Chapter 6. Dynamic. 6.1 Introduction. 6.2 Case Study/Engineering Application
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1 Chapter Dynamic. Introduction In the last chapters, we have discussed the static analysis of structures. Static analysis holds when the loads are slowly applied. When the loads are suddenly applied, or when the loads are of a variable nature, the mass and acceleration eects come into the picture. If a solid body, such as an engineering structure, is deformed elastically and suddenly released, it tends to vibrate about its equilibrium position. This periodic motion is due to the restoring strain energy in the element and is called free vibration. The number of cycles per unit time is called the frequency. The maximum displacement from the equilibrium position is the amplitude.. Case Study/Engineering Application Figure. and. below show a failed shaft of an air conditioning blower. The blower operating at rpm. Observation from Figure. at the colour and surface texture shows brittle fracture and ductile fracture. The arrow in Figure. shows torque direction. The deformation in the red circle suggest that after britte fracture,
2 it continues with ductile fracture. Early conclusion from observation suggest that the shaft failed because of fatigue and continues with plastic shear deformation due to the electric motor torque and rotational energy from the blower. To study the real factor contributing to the shaft failure, four analysis were carry out which are hardness test, ultrasonik analysis, static analysis and modal analysis. Figure : Figure :.. Ultrasonic Analysis Ultrasonic analysis was carried out to detect microcrack in the shaft. The measurement is done laterally along the shaft. Figure. below shows an example of the measurement result. All the result show that the rst peak is mm which prove that there are no microcrack present
3 Figure :.. Hardness Test This test is carried out to compare the strength of the failed shaft with the strength of the new shaft. The average hardness of the failed shaft is. and the hardness range is between. and.. However, for the new shaft, the hardness is between. and. with average value of.. From the experiment, the hardness of the failed shaft is lower than the new shaft... Static Analysis The purpose of this analysis is to determine the shaft deection due to the blower's weight.. The shaft's boundary condition is shown in Figure. below. Figure :
4 The load due to the blower's weight at element,, and is -. N while at element is - N. Input data for BEAM program: Result from BEAM program:
5 Figure. shows the deection of the shaft. Figure :
6 .. Modal Analysis The purpose of the modal analysis is to obtain the lowest eigenvalue and mode shape for the shaft with blower. This analysis will not consider unbalance condition. Input data for BeamKM program: PROGRAM BeamKM << for Stiffness and Mass Matrices Shaft Analysis of Air Conditioning Blower NN NE NM NDIM NEN NDN ND NL NMPC NODE# X-COORD..... ELEM# N N MAT# Mom_In Area.E+..E+..E+..E+..E+..E+..E+..E+..E+..E+..E+..E+..E+..E+..E+..E+. DOF# Displ. MAT# E Rho << Properties E and MassDensity.E+.E- SPRING SUPPORTS <DOF#= Exits this DOF# Spring Const LUMPED MASSES <DOF#= Exits this DOF# Lumped Mass.E+.E+.E+.E+.E- Result from BeamKM program as input for Jacobi program:
7 Banded Mass Matrix.E+ -.E+.E+ -.E+.E+ -.E+ -.E+ -.E+.E+ -.E E+ -.E+ -..E+ -.E E+ -.E E+ -.E+ -..E+.E+ -.E E+ -.E+ -...E+ -.E+ -...E+ -.E E+ -.E+ -...E+ -.E+ -...E+ -.E E+..E+ -.E+.E+ -.E+.E+ -.E+.E+ -. Banded Stiffness Matrix BandWidth NumDOF Shaft Analysis of Air Conditioning Blower Results from Program BeamKM Banded Mass Matrix.E+ -.E+.E+ -.E+.E+ -.E+ -.E+ -.E+.E+ -.E E+ -.E+ -..E+ -.E E+ -.E E+ -.E+ -..E+.E+ -.E E+ -.E+ -...E+ -.E+ -...E+ -.E E+ -.E+ -...E+ -.E+ -...E+ -.E E+..E+ -.E+.E+ -.E+.E+ -.E+.E+ -. Banded Stiffness Matrix BandWidth NumDOF Shaft Analysis of Air Conditioning Blower Results from Program BeamKM Result from Jacobi program:
8 -...E E-.E E E- -.E E E- -.E E E-.E E E-.E E E-.E E E- -.E Mode shape :. rpm Pesongan aci Nod
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