Cutting Processes I
Reading assignment: ~
Cutting processes I Cutting processes ~
Process planning, Cost, Quality, Rate and Flexibility
Modeling: Orthogonal cutting ~
Video, geometry, forces and power
Demonstration
20.1 – 20.3, 20.5
Cutting equipment/tools Design for Manufacturing: Cutting Process variation
Material removal processes Market research
Conceptual design
Design for manufacture
Unit mfg. processes
Mechanical removal processes ~
Milling
Turning
~
Grinding
Broaching
Shaping
Others ~
Thermal
Electrochemical
Chemical
Machining
Assembly
Injection molding Casting
Welding
Factory, systems & enterprise
Stamping
Bolting
Forging
Riveting
Others…
Soldering Others…
In general: Cost Expensive
Flexibility Complex shapes
Quality Depends
Rate Slow
1
Understanding what is going on
Process planning & cutting process
Key issues ~
How does cutting work?
~
Linking the Cost, Flexibility, Quality and Rate to process parameters
Today
Available methods to design process parameters: ~
Analytic
Numerical
Experimental
Steps we will take to get there
Next
Next2
Settings:
Materials:
Equipment:
- Speed - Tool orientation - Feed/depth
- Tool - Coating - Lubricant
- Tool geometry - Machine tool - Fixture
Inputs: - Material - Energy - Others
Outputs: - Parts - Chips - Energy - Others
Cutting Process
Basic cutting geometries z
Step I: Geometry & Motion
z Tool and material
x x Step II: Forces
Cutting, shearing, friction
y y
Specific energy Cutting, shearing, friction
Step III: Material & Power
Geometry & Motion → Forces → Material & Energy/Power
Orthogonal (2D)
Oblique (3D)
Orthogonal →
Provides insight for understanding
Oblique
Complex, diminishing returns
→
Geometry & Motion → Forces → Material & Energy/Power
2
Orthogonal cutting in a lathe
Orthogonal cutting zone geometry Important Angles
tc
- Shear angle: φ - Rake angle: α - Relief angle: ε
Chip Shear plane
− + Motion
α
w
Tool to
φ
ε
Work piece Geometry & Motion → Forces → Material & Energy/Power
Geometry & Motion → Forces → Material & Energy/Power
Velocity diagram of cutting zone Need velocities to obtain power estimates
CUTTING VIDEO Key issue: ~Motion ~Types ~How
and material flow
of chips
chip type relates to material
Geometry & Motion → Forces → Material & Energy/Power
90ο−φ+α
Vc α
t c
Vs
φ−α 90ο−α
Chip
φ
Vc
V V Vs Vc = = ⎛π ⎞ sin (φ ) ⎛π ⎞ sin⎜ − φ + α ⎟ sin⎜ − α ⎟ ⎝2 ⎠ ⎝2 ⎠
Tool V
φ
Vs
Vs Vc V = = cos(φ − α ) cos(α ) sin (φ )
Geometry & Motion → Forces → Material & Energy/Power
3
Cutting ratio, r
Analysis of shear strain
From mass conservation:
d
ρ ⋅ to ⋅ w ⋅ V = ρ ⋅ tc ⋅ w ⋅ Vc
a
φ
tc
From velocity diagram: V
cos(φ − α )
=
Vc to sin (φ ) = =r= V tc cos(φ − α )
d
α
− +
∆x bc + cd γ = = = cot (φ ) + tan (φ − α ) A ac
α
w
Cutting ratio:
φ−α
Chip
Vc sin (φ )
∆x
A
b
c
90−α
φ
Tool to
φ
b
a
What does this mean: Work piece
Geometry & Motion → Forces → Material & Energy/Power
~
φ↓=γ↑
Geometry & Motion → Forces → Material & Energy/Power
Cutting forces and power
Cutting forces
Why do we need to know the cutting force/power?
Forces:
~
Designing parts / machine tools (power and stiffness)
~
Part, machine and tool deflection
~
Trade offs in process planning, CFQR…
~
Equipment suitability
~
Others….
t
~
Thrust
Ft
~
Cutting
Fc
~
Friction
Ff
~
Tool normal
N
~
Shear
Fs
~
Chip normal
Ft
Chip −
+ Ff α
Fn
φ
Fs
c
Fc
N Tool
Fn Work piece Geometry & Motion → Forces → Material & Energy/Power
Geometry & Motion → Forces → Material & Energy/Power
4
Merchant’s diagram: Force relationships
Ft = Fc tan (β − α)
Shear plane forces: R Fs
Ff
Fs = Fc ⋅ cos(φ ) − Ft ⋅ sin (φ )
R
N
Ft
Fn = Fc ⋅ sin (φ ) + Ft ⋅ cos(φ )
Fc
Fn R
Fc
φ
β < α tool is pulled into part
~
β > α tool is pushed away
~
β = α no thrust force
Ft
β−α
Ff
α
Geometry & Motion → Forces → Material & Energy/Power
Merchant’s relationship
Magnitude of shear stress varies with angle of shear plane Fs Fc ⋅ cos(φ ) − Ft ⋅ sin (φ )
Merchant’s assumption:
Fc α β to w τs
35 0.61 225 20 0.35 40 0.70 0.015 0.075 70021
~
⎡ to ⎤⋅w ⎢⎣ sin (φ )⎥⎦ degrees radians lbf degrees radians degrees radians inches inches psi
τs =
Shear stress along shear plane
100000
Shear angle adjusts to maximize τs
Fs Fc ⋅ cos(φ ) − Ft ⋅ sin (φ ) = As ⎡ to ⎤⋅w ⎢⎣ sin (φ )⎥⎦
Ft = tan (β − α ) Fc
90000
⎤ ⎤ dτ s F ⎡ F F ⎡ F = c cos2 (φ ) − sin 2 (φ ) − t ⋅ 2 ⋅ sin (φ ) ⋅ cos(φ )⎥ = c ⎢cos(2φ ) − t ⋅ sin (2φ )⎥ dφ to ⋅ w ⎢⎣ Fc Fc ⎦ to ⋅ w ⎣ ⎦
80000 70000
τs [psi]
φmax
α
= tan (β ) N Typcially : 0.5 < µ < 2
µ=
φ and τs =
α
Use high α for thin cuts?
Geometry & Motion → Forces → Material & Energy/Power
As
β
Ff
β
Ff
α
τs =
R
N
N = Fc ⋅ cos(α ) − Ft ⋅ sin (α )
N
~
F f = Fc ⋅ sin (α ) + Ft ⋅ cos(α )
R φ
Fc
Tool-chip forces:
Fs
Fn Ft
Cutting and thrust forces
60000
⎡ cos(2φ ) Ft ⎤ dτ s cos(2φ ) sin (β − α ) − =0→⎢ − ⎥=0= dφ sin (2φ ) cos(β − α ) ⎣ sin (2φ ) Fc ⎦
50000 40000 30000 20000
cos(2φ ) ⋅ cos(β − α ) − sin (2φ ) ⋅ sin (β − α ) = 0 = cos(2φ + β − α )
10000 0 0
15
30
45
60
75
φ [degrees]
Geometry & Motion → Forces → Material & Energy/Power
90
2φ + β − α =
π 2
→φ =
π 4
−
β 2
+
α 2
Merchant’s relationship [radians]
Geometry & Motion → Forces → Material & Energy/Power
5
The use of Merchant’s relationship φ=
π 4
−
β 2
+
As rake angle ↓
Power/energy requirements What happens to energy you put in?
α
Merchant’s relationship [radians]
2 or as friction angle ↑
~
Shear angle ↓
~
Chip thickness ↑
~
Energy dissipation via shear ↑
~
Heat generation ↑
~
Temperature ↑
~
Shear
~
Friction
~
Others?
Chip
Tool
Work piece
Geometry & Motion → Forces → Material & Energy/Power
Specific energy (table from Kalpajkian) us =
Energy Volume certain conditions
Approximate Energy Requirements in Cutting Operations
Geometry & Motion → Forces → Material & Energy/Power
Power and specific energy Specific energies to consider: Shear us =
Fs ⋅ Vs w ⋅ to ⋅ V
us =
τ s Vs ⋅ sin (φ ) V
Assumed for 80 % motor efficiency J / mm3 Aluminum alloys
0.40 – 1.10
Copper alloys
1.40 – 3.30
Cast irons
1.60 – 5.50
Steels
2.70 – 9.30
Stainless steels
3.00 – 5.20
Geometry & Motion → Forces → Material & Energy/Power
+
Friction uf =
F f ⋅Vc
+
Others
w ⋅ to ⋅ V
Others
~20%
~5%
=
Total ut =
Fc ⋅ V w ⋅ to ⋅ V
us = τ s ⋅ γ
~75%
100%
Geometry & Motion → Forces → Material & Energy/Power
6
Cutting processes II
Cutting Processes II 20.6 – 20.8
~
21.1 – 21.6, 21.13
~
Process planning, Cost, Quality, Rate and Flexibility
Modeling: Orthogonal Cutting ~
Video, geometry, forces and power
Demonstration Equipment and tools
Reading assignment: ~
Cutting processes
Design for Manufacturing Process variation
Process planning & cutting process Market research
Conceptual design
Design for manufacture
Last
Unit mfg. processes Machining
Assembly
Injection molding Casting
Welding
Factory, systems & enterprise
Stamping
Bolting
Forging
Riveting
Others…
Inputs: - Material - Energy - Others
Today
Next
Settings:
Materials:
Equipment:
- Speed - Tool orientation - Feed/depth
- Tool - Coating - Lubricant
- Tool geometry - Machine tool - Fixture
Cutting Process
Outputs: - Parts - Chips - Energy - Others
Soldering Others…
7
Review: Cutting forces
Merchant’s minimum energy assumption
Forces:
t
Thrust
Ft
~
Cutting
Fc
~
Friction
Ff
~
Tool normal
N
~
Shear
Fs
~
Chip normal
Fn
Assumption: φ adjusts to value that minimizes cutting energy ~
Ft
Chip
−
c
+ Fc
=
N
=
P cut
Minimized
Fc ⋅V
Minimized
Constant
Fc is minimum when shear plane is plane of maximum shear stress
~
Example: Fc = minimum and τs = maximum for φ = 35o (for same α and β) τ s on shear plane if shear plane at φ
Fc dependance on of φ
1000
Tool
Fs
(E cut )
~
80000
900
70000
800
60000
700
Fc [lbf]
φ
∂ ∂t
Minimize
Ff
α
If Energy need to cut is minimized, Fc is minimized for a given V
Fn Work piece
600
τs [psi]
~
500 400 300
50000 40000 30000 20000
200
10000
100
0
0 0
15
30
45 60 φ [degrees]
75
90
0
15
30
45
60
Merchant’s relationship
Review: Power and specific energy
Merchant’s relationship:
Specific energies to consider:
π
β
α
~
φ=
~
It is an idealization, not always accurate, BUT the trend is consistent
4
−
2
+
Shear energy +
2
us =
Fs ⋅ Vs w ⋅ to ⋅ V
us =
τ s Vs ⋅ sin (φ ) V
Friction energy + uf =
75
90
φ [degrees]
Others
F f ⋅Vc w ⋅ to ⋅ V
Others
~20%
~5%
= Total energy ut =
Fc ⋅ V w ⋅ to ⋅ V
us = τ s ⋅ γ
~75%
100%
Chart adapted from: Metal Cutting Theory and Practice, Stephenson and Agapiou
8
Caution on modeling and reality Our assumptions: Plastically Deformed Chip −
Not deformed
+
α
Fs
φ
Vs
Vchip
~
Slow, orthogonal cutting
~
Material properties invariant
~
Constant temperature
~
Simple sliding friction
~
No strain hardening
Fc
Ff
V
Use our analysis for: ~
Trends & building intuition
~
Basis for detailed study
Chip types (source: Kalpajkian)
Chip types (source: Kalpajkian)
A) Continuous chip with narrow primary shear zone
D) Continuous chip with build up edge (BUE)
~
Ductile materials @ high speed
~
Bad for automation (use chip breakers)
~
E) Serrated chip:
B) Secondary shear zone at chip-tool interface ~
A
High plastic working and bad for automation
Secondary shear zone -> increased energy dissipation
~
Low thermal conductivity materials
F) Discontinuous chip (good chips) ~
B
D
Source: Kalpajkian
Low ductility materials and/or negative rake angles
E
F
Source: Kalpajkian
9
Example Given: ~
CUTTING DEMONSTRATION
to
w
ω
Plathe
Find: ~
Velocity at which lathe stalls
~
Cutting force
Cutting tool requirements Maintain:
TOOL MATERIALS AND TOOL WEAR
~
Hardness at operating temperature
~
Toughness
~
Low wear rate
Should be easy to repair/sharpen
Tool-part combination should be chemically inert ~
Diamond and steel….
10
Cutting tool characteristics
Cutting tools: Geometry
Why do we worry about tool wear? ~
Tool can cease to cut
Dimensional accuracy
~
Surface finish
Cutting force/power
~
Cost
Flexibility
Rate
Quality
Is a function of many parameters ~
Coolant
Geometry
Lubricant
Process parameters
Cutting tools: Geometry
Tooling hardness and temperature Things to note: ~
Performance ↑
~
Rate of change ↓
time
Source: Kalpajkian
Source: Kalpajkian
11
Temperature and wear
Tool wear up close
Diffusion is thought to dominate crater wear
Crater wear affected by same parameters as flank wear
This is a function of temperature
In addition: ~
Material affinity and temperature
Flank wear
Source: Kalpajkian
Depth of cut
Taylor’s wear relationship (flank wear)
Defining tool failure
Relationship between tool life and cutting speed
Wear “snowballs” to set limit
~
Use to set optimum cutting speed for CFRQ
~
Represents a given wear condition
~
Define wear condition for failure
Crater wear
Source: Kalpajkian
Force/power increase to set limit
Surface finish becomes unacceptable
Wear land size for given process
Source: Kalpajkian
12
Taylor’s wear relationship (flank wear)
Taylor’s tool life curves (Experimental)
C = constant & n = exponent (from experimental data)
Coefficient n varies from:
v ⋅ tn = C
v = cutting velocity ( fpm )
t = time to failure (min)
Steels
Ceramics
0.1
0.7
Source: Kalpajkian
v ⋅ tn = C v = cutting velocity ( fpm ) t = time to failure (min)
As n ↑, wear is less sensitive to cutting speed Source: Kalpajkian
Preventing tool failure with coatings Tools may be coated for many reasons: ~
Chemically inert
~
Temperature resistance
~
Surface energy/specific energy
~
Low friction
Common coatings ~
Titanium nitride (TiN)
~
Cubic boron nitride (cBN)
~
Multi-phase coatings
Multi-phase coating Layers ½ – 10 µm thick
CUTTING PROCESS DFM
13
DFM for cutting: Surface roughness
Finish by process (source = machinery handbook)
Surface roughness: ~
Definition
Depends on : ~
Mass removed
~
Size of tool
~
Cutter
~
Speed
DFM for cutting: Part geometry
DFM for cutting: Ala features
Thin sections and tubes (vibration)
Use common dimensions / parts / shapes / sizes
Overhanging parts
~
Proper tolerance
~
Use common/important datums
~
Standard features (i.e. don’t use octagon shaped holes)
Inclined planes and drilling….
14
DFM for cutting: Ala tooling
DFM for cutting: Ala equipment
Avoid deep pockets and holes
Beware of fixturing needs ~
Minimize number of fixture cycles
~
Design an interface for part-fixture
Design should include real shape tool makes ~
Tapped holes
~
Pocket corners
Machine and tool access to create features
15
