4-20 mA Calculator (Info)This calculator converts the measurement of overall vibration transducers in the range

of 4-20 mA to the actual vibration units.

Features

Common used vibration units: g rms, mm/s rms, ips pk, mil pk-pk.

You can specify any other units you want.

Also available in the chrome web store:

Directions for use

1. Select from the list or enter the units of the physical quantity you are converting.

2. Enter the range of the measured variable corresponding to the 4-20 mA range.

3. Enter the current value in mA to obtain the physical value in the selected units or vice

versa.

Formulas

4-20 mA transducers provide an output proportional to the vibration within a specified

range, from 0 to a maximal amplitude Vmax, as shown in the following picture:

4-20 mA transducer input/ouput relationship

Calling I the output current and V the vibration—or other physical measure—

between Vmin (which is usually 0) and Vmax; the conversion formulas are as follows:

I [mA] = ( ( (V − Vmin) / ( Vmax − Vmin) ) × 16 ) + 4

V[units] = ( (I − 4 ) / 16) × ( Vmax − Vmin ) + Vmin

Note that the values and units of Vmin and Vmax are specified by the manufacturer. You

must enter Vin the same units.

Conversion Between Displacement, Velocity and AccelerationVibration is a form of movement; in consequence, the relations between acceleration,

velocity and displacement are governed by simple kinematics; acceleration is the

derivative of velocity, which in turn is the derivative of displacement:

Conversely, displacement is the integral of velocity, which in turn is the integral of

acceleration:

For an arbitrary vibration signal, the only way to convert one of these measures into

another would be to know the complete time waveform and differentiate or integrate it.

Fortunately, the integral and derivative of a sinusoidal function are also sinusoidal

functions, so for sinusoidal waveforms these relations simplify to (the intermediary

math has been omitted):

From displacement to velocity and acceleration:

From acceleration to velocity and displacement:

With frequency in Hz and phase in radians.

It is important to observe that if one of the three variables —acceleration, velocity or

displacement— is sinusoidal, the other two are also sinusoidal at the same frequency;

only amplitude and phase change.

Phase Relations

Phase relations are fairly intuitive and independent of amplitude and frequency. The

phase difference between acceleration and displacement is always 180°, which means

that when the object reaches its maximum displacement from the equilibrium position,

the acceleration is maximum in the opposite direction (see points 1 and 2 in the figure

below). Velocity always lags acceleration by 90° and leads displacement by 90°: it is

maximum when both acceleration and displacement are zero, that is, when passing

trough the equilibrium position (points 3 and 4).

Phase difference between acceleration, velocity and displacement

Amplitude Relations

The amplitude of acceleration, velocity and displacement are related by factors that

depend on vibration frequency. For a given velocity amplitude, for example, the

corresponding displacement amplitude is higher at low frequencies by a factor

proportional to 1/f and acceleration is higher at high frequencies, by a factor

proportional to f. This relations explain why low frequency vibration is emphasized by

displacement measures and high frequency vibration by acceleration, as illustrated in

the following figure:

Sinusoidal acceleration and displacement amplitude as a function of frequency for a fixed

velocity amplitude of 1 mm/s rms

Units in this figure were chosen because they are commonly used and to make the

curves fit in the plot. If different units are used, the scale of the curves will vary but

their general form remains the same.

Conversion Formulas

The conversion formulas for amplitude only are summarized in the following table:

Amplitude conversion between sinusoidal acceleration, velocity and displacement.

You want

You have

A, f[Hz] V, f[Hz] X, f[Hz]

Acceleration, A = — 2πf V  (2πf)2 X 

≈ 6.28f V ≈ 39.5f2 X

Velocity, V =1/(2πf) A

≈ 1/(6.28f) A—

2πf X ≈ 6.28f X

Displacement, X =1/(2πf)2 A

≈ 1/(39.5f2) A1/(2πf) V 

≈ 1/(6.28f) V—

To take into account the phase, the formulas are (using the notation aplitude@phase):

Amplitude and phase conversion between sinusoidal acceleration, velocity and displacement.

You want

You have

A, f[Hz] V, f[Hz] X, f[Hz]

Acceleration, A@φa =

—2πf V@(φv+90°) 

≈ 6.28f V@(φv+90°)

(2πf)2 X@(φx+180°) ≈

39.5f2 X@(φx+180°)

Velocity, V@φv =

1/(2πf) A@(φa−90°) ≈ 1/(6.28f) A@(φa−90°)

—2πf X@(φx+90°) 

≈ 6.28f X@(φx+90°)

Displacement, 

X@φx =

1/(2πf)2 A@(φa−180°) ≈ 1/(39.5f2)

A@(φa−180°)

1/(2πf) V@(φv−90°) ≈ 1/(6.28f) V@(φv−90°)

—

Units

The formulas presented do not modify the type of amplitude measurement (pk, pk-pk or

rms). They do not transform the units used, either. When applying these formulas, care

has to be taken to convert the result to the desired units.

Example

If we want to convert a sinusoidal acceleration of 0.1g rms into velocity in in/s pk, and

we don't care about the phase, we can proceed as follows:

A = 0.1g  = 0.1 x 32.17ft/s2  = 3.217ft/s2  ≈ 38.6in/s2 

f = 4500 cpm = (4500/min)x(1min/60s) = 75/s

V = A/(2πf) ≈ (38.6m/s2) / (6.28 x 75/s) = 0.082in/s

As the acceleration amplitude was rms, so is the obtained velocity. We use the formulas

in theAmplitude section to get:

V ≈ 0.11in/s pk

As you seem, calculations can be tricky... These are the formulas used by the sinusoidal

vibration calculator to convert between sinusoidal displacement, velocity and

acceleration.

Sinusoidal Vibration Calculator (Info)Use the online vibration calculator to convert amplitudes of sinusoidal vibration between

different unit systems, physical variables and overall amplitude values.

Features

The calculator handles displacement, velocity and acceleration units commonly used in

mechanical vibration analysis:

Vibration in mil, µm, ips (in/s), mm/s, ft/s², m/s², g

Peak (pk), peak to peak (pk-pk) or rms amplitude

Vibration frequency in Hz, cpm or rad/s

Converts phase shift measurements

Solve for the frequency at which two different vibration quantities are equal

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Directions for use

With the "solve for frequency" box unchecked: the calculator will convert the entered

vibration amplitude (and phase angle) to the other physical variables and units, at the

given frequency:

1. Set the vibration frequency (Hz or CPM, only one), press 'Enter'.

2. Set the vibration amplitude (only one), press 'Enter'.

3. Optionally, set the vibration angle (only one), press 'Enter'.

With the "solve for frequency" box checked: the calculator will find the frequency at

which the vibration amplitude corresponds to two given vibration amplitude values:

1. Set a vibration amplitude, press 'Enter'.

2. Set vibration amplitude of another physical variable, press 'Enter'.

Rotor Balancing Simulator (Info)

This online balancing simulator allows you to test your balancing skills in one or two

planes with a rigid rotor model. Go ahead and play with different rotor geometries and

operation conditions, pure static or couple unbalance, add balancing weights and see if

you can make the rotor run smoothly.

You can also use the simulator to follow the Single plane balancing tutorial.

Features

Models a rigid rotor of variable size and geometry.

Simulation of unbalance and vibration readings in the supports.

Variation of operating speed and bearing stiffness.

Vibration indication in displacement or velocity.

Arbitrary placement of balancing weights.

Elapsed time simulation.

Also available in the chrome web store:

Directions for use

Most of the options and controls are self-describing, below are some which may require

further explanation.

Set up tab

Initial unbalance: the application simulates an uneven distribution of mass in the rotor

which can bestatic, causing the principal inertia axis of the rotor to be offset but parallel

to the shaft axis, ordynamic (static and couple combination), which causes the principal

inertia axis to be not parallel to the shaft axis. In a rotor supported between the

bearings a static unbalance produces in−phase vibration at the bearings and a couple

unbalance produces out of phase vibration. In a overhung rotor, however, even a pure

static unbalance will produce out of phase vibration at the bearings.

Mount stiffness: This is the total dynamic stiffness of the bearings and supporting

system. For the same mass unbalance, a softer mounting (lower stiffness) will result in

higher vibration at the bearings than a more rigid one (higher stiffness) and will require

less residual unbalance to attain the vibration tolerance.

Balance tab

Balancing weights: The weight's angular position is refered to the keyway (which is

also the reference for the phase of vibration measures) and the angle increases in the

direction opposite to the turning sense.

Keyway position is shown when adding or removing balancing weights.

Vibration measurement: This field displays the 1X filtered absolute vibration as

measured by seismic sensors located in the radial horizontal direction at each bearing

housing (see picture below). You can select to measure vibration in metric or imperial

units, velocity or displacement. It is important to note that when you select to measure

in displacement units (µm or mils), you obtain the integrated absolute displacement at

the bearing housing and not the relative shaft-casing vibration.

Location of vibration sensors.

The phase reference signal is triggered when the rotor keyway is in the same direction

as the sensors (horizontal, facing forward in the front view and to the left in the side

view), and the lag phase convention is used.

The background color of the vibration value changes according to the zones defined in

the ISO 10816-3 standard "Evaluation of machine vibration by measurements on non-

rotating parts", for a group 2 machine operating below its first critical speed, and they

mean (in short):

Red: Zone D, vibration of sufficient severity to damage machine.

Orange: Zone C, unsatisfactory for long term continuous operation.

Yellow: Zone B, unrestricted, long-term operation allowed.

Green: Zone A: Typical of new machinery.

For a good field balancing you would want to attain zone A or, at the very least, zone B.

Color indicating vibration severity.

Elapsed time: Operations like starting and stopping the machine and working with

balancing weights increase the elapsed time by several minutes to simulate a real life

condition.

Shaft Alignment Assistant (Info)This online shaft alignment software helps you to align machinery using the reverse

indicator method. Just enter the indicators' readings to obtain the plot of the relative

position of the shafts centerlines and the corrections needed.

Features

The alignment assistant supports:

Two machines.

Short coupling.

Short coupling tolerances.

Reverse dial indicator method.

Metric and US/Imperial units.

Fixed/movable machine model, typically used for pump-motor or fan-motor sets where

it is not desirable to move the pump or fan. It can also be used in many other cases of

course.

Directions for use

The main components of the application are the alignment plot, the set up tab and

the alignment tab.

Alignment plots

The alignment plots show the relative positions of the shaft centerlines of the machines,

and allow you to easily interpret and follow the entire alignment status. There are two of

plots:

vertical (as viewed from the side) and horizontal (as viewed from above).

The alignment plots display also hints for the different dimensions you will have to enter

to configure

the alignment job, the position of the dial indicators when measuring and the tolerances

attained.

Alignment plots

Hint:

The default reference directions for the horizontal plot are "north" and "south",

but you can change them to whatever you want by clicking on the labels next to the

plot,

for example "wall" and "tank".

Changing names for horizontal directions

Set up tab

Measuring tape units: these units will be used to specify the dimensions of the

movable machine and the position of the dial indicators relative to the coupling center.

You can select centimeters or inches.

Coupling to front foot: this is the distance in the axial direction between the center of

the coupling and the bolt hole of the inboard feet on the movable machine. When you

edit this field, you will see a hint in the alignment plot, like this:

Coupling to front foot hint

Feet separation: this is the distance in the axial direction between the center of the

bolt holes of inboard and outboard feet. When you edit this field, you will see a hint in

the alignment plot, like this:

Feet separation hint

Operating speed: the operating speed is used to calculate the alignment tolerance

according to the following tables for metric and imperial/US units:

Short coupling alignment tolerances (metric units)

Operating speed[rpm]

Offset[mm/100]

Angularity (slope)[mm/100 / 100mm]

Acceptable

Excellent

Acceptable

Excellent

750 19 10 12.5 8.5

1000 13 7 9 6

1500 8.5 5.5 6 4

3000 4.5 3 3.5 2

6000 3 1.5 2 1

Short coupling alignment tolerances (imperial/US units)

Operating speed[rpm]

Offset[mil]

Angularity (slope)[mil / 10in]

Acceptable

Excellent

Acceptable

Excellent

600 9 5 15 10

900 6 3 10 7

1200 4 2.5 8 5

1800 3 2 5 3

3600 1.5 1 3 2

7200 1 0.5 2 1

Dial indicator units: these units will be used to specify the alignment measurements

themselves. You can select hundreds of a millimeter or thousands of an inch.

Indicator 1 to coupling center: indicator 1 is the indicator that turns with the

movable machine and which measures on the shaft of the fixed machine. When you edit

this field, you will see a hint in the alignment plot, like this:

Indicator 1 to coupling center hint

Indicator 2 to coupling center: indicator 2 is the indicator that turns with the fixed

machine and which measures on the shaft of the movable machine. When you edit this

field, you will see a hint in the alignment plot, like this:

Indicator 2 to coupling center hint

Bar sag readings: enter here the bar and bracket sag readings for each indicator.

After this, the alignment assistant will compensate your alignment measurements. Note

that these values must be negative and they should be both almost the same if you use

a symmetric arrangement.

Align tab

Measurement: enter the readings of the dial indicators. You do not need to

compensate for the bar sag, the readings will be compensated according to the amount

you entered in the Bar sag readings field in the set up tab. When you edit each field a

hint will be displayed in the alignment plot showing the position of the corresponding

measurement so you don’t need to deal with 12-3-6-9 o’clock conventions.

Dial indicator measure and hint

After entering the readings press the Update button to have the alignment plot display

the positions of the shafts centerlines and the corrections at the feet updated in the

corrections information box.

Corrections: this box displays the required corrections at the feet of the movable

machine and the tolerance attained for the vertical and horizontal direction. The

tolerances are also displayed in the alignment plot by means of a color shade over the

coupling with the following convention:

Excellent: green

Acceptable: yellow

Bad: Red

Alignment measurement, tolerances, corrections and plot

Sinusoidal Vibration BasicsThis tutorial is about the basic quantities that characterize sinusoidal vibration:

amplitude, frequency and phase. Also, some interesting properties of sinusoidal

vibrations are explored such as amplitude units conversion and polar representation.

Motivation

Sinusoidal vibration is an idealization. There are few machines that will vibrate in a pure

sinusoidal fashion (although a notable example are machines that exhibit pure mass

unbalance); most real vibration waveforms are much more complex. However,

understanding sinusoidal vibration is useful for a number of reasons:

For sinusoidal waveforms it is easy to convert overall amplitude values between peak,

peak to peak and rms. It is also easy to convert between acceleration, velocity and

displacement.

Sinusoidal vibration allows to introduce the concept of phase, which is used in some

advanced diagnostic techniques and the basic concept used in rotor balancing: if you

want to balance a rotor —and understand that is happening— you must definitely

understand sinusoidal vibration and phase.

Any vibration waveform, no matter how complex, can be decomposed into sinusoidal

components. This fact is the base of frequency analysis, perhaps the most known tool

for vibration diagnostics.

Sinusoidal vibration

Sinusoidal vibration is the simplest form of vibration, in which a body moves around an

equilibrium position in a periodic and smooth way. Perhaps the best known example of

sinusoidal motion is the motion of a mass attached to an ideal spring and subject to no

friction.

In a formal sense, a vibration is said to be sinusoidal if it corresponds to a sinusoidal

function of time, and it can be described with the following equation:

x(t) = X·cos(2πft − φ)

Such a function looks like this:

Sinusoidal vibration waveform

A sinusoidal waveform is completely determined by three parameters:

X, the amplitude.

f, the frequency.

φ, the phase.

In the following sections we will describe more in detail these quantities and their

properties.

Notation

We will use the following notation throughout this tutorial:

Sinusoidal displacement waveform: x(t) = X·cos(2πft − φx)

Sinusoidal velocity waveform: v(t) = V·cos(2πft − φv)

Sinusoidal acceleration waveform: a(t) = A·cos(2πft − φa)

The properties of sinusoidal vibration apply regardless of the physical quantity

measured (displacement, velocity or acceleration). For simplicity, in most formulas we

will use displacement vibration, x(t); you can replace "x" by "v" or "a" as needed.

Tutorial Contents

Frequency

Amplitude

Phase

Conversion Between Displacement, Velocity and Acceleration