UNIVERSITY OF NAIROBI
DEPARTMENT OF MECHANICAL AND MANUFACTURING
ENGINEERING
FME 311: THEORY OF MACHINES LABORATORY
GEAR TRAIN EFFICIENCY TEST
Introduction
Gear trains are used for transmitting power from a driving unit to a driven unit, often with
a change of speed. The output from the gear train can have a higher or a lower speed,
depending on the requirements of the driven unit.
Power loss in the enclosed gear train results from viscous friction of lubricants, sliding
friction between the meshing teeth and losses of energy due to vibration and noise,
among other causes. Therefore, the power supplied to the gear train is always greater
than the power delivered to the driven unit. This laboratory session demonstrates a
method for determining power losses.
Theory and Apparatus
The straight forward approach to measuring power losses in a gear train would be to
measure the power supplied to the train by the motor and the power supplied to the driven
unit from the gear train so that the losses can be determined as the difference between the
two measurements.
However, the value of the power losses is very much less than the two measurable values
and the method described above would be very inaccurate, if used. This difficulty is
overcome by feeding the power output from the gear train back to the input shaft. Figure
1 illustrates the principle.
In Figure 1:

The total power loss in the system is the sum of the power loss in the motor and the
power loss in the gear train:
L  Lm  Lg
(1)
In equation (1), L is the total power loss in the drive, Lm is the power loss in the
motor and L g is the power loss in the gear train.
Gear Train Efficiency Test
Lg
G4
G3
Lm
Hi
Ho
Ho
G1
G2
C1
C2
H o  Lg
Motor
Figure 1 – The Four-Square Gear Test Rig

Once the system attains a steady speed (no acceleration), the power balance for the
drive can be represented as follows:
H i  Lm  Lg  0


H i  Lg  Lm 

Hi  L


(2)
The power denoted by H o is re-circulated and has no net effect on the power
balance as expressed in equation (2). However, if a torque can somehow be built
into the drive then H o will have a value that needs to be determined in order to
calculate the efficiency of the gear train. Once the value of H o is known, the
efficiency of the gear train is determined as follows:

Ho
H o  Lg
(3)
A schematic arrangement of the apparatus is shown in Figure 2.
The variac enables the supply of power at variable voltage to the DC motor and thus
provides a means of varying the speed of the motor. The wattmeter is an instrument for
measuring the electrical power supplied to the motor and denoted by H i in Figure 1.
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Gear Train Efficiency Test
DC
Power
To Gear
Train
Wattmeter
Variac
Tachometer
Motor
Figure 2 – Schematic of the Apparatus
Torque can be built into the system by use of coupling C2 (Figure). The speed of the
motor shaft can be set by use of the variac and the hand-held tachometer shown in Figure
2. With the built-in torque, T , and the speed of the motor shaft,  , known, H o is
determined as follows:
H o  T
(4)
In equation (4), T is in Newton-metres and  is in radians per second.
Procedure
1.
Determination of power losses in the motor alone:
Disconnect the motor from the gear train at coupling C1 and set the motor running
at a chosen speed. The power supplied to the motor then goes to overcome losses in
the motor windings, and bearing friction. This power is read off the wattmeter as
Lm . Repeat this procedure for higher speeds in incremental steps of 100 rpm such
as 900, 1000, 1100,…, to 1800 rpm.
2.
Determination of power losses in both the motor and the gear train:
Reconnect the motor to the gear train at coupling C1 and build a torque into the gear
train at coupling C2 by holding one half of C2 using a spanner and applying a
moment onto the other half. The moment is applied by hanging masses on a steel
rod fixed in the movable half of coupling C2 and then locking the two halves of the
coupling together. Figure 3 illustrates application of the built-in torque.
The built-in torque is calculated as follows:
T  MgRcos
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Gear Train Efficiency Test
Measure angle  using a protractor furnished with a spirit level.
R

Mg
Figure 3 – Applying the Built-in Torque
After building in the torque, run the experiment at the same speeds that were used in step
1 above and record the wattmeter reading at each speed, which now gives the values of
total power loss, L . Repeat this procedure using 1 kg, 2 kg, 3 kg and 4 kg masses to
build in the torque. Tabulate all your results. A sample table is appended to this
document.
Analysis
1.
Plot the four graphs of power lost in the gear train versus speed on a single sheet of
paper.
2.
Plot the graphs of efficiency versus speed for the four values of built-in torque on a
single sheet of paper.
Discussion and Conclusions
Discuss the results and draw conclusions from them.
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Gear Train Efficiency Test
Sample Table of Observations
Mass used to build-in torque, M (kilograms):
Radius of the torque arm, R (metres):
Angle of the torque arm,  (degrees):
Motor speed, N , (rpm)
Motor power loss, Lm (kW)
Total Power Loss, L (kW)
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
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