You are asked to design a data acquisition system for a vibration testing setup

Question

You are asked to design a data acquisition system for a vibration testing setup for a certain mechanical machine. The data acquisition is expected to have the components shown in Figure 3. The expected vibrational acceleration range is within +/- 600 m/s^2 with a frequency range from 1 to 8000 Hz. It is desired to collect the vibrational signal with a resolution of 0.05 m/s^2 or better. Answer the following questions to collect the data acquisition components considering low cost solution. a) For the first design step, what is the required number of bits of the A/D? b) Assume that the available accelerometers are as listed in Table 1. Find which sensor would be suitable for the required data acquisition system. Explain your answer in the space below Table 1. c) What is the cost-off frequency of the low-pass filter? Show your calculations. d) What is the least required sampling frequency of the A/D converter? Show your Calculation. e) Most of the available A/D converter can be set at either plusminus 5V, plusminus 2.5 V, plusminus 1.25 V, plusminus 1 V, 0 to 5V, 0 to 2.5V, 0 to 1.25 V, or 0 to 1V and the amplifier has a gain, K, that can be set at either 1, 10, or 100. What is the best combination of the amplifier gain and the A/D range such that the A/D converter range of each channel is best utilized? f) Double check if the required resolution is still maintained (by finding the effective resolutions). If it is not, adjust the corresponding parameter and all requirements are satisfied. g) How much memory is required to store 10 seconds of the vibration signal in Mega Bytes (MB)? h) Imagine an experiment is being made with a system of your choice. As per the given specifications and your previous calculations; fill in the table below with the matching values at the points specified in Figure 3. Write any required in the space below.

Explanation / Answer

a) We know that Formula, Resolution= (Range/2^n); where n is the number of bits of ADC.

For sensor 1: given, Resolution =0.25

                            Range = 2*49000= 98000

                           2^n= (98000/0.25)= 392000

then taking log on both side.  

                              n=18.580

This indicates 19bit ADc is required. For specific if 8 bit, 16bit then 24 bit are available choose 24bit ADC.

In the same way for sensor 2: Resolution =0.025

                            Range = 2*4905

n= 18.58 bits.(Use 24bit)

For sensor 3: Resolution =0.005

                            Range = 2*4900

n= 29.83 (Use 32bit)

For sensor 4: Resolution =0.0015

                            Range = 2*490

n=19.31(Use 24 bit)

For sensor 5: Resolution =0.03

                            Range = 2*4905

n=18.31(Use 24 bit)

b)

Cutoff frequency should be greater that fS = 2fMAX.

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