Term Used In Worm Gearing

Machine Design

Gear Drives

Introduction:

The worm gears are widely used for transmitting power at high velocity ratios between non-intersecting shafts that are generally, but not necessarily, at right angles.

Terms used in Worm Gearing

1. Axial pitch.

It is also known as linear pitch of a worm.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.It may be noted that the axial pitch (p_a) of a worm is equal to the circular pitch ( p_c ) of the mating worm gear, when the shafts are at right angles.

2. Lead.

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

Lead, l = p_a . n
where p_a = Axial pitch ; and n = Number of starts.

3. 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. It is denoted by λ.If one complete turn of a worm thread be imagined to be unwound from the body of the worm, it will form an inclined plane whose base is equal to the pitch circumference of the worm and altitude equal to lead of the worm,

From the geometry of the figure, we find that

where m = Module, and
DW = Pitch circle diameter of worm.

The lead angle (λ) may vary from 9° to 45°. It has been shown by F.A. Halsey that a lead angle less than 9° results in rapid wear and the safe value of λ is 12½°.For a compact design, the lead angle may be determined by 

the following relation, i.e. 

where N_G is the speed of the worm gear and N_Wis the speed of the worm.

4. Tooth pressure angle. It is measured in a plane containing the axis of the worm and is equal to one-half the thread profile angle

5. Normal pitch. It is the distance measured along the normal to the threads between two corresponding points on two adjacent threads of the worm. Mathematically, Normal pitch, p_N = p_a.cos λ

6. Helix angle. It is the angle between the tangent to the thread helix on the pitch cylinder and the axis of the worm. It is denoted by
α_W,The worm helix angle is the complement of worm lead angle, i.e.

α_W λ = 90°

the helix angle on the worm is generally quite large and that on the worm gear is very small. Thus, it is usual to specify the lead angle (λ) on the worm and helix angle (α_G) on the worm gear. These two angles are equal for a 90° shaft angle.

7. Velocity ratio. It is the ratio of the speed of worm (N_W) in r.p.m. to the speed of the worm gear (N_G) in r.p.m. Mathematically, velocity ratio, 

Let l = Lead of the worm, and
D_G = Pitch circle diameter of the worm gear.

We know that linear velocity of the worm,  

and linear velocity of the worm gear,