OBJECTIVE: To evaluate the power loss in a gear train for different values of power transmitted and the resulting efficiencies.
INTRODUCTION: Gears are compact, positive-engagement, power transmission elements that determine the speed, torque, and direction of rotation of driven machine elements. Gear types may be grouped into five main categories: Spur, Helical, Bevel, Hypoid, and Worm. Typically, shaft orientation, efficiency, and speed determine which of these types should be used for a particular application.
Gear contact is normally simultaneous across the entire width of the meshing teeth, resulting in a continuous series of shocks. These rapid shocks result in some objectionable operating noise and vibration. Moreover, tooth wear results from shock loads at high speeds. Noise and wear can be minimized with proper lubrication, which reduces tooth surface contact and engagement shock loads. The main advantage of the gear is the property of self-holding, i.e. providing the immobility of the screw with its loading only by the axial force . The efficiency of a gear is equal to the relation between the useful (output) power and the applied (input) power.
Gear trains are used for transmitting power from a driving unit to a driven unit, with a change of speed. The output from the gear box can have a higher or a lower speed depending on the requirement. Power losses in the gear box which encloses the gear train results from viscous friction of lubricants, sliding friction, losses of energy due to vibration and noise etc. Therefore power supplied to the gear train is more than power delivered to the power absorber. This experiment demonstrates a method of determining these losses.
Evaluate how the various gear types are combined into gear drives; and consider the principle factors that affect gear drive selection.
The efficiency of a mechanism is determined by:
Where is the power input in the mechanism
and is the output power.
This main dependency in engineering is used to evaluate the theoretical and the real (experimentally determined) values of efficiency of a gear.
To measure power losses in a gearbox, the straight forward approach is to measure the power supplied to the motor and the powers absorbed by the power absorber so that the loss can be found as the difference between the two.
The value of losses is very much less than either of the two values measurable and the method described above would be very inaccurate if employed. This difficulty is overcome by feeding the power output from the gearbox back into the input. Fig. 1 below illustrates the principle.
Let power output from gear be , then
T = torque built into the train and W= angular velocity of the motor shaft
Losses = sum of losses in the motor and in the gear train
Figure 1: The gear train principle
Then the equivalent of power supplied
Note that is a calculated value. It is not read off the wattmeter. Once the system attains a steady speed, the only power supplied from the mains is the power required to overcome losses.
Fig. 2 shows the layout of the apparatus. A wattmeter is used for giving a reading of the power supplied to overcome losses. A variance enables a supply of variable voltage to the DC motor hence a variable speed can be achieved. The torque is incorporated into the system using coupling (Fig 1). The speed of the motor shaft is measured by a tachometer pressed lightly at the end of the shaft.
Figure 2: Experiment set up
1. Determination of losses in the motor alone.
The motor is disconnected from the gear tat coupling and set to run at a chosen speed. The power supplied to the motor to overcome losses in the winding and bearing friction is read off the wattmeter. Run the motor steadily at 800 rev/min and record the wattmeter reading as. Repeat for higher speeds increasing the speed in steps of 100 rev/min. i.e. at 900, 1000, to 1800 rev/min.
2. Determination of losses in both the motor and the gear train
Connect the motor to the gear train at and build a torque into the gear train at coupling, by holding one half of with a spanner and applying a moment on a steel rod fixed in the coupling, and tightening the two halves of the coupling together. Fig. 3 shows how to determine the torque.
Figure 3: Determination of the torque
Measure using a vernier protractor.
After building the torque, run the system at the same speeds as above and record the corresponding wattmeter readings representing LT. Take four sets of readings using 1Kg, 2Kgs, 3Kgs, and 4Kgs. masses. Tabulate all the results.
1. Plot the four graphs of power lost in the gear train vs. speed on the same sheet.
2. Plot the efficiency vs. speed for the four torques on the same sheet.
DISCUSSIONS AND CONCLUSION
Discuss and draw conclusions on your results.