Full Travel Range Research Articles

Design of a micro machine tool with double-toggle mechanisms

Micro machining plays an important role in manufacturing the miniature products which are made of various materials with complex 3D shapes and tight machining tolerance. In this paper, a new design of CNC micro machine tool with double-toggle mechanism is proposed. The machine has the characteristics of low cost, ultra-fine feed resolution, and high accuracy. With the double-toggle mechanism and regular driving components including AC motors, ballscrews, and a PC-based controller, the micro machine tool can perform good micro machining for miniature components. Because of the geometrical drive function, the errors of the machine are reduced by the double toggle structure without using high-end driving components and controller. In addition, the design of the structure avoids the drawback of the regular toggle mechanism which cannot have stable feed resolution for the full travel range. The kinematics model and characteristics of the machine were derived and analyzed. Modal analysis and dynamic compliance analysis were also conducted to evaluate stiffness and dynamic characteristics of the machine. A prototype of the machine was built, and the accuracy calibration results showed the machine can reach a positioning accuracy of 470nm.

Robust control of the electrostatic torsional micromirrors

In order to simplify the sensors subsystems of the electrostatic torsional micromirrors (ETMs), the output feedback control for the ETM systems is investigated in this paper. The dynamics of the systems is established by combining the dynamics of both the mechanical and electronic subsystems, and it is proved that the dynamics of the overall system with uncertainties in electrical parameters can be exactly transformed into the third order linear system. Then an output feedback finite-time stabilizing (FTS) controller is presented by composing of a full state FTS observer and a state feedback FTS controller for the third order linear systems, such that the ETM systems can be stabilized in its full travel range by merely measuring the tilt angle. Some numerical simulations demonstrate the stability of the proposed output feedback FTS controller.

A technique for accuracy improvement of squareness estimation using a double ball-bar

Squareness measurement and its compensation are important for improving the performance of machine tools. A double ball-bar is widely used to measure squareness because of its simple, convenient setup and measurement procedures. This study addresses two important issues affecting the accuracy of squareness estimation when a simplified model of the geometric errors is used and estimation is carried out over constrained local ranges of the moving axes. A simplified model is frequently applied to geometric error estimation using a double ball-bar to avoid singularity problems while solving the double ball-bar equation. However, the use of a simplified error model significantly affects the accuracy of the squareness estimation. In this article, a squareness estimation technique using double ball-bar measurements and a laser interferometer is proposed. In addition, a convenient squareness estimation method involving only single double ball-bar measurements is suggested for the full travel range utilizing the straightness error data. The validity of the proposed method is verified by comparison with laser interferometer measurement results using an optical square on the XY-plane of a three-axis machine tool.

Focus on vacuum and cryogenics

Focus on vacuum and cryogenics

Analysis of squareness measurement using a laser interferometer system

Squareness measurements of the driving axes of a machine tool are very important in order to evaluate the performance of the machine. A laser interferometer measurement is one of the most reliable ways to measure squareness. However, a squareness measurement using a laser interferometer system with an optical square causes restrictions in the straightness interferometer setup, which results in the occurrence of Abbe’s offset. The Abbe’s offset combined with angular errors during the motion of an axis causes Abbe’s error. In addition, difficulty in the optical square setup causes restrictions on other optics and limitations of the measurable range. We present mathematical approaches that can be used to eliminate Abbe’s error and to estimate squareness over the full range by using the best fit of straightness data measured without an optical square. Experiments for squareness measurements of a threeaxis machine tool are conducted. The proposed techniques are used for squareness evaluation with the elimination of Abbe’s error and also for squareness estimation for the full travel range.

레이저 간섭계를 이용한 직각도 측정에 관한 분석

The squareness measurement of driving axes of a machine tool is very important to evaluate the performance of the machine. Laser interferometer measurement system is one of the most reliable equipment to measure the squareness. However, squareness measurement using laser system with an optical square result in restriction of straightness optics setup and Abbe’s offset. This offset combines with angular errors during the motion of an axis to cause Abbe’s error. In addition, the difficulty in optical square setup causes restriction of other optics and limitation of measurable range. In this paper, mathematical approaches are presented to eliminate the Abbe’s error and to estimate squareness for full range by using the best fit of straightness data measured without an optical square. Experiments for squareness measurement of 3 axis machine tool were conducted and the proposed techniques were used for squareness evaluation with elimination of Abbe’s error and squareness estimation for the full travel range.

Finite-Time Stabilization of a Comb-Drive Electrostatic Microactuator

The inherent nonlinear characteristic between the electrostatic force and the applied voltage causes electrostatic microactuators to show the pull-in bifurcation phenomenon. Exploiting a closed-loop control for stabilizing the electrostatic microactuators in its full travel range is the primary objective in the control of such devices. In this paper, the dynamics of a transverse comb-drive electrostatic microactuator is established with considering the presence of parasitic and parametric uncertainties, and it is shown that the dynamics can be transformed into the third-order Brunovsky's canonical form. Then, a finite-time stabilizing controller is proposed for the third-order Brunovsky's canonical form systems, and the finite-time stability of the presented controller is shown. The robust finite-time stability of the controller under the parasitic and parametric uncertainties is also verified using numerical simulations.

A surface micromachined offset-drive method to extend the electrostatic travel range

A surface micromachined offset-drive mechanism is demonstrated to address the pull-in problem of electrostatic actuation in microelectromechanical systems (MEMS). Similar to the vertical comb drive method, our offset-drive method uses fabricated electrodes that are laterally offset rather than directly opposite to each other. As a consequence, the electrodes are never engaged and are driven mostly by fringing fields. An offset electrode capacitance model is proposed for analysis. Simulations show that the proposed offset scheme may require lower operating voltages than some competing methods, and a full travel range can be achieved without pull-in. It is also found that drive performance is influenced by the structure's lateral gap. Lateral gaps smaller than a critical value are still susceptible to the pull-in problem. For devices on a planar semiconductor substrate, this method is electrically equivalent to the series capacitor mechanism due to the high substrate dielectric constant. We demonstrate that the substrate may be etched to improve the performance of this offset-drive method. An offset-drive test structure consisting of an aluminum beam suspended across two posts is designed and fabricated, with an etched substrate underneath. By measuring the maximum beam deflection, the offset-drive method is characterized experimentally.

Experimental study of micromachined electrostatic torsion actuators with full travel range

By studying pull-in behavior, we investigate the stability of single-crystal silicon, rectangular, electrostatic torsion actuators in a variety of ambients and configurations. These structures are designed for full travel range using partial-plate buried electrodes on either oxidized silicon or nitrided glass substrates. We find that the presence of charge in both systems, due at least in part to moisture on insulating surfaces surrounding the buried partial plate, has a large effect on pull-in performance, even in vacuum and flowing dry nitrogen. We are able to minimize this charge effect by using devices fabricated with ground shield electrodes. These improved structures exhibit stable actuation in air without pull-in at a travel range that exceeds 90%. This is among the highest measured stable values reported in the literature.

Analytical and finite element model pull-in study of rigid and deformable electrostatic microactuators

A general theory and method are presented and employed to analyze the static behaviors of rigid and deformable electrostatic actuator systems with various electrode configurations. This method utilizes capacitance-based generalized equations and provides an easy and time-saving platform over complicated coupled finite element method (FEM) simulations for pull-in analysis of a complex system. Analytical results show that the travel range of rigid electrostatic actuators can be extended by manipulating the shape of the electrode. Even a full travel range (100%) can be realized by a general power function shaped electrode. It is found that the partial actuation can avoid pull-in and reach full travel ranges with the sacrifice of the bias voltage. Analytical results of cantilever rectangular and circular actuators with a partial electrode are in good agreement with simulation results. Actuation curves of various actuators are also derived using this method. It is found that partial actuation curves are exactly the same as full actuation curves, and all types of cantilever torsion actuators with various electrode shapes follow the same actuation curve. Analytical and FEM simulations are carried out to study the pull-in behavior of deformable electrostatic actuators of three electrode configurations. The analytical results agree with FEM simulation results. It is found that the normalized deformation curves of these three electrode configurations are independent of geometry and voltage. The fringing field is considered in this analytical method.