TEQIP Workshop on Machining Dynamics Machining Process Modelling + Machine Tool Dynamic Testing + Avoidance of Chatter Vibrations 18-22 July 2016 Experimental characterization of machining processes Dr. Mohit Law mlaw@iitk.ac.in
Depth of cut (axial/radial) Mag. [m/n] Machining dynamics Machining models F t = K t bh F f = K f bh Dynamics Tools Freq. [Hz] Chatter Stable Spindle Speed [RPM] Source: MAL, UBC 2
Objectives of experimental characterization Process planning Identify cutting force coefficients, these give us a sense of machinability of materials Cutting coefficients are inputs into chatter prediction models Outline Identification of cutting force coefficients Turning Milling 3
Orthogonal cutting force coefficients F t = F tc + F te ; F f = F fc + F fe ; F t = bh τ s cos β a α r sin φ c cos φ c + β a α r F f = bh τ s sin β a α r sin φ c cos φ c + β a α r F t = K tc bh + K te b; F f = K fc bh + K fe b; cos β a α r K t = τ s sin φ c cos φ c + β a α r sin β a α r K f = τ s sin φ c cos φ c + β a α r 4
Oblique cutting force coefficients F t = bh τ s cos β n α n + tan i tan η sin β n sin φ n cos 2 φ n + β n α n + tan 2 ηsin 2 β n F t = F tc + F te ; F r = F rc + F re ; F a = F ac + F ae ; F f = bh τ s sin φ n cos i sin β n α n cos 2 φ n + β n α n + tan 2 ηsin 2 β n F r = bh τ s cos β n α n cos β n α n tan i tan η sin β n sin φ n cos 2 φ n + β n α n + tan 2 ηsin 2 β n K tc = τ s cos β n α n + tan i tan η sin β n sin φ n cos 2 φ n + β n α n + tan 2 ηsin 2 β n F t = K tc bh + K te b; F r = K rc bh + K re b; F a = K ac bh + K ae b; K fc = τ s sin φ n cos i sin β n α n cos 2 φ n + β n α n + tan 2 ηsin 2 β n K fc = τ s cos β n α n cos β n α n tan i tan η sin β n sin φ n cos 2 φ n + β n α n + tan 2 ηsin 2 β n 5
Orthogonal cutting coefficients Step 1 Select material of interest Step 2 Setup tube on a lathe Step 3 Turning tool with zero inclination angle, flat rake face, and no chip breaker Step 4 Select speeds most often used in your application Step 5 Measure cutting forces using dynamometer Source: CutPro Guide, MAL Inc. Step 6 Repeat tests for a range of feed rates Repeat tests for different speeds and tool geometries as necessary Run cutting coefficient identification algorithm 6
Orthogonal cutting coefficients Advantages: Experiments and measurements are not very difficult Identified coefficients can be transformed using the orthogonal to oblique transformation methods This enables prediction of cutting coefficients for oblique cutting using experiments from orthogonal cutting Source: CutPro Guide, MAL Inc. Disadvantages: Need to specially prepare tubes and tools Need to conduct quite a many tests for complete characterization of speeds, feeds and geometry Not directly applicable to tools with proper geometry and chip breakers used in many applications 7
Oblique cutting tests for identification Conduct a dedicated series of tests at different feed rates and identify coefficients directly for the tool-workpiece-cutting parameter combination of interest Feed Rate Measured Measured Test No: h [mm/rev] Ftc [N] Ffc [N] 1 0.050 101 32 2 0.075 140 35 3 0.100 175 39 4 0.125 213 41 240 220 200 Test 1 F f F t 300 250 Test 4 F f F t 180 160 200 140 120 100 150 80 60 100 40 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 50 0 1000 2000 3000 4000 5000 6000 8
Prediction Oblique cutting tests for identification Forces are composed of shearing and edge rubbing force components F t = F tc + F te ; F f = F fc + F fe ; or F t = K tc bh + K te b; F f = K fc bh + K fe b; Consider only shearing components (since edge forces do not contribute to cutting): F tc = K tc bh; F fc = K fc bh; Hence the cutting coefficients are: Slopes from graph: K tc b and K fc bh K tc = F tc bh ; K fc = F fc bh ; K te = F te bh ; K fe = F fe bh ; Slopes from graph: 1484 and 124 K tc = 712; K fc = 62; K tc = 14; K fc = 13; Units: N mm 2 9
Identification in milling Conduct a dedicated series of tests at different feed rates and identify coefficients directly for the tool-workpiece-cutting parameter combination of interest Use a small workpiece Ensure dynamometer is clamped rigidly to the table Measure cutting forces at stable DOC and at low cutting speed Collect cutting forces for a full number of revolutions Conduct set of milling tests at different feeds but constant axial DOC and immersion (preferably slotting) Run Axial DOC [mm] Radial engagement [% of D] Feed/tooth [mm/tooth] Cutting speed [m/min] Spindle speed [RPM] Feed [mm/min] 1 1 100 0.1 180 3570 1428 2 1 100 0.125 180 3570 1785 3 1 100 0.15 180 3570 2142 4 1 100 0.175 180 3570 2500 10
Force, F(N) Force, F(N) Cutting force measurements in milling Run Axial DOC [mm] Radial engagement [% of D] Feed/tooth [mm/tooth] Cutting speed [m/min] Spindle speed [RPM] Feed [mm/min] 1 1 100 0.1 180 3570 1428 2 1 100 0.125 180 3570 1785 3 1 100 0.15 180 3570 2142 4 1 100 0.175 180 3570 2500 Run 1 Run 4 200 150 100 Force components 300 F x 250 F y F z 200 150 Force components F x F y F z 50 100 0 50 0-50 -50-100 -100-150 0.1 0.15 0.2 0.25 time, t(s) -150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 time, t(s) 11
Force (N) Identification in milling (slotting) Average milling force per tooth period F q = 1 φ ex F φ q φ j dφ; q = x, y, z p φ st when φ st φ φ ex For full immersion slotting, φ st = 0; φ ex = π Average milling force per tooth period, simplified: F x = N ta 4 K rcc N ta π K re F y = N ta 4 K tcc + N ta π K te F z = N ta 4 K acc + N ta π K ae F q = F qc c + F q ; q = x, y, z Cutting coefficients 250 200 150 100 50 0-50 Mean Force Component vs feed rate -100 0 0.05 0.1 0.15 0.2 feed rate (mm/rev) F x F y F z regr. F x regr. F y regr. F z K tc = 4F yc N t a K rc = 4F xc N t a K rc = πf zc N t a K te = πf ye N t a K rc = πf xe N t a K rc = 2F ze N t a 12
Cutting force coefficient identification Conduct a dedicated series of tests at different feed rates and identify coefficients directly for the tool-workpiece-cutting parameter combination of interest Process planning Identified cutting force coefficients give us a sense of machinability of materials Cutting coefficients are inputs into chatter prediction models Questions? 13