Methods of validation and optimization techniques
Transcription
Methods of validation and optimization techniques
Methods of validation and optimization techniques Simulation Techniques in Manufacturing Technology Lecture 11 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 © WZL/Fraunhofer IPT Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 2 Objectives of the Lecture This lecture is intended to… … Help you to understand the relevant variables from the perspective of cutting. … Explain the design and function of industrial sensors. … Convey basics of measurement techniques. … Clarify the validation of cutting process models. … Teach the optimization technique. © WZL/Fraunhofer IPT Seite 3 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 4 Relevant Process Quantities in Cutting Tools ■ Force ■ Moment ■ Active Power ■ Temperature ■ Acceleration ■ Mechanical Vibration (AE) ■… © WZL/Fraunhofer IPT Seite 5 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 6 Cutting force Acceleration Technical Sensors in Metal Cutting Measuring platform Rotating cutting force dynamometer Acceleration sensor Force measuring pin vc Process remarks Load ring Pyrometer Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 7 Procedure for measuring value in a Sensor Measuring signal & Sensor selection processing & application Process related signals AE-Signal [U ] Ze it [s] Measure Filtering offset corrector Measuring principle m Temperature [°C ] Amplification Force m [N ] Sensor selection Application A/D Converter A D Acceleration m 2 s I Active Power [A ] © WZL/Fraunhofer IPT Seite 8 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 9 Strain Gauges - DMS Function: ■ An external force causes stress and eventually strain in the component ■ Strain gauges convert mechanical strain into electric resistance. Messmäander SiO2 Isolation Measuring direction Stress Strain © WZL/Fraunhofer IPT F E A L L Contact Träger, Klebstelle Class: Passive Sensor Seite 10 Measuring Principle R0 + R R0 R l A R l A0 R0 0 l0 A © WZL/Fraunhofer IPT R R0 k R0 - R l l0 R / R0 k Seite 11 Load Cell Load [kg] Deformation of the body [mm/m] Display in kg Resistance change at DMS [R/R] Standardized Transducer Ex – Load Cell after consideration of principle of Double beam Source: HBM © WZL/Fraunhofer IPT Seite 12 Stress Measurement ■ Component Optimization (R&D) ■ Operations Monitoring ■ Vulnerability analysis to identify the causes of damage Load induced Stress: F A Residual Stresses (for resolution) E Thermally induced Stress: E Source: HBM © WZL/Fraunhofer IPT Seite 13 Advantages and Disadvantages of Strain Gauges Advantages Disadvantages Universally and easily applicable Relative change in resistance is very low Small / Low Mass Wide Frequency Range (0… > 50kHz) Low Reaction on the measuring object Excellent Linearity over a wide range of strain range Low and predictable temperature effects High stability over a long usage Low Cost (electrical bridge circuit is always used) Temperature Limits Cannot be reused Precautions required against: – Humidity – Temperature (Temperature gradient!) – Ionizing Radiation – Magnetic Field Source: HBM © WZL/Fraunhofer IPT Seite 14 Piezoelectric Sensor Greek. piézein = drücken, pressen Force and Moment Piezoelectric Effect: Deformation along polar axis produces a dipole moment on opposite surfaces. Charge displacement is converted by a charge amplifier to a voltage signal. Class: Active Sensor Acceleration Strain Mechanical Vibration Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 15 Piezoelectric Material Suitable Material: Quartz Tourmaline Ferroelectric Ceramics Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 16 Longitudinal effect (1) unbelasteter Kristall belasteter Kristall Fx ---------+ Si Q ~ F: + O - - - - Qx d11 Fx n x y + - + + + ++++++++++ Fx © WZL/Fraunhofer IPT (1) The charge occurs on the mechanical surface by pressure with d II Piezoelectric co-efficient in x-direction Fx n Load in x-direction Number/Valency in piezo element Seite 17 Shearing effect (2) unbelasteter Kristall belasteter Kristall Fx --------O Si y + - + - x - © WZL/Fraunhofer IPT (2) The charge occurs on the mechanical surface by shear stress Q ~ F: + - + Qx 2 d11 Fx n + + +++++++++ with Fx d II Piezoelectric co-efficient in x-direction Fx n Load in the x-direction Valency / Number of the piezo element Seite 18 Transversal effect (3) unbelasteter Kristall belasteter Kristall unbelasteter Kristall belasteter Kristall Fy Fy O O + - y + + Si + - Si xx y -- - ++ - ++ ++ ++ ++ + - + - y + + - x - - + + -- Fy F y © WZL/Fraunhofer IPT Q ~ F: b - Qx d11 Fy a Mit: b a (3) The charge occurs on the vertical surface by mechanical stresses c d II Piezoelectric co-efficient in x-direction Fy Load in the y-direction b a Geometric relationship Seite 19 Piezoelectric Co-efficients Materials Quarz Li2B4O7 GaAs ZnO LiNbO3 LiTaO3 PZT PVDF Piezo- und Ferroelectric Materials Piezoelectric Co-efficient d [pC/N] 2,31 19,4 2,69 12,4 69,4 23,1 380 – 590 20 – 35 TCurie [°C] ca. 570 ca. 150 ca. 150 ca. 150 1145 603 190 – 360 170 – 200 Jaques und Pierre Curie in 1880 discovered the Piezoelectric effect. Upon reaching the Curie temperature Piezoelectric effect ceases. Development of a mixed crystal of Pb(Zn1/3 Nb 2/3)O3 und PbTiO3 with Piezoelectric co-efficient of d = 1500 pC/N © WZL/Fraunhofer IPT Seite 20 Construction of 3 force component sensors (Fx, Fy, Fz) Multi-layered structure by pairs of dics Shear effect Longitudinal effect Isolation Shear effect Isolation Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 21 4-Component Sensor (Fx, Fy, Fz, Mz) Fs r Torque Measurement: Arrangement of shear sensitive elements to form a ring M = Fs • r Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 22 Force Sensors and Dynamometer Measuring Range Fx, Fy: +/- 1 to 60 kN Fz: +/- 2 to 100 kN Measuring Range Fx, Fy: +/- 5 kN Fz: +/- 10 kN Measuring Range Fx, Fy: +/- 5 kN Fz: - 5 bis +20 kN Mz: +/- 200 Nm Measuring Range Fx, Fy: +/- 5 kN Fz: +/- 20 kN Mz: +/- 200 Nm Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 23 3-Component force measurement platform: Measuring Fc, Ff, Fp Kraft [N] Force /N Cutting Force Measuring in Turning 200 Fc 150 FP Ff 100 50 Fx Vorschubkraft 0 Fy Passivkraft Fz Schnittkraft -50 0 5 10 15 20 25 Cutting time Zeit tc /[s]s © WZL/Fraunhofer IPT Seite 24 Wirkleistung [V] Source: Kistler Instrumente AG © WZL/Fraunhofer IPT 1.5 1.25 1 0.75 0 2 4 6 8 10 12 Vorschubkraft Fz [N] 3 2.75 2.5 2.25 2 1.75 1.5 1.25 1 0.75 0.5 0.25 0 0 1.5 1000 Feed force Fz / N Wirkleistung [V] 3 2.75 2.5 2.25 2 1.75 1.5 1.25 1 0.75 0.5 0.25 0 Vorschubkraft Fz [N] Drehmoment Mz [Nm] Drehmoment Mz [Nm] Rotating Tool Dynamometer Measuring Mz, Fx, Fy, Fz Torque Mz / Nm Cutting Force Measuring in Drilling, Milling, Tapping, Reaming 14 16 18 20 Bohrweg [mm] 2 4 6 8 10 12 14 16 18 20 Drilling depth / mmBohrweg [mm] 900 1.25 800 1 700 600 0.75 500 400 0.5 300 0.25 200 100 0 00 0 2 2 4 4 6 6 8 8 10 10 12 12 14 16 18 20 14 16 18 20 Bohrweg [mm] Bohrweg [mm] Drilling depth / mm Seite 25 Strain Sensor Main expansion direction Elongation F Dl l F l0 A E Equivalent strain l0 q d d0 Sensitivity weakening d0 d 2 Poisson equation A © WZL/Fraunhofer IPT q m Typical Values: 1/m 3 … 4 for Steel 1/m 5 … 9 for Cast Iron Seite 26 Acceleration Sensor Basic Components Housing Seismic mass Electrode Piezoelectric Material Female connector Base Plate Various 3 axis acceleration sensors Measuring range: Frequency range: Sensitivity: Mass: +/- 5 g m/s² 1 – 3.000 Hz 1000 mV/g 16 g Measuring range: Frequency range: Sensitivity: Mass: +/- 50 g m/s² 0,5 – 5.000 Hz 100 mV/g 29 g Measuring range: Frequency range: Sensitivity: Mass: +/- 500 g m/s² 2,5 – 10.000 Hz 10 mV/g 7,6 g Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Seite 27 Application of three axis acceleration sensor Tool revolver Tool Magnet Acceleration sensor © WZL/Fraunhofer IPT Seite 28 Structure-borne sound Structure-borne sound is sound that propagates as a transverse wave in a solid body Basic Components Piezoelectric piezoelektrisches Element Element Dämpfungsmasse Damping mass Housing The measuring ranges of the sensors are limited for the reason of resonance. Membrane Coupling Membran und and Koppelelement Source: Kistler Instrumente AG © WZL/Fraunhofer IPT Accessible range 50 - 400 kHz bzw. 100 - 900 kHz Element Seite 29 Causes for Structure-borne sound (AE = Acoustic Emission) 5 1 Plastic Deformation in the Shear Plane 2 Friction on the rake face. 3 Crack initiation and crack propagation. 6 4 Friction between tool and workpiece. 7 5 Impact of the chip on the workpiece or tool. 1 6 Chip Breaking. 3 4 vc © WZL/Fraunhofer IPT 2 7 Friction through check of the chip on the rake face. Seite 30 Fields of Application and Application notes Fields of Application ■ Monitoring of the finishing process ■ Wear monitoring in turning, drilling and milling. ■ Recognizing unfavorable chip shapes. Joined Time Frequency Analysis for wear indication ■ Detection of overheating. 400 kHz 900 µm ■ The damping of the joints is highly dependent on frequency and is approximately 11 db i.e. application close to site of action. ■ Good coupling conditions require a high Amplitude [dB] Application notes surface quality at the installation site. ■ Coupling via liquid jet possible. © WZL/Fraunhofer IPT Seite 31 Pressure Sensors Basic components Fields of application. Monitor the clamping transported away Plug during deep drilling. Monitoring of contact pressure of the ceramic balls for hard burnishing. Monitoring systems for high pressure Sensor housing coolant supply Sealing shoulder Contact spring Transversal sensitive Quartz rod Connecting Piece Sleeve Membrane Source: Chip Blaster © WZL/Fraunhofer IPT Seite 32 Application for flow measurement Monitor the clamping during deep drilling. Absolute Pressure Sensor For a flow rate Orifice QC 2 p with Differential Pressure Sensor © WZL/Fraunhofer IPT Q Flow rate C p Constant Pressure difference Density Seite 33 Advantages and Disadvantages of Piezoelectric Sensor Advantages Disadvantages Large Measuring Range Suitability only for dynamic and quasi- High Resolution, ex. <10 mN within a measuring range of 5 kN Good Linearity and very less hysteresis. Easy handling through reset. High Curie Temperatures crystals used static measurements. Crosstalk between the axis. Structural weakness through sensor integration. High Cost with DMS. available from 573°C to 400°C. High overload protection with DMS No aging © WZL/Fraunhofer IPT Seite 34 Temperature Sensor Thermo-element Two color pyrometer Resistance thermometers Infrared camera © WZL/Fraunhofer IPT Seite 35 Thermo-element Two dis-similar metals are connected at one end electrically. A Temperature difference between TM und Tref generates a small electrical voltage Uth U th k A k B TM Uth + - (Seeback-Effect) TM Tref Uth is also influenced by materials A & B and B their reference temperatures. Manager Type positive negative Temperature Uth [mV] Seeback-range [°C] coeff. ar0°C [µV/°C] E Chrome Constantan -270 to 1000 -9.835 bis 76.358 58.70 J Iron Constantan -210 to 1200 -8.096 bis 69.536 50.37 K Chrome Aluminium -270 to 1372 -6.548 bis 54.874 39.48 -6.258 bis 20.869 38.74 T Copper © WZL/Fraunhofer IPT Constantan -270 to 400 Material kxPt [mV/100 K] Constantan -3.47…3.04 Nickel -1.9…-1.3 Platin 0.0 Copper 0.75 Iron 1.9 Nickel-Chrom 2.2 Ferro-silicon 42..50 Seite 36 Two Color Pyrometer The Planck's radiation law E T C1 1 5 exp C2 T …Provides for the ratio of radiation intensities of two wavelengths Eλ and λ1,2: 1 1 1 TR ln 2 T C 1 1 2 1 2 1 with: T = True Temperature TR = Measured Temperature ε1,2 = Emissivities C1,2 = Constants Features Measuring the radiation density at two different wavelengths. No reference is required (absolute measuring method) Contactless Spatial and temporal high resolution. Low influence of surface type on emissivity. Sensitive incident against ambient light and contamination of optics. Source: WSA RWTH Aachen © WZL/Fraunhofer IPT Seite 37 Measuring the Surface Temperature of the Workpiece Workpiece Chip HM-Tip Quarz fibre of two colour pyrometer (0,42 mm dia) vc Preparation of the insert is required. Perform thermal radiation of the component 1 mm Heat radiation surface(secondary cutting) through Quartz fiber unit. Bare metal surfaces have low emmisivity. Therefore, can be measured only from 200 degree Celsius. Not suitable for wet processing. © WZL/Fraunhofer IPT Seite 38 Temperature Measurement by a Two-Color-Pyrometer workpiece fiber chip measuring spot major cutting edge insert 0.5 mm Technical specifications quartz fiber ( 0.26 mm) Temperature range: app. 250 -1200 °C Maximum time resolution: 2 ms Measured temperature independent of surface emissivity © WZL/Fraunhofer IPT Seite 39 Combination of Temperature and Force Measurement Chip temperature aluminium feed 0,25 mm depth of cut 2 mm steel / titanium 0,1 mm 1 mm Cutting speed Cutting force Fc 500 N 300 200 100 0 © WZL/Fraunhofer IPT Seite 40 Alternative Measurement Position - Workpiece Surface °C 700 Measuring point Temperature distance to cutting edge 1 mm quartz fibre 600 500 4.5 mm 400 300 200 © WZL/Fraunhofer IPT 0 20 40 60 Cutting speed 80 100 m/s Seite 41 Alternative Measurement Position - Top of the Chip 1000 °C Quartz fibre Measuring point Temperatur Temperature Cemented carbide tip 800 optic Optik 600 400 Cutting insert © WZL/Fraunhofer IPT Hartmetallspitze cemented carbide tip 0 1000 2000 3000 4000 5000 6000 m/min Schnittgeschwindigkeit Cutting speed Seite 42 Surface Metrology tactile/stationary optical/ stationary Quelle: Wyko tactile/mobile © WZL/Fraunhofer IPT Quelle: Hommel Seite 43 3D Coordinate Measuring © WZL/Fraunhofer IPT Seite 44 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 45 Features and Technical Data of the Test Bench Excellent accessibility for filming and measuring 𝑣𝑐 relevant characteristics of the chip formation process Synchronised measurement of: – Cutting force components – Thermal imaging and pyrometer temperature measurement – Highspeed video analysis of chip formation New level validation of metal cutting simulations Highspeed Videocamera Workpiece + Fixture Tool holder for Friction Experiment (Slide 4) Cutting Tool Dynamometer x-y-Feed Drive © WZL/Fraunhofer IPT Also serves as experimental basis for cutting, friction and material modelling Technical Data: Machine tool: Forst RASX 8x2200x600 M / CNC Cutting velocity: 0.5 ≤ vc ≤ 150 m/min Cutting length: 0 - 500 mm Width / Depth of cut 0 - 15 mm Max. cutting force: 80 kN Seite 46 Features and Technical Data of the Test Bench Shaftholder max. 32x32 Grooving / Parting Tool holders for orthogonal cutting (Inclination angle = 0°, tool edge angle = 0°) Phantom v7.3 Highspeedvideocamera, LED Illumination vc= 20 m/min f = 0,3 mm © WZL/Fraunhofer IPT workpieceholder workpiece vc 1 mm Seite 47 Experimental Determination of Friction Coefficients – Test setup Force measurement with 3-Component-Dynamometer Temperature measurement on Tool surface of the workpiece with Two-Color-Pyrometer Workpiece part: sheets/flat material Tool insert: Indexable inserts y z Pyrometer fiber © WZL/Fraunhofer IPT Seite 48 High Speed Filming of Friction Process Sliding speed Vrel = 60 m/min Uncut chip thickness: t = 0.5 mm Cutting width: b = 1.5 mm Cutting tool material: Sandvik 1005 Workpiece material: C45E+N Frame rate: 6700 FPS © WZL/Fraunhofer IPT Seite 49 Advanced Experimental Setup: Orthogonal Cut on Broaching Machine tool tool holder workpiece High-Speed Filming workpiece holder HS camera measurement platform High speed camera: – Type: Vision Research Phantom v7.3 – Frame rate: 6.688 fps by 800 x 600 pixel 500.000 fps by 32 x 16 pixel tool © WZL/Fraunhofer IPT workpiece holder workpiece IR camera High-Speed Thermography High speed external broaching machine: – Type: Forst RASX 8x2200x600 M/CNC – Max. force: 80 kN – Power: 40 kW – Max. cutting speed: 150 m/min – Tool fixed und workpiece moved – Optimal filming of the cutting zone High speed IR camera: – Type: FLIR SC7600 – Frame rate: 100 fps by 640 x 512 pixel 800 fps by 160 x 128 pixel – Measurement range: -20°C - 3000 °C (±1°C) Seite 50 High Speed Filming of Chip Formation (vC = 150 m/min, dry cut) h = 0.20 mm Workpiece: AISI 1045 normalized 3.5 x 50 x 200 mm © WZL/Fraunhofer IPT h = 0.40 mm Tool: Carbide, uncoated Sharp (rß 5 µm) Seite 51 High Speed Thermography During Chip Formation (vC = 150 m/min) h = 0.10 mm h = 0.50 mm 600 400 °C 350 300 250 200 50 0 Workpiece: AISI 1045 normalized 3.5 x 50 x 200 mm © WZL/Fraunhofer IPT Tool: Carbide, uncoated Sharp (rß 5 µm) Seite 52 High Speed Thermography During Chip Formation (vC = 150 m/min) Tool Chip t = 82 ms t = 86 ms End of the cut 50 0 200 250 350 °C 300 Time after tool-workpiece contact t = 43 ms 400 t = 6 ms 600 h = 0.5 mm h = 0.1 mm End of the cut t = 20 ms © WZL/Fraunhofer IPT t = 90 ms t = 100 ms t = 160 ms Seite 53 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 54 FE Validation of a Developed FE Cutting Model Tool Cutting parameters Workpiece material: Tool material: Cutting speed: Feed: Cooling: AISI 1045 Sandvik H13A, = 6° α = 3°, rß 5 µm 150 m/min variabel dry y Workpiece vC x Developed friction model: µ = µ (h,vc) µ < 0.577 only sliding friction (Coulomb friction) µ 0.577 sliding + sticking friction (hybrid friction) Boundary conditions Cutting tool: Rigid Workpiece: Visco-Plastic With heat dissipation Contact: Heat transfer (Conduction & Convection) Modified Johnson-Cook material law: (546 MPa 487 MPa 0.25 ) (1 0.015 ln( / 0 )) exp( 1.67 [T T 0 ] / Tm ) © WZL/Fraunhofer IPT Seite 55 Material and Friction Laws Validation: Chip Formation (Orthogonal Cut, vC = 150 m/min, AISI 1045) h = 0.5 mm FE simulation Experiment h = 0.2 mm FE simulation Experiment © WZL/Fraunhofer IPT h = 0.4 mm FE simulation Experiment h = 0.04 mm FE simulation Experiment h = 0.3 mm FE simulation Experiment h = 0.02 mm FE simulation Experiment Seite 56 Material and Friction Laws Validation: FE Cutting Simulation (vC = 150 m/min, h = 0.50 mm, DEFORM) Plastic strain [-] Effective stress [MPa] © WZL/Fraunhofer IPT Strain rate [1/s] Temperature [ C] Seite 57 Turning: Comparison of Simulation and Real Chip Flow CNMG120408 Chip breaker NF HC-P15 kr = 95° n = -6° s = -6° C45E+N ap = 1,9 mm f = 0,25 mm vc = 200 m/min dry vf © WZL/Fraunhofer IPT vc Seite 58 Milling: Verification of the FE Model Experiment . Simulation Full agreement © WZL/Fraunhofer IPT Seite 59 Drilling: Verification of the Chip Formation Experimental chip formation Chip formation in the simulation Workpiece material: C45E+N Cutting speed: vc = 35 m/min Cutting tool material: HW K20 Feed: © WZL/Fraunhofer IPT f = 0.012 mm Seite 60 FE-Based Calibration Process for the Tool Wear Model Modeling Verschleißmarkenbreite über die Schnittzeit 16MnCr5 (einsatzgehärtet), Stegbreite = 1 mm, cBN bestückte Einstechplatte der Sorte N151.2-600-50E-G Schnittgeschwindigkeit vc = 150, 200, 300 m/min und Vorschub f = 0,06 mm Wear curve Machining experiments 120 vc = 200 m/min vc = 150 m/min Verschleißmarkenbreite VB [µm] Tool-wear VB vc = 250 m/min 100 80 t = 10 min t = 6 min t = 4 min t = 1 min 60 40 20 0 0 5 10 15 20 25 Cutting time t 30 35 40 Schnittzeit t [min] dW σ n v ch C1 e dt C ( 2 ) T lg C1 lg {w /( n VS)} Determination of the specific material parameters C1 and C2 dW/dt Regression analysis FE-analysis Temperature Normal- C2 tension Sliding speed 1/T © WZL/Fraunhofer IPT Seite 61 Verification of the Tool Wear Simulation for the Flank Wear vc = 150 m/min, f = 0.06 mm, ap = 1 mm, dry eff = -26° Tool [mm] Flank wear VB [mm] Width VB/ Wearwidth Flank Time: 5 min 0 = 7° Time: 15 min Time: 25 min Time: 35 min 93 µm 0,1 Experiment 0,08 0,06 Simulation 0,04 0,02 0 0 5 10 15 20 25 30 35 Cutting time t [min] Time [min] © WZL/Fraunhofer IPT Seite 62 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 63 What is Optimization? „Optimization is the act of obtaining the best result under given circumstances” “Optimization is a branch of mathematics concerned with the application of scientific methods and techniques to decision making problems and with establishing the best or optimal solutions” “Optimization can be defined as the process of finding the conditions that give the maximum or minimum of an objective function” „Making things better“ „Generating more profit„ „Determining the best“ „Improving the performance of systems“ „Do more with less“ “Optimization is the mathematical discipline which is concerned with finding the maxima and minima of functions, possibly subject to constraints” Source: Papalambros, Altair Engineering © WZL/Fraunhofer IPT Seite 64 Historical Development Newton, 1642-1727: The development of differential calculus methods of optimization Bernoulli, 1697: Brachistochrone Problem Leibnitz, 1646-1716: Differential calculus methods of optimization Euler, 1707-1783: Calculus of variations, minimizing functions Lagrange, 1736-1813: Optimization of constrained problems Cauchy, 1789-1857: Steepest descent method for unconstrained optimization Von Neumann, 1903-1957: Game theory Bellman, 1920-1984: Principle of optimality in dynamic programming problems Karmarkar, 1957: Interiot point method for linear programming problems Bendsoe, Kikuchi, 1988: Topology optimization Tucker, 1905-1995: Optimality conditions Dantzig, 1914-2005: Linear programming and Simplex method Source: Nocedal, Spall, Rao, Gill, Goldberg © WZL/Fraunhofer IPT Seite 65 Main Benefits of Optimization More efficient and thorough research Decrease of product development costs and time to market Reduction of production time and better utilization of capital Acceleration of process and product development Increase of competitive advantages and innovation More engineers having optimization knowledge Making a system reliable and robust Providing insight in system problem, underlying physics and model weaknesses Improving process performance and product quality Opening up new research fields and technologies Promotion of interdisciplinary research and applications Creation of new jobs, new skills and new growth opportunities Source: Chong, Zak, Rao, Gill © WZL/Fraunhofer IPT Seite 66 Disadvantages of Optimization Proper problem formulation critical! Choosing the right algorithm for a given problem Many algorithms contain lots of control parameters Optimization tends to exploit weaknesses in models Optimization can result in very sensitive designs Some problems are simply too hard / large / expensive Large problems optimization requires lots of computing power Source: Chong, Zak, Rao, Gill © WZL/Fraunhofer IPT Seite 67 What is the Optimization Problem? Minimize (or maximize) an objective „performance“ function: taking into account the constraints: (x1,x2,…,xn) F(x1,x2,…,xn) Gi(x1,x2,…,xn) = 0, i=1,2,…,p Hj(x1,x2,…,xn) < 0, j=1,2,…,q are the n system variables Gi(x1,x2,…,xn) are the p equality constraints Hj(x1,x2,…,xn) are the q inequality constraints Source:Papalambros © WZL/Fraunhofer IPT Seite 68 System Definition Input System approach Output Environment What belongs to system / environment? What is the level of details? What is the system function? What is input / output? © WZL/Fraunhofer IPT Seite 69 System Example: Catilever Beam L Steel (E, ρ) h b U(t), Mb(t), V(t) h Mathematical model: FL3 U 3EI System variables: FL3 bh 3 3E 12 © WZL/Fraunhofer IPT F(t) System U(t) U(t) System F(t) F(t) System Mb(t) h, b, L E, ρ System V(t) F(t), U(t), Mb(t), V(t) System parameters: h, b, L System constants: 4 F L3 E b h3 E, ρ F(t) Seite 70 The Optimization Procedure Constants Cj Responses System model f, g, h System variables xi Optimizer Derivatives of responses (System sensitivities) f g h , , xi xi xi © WZL/Fraunhofer IPT Seite 71 Applications of Optimization Mechanic, manufacturing, architecture, electrical circuits, economic, transportation, etc. – Improving structure Automotive Civil infrastructure – Protein folding – System identification – Logistics – Financial market forecasting (options pricing) – Traveling salesman problem – Route planning – Operations research Biomedical Aerospace – Controller design – Spacecraft trajectory planning Source: Red Cedar Technology © WZL/Fraunhofer IPT Seite 72 Categories of Structural Optimization Topology optimization: Size optimization: Shape optimization: Material optimization: Body in White of BMW 5 GT Source: Altair Engineering, BMW, Wikipedia © WZL/Fraunhofer IPT Seite 73 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 74 Optimization Algorithms Analytical methods Numerical stochastic methods – Variational method – Robbins-Monro algorithm – Simultaneous-Mode-Design method – Kiefer-Wolfowitz algorithm Numerical deterministic methods – Stochastic gradient descent – Grid/raster method – Simultaneous perturbation stochastic approximation – Gradiant method – Scenario optimization approach – Steepest descent method – Simulated / Quantum annealing – Simplex method – Swarm algorithms – Penalty function methods – Genetic algorithm – Levenberg-Marquardt algorithm – Evolution strategies – Etc. – Etc. Source: Wegener, Robbins, Roberto, Dixit, Malliaris © WZL/Fraunhofer IPT Seite 75 Commercial Software for Optimization Company General optimization Web address Structural optimization Altair Engineering www.altair.com HyperOpt OptiStruct Ansys www.ansys.com - Ansys-CADOE Engineous Software www.engineous.com iSIGHT - MSC Software www.mscsoftware.com - MSC.Nastran Noesis www.noesissolutions.com Optimus - Opttek www.optteck.com OptQuest - Oculus Technologies www.oculustech.com CO - Phoenix Integration www.phoenix-int.com Model Center - UGS PLM www.ugs.com - NX.Nastran Vanderplaats R&D www.vrand.com VisualDOC, BIGDOT GENESIS © WZL/Fraunhofer IPT Seite 76 Example: Design Optimization Problem Definition Initial Models Database Multi-Models Generation Multidisciplinary Computations Optimization Algorithm Objective Constraints Optimized Models Database Source: Selmin © WZL/Fraunhofer IPT Seite 77 Topology Driven Vehicle Concepts: Concept Development Process Define all available package space, loading and BC’s Topology optimization for gross concept features Interpret into first concept design Topology optimization for concept refinement Interpret concept for final optimization and design details Final concept Source: Altair Engineering © WZL/Fraunhofer IPT Seite 78 Topology Driven Vehicle Concepts: Results Final concept design – – – – – – – Primary Hydroformed Sections Mid-Rail “C” Section Welded Body Mount Brackets 23% lower mass 25% fewer parts 50% less weld length Cost penalty: $0.25 cost per lb saved Performance results – – – – – Twist: Vertical bend: Lateral bend: Bending stiffness: Torsion stiffness: 25.0 Hz (+34%) 27.8 Hz (+2.5%) 26.4 Hz (-9%) 3278 N/mm (0%) 159 kNm/rad (+31%) Source: Altair Engineering © WZL/Fraunhofer IPT Seite 79 Hydroformed Lower Rail Crush zone Crush zone 67 design variables Maximize energy absorbed in crush zone Identify the rail shape and thickness 66 control points and one gage thickness Subject to constraints on: – Peak force – Mass – Manufacturability Source: Red Cedar Technology © WZL/Fraunhofer IPT Seite 80 Validation: Lower Rail Benefits Compared to 6-month manual design effort: – Overall crash response resulted in equivalent of five star rating – Energy absorption increased by 100% – Peak force reduced by 30% – Weight reduced by 20% Source: Red Cedar Technology (Goodman) © WZL/Fraunhofer IPT Seite 81 Outline 1 Learning Goals 2 Relevant Process Quantities in Cutting Tools 3 Technical Sensors in Metal Cutting 4 Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature 5 Measurement Integration in the Cutting Process 6 Validation of Cutting Process Models 7 Optimization: Definition, History, Procedure and Applications 8 Optimization Algorithms, Software and Examples 9 Integration of Optimization in FE Cutting Simulation © WZL/Fraunhofer IPT Seite 82 The Great Challenges of the Cutting Process Process Strain Strain rate / s-1 Thomolog Extrusion 2–5 10-1 – 10-2 0,16 – 0,7 Forging / Rolling 0,1 – 0,5 10 – 10+3 0,16 – 0,7 Sheet metal forming 0,1 – 0,5 10 – 10+2 0,16 – 0,7 Cutting 1–5 10+3 – 10+6 0,16 – 0,9 Cutting process Extreme conditions in the cutting process Source: Jaspers © WZL/Fraunhofer IPT Seite 83 Influencing Factors on the Cutting Process Bild eines Prozesses Workpiece material structure Cutting zone chip forming mechanisms texture mechanical properties hardness residual stresses © WZL/Fraunhofer IPT Tool cutting material Machine machine design coating cooling lubricant geometry cutting parameters contact conditions e.g.: friction, wear heat transfer drive system M tool holder clamping device Seite 84 Cutting Simulation: Input- und Output Parameters Chip formation Temperature Tension Deformation Rate of deformation Chip type Chip flow Chip crack Component / tool Geometry Material data Contact conditions Boundary conditions Cutting conditions © WZL/Fraunhofer IPT Tool Strain Tension Temperature Cutting forces Wear Component Strain Temperatures Deformation Burr formation Distortion Future: Residual stresses Surface quality, e.g.: roughness, changes in shape, Measurement and position Seite 85 Integration of the Optimization in the FEM Change physical problem Physical problem Improve mathematical model Mathematical model Numerical model Optimization FEM Does answer make sense? No! Refine analysis Process improvement and optimization Yes! © WZL/Fraunhofer IPT Seite 86 FE Based Sensitivity Analysis Varied input parameters: Goal output parameters: Heat capacity Thermal conductivity Cutting force Fc Passive force Fp Flow stress Feed force Ff Friction coefficient Temperature T Tool micro-geometry Legend Influence Heat capacity Thermal conductivity Flow stress Tool micro-geometry Friction Cutting force low Feed force medium Passive force high © WZL/Fraunhofer IPT Temperature Seite 87 Benchmark-Analysis to Choose the Best Tool Geometry Fixed input parameter material parameter, friction coefficients Cutting parameter 2 vc2, ap1, f1 + Tool B C Determination of the thermomechanical loadspectrum, chip flow, chip form A Temp + Coating TiN TiAlN AlO2 © WZL/Fraunhofer IPT Flank wear VB Q, T, Fi, Cutting parameter 1 2 A Cutting parameter 1 # + vc1, ap1, f1 Benchmark-Analysis Cutting simulation Wear B Tool Stress C Chip flow Tool A + - ++ - Tool B - -- o + Tool C ++ ++ + + Optimised tooland tool carriergeometry Seite 88 Thank you for your attention! © WZL/Fraunhofer IPT Seite 89 Questions Which measuring sensors do you know? Describe the Piezoelectric effect. What is the Seeback effect? What is Optimization? Name the main benefits and disadvantages of optimization. Please describe the Optimization Problem. What are the categories of structural optimization? Please give some optimization Algorithms. Which influencing factors on the cutting process do you know? List the input- und output parameters of cutting simulation. Please characterize the Integration of the Optimization in the FEM. © WZL/Fraunhofer IPT Seite 90