshaft.
To simplify the problem you can assume for your initial analysis and design that the pressure in the
combustion chamber can be modeled as shown in Figure 3.
2
Pressure, MPa
13.789
10.342
- 200
- 160
- 120
- 80
- 40
0
20
60
100
Crank angle, degs.
TDC
Figure 2. The pressure against the crank position.
Pressure, MPa
10.342
8.618
540
630
90
0,720
Compression
180
Crank angle, degs.
Expansion
TDC
Figure 3. Initial model of the pressure against the crank position.
3
Suggestions for the solution procedure: The following steps are guidelines for completing this project:
(i) Determine the acceleration of the piston from a kinematic analysis of the slider-crank mechanism
shown in Figure 4. (A kinematic analysis of a single cylinder engine is presented in Uicker, et al, Fourth
Edition, 2011, see Chapter 3, Section 3.9, Chapter 4, Section 4.9, and Chapter 16, Section 16.4).
Figure 4. The slider-crank mechanism.
(ii) Determine the reaction forces acting on the crankshaft as a function of the crank position θ.
In the initial dynamic force analysis you need only include the mass of the piston; that is, you can
neglect the mass of the connecting rod and the crankshaft. Also, you can neglect the effects of friction in
the mechanism (that is, friction in the journal bearings and between the piston and the cylinder wall).
(iii) Generate shear force diagrams, bending moment diagrams, and torque diagrams for each piece of
the crankshaft (i.e., at least five total pieces must be documented in order to help model the crankshaft as
a simple shaft) to determine the critical planes of the crankshaft for a stress analysis. Note that these
loads will be a function of the crank position because the loads vary with the crank position. Assume
that the loading on the crankshaft is symmetric. For example, half of the crankshaft torque is transmitted
by the left half of the shaft and half of the torque is transmitted by the right half of the shaft.
(iv) Within the critical planes of the crankshaft locate the critical elements of the crankshaft. Try to limit
the number of critical elements that you need to consider by careful logic. Clearly document the number
of critical elements that you have identified.
(v) Find the state of stress on each critical element and determine the mean stress component and the
alternating stress component acting on each critical element.
(vi) Apply both static failure theories and fatigue failure theories to size the geometry of the crankshaft.
Select the most appropriate material for the crankshaft. Specify the material properties and the
recommended heat treatment for the crankshaft. Recall that fatigue is caused by time-varying stresses
which initiate at a crack, usually at a local surface imperfection such as a machining mark or a notch in
the geometry. Therefore, the stress concentration effects are important. As the stresses are cycled, even
at levels below the yield strength of the material, the crack propagates reducing its cross-sectional area.
Eventually, the area decreases sufficiently to push the stresses beyond the yield or ultimate strength of
the material, in which case the part will break or fracture.
Since this is an open-ended project then more information may be made available, upon request, in
order to complete a detailed failure analysis and design of the crankshaft.
The formal report must include all of your work, clearly showing and detailing your important
results. Detail your iteration procedures, your findings, and include a discussion of the practical
significance of your results. Include a copy of your computer program (spreadsheets). Also, include the
important design charts and plots which should clearly show the important data points.
4