Kinematics of Spiral Gear

2. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Subject :- Theory of Machines II
T.E. Mechanical (302043)
Unit 2
2.2 SPIRAL GEAR
By
Prof. K. N. Wakchaure(Asst Professor)
Department of Mechanical Engineering
Sanjivani College of Engineering
(An Autonomous Institute)
Kopargaon, Maharashtra
Email: wakchaurekiranmech@Sanjivani.org.in Mobile:- +91-7588025393

3.  spiral gears (also known as skew gears or screw gears) are used
to connect and transmit motion between two non-parallel and
non-intersecting shafts.
 The pitch surfaces of the spiral gears are cylindrical and the
teeth have point contact.
 These gears are only suitable for transmitting small power.
 helical gears, connected on parallel shafts, are of opposite hand.
But spiral gears may be of the same hand or of opposite hand.

4. A pair of spiral gears 1 and 2, both having left hand helixes.
The shaft angle θ is the angle through which one of the shafts
must be rotated so that it is parallel to the other shaft, also the
two shafts be rotating in opposite directions.
𝜽 = 𝑺𝒉𝒂𝒇𝒕 𝒂𝒏𝒈𝒍𝒆 = 𝜶 𝟏 + 𝜶 𝟐 For Same hand of Helix
𝜽 = 𝑺𝒉𝒂𝒇𝒕 𝒂𝒏𝒈𝒍𝒆 = 𝜶 𝟏 − 𝜶 𝟐 For Opposite hand of Helix

5. 𝒅 𝟏 = 𝒑𝒊𝒕𝒄𝒉 𝒄𝒊𝒓𝒄𝒍𝒆 𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝑮𝒆𝒂𝒓 𝟏 (𝒑𝒊𝒏𝒊𝒐𝒏)
𝒅 𝟐 = 𝒑𝒊𝒕𝒄𝒉 𝒄𝒊𝒓𝒄𝒍𝒆 𝑫𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝑮𝒆𝒂𝒓 2
𝜶 𝟏 = 𝑯𝒆𝒍𝒊𝒙 𝒂𝒏𝒈𝒍𝒆 𝒇𝒐𝒓 𝑮𝒆𝒂𝒓 𝟏
𝜶 𝟐 = 𝑯𝒆𝒍𝒊𝒙 𝒂𝒏𝒈𝒍𝒆 𝒇𝒐𝒓 𝑮𝒆𝒂𝒓 𝟐
𝜽 = 𝑺𝒉𝒂𝒇𝒕 𝒂𝒏𝒈𝒍𝒆 = 𝜶 𝟏 + 𝜶 𝟐
𝝎 𝟏 = 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝑮𝒆𝒂𝒓 𝟏
𝝎 𝟐 = 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝑮𝒆𝒂𝒓 𝟐
mn= Normal Module
pn= Normal pitch
mt1= Transverse module of Gear 1
mt2= Transverse module of Gear 2
pc1= Transverse pitch of Gear 1
pc2= Transverse pitch of Gear 2
Gear Ratio (G) =
𝑻𝟐
𝑻𝟏
T1and T2 = Number of teeth on gears 1 and 2,
N1 and N2 = Speed of gears 1 and 2
NOTATIONS

6. Since the normal pitch is same for both the spiral gears,
therefore

7. EFFICIENCY OF SPIRAL
GEAR
Ft1 = Force applied tangentially on the driver,
Ft2= Resisting force acting tangentially on the
driven,
Fa1 = Axial or end thrust on the driver,
Fa2 = Axial or end thrust on the driven,
FN = Normal reaction at the point of contact,
Φ = friction angle,
R = Resultant reaction at the point of contact, and
θ = Shaft angle = α1+ α2
Work input to the driver
= Ft1 × π d1.N1/60 = R cos (α1 - Φ) π d1.N1/60
Ft1
R
Fn
α1
α1
Fa1 ϕ

8. EFFICIENCY OF SPIRAL
GEAR
Ft1 = Force applied tangentially on the driver,
Ft2= Resisting force acting tangentially on the
driven,
Fa1 = Axial or end thrust on the driver,
Fa2 = Axial or end thrust on the driven,
FN = Normal reaction at the point of contact,
Φ = friction angle,
R = Resultant reaction at the point of contact,
and
θ = Shaft angle = α1+ α2
Work input to the driven gear
= Ft × π d2.N2/60 = R cos (α2 + Φ) π d2.N2/60
Ft2 Fn
α2
Rα2

9. EFFICIENCY OF SPIRAL
GEAR
Ft1 = Force applied tangentially on the driver,
Ft2= Resisting force acting tangentially on the
driven,
Fa1 = Axial or end thrust on the driver,
Fa2 = Axial or end thrust on the driven,
FN = Normal reaction at the point of contact,
Φ = friction angle,
R = Resultant reaction at the point of contact,
and
θ = Shaft angle = α1+ α2
Work input to the driver
= Ft1 × π d1.N1/60 = R cos (α1 - Φ) π d1.N1/60
Work input to the driven gear
= Ft2 × π d2.N2/60 = R cos (α2 + Φ) π d2.N2/60
Ft1
Ft2
Fn
Fn
R
Fa1
Fn
Fn
R

10. As and
Ft1
Fn
Fn
R
Fa1
Ft1
R
Fa2
α2
α1
θ
ϕ
α1
α2
ϕ
α1
Work input to the driver
= Ft1 × π d1.N1/60 = R cos (α1 - Φ) π d1.N1/60
Work input to the driven gear
= Ft2 × π d2.N2/60 = R cos (α2 + Φ) π d2.N2/60

11. Maximum Efficiency
Since the angles θ and φ are constants, therefore the
efficiency will be maximum, when cos (α1 – α2 – φ) is
maximum, i.e.
Ft1
Fn
Fn
R
Fa1
Ft1
R
Fa2
α2
α1
θ
ϕ
α1
α2
ϕ

12. 12
Subject :- Theory of Machines II