Parameter Identification of a Cantilever Beam Immersed in Viscous Fluids With Potential Applications to the Probe Calibration of Atomic Force Microscopes

Abstract

The main objective of the report is to present a new identification method has been derived for single-degree, base-excited systems. The system is actually to mimic a probe of cantilever type of AFMs. In fact, the idea of the present report was initiated by needs for in situ spring constant calibration for such probe systems. Calibration processes can be treated as parameter identification for the stiffness of the probe before it is used. However, sine a real probe is too small to be seen by bare eyes and too costly to verify, a cantilever beam was adopted to replace it during the study. The present method starts with giving a chirp excitation to the target system, and to lock the damped natural frequency. Once the damped natural frequency is obtained, it is possible to locate the frequency at which the phase lag is equal to π/2. From which, the excitation frequency is then purposely changed to that frequency and the corresponding steady-state responses are measured. In the meantime, the system dissipative energy or power may also need to be stored. In fact, the present identification formulation is to express the spring constant of the target systems in terms of two measurable parameters: the phase angle and the system damping. The former can be computed from the damped natural frequency while the latter can be identified along with measuring the input power. The novel formulation is then numerically simulated using the Simulink toolbox of MATLAB. The simulation results clearly showed the current identification method can work with good accuracy. Following the numerical simulation, experimental measurements were also carried out by a cantilever beam that its free end was immersed to viscid fluids. The fluids of different viscosity were used to mimic the environments of a probe in use. The experimental results again substantiated the correctness of the present method. Thus it is accordingly concluded that the new recognition algorithm can be applied with confidence.