Metric Formulas & Terminology

Formula Terminology

xπxn D = Machined diameter mm

V =Dm
mCutting speed (m/min)
c1000 V=Cutting speedm/min
c
n=Spindle speedrev/min
V x 1000=Period of engagementmin
n = cTc
DmxπSpindle speed (rev/min)
Q=Metal removalcm /min
z3
l=Machined lengthmm
Vm
c x ap x fn x kc=Power demandkW
=Power demand (kW) Pc
60 x 1000 x Pc
h=Specific cutting forceN/mm
Kc2
f=Feed per revolutionmm/rev
n
= Vk=Cutting edge angledegree
Qz x f x aMetal removal (cm3/min) r
cp n
R max =Profile depthµm
r=Insert nose radiusmm
e
lm=Depth of cutmm
=ap
TcPeriod of engagement (min)
fn x n h=Efficiency

Trigonometrical Equivalents

DimensionPart to be Found
GivenABabc
a & csinA=a÷ccosB=a÷cb = c2- a2
a & btanA=a÷bcosB=a÷bc = a2+ b2
c & bcosA=b÷csinB=b÷ca = c2- b2
A & aB = 90º - Ab=axcotAc=a÷sinA
A & bB = 90º - Aa=bxtanAc=b÷cosA
A & cB = 90º - Aa=cxsinAb=cxcosA

Trigonometrical Equivalents

Dimension GivenParts to be FoundFormula
abcAcos A = b2+c2-a2÷ 2bc
abABsinB=bxsinA÷a
abACC = 180 -(A + B)
aABbb=axsinB÷sinA
aABcc = (a x sin C ÷ sin A) x
(a x sin(180 - A - B)÷ sin A)
abCBB = 180 - (A + C)