V.

Tractor Transmission Performance:

The relationship between engine brake power and power in the drive wheels of tractor
are discussed below.

i. Engine Brake power

The engine brake power (W) is given by the following equation

... (11.10)

Where, W= engine brake power, kW

Ne = engine RPM

Te = engine torque, N-m

Or ...
(11.11)

Where, W= engine brake power, HP

Ne = engine RPM

Te = engine torque, Kg-m

ii. Power in the drive wheels of tractor

The power in the drive wheels of tractor is given by

... (11.12)

Where, Ww = power in drive wheels of tractor, kW

Tw = drive wheel torque, N-m

Nw = drive wheel RPM

Based on torque speed relationship of tractor power transmission as given in eqns. 8.2
and 8.3, the transmission efficiency (ηt) is given by the following equation.
 ...
(11.13)

Where, Te = engine torque, N-m or Kg-m

Ne = engine RPM

Tw = drive wheel torque, N-m

Nw = drive wheel RPM

ηt = transmission efficiency, %

iii. Drawbar power of tractor

It primarily depends on drawbar pull developed by the tractor and its speed of operation.
The drawbar power of tractor is given by

...(11.14)

Where, Wd= drawbar power, kW

P = drawbar pull, kN

S = speed, km/hr

Or, ...(11.15)

Where, Wd = drawbar power, HP

P = drawbar pull, Kg

S = speed, m/s

VI. Design Procedure for Gearbox of a Tractor

i. Design Considerations

1. To reduce the size of gearbox, the intermediate shaft should have as high speed as
possible.
2. At any point of time only one set of gears should be in mesh. In other words, one set
of gears must be completely disengaged before the other starts to engage.

3. The transmission ratio (TR) of a pair of gears in a gearbox should satisfy following
condition.

4. The speed range ratio (Maximum shaft speed divided by minimum shaft speed)
should not be more than 8.

5. In case of sliding gearbox, the centre distance between two shafts should remain
constant. Or in other words the sum of number of teeth of meshing gears must be
constant.

6. In a gearbox same module (m) of the gear set must be used.

7. The minimum difference between the numbers of teeth of adjacent gears must be 4.

8. The minimum numbers of teeth (in a set for spindle drives) should be greater than 17
to avoid interference of tooth.

VII. Differential

Differential of a tractor consists of planetary gear system which has four bevel gears
(two side gears and two pinions). It also has a pair of bevel gears consisting of a pinion
and crown wheel fitted at right angle to each other to transmit power received from the
gearbox to the rear axles. In other words, the input power to the planet carrier attached
to the crown wheel and output power to the side gears mounted on the counter shafts
gives drive the rear wheels. It acts as a speed reduction and transmission of power at
90°. The differential divides the power into equal parts and finally to the rear wheels. It
allows one wheel of tractor to move faster than the other wheel while taking turns. When
the tractor is moving straight ahead, the bevel pinions of differential do not rotate on
their carrier shafts and both the side gears rotate at same speed. A differential lock is
also provided to prevent excessive spin of one wheel than the other when a resistance
to wheel is different. If one wheel of tractor gets in the mud or loose soil, the other wheel
on the solid ground will not move while the other wheel spins around due to differential
action. To overcome this problem differential lock is provided which allow both the
wheels to move with same speed and apply equal torque.

The torque transmitted by both the axles of tractor would be equal as the bevel pinions
of differential are exerting equal torque on both the side gears.
Transmission efficiency of differential of tractor is given by

... (11.16)

Where, ηd = Transmission efficiency of differential

Wa = power output through both the axles, kW

Wbp = power input to differential through bevel pinion, kW

Also,

... (11.17)

Where, Tbp = torque input to bevel pinion of differential, Nm

Nbp = RPM of bevel pinion

Tal = torque output from left axle, N.m

Tar = torque output from right axle, N.m

Nal = RPM of left axle

Nar = RPM of right axle

ηd = transmission efficiency of differential, %

While moving straight, the torque in both the axles should be equal

Therefore Tal = Tar = Ta …. (11.18)

Where, Ta = rear wheel axle torque.

And average speed of the axle (Na) would be

…..
(11.19)

From eqns. 11.17, 11.18 and 11.19

We get,
Or ... (11.20)

...
(11.21)
ii. Speed division by the differential

While taking turns, the role of differential comes into picture and as per the principles of
differential gears, the reduction in speed of inner sun gear will be added up to the speed
of outer sun gear. The speed of crown wheel during turnings would be average speed of
two drive wheels of the tractor as given by following equation.

..
. (11.22)

Where,Nc = crown wheel speed, rpm

Ni = inner wheel speed, rpm

No = outer wheel speed, rpm

iii. Design of Bevel Gears of differential

The following points should be taken into account while designing a bevel gear drive for
a differential:

1. The gear should have sufficient strength so that, it does not fail at starting
torques under dynamic running conditions.
2. The teeth must have very good wear characteristics so that the life of gear is
long.
3. The suitable material must have very good wear characteristics so that life of
gear is long.
4. The drive should be compact and properly designed.
5. The proper lubrication arrangement should be made.

Design procedure
1. Pitch diameters of bevel gears: Let the number of teeth be N and module be m,.

Then,

Velocity ratio =VR =1.7

Take

Thus, the reference angle for tooth of gear = 30.4º

Thus, the reference angle for tooth of pinion= 59.6º

Pitch line velocity: Pitch line velocity of pinion and gear is calculated by

...
(11.23)

2. Determination of Maximum Tooth Load: Assuming that the full load acts on entire
length of rotor which is driven by these gears. So, the transmitted teeth load is given by

...
(11.24)

3. Materials for bevel gears and Designed Stresses: Let the material for gears be
15Ni2Cr1Mo15 (Nickel chromium molybdenum steel) having ultimate strength-

Taking factor of safety 2.5 for the case hardened steel

Then, design stress

...(11.25)

4. Dynamic load on Bevel Gears: Given in machine design hand books

... (11.26)
 Where, Fd = dynamic load, kgf

Cv = Velocity factor =

Vm = mean velocity

Nsf = service factor =1.5

Km = load distribution factor = 1.25

Ft = tooth load

5. Calculation of Pc and Pd : The circular pitch = Pc = λm

Diameter pitch = Pd = 1/m

6. Calculation of face width: Adopting a 20º in volute teeth (the gear Lewis form factor
is given by

... (11.27)

For straight bevel gears = Z1 / cos σ1 or Z1 / cos σ2 =Zv

Zv = virtual number of teeth

Z1 and Z2 = number of teeth in pinion and gear respectively

σ1 and σ2 = reference cone angle in degrees

Yv = π X Y v

Applying Lewis eqns.

...
(11.28)

Where, Fs = strength of tooth in kgf

σu = design bending stress, 3200kg/cm2 for used material

R = cone distance
 b = face width

Pd = diametrical pitch

If b is small, then we can take another value.

Check for dynamic load:

Dynamic load is given by Buckingham equation.

…
(11.29)

Where,Vm = pitch line velocity m/s

c = constant whose values for 20º full length steel gear is given by c = 11860 × e

E = permissible error in action corresponding to a pitch line velocity (V)

Therefore, Fd must be below the maximum permissible contact compressive stress.

Check for maximum wear:

Formula for maximum wear is given by

Fw =d X Q X K X b ... (11.30)

Where, Fw = wear load

d = Pitch circle diameter

Q = ratio factor 22/(2+1)

k = load factor = (σ)2 × ...

α = pressure angle

b = face width

c = design compression strength