Design of a six-degree-of-freedom geometric errors measurement system for a rotary axis of a machine tool

2020 ◽  
Vol 127 ◽  
pp. 105949 ◽  
Author(s):  
Chien-Sheng Liu ◽  
Hung-Chuan Hsu ◽  
Yu-Xiang Lin
Keyword(s):  
Machine Tool ◽  
Measurement System ◽  
Degree Of Freedom ◽  
Geometric Errors ◽  
Rotary Axis ◽  
Six Degree Of Freedom

scholarly journals Design of a Measurement System for Simultaneously Measuring Six-Degree-Of-Freedom Geometric Errors of a Long Linear Stage

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3875 ◽  
Author(s):  
Chien-Sheng Liu ◽  
Yu-Fan Pu ◽  
Yu-Ta Chen ◽  
Yong-Tai Luo
Keyword(s):  
Measurement System ◽  
Taylor Series Expansion ◽  
Degree Of Freedom ◽  
Geometric Errors ◽  
Linear Stage ◽  
Six Degree Of Freedom ◽  
Geometric Motion ◽  
Laser Interferometers ◽  
Interferometer Method ◽  
Conventional Laser

This study designs and characterizes a novel precise measurement system for simultaneously measuring six-degree-of-freedom geometric motion errors of a long linear stage of a machine tool. The proposed measurement system is based on a method combined with the geometrical optics method and laser interferometer method. In contrast to conventional laser interferometers using only the interferometer method, the proposed measurement system can simultaneously measure six-degree-of-freedom geometric motion errors of a long linear stage with lower cost and faster operational time. The proposed measurement system is characterized numerically using commercial software ZEMAX and mathematical modeling established by using a skew-ray tracing method, a homogeneous transformation matrix, and a first-order Taylor series expansion. The proposed measurement system is then verified experimentally using a laboratory-built prototype. The experimental results show that, compared to conventional laser interferometers, the proposed measurement system better achieves the ability to simultaneously measure six-degree-of-freedom geometric errors of a long linear stage (a traveling range of 250 mm).

scholarly journals Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool

Sensors ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 5 ◽  
Author(s):  
Chien-Sheng Liu ◽  
Jia-Jun Lai ◽  
Yong-Tai Luo
Keyword(s):  
Degree Of Freedom ◽  
Geometric Errors ◽  
Light Path ◽  
Linear Guide ◽  
Positioning Errors ◽  
Speed Up ◽  
Analysis Design ◽  
Six Degree Of Freedom ◽  
Straightness Error ◽  
The Mathematical Model

This paper proposes a system utilizing a Renishaw XL80 positioning error measuring interferometer and sensitivity analysis design to measure six-degree-of-freedom (6 DOF) geometric errors of a machine tool’s linear guide. Each error is characterized by high independence with significantly reduced crosstalk, and error calculations are extremely fast and accurate. Initially, the real light path was simulated using Zemax. Then, Matlab’s skew ray tracing method was used to perform mathematical modeling and ray matching. Each error’s sensitivity to the sensor was then analyzed, and curve fitting was used to simplify and speed up the mathematical model computations. Finally, Solidworks was used to design the set of system modules, bringing the proposed system closer to a product. This system measured actual 6 DOF geometric errors of a machine tool’s linear guide, and a comparison is made with the Renishaw XL-80 interferometer measurements. The resulting pitch, yaw, horizontal straightness, and vertical straightness error deviation ranges are ±0.5 arcsec, ±3.6 arcsec, ±2.1 μm, and ±2.3 μm, respectively. The maximum repeatability deviations for the measured guide’s pitch, yaw, roll, horizontal straightness, vertical straightness, and positioning errors are 0.4 arcsec, 0.2 arcsec, 4.2 arcsec, 1.5 μm, 0.3 μm, and 3 μm, respectively.

Six-degree-of-freedom displacement and angle measurement system based on two-dimensional position-sensitive detector

2018 ◽  
Vol 26 (12) ◽  
pp. 2930-2939 ◽  
Author(s):  
高玉娥 GAO Yu-e ◽  
刘 伟 LIU Wei ◽  
吕世猛 L Shi-meng ◽  
张永康 ZHANG Yong-kang ◽  
董文博 DONG Wen-bo
Keyword(s):  
Measurement System ◽  
Angle Measurement ◽  
Degree Of Freedom ◽  
Position Sensitive Detector ◽  
Two Dimensional ◽  
Sensitive Detector ◽  
Position Sensitive ◽  
Six Degree Of Freedom

Error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool

2018 ◽  
Vol 233 (6) ◽  
pp. 1637-1652 ◽  
Author(s):  
Xuan Luo ◽  
Fugui Xie ◽  
Xin-Jun Liu ◽  
Jie Li
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Jacobian Matrix ◽  
Error Modeling ◽  
Degree Of Freedom ◽  
Geometric Errors ◽  
Parallel Kinematic Machine ◽  
Parallel Kinematic ◽  
Position And Orientation ◽  
Five Axis

5-Degree-of-freedom parallel kinematic machine tools are always attractive in manufacturing industry due to the ability of five-axis machining with high stiffness/mass ratio and flexibility. In this article, error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool are discussed for its accuracy issues. An error modeling method based on screw theory is applied to each limb, and then the error model of the parallel kinematic machine tool is established and the error mapping Jacobian matrix of 53 geometric errors is derived. Considering that geometric errors exert both impacts on value and direction of the end-effector’s pose error, a set of sensitivity indices and an easy routine for sensitivity analysis are proposed according to the error mapping Jacobian matrix. On this basis, 10 vital errors and 10 trivial errors are identified over the prescribed workspace. To validate the effects of sensitivity analysis, several numerical simulations of accuracy design are conducted, and three-dimensional model assemblies with relevant geometric errors are established as well. The simulations exhibit maximal −0.10% and 0.34% improvements of the position and orientation errors, respectively, after modifying 10 trivial errors, while minimal 65.56% and 55.17% improvements of the position and orientation errors, respectively, after modifying 10 vital errors. Besides the assembly reveals an output pose error of (0.0134 mm, 0.0020 rad) with only trivial errors, while (2.0338 mm, 0.0048 rad) with only vital errors. In consequence, both results of simulations and assemblies validate the correctness of the sensitivity analysis. Moreover, this procedure can be extended to any other parallel kinematic mechanisms easily.

Six-degree-of-freedom displacement measurement system using a diffraction grating

2000 ◽  
Vol 71 (8) ◽  
pp. 3214-3219 ◽  
Author(s):  
Jong-Ahn Kim ◽  
Kyung-Chan Kim ◽  
Eui Won Bae ◽  
Soohyun Kim ◽  
Yoon Keun Kwak
Keyword(s):  
Measurement System ◽  
Diffraction Grating ◽  
Degree Of Freedom ◽  
Displacement Measurement ◽  
Six Degree Of Freedom

Geometric Error Compensation With a Six Degree-of–Freedom Rotary Magnetic Actuator

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Alexander Yuen ◽  
Yusuf Altintas
Keyword(s):  
Real Time ◽  
Kinematic Model ◽  
Geometric Error ◽  
Degree Of Freedom ◽  
Geometric Errors ◽  
Working Volume ◽  
Quintic Polynomial ◽  
Gradient Descent Algorithm ◽  
Forward Kinematic ◽  
Six Degree Of Freedom

This paper presents a methodology to compensate the tooltip position errors caused by the geometric errors of a three-axis gantry type micromill integrated with a six degree-of-freedom (6DOF) rotary magnetic table. A geometric error-free ideal forward kinematic model of the nine-axis machine has been developed using homogenous transformation matrices (HTMs). The geometric errors of each linear axis, which include one positioning, two straightness, pitch, roll, and yaw errors, are measured with a laser interferometer and fit to quintic polynomial functions in the working volume of the machine. The forward kinematic model is modified to include the geometric errors which, when subtracted from the ideal kinematic model, gives the deviation between the desired tooltip position with and without geometric errors. The position commands of the six degree-of-freedom rotary magnetic table are modified in real time to compensate for the tooltip deviation using a gradient descent algorithm. The algorithm is simulated and verified experimentally on the nine-axis micromill controlled by an in-house developed virtual/real-time open computer numerical controlled (CNC) system.

scholarly journals Embedded Sensor System for Five-degree-of-freedom Error Detection on Machine Tools

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Yubin Huang ◽  
Kuang-Chao Fan ◽  
Wei Sun
Keyword(s):  
Machine Tool ◽  
Error Detection ◽  
Degree Of Freedom ◽  
Sensor System ◽  
Volumetric Error ◽  
Working Space ◽  
Depth Study ◽  
Nc Milling ◽  
Six Degree Of Freedom ◽  
Cutting Point

Any linear stage of machine tool has inherent six-degree-of-freedom (6-DOF) geometric errors. Its motion control system, however, has only the position feedback. Moreover, the feedback point is not the commanded cutting point. This is the main reason why the positioning error along each axis and the volumetric error in the working space are inevitable. This paper presents a compact 5-DOF sensor system that can be embedded in each axis of motion as additional feedback sensors of the machine tool for the detection of three angular errors and two straightness errors. Using the derived volumetric error model, the feedback point can be transferred to the cutting point. The design principle of the developed 5-DOF sensor system is described. An in-depth study of systematic error compensation due to crosstalk of straightness error and angular error is analyzed. A prototype has been built into a three-axis NC milling machine. The results of a series of the comparison experiments demonstrate the feasibility of the developed sensor system.

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