Engineering Mechanics

(^214) „„„„„ A Textbook of Engineering Mechanics

2. In general, if the worm wheel is n threaded, then
   2
   V.R.
   lT
   np

π

=

Example 11.23. A worm geared screw jack has the following particulars :

Length of handle = 300 mm

No. of teeth in the worm wheel = 50

Pitch of screw = 10 mm

Effort applied = 100 N

Load lifted = 100 kN

If the worm is double threaded, find the efficiency of the jack.

Solution. Given: Length of handle (l) = 300 mm ; No. of teeth in the worm wheel (T) = 50 ;

Pitch of screw (p) = 10 mm ; Effort (P) = 100 N ; Load lifted (W) = 100 kN = 100 000 N and no. of

threads (n) = 2.

We know that velocity ratio of a worm geared screw Jack,

2230050

V.R. 4712

210

lT

np

ππ××

== =

×

and M.A. 100 000 1000

100

W

P

== =

∴ Efficiency,

M.A. 1000

0.212 21.2%

V.R. 4712

η= = = = Ans.

EXERCISE 11.3

1. In a first system of pulleys, there are 5 movable pulleys. If the efficiency of the machine is
   75%, what effort can lift a load of 4 kN? [Ans. 166.7 N]


2. In a second system of pulleys, there are nine pulleys in the two blocks. Find the efficiency
   of the machine, if an effort of 50 N can lift a load of 300 N. [Ans. 66.7%]


3. There are three pulleys arranged in the third system of pulleys. Find the load that can be
   lifted by an effort of 50 N, if efficiency of the machine is 80%. [Ans. 280 N]


4. A simple screw jack has a thread of pitch 12 mm. Find the load that can be lifted by an
   effort of 20 N applied at the end of handle 500 mm long. Take efficiency of the machine as
   50%. [Ans. 2.094 kN]


5. In a simple screw jack, the pitch of the screw is 10 mm and length of the handle is 450 mm.
   Find the velocity ratio. If an effort of 25 N applied at the end of the handle can lift a load
   of 3 kN, find the efficiency of the jack. Also calculate the amount of effort wasted in
   friction and the frictional load. [Ans. 282.7 ; 42.4% ; 14.4 N ; 4.068 kN]


6. A differential screw jack has threads of 10 mm and 6 mm. It was found that an effort of
   14.7 N applied at the end of handle 400 mm long can lift a load of 2.5 kN. Find the
   efficiency of the screw jack. [Ans. 27.1%]


7. A worm geared screw jack has the following particulars :
   Handle length = 400 mm
   No. of teeth in the worm wheel = 45
   Pitch of screw = 12 mm
   If the worm is single-threaded, find the load that can be lifted by an effort of 20 N. Take
   efficiency of the machine as 20%. [Ans. 37.7 kN]