Investigation of the machinability of commercially pure titanium in ultrasonic machining using graph theory and matrix method
Abstract
Any type of machining operation is well influenced by the machinability of work material under processing. This work proposes a graph theory and matrix method based technique for the assessment of machinability of titanium in ultrasonic machining. Identification of various machining attributes along with their relative importance has been considered and analyzed by developing a mathematical function by employing graph theory and matrix method. An attribute digraph is developed, which provides a visual illustration of considered attributes with their relative interactions. This digraph is further represented by using matrix expression. A permanent machinability index for all the experimental runs is also obtained from matrix form demonstration based on attribute digraph. The combination of all the attributes for any machining operation makes this method quite versatile. The results reveal that an experimental run having the combination consisting tool material of titanium, grit size of 500, and power supply of 300 W yields optimized results for machinability.
References
Dvivedi, A. & Kumar, P. 2007. Surface quality evaluation in ultrasonic drilling through the Taguchi technique. International Journal of Advanced Manufacturing Technology 34:131-140.
Gauri, S. K., Chakravorty, R. & Chakravorty, S. 2011. Optimization of correlated multiple responses of ultrasonic machining (USM) process. International Journal of Advanced Manufacturing Technology 53:1115-1127.
Jadoun, R. S., Kumar, P. & Mishra, B. K. 2009. Taguchi’s optimization of process parameters for production accuracy in ultrasonic drilling of engineering ceramics. Production Engineering Research and Development 3:243-253.
Jadoun, R. S., Kumar, P., Mishra, B. K. & Mehta, R. C. S. 2006. Optimization of process parameters for ultrasonic drilling (USD) of advanced engineering ceramics using Taguchi approach. Engineering Optimization, 38(7):771-787.
Jangra, K., Grover, S., Chan, F. T. S. & Aggrawal, A. 2011. Digraph and matrix method to evaluate the machinability of tungsten carbide composite with wire EDM. International Journal of Advanced Manufacturing Technology 56:959-974.
Kataria, R., Kumar, J. & Pabla, B. S. 2014. Experimental Investigation into the Hole Quality in Ultrasonic Machining of WC-Co Composite, Materials and Manufacturing Processes, Article in press, http://dx.doi.org/10.1080/10426914.2014.995052.
Kumar, J. & Khamba, J. S. 2008. An Experimental Study on Ultrasonic Machining of Pure Titanium Using Designed Experiments. Journal of the Brazilian Society of Mechanical Sciences and Engineering 30(3):231-238.
Kumar, J. & Khamba, J. S. 2009. An investigation into the effect of work material properties, tool geometry and abrasive properties on performance indices of ultrasonic machining. International Journal Machining and Machinability of Materials 5(2/3):347-366.
Kumar, J. & Khamba, J. S. 2010. Modeling the material removal rate in ultrasonic machining of titanium using dimensional analysis. International Journal of Advanced Manufacturing Technology 48:103-119.
Kumar, J. & Khamba, J. S. 2010. Multi-response optimization in ultrasonic machining of titanium using Taguchi's approach and utility concept. International Journal of Manufacturing Research 5(2):139-159.
Kumar, J. 2013. Ultrasonic machining-A comprehensive review. Machining Science and Technology: An International Journal 17(3):325-379.
Kumar, J., Khamba, J. S. & Mohapatra, S. K. 2008. An investigation into the machining characteristics of titanium using ultrasonic machining. International Journal Machining and Machinability of Materials 3(1/2):143-161.
Kumar, V. & Khamba, J. S. 2008. Statistical Analysis of Experimental Parameters in Ultrasonic Machining of Tungsten Carbide Using the Taguchi Approach. Journal of the American Ceramic Society 91(1):92-96.
Kumar, V. & Khamba, J. S. 2009. Parametric optimization of ultrasonic machining of co-based super alloy using the Taguchi multi-objective approach. Production Engineering Research and Development 3:417-425.
Lalchhuanvela, H., Doloi, B. & Battacharyya, B. 2012. Enabling and Understanding Ultrasonic Machining of Engineering Ceramics Using Parametric Analysis. Materials and Manufacturing Processes 27:443-448.
Paramasivam, V. & Senthil, V. 2009. Analysis and evaluation of product design through design aspects using digraph and matrix approach. International Journal on Interactive Design and Manufacturing 3:13-23.
Rao, R. V. & Gandhi, O. P. 2002. Digraph and matrix methods for the machinability evaluation of work materials. International Journal of Machine Tools & Manufacture 42:321-330.
Rao, R. V. & Padmanabhan, K. K. 2006. Selection, identification and comparison of industrial robots using digraph and matrix methods. Robotics and Computer-Integrated manufacturing 22:373-383.
Rao, R. V. 2007. Decision making in manufacturing environment. Springer Publications.
Rao. R. V. & Padmanabhan, K. K. 2007. Rapid prototyping process selection using graph theory and matrix approach. Journal of Materials Processing Technology 194:81-88.
Singh, R. & Khamba, J. S. 2007. Investigation for ultrasonic machining of titanium and its alloys. Journal of Materials Processing Technology 183:363-367.
Singh, R. & Khamba, J. S. 2008. Comparison of slurry effect on machining characteristics of titanium in ultrasonic drilling. Journal of Materials Processing Technology 197(1-3):200-205.
