An Approach for Nonlinear Damping Characterization for Linear Optical Scanner

Abstract

Vibratory systems that are used in linear optical scanners are significantly influenced by the properties of the surrounding fluid. Although, the dominant energy loss in scanner vibrations is caused by viscous effects, especially in nonmicroelectromechanical system (MEMS) scanners, the relative importance of viscous damping model is not well studied. In this study, a piece-wise method for calculating the damping ratio with logarithmic decrement to produce a numerical model which is able to predict the free response of a linear optical scanner is developed. The damping ratio function used in the model was derived by comparing and minimizing the deviation between the amplitude predicted by numerical model and the experimental data. The efficiency of this approach was tested on the basis of a torsional spring scanner. The results show significant improvement whereby the proposed model predicted the free response with a deviation of only 8% while the general exponential damping model produced a deviation of 20%.

An Investigation on the Damping Characteristics of a Linear Optical Scanner

“…20 Several factors contribute to the nonlinearity, for instance, operating temperature, resonance frequency, strain, and strain rate of deformation in various components of system. 21 In deriving the mathematical models for damping performed in previous study, 22 the damping elements are assumed to have either inertia or the means to store or release potential energy. As the free response of the system developed in this study is that of an underdamped system, an exponential damping model for the numerical analysis is selected for the study as given below:…”

Improvement and Quantification of Spatial Accessibility and Disturbance Responsiveness of Shoulder Prosthesis

“…This measurement was repeated 10 times for all 11 configurations in Table 2. Their oscillatory waveform is represented by (4) and is shown in Figure 7 [17]. The displacement, natural angular frequency, damped angular frequency, damping ratio, time, and arbitrary constant are denoted by x, w n , w d , ζ, t, and C 1 , respectively.…”

“…In Figure 7, the vibration amplitudes are x 1 , x 2 , x 3 ,... x i ; thus, the amplitude ratio after cycle T is shown by (5). Generally, the amplitude ratio after iT is x 1 /x i ; the logarithmic decrement δ, damping ratio ζ, and viscous damping coefficient c are defined in ( 6)-( 8), respectively [17]. Because the equilibrium position of the measured oscillatory waveform was difficult to read, a i was read as shown in Figure 7; (6) was doubled to become the logarithmic decrement δ, as shown in (9).…”

“…In Figure 7, the vibration amplitudes are x 1 x 2 , x 3 ,… x i ; thus, the amplitude ratio after cycle T is shown by (5). Generally, the amplitude ratio after iT is x 1 / x i ; the logarithmic decrement δ, damping ratio ζ, and viscous damping coefficient c are defined in (6)–(8), respectively [17].…”