Mechanics and Dynamics of 5-axis Ball-end Milling Operations

Mechanics and Dynamics of 5-axis Ball-end Milling Operations Erdem OZTURK, PhD.Candidate L.Taner TUNC, PhD. Candidate Assoc.Prof. Erhan BUDAK Manufacturing Research Laboratory, SABANCI UNIVERSITY, ISTANBUL 06 November 2009 ATILIM UNIVERSITY, ANKARA

Mechanics 5-axis ball-end milling Dynamics Process Geometry Force & Deflection Model Parameter selection considering force/deflections Applications Interfacing with CAM PM software Stability Models Freq.,time-domain solutions Effect of lead and tilt angles on stability Application on a compressor disk

Manufacturing Research Laboratory People Director: Assoc. Prof. Erhan Budak 1 Research Fellow, 2 PhD., 4 MSc. and 10 undergrad. senior students 2 technicians, 4 interns Research Areas Mechanics and dynamics of machining Advanced CAM applications Machine tool vibrations

Manufacturing Research Laboratory Facilities Machine Tools Deckel Maho DMU 50evo 5-axis machining center. Mori Seiki NL1500 Turning Center Mazak NEXUS 510 CII 3 Axis Machining Center Measurement Instruments Kistler Table/ Rotary Dynamometers Various vibration and displacement sensors, modal test kits Inspection Equipment Mitutoyo Coordinate Measuring Machine (CMM) Euro-C-A544) Surface Roughness measurement system Roundness measurement device Microscopes

Mechanics 5-axis ball-end milling Dynamics Process Geometry Force & Deflection Model Parameter selection considering force/deflections Applications Interfacing with CAM PM software Stability Models Freq,time-domain solutions Effect of lead and tilt angles on stability Application on a compressor disk

5-axis Ball-end Milling Common process Aerospace, Automotive, Die/mold Industries Application Complex Surfaces Lead angle Tilt angle

Technology Special Machine Tools Additional 2 rotational axes Different kinematic designs CAD/CAM More complex wrt. 3-axis CAM softwares provide no info about the physics of the process Forces, Form Errors, vibrations Current work flow CAD CAM CL file Post processor G code Machine tool Product

Technology Special Machine Tools Additional 2 rotational axes Different kinematic designs CAD/CAM More complex wrt. 3-axis CAM software provides no info about the physics of the process Forces, Form Errors, vibrations Current work flow CAD CAM CL file Post processor G code Machine tool Product Problems Torque/power limits High form errors, tool breakage Chatter vibrations

Method Special Machine Tools Additional 2 rotational axes Different kinematic designs CAD/CAM More complex wrt. 3-axis CAM software provides no info about the physics of the process Forces, Form Errors, vibrations Proposed work flow CAD CAM CL file Post processor G code Machine tool Product Process Models Increased productivity and quality

Mechanics 5-axis ball-end milling Dynamics Process Geometry Force & Deflection Models Parameter selection considering force/deflections Applications Interfacing with CAM PM software Stability Models Freq,time-domain solutions Effect of lead and tilt angles on stability Application on a compressor disk

Process Geometry Three coordinate systems Variable geometry along the tool axis Complex engagement region* Cutting Types: First cut, Following cut, Slotting Ozturk, E. and Budak, E., (2007), Modeling of 5-axis Milling Processes, Machining Science and Technology, 11:3, 287 311

Engagement Criteria Common engagement criteria Local chip thickness 0 N a Ro Following-cut case (positive cross-feed direction)

Scallop Height Two different cases depending on the step over value s 2R o cos t i s 2R o cos t i

Material Removal Rate(MRR) Flat-end Milling s 2R o cos t i s 2R o cos t i Area proj Roa R wdn o MRR F vel Area proj

Process Mechanics Variable mechanics along the tool axis Start and exit angles, Chip thickness, Cutting force coefficients

Force & Deflection Models Differential elements Oblique model for differential forces df df rj df (φ (z)) K tj aj (φ (z)) K j j (φ (z)) K j ds+ K ds+ K ds+ K (h)db (h)db (h)db Simulated vs. measured forces re te ae rc tc ac Over 70 cutting tests performed Statistical analysis max. error<20%

Cutting Forces(N) Indentation case If tool tip is in cut Extra indentation forces 600 400 Fz Fy 200 0-90 -200 0 90 180 270-400 Fx -600 Tool rotation angle(deg) Lead,tilt (deg) Step over (mm) Cutting type Cross feed direction Cutting depth(mm) feed mm/tooth n (rpm) -15,0 7.2 First cut Positive 3 0.1 500

Tool tip contact avoidance* Lead angle non-negative Cutting depth,a <R o (1-cos(tilt)cos(lead)) Step over, tool orientation selection * Ozturk, E., Tunc, L., T., Budak, E., (2009), Investigation of Lead and Tilt Angle Effects in 5-Axis Ball-End Milling Processes, International Journal of Machine Tools and Manufacture, 49,1053-1062

Parameter Selection: Lead and Tilt Angles Roughing: Minimize force Cutting depth (mm) 5 Step over(mm) 5 Cutting Type Following cut Cross-feed direction Negative Spindle (rpm) 1000 Feed (mm/tooth) 0.05 Material Cutting Tool Ti6Al4V 12 mm diameter 2 flute ball-end mill helix angle :30 deg rake angle:8 deg

Parameter Selection: Lead and Tilt Angles Roughing: Minimize force Point (lead, tilt) deg Simulated maximum F xy (N) Measured maximum F xy (N) 1 0,10 692 653 2 0,50 821 786 3 30,-50 1190 1110 Cutting depth (mm) 5 Cutting type Slotting Lead(deg) [0,5,..,60] Tilt(deg) [-60,55,...55,60] Spindle (rpm) 1000 Feed (mm/tooth) 0.05 Material Cutting Tool Ti6Al4V 12 mm diameter 2 flute ball-end mill helix angle :30 deg rake angle:8 deg

Parameter Selection: Lead and Tilt Angles Finishing: Minimize deflection in the surface normal direction Tool diameter (mm) 12 Cutting depth (mm) 1 Step over(mm) 1 Cutting Type Following cut Cross-feed direction Negative Spindle (rpm) 1000 Feed (mm/tooth) 0.05 Material Ti6Al4V Lead,tilt=0 Lead(+) Cutting Tool 12 mm diameter 2 flute ball-end mill helix angle :30 deg rake angle:8 deg Tool tip mark

Mechanics 5-axis ball-end milling Dynamics Process Geometry Force & Deflection Model Parameter selection considering force/deflections Applications Interfacing with CAM PM software Stability Models Freq,time-domain solutions Effect of lead and tilt angles on stability Application on a compressor disk

Stability Models Chatter marks Aim: Elimination of chatter vibrations Dynamic cutting forces on a disc l l l T l F ( ) F ( ) F ( ) ab ( ) d x y z 3D dynamics Cutting zone discretized Dynamic forces integrated Fourier expansion Dynamic displacement vector d x ( t) x( t ) y( t) y( t ) z( t) z( t ) T Directional coefficient matrix: Time varying and periodic r p l l irn l 1 l B ( ) Br e, Br B r p 0 ( ) e irn d

Single frequency method B l () represented by B ol only Dynamic displacements occur at chatter frequency ω c Eigenvalue problem: Iterative procedure for stability diagrams. Multi frequency method Effect of multi-frequencies included Eigenvalue problem both depends on ω c and ω t A numerical solution procedure T z y x c i t F t F t F i e c ) ( ) ( ) ( ) ( ) 1 ( G d in h l h in h l h in l in l l o l s s s s e e e e B B B B B B.... ) ( 1 1 Single vs. multi-frequency method in h l h in h l h in l in l l o l s s s s e e e e B B B B B B.... ) ( 1 1

Process Directional Simulationcoefficient matrix, B() Flat-end milling Small step over Small immersion Added lobes Ball-end milling Small step over Not so small immersion Negligible multifreq. effects

Time-domain simulation Simulation in discrete time intervals Calculation of dynamic forces, displacements Non-linearities included Unstable Marginally stable Stable

Experimental Case 1: Slotting 5-axis ball-end milling lead, tilt= 15 o,-15 o - D= 20 mm Direction f n (Hz) z (%) k (N/mm) X 747 3.89 26300 Y 766 3.98 36000 stable chatter

Experimental Case 2: following cut 5-axis ball-end milling Lead, tilt= 15 o,15 o, step over 0.1 mm D= 8 mm,cross-feed direction: (+) Modal data Mod e # f n (Hz) z m(kg) 1 1826.7 0.99 0.0418 2 1934.4 0.96 0.0824 3 2028.4 0.97 0.0852 Addition of multifrequency terms Negligible effect on stability diagram

Lead and tilt effects on stability Lead tilt angles may change the feed direction Measured transfer function matrix H needs to be oriented ' G T G HT G Lead and tilt effect on abs. stability T ( feed wrt. workpiece, lead, tilt) G T G Before lead, tilt After lead, tilt Stability limit can be increased by: - optimizing feed direction (lead & tilt) - part clamping orientation

Mechanics 5-axis ball-end milling Dynamics Process Geometry Force & Deflection Model Parameter selection considering force/deflections Applications Interfacing with CAM PM software Stability Models Freq,time-domain solutions Effect of lead and tilt angles on stability Application on a compressor disk

Process Simulation: Interfacing with CAM Cutter Location File Workpiece Information Geometrical Calculations Process Model

Extracting Cutting Conditions Determine tool orientation (lead, tilt) from CL file Use CL points between successive passes Determine step over and cutting depth analytically using CL points Very fast, practical and accurate - Works for smooth and continuous surfaces!

Parameter Extraction & Process Simulation:

Point Mill Software

Industrial Applications

Application: Machining of a Compressor Disk Roughing Pass 20 mm tool dia., 0.16 mm/tooth Semi-Finishing Pass 16 mm diameter tool 0.12 mm/tooth 2 mm constant stock

Results & Improvements Feed rate scheduling Leveled cutting forces Approx. 25% saving in machining time Chatter analysis in Roughing & Semi Finishing 40% saving in Roughing 50% saving in Semi Finishing

Feed rates in 5-axis milling Not always accurate! Rotary motions neglected or miscalculated Depends on CNC and/or post processor G94: Constant feed (CNC) F1000 => feed=1000mm/min G93: Inverse time feed (post) F1000 => time=0.001 min

Conclusions Geometry, mechanics and stability of 5-axis milling modeled Lead and tilt angle effects on forces and stability demonstrated Models used in parameter selection for increased productivity Part program interfacing provides continuous simulation capability Models verified experimentally and applied on industrial parts

Publications Refereed Journal Papers Ozturk, E., Tunc, L., T., Budak, E., (2009), Investigation of Lead and Tilt Angle Effects in 5- Axis Ball-End Milling Processes, International Journal of Machine Tools and Manufacture, 49,1053-1062. Budak, E., Ozturk, E., Tunc,L., T., (2009), Modeling and Simulation of 5-Axis Milling Processes, Annals of CIRP, Manufacturing Technology, 58, 347-350. Ozturk, E. and Budak, E., (2007), Modeling of 5-axis Milling Processes, Machining Science and Technology, 11:3, 287 311 Ozturk, E., Budak, E., (2009), Dynamics of 5-axis Ball-end Milling, Part I: Using Singlefrequency Solution, Journal of Manufacturing Science and Engineering, in review. Ozturk, E., Budak, E., (2009), Dynamics of 5-axis Ball-end Milling, Part II: Multi-Frequency Solution, Journal of Manufacturing Science and Engineering, in review.

Publications Refereed International Conference Proceedings Ozturk, E., Budak E., (2008), Chatter Stability of 5-Axis Milling Using Multi-Frequency Solution, Proceedings of the 3rd CIRP International Conference: High Performance Cutting, Dublin, Ireland, 1: 429-444. Ozturk, E., Ozlu, E., Budak E., (2007), Modeling Dynamics and Stability of 5-axis Milling Processes, Proceedings of the 10th CIRP Workshop on Modeling of Machining Operations, Reggio Calabria, Italy, 469-476. Ozturk, E., Tunc, L., T., Budak E., (2007), Machining Parameter and Strategy Selection in Multi Axis Milling of Sculptured Surfaces, Proceedings of the 4th International Conference and Exhibition on Design and Production of Machines and Dies/Molds, Cesme, Turkey, Tunc, L., T., Budak E., Ozturk, E., (2006), Optimization of 5-axis Milling Processes Using Process Models, Proceedings of the 9th CIRP Workshop on Modeling of Machining Operations, Bled, Slovenia, 179-186. Ozturk, E., Budak, E., (2005), Modeling of 5-axis Milling Forces, Proceedings of the 8th CIRP Workshop on Modeling of Machining Operations, Chemnitz, Germany, 319-326

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