# Worm Gearing Terminology, Rules and Formulae

Worm Gearing Terminology

(a) Lead. It is the linear distance through which a point on thread moves ahead in one revolution of the worm. For single start thread, lead is equal to the pitch, but for multiple start threads, lead is equal to the product of pitch and number of starts.

For multi-start worm, lead = Linear pitch x No. of starts

(b) Linear Pitch (LP). It is the distance measured axially (i.e. parallel to the axis of worm) from a point on one thread, to the corresponding point on the adjacent thread on the worm.

(c) Helix Angle. It is the angle between the tangent to the thread helix on the pitch cylinder and the axis of the worm.

(d) Lead Angle. It is the angle between the tangent to the thread helix on the pitch cylinder and the plane normal to the axis of the worm.

(e) Whole Depth. It is the complete one side depth of thread. It is from the crest to the root measured normal to the axis.

• Whole depth = 0.6866 of linear pitch
• Width at the top of the thread (f) = 0.335 of pitch.
• Width at the bottom of thread (c) = 0.31 of pitch
• Root diameter of worm = OD (Outside dia) – 2WD (Whole depth)

(f) Pressure Angle. It is measured in a plane containing the axis of the worm and is equal to one half the thread profile angle. The following table shows the recommended values of lead angle and pressure angle.

Recommended Values of Lead Angle and Pressure Angle

 Lead angle in degrees 0-16 16-25 25-35 35-45 Pressure angle in degrees 14 ½ 20 25 30

(g) Velocity Ratio. It is the ratio of the speed of worm (Nw) in RPM to the speed of the worm gear (Ng) in RPM

Velocity ratio  = Nw / Ng

(h) Circular Pitch (CP). Circular Pitch of the worm wheel is equal to linear pitch of the worm. Therefore, the circumference of pitch circle of the worm wheel = (Linear pitch of worm x No. teeth of worm wheel).

(i) Throat Radius. This is the radius of the face curve and is made to suit the curvature of worm.

(j) Throat Diameter. This is equal to the outside diameter of a spur gear with same number of teeth and pitch as the worm wheel. The out side diameter at the centre of the worm wheel is called throat diameter.

(k) Face Angle. This is the angle to which the face of the wheel is turned. It is usually 60 degrees to 80 degrees but 75 deg is mostly adopted.

(l) Out Side Diameter at the Sharp Corners. It is the over all diameter of the worm wheel.

(m) Normal Circular Pitch (NCP). It is the distance between two corresponding points of the adjacent teeth measured along the pitch circle.

NCP = LP x Cos of helix angle

The term pitch circle, circular pitch, diametrical pitch, pressure angle, width of the face, addendum, dedendum and clearance are used in the same way as for ordinary spur gears. For pressure angle greater than 14½ deg the tooth proportions are calculated using normal circular pitch.

Whole depth (WD) = 0.6866 x NCP

Width of the thread tooth at end = 0.31 x NCP

Rules and Formulae for Worm Gearing

(a) Linear Pitch (LP) = (Lead of the Worm) / (No. of start of Worm)

(b) Circular Pitch of worm wheel (CPg). It can be calculated by dividing circumference of pitch circle by number of teeth of the worm wheel.

CPg = Pitch Circumference/ No. of Teeth of Worm Wheel

= {Pitch Dia of Worm Wheel (PDg) x p} / {No. of Teeth (Ng)}

= (PDg x p) / Ng

(c) Pitch Dia of Worm Wheel (PDg) = {No. of Teeth of Worm Wheel (Ng)} x

{Linear Pitch of the Worm (LP)} / p

PDg= (Ng x LP) /p

(d) Pitch Dia of Worm (PDw) ={Outside Dia of the worm (ODw)} – 2 Addendum of worm tooth

PDw   = (ODw – 2 a)

(e) Addendum of Worm Tooth (a)   = 0.3183 x LP

(f) Dedendum of Worm Tooth (d)   = 0.3683 x LP

(g) Whole Depth of Worm Tooth (WDw) = 0.6866 x LP

(h) Centre Distance (CD) = {(PDg +PDw) / 2}

(j) Root Dia of Worm (RD) = ODw – 2 WD

(k) Helix Angle of Worm =Tan of Helix angle = Lead / (PDw x p)

(l) Throat Dia of Worm Wheel (TD) = PDg + 2 Addendum

(n) Outside Dia of Worm Wheel (ODg) at Sharp Corners (O)

= 2{R – R Cos (Face Angle/2)} + TD (where R= Throat Radius)

(o) Minimum Length of Worm for Complete Action (X) = (√8 PDg x Addendum)

(p) Outside Dia of Worm (ODw) = PDw +2 Addendum

(q) Velocity Ratio (V) = RPM of Worm/ RPM of Wheel, Also (V) = (No. of Teeth of Worm Wheel}/ {(No. of Start of Worm (Nw)} = Ng / Nw

(r) Maximum Width of Face of RIM (F) = 2 /{√ a2 + (PDw x a)}

(s) Face Angle (B) = 60to 800  usually 75

(t) Width of Thread Tooth at End (t) = 0.31 x LP

(u) Root Diameter = ODw – 1.273 Linear Pitch

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