2. An internal slot, its shape is shown in Figure 2 below, is machined through a cylindrical workpiece using a broaching bar with tungsten carbide cutting edges. It can be assumed that a sufficiently large hole has been previously machined to allow the broach to be pulled through and thus to produce the internal slot right through the workpiece. Each tooth of the broach has a rake angle of a degrees and the depth of cut per tooth is d mm. Assume that all the teeth are cutting under exactly the same conditions and that cutting is occurring all around the slot periphery. The process can be regarded as a two-dimensional one and that the Merchant minimum energy principle applies. The yield shear stress of the workpiece material is 230 MPa. The coefficient of friction at the rake face is 1.1. (a) If the power available from the driving motor, after mechanical losses have been taken into account, is P kW and the cutting speed is 20 m/min, determine the maximum number of teeth that can be cutting at the same time through the workpiece. (12 marks) (b) Assuming that as the broach is pulled right through the workpiece, each tooth is in contact with the job (i.c. cutting) for f minutes, calculate how many workpieces can be machined before the cutting edges have to be replaced. For this tool, Taylor's Tool Life equation is: 72-50, where Vis the cutting speed (in m/min) and 7 is the tool-life (in minutes). Use the following formulae to determine the values of the parameters (units in brackets): a = 2 x b d = (5+b)/100 P-8.0+3xa = (deg) (mm) (kW) f [10 (5xb)]/10 (min) (8 marks) Note: alast digit of your student ID b second last digit of your ID Search W 5-a (4+b) Rad. Cross-section of a broach showing cutting teeth in contact Cross-section of finished workpiece (dimensions in mm) Figure 2