Sign up
Fill in the fields and send the application for registration. Your application will be reviewed as soon as possible.
If you already have an account, please sign in, or restore your password.
Sign in
To log in, fill in the fields below.
And have a good day.
If you do not have an account, please sign up, or restore your password
Restore password
To reset your password, fill in the field below. After that, you will be notified in the email.
If you do not have an account, please sing up, or sign in if you have one.
Sine
Relation between Acceleration, Velocity, and Displacement
The formulas here describe the relation between acceleration, velocity, and displacement. The formulas are:
where:
- A – acceleration in m/s2;
- V – velocity in m/s;
- D – displacement in m. Please note that displacement D is listed in a zero-to-peak value;
- F – sine frequency in Hz.
We then use the above relations to derive the formulas for crossover points in Sine tests:
where:
- A – acceleration in m/s2
- V – velocity in m/s;
- D – displacement in m. Please, note that displacement D is listed in zero-to-peak value;
- Dmm – displacement D in mm.
- F(A-V) — crossover point between acceleration and velocity;
- F(V-D) — crossover point between velocity and displacement;
- F(A-D) — crossover point between acceleration and displacement.
Sweep rate calculations
There are two common sweep rate types in Sine: linear and logarithmic. The linear sweep rate is usually nominated in Hz/sec, the logarithmic — in oct/min.
We can calculate the sweep time of a linear sweep using the following formula:
where:
- Tlin – sweep time in seconds;
- Fe – end sweep frequency;
- Fs – start sweep frequency;
- S – sweep rate.
Vice versa, the required sweep rate can be calculated using the desired sweep time:
If we are speaking of the logarithmic sweep rate, the base term here is an octave – the interval between a frequency and its double value.
Therefore, if we want to know the number of octaves between sweep frequencies, we have to use the formula below:
Using the formula below, we can calculate the sweep time of a logarithmic sweep:
where Tlog is the logarithmic sweep time in seconds.
The required sweep rate also can be calculated using the following formula:
Random vibration
Calculation of Acceleration RMS value
Generally, a random profile is defined as a table of PSD and frequency, as shown below:
| Frequency (Hz) | Amplitude, g2/Hz |
| 20 | 0.00040 |
| 100 | 0.01 |
| 1000 | 0.01 |
| 2000 | 0.0025 |
To calculate the RMS value of acceleration we should calculate the area under the task line. This requires two actions: 1) calculating the area under each line of the spectrum and 2) summing the areas.
The best way to calculate the area depends on the slope of the line. The slope can be calculated using the formula:
where:
- Ae – end amplitude;
- As – start amplitude;
- Sl – slope.
The area P is calculated using the formula:
The acceleration RMS value is calculated using:
Calculation of Velocity and Displacement Values
Calculating velocity is based on the same principle, as calculating the acceleration, however. the values of amplitude are divided by (2π)2:
Two peculiarities have to be mentioned here:
- As and Ae should be in (m/s2)2/Hz units;
- not RMS, but peak values are usually taken into account. Therefore, we have to multiply the RMS value by the sigma factor:
where ς
– sigma factor.
The same principle is used for displacement calculations:
However, the third peculiarity appears here: Dpeak is a zero-to-peak value, so if we want to calculate the peak-to-peak value, we have to multiply Dpeak by two:
If you want to learn more about the formulas we use, contact our 24/7 technical support via email or call +371 6610 2166.
