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Worm Gear

Worm Gears
Worm Gear

A worm is a gear with one or more cylindrical, screw-like threads and a face width that is usually greater than its diameter. A worm has a center hole (bore) for mounting the worm on a shaft.

Worm gears, like worms, also are cylindrical and bored for mounting on a shaft. However, unlike a worm, a worm gear’s diameter is usually much larger than the width of its face. Worm gears differ from spur gears in that their teeth are somewhat different in shape and are always formed on an angle to the hole (axis) in order to mate with worms.

In worms and worm gear sets, both the worm and worm gear are of the same hand. Right-hand sets are considered standard. As a result, right-hand sets will always be furnished unless otherwise specified.


The efficiency of worm gear depends on the lead angle, sliding speed, and lubricant, surface quality and installation conditions. They offer smoothest, quietest form of gearing. They provide high-ratio speed reduction in minimal spaces.

Worm gears are used when large gear reductions are required. Worm gear has a unique property of easily turning the gear. The gear cannot turn the worm because the angle on the worm is shallow and when the gear tries to spin the worm, the friction between the two holds the worm in place. Worm gears work under difficult conditions, presenting unique lubrication demands. The types of oils most commonly used to lubricate worm gears are compounded mineral oils, EP mineral gear oils and synthetics.

Worm gear is always used as the input gear. For the operation of worm gear, torque is applied to the input end of the worm shaft by a driven sprocket or electric motor. The worm and the worm shaft are supported by anti-friction roller bearings. Because of high friction worm gears are very inefficient. There is lot of friction between a worm gear and the gear being driven by the worm gear. When used in high torque applications, the friction causes the wear on the gear teeth and erosion of restraining surface.

Worm Gear-Basic Dimensions

Gear dimensions are important because they provide valuable information when determining how best to meet a customer’s needs. Here are definitions we need to know in order to determine the basic dimensions of worm gears.
1. Pitch Diameter –The diameter of the pitch circle is the “imaginary” circle on which the worm and worm gear mesh.
2. Working Depth – The maximum distance the worm thread extends into the tooth space of the gear.
3. Throat Diameter –The diameter of the throat circle at the center line of the worm gear face (the lowest point on the tooth face).
4. Outside Diameter – The largest diameter of the worm gear teeth. It is equal to the diameter of the outside circle.
5. Root Diameter – The smallest diameter of the worm gear. It is equal to the diameter of the root circle.

Worm Gear-Tooth Dimensions

Worm Gear-Tooth Dimensions

1. Addendum – The distance from the pitch circle to the throat circle.
2. Dedendum – The distance from the pitch circle to the base of the tooth. It is equal to the addendum plus the working clearance.
3. Whole Depth – The distance between the throat and the base of the tooth. It is equal to the addendum plus the dedendum.
4. Working Clearance – The space between the top of the worm thread and the bottom of the worm gear tooth when properly

Worm and Worm Gear Formulas

    S. no.

    To Obtain



    1 Circular Pitch Diametral Pitch Divide 3.1416 by the Diametral Pitch.
    2 Diametral Pitch Circular Pitch Divide 3.1416 by the Circular Pitch.
    3 Lead (of Worm) Number of Threads
    in worm & Circular Pitch
    Multiply the Circular pitch
    by the number of threads.
    4 Circular Pitch
    or Linear Pitch
    Lead and number of
    threads in worm
    Divide the lead by the
    number of threads
    5 Addendum Circular Pitch Multiply the Circular pitch by .3183.
    6 Addendum Diametral Pitch Divide 1 by the Diametral Pitch.
    7 Pitch Diameter
    of Worm
    Outside Diameter
    and Addendum
    Subtract twice the Addendum
    from the Outside Diameter.
    8 Pitch Diameter
    of Worm
    Select Standard
    Pitch Diameter
    when Designing
    Worm Gears are made to
    suit the mating worm.
    9 Pitch Diameter
    of Worm Gear
    Circular Pitch and
    Number of Teeth
    Multiply the number of teeth in
    the gear by the Circular Pitch and
    divide the product by 3.1416.
    10 Pitch Diameter
    of Worm Gear
    Diametral Pitch
    and No. of Teeth
    Divide the number of teeth
    in gear by the Diametral Pitch
    11 Center Distance
    between Worm
    and Worm Gear
    Pitch Diameter of
    Worm and Worm Gear
    Add the Pitch Diameters of
    the worm and worm gear
    then divide the sum by 2.
    12 Whole Depth of
    Circular Pitch Multiply the Circular Pitch by .6866.
    13 Whole Depth of
    Diametral Pitch Divide 2.157 by the Diametral Pitch.
    14 Bottom Diameter
    of Worm
    Whole Depth and
    Outside Diameter
    Subtract twice the whole
    depth from the Outside Diameter
    15 Throat Diameter
    of Worm Gear
    Pitch Diameter of
    Worm Gear and Addendum
    Add twice the Addendum to the
    pitch diameter of the Worm Gear.
    16 Lead Angle of
    Pitch Diameter of the
    Worm and the Lead
    Multiply the Pitch Diameter of the Worm
    by 3.1416 and divide the product by the
    Lead, the Quotient is the cotangent of
    the Lead Angle of the Worm.
    17 Ratio Number of Starts (or threads)
    in the Worm and the number
    of teeth in the Worm Gear
    Divide the number of teeth in
    Worm Gear by number of starts
    (or threads) in worm.


Worm gears are a compact, efficient means of substantially decreasing speed and increasing torque. Worm-drives have also been used in a few automotive differentials. The worm-wheel carries the differential gearing. This protects the vehicle against rollback. This has largely fallen from favour due to the higher than necessary reduction ratios. Worm gears are widely used in packaging machinery, material handling, machine tools, indexing and food processing. They are used widely in conveyor systems. They are also used in torsen differential, used on some high-performance cars and trucks. They serve as speed reducers in many different industries.


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