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Vibration analysis mathematics

Started by shantanu@india, Mar 04, 2022, 06:01 AM

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I am using a 3-axis accelerometer ADXL345 to measure bearing housing vibration of pumps. The sensor is providing acceleration data in terms of 'g'. I have to evaluate the RMS velocity in mm/sec as per hydraulic standards.
Can I do it with the limited resources of a microcontroller? Here I am using a 32-bit ESP8266 running at 80MHz as the core device a PIC to carry out the peripheral activities.
My ultimate objective is to upload the vibrational speed , temperature & pressure values to the cloud.


Hello shantanu,

Do you mean the rate of vibration's amplitude change when you say vibrational speed?
I've been using those sensors for other purposes and my observation is that they are too noisy at high data rates which are needed for accurate integration to calculate velocity and displacement. Also the 0-value of the z-axis tends to have a significant initial offset.
Maybe strain gauges, adhered to the correct places,  will be more accurate and precise? But then you will need a bit more complicated analog circuit and more complex math.



I have used the ADXL345 accelerometer to detect movement but not an application similar to yours. There is a characteristic of this accelerometer that is that you set some vibration margins in the axes and if they are exceeded, an interruption is triggered. This helps you to check when something is going wrong and therefore if it's not going wrong then it's okay. This does not require any math on the part of the processor, the entire accelerometer does. On the other hand, if you want an acceleration measurement at all times and calculate everything yourself, then I think it's best to buy an accelerometer evaluation board that comes with a USB connection and PC software and characterize the system you want to size.

Long live for you


Thanks Trastikata and Gamboa.
Yes... I know its difficult to replicate vibration analyzers from leaders like Bruel and Kjaer but at least I can give an honest effort. I have seen Bruel and Kjaer handheld analyzers with a bandwidth of 10kHz where you can record, visualize, analyze and download vibration signatures. Highly sophisticated and enormously expensive!! Obviously they use FPGA's or custom ASIC's that can do number crunching at a fantastic rate including FFT for harmonic analysis. My humble machine cannot do all that.
Gamboa's idea of setpoint is attractive... but would not be convincing to my users who need to quantify the vibration levels of their machines.
I am now thinking of sending the raw acceleration values to any PC by the ESP8266 Wi-Fi and do the analysis in the PC program.
The ADXL345 acceleration values seem to be accurate as per the datasheet and if I am able to do the maths properly then the vibration results should not be way off the mark.
What do you think?