A Mathematical Model to Predict Crack Growth Rate along a Cantilever Beam under Forced Vibration

R Prasad, R Mishra, Verma
Management and Applied Sciences www.ijetmas.comJune 2017   unpublished
It was observed that most of the vibrating components used in real life fail unpredictably. Need of monitoring vibration, henceforth emerges. In many instances it is difficult to take any preventive action immediately on fault detection. In such cases it becomes very important to read vibration continuously to know crack growth rate, in order to know time in hand for needful action to be taken within safe zone. Cases in which crack growth rate is very high and critical, automated security
more » ... ated security system can be introduced. In present investigation efforts have been made to develop a mathematical model to calculate crack growth rate of a vibrating component. Six variables were considered to analyze the vibrating system and were correlated using Bukingham Pi Theorem. Three dimensionless groups were obtained and were found pure numbers determined by the specific values of the defined problem parameters. Velocity of vibration were observed and recorded at frequency (i.e., 60 Hz, 80 Hz, 100 Hz and 120 Hz) of vibration and at different positions (i.e., 50 mm, 100 mm, 150 mm, 200 mm and 250 mm from the free end) on the beam. Anticipation of behavior of vibrating cantilever beam was made simple by assuming crack growth rate of the order of 0.01 micrometer/hour. The values of crack growth rate as well as dimensionless groups were calculated. Specimens were heat treated in order to assure more prominent behavior of material during experimental work. The calculated value of crack growth rate at different experimental condition were plotted and compared to conclude.