MODEL ANALYSIS ON PROPOSED COUPLING AND DESIGN OPTIMIZATION
The energy crisis has created a booming demand for large industrial engines that are efficient, powerful, and sturdy. But husky engines, especially diesels, can easily induce destructive vibrations in driven machinery such as generators, pumps, or marine propulsion systems. Large industrial engines tend to produce high firing pressures that produce impulsive turning forces on the crankshaft. These forces, in turn, can set up severe torsional vibration.
When these engines are connected to driven machines such as pumps, generators, or marine propulsion drives, there is a potential for damage from driven machine modes of vibration. The engine is often protected by a front end damper added to the crankshaft. However, the combined system of engine, coupling and load set up new modes of vibration as the engine masses swing against the load masses.
In this project a new coupling model is modeled and analysis is made in order to reduce the transmission of torsional vibration, which exists because of secondary forces acting at the crank shaft bearing or main bearing, from the engine to the load (generator or pump). The dimensions of the proposed coupling i.e. diameter of the circular cross section pin, thickness of rubber bush, pin length and the number of pins are optimized based on the induced torsional shear stress in the coupling for a given input speed and torque applied on the input shaft of the coupling. Modal analysis is done with the proposed optimized coupling and natural frequencies and mode shapes are plotted.
INTRODUCTION TO MODAL ANALYSIS :
Modal analysis is used to determine the vibration characteristics (natural frequencies and mode shapes) of a structure or a machine component while it is being designed. It also can be a starting point for another, more detailed, dynamic analysis, such as a transient dynamic analysis, a harmonic response analysis, or a spectrum analysis.
Overview of steps in modal analysis
The procedure for a modal analysis consists of four main steps:
1. Build the model.
2. Apply loads and obtain the solution.
3. Expand the modes.
4. Review the results.
Design and optimization of a coupling for reducing torsional vibration in rotating shafts. When rotating shafts are connected by means of a coupling for power transmission, the output shaft has a vibration due to the input vibration which is because of the secondary forces acting at the crankshaft bearing or main bearing. In I.C.engines, the effect of the reciprocating parts is to produce a shaking force and a shaking couple. Since the shaking force and a shaking couple vary in magnitude and direction during the engine cycle, therefore they cause very objectionable vibrations. We can reduce the shaking force and a shaking couple by adding appropriate balancing mass, but it is usually not practical to eliminate them completely. In other words, the reciprocating masses are only partially balanced.
Here the transmission of torsional vibration is reduced that exists in the engine through the new proposed coupling model from the I.C. engine to the driven load such as generators, pumps, marine propulsion systems. The aim of this project is to reduce the induced torsional vibration stresses in the output shaft than the input shaft of the proposed coupling.
DESCRIPTION OF THE COUPLING MODEL:
The output and input shafts are connected by means of square key. Mild-steel is considered for both the input and output shafts and the keys. The input flange has pins and the cross section of pin is considered here as circular. Over this pin a circular natural rubber bush is provided and its length is equal to the length of pin and its thickness varying from 3 to 4mm. The cast-iron material is chosen for both left and right flanges and pins and the natural rubber is for bush.
REQUIREMENTS OF COUPLINGS:
Â¢ It should be easy to connect or disconnect.
Â¢ It should transmit the full power from one shaft to the other shaft without losses.
Â¢ It should reduce the transmission of shock loads from one shaft to another shaft.
Â¢ It should have no projecting parts.
Â¢ Excellent kinematics properties.
Â¢ High torsional stiffness.
Â¢ Complete absorption of angular and parallel misalignment.
Figure 1. Proposed coupling model in front view
Figure 2 Proposed coupling model in 3-D, modeled in Pro E wildfire
The following parameters are considered in the design optimization of the coupling in order to reduce vibration transmission from the input shaft to the output shaft.
Â¢ Shape of the input flange pin
Â¢ Diameter of the input flange pin
Â¢ Length of the pin
Â¢ No of pins
Â¢ Bush material and thickness
Â¢ Thickness of the flange
Â¢ Using of bimetallic materials for flanges
Â¢ Engine AV1 water cooled diesel
Â¢ Power 3.7 k.w.
Â¢ Speed 1500 rpm
Â¢ Torque 23.55 N. m.
PROPOSED COUPLING DATA (A CASE)
Â¢ Material: Coupling, Pin (cast iron, = 14 to 20 MPa)
Shaft, Key (mild steel, = 40 to 50 MPa)
Bush (natural rubber)
Â¢ Shaft diameter, d = 20mm
Â¢ Outer diameter of hub , =2d = 40mm
Â¢ Length of hub, L=1.5d = 30mm
Â¢ Pitch circle of pins, =3d = 60mm
Â¢ Outer diameter of flange, =4d = 80mm
Â¢ Thickness of flange, t=0.5d = 10mm
Â¢ Length of shaft, L=3d = 60mm
Â¢ Pin diameter, = 5mm
Â¢ No of pins = 4
Â¢ Length of pin (circular) = 8.5mm
Â¢ Bush thickness = 4mm
Â¢ Diameter of hole = 13mm
Â¢ Square Key, t=w = 5mm
Â¢ Length of key, l=L=1.5d = 30mm
Material properties such as youngâ„¢s modulus, poisson ratio and density of cast-iron, mild steel and natural rubber are tabulated below, shown in table 1.
Table 1. Material properties considered for coupling
Cast-iron Mild steel Rubber
Youngâ„¢s modulus, (MPa)
Poisson ratio 0.23
Density, (kg/mm )
Fig.3 Free meshed model of the coupling, done in Ansys 8.0
The constrained degrees of freedom are Ux, Uy, Uz, ROTy and ROTz. So the coupling rotates in x-axis direction i.e. about the axis of shaft. The nodes at the left and right faces of shafts, the inner and outer surfaces of all bushes, the 8 mating surfaces of keys with the shaft and hub and the inner surface of hub that is mating with the outer surface of shaft are constrained and the model is shown in figure4.
Fig.4 Boundary conditions and loads applied model
The applied global angular velocity (inertia load) is 157 rad/sec and the torque applied on the input shaft is 23.55 N.mm.
SOLUTION AND POST PROCESSOR:
After specifying the above inputs, solving the problem and obtaining the nodal solution. From the nodal solution the maximum induced shear stress in the coupling is obtained.
RESULTS AND ANALYSIS:
The coupling having dimensions as pin diameter is 6 mm, bush thickness is 3.5mm, number of pins are 8, and the pin length is 8.5mm is taken as set1, and the induced maximum shear stress in the coupling for these dimensions is shown in figure 5.
Figure 5. Shows the location where the maximum shear stress occurring
Table 2. Shear stresses induced in the coupling for a pin length, L=8.5mm
Pin dia, d = 7mm
Pin dia, d = 6mm
Pin dia, d = 5mm
4 100.536 -95.94 66.697 -91.755 62.945 -44.1
5 85.363 -71.273 85.076 -87.08 96.568 -77.2
6 82.656 -311.48 76.197 -63.308 80.781 -85.976
7 86.979 -299.8 61.422 -64.4 68.8 -69.1
8 92.978 -263.9 34.456 -70.389 35.855 -28.9
Table 3. Shear stresses induced in the coupling for a pin length, L=7.5mm
Pin dia, d = 7mm
Pin dia, d = 6mm
Pin dia, d = 5mm
4 91.726 -88.8 91.89 -87.6 70.41 -75.2
5 91.286 -82.28 86.7 -70.4 132.06 -80.9
6 90.897 -81.8 97.88 -67.7 96.8 -78.8
7 81.459 -85.8 78.28 -71.32 92.021 -96.3
8 93.4 -280.7 88.7 -89.3 88.34 -73.4
Table 4. Shear stresses induced in the coupling for a pin length, L=6.5mm
Pin dia, d = 7mm
Pin dia, d = 6mm
Pin dia, d = 5mm
4 58.3 -57.5 86.04 -73.7 77.7 -80.35
5 95.4 -70.7 88.2 -74.3 121.2 -84.5
6 100.264 -66.7 117.29 -59.8 99.6 -86.2
7 86.36 -84.5 89.253 -85.7 86.218 -32.78
8 118.28 -89.9 87.032 -63.1 76.8 -86.5
Table.5.Natural frequencies of the coupling using Block lanczos, Subspace method
Mode order 1 2 3 4 5 6 7 8
Natural freq, Hz 202.4 203.4 213.5 234.1 234.2 248.7 250.8 255
Figure 6. For Pin diameter, d = 5mm, 4mm, = 13mm
Figure 7. For Pin diameter, d = 6mm, 3.5mm, = 13mm
Figure 8. For Pin diameter, d = 7mm, 3mm, = 13mm
Mode 1 at 202.4 HZ Mode 3 at 213.5 Hz
Mode 4 at 234.1 Hz Mode 6 at 248.7 Hz
Mode 7 at 250.8 Hz Mode 8 at 255 Hz
CONCLUSION AND FUTURE SCOPE OF WORK:
From the above graphs it is concluded that the first minimum shear stress, 34.4MPa is occurring in the coupling when the pin length is 8.5mm, no of pins are 8, pin diameter, d is 6mm, 3.5mm, and the is 13mm. The second minimum shear stress, 35.8MPa is occurring in the coupling when the pin length is 8.5mm, no of pins are 8, pin diameter is 5mm, 4mm, and the is 13mm and the third minimum shear stress, 58.3MPa is occurring when the pin length is 6.5mm, no of pins are 4, pin diameter, d is 7mm, 3mm, and the = 13mm.
From the modal analysis of coupling, the first 8 natural frequencies and their corresponding mode shapes are extracted by using block lanczos method. At the first two natural frequencies (202.4, 203.4 MPa) the system is in safe mode but at the remaining frequencies the system gets failure.
Analysis of coupling is done only for circular type of pin and it can be extended to square and hexagonal type of pin and further work can be carried out by using bimetallic materials to the coupling.
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