Helical gears have teeth formed in a helix around the gear. This allows two parallel shafts to be connected using helical gears instead of spur gears. The key characteristics of helical gears are: - Teeth are formed in a helix rather than parallel to the axis, providing gradual engagement between gears. - Recommended pressure angle is 15-25 degrees and helix angle is 20-45 degrees. - The normal tooth load on helical gears has both tangential and axial components due to the helical teeth. - Helical gears are designed to have more than one pair of teeth in contact at a time to smoothly transmit torque between parallel shafts.

1. Helical Gears
• A helical gear has teeth in form of helix around the gear. Two such
gears may be used to connect two parallel shafts in place of spur
gears. The helixes may be right handed on one gear and left handed
on the other. The pitch surfaces are cylindrical as in spur gearing, but
the teeth instead of being parallel to the axis, wind around the
cylinders helically like screw threads.
• The teeth of helical gears with parallel axis have line contact, as in
spur gearing. This provides gradual engagement and continuous
contact of the engaging teeth

2. Terminology
• 1. Pitch circle. It is an imaginary circle which by pure rolling action,
would give the same motion as the actual gear.
• 2. Pitch circle diameter. It is the diameter of the pitch circle. The size
of the gear is usually specified by the pitch circle diameter. It is also
called as pitch diameter.
• 3. Pitch point. It is a common point of contact between two pitch
circles.
• 4. Pitch surface. It is the surface of the rolling discs which the
meshing gears have replaced atthe pitch circle.

3. Proportions for helical gears
Though the proportions for helical gears are not standardised, yet the
following are recommended
by American Gear Manufacturer's Association (AGMA).
Pressure angle in the plane of rotation,
φ = 15° to 25°
Helix angle, α = 20° to 45°
Addendum = 0.8 m (Maximum)
Dedendum = 1 m (Minimum)
Minimum total depth = 1.8 m
Minimum clearance = 0.2 m
Thickness of tooth = 1.5708 m

4. Forces components on a tooth of helical gear
• In order to have more than one pair of teeth in contact, the tooth
displacement (i.e. the advancement of one end of tooth over the
other end) or overlap should be at least equal to the axial
• pitch, such that Overlap = pc = b tan α ...
• The normal tooth load (WN) has two components ; one is tangential
component (WT) and the
• other axial component (WA), WA = WN sin α = WT tan α

5. Virtual number of teeth
• The formative or equivalent number of teeth for a helical gear may be
defined as the number of teeth that can be generated on the surface
of a cylinder having a radius equal to the radius of curvature at a
point at the tip of the minor axis of an ellipse obtained by taking a
section of the gear in the normal plane.
• equivalent number of teeth on a helical gear, TE = T / cos3 α
where T = Actual number of teeth on a helical gear α = Helix angle.

6. Beam strength of helical gears
In helical gears, the contact between mating teeth is gradual, starting at
one end and moving along the teeth so that at any instant the line of
contact runs diagonally across the teeth. Therefore in order to find the
strength of helical gears, a modified Lewis equation is used. It is given
by WT = (σo × Cv) b.π m .y'
where WT = Tangential tooth load,σo = Allowable static stress,
Cv = Velocity factor ,b = Face width, m = Module, and
y' = Tooth form factor or Lewis factor corresponding to the formative
or virtual or equivalent number of teeth.

7. wear strength of helical gears
• The maximum or limiting wear tooth load for helical gears is given by
• Ww = P2. . .cos D bQKαwhere DP, b, Q and K have usual meanings as
discussed in spur gears.
• In this case, K =2NP G( ) sin 1 11.4esE Eσ φ ⎡ + ⎤ ⎢ ⎣ ⎦ where φ N =
Normal pressure angle

8. Dynamic load on helical gears
• The dynamic tooth load on the helical gears is given by
• WD = WT +2T2 T21 ( . cos ) cos21 . Cos v b C W v b C Wα + α+ α+
• where v, b and C have usual meanings as discussed in spur gears.

9. Design of helical gears
Lead : Distance from any point on a thread to the corresponding point on the next turn of the same thread, measured parallel
to the axis.
Linear pitch, p : Distance from any point on a thread to the corresponding point on the adjacent thread, measured parallel to
the axis. For a single-thread worm, lead and linear pitch are the same.
Lead angle, Angle between a tangent to the helix and a plane perpendicular to the axis. Note that the complement of the helix
angle is usually given for helical gears.
Pitch diameter, Same as described earlier in this list. Note that for a worm it is still measured in a plane perpendicular to the
gear axis, not a tilted plane . The complement of the angle between the direction that the teeth exert force on each other, and
the line joining the centers of the two gears.
Outside diameter, Diameter of the gear, measured from the tops of the teeth.
Root diameter Diameter of the gear, measured at the base of the tooth.
Addendum, a Radial distance from the pitch surface to the outermost point of the tooth.
Dedendum, b Radial distance from the depth of the tooth trough to the pitch surface. Whole depth, The distance from the top
of the tooth to the root; it is equal to addendum plus dedendum or to working depth plus clearance.
Clearance Distance between the root circle of a gear and the dedendum circle of its mate