Nomenclature Gear

1 nomenclature

1.1 general nomenclature
1.2 helical gear nomenclature
1.3 worm gear nomenclature
1.4 tooth contact nomenclature
1.5 tooth thickness nomenclature
1.6 pitch nomenclature

nomenclature

general nomenclature

rotational frequency, n 
measured in rotation on time, such revolutions per minute (rpm or rpm).
angular frequency, ω 
measured in radians/second. 1 rpm = 2π rad/minute = π/30 rad/second.
number of teeth, n 
how many teeth gear has, integer. in case of worms, number of thread starts worm has.
gear, wheel 
the larger of 2 interacting gears or gear on own.
pinion 
the smaller of 2 interacting gears.
path of contact 
path followed point of contact between 2 meshing gear teeth.
line of action, pressure line 
line along force between 2 meshing gear teeth directed. has same direction force vector. in general, line of action changes moment moment during period of engagement of pair of teeth. involute gears, however, tooth-to-tooth force directed along same line—that is, line of action constant. implies involute gears path of contact straight line, coincident line of action—as indeed case.
axis 
axis of revolution of gear; center line of shaft.
pitch point 
point line of action crosses line joining 2 gear axes.
pitch circle, pitch line 
circle centered on , perpendicular axis, , passing through pitch point. predefined diametral position on gear circular tooth thickness, pressure angle , helix angles defined.
pitch diameter, d 
a predefined diametral position on gear circular tooth thickness, pressure angle , helix angles defined. standard pitch diameter basic dimension , cannot measured, location other measurements made. value based on number of teeth, normal module (or normal diametral pitch), , helix angle. calculated as:




d
=



n

m

n




cos
⁡
ψ





{\displaystyle d={\frac {nm_{n}}{\cos \psi }}}

in metric units or



d
=


n


p

d


cos
⁡
ψ





{\displaystyle d={\frac {n}{p_{d}\cos \psi }}}

in imperial units.
module or modulus, m 
since impractical calculate circular pitch irrational numbers, mechanical engineers use scaling factor replaces regular value instead. known module or modulus of wheel , defined as




m
=
p

/

π


{\displaystyle m=p/\pi }


where m module , p circular pitch. units of module customarily millimeters; english module used units of inches. when diametral pitch, dp, in english units,




m
=
25.4

/

d
p


{\displaystyle m=25.4/dp}

in conventional metric units.
the distance between 2 axis becomes




a
=
m
(

z

1


+

z

2


)

/

2


{\displaystyle a=m(z_{1}+z_{2})/2}


where axis distance, z1 , z2 number of cogs (teeth) each of 2 wheels (gears). these numbers (or @ least 1 of them) chosen among primes create contact between every cog of both wheels, , thereby avoid unnecessary wear , damage. uniform gear wear achieved ensuring tooth counts of 2 gears meshing relatively prime each other; occurs when greatest common divisor (gcd) of each gear tooth count equals 1, e.g. gcd(16,25)=1; if 1:1 gear ratio desired relatively prime gear may inserted in between 2 gears; maintains 1:1 ratio reverses gear direction; second relatively prime gear inserted restore original rotational direction while maintaining uniform wear 4 gears in case. mechanical engineers, @ least in continental europe, use module instead of circular pitch. module, circular pitch, can used types of cogs, not evolvent based straight cogs.
operating pitch diameters 
diameters determined number of teeth , center distance @ gears operate. example pinion:





d

w


=



2
a


u
+
1



=



2
a





z

2



z

1




+
1



.


{\displaystyle d_{w}={\frac {2a}{u+1}}={\frac {2a}{{\frac {z_{2}}{z_{1}}}+1}}.}


pitch surface 
in cylindrical gears, cylinder formed projecting pitch circle in axial direction. more generally, surface formed sum of pitch circles 1 moves along axis. bevel gears cone.
angle of action 
angle vertex @ gear center, 1 leg on point mating teeth first make contact, other leg on point disengage.
arc of action 
segment of pitch circle subtended angle of action.
pressure angle,



θ


{\displaystyle \theta }

 
the complement of angle between direction teeth exert force on each other, , line joining centers of 2 gears. involute gears, teeth exert force along line of action, which, involute gears, straight line; , thus, involute gears, pressure angle constant.
outside diameter,




d

o




{\displaystyle d_{o}}

 
diameter of gear, measured tops of teeth.
root diameter 
diameter of gear, measured @ base of tooth.
addendum, a 
radial distance pitch surface outermost point of tooth.



a
=
(

d

o


−
d
)

/

2


{\displaystyle a=(d_{o}-d)/2}


dedendum, b 
radial distance depth of tooth trough pitch surface.



b
=
(
d
−

root diameter

)

/

2


{\displaystyle b=(d-{\text{root diameter}})/2}


whole depth,




h

t




{\displaystyle h_{t}}

 
the distance top of tooth root; equal addendum plus dedendum or working depth plus clearance.
clearance 
distance between root circle of gear , addendum circle of mate.
working depth 
depth of engagement of 2 gears, is, sum of operating addendums.
circular pitch, p 
distance 1 face of tooth corresponding face of adjacent tooth on same gear, measured along pitch circle.
diametral pitch, dp 




d
p
=
n

/

d
=
π

/

p


{\displaystyle dp=n/d=\pi /p}


ratio of number of teeth pitch diameter. measured in teeth per inch or teeth per centimeter, conventionally has units of per inch of diameter. module, m, in metric units




d
p
=
25.4

/

m


{\displaystyle dp=25.4/m}

in english units
base circle 
in involute gears, tooth profile generated involute of base circle. radius of base circle smaller of pitch circle
base pitch, normal pitch,




p

b




{\displaystyle p_{b}}

 
in involute gears, distance 1 face of tooth corresponding face of adjacent tooth on same gear, measured along base circle
interference 
contact between teeth other @ intended parts of surfaces
interchangeable set 
a set of gears, of mates other

helical gear nomenclature

helix angle,



ψ


{\displaystyle \psi }

 
angle between tangent helix , gear axis. 0 in limiting case of spur gear, albeit can considered hypotenuse angle well.
normal circular pitch,




p

n




{\displaystyle p_{n}}

 
circular pitch in plane normal teeth.
transverse circular pitch, p 
circular pitch in plane of rotation of gear. called circular pitch .




p

n


=
p
cos
⁡
(
ψ
)


{\displaystyle p_{n}=p\cos(\psi )}

several other helix parameters can viewed either in normal or transverse planes. subscript n indicates normal.

worm gear nomenclature

lead 
distance point on thread corresponding point on next turn of same thread, measured parallel axis.
linear pitch, p 
distance point on thread corresponding point on adjacent thread, measured parallel axis. single-thread worm, lead , linear pitch same.
lead angle,



λ


{\displaystyle \lambda }

 
angle between tangent helix , plane perpendicular axis. note complement of helix angle given helical gears.
pitch diameter,




d

w




{\displaystyle d_{w}}

 
same described earlier in list. note worm still measured in plane perpendicular gear axis, not tilted plane.

subscript w denotes worm, subscript g denotes gear.

tooth contact nomenclature































































point of contact 
any point @ 2 tooth profiles touch each other.
line of contact
a line or curve along 2 tooth surfaces tangent each other.
path of action 
the locus of successive contact points between pair of gear teeth, during phase of engagement. conjugate gear teeth, path of action passes through pitch point. trace of surface of action in plane of rotation.
line of action 
the path of action involute gears. straight line passing through pitch point , tangent both base circles.
surface of action 
the imaginary surface in contact occurs between 2 engaging tooth surfaces. summation of paths of action in sections of engaging teeth.
plane of action
the surface of action involute, parallel axis gears either spur or helical teeth. tangent base cylinders.
zone of action (contact zone) 
for involute, parallel-axis gears either spur or helical teeth, rectangular area in plane of action bounded length of action , effective face width.
path of contact
the curve on either tooth surface along theoretical single point contact occurs during engagement of gears crowned tooth surfaces or gears engage single point contact.
length of action
the distance on line of action through point of contact moves during action of tooth profile.
arc of action, qt 
the arc of pitch circle through tooth profile moves beginning end of contact mating profile.
arc of approach, qa 
the arc of pitch circle through tooth profile moves beginning of contact until point of contact arrives @ pitch point.
arc of recess, qr 
the arc of pitch circle through tooth profile moves contact @ pitch point until contact ends.
contact ratio, mc, ε 
the number of angular pitches through tooth surface rotates beginning end of contact. in simple way, can defined measure of average number of teeth in contact during period during tooth comes , goes out of contact mating gear.
transverse contact ratio, mp, εα 
the contact ratio in transverse plane. ratio of angle of action angular pitch. involute gears directly obtained ratio of length of action base pitch.
face contact ratio, mf, εβ 
the contact ratio in axial plane, or ratio of face width axial pitch. bevel , hypoid gears ratio of face advance circular pitch.
total contact ratio, mt, εγ 
the sum of transverse contact ratio , face contact ratio.





ϵ

γ


=

ϵ

α


+

ϵ

β




{\displaystyle \epsilon _{\gamma }=\epsilon _{\alpha }+\epsilon _{\beta }}







m


t



=

m


p



+

m


f





{\displaystyle m_{\rm {t}}=m_{\rm {p}}+m_{\rm {f}}}


modified contact ratio, mo 
for bevel gears, square root of sum of squares of transverse , face contact ratios.





m


o



=



m


p



2


+

m


f



2






{\displaystyle m_{\rm {o}}={\sqrt {m_{\rm {p}}^{2}+m_{\rm {f}}^{2}}}}


limit diameter 
diameter on gear @ line of action intersects maximum (or minimum internal pinion) addendum circle of mating gear. referred start of active profile, start of contact, end of contact, or end of active profile.
start of active profile (sap) 
intersection of limit diameter , involute profile.
face advance 
distance on pitch circle through helical or spiral tooth moves position @ contact begins @ 1 end of tooth trace on pitch surface position contact ceases @ other end.

tooth thickness nomenclature







































circular thickness 
length of arc between 2 sides of gear tooth, on specified datum circle.
transverse circular thickness 
circular thickness in transverse plane.
normal circular thickness 
circular thickness in normal plane. in helical gear may considered length of arc along normal helix.
axial thickness
in helical gears , worms, tooth thickness in axial cross section @ standard pitch diameter.
base circular thickness
in involute teeth, length of arc on base circle between 2 involute curves forming profile of tooth.
normal chordal thickness
length of chord subtends circular thickness arc in plane normal pitch helix. convenient measuring diameter may selected, not standard pitch diameter.
chordal addendum (chordal height) 
height top of tooth chord subtending circular thickness arc. convenient measuring diameter may selected, not standard pitch diameter.
profile shift 
displacement of basic rack datum line reference cylinder, made non-dimensional dividing normal module. used specify tooth thickness, 0 backlash.
rack shift 
displacement of tool datum line reference cylinder, made non-dimensional dividing normal module. used specify tooth thickness.
measurement on pins 
measurement of distance taken on pin positioned in tooth space , reference surface. reference surface may reference axis of gear, datum surface or either 1 or 2 pins positioned in tooth space or spaces opposite first. measurement used determine tooth thickness.
span measurement 
measurement of distance across several teeth in normal plane. long measuring device has parallel measuring surfaces contact on unmodified portion of involute, measurement wis along line tangent base cylinder. used determine tooth thickness.
modified addendum teeth 
teeth of engaging gears, 1 or both of have non-standard addendum.
full-depth teeth 
teeth in working depth equals 2.000 divided normal diametral pitch.
stub teeth 
teeth in working depth less 2.000 divided normal diametral pitch.
equal addendum teeth 
teeth in 2 engaging gears have equal addendums.
long , short-addendum teeth 
teeth in addendums of 2 engaging gears unequal.

pitch nomenclature

pitch distance between point on 1 tooth , corresponding point on adjacent tooth. dimension measured along line or curve in transverse, normal, or axial directions. use of single word pitch without qualification may ambiguous, , reason preferable use specific designations such transverse circular pitch, normal base pitch, axial pitch.

circular pitch, p 
arc distance along specified pitch circle or pitch line between corresponding profiles of adjacent teeth.
transverse circular pitch, pt 
circular pitch in transverse plane.
normal circular pitch, pn, pe 
circular pitch in normal plane, , length of arc along normal pitch helix between helical teeth or threads.
axial pitch, px 
linear pitch in axial plane , in pitch surface. in helical gears , worms, axial pitch has same value @ diameters. in gearing of other types, axial pitch may confined pitch surface , may circular measurement. term axial pitch preferred term linear pitch. axial pitch of helical worm , circular pitch of worm gear same.
normal base pitch, pn, pbn 
an involute helical gear base pitch in normal plane. normal distance between parallel helical involute surfaces on plane of action in normal plane, or length of arc on normal base helix. constant distance in helical involute gear.
transverse base pitch, pb, pbt 
in involute gear, pitch on base circle or along line of action. corresponding sides of involute gear teeth parallel curves, , base pitch constant , fundamental distance between them along common normal in transverse plane.
diametral pitch (transverse), pd 
ratio of number of teeth standard pitch diameter in inches.





p


d



=


n
d


=


25.4
m


=


π
p




{\displaystyle p_{\rm {d}}={\frac {n}{d}}={\frac {25.4}{m}}={\frac {\pi }{p}}}


normal diametral pitch, pnd 
value of diametral pitch in normal plane of helical gear or worm.





p


n
d



=



p


d




cos
⁡
ψ





{\displaystyle p_{\rm {nd}}={\frac {p_{\rm {d}}}{\cos \psi }}}


angular pitch, θn, τ 
angle subtended circular pitch, expressed in radians.




τ
=


360
z




{\displaystyle \tau ={\frac {360}{z}}}

degrees or






2
π

z




{\displaystyle {\frac {2\pi }{z}}}

radians




^ iso/dis 21771:2007 : gears – cylindrical involute gears , gear pairs – concepts , geometry , international organization standardization, (2007)
^ gunnar dahlvig, construction elements , machine construction , konstruktionselement och maskinbyggnad (in swedish), 7, isbn 9140115542 
^ cite error: named reference ansiagma invoked never defined (see page).