Ingersoll-Rand (IR) produces both a vibrating-drum soil and asphalt roller. The noise generated from these machines will be too high to pass European environmental laws which take effect in the year 2006. It is believed that the shell of the drum generates most of this noise. Currently, testing of the drum is done with a full size impact analysis. Testing on the full size drum is difficult due to its large size and inability to completely isolate it during testing. A method to construct and test a scale model has been proposed to solve this problem.

This project demonstrates the feasibility of the proposed solution using dimensional analysis to analyze the vibrational response of a full size soil compactor using a scale model. A model with a scale factor of 0.1399 or 1/7.15 scale was constructed from aluminum piping and sheet metal. This scale factor was chosen to take advantage of commercially available materials. Dimensional analysis was researched to provide a prediction frequency scaling factor. The full size drum’s frequency response is predicted to be 0.142 times that of the scale model.

The purpose of the project is to build a scale model of the soil compactor’s drum so that testing may be conducted to find its natural frequencies and modal shapes. These experimental values will then be used to predict the natural frequencies and modal shapes of the full-scale drum through the use of dimensional analysis.

When using a 1/7.15 scale, the natural frequencies obtained during testing will be used to predict the full size drum response according to the following formulae:

m = scale model
p = prototype (full size drum)

The final form of the equation shows that the frequency of the full size drum is 0.142 times the frequency of the model.

Two scale models were built. The only difference between the two is the type of joining. One of the model is welded while the other one is joined using the epoxy, Belzona. Results from the two models are compared. The figures below show the two scale models.

With the scale model now constructed, attention turns to testing to determine the natural frequencies and modal shapes. To conduct impact testing, the model will be hung vertically with rubber bands. The rubber bands are used to ensure negligible damping and to provide as close to a free response as possible. In this way, only the natural frequencies of the model will be excited. Attached to the model’s surface is an accelerometer. The accelerometer has a piezo-electric crystal inside which creates a charge when excited. The ICP Power Supply converts this charge to a voltage and outputs it to the signal analyzer. The impact hammer works in a similar way as the hammer’s ICP Power Supply produces a voltage corresponding to the force created by the hammer’s head. This signal also passes through the signal analyzer. Using the program SigLab, the voltages may be analyzed to determine the frequency content and an input / output function. A schematic of the impact testing setup can be seen in the figure below.

In each experiment, the accelerometer will be stationary but the hammer’s impact location will change. A grid on the model will help in making the testing systematic and manageable. The grid will determine the places where the hammer creates impact and the respective frequency response of the model as well as the force input. The size of the grid will be determined through trial and error during testing so as to provide a detailed vibrational response. The best spacing will be the largest grid that still reveals natural frequencies and modal shapes. The results from the impact testing will aid in predicting the full size drum’s response.

The following table summarized the primary frequencies and at which rings they occur. The predicted full size frequencies are equal to the 0.142 of the model frequencies.

		Ring										Ring
Model Frequency Peak (Hz)	Predicted Full Size Frequency Peak (Hz)	A	B	C	D	E	F	G		Model Frequency Peak (Hz)	Predicted Full Size Frequency Peak (Hz)	A	B	C	D	E	F	G
1537.50	218.33						X	X		3168.75	449.96						X	X
1556.25	220.99			X	X	X				3200.00	454.40	X	X
1643.75	233.41						X	X		3206.25	455.29			X	X	X
1650.00	234.30	X	X	X						3393.75	481.91	X	X
1656.25	235.19				X	X				3437.50	488.13			X	X	X
1693.75	240.51						X	X		3600.00	511.20			X	X	X
1706.25	242.29			X	X	X				3606.25	512.09							X
2125.00	301.75	X	X							3843.75	545.81			X	X	X
2162.50	307.08			X	X	X				3850.00	546.70	X	X					X
2243.75	318.61	X	X							4056.25	575.99			X	X	X
2262.50	321.28					X				4237.50	601.73						X	X
2293.75	325.71						X	X		4406.25	625.69			X
2318.75	329.26					X				4418.75	627.46	X	X
2531.25	359.44	X	X							4475.00	635.45			X
2537.50	360.33			X	X					4481.25	636.34				X
2543.75	361.21					X				4600.00	653.20			X	X
2593.75	368.31	X	X							4606.25	654.09					X
2625.00	372.75			X	X	X				4825.00	685.15			X	X	X
2818.75	400.26			X						4831.25	686.04							X
2825.00	401.15				X	X				4837.50	686.93	X	X
2987.50	424.23			X	X	X				4881.25	693.14						X
3081.25	437.54			X	X	X

Matlab code was utilized to analyze the enormous data. This reduces analysis time, increases flexibility in data modifications and also makes data presentation more user friendly. The code was developed with the help from Dr. John S. Lamancusa. When the M code is run, Matlab will compile all the data from excel files. At any frequencies available, the M code would be able to produce 2D mode shapes at any rings, 3D mode shapes and animated 3D mode shapes. The frequencies available are between 0 - 5000 Hz and should be a mutiple of 6.25. The following figures show examples of 3D mode shapes from the M code.

Mode Shape at Model Frequency of 2987.5 Hz

Team Picture
Ingersoll Rand