σ=F/A

where F = applied force

A= initial (engineering stress/safety calcs) or instantaneous (true stress) cross sectional area

ε=ln(L/L₀)

Always use true strain

Yield Strength (Y)

Tensile Strength (UTS)

Modulus of Elasticity (E)

σ=Kεⁿ

Only use true stress and strain

σ=Eε

for elastic region

flow curve K=Y and n=0

metals above recrystallization temperature

K>Y and n>0

most metals

τ=F/A=T/2πr²t

F=applied force

A=deflection area

T=applied torque

r=tube radius

t=tube wall thickness

γ=δ/b=Rα/L

where δ=deflection

b=deflection distance

α=angular deflection

L=gauge length of tube

τ=Gγ

where G= Shear modulus

τ=Sγⁿ

where S=shear strength

n=strain hardening exponent

S=0.7TS

where TS is tensile strength

HB=2F/πDb(Db-√D_b²-D_i²)

where F=indentation load

D_b=diameter of ball

D_i=diameter of indentation

TS=K_h(HB)

where K_h=3.45 for MPa or 500 for psi

TS decreases

Y decreases

ductility increases

no longer strain hardens

new grains form free of strain

T_r=0.5T_m (IN KELVIN)

Resitance to flow characteristic of given fluid

A meausure of the internal friction when velocity graidents are present in the fluid

Liquid Based

Solid Based

Powder Based

T_i=A_i/(vD)+T_D

where T_i = Time to complete layer i

A_i= area of layer i

v=average scanning speed of laser beam at surface

D=diameter of spot size

T_d=delay time between layers

fewer support structures than other methods

highest resolution surface features

must cut away support structures

messy to clean

potential for high resolution

inexpensive

overhanging features require many support structures

very slow at high resolution

difficult to achieve flat surface

Prototypes

Pattern for casting mold

Assembly testing

Parts with intricate internal geometries

Medical one of a kind parts

M_RR=vfd

where v= cutting speed

f=feed

d=depth of cut

Roughing:remove large amounts of material

-large feeds and depths

-slow cutting speeds

Finishing:final dimenions, tolrances and finish

-small feeds and depths

-fast cutting speeds

r=t₀/t_c

always less than 1

Shear plane angle (chip formation)

tanφ=rcosα/(1-rsinα)

r=chip thickness raio

α=rake angle

Work material: brittle

Cutting speed: slow

Feed and depth of cut: large

Tool-chip friction: large

Work material: ductile

Cutting speed: fast

Feed and depth of cut: small

Tool-chip friction: low

sharp cutting edge

Work material:ductile

Cutting speed:low-med

Tool-chip friction: large, causing portinos of chip to adhere to rake face

Semi-continuous sawtooth appearance

Alternating high shear strain and low shear strain

Difficult to machine metals at high cutting speeds

μ=F/N=tanβ

where β=friction angle

S=F_s/A_s

where S=shear strength

A_s=t₀w/sinφ

where t₀=cut depth

w=cutting edge width

φ=shear plane angle

φ=45+α/2+β/2

in degrees

increase rake angle α

decrease friction angle β

Reduced tool life

Hazardous hot chips

Inaccuracies in part dimensions due to thermal expansion

ΔT=(0.4U/ρC)(vt₀/K)^0.333=(0.4F_c/ρCfd)(vt₀/K)^0.333

where T=temperature at tool chip interface

U=specific energy

v=cutting speed

t₀=chip thickness before cut

ρC=volumetric specific heat of work material

K=thermal diffusivity of work material

M_RR=πD²Nf/4

where D=drill diameter

N=spindle speed(rev/min)

f=feed (length/rev)

d=depth of cut

M_RR=Wdv

where W=width of cut

d=depth of cut

v=feed rate

1.Excessive or dynamic cutting force, leading to brittle fracture (fracture failure)

2. Cutting temperature is too high for tool material (temperature failure)

3. Preferred wearing method (gradual wear)

vTⁿ=C

where v=cutting speed

T=tool life

n is the slope of log-log plot

C is the intercept on the speed axis at 1 minute tool life

change in sound emitted

chips become ribbon like, stringy

degradation of surface finish

increased power required to cut

Improve cutting performance

-improve chip removal

-reduce cutting temp

-improve surface finish

Types:

Coolant (generally water-based)

-more effective at very high cutting speeds

Lubricant (generally oil based)

-more effective at low cutting speeds

R_i=f²/32NR

where f=feed

NR=nose radius

1. Add stiffness and or damping

2. Operate at speeds that avoud natural frequency of machine/tool system

3. Reduce feed (sometimes depth)

4. Change cutter design

5. Use Cutting fluid

T_c=T_h+T_m+T_t/n_p

where T_h=handling time per part

T_m=machining time per part

T_t/n_p=tool change time per part, where n_p=number of pieces cut in one tool life (round down)

Cc=C_oT_h+C_oT_m+C_oT_t/n_p+C_t/n_p

where C_oT_h=Cost of part handling time (C_o=cost rate for operator and machine)

C_oT_m=cost of machining time

C_oT_t/n_p=cost of tool change time

C_t/n_p=tooling cost (C_t=cost percutting edge)