GrindingGrindingIllegitimi non carborundumgver. 1ver. 1ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20091OverviewOverview• Processes•AnalysisAnalysisME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20092ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20093Horizontal GrindingME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20094ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20095Horizontal grindingVertical grindingME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20096Centered grindingCentered grindingCenterless grindingME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20097Creep Feed GrindingCreep Feed GrindingME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20098ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20099ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200910ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200911ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200912Grinding WheelsGrinding WheelsME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200913Grinding WheelsGrinding WheelsME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200914Grinding Wheel InformationME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200915Correctly Mounted WheelME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200916Grinding Wheel SurfaceGrinding Wheel SurfaceME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200917Grind Wheel DressingGrind Wheel DressingME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200918Grinding Wheel DressingGrinding Wheel DressingME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200919Grinding ChipsGrinding ChipsME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200920Chip formation geometryChip formation geometrywlDθtlVdtθlvME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200921Chip geometryChip geometry•As with rolling contact length, the chip length,As with rolling contact length, the chip length, l– D = wheel diameter, d = depth of cutdDl ⋅=• Material removal rate, MRR–v= workpiece velocity, d= depth of cut, b = width pypof cutbdvMRR⋅⋅=ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200922Material removal rateMaterial removal rateTh hi h t i l•The chips have a triangular cross-section, and ratio (r) of chip thickness (t) t hi idth ()wto chip width (w)2010tww•So, the average volume per chip2010totr≈=tlSo, the average volume per chipwtlltwVolchip412121=⋅⋅=ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200923chip422ChipsChips•The number of chips removed per unit•The number of chips removed per unit time (n), where c = number of cutting edges (grains) per unit area (typ 0 1 toedges (grains) per unit area (typ. 0.1 to 10 per mm2, and V = peripheral wheel velocityvelocity cbVn⋅⋅=ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200924CombiningCombiningVolnbdvMRR⋅=⋅⋅=chipVolnbdvMRR==1wtlVbcbdv41⋅=⋅⋅trw ⋅=dDl ⋅=dDttrbcVbdv ⋅⋅⋅⋅⋅⋅⋅=⋅⋅41ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 2009254Chip thicknessChip thicknessdv4dDrcVdvt⋅⋅⋅⋅=42orDdVvt=4DrcV⋅⋅ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200926Specific grinding energyuSpecific grinding energy, u• Consist of chip formation, plowing, and slidingguuuu++=slidingplowingchipuuuu++=ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200927Total grinding forceTotal grinding force•Get force from power•Get force from powerMRRuPower×=MRRuPowerbdvuVF⋅⋅×=⋅bdvuVFgrinding⋅⋅×=⋅bdvuF⋅⋅×=VuFgrinding×=ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200928Total grinding forceTotal grinding forceFiillttd•From empirical results, as tdecreases, the friction component of u increasestu1∝tKu11⋅=ortsubstitutingbd1VbdvtKFgrinding⋅⋅⋅⋅=11ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200929Total grinding forceTotal grinding forceSubstituting for tVbdvdKFgrinding⋅⋅⋅⋅=411VDdrcVv⋅⋅⋅4irearrangingvrcddDVvrcdbKFgrinding⋅⋅⋅⋅⋅⋅⋅=41ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200930Force on a grainForce on a grain•The force per grain can be calculatedThe force per grain can be calculatedAreauFgrain×=gwtuFgrain21×=rtw=andKu1=grain2tKu1⋅=11ttrtKFgrain⋅⋅⋅×⋅=2111ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200931Force on a grainForce on a grainsubstituting for t, and rearrangingdvrKFi⋅⋅=41DrcVrFgrain⋅⋅2DdcVrvKFgrain⋅⋅⋅=1ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200932Grinding temperatureGrinding temperature• Temperature rise goes with energy delivered per unit areainputEnergyKTΔareapgyKT⋅=Δ2dlbu⋅⋅×1dtKKlbdlbuKT⋅⋅⋅=⋅⋅⋅×⋅=Δ11221DdVcrvdKKT4121⋅⋅⋅=ΔME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200933DVcrGrinding temperatureGrinding temperature• RearrangingdDvrcVKKT ⋅⋅⋅⋅⋅=Δ421• Temperatures can be up to 1600oC, but for a short time.ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200934Grinding –Ex. 1-1g• You are grinding a steel, which has a specific grinding energy (u) of 35 W-s/mm3.• The grinding wheel rotates at 3600 rpm, has a diameter (D) of 150 mm thickness (b) of 25 mm anddiameter (D) of 150 mm, thickness (b) of 25 mm, and (c) 5 grains per mm2 (c). The motor has a power of 2 kW.• The work piece moves (v) at 1.5 m/min. The chip thickness ratio (r) is 10.•Determine the grinding force and force per grain•Determine the grinding force and force per grain.• Determine the temperature (K2is 0.2oK-m/N). Room temperature is 20oC.ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200935GrindingEx 12Grinding –Ex. 1-2• First we need to calculate the depth of pcut. We can do this from the power.bdvuMRRuPower⋅⋅⋅=×=min2mmmsWsec60min1025min5.1352000263××⋅⋅⋅−=mmmmmdmmmsWWmd6104.91−×=ME 6222: Manufacturing Processes and Systems