MATERIAL REMOVAL PROCESSES Theory of Metal Machining 1

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MATERIAL REMOVAL PROCESSES Theory of Metal Machining 1. Overview 2. Theory of Chip Formation 3. Force Relationships 4. Power and Energy Relationship 5. Cutting Temperature 1 Introduction

• Everyday Experience: Scraping the ice from your windshield – Edge angle of the ice scraper – Force required depending on the characteristics of ice • Incentives: Making a ceramic vase out of clay – Shaping – Removal of excess materials - ‘machining’ • Powder Metal or Cast – Exact dimension – Tolerance & Surface Finish

2 Classification Turning and Related Operations Drilling and Related Conventional Operations Machining Milling Other Machining Operations Material Removal Grinding Processes Abrasive Processes Processes Other Abrasive Processes Mechanical Energy Processes Electrochemical Nontraditional Processes machining Thermal Energy Processes Chemical Machining 3 Material Removal Processes

A family of shaping operations through which undesired excess material is removed from a starting workpart so the remaining part become closer to the desired shape • Categories: – Machining – material removal by a sharp cutting tool, e.g., turning, milling, drilling – Abrasive processes – material removal by hard, abrasive particles, e.g., grinding – Nontraditional processes - various energy forms other than sharp cutting tool to remove material

4 Machining

• A shearing process in which excess materials is removed by cutting tools. – A variety of work materials – ‘Repeatable’ regular geometries – Close tolerance (<0.025μm) – Smooth surface finish (0.4μm) – Waste, Expensive: Cost and Time – Other processes such as casting, forging, and bar drawing create the general shape – Machining provides the final shape, dimensions, finish, and special geometric details

5 1. Overview Work • Types New Surface Speed motion Feed Motion – Turning - Lathe (tool) (work) Speed motion – Drilling – Drill press Cutting tool (Tool) – Milling – Milling Machine Feed Motion Drill bit • Peripheral (tool) • Face • Cutting Tool Work Speed motion Speed motion Milling Cutter Milling Cutter New Surface New Surface

Feed Motion (work) Feed Motion (work) Work material Work Peripheral (End) Milling Face (Slab) Milling 6 Cutting condition

• Relative motion between tool and work • Cutting conditions – Cutting speed, v (m/s) – Surface speed – Feed f (m): the lateral distance traveled by the tool during one revolution. – Depth of cut d (m) • Material Removal Rate: = dfvMRR – Roughing - removes large amounts of material, at high feeds and depths, low speeds – Finishing - Achieves final dimensions, tolerances, and finish, Low feeds and depths, high cutting speeds 7 Machine Tools

• A power-driven machine that performs a machining operation – Holds workpart – Positions tool relative to work – Provides power and controls speed, feed, and depth. – Pumps a Cutting fluid v

f 8 2. Theory of Chip Formation • Orthogonal Cutting Model Rake angle: α α Shear angle: φ Shear Chip thickness ratio: Plane Tool t l sinφ r o == s tc tc ls cos()−αφ to φ By rearranging l Work s r cosα tanφ = − r sin1 α r is always less than 1.0. 9 Shear Strain in chip α

B A D C sin( ) sincoscossin φ Using α ± β = α β ± α β cos()=± m sinsincoscos βαβαβα B A φ AC + ADDC φ−α γ == tan()+−= cotφαφ BD BD sin()−αφ cosφ cosα D α = =+ cos()−αφ sinφ cossin ()−αφφ C As φ (from 10° to 35°) increase, γ (from 5 to 2) decreases. 10 Velocity α

Vc Vs α 90-φ+α φ-α Tool 90-α φ Vc V V φ Vs V VV Work = s = c ⎛π ⎞ ⎛π ⎞ sinφ sin⎜ +− αφ⎟ sin⎜ −α ⎟ V cosα V ⎝ 2 ⎠ ⎝ 2 ⎠ γ& = s = Δy cos()αφΔ− y V s VV c == where Δy is the finite thickness of cos()− sincos φααφ the shear plane, typically 0.03mm. Shear Strain rate is around 103-105sec-1 11 Actual Chip Formation

(a) Discontinuous chip •Brittle materials at low cutting speed •High tool-chip friction and large feed and Secondary depth Shear Zone (b) Continuous chip •Ductile materials with high speeds and small feed and depth of cut (c) Continuous chip with built-up edge •Ductile material at low to medium speeds (d) Serrated chip Tool •Difficult-to-machine metals at high cutting speeds Effective φ

Primary Shear Zone Work12 The ‘Real’ Cutting Force

Cutting Forces are measured with Dynamometer.

Normal Ft

Shear Fr •Area: A=bh σ Fn where b=chip width F t h=chip thickness •Temperature (500-1000oC) R • Pressure (1000-3000 MPa) Sticking Zone Sliding Zone

13 3. Force Relationships

α Tool Tool F φ R Fs β Fc R’ N Work F Work Fn R” t

F: Friction Force Fs: Shear Force Fc: Cutting Force N: Normal Force Fn: Normal Force Ft: Thrust Force

14 Force Diagram F F φ s c = c sinα + FFF t cosα

β−α c cos −= FFN t sinαα

cs cos −= FFF t sinφφ Fn sin += FFF cosφφ Ft cn t

F F R = s β cossin ()−+ αβφφ τ wt α = os cossin ()−+ αβφφ α F cos()−αβ N F = s c cossin ()−+ αβφφ

Fs sin()−αβ Ft = cossin ()−+ αβφφ15 Cutting Force

⎡ cos( −αβ) ⎤ 2 • Cutting Force: c = bhF τ s ⎢ ⎥ = c c []/ mmNKbhK ⎣ cossin ()−+ αβφφ⎦ • Thrust Force: ⎡ cos()−αβ ⎤ t = bhF τ s ⎢sin ⎥ = tbhK ⎣ cossin ()−+ αβφφ⎦

τ sbh RF cos()αβφcos FF sinφφ=−=−+= c = RF cos(β −α) s c t sinφ t RF sin()−= αβ

n RF sin()c sin +=−+= FF t cosφφαβφ

Kc and Kt must be calibrated α through machining experiments. t b c Tool d

φ h to f Fc R F Work 16 t Top View Chatter Analysis • Mechanical vibration k c Free Vibration: + &&& + kxxcxm = 0 Forced Vibration: &&& =++ o sinωtFkxxcxm sin)(Assume ()wtXtx += φ F kx xc& Or using complex harmonic functions

ωαtjj &&& =++ o eeFkxxcxm Φ()w F )(Assume = Xetx ()tj +φω tx )( 2 2 ωφtjj ωαtjj ()+− ωω ()== o eeFtFeXecjmk 1 X 11 Magnitude ratio: ()w ==Φ kF 2 o ()2 +− ()21 ζrr 2 r φ 1 − 2ζr Phase: φ = tan −1 +α 0 1− r 2 where r = ω ζ = 2 kmc -90 ωn k 17 and ω = n m -180 r The Merchant Equation F • Shear stress: τ = s As wt • Shear Plane Area: A = o s sinφ cosφ − FF sinφ • Shear stress: τ = c t owt sinφ • Merchant’s Assumption: Shear plane angle will form to minimize energy • After differentiating τ w.r.t φ, Merchant’s Equation: α β φ 45 −+= 22 18 Implication of Merchant’s Eq. α β φ 45 −+= 22 • An increase in rake angle causes the shear plane angle to increase. • A decrease in friction angle cause the shear plane angle to increase. • The analysis from orthogonal cutting can be used in a typical turning if the feed is small relative to depth of cut. Effect of shear plane angle φ : (a) higher with a resulting φ Tool lower shear plane area; Tool (a) smaller φ with a resulting larger shear plane area.

19 Turning vs. Orthogonal

Feed f Uncut Chip thickness to Depth d Width of cut w

Cutting speed v Cutting speed v

Cutting force Fc Cutting force Fc

Feed force Ff Thrust force Ft

α d t c Tool

t φ f oF c Ft Work

20 4. Power & Energy Relation

= VFP • Power (energy per unit time) cc VF HP = c c 000,33 P hp = c 000,33 P in ft-lb/min P hp • Horse power P = c or hp = c g E g E with mechanical efficiency E=90% P • Unit Power P = c u MRR

P cc vF Fc • Specific energy PU u ==== MRR owvt owt 21 Size Effect & Energy Distribution

0.01 0.04(in) 1.6 100 1.4 Tool

1.2 Work 1.0

0.8 50

0.6 Correction Factor Chip

0.4 Proportion of Energy 0 0.125 0.25 0.5 1.0 1 2 3 Chip thickness before cut (mm) Cutting Speed (m/s)

22 Specific Energy for various work

materials (to=0.25mm) Materials Brinell Specific Energy (U) Hardness N·m/mm3 In-lb/in3 Hp/in3/min Carbon Steel 150-200 1.6 240,000 0.6 200-250 2.2 320,000 0.8 251-300 2.8 400,000 1.0 Alloy Steels 200-250 2.2 320,000 0.8 251-300 2.8 400,000 1.0 301-350 3.6 520,000 1.3 351-400 4.2 640,000 1.6 Cast iron 125-175 1.1 160,000 0.4 175-250 1.6 240,000 0.6 Stainless steel 150-200 2.8 400,000 1.0 Aluminum 50-100 0.7 100,000 0.25 Aluminum Alloys 100-150 0.8 120,000 0.3 Magnesium Alloys 50-100 0.4 60,000 0.15 23 Problem 21.30 A lathe performs a turning operation on a work piece of 6in diameter. The shear strength of the work=40,000lb/in2. The rake angle of the tool =10o. The machine settings are: rotational speed=500rev/min, feed=0.0075in/rev. and depth=0.075in. The chip thickness after the cut is 0.015in. Determine: (a) the horsepower required (b) the unit horsepower for this material,

(a) To get HP, Fc and v are needed t 0075.0 r o === 5.0 t 015.0 r cosα ⎛ 10cos5.0 ⎞ tanφ = ; φ = arctan⎜ ⎟ = 3.28 o − r sin1 α ⎝1− 10sin5.0 ⎠ βα ⎛ 10 ⎞ (b) HP φ 45 β ⎜452; −+=−+= ⎟ = 4.433.28 o u 22 ⎝ 2 ⎠ vfdMRR == = 3 minin3.5)075.0)(0075.0(785

o wt ⋅ 075.00075.0 2 HP 2 3 As == = in00119.0 HP === hp/(in375.0 /min) sinφ 3.28sin u MRR 3.5

SAF ss == = lb5.47)00119.0(000,40 (c) HPu with the correction factor Fig. 21.14 Fs cos()−αβ − )103.43cos(5.47 Fc = = = lb6.83 HP 375.0 cos()−+ αβφ −+ )104.433.28cos( HP u === hp/(in326.0 3/min) u f 15.1 ωrv == π = minft/785rev/ft)12/6min(/rev500 vF )785(6.83 HP c == = hp2 24 000,33 000,33 5. Cutting Temperature • Cook’s dimensional analysis 333.0 U ⎛ vt ⎞ T = 4.0 ⎜ o ⎟ ρC ⎝ K ⎠ • Experimental Measurement – Tool-chip thermocouple – Trigger’s results = KvT m • RC-130B Ti (T=479v0.162) • 18-8 Stainless steel (T=135v0.361) • B113 Free machining steel (T=86.2v0.348)