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:
- Quasi-Static: : all presses : sec – hour
- Intermediate::all hammers: mille sec.
- Impact(Dynamic): : all MRP: micro sec.
Types of Chips:
- Continuous: ductile materials, high cutting speed, high
- Built-up Edge: high n. To get rid of it: increase cutting speed, increase , decrease d, decrease rt, use cutting fluid.
- Serrated: low thermal conductivity.
- Discontinuous: brittle materials, very high cutting speed, very high hardness, very high d, low , no cutting fluid.
- Curly: extremely ductile materials.
Tool Failure:
- Turning: gradual wear, fracture, fatigue(thermal, normal), crator formation.
- Milling: gradual wear, fatigue(thermal, normal).
- Grinding: gradual wear, break-up of grains, brake-up bracelets, overall wear (G).
Rake Angle :
- Diamond : zero.
- Cast Steel : (30-40)o.
- 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):
- Axis of the cutter is perpendicular to the workpiece.
- Slab (Horizontal):
- Axis of the cutter is parallel to workpiece.
- There are two types:
a)Up Milling:
- The workpiece & the cutter move in opposite directions.
- Thickness increases from zero to maximum.
- Used in case hardening & oxides.
- Fv is upward.
b)Down Milling:
- The workpiece & the cutter move in the same direction.
- Thickness decreases from maximum value to zero.
- Used in homogenous materials
- 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