Simulation in Manufacturing Technology

Simulation in Manufacturing Technology Lecture 8: Principles of Cutting Prof.Dr.-Ing. ritz Klocke Seite 1 Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-Hand System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E- Model of Chip ormation Seite 2

Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-Hand-System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E- Model of Chip ormation Seite 3 Cutting: Machining with geometrically defined cutting edge Manufacturing Processes major groups 1 primary shaping 2 secondar y shaping / forming 3 cutting 4 joining 5 coating 6 changing material properties source: DIN 8580 3.2 cutting with geometrically defined cutting edges (DIN 8598-0) Seite 4

Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-hand system Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip ormation Seite 5 Cutting edges on the cutting part of a turning tool primary motion shank feed motion major second face A γ minor cutting edge S' minor flank A' α major cutting edge S major second flank cutting edge corner A α Seite 6

Tool and workpiece motions trace of the plane of the face A g chip tool trace of the plane of the flank A a cutting speed η resultant cutting speed β ϕ workpiece feed speed trace of the plane of the transient surface Seite 7 Tool-in-hand system assumed working plane P f λ s P n cutting edge normal plane P n v r c tool cutting edge plane P s P s P p κ r v r f Pf P o tool orthogonal plane P o tool back plane P p P r tool reference plane P r Seite 8

Differences between reference systems assumed direction of primary motion tool back plane P p working back plane P pe direction of the resultant cutting speed assumed working plane P f v r c selected point on the cutting edge v r e working plane P fe assumed direction of feed motion tool-in-hand system tool-in-use system direction of feed motion tool reference plane P r working reference plane P re Seite 9 Tool-in-hand system (ISO 3002) assumed working plane P f tool cutting edge plane P s Variable with the process! P f P s κ r ix with the tool! v r f v r e v r c P n ix with the tool! cutting edge normal plane P n λ s ix with the machine by turning, if the cutting edge is positioned in the centre of the spindle. z C y B P r γ n i x with the tool! This is the plane of the face A γ. machine coordinate system A x (DIN EN ISO 841) tool reference plane P r Seite 10

Theoretical terms at the process trace of the working reference plane P re γ ne trace of the shear plane trace of the working cutting edge plane P e P se h r h r ch tool workpiece selected point on the cutting edge z P oe P fe P ne y Seite 11 Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-Hand System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip ormation Seite 12

Chip formation: types of chips I segmented chip continuous chip chip with build-up edge Seite 13 Chip formation: types of chips II shearing chip discontinuous chip Seite 14

Chip formation: The cutting operation 1. bring up gathering 2. split up, crack segment formation 3. shearing and next bring up 4. second segment formation and bring up 5. shearing and next crack source: Codron 1906 6. third segment formation and bring up 7. shearing and next crack t dynamic cutting force Seite 15 Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-Hand system Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip ormation Seite 16

The shear plane model trace of P p shear plane accounts: plastic deformation only in the shear plane biaxial stress condition ideal sharpness of the cutting edge realisation: the orthogonal cut All the force components are in the tool orthogonal plane P o. tool cutting edge angle k r = 90 tool cutting edge inclination l s = 0 This model is acceptable, because the biaxial and the triaxial stress condition are in neighbourhood. Seite 17 Consideration of energy h shear plane h model v c v ch h ch x shear energy: specific shear energy: E e = s E s s = = = τ V A x x s A A = sin b h = sin Seite 18

Krystoff 1939: shear angle determination ( ρ ) + = 45 z γ o 2 n trace of the shear plane 90 major axis system machine coordinate system principle of maximum shear stress 3 y z workpiece ρ γ o tool γ o trace of the tool reference plane P r π = + γ o ρ 4 α o P o P f P n Seite 19 Ernst and Merchant 1941: force equilibrium and shear angle γn ρ f z n c ρ γ o trace of the shear plane shear stress in the shear plane: τ = A dτ = 0 d = ( cos sin ) c f b h π 1 = + 4 2 sin ( γ ρ ) o γ γ o trace of the tool reference plane P r workpiece tool α o P o P f P n Eugene M. Merchant Seite 20

Application: theory of the ideal plastic body Lee/Shaffer (1951) τ C A trace of the shear plane A σ = 0 τ = 0 B D C γ o η π 4 B trace of the tool reference plane P r Mohr s circle diagram τ a, d e η 2 ρ ρ b c, f σ workpiece α o tool P o P f P n π = + γ o ρ 4 Seite 21 Shear plane model: force calculation demonstration of the total force as a function of the shear stress with consideration of: shear work friction work at the face z τ b h = sin cos ( + ρ γ ) 0 By using the circle of Thales, the total force can be substitute with the two force components cutting force and feed force. (in the orthogonal cut) cos ( ρ γ o ) sin( ρ γ o ) τ b h fortho cos( + ρ λ ) sin cos( + ρ γ ) cortho = sin o = o τ b h Calculation of the force components with a physical and theoretical background! (advantage of analytical models) Seite 22

Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-Hand System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip ormation Seite 23 orce components feed speed v e resultant cutting speed v c cutting speed the three force components c, f and p are perpendicular the total force z is their geometrical sum back force p does not influences the power v f primary motion (workpiece) back force p f feed force feed motion (tool) c a active force cutting force z total force Seite 24

Dependencies of the force components distribution of force c area of the rounded corner c force f p f force c f p v force c feed cutting speed tool cutting edge angle depth of cut c f p κ r force f p a p The maxima are produced by the build up cutting edge during the area of low cutting speed. At the area of the rounded corner the trend line of the force components are not linear! Seite 25 primary influence of the force components technical cutting mechanics technical terms: v c, v f, a p, geometrical relation k r, l s, a o, g o, theoretical cutting mechanics theoretical terms: b, h, h ch, In the theoretical cutting mechanics, the cross-sectional area was identified as primary factor and for the calculation the following parameters were defined: thickness of cut h width of cut b z = f ( b, h) Plagens has found a good approximation of the cutting force with a linear function of the width of cut (b). The approximation of the force components with a function of the thickness of cut h was often discussed and lead to empirical models: Seite 26

orce approximation: empirical models linear approximation: potential approximation: i = A b h + B b i = k i1.1 b h ( 1 ) m i result of a curve fit first part has a basis of the shear plane theory very easy function not so precise all calculations are not so protected (low number of user) Schlesinger (1931) Pohl (1934) Klein (1938) Richter (1954) Hucks (1956) Thomson (1962) Altintas (1998) researcher result of a curve fit calculation of the cutting force statistic protected very precise a theoretical reason is missing calculation of the other force components are not protected Taylor (1883/1902) ischer (1897) riedrich (1909) Hippler (1923) Salomon(1924) Kronenberg (1927) Klopstock (1932) Kienzle (1952) Seite 27 Example: linear approximation force / N Kraft [N] 600 500 400 300 200 v c = 242 m min h = 100 µm v c =242 m/min h =100 µm c f c f force / N Kraft [N] 800 700 600 500 400 300 Ac=131,69 N Bc=3,98 N/µm Af=154,71 N Bf=2,48 N/µm c242 f242 Linear it of Data1_c242 Linear it of Data1_f242 100 0 1 2 3 4 5 Zeit [s] time/ s.. 200 100 0 20 40 60 80 100 120 140 160 180 Spanungsdicke [µm] thickness of cut / µm linear approximation: i = A b h + B b i i Seite 28

Example: potential approximation scaled force nomogram 10000 scaled force i ' / N/mm tane i =1-m i ' i1 1000 B e i A log( ib )-log( ia ) log(h B )-log(h A ) 100 0,1 1 thickne ss of cu t h / mm i Otto Kienzle (1893-1969) k = ki b h i 1. i = mi h k 1 logarithmic scale of the axes! triangle of the slope! potential approximation: i = k i1.1 b h 1 m i Seite 29 Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-hand System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip ormation Seite 30

Types of wear face A γ tool clearance A α flank wear land crater C B A N A KM SV α VB B KT SV γ A K flank A α face Aγ Seite 31 Taylor s tool life theory Standzeitdiagramm tool life diagram tool life straight line or Taylor s straight line 100 y = m x + b Application of the general equation of a straight line! tool Standzeit life T T / min / min 10 Consideration of the logarithmic scale of the axes! log T + = tanδvc logvc logcv tanδ vc = kvc log T = k logv + logc vc c v δ vc k vc T = v c C v 1 10 100 cutting speed v c / m/min Schnittgeschwindigkeit v c / m/min rederick Winslow Taylor (1856-1915) Seite 32

Wear diagram: flank wear Verschleißdiagramm wear the choice of the tool life criterion VB / mm 0,4 vc=160 m/min 0,3 vc=200 m/min vc=300 m/min 0,2 under fix 0,1 cutting edge geometries and 0 cutting conditions 0 5 10 15 20 25 30 t c / min determination of the tool life consideration of the boundary conditions Seite 33 Tool life straight line determination of the cutting speed for a tool life of 15 minutes 100 Standzeitdiagramm tool life diagram T=15 min Standzeit tool life / T / min 10 HW - P25 1 100 1000 Schnittgeschwindigkeit Cutting speed / m/min / m/min m v15 VB 0,3 = 170 min Seite 34

Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-hand System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip ormation Seite 35 Engagement conditions P r κ r tool reference plane P r P 1 R t x P 2 rε rε Rt f/2 z Tschebyschow (1874): Milling Bauer (1934): Turning R t = rε rε f 4 2 R t 2 f 8 r ε Seite 36

Structure of the lecture Introduction: Metal Cutting The Cutting Part Tool-in-Hand System Terms at the Wedge Chip ormation Specification Shear Plane Model Machinability orce Components Tool Life Surface Integrity Chip orm Modeling of Machining E-Model of Chip formation Seite 39 E-Model: orthogonal cut CAD-data of the tool plastomechanic calculation thermodynamic calculation flow stress / MPa material data temperature / C strain rate E-Software nonlinear E multiphysics modeling results: stress distribution of the tool temperature distribution of the tool Seite 40