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Titanium and its alloys are attractive for many engineering applications due to
their superior properties (such as chemical inertness, high strength, and stiffness at
elevated temperatures, high strength to weight ratio, corrosion resistance, and
oxidation resistance). However, these properties also make it difficult to shape and
machine titanium and its alloys into a precise size and shape. As a result, their
widespread application has been hindered by the high cost of machining with the
current technology. Therefore, there has been a crucial need for reliable and
cost-effective machining processes for titanium and its alloys. One of the cost-effective
machining methods for titanium and its alloys is Ultrasonic Machining (USM), which is able
to machine materials irrespective of their thermal-conductive and elastic
nature. Although the Material Removal Rate (MRR) of USM is low, it has been widely
used because the process does not thermally damage or introduce stresses in the
workpiece. The schematic of the USM process is shown in Figure 1. Most of the research in
the past has been concentrated on the machining of hard and brittle materials
using USM, but very little effort has been put in to explore the machining capability
of USM for tough materials like titanium. Singh and Khamba (2004) outlined
machining characteristics comparison of titanium alloys in ultrasonic machining. The main
emphasis was on comparing workpiece material properties which affect MRR while
machining with USM.
For the stationary USM of titanium and its alloys, an approach to model the
MRR was proposed and applied for predicting the MRR for the case of titanium and
its alloys as a macro model (Benedict, 1987). The model is mechanistic in the sense
that parameters can be observed experimentally from a few experiments for a
particular material and then used in the prediction of MRR over a wide range of
process parameters. This was demonstrated for titanium and its alloys, where very
good predictions were obtained using an estimate of multi-parameters at a time. In
this model, the effects of six process parameters (tool material, power rating, slurry
type, slurry temperature, slurry concentration and slurry grit size) were revealed. Table
1 shows the various input and output parameters used in the experimental study
and Table 2 shows the chemical analysis of TITAN15 (ASTM Gr. 2), pure titanium
and TITAN31 (ASTM Gr. 5) titanium alloy work material selected for the study.
The relationships were studied by considering the interaction between these
variables. These relationships agree well with the trends observed by experimental
observations made otherwise (Buckingham, 1915; Farago, 1980; Kumar, 1987; Clifton et al., 1993; and Ghosh and Mallik, 1996). The study under consideration deals primarily
with obtaining optimum system configuration in terms of response parameters
with minimum expenditure of experimental resources. The parameters that influence
the output were identified and divided into two classes: noise factors and control
factors. Figure 2 shows the details of noise factors and signal factors for the `process
diagram', representing machining conditions of titanium and its alloys. The best settings
of control factors have been determined through experiments, as shown in Table 3,
as geometric model (Benedict, 1987). Now based upon the geometric
model, Buckingham-p approach has been applied to study the relationships between
MRR and controllable machining parameters. |
