Measurements Lab report

EXPERIMENT TITLE HERE
Name Date Mechanical Engineering Department California State University, Northridge
The total length of the “Summary Report” is 4 pages in 12 point font size. Follow the guidelines below.
Abstract The abstract should be brief, self-contained and explicit. It should state the experiment objectives, experimental techniques, main results and conclusions. It should be ~100 words long.
Introduction This should outline the objectives of the experiment and briefly describe the scope and methods employed in about 1-2 paragraphs.
Theory The theory should be stated briefly, and any references to sources such as lecture notes or textbooks should be cited. The theory should then be developed, if relevant, so that it relates to the variables of the experiment. Any theory involves some assumptions, and the experimental equipment or method may not be consistent with one or more of these. Be certain to consider the limitations of the theory and/or experiment in the `Discussion’ section. This section should be about 2-3 paragraphs.
Apparatus and Procedure The apparatus section provides a brief description of the apparatus and experimental set-up used to carry out the experiment (1 paragraph). It also describes the method by which the experimental data were obtained. Write in the past tense and describe what you actually did (1 paragraph).
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Results The results section presents results (main results) in the form of graphs or tables. These are used to facilitate the comparison of experimental results and theoretical predictions, variations in test results obtained from different sources, and sizes of errors relative to magnitudes of effects in about 1 page. The uncertanity analysis is mandatory (10% of lab report score automatically deducted is uncertanity analysis is not included). Discussion This section should include comments on the results obtained and interpretation of them in relation to the stated objectives of the experiment. The discussion may include: how well the experimental results compare with experiments, comments on the forms of graphs and pattern of results, The effects of theoretical approximations and assumptions and of experimental, and magnitude and significance of experimental errors. 1-2 paragraphs.
Conclusions The conclusions are intended to highlight what the author considers to be the significant findings or outcome of the experiment in about 1 paragraph.
References

Measurement of the Damping Coeﬃcient of an Air Damper
7.1.1 Objective
The purpose of this experiment is to measure the damping coeﬃcient of a small commercial damper using our laboratory data acquisition system. You will be required to make use of the LabView vi ﬁle created in previous lab exercises, and employ some of the data analysis techniques which were discussed in previous lectures.
7.1.2 Theory
The resistance force of an ideal damper or shock absorber is proportional to the speed of the motion. Thus we can write
F = C ×
dx dt
, (7.1)
where C is the damping coeﬃcient. “C” can be determined by applying a known force on the damper and measuring the resulting velocity. To determine whether the damper truly behaves according to the ideal model, one must repeat the measurements at several known forces. In this experiment, the known force is produced by placing weights on a platform which is connected to one end of the damper. The resulting motion of the damper is measured using a linear potentiometer (see Figure ). The damper is adjustable with a knob on one end. The instructor will adjust the damper so that an appropriate velocity range is obtained for the weights used in the experiment. Measurements will be taken for each weight to determine the velocity of motion. Subsequently the force and velocity data will be plotted to determine the coeﬃcient C. Note that the force-velocity plot will be linear if the damper behaves according to the ideal model.
7.1.3 Procedure
1. Open LabView and access an appropriate vi ﬁle. It will probably be easier to modify this ﬁle for use in this experiment, although you can start from scratch if
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Figure 7.1: Schematic of the experimental setup used for estimating damping coeﬃcient of air damper.
you wish. It will probably be best to create two vi ﬁles for this experiment one to do the potentiometer calibration, and the other to take the data for velocity measurements. For the calibration vi, you can take the ﬁle from Exercise-2 and delete the icons associated with the chart output and spreadsheet ﬁle storage.
2. Calibrate the linear potentiometer by measuring the voltage output at speciﬁc “x locations. The distance “x can be measured with the scale attached to the test stand. Use either the top or bottom of the moveable platform as the reference for the measurement (but be consistent!). It is probably easiest to lay the test stand horizontally on the workbench during the calibration procedure. Collect data at six or more x locations.
3. Enter the data collected in Step -2 in an Excel worksheet. Plot the distance “x versus voltage (i.e. volts should be on the horizontal axis). Insert a linear trendline and check the appropriate box so the linear equation is displayed on the chart. Save the Excel worksheet for later reference and return to the LabView ﬁle.
4. Make sure that the instructor has checked the damper adjustment knob so that good data will be obtained (i.e. velocities are in an appropriate range). Generally, the adjustment should be set so that the damper moves very slowly with the lightest weight placed on the test stand. Some capabilities need to be added to the vi ﬁle from Exercise-2 to perform this step speciﬁcally the ability to apply a linear calibration equation to the measured voltage (i.e. multiply by a slope and add an intercept these values will be entered via the front panel). Modify the vi ﬁle to accommodate these changes by adding two Controls on the front panel and then adding the appropriate math functions and connections on the wiring diagram. Enter the slope and intercept values from Step-3 in the appropriate Controls, so that the output of the LabView ﬁle will now be the distance “x.
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5. Data should now be collected for each of the seven supplied weights. For each weight the procedure involves placing a weight on the test stand, and then running the LabView ﬁle to collect data of distance versus time. You will probably need to experiment with the sampling frequency and the number of points in order to get good data. Make sure that the linear portion of the output representing the motion, as viewed on the LabView chart output, consists of at least ten points so that a good estimate of dx/dt (i.e.velocity) can be evaluated. Save the results in a ﬁle with an appropriate name so it can be recognized later and opened in Excel. After this step you should have seven output ﬁles corresponding to the seven weights.
6. After the data collection is complete, open each output ﬁle in Excel and determine the velocity of the damper. Locate the range of data values corresponding to the motion and ﬁt a linear trend line to this data. Also ﬁnd the “1σ” uncertainty in the slope (Sa1) using the LINEST function. Now, the velocity of the damper can be expressed as the absolute value of the slope ±2 * (1 σ uncertainty) (95%). (Or use the t factor instead of 2 if the number of points is less than 20.) Complete this analysis for each of the seven output ﬁles.
7. Make a table in an Excel worksheet with the values calculated from Step-6. Put the velocity values in the ﬁrst column, the 95% uncertainty in velocity in the second column, and the force (weight) values in the third column. Plot the force versus velocity on a chart, and use the velocity uncertainty values to create x-error bars. Observe the trend in the data is it linear? The error bars on the velocity values help to determine whether deviations from the linear trend are explainable from the measurement uncertainties. Evaluating the slope (and its uncertainty) of the linear ﬁt through the force-velocity data will provide an estimate of the damping coeﬃcient and its uncertainty.
7.1.4 Results
Your results should address the following points:
1. Make sure that the following plots are included in the results section of the report: potentiometer calibration, distance-time plots for each weight, and force-velocity plot for the damper. (Exception some of the distance-time plots can be put in the appendix, if you wish.) Worksheets containing the data values and analysis can be shown in the appendix.
2. Comment on the linearity of the potentiometer calibration plot are there signiﬁcant deviations between any of the data points and the best ﬁt line?
3. Comment on the distance time plots for each weight. Are these linear in the range corresponding to the damper motion? Note that non-linearities may indicate errors in the data, friction in the test stand, etc. The velocities and their uncertainties corresponding to a 95% conﬁdence level should be summarized in a table in the results section of the report.
4. Evaluate the damping coeﬃcient (with proper units!) and its uncertainty (95% conﬁdence) from the force-velocity data. (The uncertainty in C is the uncertainty of the slope of the force-velocity plot.) Does the plot support the assumption that the air damper acts as an ideal damper? Allow for the uncertainties in velocity
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while making your assessment. Note that non-linearities in this plot may indicate errors in the data, non-ideal behavior by the damper, friction in the test stand, etc.

……………….Answer Preview………………

Abstract

The damping of a system are classified as follows: Over-damped- is when the system returns to equilibrium state without oscillating. The graph is exponentially decaying. Critically damped is when the system comes back to equilibrium condition as fast as possible and without oscillating. Underdamped describes the state of a system oscillating very low frequency that has amplitude gradually tending to zero. Finally, un-damped is when the systems oscillate at their normal natural frequency known as resonant frequency (ω_o) (Hartono & Burgh, 2012).

Objective

To determine the damping coefficient of an object hanging in air.

Introduction and theory

The experiment was performed to determine the damping………………..

APA

663 Words