XN-8000 Frequently Asked Questions
Question number FAQ-1102
In both the XN-0821 and DS-0221 software, what is the order of differential and integral operations when the value is 1/H?
The DS-0221 general-purpose FFT analysis software performs differential and integral operations on the frequency response function "H," followed by the operation of its reciprocal. In contrast, the XN-0821 FFT analysis software performs the operation of the reciprocal of the frequency response function "H" (1/H), followed by the operation of differential and integral operations.
For example, when measuring the frequency response function H = A/F, where acceleration = A and force = F, and determining the stiffness using reciprocal calculation (1/H) and calculus, the "X" in stiffness = F/X is obtained by double integrating the acceleration A and calculating the displacement X = A * {1/jω} 2. However, since A is included in H, the order of the 1/H calculation and the calculus calculation becomes important. Since A is in the numerator of H, double integrating H gives "X/F", and the reciprocal calculation of this gives "F/X". If 1/H is performed first, it becomes "F/A", and A comes into the denominator, so "1/X" becomes the second derivative of "1/A", and as a result, "F/X" is obtained (Equation 1).
formula 1
■In the case of DS-0221
To calculate stiffness (F/X), set the inverse operation function for the frequency response function (A/F) to ON and the double integral to ON.
■In the case of XN-0821
To calculate stiffness (F/X), enable the inverse operation function for the frequency response function (A/F) and set the second derivative.
| -- | （jω） | （jω）2 | 1/（jω） | 1/（jω）2 | |
| -- | First derivative | Second derivative | Single integral | double integral | |
| H | A/F Inertance | -- | -- | V/F Mobility | X/F compliance |
| 1/H | F/A Apparent Mass | F/V Mechanical impedance | F/X Stiffness | -- | -- |
F: Force (N), A: Acceleration (m/ s²), V: Velocity (m/s), X: Displacement (m)
■XN-0821 Operation to calculate stiffness from frequency response function A/F
(Frequency response - inverse operations and calculus)
- Double-click the frequency response function graph to open the Graph properties.
- Click the "Advanced Settings" button on the "Display Data" page to open the "Frequency Response Function" page.
- On the [Frequency Response Function] page, check "Reciprocal Calculation: on" and click the OK button (Figure 1).
Figure 1 - Click the [Operations] tab and set "Calculus: Second Derivative" on the [Operations] page (Figure 2).
Last updated: 2006-11-20