Download Seokho Hong Period 6 The Effect of Gear Ratio from Wind Turbine

Seokho Hong
Period 6
The Effect of Gear Ratio from Wind Turbine to Generator on Power Generation
Design
This lab seeks to answer: how does the gear ratio of the wind turbine to the
generator affect the amount of power generated? The equation for determining the
amount of power generated by a generator is: power = torque * 2 * PI * rotational speed.
Gear ratios are not sources of power nor do they reduce the amount of useful energy in
the system except some negligible amount of heat and friction. They work by changing
the nature of the mechanical energy by shifting the balance between torque and rotational
speed, which are inversely related as shown by the previous equation. Using gears to
reduce rotational speed increase torque proportionately, and vice versa. Because of the
law of conservation of energy, and because gearboxes do not transform the nature of the
energy in any significant amount, gearboxes do not deprive the system of power. Given
that the amount of power applied onto the generator is the same, the amount of energy
generated by the generator should not be affected by the gear ratio modifying the
mechanical energy. Therefore, if the gear ratio on the wind turbine is changed, there will
be no effect on the power generated. This will occur because the gearbox will not add or
remove useful energy in the system.
The equipment for this lab includes the materials for the wind turbine, a large fan,
two resistors of 100 and 330 ohms, and two multimeters. The wind turbine contains many
different parts, which include the following relevant parts: 4, 18-inch fan blades, a
generator of unknown efficiency, a 64-tooth gear, 32-tooth gear, and an 8-tooth gear. To
conduct the experiment, the constructed wind turbine was placed in front of a large fan
that was turned on. On the first test, the turbine was connected to the 64-tooth gear while
the generator had an 8-tooth gear resulting in an 8:1 gear ratio. With the black and red
wires, the 100ohm resister was placed between them. Multimeters were attached to the
circuitry: one in parallel across the resistor and one in series. The one in parallel would
measure the voltage drop across the resister while the one in series would measure the
current. They were measured in volts and amperes respectively after the fan was turned
on to the setting of ‘low’ from 1 meter away from the turbine. The following test
involved readjusting the gearbox to have a 4 to 1 ratio. Then both ratios were tested with
the 330ohm resistor to obtain more data points.
The dependent variables of this experiment include the gear ratio in the gearbox
and the strength of the resistor. Only two gear ratios were possible: the 8-1 and 4-1 ratios,
and to add more data points, we used two resistors for each gear ratio, the 100ohm and
330ohm resistors. The controlled variables include the shape, number, pitch, and
distribution, and length of fan blades, the speed of the fan, the distance between the fan
and the turbine, and other minor variables including temperature and other sources of
wind. Using the same wind turbine and maintaining the setup 1 meter away from the fan
ensured that many of the variables were controlled. The fan was always turned onto the
‘low’ setting when in use. Temperature and stray wind were not controlled as well, but
the indoor environment ensured that these variables were kept to a minimum. Efforts
were made to ensure that no other forces acted upon the spinning of the wind turbine. For
this experiment, no particular safety precautions were needed because the wind turbine
would not spin fast enough to hurt anyone and the current generated would not be
harmful either.
Data Collection and Processing:
The changing of the variables, including gear ratio and resistor, had no visible
effects on the spinning of the wind turbine.
Raw Data:
Table 1. Measured Voltage and Current for each Trial
Gear Ratio
Resistor
Voltage
Current
1:4
100 ohm
.6V+/-.05V
.006A+/-.001A
1:4
330 ohm
.7V+/-.05V
.002A+/-.001A
1:8
100 ohm
1.1V+/-.05V
.011A+/-.001A
1:8
330 ohm
1.5V+/-.05V
.005A+/-.001A
Calculations:
Power can be calculated from the following equation:
Power = Voltage * Current
For the first trial: .6V+/-.05V * .006A+/-.001A = .0036A+/-.0009A
The uncertainty associated with this trial: .05V/.6V + .001A/.006A = .25
.25 * .0036A = .0009A
Power was calculated in a similar way for the rest of the trials.
Table 2. Calculated Power
Gear Ratio
Resistor
Power
1:4
100 ohm
.0036A+/-.0009A
1:4
330 ohm
.0014A+/-.0008A
1:8
100 ohm
.0121A+/-.00165A
1:8
330 ohm
.0075A+/-.00175A
The ratio of power generation from the 1:4 to 1:8 gear ratios can be calculated by :
Power of 1:8 / Power of 1:4 = power ratio
For example, for the 100ohm resistor tests: .0121A/.0036A = 3.36
Uncertainty: ( .00165A/.0121A + .0009A/.0036A ) *3.36= 1.30
Table 3. Power ratios of 100ohm resistor tests and 330 ohm resistor tests
Resistor
Power Ratio
100ohm
3.36+/-1.3
330ohm
5.357+/-4.31
Conclusion:
The gearbox ratio in the wind turbine does affect power generation. A faster speed
in rotation increases the amount of power generated. This is inconsistent with the power
equation presented in the introduction, but is consistent with winds turbines used today,
which use gearboxes to increase the rotational speed at the cost of torque. According to
Table 3, the power ratios for both resistors are higher than 1 meaning that higher gear
ratio of 1:8 produces more energy than the 1:4. Although the 330ohm data is relatively
meaningless because of the extraordinarily high uncertainty, even the lower estimates
would give a power ratio greater than 1. Clearly the gear ratio does have an effect on the
amount of power generated and therefore the results of this experiment do not support my
original hypothesis.
The main limitation resulting from the use of school equipment was the increase
in random error in the measurements of voltage and current. Since a propeller fan was
used to turn the turbine, the wind hitting the turbine was erratic and turbulent. This
resulted in the turbine spinning slightly slower or faster at other times contributing to a
less accurate reading on the multimeters. Given a wind tunnel producing much more
consistent wind, the experiment may have had much less random error because the
turbine would spin with less volatility.
One weakness of this experiment was the lack of experimental data. The materials
prevented the testing of other gear ratios and therefore this experiment dealt with only
two settings of the dependent variable. Given additional gears of different sizes, the
experiment may have been able to generate a more complete and convincing set of data.
Using other gear ratios, especially very low or very high gear ratios would be the next
step to extending the inquiry.