Gear drives

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Worms &
Worm Gears

o Worm gearing is used to transmit power between nonintersecting

shafts, nearly always at right angles to each other (Faires, 1965).

o Worm gearing is mostly used as a speed reducer, which consists of

worm and a worm wheel or gear (Khurmi; Gupta, 2005).

o When properly mounted and lubricated they function as the quietest

and smoothest running type of gearing.

It can give velocity ratios as high as 300:1 or more in a single step in a minimum of
space, but it has a lower efficiency. The worm (which is the driving member) is usually of a
cylindrical form having threads of the same shape as that of an involute rack. The worm is
generally made of steel while the worm gear is made of bronze or cast iron for light service.
Efficiency of worm gear drives depends to a large extent on the helix angle of the worm.
Multiple thread worms and gears with higher helix angle prove 25% to 50% more efficient than
single thread worms1.

Types of Worms

Cylindrical or straight worm is most commonly used and the shape of the thread is
involute helicoid of pressure angle 14 ½° for single and
double threaded worms and 20° for triple and quadruple
threaded worms.

1
http://www.rushgears.com/Gear_Types/wormGears.php. Retrieved Sept. 18, 2012

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Cone or double enveloping worm is used to some extent, but it requires extremely accurate
alignment.

Figure 7-1. Types of Worms

Material recommended for worms is hardened steel and bronze for worm gears.
However, depending on the application unhardened steel worms operate adequately and more
economically with cast iron worm gears at 50% horsepower ratings. In addition to steel and
hardened steel, worms are available in stainless, aluminum, bronze and nylon; worm gears are
available in steel, hardened steel, stainless, aluminum, nylon and non-metallic (phenolic).

Worm Gear terms:

Axial pitch 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. Axial pitch (Pa)
of a worm is equal to the circular pitch (Pc) of the mating
worm gear, when the shafts are at right angles.

Figure 7-2. Worm and worm gear

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Lead is the linear distance through which a point on a thread

moves ahead in one revolution of the worm.

where: Pa = axial pitch ; and n = number of starts

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

where: m – module; and Dw – is pitch circle diameter of the

worm.

The lead angle (λ) may vary from 12 ½ ° to 45°. Lead angle less than 12½0 may results to
rapid wear.

For a compact design2 Lead angle

2
Khurmi; Gupta, 2005

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

For automotive applications, the pressure angle of 30° is recommended to obtain a high
efficiency and to permit overhauling.

Normal pitch is the distance measured along the normal to the threads
between two corresponding points on two adjacent threads
of the worm.

For single start thread,

For multiple start threads,
Norma lead,

Helix angle (w) is the angle between the tangent to the thread helix on the
pitch cylinder and the axis of the worm.

Velocity Ratio is the ratio of the speed of worm in r.p.m. to the speed of
the worm gear in r.p.m.

Efficiency of worm gear defined as the ratio of work done by the worm gear to the
work done by the worm.

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If the efficiency of worm gearing is less than 50%, then the worm gearing is said to be self-
locking (it cannot be driven by applying a torque to the wheel). This property is desirable in
hoisting machinery applications.

PROBLEM
A 3-start worm set has d = 60 mm, px = 12 mm, mG = 60. Find the lead, lead angle, worm gear
diameter, and center distance. N1 = 2500 rpm. Will it self-lock?

SOLUTION

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PROBLEM
A 2-start worm set has L = 2.00 in, C = 9.00 in, mG = 20, and the angle between the shafts is
900. Find the pitch diameters of the worm and worm gear, the lead angle, and the axial pitch.

SOLUTION

PROBLEM
A triple threaded worm has teeth of 6 mm module and pitch circle diameter of 50 mm. If the
worm gear has 30 teeth of 14½° and the coefficient of friction of the worm gearing is 0.05, find
the lead angle of the worm, velocity ratio, center distance, and efficiency of the worm gearing.

SOLUTION

Ans. 19.8°, 10, 115 mm, 85.8%

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Design Exercises

PROBLEM
A 5-start worm set has lead = 200, C = 2.75 in, Ng = 33, and the angle between the shafts is 900.
Find the pitch diameters of the worm and worm gear, the lead, and the axial pitch.

SOLUTION

PROBLEM
A double threaded worm has a pitch circle diameter of 84mm with a axial pitch of 20 mm
determine the helix angle.

SOLUTION

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PROBLEM
A hardened steel worm transmits power to a phosphor bronze with a velocity ratio 20 the center
distance is 400 mm determine, a)Axial module b) Lead Angle (helix angle) c) Power rating
based on heat dissipation criterion d)Power rating based on wear if worm rotates at750 rpm.

SOLUTION

PROBLEM
For a worm and worm wheel the a center distance is given as 225mm worm is made of hardened
steel and rotates at 1250 rpm worm transmits power to a phosphor bronze gear (σb=35 Mpa with
a transmission ratio of 15 the tooth on gear are 20 degree full depth involute(y=0.125).
Determine the diameter of the shaft of worm as well as the worm gear for the arrangement of the
bearing assume coefficient of friction M=0.1

SOLUTION

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Assignment # __
Find machinery or device/machines that have worm gear application. Have a picture of it and
identify the details of the gear (i.e. tooth thickness, face width, pitch diameter, etc.) and compute
the power needed to operate such machine. Submit this requirement(s) on ___________.

Notes

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DESIGN PROBLEM # 7

Name: Rating:
Course/Yr: Date:

WORM GEAR DESIGN

PROBLEM
For a worm and worm wheel the a centre distance is given as 225mm worm is made of hardened
steel and rotates at 1250 rpm worm transmits power to a phosphor bronze gear (σb=35 Mpa with
a transmission ratio of 15 the tooth on gear are 20 degree full depth involute (y = 0.125)
determine all the design parameters and recommitted safe power that the drive can transmit.

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DESIGN PROBLEM # 7 worm gear continuation

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