A novel method of angular positioning error analysis of rotary stages based on the Abbe principle

2017 ◽  
Vol 232 (11) ◽  
pp. 1885-1892 ◽  
Author(s):  
Yi-Tsung Li ◽  
Kuang-Chao Fan
Keyword(s):  
Lateral Displacement ◽  
Linear Displacement ◽  
Open Loop ◽  
Positioning Error ◽  
Motion Error ◽  
Rotational Angle ◽  
Rotary Stage ◽  
Measured Angle ◽  
Abbe Error ◽  
Circular Grating

Abbe error is the inherent systematic error in linear displacement measurement due to the measuring axis being out of line with the moving axis. The resulting gap is called the Abbe offset, which will multiply the angular pitch error of the moving stage to become the positioning error of the linear stage along the moving axis. Analogous to the Abbe principle, in the rotary stage, the rotary encoder is used to detect the worktable’s rotational angle. The encoder is normally mounted at a distance from the bearing. This distance can be also regarded as Abbe offset. Due to the inherent tilt and radial motions of the axis of rotation, the encoder’s rotating component, that is, the circular grating, would result in a lateral displacement relative to its sensing head that is fixed inside the stage housing. The actual measured angle is, therefore, different from the commanded angle, causing the angular positioning error of the rotary stage in machine tools and open-loop controlled system. In this article, the angular positioning error of the rotary stage caused by the tilt motion error and radial motion error of the spindle, the offset and the size of encoder is analyzed and experimentally verified.

Active Control of Flexible Riser Vibration by Boundary Control Based on LQR Controller

2019 ◽  
Author(s):  
Jinxin Yu ◽  
Weimin Chen
Keyword(s):  
Boundary Control ◽  
Vibration Suppression ◽  
Lateral Displacement ◽  
Open Loop ◽  
Loop System ◽  
Ocean Current ◽  
Control Law ◽  
Flexible Riser ◽  
Linear Quadratic ◽  
Rotational Angle

Abstract The lateral displacement and the rotational angle of marine riser are likely to get larger as it is in stronger ocean current and, particularly, undergoes the consequences such as vortex-induced vibration or collisions between individual risers. The riser vibration with large amplitude value will lead to fatigue or coating damage of the structural body. In this study, the active vibration control, in terms of its angle and the displacement reductions, of a flexible riser under time-varying distributed load are considered using boundary control. The governing equations of the structural dynamics involving the control system of a flexible riser are built. The riser is modeled as an Euler-Bernoulli beam under the actions of ocean loads and the feedback controller. A torque actuator is introduced at the upper riser boundary, and the control law is employed to generate the required signal for riser angle control and displacement reduction. The feed-back control law is designed in state space, and the optimization of the control law is implemented based on the LQR approach. The linear quadratic regulator is used to determine the gain matrix, which can calculate the boundary control law by solving the Recatti equation. Based on the numerical simulations, the responses of the open-loop system and closed-loop system are presented and compared. The effectiveness of the vibration suppression of the flexible riser is examined.

scholarly journals Simultaneous Measurement Method and Error Analysis of the Six Degrees-of-Freedom Motion Errors of a Rotary Axis

2018 ◽  
Vol 8 (11) ◽  
pp. 2232 ◽  
Author(s):  
Chuanchen Bao ◽  
Qibo Feng ◽  
Jiakun Li
Keyword(s):  
Simultaneous Measurement ◽  
Error Compensation ◽  
Degrees Of Freedom ◽  
Translational Motion ◽  
Laser Interferometry ◽  
Positioning Error ◽  
Motion Error ◽  
Measuring Device ◽  
Six Degrees Of Freedom ◽  
Rotary Axis

Error measurement of a rotary axis is the key to error compensation and to improving motion accuracy. However, only a few instruments can measure all the motion errors of a rotary axis. In this paper, a device based on laser collimation and laser interferometry was introduced for simultaneous measurement of all six degrees-of-freedom motion errors of a rotary axis. Synchronous rotation of the target and reference rotary axes was achieved by developing a proportional–integral–derivative algorithm. An error model for the measuring device was established using a homogeneous transformation matrix. The influences of installation errors, manufacturing errors, and error crosstalk were studied in detail, and compensation methods for them were proposed. After compensation, the repeatability of axial and radial motion errors was significantly improved. The repeatability values of angular positioning error and of tilt motion error around the y axis and x axis were 28.0″, 2.8″, and 3.9″. The repeatability values of translational motion errors were less than 2.8 μm. The comparison experiments show that the comparison errors of angular positioning error and tilt motion error around the y axis were 2.3″ and 2.9″, respectively. These results demonstrate the effectiveness of our method and the error compensation model.

scholarly journals Eigenmode operation of piezoelectric resonant gyroscopes

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Mojtaba Hodjat-Shamami ◽  
Farrokh Ayazi
Keyword(s):  
Open Loop ◽  
Excess Noise ◽  
Mode Shapes ◽  
Mode Matching ◽  
Vibratory Gyroscopes ◽  
Frequency Matching ◽  
Out Of Plane ◽  
Measured Angle ◽  
Operation Results ◽  
Bias Instability

AbstractThe theory of eigenmode operation of Coriolis vibratory gyroscopes and its implementation on a thin-film piezoelectric gyroscope is presented. It is shown analytically that the modal alignment of resonant gyroscopes can be achieved by applying a rotation transformation to the actuation and sensing directions regardless of the transduction mechanism. This technique is especially suitable for mode matching of piezoelectric gyroscopes, obviating the need for narrow capacitive gaps or DC polarization voltages. It can also be applied for mode matching of devices that require sophisticated electrode arrangements for modal alignment, such as electrostatic pitch and roll gyroscopes with slanted electrodes utilized for out-of-plane quadrature cancellation. Gyroscopic operation of a 3.15 MHz AlN-on-Si annulus resonator that utilizes a pair of high-Q degenerate in-plane vibration modes is demonstrated. Modal alignment of the piezoelectric gyroscope is accomplished through virtual alignment of the excitation and readout electrodes to the natural direction of vibration mode shapes in the presence of fabrication nonidealities. Controlled displacement feedback of the gyroscope drive signal is implemented to achieve frequency matching of the two gyroscopic modes. The piezoelectric gyroscope shows a mode-matched operation bandwidth of ~250 Hz, which is one of the largest open-loop bandwidth values reported for a mode-matched MEMS gyroscope, a small motional resistance of ~1300 Ω owing to efficient piezoelectric transduction, and a scale factor of 1.57 nA/°/s for operation at atmospheric pressure, which greatly relaxes packaging requirements. Eigenmode operation results in an ~35 dB reduction in the quadrature error at the resonance frequency. The measured angle random walk of the device is 0.86°/√h with a bias instability of 125°/h limited by the excess noise of the discrete electronics.

scholarly journals Open loop control of piezoelectric tube transducer

2018 ◽  
Vol 38 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Frederik Stefanski ◽  
Bartosz Minorowicz
Keyword(s):  
Piezoelectric Actuator ◽  
Harmonic Functions ◽  
Open Loop ◽  
Control Line ◽  
Positioning Error ◽  
Open Loop Control ◽  
Hysteresis Model ◽  
Modeling Error ◽  
Loop Control ◽  
Inverse Hysteresis

Abstract This paper is focused on the open loop control of a piezoelectric tube actuator, hindered by a strong hysteresis. The actuator was distinguished with 22 % hysteresis, which hinders the positioning of piezoelectric actuator. One of the possible ways to solve this problem is application of an accurate analytical inversed model of the hysteresis in the control loop. In this paper generalized Prandtl-Ishlinskii model was used for both modeling and open loop control of the piezoelectric actuator. Achieved modeling error does not exceed max. 2.34 % of the whole range of tube deflection. Finally, the inverse hysteresis model was applied to the control line of the tube. For the same input signal (damped sine 0.2 Hz) as for the model estimation the positioning error was max. 4.6 % of the tube deflection. Additionally, for a verification reason three different complex harmonic functions were applied. For the verification functions, still a good positioning was obtained with positioning error of max.4.56 %, 6.75 %and5.6%of the tube deflection.

Spindle radial motion error measurement using a circular grating and a autocollimator

2019 ◽  
Vol 27 (9) ◽  
pp. 2053-2061
Author(s):  
娄志峰 LOU Zhi-feng ◽  
郝秀朋 HAO Xiu-peng ◽  
刘 力 LIU Li ◽  
王晓东 WANG Xiao-dong
Keyword(s):  
Radial Motion ◽  
Error Measurement ◽  
Motion Error ◽  
Circular Grating

Crack Propagation Analysis of Statically Indeterminate Beam by Elastic-Plastic Fracture Mechanics

2002 ◽  
Vol 18 (3) ◽  
pp. 119-126
Author(s):  
Sung-Po Liu ◽  
C. J. Shih ◽  
Liang-Yu Kuo
Keyword(s):  
Fracture Mechanics ◽  
Crack Propagation ◽  
Plastic Hinge ◽  
Linear Displacement ◽  
Plastic Collapse ◽  
Rotational Angle ◽  
Elastic Plastic ◽  
Rectangular Beam ◽  
Propagation Analysis ◽  
Leak Before Break

AbstractThis paper develops an analytical model for the plastic collapse of a statically indeterminate rectangular beam containing a crack. Limit analysis, elastic-plastic fracture mechanics, compliance and J-integral concepts are used to study JIC and dJ/da that influence the crack propagation. The relations among the plastic hinge, applied load, linear displacement, rotational angle and crack growth leads to a better understanding of the problem as a consequence of this study. The conclusions are: (1) Unstable ductile fracture occurs at the crack propagates before plastic collapse or at dJ/da is smaller than the minimum critical value. (2) LBB (leak-before-break) characteristic of the statically indeterminate rectangular beam is valid if the crack propagates before plastic collapse.

scholarly journals Positioning Control and Operational Evaluation of A One Mass Rotary System using NCTF Controller

2018 ◽  
Vol 7 (3.28) ◽  
pp. 111
Author(s):  
Rozilawati Mohd Nor ◽  
Sahazati Md Rozali ◽  
Chong Shin Horng
Keyword(s):  
Tracking Control ◽  
Open Loop ◽  
Object Motion ◽  
Motion Error ◽  
Positioning Control ◽  
Proportional Integral ◽  
Control Scheme ◽  
Controller Performance ◽  
Motion Performance ◽  
Trajectory Following

A practical control scheme is proposed for a one mass rotary system. It was written to demonstrate the controller performance towards positioning and tracking control. For this system, the Nominal Characteristic Trajectory Following (NCTF) controller is proposed and improved. The objective of NCTF controller is to make the object motion to follow the NCT and ends at it origin. Generally, the NCTF controller consists of a Nominal Characteristic Trajectory (NCT) obtained from open loop response and Proportional Integral (PI) compensator. The CM-NCTF controller is proposed for evaluating the motion performance and compare with the conventional NCTF controller. For positioning control, both NCTF controllers demonstrate almost identical positioning performance. However, for tracking control, CM-NCTF controller demonstrates better tracking performance than the conventional NCTF controller with the smallest motion error presented. Besides, the robustness of the CM-NCTF controller to the variation load is examined. 

Design and Analysis of a Micro-Positioning Stage

2011 ◽  
Author(s):  
Jau-Liang Chen ◽  
Yan-Ming Chen
Keyword(s):  
Piezoelectric Actuator ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Flexure Hinge ◽  
Open Loop Control ◽  
Maximum Displacement ◽  
Rotational Angle ◽  
Loop Control ◽  
Positioning Stage

The purpose of this research is trying to design a 6 degree-of-freedom micro-precision positioning stage with monolithic mechanism. It is hoped that this stage can reach 10 μm strokes along linear axis and with rotational angle no less than 50 μrad. The dimension of this positioning stage should be less than 200 mm × 200 mm × 50 mm. By using flexure hinge and piezoelectric actuator, this stage can achieve nanometer resolution. From the experimental results, it is found that the stage can achieve a maximum displacement of 29.3 μm in X axis; 11.94 μm in Y axis; and 6.74 μm in Z axis. The stage can also achieve a maximum rotation of 405.41 μrad around Z axis; 57.18 μrad around X axis; and 63.72 μrad around Y axis. With open loop control, we have shown that the minimum step for the stage is 110 nm in X-axis; 45 nm in Y axis; and 30 nm in Z-axis.

scholarly journals An Embedded Sensor System for Real-Time Detecting 5-DOF Error Motions of Rotary Stages

Sensors ◽  
2019 ◽  
Vol 19 (13) ◽  
pp. 2855 ◽  
Author(s):  
Zhi-Feng Lou ◽  
Xiu-Peng Hao ◽  
Yin-Di Cai ◽  
Tien-Fu Lu ◽  
Xiao-Dong Wang ◽  
...  
Keyword(s):  
Real Time ◽  
Geometric Error ◽  
Sensor System ◽  
Measuring Instruments ◽  
Rotational Angle ◽  
Measuring Device ◽  
Radial Error ◽  
Real Time Measurement ◽  
Rotary Stage ◽  
External Forces

The geometric error motions of rotary stages greatly affect the accuracy of constructed machines such as machine tools, measuring instruments, and robots. In this paper, an embedded sensor system for real-time measurement of two radial and three angular error motions of a rotary stage is proposed, which makes use of a rotary encoder with multiple scanning heads to measure the rotational angle and two radial error motions and a miniature autocollimator to measure two tilt angular errors of the axis of rotation. The assembly errors of the grid disc of the encoder and the mirror for autocollimator are also evaluated and compensated. The developed measuring device can be fixed inside the rotary stage. In the experiments, radial error motions of two points on the axis (h = 5 mm and 60 mm) were measured and calibrated with LVDTs, and the data showed that the radial error motions of the axis were less than 20 μm, and the calibration residual errors were less than 2 μm. When intermittent external forces were applied to the stage, the change of the stage’s error motion could also be monitored accurately.

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