1. Pimpri Chinchwad Education Trust’s
Pimpri Chinchwad College of Engineering and
Research, Pune
Course- Theory of Machines-II
Topic –Spiral Gear
By
Prof.Fodase G.M.
2. Spiral Gears
• Skew Gears / Crossed Helical Gears
• Used for Non-parallel & Non-intersecting shafts
• Point contact between mating teeth
• Low load transmission
• Used in distribution devices of automobile engines/
measurement instruments
3. Spiral Gears
• Two meshing gears can have same or opposite hands
• Helix angle in case of spiral angle is known as Spiral Angle
• If spiral angles are different, Transverse module mt is also
different
• For specifying size of spiral gears Normal module mn is
always used
5. Shaft Angle Of Spiral Gears
21
21
• The shaft angle (θ) is the angle through which one of the
shaft must be rotated so that it is parallel to the other
shaft
• If the hands of two meshing spiral gears are same, then
the shaft angle θ is given by,
• If the hands of two meshing spiral gears are different,
then the shaft angle θ is given by,
6. Centre Distance Between Spiral Gears
l= C.D. between spiral gears
α1,α2= Spiral angles for gear 1 & 2
T1,T2 = No. of teeth on gear 1 & 2
N1,N2= Speed of gear 1 & 2
G= Gear ratio=T2/T1=N1/N2
mt1,mt2= Transverse module for 1 & 2
mn= Normal module for 1& 2
r1,r2 = PC radius for 1 & 2
7. Centre Distance Between Spiral Gears
2
22
2
Tm
r
t
2
11
1
Tm
r
t
2
Tm
r
t
We know that pitch circle radius of gear is,
Pitch circle radius of gear 1 is,
Pitch circle radius of gear 2 is,
8. Centre Distance Between Spiral Gears
21
1
2
12
1
1
2
2
1
1
2
2
1
1
2211
coscos
1
2
cos
/
cos
1
2
coscos2
2cos2cos
22
21
GTm
l
TTTm
l
TTm
l
TmTm
l
TmTm
l
rrl
n
n
n
nn
tt
The centre distance between two spiral gear is, 1
2
l
10. Efficiency Of Spiral Gears
Ft1 = Tangential force acting on gear 1
Ft2 = Tangential force acting on gear 2
Fa = Axial force acting on gear 1
Fa2 = Axial force acting on gear 2
FN = Normal reaction at the point of contact
F = Resultant force/ Resultant reaction at pt of contact
α1 = Spiral angles for gear 1
α2 = Spiral angles for gear 2
11. • θ = Shaft angle = α1 + α2
• Φ = Angle of friction
• N1 = Speed of gear 1
• N2 = Speed of gear 2
• G = Gear ratio = T2/T1 = N1/N2
• mt1 = Transverse module for 1
• mt2 = Transverse module for 2
• mn = Normal module for 1 & 2
• d1 = PC diameter for 1
• d2 = PC diameter for 2
Efficiency Of Spiral Gears
12. Efficiency Of Spiral Gears
)1.........().........(cos
60
)/(
60
)/(
260
2
)/(
60
2
)/(
60
2
)/(
)cos(
,....
1
11
1
11
1
1
1
11
1
1
1
11
F
Nd
piwork
F
Nd
piwork
d
F
N
piwork
rF
N
piwork
M
N
piwork
FF
PABFrom
t
t
t
t
t
Work i/p or i/p power to the driver is;
13. Efficiency Of Spiral Gears
)2........().........(cos
60
)/(
60
)/(
260
2
)/(
60
2
)/(
60
2
)/(
)cos(
,....
2
22
2
22
2
2
2
22
2
2
2
22
F
Nd
powork
F
Nd
powork
d
F
N
powork
rF
N
powork
M
N
powork
FF
PCDFrom
t
t
t
t
t
Work i/p or i/p power to the driver is;
14. Efficiency Of Spiral Gears
)(cos
)(cos
)(cos
60
)(cos
60
)/(
)/(
111
222
1
11
2
22
Nd
Nd
F
Nd
F
Nd
piwork
powork
The Efficiency of Spiral gear is;
15. Efficiency Of Spiral Gears
)4(....................
cos
)3(....................
cos
................cos
cos
2
2
2
1
1
1
1
1
1
11
Tm
d
Tm
d
T
d
m
T
d
m
mm
n
n
tn
tn
We know that;
16. Efficiency Of Spiral Gears
)5....(..............................
cos
cos
cos
cos
cos
cos
cos
cos
2
1
1
2
2
1
11
22
2
1
1
2
1
2
2
1
11
22
11
22
1
1
1
2
2
2
11
22
N
N
T
T
G
Nd
Nd
T
T
d
d
NT
NT
Nd
Nd
N
Tm
N
Tm
Nd
Nd
n
n
From eq (3) & (4);
18. Efficiency Of Spiral Gears
Angles Φ & θ are constants,
Therefore, Efficiency will be maximum when
cos(α1-α2-Φ) is maximum i.e.,
12
21
21
21
21
0
1)cos(
OR
22. Velocity Of Sliding Between Spiral Gears
222
111
rV
rV
22
11
sin
sin
V
V
222111
2211
sinsin
sinsin
rrV
VVV
s
s
Circumferential velocity/ Tangential velocityof gear 1 at pitch pt;
Circumferential velocity/ Tangential velocityof gear 2 at pitch pt;
Component of V1 along the tooth profile
Component of V2 along the tooth profile
Velocity of sliding between gear 1 & 2 is;
