ME 338

Manufacturing Processes II

HW#2 Instructor: Ramesh Singh Assigned Date: August 28, 2015

Due Date: September 4, 2015

1. A single point cutting tool has the ASA designation as 10-8-8-6-15-30-1(mm). The tool designer

intends to design the tool holder which may change the side cutting edge angle of tool by 50

a. Compute and plot the variation of side and back rake angles of the tool due to these design

variations.

b. Comment on the trends of variation of side and back rake angles and their effect on the

machining process.

2. An orthogonal free cutting tool is ground to have rake and clearance angles of 100 and 200

respectively. Calculate the limiting inclination angle at which the tool can be set for oblique

machining, so that the clearance angle does not drop below 180. Calculate the effective rake angle

in the limiting condition.

3. You are grinding a steel, which has a specific grinding energy (u) of 25 W-s/mm3. The grinding wheel rotates at 3000 rpm, has a diameter (D) of 120 mm, thickness (b) of 20

mm, and 5 grains per mm2

(c). The motor has a power of 2 kW. The work piece moves

(v) at 1.5 m/min. The chip thickness ratio (r) is 10.

a) Determine the grinding force and force per grain. b) Determine the temperature (K2 is 0.2

oK-mm/N). Room temperature is 20

oC.

c) Find the minimum strength in the binder to prevent uprooting of the grain. Let the grain be a SiC grain modeled as a continuously varying circular beam as shown in Fig. 1. Assume

the force/grain is acting as a linearly varying load. Use cantilever beam theory to find the stress as a

function of x ((x)) and the magnitude and location of maximum stress. Are these stresses sufficient to fail the grain? What will be the mode of failure?

Assume sintered -SiC has a strength of 4.6 GPa.

Fig. 1. SiC grain geometry

4. Machining Economics d) Derive the optimal cutting velocity and tool life for lowest unit cost. e) Compare the optimal cutting velocity and tool life for maximum profit and maximum

production rate for the following conditions.

f) Find the costs for maximum production rate and minimum cost. Given:

u = uo + um + ut = kotp + (ko + km) tm + [kt + kotc] (tm/T). Machining time, tm, is given by f V

,

where is a constant, f is the feed and V is the cutting velocity. The maximum spindle power available is 5 kW and the specific cutting energy is 4 J/mm

3. Note that r is the tool edge radius.

Taylor tool life equation p qT CV f , V (m/min), f(mm/rev), T(min)

p=3; q=2; and C=3.2 x 106

Machining (turning) parameters Depth of cut, d = 1.00 mm Feed, f =? Edge radius =5 mm

Maximum allowable Ra = 1 m Workpiece geometry

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

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

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

Using the modified Taylors tool life equation, first find the expression for cutting velocity and tool life for lowest cost and use the data to get numerical estimates for optimal velocity and cost.

5. Please refer to the attached paper (HW2_paper). Start from Eq. (1) and arrive at Eq. (7). Derive Eqs. (23) and (24). Plot and explain Fig. 1 in the paper.