Useful Formulas:

Reselience= “total energy”

 “specific energy”

In simple tension:

Representable stress:

At instability:

Total work:

Plastic work:

Rate sensitivity:

Homologous temperature: , “in Kelvin”

Heat:

Temperature rise:

, “intermediate”

Energy consumed:

  • Tresca criterion:
  • Hencky-Mises criterion:

Important Definitions, Relationships & Types:

  • Definitions:

Resilience: a mechanical property which indicates the ability of the material to absorb energy in the elastic region.

Ductility: a mechanical property which indicates the ability of the material to have some plastic deformation before fracture.

Toughness: a mechanical property which indicates the ability of the material to absorb energy before fracture.

Hardness: a mechanical property which indicates the ability of the material to resist scratching, indentation, penetration & perforation.

Joint strength: the force at the interface between the two contacted surfaces.

Formability: the ability of the material to be formed within the accepted dimensional accuracy.

Machinability: the ability of the material to be machined under certain cutting conditions within an accepted surface quality, measured by dimensional accuracy & surface roughness.

Machinability rating: a cutting speed (feet/m) if the material is worked on, it gives a tool life of 60 min.

Diffusivity: dissipation of heat within the particles of the material itself.

Conductivity: dissipation of heat between the whole body & the surrounding environment.

  • Types:

Manufacturing Processes:

  1. Quasi-Static: : all presses : sec – hour
  2. Intermediate::all hammers: mille sec.
  3. Impact(Dynamic): : all MRP: micro sec.

Types of Chips:

  1. Continuous: ductile materials, high cutting speed, high 
  2. Built-up Edge: high n. To get rid of it: increase cutting speed, increase , decrease d, decrease rt, use cutting fluid.
  3. Serrated: low thermal conductivity.
  4. Discontinuous: brittle materials, very high cutting speed, very high hardness, very high d, low , no cutting fluid.
  5. Curly: extremely ductile materials.

Tool Failure:

  1. Turning: gradual wear, fracture, fatigue(thermal, normal), crator formation.
  2. Milling: gradual wear, fatigue(thermal, normal).
  3. Grinding: gradual wear, break-up of grains, brake-up bracelets, overall wear (G).

Rake Angle :

  1. Diamond : zero.
  2. Cast Steel : (30-40)o.
  3. High Speed Steel : (10-15) o.
  • Relationships:

 Temperature : yield , flow , fracture ,  n .

 :  Temperature.

 Phydrostatic :  ductility.

 Brinnel Hardness Number :  Tadh.

 Hardness :  machinability.

 Strength :  machinability.

Tool’s Material Components:

Carbon (C) :  Hardness ,  Heat resistance.

Manganese (Mn) :  Brittleness ,  Toughness.

Silicon (Si) & Vanadium (V) :  Wear resistance.

Chromium (Cr), Tungsten (W) :  Hot hardness.

Cobalt (Co):  Wear resistance,  Crator resistance,  Hardness.

Titanium Carbide & Tantalum Carbide (TiC & TaC):

 Crator resistance,  Impact resistance,  Hardness,  Tadh.

Milling & Turning:

Surface quality: in turning worse than in milling.

d : in turning larger than in milling.

f : in turning larger than in milling.

: in tuning smaller than in milling.

ut : in turning smaller than in milling.

: in turning smaller than in milling.

Turning:

Merchant’s Circle

Coefficient of friction:

Cutting ratio:

Comparison ratio:

Cutting speed:

Friction speed:

Shear stress:

Shear strain:

Shear specific energy =

Time =

Efficiency:

Material removal rate:

Total unit power consumption = specific energy =

Total unit power consumption:

Shear unit power consumption:

Friction unit power consumption:

Power consumed in shearing: Fs* Vs

Power consumed in friction: F * Vc

Average temperature:

Max. temperature:

Specific total power:

Total power:

For HSS:

:     FH FV us ut uf 

 For Steel with carbide center:

+ :     FH FV us ut uf  V

- :     FH FV us ut uf  V

Milling:

Approaching length:

Chip thickness:

Total feed= Workpiece speed = Table speed =

Height of ridges:

Total motor efficiency:

Material removal rate:

Cutting power:

Cutting time: “Face milling”

“Slab milling”

Milling

  • End (Vertical, Face):
  1. Axis of the cutter is perpendicular to the workpiece.
  • Slab (Horizontal):
  1. Axis of the cutter is parallel to workpiece.
  2. There are two types:

a)Up Milling:

  1. The workpiece & the cutter move in opposite directions.
  2. Thickness increases from zero to maximum.
  3. Used in case hardening & oxides.
  4. Fv is upward.

b)Down Milling:

  1. The workpiece & the cutter move in the same direction.
  2. Thickness decreases from maximum value to zero.
  3. Used in homogenous materials
  4. Fv is downward.

Horizontal Milling Vertical Milling

Grinding:

  • There are 3 types of grinding: Surface, Cylindrical, Off-Hand.
  • Chip thickness increases from zero to its maximum value.
  • Surface quality decreases when G increases.

Grinding ratio:

Approaching length:

Ratio of chip width over average chip thickness:

Material removal rate:

Chip thickness:

Velocity:

Temperature rise:

In external grinding: , D < Dw

In internal grinding: , D > Dw