Figure 13.10 shows a worm and worm wheel arrangement. It consists of a threaded screw B called worm and a toothed wheel C called worm wheel. The worm B is in mesh with worm wheel C and their axes are perpendicular to each other.
Figure 13.10 Worm and Worm Wheel
On the axis of worm B, an effort wheel A of larger diameter is attached, over which a string passes. The effort P is applied at the end of this string. On the axis of worm wheel C, a small pulley or load drum is provided over which a string passes. One end of the string is attached to the load drum and other end is connected to the load W.
Let W = Load lifted by the load drum L
P = Effort applied at the effort wheel
D = Diameter of the effort wheel A
d = Diameter of load drum L
T = Number of teeth on worm wheel C
There are three variants of worm and worm wheel: single start, double start, and triple start.
Single Start: If the worm B be single threaded then with one revolution of worm B, there will be movement of one tooth on worm wheel C.
First one revolution of effort wheel A, the distance moved by the effort P = π D
Load drum L will rotate by 
revolution
Now, the distance moved by load 
Double Start: If the worm B be double threaded then with one revolution of worm B, there will be movement of two teeth on worm wheel C.
First one revolution of effort wheel A, the distance moved by the effort P = π D
Load drum L will rotate by 
revolution
Now, the distance moved by load 
Triple Start: If the worm B be triple threaded then with one revolution of worm B, there will be movement of three teeth on worm wheel C.
Similar to single start and double start, VR and MA for triple start worm.
Example 13.10: A worm of pitch 10 mm, single start has a hand wheel of radius 50 mm. It is meshed with a worm wheel of 120 teeth. Worm wheel consists of co-axial drum or pulley of diameter 40 mm. A string is wrapped around the drum and one end is connected to the load. If effort required raising a load of 1,000 N is 100 N. Find the efficiency of the machine.
Solution:
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