Analytical Expressions for Chip Area in Three-insert Rotary Boring Operation

Compacted-graphite iron (CGI) has been promoted as the material of choice for diesel engines as popular alternatives to conventional gray cast iron. CGI has higher strength and elastic modulus than gray iron but retains the damping properties, thermal conductivity, and castability of gray iron. But for all the advantages of higher strength and wear resistance offered by CGI, it is precisely these properties that make it difficult to machine. Rotary-insert tooling is a patented boring tool that shows promise for reducing the machine horsepower needed for cylinder boring operations. Holes with large diameters are usually bored with boring heads having multiple inserts. The boring heads are used as alternatives to single point boring bars. The diameter of the boring head is equal to the finish diameter of the hole, and inserts are symmetrically distributed around the circumference of the boring head in order to provide force cancellations in the plane perpendicular to hole axis. The entire hole can be bored using larger feed rates due to the presence of multiple inserts on the boring head. Atabey et al. presented a mathematical model for the cutting force system as a function of tool geometry, chip load, cutting edge contact length and process parameters (such as feed rate, cutting speed, radial depth of cut) based on the physics, kinematics and mechanics of the boring process with 2 inserts. Three cutting force components, tangential, radial, and feed forces are expressed as functions of chip load and chip-cutting edge contact length and cutting coefficients. These authors studied the effect of boring heads with radial and axial run outs and also the effect of deviation of the boring head from the hole center. Approximate expressions were developed for chip area removed by each insert. In the present paper the authors their work to presenting analytical expressions for the exact chip area cut by each insert in a boring head with 3 inserts in a boring operation. These areas of chip cut by each insert can be used in other expressions for computing the cutting forces on each insert. The three inserts are placed symmetrically at 120-deg apart. Two inserts are offset in feed and radial direction and these in turn affect the area of chip cut by each insert. These offsets can be manipulated for equating the chip load on each insert. The offsets may be also be suitably manipulated to use the first insert for rough cut with largest chip load followed by the second insert with medium chip load for semi-finish cut and the third insert taking the minimum chip load to function as the finish cut. The authors have made these propositions very simple by providing exact analytical expressions. These expressions will be very useful in precise boring operations on a micro or a nanoscale where accuracy in computation of the chip area is paramount . Since computation of area in such a geometric configuration is a very tedious process only selected expressions will be presented in the paper.