Use the following to calculate the amplitude and phase when switching between vibration units.
a → v → x
Integration is equivalent to dividing the amplitude by 2Πf and shifting by +90°. To integrate twice (a→d), divide and shift twice.
a = A sin 2Πft
| v = ∫a = - | A | cos 2Πft |
| 2Πf |
| x = ∫v = ∫∫a = - | A | sin 2Πft |
| (2Πf)2 |
x → v → a
Differentiation is equivalent to multiplying the amplitude by 2Πf and shifting by -90°. To differentiate twice (d→a), multiply and shift twice.
x = X sin 2Πft
| v = | dx | = (2Πf) X cos 2Πft |
| dt |
| a = | dv | = | d2x | = - (2Πf)2 X sin 2Πft |
| dt | dt2 |
Notes:
1) Conversion by 2Πf applies to like units only. For example m/s2 → m/s and not G → inch/s. For conversion of common English units, refer to table below.
2) Amplitude conversions may be used for overall measurements but only if vibration is a single sinusoid.
| A | V | X | Multiply By |
Phase Shift |
| A → V → X | ||||
| gRMS → | inches/sec PK | 86.901/f | +90 | |
| gRMS → | → | inches PK-PK | 27.661/f | +180 |
| gRMS → | → | mils PK-PK | 27,661.40/f | +180 |
| inches/sec PK → | inches PK-PK | 0.318/f | +90 | |
| inches/sec PK → | mils PK-PK | 318.31/f | +90 | |
| A ← V ← X | ||||
| gRMS | ←inches/sec PK | 1.15E-02*f | -90 | |
| gRMS | ← | ←inches PK-PK | 3.62E-02*f | -180 |
| gRMS | ← | ←mils PK-PK | 3.62E-05*f | -180 |
| inches/sec PK | ←inches PK-PK | 3.14E+00*f | -90 | |
| inches/sec PK | ←mils PK-PK | 3.14E-03*f | -90 | |
