Analysis of Change in Motional Capacitance of the Electrical Equivalent Circuit of Quartz-Crystal Tuning-Fork Tactile Sensor at Resonance by Combining Analytical Models for Elastic Foundation and L-Shaped Bar with Torsion Spring

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We derived the analytical formula of the motional capacitance $C_{a}$ of a quartz-crystal tuning-fork tactile sensor by use of the conservation law of energy that the electrostatic energy in $C_{a}$ is equal to the sum of the strain energy of its arm and the elastic energy of the material in contact with its base. In this analysis, the strain energy of the arm and the elastic energy of the material in contact with its base were obtained by applying the torsion spring model to the joint of the arm and the base, which were depicted as an L-shaped bar, and the elastic foundation to the materials in contact with its base, and the electrostatic energy of the arm was derived by applying the bimorph flexural model to the arm treated as a piezoelectric material. As a result of calculation, we found that the calculated value of the change in reciprocal motional capacitance $\Delta(1/C_{a})$ of the quartz-crystal tuning-fork tactile sensor by our model is closer to the measured one for plastics than that given by the theoretical formula of motional capacitance of only one arm and $\Delta(1/C_{a})$ is affected by the Young’s moduli of materials in contact with the sensor’s base.
2010-12-25