In this study it required to perform the modal analysis, harmonic analysis and compare the total deformation of the three engine shafts using ANSYS Workbench 2021. The analysis to be done on the shafts are the harmonic analysis to and response spectrum to examine the effect of the shaft under the action of the loading that gives rise to certain frequencies which are distinct to the type and magnitude of the force that acts. That frequency is called the natural frequency and when the natural frequency matches with the frequency of vibration resonance occurs which might be the root cause of the propagation of cracks within the surface. Along with this, Harmonic analysis is the study of linear actions of groups on vector spaces. Any action of a group on a set gives rise to actions on vector spaces of functions defined on that set. Group actions, in turn, are important because many mathematical structures can be analyzed by studying the group of transformations which preserve that structure. Projective actions of groups are closely related to linear ones and play a central role in quantum mechanics; there is a close relationship between elementary particles and the ways that these representations interact.
3.1 Engine Shaft (AISI 316 Stainless steel)
ASS parent alloy, 304, has considerably good resistance to a wide range of atmospheric environments and many corrosive media but when certain amount of Mo is added in base 304 alloy then the resultant alloy becomes excellent material to be used in highly corrosive environment (Pitting and crevice corrosion) (Islam M. El-Galy, 2019). This alloy with increased Resistance to pitting and crevice corrosion is called 316 SS. Some important characteristics of the chosen material for engine are:
Stainless steel is a good choice for selection because of its immune protection against corrosion, its high strength, and the ability to resist fracture. These make it a very good choice for working in harsh conditions. Given below in Table 1. the set of properties taken from ANSYS of the material used are listed.
Table 1 Properties for Stainless steel 316 (Azom, 2021)
Stainless Steel 316
|
Property
|
Value
|
Density
|
8000 kg/m3
|
Atomic Volume (average)
|
0.007 m3/kmol
|
Bulk Modulus
|
145 GPa
|
Elastic Limit
|
250 MPa
|
Endurance Limit
|
270 MPa
|
Fracture Toughness
|
200 MPa.m1/2
|
Tensile Strength
|
500 MPa
|
Thermal Conductivity
|
15 W/m.K
|
Resistivity
|
75 10-8 ohm*m
|
The part made in SolidWorks is shown in Figure 3 below: -
Table 2 represents the variation of frequency for every mode shape as the engine shaft is subjected to vibrations due to load. The given natural frequencies correspond to the behavior of the object when it is subjected to loadings and intensities which then lead to failure.
Table 2 frequencies for mode shapes (SS-316)
Mode
|
Frequency (Hz)
|
1
|
1634.3
|
2
|
1697.1
|
3
|
2805.8
|
4
|
4718.3
|
5
|
4823.1
|
6
|
7807.6
|
7
|
8800.2
|
8
|
9011.6
|
9
|
11165
|
10
|
13878
|
In Figure 4 the graphical representation of frequency obtained from the mode shapes in ANSYS is shown. The maximum natural frequency for a mode shape tells us about the highest vibrational intensity that the shaft will be subjected to during its operation. As opposed to the minimum, both parameters along with the no. of cycles play an important role in determining the total deformation that occurs. Later, the maximum frequencies, amplitude, and the total deflection for the three cases will be compared to choose the best material for the engine shaft.
Some insights about total deformation in this scenario are:
Deformation generally stands for the case when an exerted force causes a change in a body’s nodal displacement, and it loses its shape and rigidity. From ANSYS, the results of total deformation in the shaft have been computed and attached below.
The Figure 5 above explains the Deformation that is the variation or change in the object’s nodal displacement. The deformation occurs when the displacement of the nodes is beyond a certain benchmark and then the object adopts a shape different from the original. It is a result of successive loadings that insinuate that whether a part or a certain material is ready or enough for a part or not
Harmonic response analysis in ANSYS (as well as in any other FEA program) can be used to obtain steady-state response of a model subjected to a load that changes harmonically (sinusoidally) in time. Such load has specific amplitude and frequency at which it acts. The load causes forced vibrations. The calculated response is a function of frequency. These simulations can only be linear and are often performed after eigenfrequency analysis since extracted natural frequencies can be used as a harmonic load frequency to obtain actual stress and displacement in such conditions (eigenfrequency analysis only gives mode shapes with arbitrary magnitudes instead of actual displacement values). The frequency response for engine shaft- SS 316 is shown in Fig. 6.
3.2 Engine Shaft (Carbon Fiber)
Carbon fiber is one of the allotropic crystalline forms of the element. Among the other forms are diamond, graphite and bucky balls. Carbon fiber is essentially a one-dimensional form, as diamonds and buckyballs are three dimensional, and graphite a 2-dimensional form. Carbon fiber can be visualized as a helix of atoms around a hollow center. The fiber winds around with each layer translated up by one atom from the layer below. The fiber grows along the central core and expands chemically. With this crystalline structure an incredibly strong fiber is achieved. Carbon fiber is the material that consists of various strands of carbon that are bonded tightly together, and the result is a stiff, lightweight, and strong material which can be employed for various constructional purposes. It is widely used in manufacture and our studies revolves around finding the epitome of optimized working for our engine shaft.
Table 3 Properties of Carbon Fiber
(Azom, 2021)
Carbon Fiber
|
Property
|
Value
|
Density
|
2000 kg/m3
|
Atomic Volume (average)
|
0.002 m3/kmol
|
Bulk Modulus
|
228 GPa
|
Elastic Limit
|
200 MPa
|
Endurance Limit
|
Not specified
|
Fracture Toughness
|
50 MPa.m1/2
|
Tensile Strength
|
3.5 GPa
|
Thermal Conductivity
|
21 W/m.K
|
Resistivity
|
884 10-8 ohm*m
|
Table 3 shows the different parameters on which the standard and performance of the engine shaft depends. Hence it will be examined whether if carbon fiber is a good choice or not for our development of an engine shaft. In the pursuit, different tests are conducted on the three models made and the conclusions have been derived later on in the document. Carbon fiber is known for its stiff nature, it is also compared at the end to provide with a good and sound reasoning for making engine shafts on a commercial scale.
In Figure 7 the 3d-model of the shaft made in solid works with Carbon fiber applied on it is shown. Firstly, the various natural frequencies that arise when the engine shaft is loaded are discussed.
The variation for carbon fiber can be examined in Fig. 8. A comparative analysis of Figures 4,8 and 12 tells us that the maximum natural frequency of vibration is more in the case of carbon fiber as compared to Stainless steel- 316. The increasing values of frequencies tell us that the increasing intensities of vibration put the engine shaft under successive vibrations. A certain span that is distinct for every material being used comes when the frequencies result in shaft failure.
Table 4 Natural Frequencies of Carbon fiber
Mode
|
Frequency (Hz)
|
1
|
1182.1
|
2
|
1214.6
|
3
|
1975.3
|
4
|
3419.6
|
5
|
3428.2
|
6
|
5640.7
|
7
|
6365.7
|
8
|
6393.2
|
9
|
7847
|
10
|
9884.2
|
Table 4. shows us the natural frequencies for carbon fiber. The report focuses on preventing that scenario and proposes a solution by comparing the performance of engine shafts of a homogenous material, a composite, and a functionally graded material.
The total deformation in the carbon fiber is shown in Fig. 9. At low loads, most materials deform elastically. Many people mechanical deformation to refer to this sort of elastic deformation. Deformation is often described as strain. In the oilfield, it can be described as the pressure and resultant change in the rock that is hydraulically fractured.
Figure 10 shows the frequency response for carbon fiber obtained from ANSYS. The behavior of the shafts pertaining to steady state responses will be discussed below. It involves the evaluation of an objects performance when it is subjected to loadings.
3.3 Engine Shaft (Ti-6Al-4V) FGM
The most used alloy is 6al4v (Grade 5) Titanium (Radhi, 2018). This alloy is made of about 6% aluminum, 4% Vanadium, a tiny number of miscellaneous elements, and the rest Titanium. This has a combination of excellent strength and corrosion resistance. It is heat treatable as well.
Titanium (Ti) has two primary advantages over steel: It is lighter than steel. Iron (Fe) has a density of 7.8 grams/cm^3, but Ti has a density of 4.5 grams/cm^3. That gives Ti as much higher specific strength, which is defined as the strength divided by the density. Contrary to popular mythology and marketing, Ti is not stronger than steel, in general. There are some alloys of steel that are not as strong as some heat treatments of many materials but there is no Ti-6Al-4V that has the yield strength that high strength steels like AISI 4340 and 300M can have. It is all a question of heat treatments. But in any event, Ti alloys have a higher specific strength than any ferrous alloys.
Table 5 Properties of Ti-6Al-4V
FGM (Ti-6Al-4V)
|
Property
|
Value
|
Density
|
4500 kg/m3
|
Atomic Volume (average)
|
0.011 m3/kmol
|
Bulk Modulus
|
130 GPa
|
Elastic Limit
|
850 MPa
|
Endurance Limit
|
550
|
Fracture Toughness
|
95 MPa.m1/2
|
Tensile Strength
|
1000 MPa
|
Thermal Conductivity
|
7.2 W/m.K
|
Resistivity
|
169 10-8 ohm*m
|
Table 5 shows the properties of the FGM chosen. Composites are by and large homogenous through their material volume when managing a two-segment framework, and their properties are then additionally uniform through that material volume (in a specific course). FGMs could likewise be constrained by the advancement of various material stages or designs (consider varieties in precipitation solidifying), if it is done in a controlled matter through the volume by means of the creation technique (Charnont Moolwana, 2012). Ti alloys can be used at much higher temperatures than steel alloys. Ferrous alloys rapidly lose strength as the temperature goes up beyond about 300C, but Titanium alloys maintain good strength to over 500C. 3D printing is a pleasant illustration of how practical material properties can be characterized through a material construction by variety in cell structure (going from a low to high filling level in smoother progress) and changing the solidness or directional properties. In Fig. 11 the 3-d model made in solid works is and the FGM applied to it.
Given below in Table 6 is the tabular representation of the increasing values of natural frequencies pertaining to the mode shapes resulted.
Table 6 Natural Frequencies for FGM
Mode
|
Frequency (Hz)
|
1
|
1657.9
|
2
|
1728.5
|
3
|
2745.1
|
4
|
4818.9
|
5
|
4950.3
|
6
|
7986.8
|
7
|
8983.7
|
8
|
9223.4
|
9
|
11012
|
10
|
14118
|
Given below in Figure 12 is the variation of natural frequency in our third case of interest.
Figure 12 shows the frequency variation for the FGM engine shaft obtained from ANSYS. The results obtained from ANSYS for total deformation have a colored representation of the concentration of stresses in the body. It gives insights onto the most vulnerable portion of the component. Some important Key Performance indicators will be elicited that lead to various shaft failures. As most of the shafts have a circular cross-section.
In that case, stress concentration is mostly around the edges of the diameters and hence there is a fatigue failure close to the circumferential boundary of the shaft (Charnont Moolwana, 2012). Figure 13 represents the total deformation for the engine shaft made from Functionally Graded Material (FGM).
In Figure 13, the total deformation in the engine shaft of FGM can be examined. It is obvious that the stress concentration is lesser when compared to the above two cases discussed.
Figure 14 depicts the frequency response for the engine shaft of FGM, obtained from ANSYS.