Engineering lab report rewrite(paraphrasing)

Abstract

As we know to find the output power of a motor (shaft power) and its efficiency, dynamometer is widely used in that operation. Our goal out of this experiment is to find motor shaft power and the efficiency by increasing the speed of the rotations (RPM). The experiment was successfully done, and the motor shaft power data were recorded down several in each increment by RPM, the rotational speed was increased a bit. According to the data recorded we noticed that both of the power and the efficiency were increasing as the RPM was increasing too, but after reaching a certain number of RPM which was about 1398 RPM, the shaft power and efficiency decreased significantly. The highest shaft power and efficiency recorded were 0.0965 hp and 0.6256 respectively. As we know that increasing the rotational speed the uncertainties of power and efficiency will increase too.

Introduction

In general, a dynamometers are mostly operated to find the power output of the rotating shaft or tire (in case of a motor vehicle was tested.) In this experiment, a hydraulic brake dynamometer efficiency had to be determined. The hydraulic dynamometer uses the shearing of a red, oily fluid caused by the rotation of a rotor mounted to the shaft. This load against the shaft can be varied by changing the elevation of the fluid inside the housing. This causes a huge difference between the power input and output, and the ratio of the output to the input is the efficiency. Before that, the fundamental equation that relates the power to the toque and the rotational speed is:

P = T ω … (1)

Where:

P is the power of the shaft.

T is the torque of the lever arm, T = L N.

ω is the rotational speed.

The uncertainty of the shaft power, up, can be found using the following equation:

up = P * [ (uF / F)2 + (uL / L)2 + (uω / ω)2 ]1/2 … (2)

Where:

F is the force exerted by the lever arm.

L is the length of the lever arm.

The efficiency of the dynamometer, η, can be solved for using the following equation:

η = Pshaft / Pelectrical … (3)

Also the uncertainty of efficiency can be found using the following:

uη = η * [ (up shaft / Pshaft)2 + (up electrical / P electrical)2 ]1/2 … (4)

Description of Work

First, the wattmeter plugs were checked if they were connected properly. Since the dynamometer was used by a previous group, the housing was drained from the fluid. After that, the housing was filled with the fluid by letting the output tube open to let the air escapes. The shaft was rotated slowly to speed up the previous step. When the housing was filled, the inlet tube was closed. Next, the speed of the motor was set to 100 and the force meter was zeroed. The motor is then turned on the by adjusting the toque knob, and the motor speed was set to 1180 RPM. To measure the rotational speed, a strobe light was used. The frequency of the light is to be adjusted until the white marker on the shaft appears on the 12 o’clock position. The force and the electric power was recorded as well. These measurements were done several times, and in each time the force was lowered by letting some of the fluid from the housing. Approximately an increase of around 100 RPM in the rotational speed had to be reached when emptying the housing. The figures below show the experiment set up.

Figure 1: The entire experiment setup (probe on the right has a resolution of 0.1 RPM).

Figure 2: Motor control knobs.

Figure 3: Chatillon force meter with a resolution of 0.02 lb.

Figure 4: Weston wattmeter with a resolution of 10 watts

Results and Discussion

In Table 1 below, the electric input power was converted from watts to horsepower by dividing the power data by a factor of 745.7. Also the rotational speed was converted from RPM to rad/sec by dividing by a factor of 9.55. Lastly the force input was converted to torque by multiplying by the lever arm length which was 7.5 inch = 0.625 ft.

Table 1: Converted measurements of power, rotational speed and toque.

Table 2 below shows the calculated shaft power, efficiency and the uncertainties. The shaft power was calculated using Equation (1) where the toque was in ft-lb. and the rotational speed was in rad/sec. This yields the power in units of ft-lb/sec, and to convert it to horsepower it was divided by a factor of 550. The uncertainty of the shaft power was calculated using Equation (2). The units of the force, length, and rotational speed were lb, inch, and RPM respectively since they will cancel out units once half of their resolutions (uF, uL, uω) is divided by them. Efficiency was calculated using Equation (3). Both shaft output power and electric input power were in horsepower. The uncertainty of the efficiency was calculated using Equation (4).

Table 2: Shaft power and efficiency, and their uncertainties.

To fully understand the relationship between the shaft power and the rotational speed, a plot of was created as seen in Figure 5. Obviously, the shaft power tends to increase linearly as the rotational speed increases until a critical point (in our case it was 0.0965 hp) is reached, which after that it starts to decrease significantly. Another notable trend is the increase in the uncertainty values as the rotational speed increases. It started with a value and almost doubled at the end. Similarly, when Figure 6 was plotted, a similar trend with the efficiency was noted. As the efficiency increases with the RPM until it hits the same critical point (0.6256) then it decreases significantly. It is noted that both critical points were at 1398 RPM. The values of the raw data can be seen in Table 3 in the Appendix section.

Figure 5: Shaft power as a function of motor rotational speed.

Figure 6: Efficiency as a function of motor rotational speed.

Conclusion

The purpose of the experiment is to figure the trend of the shaft power and the efficiency as the RPM increases. Both, the power and the efficiency reached a critical maximum value when the rotational speed reached a certain critical value of 1398 RPM. Furthermore, a trend of the uncertainty in our measurements had to be found. What was found from the uncertainty is that its range increased as the rotational speed increased. Meaning that less accurate values as the RPM increases. One source of error I think we could pass it by collecting more data between the 2nd and the 4th shaft power data point. If more data in the range between 1100 and 1300 RPM were taken, it is conceivable that clearer interpretation of the plot might have been reached. Plus, the : Chatillon force meter wasn’t functioning properly but that was after doing the experiment so we didn’t count for that error. All in all, the trend of the shaft power and the efficiency somehow matches the expected trend, which proves that this experiment happens to be successful.

Appendix

Table 3: Raw data.

Sample Calculation

· To convert rotational speed from RPM to rad/sec:

ω = 662.5 RPM * (2π rad / revolution) * (1min / 60sec)

ω = 662.5 / (9.55) rad/sec

ω = 69.4 rad/sec

· To convert force in lb. to toque in ft-lb, T = L F:

T = 7.25in * (1ft / 12in) * 0.73lb.

T = 0.4410 ft-lb.

· To calculate the shaft power in hp, P = T ω

T = 0.4410 ft-lb.

ω = 69.4 rad/sec

P = 0.4410 ft-lb. * 69.4 rad/sec

P = 30.605 ft-lb/sec * (1hp /550 ft-lb/sec)

P = 0.0556hp

Shaft power V.S Motor speed

2.9033354381009409E-3 3.0267244834022589E-3 3.1514560863468081E-3 3.4227682256313496E-3 3.6996157941110437E-3 4.1223843182077377E-3 4.1416584626840763E-3 4.162202141147809E-3 2.9033354381009409E-3 3.0267244834022589E-3 3.1514560863468081E-3 3.4227682256313496E-3 3.6996157941110437E-3 4.1223843182077377E-3 4.1416584626840763E-3 4.162202141147809E-3 1180 1231.4000000000001 1284.7 1398 1521.9 1715.1 1728.6 1742.3 1751.6 1761.9 8.8457877201332691E-2 9.084578772013327E-2 9.172060923369825E-2 9.6482627320323658E-2 9.0546168491194665E-2 6.9387672536887199E-2 5.7592574964302708E-2 4.3536768205616368E-2 3.5432175154688238E-2 2.0965016658733938E-2

Rotational Speed (RPM)

Shaft power (hp)

Efficiency V.S Motor speed

5.7959083504298799E-2 5.9627998289245476E-2 6.0428238046283528E-2 5.8755484068179473E-2 5.6410254728439746E-2 6.5833627477352982E-2 7.7416878915167311E-2 7.9723369075603345E-2 5.7959083504298799E-2 5.9627998289245476E-2 6.0428238046283528E-2 5.8755484068179473E-2 5.6410254728439746E-2 6.5833627477352982E-2 7.7416878915167311E-2 7.9723369075603345E-2 1180 1231.4000000000001 1284.7 1398 1521.9 1715.1 1728.6 1742.3 1751.6 1761.9 0.59966399117303437 0.61585185366275796 0.62178234823244349 0.62562691471969878 0.58713285081638145 0.54465670958691359 0.53683478938600671 0.46379097215611609 0.48039587296092762 0.34741362049817553

Rotational Speed (RPM)

Efficiency

10