# Should the peak acceleration of a bungee jumper be 9.8 ## What is Vibration Analysis?

Vibration analysis is the process of gathering vibration levels from the surface of machinery and then analyzing them to detect various faults or failures developing inside it.

The vibration levels are gathered with the help of vibration capturing sensors called accelerometers.

## What defects can be captured with the Vibration Analysis Method?

Almost all types of faults that occur in rotating or reciprocating machines, like Unbalance, Misalignment, Looseness, Bearing defects, Belt defects, pump cavitation, etc can be determined by the Vibration Analysis technique.

## How data captured is analyzed in Vibration Analysis?

The data captured with the help of sensors can be viewed in either of the two forms-

2. Frequency Domain

Now let’s see how vibration data is analyzed in each measurement form.

## 1. Time Domain Form

The time-domain form shows data in an Amplitude(Y-axis) vs Time(X-axis) graph.

The vibration amplitude can be represented by various forms or parameters like Acceleration, Velocity, or Displacement. Although all these parameters are interrelated, each has its own importance in fault detection inside the machine which will be described later in this article.

The vibration data displayed in time domain form can also be called Overall Vibration Measurement for a machine.

### What are the Overall Vibration Measurements?

The following are referred to as overall vibration measurements:

• Displacement (Peak to Peak)
• Velocity (Peak)
• Acceleration (True Peak)
• High-Frequency Accelerations (RMS)

RMS value is defined as the square root of means of squares of instantaneous values.

Peak (Derived Peak) = √2 x RMS . The Derived Peak is usually referred to as Peak.

True Peak is the maximum value attained during one cycle of vibration waveform is called its True Peak value.

Peak to Peak is the difference between the maximum positive and the maximum negative amplitudes of a waveform.

Displacement – Is derived from the acceleration data or directly measured using an LVDT or laser probe. It is the total distance traveled by a vibrating body from one extreme to the other. Displacement is a measure of mechanical stress. It is measured in mills. Mills is 1/1000 of an inch.

Velocity – This is derived from the acceleration data and is measured in m/s or inch/sec. It is the rate of change of displacement. Velocity is a measure of mechanical fatigue.

Acceleration – Is measured using an accelerometer and is measured in g’s (g=9.8 m/s2). It is the rate of change of velocity and represents the forces experienced by the equipment.

High-Frequency Accelerations or Energy – This is the acceleration RMS or the peak in the filtered high-frequency band ( Usually 5 kHz to 50 kHz band).

### Why are they important?

These are called overall measurements as they provide an overall single value of measurement instead of a spectrum. Overall measurements can be used for identifying a developing fault in a piece of equipment. Overall measurements can be trended over time to make out the trend in machine health. Overall measurements have their own limitation and it is not possible to identify the specific fault as it requires identifying values at a specific frequency.

### How to choose the right overall measurement metrics?

You must understand the use and limitations of each overall measurement before you start using them.

Used for analyzing stress-related defects occurring in orders of rotating frequency.

Displacement is a good measure for low-frequency vibration and is not suited for high-frequency vibration. It can be used for analyzing frequencies of less than 20Hz. It can be used on equipment running up to 1200 rpm.

Used for analyzing fatigue-related defects occurring in orders of rotating frequency.

Velocity is a good measure for medium frequency vibration. It can be used in the 10Hz (600 CPM) to 1KHz (60,000 CPM) frequency range. It can be used on equipment running from 1200 to 3600rpm.

Acceleration True Peak or High-Frequency Accelerations RMS

Used for analyzing force related defects occurring in the high-frequency band.

Acceleration is a good measure of high-frequency vibration. It can be used for analyzing frequencies of more than 1KHz (60,000 CPM). It can be used for identifying bearing, cavitation, and lubrication issues.

## 2. Frequency Domain Form

Next is the Frequency Domain form where you can see the data in Frequency(X-Axis) vs Amplitude(Y-Axis) form.

This form is also known as Spectrum Form or Spectrum Graph as you view a spectrum of frequencies i.e. all the frequencies of which the composite waveform displayed in the Time(X-Axis) vs Amplitude(Y-Axis) form is made up of.

Another name is FFT Graph as the conversion from Time vs Amplitude Graph to Frequency vs Amplitude is done with the mathematical model called FFT or Fast Fourier Transform.

### How to analyze the Spectrum Graph?

The principle behind analyzing the graph and detecting the faults is that each fault displays its own characteristics inside the spectrum graph.

The below table describes the symptoms of each fault that can be detected with the help of Spectrum Graph.

Ball Bearing Problem ## Final Words

So, the above was brief on the vibration analysis technique.

The method of vibration analysis is certainly great for detecting early faults and failures in rotating machines.

In fact, it’s capable of telling you the fault (1-2) months before its arrival.

But since the vibration analysis method requires manual measuring and analyzing the data, the work becomes quite tedious and difficult when there is a large number of machines. Further adding, machine failures are sometimes uncertain also. So depending totally upon this method is definitely not a great idea.

The best way to plan, prioritize, and manage maintenance activities is by using more advanced technologies like Predictive Maintenance, where machines are wireless monitors using sensors and the complete system provides you important alerts in case of abnormal events occurring inside the machines.

We at SenseGrow offer :

ioEYE Predict: The Vibration Monitoring IoT Platform.

Our ioEYE Sensor also monitors parameters like Ultrasound, Temperature, Magnetic Flux apart from the Machine Vibrations.

The platform will show you the health condition of your rotating machines on our SaaS cloud platform ioEYE Predict, which will help you to plan your maintenance tasks.

## Should the peak acceleration of a bungee jumper be 9.8 • Category

## What are the Overall Vibration Measurements?

The following are referred to as overall vibration measurements:

• Displacement (Peak to Peak)
• Velocity (Peak)
• Acceleration (True Peak)
• High-Frequency Accelerations (RMS)

RMS value is defined as the square root of means of squares of instantaneous values.

Peak (Derived Peak) = √2 x RMS . The Derived Peak is usually referred to as Peak.

True Peak is the maximum value attained by during one cycle of vibration waveform is called its True Peak value.

Peak to Peak is the difference between the maximum positive and the maximum negative amplitudes of a waveform.

Displacement – Is derived from the acceleration data or directly measured using an LVDT or laser probe. It is the total distance traveled by a vibrating body from one extreme to the other. Displacement is a measure of mechanical stress. It is measured in mills. Mills is 1/1000 of an inch.

Velocity – Is derived from the acceleration data and is measured in m/s or inch/sec. It is the rate of change of displacement. Velocity is a measure of mechanical fatigue.

Acceleration – Is measured using an accelerometer and is measured in g’s (g=9.8 m/s2). It is the rate of change of velocity and represents the forces experienced by the equipment.

High-Frequency Accelerations or Energy – Is the acceleration RMS or the peak in the filtered high-frequency band ( Usually 5 kHz to 50 kHz band).

## Why are they important?

These are called overall measurement as they provide an overall single value of measurement instead of a spectrum. Overall measurements can be used for identifying a developing fault in a piece of equipment. Overall measurements can be trended over time to make out the trend in machine health. Overall measurements have their own limitation and it is not possible to identify the specific fault as it requires identifying values at specific frequency. ## How to choose the right overall measurement metrics?

You must understand the use and limitations of each overall measurement before you start using them.

Displacement Peak to Peak

Used for analyzing stress-related defects occurring in orders of rotating frequency.

Displacement is a good measure for low-frequency vibration and is not suited for high-frequency vibration. It can be used for analyzing frequencies of less than 20Hz. It can be used on equipment running up to 1200 rpm.

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Used for analyzing fatigue-related defects occurring in orders of rotating frequency.

Velocity is a good measure for medium frequency vibration. It can be used in the 10Hz (600 CPM) to 1KHz (60,000 CPM) frequency range. It can be used on equipment running from 1200 to 3600 rpm.

Acceleration True Peak or High-Frequency Accelerations RMS

Used for analyzing force related defects occurring in the high-frequency band.

Acceleration is a good measure of high-frequency vibration. It can be used for analyzing frequencies of more than 1KHz (60,000 CPM). It can be used for identifying bearing, cavitation and lubrication issues.

## What defects can you identify with them?

Machine faults lie in different frequency bands. Since different overall measurements are suited for different frequency bands we must select the overall measurement that is sensitive to the vibration frequency the machine will produce. You might have to use a combination of them to cover the entire frequency range.

An increasing trend in Acceleration true peak is an indication of late-stage bearing defect. Accelerations over 7g (ball bearing) and 12g (roller bearing) are a strong indicator of the defective bearing.

In most industries equipment is operating at rpm’s between 1200 to 3600. This makes Peak (Derived Peak) Velocity the preferred overall measurement to measure vibration severity at rotating frequency and orders of rotating frequency. Acceleration True peak is a good overall measurement to identify late-stage bearing defects. While High-frequency acceleration is a good indicator of the early-stage bearing defect.

It is important that you use something like ioEYE Predict and our vibration sensor to monitor and trend these overall measurements at regular intervals. You can then monitor the trends over time and set alerts thresholds on these overall measurement parameters. Trending is more important in the case of machines that normally produce high accelerations, like screw compressors. In such cases, a change in trend is more important to observe than absolute values.

Trending is also important in cases of unbalanced machines as in this case unbalance will modulate the vibration and bearing race defect frequencies will not show up. In this case, the upward trends of High-Frequency acceleration and True Peak acceleration will be indicative of the bearing defects.

Only looking at overall measurements can at times mislead you. You should only use them as an indication of fault and carry out detailed spectrum measurements and analysis to confirm your findings. Example peak velocity can mislead you to believe that the vibration level is high but you should always validate such cases with a velocity spectrum. The frequency of the peak velocity in the spectrum can help you distinguish between an actual or a false alert. If you cannot capture the spectrum you should at least measure Velocity True Peak. If True Peak is very high as compared to the Peak it means the first three harmonics are very prominent.

Overall measurements can provide you the indication that there is some problem and that further analysis is required. Using them alone without further detailed vibration analysis can lead to a lot of incorrect diagnoses.

## Abungee jumper falls for 1.3 s before the bungee cord begins tostretch. Until the jumper has bounced back up to this level, thebungee causes the jumpe

Abungee jumper falls for 1.3 s before the bungee cord begins tostretch. Until the jumper has bounced back up to this level, thebungee causes the jumper to have an average acceleration upward of4 m/s 2.
A) Howfast is the jumper going when the bungee cord begins tostretch?
B) Howfar below the diving platform is the jumper at thatmoment?
C) How long after the bungee cord begins to stretch does the jumperreach the low point of the drop?
D) How far below the diving platform is the jumper at the instantthe speed is zero?
Anyhelp on how to solve is appreciated!

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Assuming his initial velocity is zero
A)v = at
v = − 9.8 × 1.3 s
v = 12.74 m/s downwards
B) d = 1 2 a t
2d = -4.9 (1.3)
2d= -8.28 m
C)low point when velocity = 0
Vf = Vi + at
0 = -12.74 + 4t
t = 12.74 4
t= 3.185 s
D) distance after stretch
d = V 1 t + 1 2 a t
2 d = − 12.74 ( 3.185 ) + 1 2 ( 4 ) ( 3.185 )
2d = – 40.58 m +20.29m
d = -20.3 m
Total distance = distance free fall + distance after stretch
d = -8.28 – 20.3m
d = -28.6 m

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Source https://www.sensegrow.com/blog/vibration-analysis

Source https://www.sensegrow.com/blog/overall-vibration-measurements-iot-predictive-maintenance

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