Cutting with geometrically undefined cutting edges Simulation Techniques in Manufacturing Technology Lecture 10 Laboratory for Machine Tools and Production Engineering Chair of Manufacturing Technology Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. Dr. h.c. F. Klocke
Review: Modelling and simulation of grinding processes macroscopic microscopic Molecular Dynamics (MD) kinematics Finite Element analysis (FEA) fundamental regression artificial neural nets rule based mx+bx-cx = CU 0 sin(ωt) x, x, x x xx x x xx x x x xx physical empirical heuristic heuristic and empirical models are limited and difficult to transfer from one process to another Finite Element models are complex to apply and the necessary material properties are often not known Molecular dynamics are very fundamental fundamental models can be regression models with physical background kinematics models can be used for applicable simulations Source: CIRP Keynote Paper 2006, Brinksmeier et al. Seite 2
Modelled parameters in grinding roughness temperature, surface integrity Lecture 9 Lecture 10 topography, engagement forces energy wear chatter, vibration Source: CIRP Keynote 1992, Toenshoff et al. Seite 3
Common empirical regression models - Still in use and important fundamental topography fundamental chip thickness fundamental cutting force fundamental temperature fundamental roughness Nkin h = F'= = θz max Rt Rz = = = A 1 cgw cgw 1 e 1 e 1 a q 1 2 e 2 d eq 1 e 1 q 1 e e 1 a e 2 c gw c 1 wp q e a 2 e e α 1 λ a e e 2 v e w 3 v e c 1 e 4 d e eq c gw c 1 wp q e a 2 e 1 e A + c gw c 2 wp q e 1 e 5 e A a 1 d 1 d e6 e eq eq v 1 d eq c e e 1 e1 2 e 3 e7 w e 3 d e8 eq e w N St z a v 3 V ' 4 = n z Seite 4
Wear model by regression analysis regression model on basis of test results for external + internal cylindrical grinding and surface grinding wear increases with increasing specific material removal V w + decreases with higher overlap rate U d about 1100 tests ξ w = 0.1 mm³/mm l k = 1 mm with machining value ξ w = Q w / n s kinematical contact length l k = l g 1-1/q Source: Osterhaus Seite 5
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 6
Energy in grinding and turning volume related machining power turning grinding points of energy transformation Source: CIRP Keynote 1992, Toenshoff et al. workpiece a chip bonding grit b d e c tool chip d workpiece a b c about 100 µm about 10 µm a shearing zone, deformation work b rake face, friction work c cutting edge, surface work d flank, friction work e bond, friction work Seite 7
The grinding process - Chip formation in grinding grinding wheel grain trajectory F t,s F n,s bond v s bulging grain (cutting edge ) chip workpiece T µ h cu eff h cu elastic deformation I II elastic and plastic deformation III elastic and plastic deformation and chip removal Seite 8
The grinding process Heat distribution in grinding P c = F t v c = P m + Q w + Q kss + Q s + Q k grinding wheel grain trajectory F t,s bond v s environment (coolant, air) Q kss grain (cutting edge) Q s face friction chip flank friction Q k shear energy displacement energy work piece Q w Seite 9
Theoretical chip thickness at a single grain h cu,max max. undeformed chip thickness v s d eq v w f as a e cutting speed, wheel speed equivalent diameter of the grinding wheel workpiece speed feed per grain depth of cut maximum chip thickness at the single grain h cu,max, SG 2 π d eq F c, 1/Rz, r S = f (h cu ) f as v v w c a d e eq d eq h cu,max v c a e v w Seite 10
Theoretical chip thickness in a grinding process h cu,max max. undeformed chip thickness v s d eq v w f as a e C stat k cutting speed, wheel speed equivalent diameter of the grinding wheel workpiece speed feed per grain depth of cut static cutting edge density constant (material dependent) α,β,γ coefficients (depending on the grinding wheel specification and the material characteristics of the workpiece) e.g. α = β = 1/3; γ = 1/6 maximum undeformed chip thickness α β 1 v w a h e cu,max k C stat vs deq F c, 1/Rz, r S = f (h cu ) f as d eq h cu,max v s a e v w γ Seite 11
Equivalent grinding wheel diameter external cylindrical grinding surface grinding internal cylindrical grinding d s l g d s l g d s d w l g d w a e d w a e a e d eq d d d = w s = eq s d w + d s d d eq = d d w w d s d s l g d eq l g d eq s l g d seq d w? a e d w? a e d w? a e Seite 12
Contact length geometrically simplified calculation of the chip length l 2 g = ae + x l g 2 2 x 2 deq deq 2 2 a a d = e = e eq 2 ½ d s -a e ½ d s x a e l g a e Seite 13
Characteristic values of grinding processes material removal V w and specific material removal V w V w describes the ground workpiece volume V w describes the machined workpiece volume in relation to the grinding wheel width material removal rate Q w and specific material removal rate Q w Q w describes the ground workpiece volume per time Q w describes the ground workpiece volume per time in relation to the grinding wheel width an is therewith a characteristic value for the productivity G-ratio describes the ratio of the material removal and the wear volume of the grinding wheel G = V' V' w sw Seite 14
Influence of the set values on the process and the result v w a e a p f r, v fr v s, n s a p v s l w v w, n w set values forces F t,n process wear r s time t c temperature ϑ result roughness y R a,z x tolerance form-/ shape error v fr Q w (a e, v w ) v c Seite 15
Difficulties in grinding process simulation Cutting speeds: v c 15-200 m/s Temperatures: peaks above 1200 C Temperature gradients: 10 6 C/s / 10 3 C/mm Many material properties are not known within these ranges Forming speeds: ϕ up to 10 7 1/s v S v W Seite 16
There are several chip formation mechanisms! Increasing cutting speed v c Increasing engagement depth h cu Micro peeling energetically favourable mechanism high chip thickness h cu Micro continuous chipping energetically favourable mechanism high chip thickness h cu Micro ploughing energetically unfavourable removal mechanism Micro grooving V removal V forming 1 V removal V forming 1 150... 1 200 energetically very unfavourable removal mechanism Seite 17
Surface integrity of the workpiece Surface layer properties: residual stresses density structure hardness electrical, optical, thermal, magnetical properties texture structure cracks machined surface HV hardness residual stresses σ II σ Source: Brinksmeier Seite 18
Influence of abrasive material on surface integrity Residual stresses σ mechanical load plastic deformation reduction of density + increase of specific volume of plastically deformed area σ E compressive stress F ε the surrounding, not plastically deformed material hinders volume increase compressive stress in plastified zone tensile stresses beneath plastified zone mechanical load Seite 19
Influence of abrasive material on surface integrity Residual stresses s σ high thermal loads on small material area increase of specific volume + decrease of E-modulus and flow stress s E compressive stress F mechanical load e σ E tensile stress ε material volume shrinks during cooling the surrounding, not heated material hinders shrinkage tensile stresses Q thermal load Seite 20
Influence of abrasive material on surface integrity Residual stresses σ σ E compressive stress F mechanical load ε σ σ E Q thermal load tensile stress effects of thermal load during cbn machining can exceed mechanical effects positive compressive stresses near surface ε residual stresses σ [N/mm²] surface grinding v s = 30 m/s a e = 7 µm v w = 400 mm/s material 100 Cr6V 62 HRC corundum Source: Brinksmeier depth [µm] Seite 21
Surface integrity Change of structure V 40 µm w = 250 mm³/mm V 40 µm w = 1000 mm³/mm material: 16MnCr5, hard roller burnished grinding wheel: sintered corundum A 80 H 6 V grinding parameters: v c = 80 m/s; q = -120; Q w = 15 mm³/mms ext. cyl. circumferential plunge grinding cooling lubricant emulsion 5% Martensitic steels can be harmed by grinding process deformation rehardening at the surface possible annealing in deeper regions possible shown case: grinding wheel wear leads to high process temperatures V w = 1000 mm³/mm 100 µm Seite 22
Surface integrity Deformation cross-sectional view, etched, 1:500 X 53 Cr Mn Ni N 21 9 material structure can be deformed by grinding process 20 µm cross-sectional view, etched, 1:500 X 50 Cr Mn Ni Nb N 21 9 20 µm Source: Lortz Seite 23
Why is grinding process simulation so difficult? undefined cutting edges, complex tool high number of edges simultaneously in contact, dynamic process complex profiles dressing roller grinding wheel penetration area mechanisms in contact zone are still widely unknown (workpiece and tool) peak temperatures single grit forces cooling lubricant effects Seite 24
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 25
Energy distribution and heat flow thermal energy flows in all relevant components of the system: workpiece (q wp ) grinding wheel (q gw ) chip (q chip ) cooling lubricant (q cl ) the distribution of the heat flow can be manipulated bonding penetration path q cl grain q gw q chip v s chip Legend: P c = cutting power F t = tangential force v c = cutting speed A k = contact area q = heat flow source: Rowe, Stephenson q workpiece t = q cl + q gw + q chip + q wp q wp = P c = F F t t v A k c Seite 26
Das Bild kann zurzeit nicht angezeigt werden. Tasks of the cooling lubricant primary tasks reduction of the friction: grain workpiece reduction of the friction: bonding workpiece transport of thermal energy secondary tasks cleaning of grinding wheel and workpiece chip transportation corrosion protection of machine tool and workpiece Seite 27
Categorisation of cooling lubricants cooling lubricant non-water-mixed cooling lubricant oil emulgable concentrate water-mixed cooling lubricant water-soluble concentrate + water + water Source: DIN 51385 emulsion solution Seite 28
Influence of the friction on the chip formation higher friction emulsion the chip formation begins earlier bulging cutting edge chip less material flows under the cutting edge more heat generated (tendency) η Tµ cutting point h cu eff h cu I II III penetration path lower friction oil chip formation begins later bulging cutting edge chip more material flows under the cutting edge process is less efficient η Tµ cutting point h cu eff h cu lower heat production (tendency) I II III elastic springback material flow Seite 29
Cooling vs. lubricating chip formation goal: chip formation instead of material deformation the higher the lubrication, the higher the required normal force for the chip formation cooling required for heat reduction friction at the grain, bonding and workpiece surface lubrication required for friction reduction generally: the higher the v c, the more important is the lubrication surface grinding: high number of momentary cutting edges N mom, and lower cutting speed v c Seite 30
How much cooling lubricant is delivered by pores? iron core diamond tip coil grinding wheel surface maximum coolant flow within grinding gap in [l/min], v c = 100 m/s measurement direction percentage material volume [%] depth [µm] Seite 31
Calculation of heat flux total heat flux can be calculated from empirical data q cl q wp q gw F t q chip q t = P c = Ft v A k c total heat flux q t q = q + q + q + t cl cooling lubricant chip chip wp workpiece q gw grinding wheel q cl = R cl q t q chip = R chip q t q wp = R wp q t q gw = R gw q t Legend: P c = cutting power F t = tangential force v c = cutting speed A k = contact area q = heat flow R = partition ratio Quelle: Seite 32
Calculation of heat flux into workpiece 9-52 % q cl 2 12 % q gw q wp 14-84 % 3 38 % F t q chip heat flux into cooling lubricant q cl assumption: cooling lubricant can take heat flux until boiling point heat flux into chip q chip assumption: chips can take heat until melting point heat flux into grinding wheel q gw grit contact analysis grinding wheel contact analysis heat into workpiece q wp can be calculated as difference of total heat flux q t (calculated from measured forces) and the assumed heat fluxes q cl, q chip and q gw Quelle: Seite 33
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 34
Principle of the FEM 2D linking-up 3D object numerical calculation of: offset expansion stress deformation speed of deformation temperature linked-up object v ε σ ϕ. ϕ ϑ material parameters: flow sheets thermal expansion coefficient grade of emissions process parameters: thermal distribution factor k w material and process parameters in the grinding process are often not available or can only be acquired very inaccurately Seite 35
FEM for machine tool Machine optimisation by FEM FEM analysis of calculated and measured values Flexibility [µm/n] Source: WZL 1 0.1 0.01 G xx G yy G zz 0.001 0 20 Frequency [Hz] 80 100 Source: WZL measuring optimisation of grinding machine optimisation of ground workpieces Seite 36
FEM for grinding tool Tool optimisation by FEM Optimisation of grinding layer concerning influence of centrifugal forces influence of contact forces Optimisation of grinding wheel body with regard to contact forces centrifugal forces damping abilities Source: WZL Optimal grinding wheel lay-out for every particular grinding application Seite 37
FEM for single grits Process optimisation by FEM Simulation of single grit cutting process determination of temperature and stress distribution in one grit determination of local temperature and stress distribution in the workpiece Simulation of complete grinding process calculation of temperature and stress distribution in the ground workpiece Source: WZL Seite 38
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 39
Example: Measured thermal dispersal factor k w thermal flow during grinding estimation of k w F t 9-52 % q cl F n 2 12 % 3 38 % q gw q chip measuring of the temperature close to the contact zone with - thermal elements, - thermal camera q wp 14-84 % F t estimation of k w Q w = k w P c = k w F t v c - determination of k w during grinding is difficult - temperature in the contact zone cannot be measured directly iterate k w until the temperature at the measuring points in the model and in reality nearly match - thermal distribution factor depends on process parameters Seite 40
Model for temperature calculation in the grinding process adiabatic surface single-side bordered semi-infinite body l k =2l b k»l k q workpiece q v z speed of the heat source y x x model by Carslaw and Jaeger heat source has a constant and uniformly distributed heat flow density heat source moves linear and with constant speed over the surface heat source has an unlimited expansion vertical to the direction of movement the heated solid is semi-infinite, i.e. it is only limited at one side the surface of the solid is adiabatic quasi-stationary circumstances, i.e. that the residence time of the heat was long enough z Seite 41
From the real process to FEM cooling lubricant grinding wheel specification of the abstraction level - How are the thermal and mechanical loads described? fixing contact length l g seat υ 0 = +20 C l g - Where do the mechanical and thermal loads act? examples for heat sources heat source q w cooling surfacepressure p r cooling rectangular triangular clamping force p s workpiece v fg const. temperature level υ 0 = + 20 C clamping force p s trapezoid-shaped parabolically Seite 42
FEM Temperature and deformation simulation Source: Weber, IWF Braunschweig v f grinding wheel/ workpiece: grinding wheel: 89A60-219AV2 workpiece: nickel basis alloy process parameters: cutting speed v c : 26 m/s feed rate v ft : 300 mm/min specific removal rate Q : 5 mm³/mm s radial feed in f r : 1 mm contact depth a p : 12,5 mm process-/simulations parameters: tangential force F t : temperature 116 N measured 520 C at cutting measuring performance pointp c : simulated 529 C 3016 W heat distribution factor : k w = 22% Seite 43
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 44
Physical cutting simulation with FEM potential + exact simulation of the physical procedures at the grain cutting edge is possible + the elasto-plastic material behaviour will be considered challenge - exact knowledge of the material characteristics is required - material flow curves for high deformation speeds and high temperatures are necessary Seite 45
Split-Hopkinson-Bar-Test projectile tempered chamber front-end staff output staff probe v >> 50m/s. ϕ up to 10 4 s -1 SourceLFW, RWTH Aachen Seite 46
Split-Hopkinson-Bar-Test projectile tempered chamber front-end staff output staff flow stress 1 2 2600 [MPa] 2200 2000 1800 1600 y 100 [%] 60 40 thermal coefficient 1400 20 j = 0,1 1200 1000 0 RT 600 [C ] 900 temperature Source: LFW, RWTH Aachen k f = s (ϕ, ϕ ).. k f = f ( ϕ, ϕ, y ) y = s (T, j = 0,1) s (T = RT, j = 0,1) Seite 47
Single-grit scratching test kinematic: lengthwise peripheral surface grinding v f v c x v c v f y h cu,max x z L FEM-simulation v c v f h cu,max Source: WZL Aachen, IWT Bremen L Seite 48
Optimised lay-out of the FEM - model v x v y the whole component must be linked-up h cu, max grain moves on the contact track long simulation duration v x v y end max. in-feed depth v y v y v x start h cu, max partial linking-up around the grain grain moves in in-feed direction, workpiece in feed direction v x shorter simulation duration eraser window allowance area eraser window Seite 49
Optimized lay-out of the FEM - model optimized model characteristics elasto-plastic workpiece higher grid density close to the grain, to reproduce elasto-plastical material behaviour symmetry planes symmetry plane grit optimisation Seite 50
Single-grit-tests with the FEM - model indentation depth: 5 µm speed : 1.26 m/s spike radius : 2.5 µm material : 16MnCr5, carburised, tempered Seite 51
Results of the physical cutting simulation shaping of the elasto-plastic material behaviour in the model applicability to analyse and optimise of the metal removal mechanisms Seite 52
Results of the physical cutting simulation model speed vectors temperature residual stresses Seite 53 Source: WZL Aachen
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 54
Conclusion Grinding is a complex process with complex effects on the workpiece surface integrity Temperature modelling can be done with some assumptions about the heat fluxes Finite Element Analysis considers elasto-plastical material behaviour and simulates physical procedures at the grain cutting edge But FEA needs exact knowledge of material- and process parameters and high computer power (today only applicable for one or few grits and low cutting speeds) Source: Seite 55
Vision: Overall model for grinding processes numeric model of the grinding wheel process kinematic and penetrationcalculation macro- microgeometry geometry numeric modell of the workpiece macro- microgeometry geometry model to generate the abrasion of the grinding wheel kinematic cuttingparameters cutting thickness, -width, -length, -profile process models grinding forces/ -power single grain grinding wheel thermal flows process parameters superpositioning and calculating of the resulting form- and sizedeviation models to calculate the elasto-mechanic deformation spindle tool models to calculate the thermo-elastic deformation models to calculate the thermal stress Seite 56
Structure 1 Important Mechanisms in Chip Formation during Grinding for Modelling 2 Temperature Modelling 3 FEA Modelling 4 Macroscopic FEA 5 Microscopic FEA 6 Conclusion Seite 57
Molecular dynamics workpiece topography information about deformation mechanisms and surface integrity Source: CIRP Keynote Paper 2006, Brinksmeier et al. Seite 58
Modelling and simulation - Neuronal Networks Input: e.g.: process parameter Artificial Neuronal Network (NN) w 1 (i,j) w 2 (i,j) Output: e.g.:grinding result to calculation Phase 1: training of the NN until d < d max Phase 2: test of the NN if hit rate is sufficient Phase 3: execution mode of NN to evaluation Seite 59