2. What is a differential?
Differential is a device capable of transmitting torque and
rotation through three shafts, almost always used in one of
two ways. In one of these, it receives one input and
provides two outputs; this is found in most automobiles. In
an automobile and other wheeled vehicles, the differential
allows each of the driving wheels to rotate at different
speeds, while supplying equal torque to each of them.
3. Purpose of a differential
The differential is found on all modern cars and trucks,
and also in many all-wheel-drive vehicles. These all-
wheel-drive vehicles need a differential between each
set of drive wheels, and they need one between the
front and the back wheels as well, because the front
wheels travel a different distance through a turn than
the rear wheels.
5. Differential Gear Train on a Turning TRACTOR
The outer wheel traverses an arc with radius ro and the inner
wheel traverses an arc with radius ri. As illustrated, the
lengths of the arcs traversed are so, sn, and si. The outer arc so is
obviously larger than the inner arc si for a given traversed
angle theta. Some way of ensuring that the outer wheel is
able to turn slightly faster than the inner wheel must be
ensured in order to prevent binding and slippage of the tires
on the road.
6. Differential Gear Train on a Turning TRACTOR
Fortunately, the automobile differential solves
this problem with only one transmission and
one drive shaft for both driven wheels.
7. Differential Gear Train on a Turning Tractor
Since s=r(THETA), the length of the arc traversed for a given theta is
proportional to the radius. Since ro is greater than rn by the same amount
that ri is less than rn, the right wheel center must travel further than the
car center by the same amount that the left wheel center must travel less
further than the car center. As its name implies, a differential allows the
left and right drive wheels to turn differentially with respect to each
other. As can be seen by turning the drive wheels of a car on a mechanic's
lift, turning one drive wheel results in the opposite wheel turning at the
same rate in the opposite direction.
10. Differential Calculations
• The difference between the paths travelled by
left(outside) and the right(inside) wheels will
be 2∏(R-r)
• Since both sets of wheels travel over this
distance at the same time,the speed
differential between the left (outside) and
right(inside) wheels is Vo-Vi=2∏(R-r)/T,where
T is time time trevel
11. example
• Consider the open differential shown in
figure.the numbers of tooth on each gear are
as
Ni=16,Nc=57,Np=12,No=17
Suppose that we jack the right wheel up and
rev the engine up to 5100 rpm.The speed
reduction across the transmission gearbox is
3.4
12. Differential Calculations
The dimensionless velocity differential
between the outside and the inside wheels
can then be approximated by
Vdiff =Vo-Vi/Vavg =R-r/Ravg=t/Rav
Where t is the wheel base and
Ravg is the distance from the
centre of rotation to the centre of
the wheel axle
13. What is the speed of the left wheel?
What is the speed of the free rotating
right wheel?
14. Numerical Problem:
The differential in a rear axle of a farm tractor has a
ring gear with 32 teeth driven by a bevel pinion with
8 teeth. Each side gear is connected to a rear axle
through a final drive unit that provides a 5:1 speed
reduction . If the input torque of a bevel pinion is
1500Nm & input speed is 520 rpm. Calculate the
torque and power in each rear axle when the left
wheel encounters poor traction & begins turning
50% faster than right wheel. Assume differential
efficiency as .98
Sol. Given: input torque(Te)=1500 rpm,speed ratio
on rear axle=32/8=4
input speed(Ne)=520,Tr=32,Tp=8
speed reduction of final drive=5:1
speed on rear axle=520/5*4= 26 rpm
Let x be the speed reduction
15. Therefore, speed of left wheel NL=(26+x) rpm , and
speed of right wheel Nr=(26-x)rpm
(NL+x)=1.5(Nr-x)
26+x=1.5(26-x)
2.5x=13
x=13/2.5=5.3 rpm
speed of left wheel NL=26+5.3=31.3 rpm , and speed
of right wheel Nr=(26-5.3)=20.8rpm
1500*2*∏*250/60=T[2*∏*3.12/60+2∏*20.8/60]
T=14700 Nm
Again PL=2∏TNL.ήd
=2∏*14700*31.2*0.98/60
=47.06kw
Pr=2∏TNrήd
= 2*∏*14700*20.8*.98/60
=31.378kw ans.
16. Multiple choice questions:-
1.In tractor engine power at right angle is transmitted
by
(a)Differential (b) clutch assembly (c)pto shaft (d) belt
pulley
2.The crown wheel assembly of tractor differential
works as
(a)Increase speed of rear wheel
(b) Reduce speed of rotation
(c) Control pto speed
(d) Control engine speed
3.The bevel pinion of differential of a tractor drives
(a)Crown gear (b) final drive gear (c)crank shaft (d) all
above three
17. 4.Final drive in tractors provides addition speed reduction
between
(a)Engine and rear wheels (b)piston and crank shaft
(c)engine and gear box (d)engine and differential
5.Main component of tractor differential
(a)Pto shaft (b)crown wheel assembly (c)spur gear
(d)clutch
Answers:-
1-(a), 2-(b), 3-(a), 4-(a),5(b)
