As regards the problems of using absolute linear time grating sensors as the position detector for full closed-loop CNC system, it is necessary transform temporal information to spatial information with time-space transformation algorithm for absolute linear time grating sensors. Time grating sensor’ signal interpolation model is established with time series. The purpose is to extract the relation mapping between future measurement value and past measurement value. In this way, original absolute displacement signal sampled in equal time interval can be converted to continuous incremental pulses required by full closed-loop CNC system. Furthermore, the predicted error model is proposed to improve the interpolation accuracy. The experiment results prove that the interpolation accuracy can reach 0.65 μm, the resolution can reach 0.1 μm.
As regarding the errors caused by mechanical installation and signal processing, a novel self-adaptive kalman filter algorithm is proposed. According to kalman filter recursion formula, the current value can be estimated with the last estimated value and the current measured value. Therefore, the kalman filter algorithm does not need recorder the past series of the estimated value and the current measured value, the calculated load is not too heavy to implement. The respond speed and the quality of time grating can be improved significantly. Experiment results prove the valid of the proposed method.
Through analyzing errors of the length measurement system in which a linear time grating was the principal measuring component, we found that the study on the error law was very important to reduce system errors and optimize the system structure. Mainly error sources in the length measuring system, including the time grating sensor, slide way, and cantilever, were studied; and therefore total errors were obtained. Meanwhile we erected the mathematic model of errors of the length measurement system. Using the error model, we calibrated system errors being in the length measurement system. Also, we developed a set of experimental devices in which a laser interferometer was used to calibrate the length measurement system errors. After error calibrating, the accuracy of the measurement system was improved from original 36um/m to 14um/m. The fact that experiment results are consistent with the simulation results shows that the error mathematic model is suitable for the length measuring system.
A combination method for calibrating the errors of linear time grating displacement sensor is presented. Based on further analysis of time grating, periodic errors, Abbe errors and thermal expansion errors are integrated to obtain error curve for setting up error model, which is adopted to compensate errors using Fourier harmonic analysis and the principle of liner expansion, respectively. Results prove that this method solves the difficult issues about error separation in the linear measurement, and significantly improves the accuracy of linear time grating. Furthermore, this method also solves the issues about continuous automatic sampling with computer, so that the calibration efficiency has been greatly enhanced.
In order to apply original absolute time grating sensor to closed loop numerical control system, a forecasting angle
displacement method with time series analysis theory is proposed. In this way, an absolute time grating sensor can be
transformed to an incremental time grating. In addition, a discrete standard quantity interpolation method is present to
reduce dynamic forecast error. In this way, forecast error of the last measurement period will be corrected in the next
measurement period. Therefore, cumulative errors can be eliminated. The experiment results prove that dynamic errors
can be controlled within ±3″ with error correction method.
Aiming to improve the measurement accuracy of angular displacement sensor effectively and greatly reduce the
production costs under an ordinary machining accuracy. A new method of error correction called harmonic calibration
based on the closure property of circle was presented. Using this method, real-time and dynamic error separation and
correction can be realized when error curve of angular displacement sensor is uncertain. In addition, a method of
“spatial sampling” is presented to solve the problem of asynchrony for dynamic sampling. Furthermore, another method
which adopts software assist to accomplish adaptive filter is presented to eliminate the influence of random error in the
dynamic measurement. As a result a system of full-automatic real-time detection and dynamic calibration for angular
displacement sensor with intelligent functions was developed. Experiment results prove that the accuracy of time grating
can reach up to ±1” in this way. This effective dynamic method can provide a qualitative and quantitative analysis for
calibration of angular displacement sensor.
Time grating is a novel displacement sensor which employs time to measure space. A new predictive method for
predicting the dynamic angular displacement of CNC rotary table is presented with time series. In addition, feedback
interface for rotary transformer is designed to update data speed for time grating in the measurement process. Experiment
results prove that forecast error for acceleration range from -0.00026″/ms<sup>2</sup> to 0.00028″/ms<sup>2</sup>, and forecast angular
displacement error is within ±2″.