Nomenclature

xix

NOMENCLATURE

Aw = tldw Ac Br (CpP)w dcw dw dwl dw-- r

D Dw E

ex, ev and ez ei

err(z) F

Fly F,,

F~

Fx, Fv and Fz

Fo

Cross-sectional area of the uncut chip (m 2) Cross-sectional area of the chip (m 2) Briks criterion The volume specific heat of work material (J/(m3~ Depth of cold working (mm) Cutting width (orthogonal cutting) or the depth of cut (mm) Width of chip (mm) Depth of re-cutting (mm) Similarity criterion that accounts on the parameters of the uncut chip thickness Diameter of the workpiece (diameter of the hole being bored or drilled) (m) Young's modulus or the modulus of elasticity (MPa) Relative sharpness similarity criterion Direct strains Equivalent strain "Error function" encountered in integrating the normal distribution Friction force at the tool-chip interface (N) Friction force at the tool-workpiece interface (N) Normal force at the tool-chip interface (N) Normal force on the plane which approximates the surface of the maximum combined stress at its final inclination (shear plane) (N) Fs Shear force on the plane which approximates the surface of the maximum combined stress at its final inclination (shear plane) (N) Components of the cutting force in the tool coordinate system (N) Similarity criterion that accounts for the thermal properties of the tool and work materials as well as for the tool geometry Cutting feed (mm/rev)

xx g hr hs hs-opt kw

kt kwf

Kh lc lc--p lck e md tlw

N Nu Pc Pe Po Pr R

Re rct

rn tl t2 T

TD TUD

Tm Uc, ui !)

vf Vcf Vh Vopt VS Vl Ww

Wc, Ol Oln

~cf

ex, ev and e:

Nomenclature

Acceleration due to gravity (m/s 2) Radial tool wear (ram) Relative surface wear rate (~tm/103 sm 2) Optimal relative surface wear (~t m/l 0 3 sm 2) Thermal conductivity of work material (J/(m- s. C)) Thermal conductivity of tool material (J/(m. s. C)) Thermal conductivity of the working fluid (J/(m. s. C)) Cooling intensity Contact length (natural)- the length of the tool-chip contact interface (ram) Plastic part of the contact length (mm) Elastic part of the contact length (mm) Length of the workpiece (m) Drill point offset (mm) Workpiece rotational speed (rpm) Normal force at the tool-chip interface (N) Nusselt number Cutting power (W) Peclet criterion (number) Poletica criterion, Po-criterion Prandtl Number Resultant cutting force (N) Reynolds Number Physical resource of the cutting tool (W) Cutting tool nose radius (m) Uncut chip thickness (m) Chip having thickness (m) Tool life (rain) Dimension tool life (sin2) Specific dimension tool life (10 3 smZ/~tm) Melting temperature of the work material (~ Total energy entering the cutting system (Ws) Energy to fracture the layer being removed (Ws) Cutting speed (velocity) (m/min) Feed velocity (m/min) Velocity of the cutting fluid (m/rain) Dimension wear rate (~tm/min) Optimal cutting speed (m/min) Shear velocity (m/min) Velocity of the chip relative to the tool rake face (m/min) Thermal diffusivity of the work material (mZ/s) Power required by the cutting system (W) Tool flank angle (~ Tool normal flank angle (~ Thermal diffusivity of the cutting fluid (m2/s) Cutting wedge angle in the normal plane (~ Final shear strain True strains along the main axes

Nomenclature

ef

~2

Y Yn

Yxv, Yyz and ~'z.~ 17cs Kr Krl

ks # #f Us Or-av Ofl-av Of l ~ max Oct Oopt Pce

Pw Pct

PcU tT UTS O'YT O"c Crc- f

~f Gi 753, "gc 75c- f Tin

O.)a c

xxi

Strain at fracture of the work material Strain rate (l/s) Shear angle (~ Approach angle of the gundrill's outer cutting edge (~ Approach angle of the gundrill's inner cutting edge (~ Tool rake angle (~ Tool normal rake angle (~ Engineering shear strains Physical efficiency of the cutting system Tool cutting edge angle, major cutting edge (~ Tool cutting edge angle, minor cutting edge (~ Cutting edge inclination angle (~ Mean friction angle at the tool-chip interface (~ Friction coefficient Poisson's ratio Mean contact temperature at the tool-chip interface (~ Mean contact temperature at the tool-workpiece interface (~ Maximum temperature at the tool flank (~ Cutting temperature (~ Optimal cutting temperature (~ Radius of the cutting edge (m) Density of the work material (kg/m 3) Density of the tool material (kg/m 3) Density of the cutting fluid (kg/m 3) Ultimate tensile strength of the work material (MPa) Yield tensile strength of the work material (MPa) Mean normal stress at the tool-chip interface (MPa) Mean normal stress at the tool-workpiece interface (MPa) Fracture stress (MPa) von-Mises' stress Yield shear stress of the work material (MPa) Specific frictional force which is the mean shear stress at the tool--chip interface (MPa) Specific frictional force which is the mean shear stress at the tool-workpiece interface (MPa) Strength of adhesion bonds at the tool-workpiece interface (MPa) Chip compression ratio Normalized chip compression ration Angle of action