New parameter identification method for calibrating stiffness of AFM probes

• Adopted simulates a real probe system and helps in accurately identifying the parameters of SDOF and MDOF systems.
• The present method requires the external excitation frequency to purposely change to that frequency and the steady-state responses are stored for later analysis.
• The system parameters could be successfully identified even under different damping condition.

Although there are many studies in the area of system parameter identification, none of them can be used to calibrate the probes of atomic force microscopes (AFM). We had derived a single-DOF identification method that was proven reliable. However, the original, patented SDOF method was found not sufficiently accurate in some cases when applying to an AFM. This study primarily aims to generalize a method for SDOF systems to multi-DOF systems. Before doing that, we focused on two-DOF structural systems. Unlike the currently used method, the present method can be applied in situ or when the AFM probe is well installed inside the probe clip. To improve the precision of the method, a TDOF model was adopted for observing the dynamic responses. The TDOF system was decomposed into two SDOFs in principal coordinates by using their mode shapes. It is well known that by mode superposition, two modal responses can be superimposed into the system ones. Thus, the present identification method starts by giving a wideband excitation and acquires the responses that were used to lock the damped natural frequency. The excitation frequency was thus changed to find the location where the phase lag is 90°. As a result, the system dissipative energy can be computed under such conditions. Once the energy was obtained, the system damping was readily found, followed by the other system parameters. The present identification method was numerically verified using the MATLAB Simulink Toolbox. The numerical results clearly showed good consistency and very small errors. However, the system quality factors tended to have large identification errors for systems under slightly large damping. Nevertheless, the new method can identify the structural parameters of TDOF systems with viscous damping. In addition to the numerical verification, the method was also experimentally validated. The same procedures as those in an AFM were exactly followed, except that the model was a cantilever beam instead of an AFM probe. The system parameters could be successfully identified even under different damping conditions mimicking air, water as well as #40 lubricants.