The basic structure utilizes one of the MEMS processes. The nickel-plane W-type microspring processed by the quasi-LIGA process is shown as having a total length, width, and thickness of 1194, 111, 013 mm. Nickel plane W-type micro-spring electron micrograph (EM) Because of its symmetry, it is known from the material mechanics that within the linear elastic range, the force and deformation of the corresponding points of each microspring are exactly the same. Therefore, the mechanical properties of a W-type microspring can be analyzed first, and then the characteristics of the n-section are generalized. The structural form and structural parameters of the microspring used in the analysis are as shown.
Each section of the microspring is made up of straight beams and curved beams of thickness D and is in the same plane, and its cross section is rectangular. Straight beams include 5 unit beams (each length is L), half unit beams 6 (each length is L/2), and 2 end joint straight beams L1 (L1=(d+b)ctg(H /2) and 2 spring end straight beams L2 (L2 = d-2R2); curved beams include 8 spring beams connected to straight beams (the outer radius of the arc is R1 + b) and the end of the spring 4 turning curved beams (the outer arc radius is R2+b).
Mechanical Model and Formula Derivation Since the structure of each microspring is centrally symmetrical, it is only necessary to perform static analysis on any of the half sections. In the online elastic range, the second energy theorem in mechanics can be used to determine the linear displacement of the half-section microspring under tension.
The upper end face of the half-section microspring is fixed, and a pulling force F is applied to the center point O of the lower end face, which coincides with the axis of the microspring and is directed downward, as shown. In this case, the deformation caused by the axial force and the shear force on the cross section of the microspring is small, negligible, and only the deformation caused by the bending moment is considered. Therefore, the total strain energy U generated by the half-section microspring under the action of the tensile force F is U=Eni=1QlM2i(x)2EIdx, where l1, Mi(x), E, ​​I are the i-th segments respectively. That is, the length of the rod, the bending moment, the elastic modulus of the material and the moment of inertia of the section, respectively, of the 114 segment of the middle, I=(Db3)/12. The displacement S generated in the F direction at the O point is S=5U5F .
Formula Verification and Stiffness Analysis Tensile Experiment In order to verify the correctness of the calculation formula of the plane W-type microspring constant calculated above, the formula calculation result and the tensile test result of the nickel plane W-type microspring fabricated by the quasi-LIGA process The simulation results were compared. The structural parameters of the microspring (as shown) are: b = 55 Lm, d = 55 Lm, D = 300 Lm, L = 21115 Lm, H = 2 P / 3, R1 = 50 Lm, R2 = 20 Lm, n = 8.
The tensile test was carried out 4 times on a special micro-spring stretching device to obtain a mechanical property curve as shown. The linear part of the elastic tension range of the middle tensile force F elongation is obtained. After the least squares method, the tensile test stiffness is 259 N/m.
The simulation uses the finite element simulation tool) ANSYS to carry out the tensile simulation calculation of the microspring to predict its stiffness characteristics. In the simulation, according to the structural characteristics of the fabricated microspring and considering the calculation accuracy, the element model adopts the PLANE82 unit. And SOLID95 unit. In order to obtain reliable mechanical performance data of electroformed metal materials, a piece of metal piece was electroformed while electroforming the micro-spring, and a standard spline was made for tensile test, thereby obtaining a Young's modulus of the quasi-LIGA metal nickel. 180GPa. The micro-spring elongation amount $S is obtained by simulation, and then the spring constant k is calculated by the applied tensile force F through Hooke's law F=k$S. To ensure the elastic deformation of the micro-spring, the applied tension is not easy. Big. For the simulation results of the microspring under the tension of 18612mN, the elongation is 01701mm.
The result analysis lists the above two methods and the results obtained by the formula (4). It can be seen from the table that the stiffness k2 obtained by the simulation calculation and the stiffness k3 calculated by the formula are within 5% of the stiffness k1 obtained by the test. It can be seen that the simulation and formula calculation results in the elastic range of the microspring are in good agreement with the test results. The spring type k1/(Nm-1)k2/(Nm-1)k3/(Nm-1) plane W-type nickel 259266260 is calculated by ANSYS and calculated by equation (4) in order to obtain more obvious comparison results. The spring constants corresponding to the different line widths and thicknesses of the microsprings are shown in the comparison results.
It can also be seen that the stiffness of the planar W-shaped microspring increases as its line width or thickness increases. Using this method, it can be obtained that the stiffness of the W-type microspring also increases with the increase of the angle of the curved beam; with the length of the unit beam, the spacing of the beam, the radius of the inner arc of the curved middle part of the spring, and the inner circle of the curved end of the spring end The radius of the arc or the number of nodes decreases, and the effect of line width on stiffness is most pronounced.
Conclusion The authors have proved the spring constant calculation formula of the planar W-type MEMS spring derived from the second theorem of Cartesian and Hooke's law through the actual tensile test, and established the inherent relationship between the stiffness and the structural parameters. Through the analysis of formula and simulation results, the influence of structural parameters on the stiffness of microsprings is found, which provides a shortcut for quickly determining its elastic properties. At the same time, through comparison, ANSYS software is more accurate in simulating the mechanical properties of microsprings. The conclusions and analysis methods in this paper can be used as a basis for further optimizing the design of microsprings to meet the needs of MEMS.
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