Unit ii helical gears

Pimpri Chinchwad Education Trust’s
Pimpri Chinchwad College of Engineering and
Research, Pune
Course- Theory of Machines-II
Topic –Helical Gear
Online Lecture 1
By
Prof.Fodase G.M.

Helical Gears
• Terminology Of Helical Gears
• Virtual Number Of Teeth
• Force Analysis Of Helical Gears

Helical Gears
• Teeth are at an angle; Helix angle (α)70 to 230)
• Gradual engagement of teeth reduces shocks &
Stresses
• More smooth & quiet operation
• Used for high speed transmission & efficiency is frm 96 to
98%
• Tooth strength is greater because the teeth are longer
• Greater surface contact on the teeth thus carry more load
than a spur gear
• Used in automobiles

HELICAL GEARS
•Disadvantage:
-Longer surface of contact reduces the efficiency of a
helical gear relative to a spur gear
-They induce axial thrust in one direction on bearing

• Two helical gears of identical pitch & of
opposite hand
• Axial thrust of two gears act in opposite
direction, thus…
• Problem of axial thrust is eliminated
Herringbone Gears

Direction of Axial Thrust
• Note that the direction in which the thrust
load acts is determined by applying the
RH or LH rule to the driver. That is, for the
RH driver, if the fingers of the RH are
pointed in the direction of rotation of the
gears, the thumb points in the direction of
the thrust. The driven gear then has a
thrust load acting in the direction opposite
to that of the driver

Terminology Of Helical Gears
• Helix angle (α):-
It is the angle between axis of shaft
and center line of teeth. It is the angle at which teeth
are inclined to the axis of the gear. It is denoted by α
• Transverse circular pitch (Pt):-
It is the distance between the
corresponding points on adjacent teeth measured
along PC in transverse plane. It is denoted by Pt

• Normal circular pitch (Pn):-
It is the distance between the
corresponding points on adjacent teeth measured along
PC in normal plane. It is denoted by Pn
Where, mn = Normal module
mt = Transverse module





cos
cos
).....1(
,
)1.....(..........cos
cos
tn
tn
c
tn
t
n
mm
mm
eq
mP
But
PP
P
P







• Transverse pressure angle (Φt)
The pressure angle measured along the
transverse plane.
• Normal pressure angle (Φn)
The pressure angle measured along the
normal plane.
t
n



tan
tan
cos 

• Axial Pitch :It is distance between
corresponding points on adjacent teeth
measured on the surface in axial direction.

Virtual Number Of Teeth/Number Of Teeth On
Equivalent Spur Gear
If the helical gear is viewed along the normal plane, it will
appear as a spur gear

Semi-minor axis = r
Semi-major axis = r /
cosα
Where,
r- PC radius along T-T
re – PC radius of
equivalent spur gear
Pitch Cylinder cut at normal N-N
• If pitch cylinder of the helical gear is cut by the
normal plane NN ,The corresponding section is
an ellipse with major axis of d / cosα and minor
axis of d.
• The profile of helical gear tooth in the normal
plane is similar to that of spur gear tooth having
pitch circle radius equal to radius of curvature of
the ellipse at the point p.

Virtual Number Of Teeth



2
2
2
2
cos
cos
cos
axisminor-Semi
axis)major-(Semi
d
d
r
r
r
r
r
r
e
e
e
e








Let, re – PC radius of equivalent spur gear
de – PC diameter of equivalent spur gear
r– PC radius of helical gear
OR

Hence, the helical gear is equivalent to an
imaginary spur gear, which is in normal plane N-N, having
pitch circle radius r. This imaginary spur gear is called
equivalent spur gear or virtural spur gear or formative spur
gear.
The number of teeth on equivalent spur
gear is called as equivalent number teeth or virtual number
of teeth or formative number of teeth.

Let,
t = Number of teeth on helical gear
te = Number of teeth on equivalent spur gear or virtual
number of teeth
mt = Transverse module of helical gear
mn= Normal module of equivalent spur gear

• We know that module of spur gear is,


3
2
cos
cos
t
e
n
e
n
e
e
e
e
n
m
d
t
m
d
t
m
d
t
t
d
m




 cos)......1......( tn mm 
or
or
or





2
cos
............
d
de

• We know that module of helical gear is,
3
cos
t
t
m
d
t
t
d
m
e
t
t



or
From eq (1) & (2)
)2..(..........

Force Analysis Of Helical Gears

B
Resultant force F resolved into
three components:-
Ft - Tangential Force
Fr - Radial Force
Fa - Axial Force










tan
coscos
sincos
)...,2()3(
)3....(sincos
sin
)2....(coscos
cos
cos
)1.....(sin
ta
n
n
t
a
na
a
nt
t
n
nr
FF
F
F
F
F
byDividing
FF
BCF
FF
BCF
FBC
FF












From fig (a);
From fig (b); Fig. (a)
Fig. (b)

)5.(....................tan
)4..(..........
cos
tan
sin
coscos
t
r
t
t
n
tr
n
n
t
r
F
F
r
T
F
FF
F
F





















From eq (1) & (2)……
Also tangential force acting on tooth is,
Where,
T= torque transmitted by helical gear
r =pitch circle radius of helical gear
From fig(3)……………

t
n
t
r
n
F
F





tan
tan
cos
)6....(..........
tan
cos


From eq (4)…….
From eq (5) & (6)…….

Numerical :
• Two helical gears transmit 30KW with
velocity ratio 4,normal pressure angle is
20 degree and helix angle is 30 degree
,normal module is 12 mm and standard
addendum is equal to one module .the
pinion has 20 teeth and rotates at 400 rpm
.Determine the center distance and
evaluate forces acting on tooth with neat
sketch.

Unit ii helical gears

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