Papers by Keyword: Spring Constant

Abstract: Recently silicon components have been applied in mechanical watch movements. Among them, the silicon hairspring is the most attractive due to the significant improvement of accuracy and performance compared with the traditional material. However, the current device in production is unable to measure the spring constant which determines the timekeeping accuracy of the watch. This paper presents a method to measure the spring constant of silicon components. The setup is based on Variocouple with a force sensor. The data processing is realized by Matlab. The result shows that the spring constant is calculated rapidly and accurately.

Abstract: Based on the Winkler's hypothesis, this paper discusses how to determine the spring constant of groundwork in design of underground structure. When no sufficient experimental conditions are available, the method of numerical calculation can be used to determine the value of spring constant of groundwork. The resulted value is basically the same as the value of experience from the engineering criterion.

Abstract: It is not easy to simulate realistic mechanical behaviors of elastically deformable objects with most existing mass-spring systems for their lack of simple and clear methods to determine spring constants considering material properties (e.g. Young's modulus, Poisson’s ratio). To overcome this obstacle, we suggest an alternative method to determine spring constants for mechanical simulation of deformable objects under compression. Using the expression derived from proposed method, it is possible to determine one and the same spring constant for a mass-spring model depending on Young's modulus, geometric dimensions and mesh resolutions of the 3-D model. Determination of one and the same spring constant for a mass-spring model in this way leads to simple implementation of the mass-spring system. To validate proposed methodology, static deformations (e.g. compressions and indentations) simulated with mass-spring models and FEM reference models are compared.

Abstract: Pb1-xSrx (Zr0.53Ti0.47) O3 (PSZT) thin films have been fabricated on Pt/Ti/SiO2/Si substrate by a sol–gel method combined with a rapid thermal annealing process. The microstructure analysis of the thin films showed that the orientation ratio of (111) was 0.304，0.475 and 0.849 with x=0, 0.03, 0.08. The dielectric measurement suggested that the addition of Sr in Pb(Zr0.53Ti0.47) O3(PZT) thin films greatly improved the dielectric properties of PZT thin films. The dielectric constant for PZT thin films at a frequency of 2 kHz was 648，which was increased to 1239 when 3%at Sr was doped. Meanwhile, the dissipation factor was only increased from 0.02 to 0.03. Three kinds of piezoelectric micro-sensors have been prepared based on PSZT thin films and the sensing sensitivity of 0.017pc/uN, 0.033pc/uN, and 0.011pc/uN were realized as x increased, respectively. It indicated that micro-sensors with PSZT0.03 thin films showed better sensing property than other two.

Abstract: Micro cantilevers in atomic force microscopy are important force sensors in nano research, and the spring constant is one of the most important parameters of the cantilevers. Normal testing methods are not suitable for the spring constant detecting of micro cantilevers according to the strict scale of the cantilevers, and new methods are needed to the study of micro cantilevers. A method for detecting of spring constant of micro cantilevers based on combining the numerical simulation and frequency measurements is presented in this paper. The new method involves four steps, the first step is developing the vibration model of the micro cantilever studied immersed in air and determine the fluid parameters in the model during dynamic tests in atomic force microscopy presented in this paper; the second step is analyzing the vibration behavior of the corresponding cantilevers with the same geometry but different young’s modulus. The third step is measuring the natural frequencies of the micro cantilevers and comparing the experimental results with the numerical results to determine the young’s modulus of the cantilever. The last step is conducting the young’s modulus to the cantilever FEA model for determination of its spring constant. Experiments on a NSC cantilever have been done to validate the method presented in this paper.

Abstract: There are two kinds of microsprings often used: box microsprings and zig-zag (serpentine) microsprings. Box microsprings are considered with larger spring constant k and more symmetric structure keeping balance than zig-zag microspring. Density of spring number, N, is defined as the numbers of turns within a constant total spring length to investigate performance of box microspring. With applying the same force, the relation between spring constants and microspring sizes are discussed. Under different size parameters of box microsprings: B, W, T, and L, the spring constants decrease like exponential decay and approach a limit value as density of spring number increasing. The results show density of spring number has significant effect on spring constant. Rate of change on spring constant, Kt, is defined as the ratio of spring constant between N=1 and N=10. It means normalization of spring constant that increase density of spring number from minimum to maximum. The results show Kt decreases when B and W increase and increase as T and L increasing. Therefore, the spring constant is coupled affected by different size parameters due to different tendency as results shown. Such that the results can apply in microspring design by adjusting these size parameters to obtain the spring constant.

Abstract: This study tries to obtain the spring constant of welded metal bellows through experimental and numerical method respectively. The prediction of spring constant plays a great role in the design and application of the welded metal bellows. To derive the spring constant of the bellows, we employ commercial package to build up 2 axi-symmetric FEM models by using plane 42 and shell 51 elements. In the experiment, we use UTM to measure the spring constant of the bellows. And, the predicted spring constant resulting from the analysis is compared with the experimental one to discuss the rationality of spring constant analysis. The analytical results correspond well with experimental data and hence explaining the validity of FEM model.

Abstract: Atomic force microscopy (AFM) is widely used in many fields, because of its outstanding force measurement ability in nano scale. Some coating layers are used to enhance the signal intensity, but these coating layers affect the spring constant of AFM cantilever and the accuracy of force measurement. In this paper, the spring constants of rectangular cantilever with different coating thickness were quantitatively measured and discussed. The finite element method was used to analyze the nonlinear force-displacement behavior from which the cantilever’s normal and torsional spring constants could be determined. The experimental data and the numerical results were also compared with the results from other methods. By considering the influence of coating layers and real cantilever geometries, the more accurate force measurements by AFM cantilever can be obtained.