ME 338 Manufacturing Processes II

HW#1 Instructor: Ramesh Singh Assigned Date: Sept 6, 2009 Due Date: Sept 11, 2009

1. Assume the tool-workpiece contact to be a parallel spring damper system as shown in Fig. 1.

Fig. 1. Tool-workpiece spring damper system

+ + = Viscous damping ratio, =

a) For free vibrations (F(t)=0), solve the differential equation and plot solutions for critically damped(=1) and underdamped(

3. Machining Economics a) Derive the optimal cutting vb) Find optimal cutting velocity and tool life for maximum profit

rate for the following conditions. Given:

Taylor tool life equation Machining (turning) parameters Depth of cut, d = 1.00 mm Feed, f = 0.2 mm/rev Workpiece geometry

Workpiece diameter, Workpiece length,

Time parameters Setup time, Tool replacement time,

Cost parameters Machine utilization rate, Machining overhead, Tool cost,

Fig. 2. SiC grain geometry.

Derive the optimal cutting velocity and tool life for lowest unit cost. elocity and tool life for maximum profit and maximum production

rate for the following conditions.

Taylor tool life equation VT0.3 = 400, V (m/min) Machining (turning) parameters

= 1.00 mm = 0.2 mm/rev

Workpiece geometry Workpiece diameter, D = 50 mm Workpiece length, L = 200 mm

Setup time, tp = 0.80 min/pt Tool replacement time, tc = 1.5 min/edge

Machine utilization rate, ko = 0.50 $/min Machining overhead, km = 0.05 $/min Tool cost, kt = 2.50 $/edge

and maximum production