Multiple Reading Heads Research Articles

Self-Calibration Method for Circular Encoder Based on Two Reading Heads with Adjustable Positions

To improve the measuring accuracy of circular encoders in special applications, self-calibration of the circular encoder is necessary. The commonly used self-calibration method, namely the Equal Division Average (EDA) method, requires a large number of reading heads and cannot be used when the structural space is limited. In this paper, a self-calibration method for a circular encoder based on two reading heads with adjustable positions (TRAP) is proposed. This TRAP method uses two reading heads to simulate multiple reading heads, which can be used to achieve self-calibration of circular encoders in limited space. This paper investigates the principle of simulating multiple reading heads with two reading heads, designs and builds an experimental system, and obtains and analyzes experimental data. The experimental results show that the peak-valley value of the angle measurement error is reduced from 252.41″ to 18.82″ after self-calibration with the TRAP method, and the repeatability of multiple self-calibration experimental results is less than 0.75″. The TRAP method breaks through the limitation of the number of reading heads that can be installed during the self-calibration of the circular encoder and can effectively suppress the angle measurement error of the circular encoder.

On the Positional Single Error Correction and Double Error Detection in Racetrack Memories

In the era of non-volatile memories, the racetrack memory is a promising technology to pack hundreds of bits in a magnetic nanowire. A solid-state read head is grown alongside the nanowire to sense individual bits which are pushed across the head by a shifting force. However, the probabilistic nature of this shifting movement inflicts positional errors. Therefore, robust and low-cost error correcting codes are essential for a reliable alternative in on-chip memories and storage applications. Recent works focus on Varshamov-Tenengolts (VT) codes which can correct all single bit insertions and deletions. However, VT codes are incapable of detecting multiple deletions/insertions. Because a positional error corrupts multiple data words, multi-bit positional error detection is critical for racetrack memories. In this article, we propose a novel positional single error correction and double error detection (P-SECDED) code in the context of racetrack memories with a single read head. In particular, we adopt a postamble-based approach where a VT-encoded codeword appends a carefully selected bit-pattern, stored on the racetrack. We rigorously analyze the limitations of the postamble method, and deduce a criterion for postamble selection. We further provide a methodology to optimize this postamble selection in order to correct all single-bit errors and as much of two-bit errors as possible. Finally, we prove that all incurable two-bit errors are successfully detected. To the best of our knowledge, this work is the first attempt to provide P-SECDED fault-tolerance to three-dimensional racetrack memories which cannot afford multiple read heads.

Moiré Fringe Signal Subdivision System of a Stained Code Disc of a Grating Displacement Sensor

When a code disk of a displacement sensor is exposed to dust or other impurities, it causes distortion of the grating moiré fringe signal, and thereby provides wrong displacement information from the sensor. Therefore, it is necessary to analyze the distortion in the reading due to the stains. In this paper, multiple reading heads were used to collect the moiré fringe signal of the sensor and were evenly distributed on the fine code channel. Each reading head was used to subdivide the moiré fringe signal collected by it, calculate the signal amplitude value corresponding to each sampling point, and analyze the stains of the code disk corresponding to the reading head according to the signal amplitude value. According to the stains of the code disk, the subdivision value of each reading head was considered to have a certain weight. It was found that when the reading head is stained, the weight decreases, whereas when it is clean, the weight increases. Finally, the weighted average value of the two reading heads was taken as the final subdivision value of the sensor. The experimental results showed that the system provides output with high-precision displacement values even when the moiré fringe signal was abnormal due to the local stains of the sensor’s code disk, therefore it significantly increases the anti-stain ability of the sensor.

A self-calibration method for rotary tables’ five degrees-of-freedom error motions

The paper proposed a novel self-calibration method for five degrees-of-freedom error motions of rotary tables. Two encoders with multiple reading heads were installed on the spindle’s different positions to measure rotation angles. By analyzing indication differences between the reading heads, the two grid discs’ radial motions were obtained. After Fourier analysis, measurement errors caused by the installation errors of the grid discs were eliminated and two different positions’ error motions of the spindle were obtained. Therefore, the rotary table’s 5-DOF error motions, including angular positioning (ECC) error motions, radial (EXC, EYC) and tilt (EAC, EBC) error motions defined in ISO 230-7 and ANSI/AMSEB89.3.4, were self-calibrated. In order to verify the proposed self-calibration method, roundness errors of a cylinder were measured on a rotary table with a self-calibration system. During the measurement of the roundness errors, the error motions of the rotary table were measured simultaneously by the self-calibration system. After error compensations and eliminating influences of error motions of the rotary table, measurement data of the roundness errors were obtained. Compared with the calibration of three-point method for measuring roundness errors, the residual errors were less than ±0.5 μm. In order to verify dynamic measurement, external forces were loaded on the rotary table intentionally during the measurement process. The error motions of the rotary table changed with intermittent external forces, which were also detected accurately by the self-calibration system on line. After error compensations, the calibrations trend and magnitude with three-point method showed that error motions self-calibration of the rotary table are effectiveness and feasibility.

A Simplified Self-Calibration Method for Cylindrical Grating

Cylindrical grating angle sensor is a common angle measuring device with high precision. Due to the reflecting arc surface of the cylindrical grating the effects of relative displacement of graduation line and gap variation will interact. Significant residual errors still exist even with high precision cylindrical grating and multiple reading heads around the scale disc .In this paper, based on the principle of circumference closure, the principle of self-calibration is deduced and analyzed in detail. The calibration curve is obtained by obtaining the deviation between the certain position and an ideal position of the graduation line position in real time. A simple self-calibration method of cylindrical grating is acquired. It can calibrate random errors and system errors with time and improve the angle measurement accuracy. The method has the advantages of simple structure and strong maneuverability, and provides technical means for the miniaturization and high precision of cylindrical grating.

Utilization of multiple read heads for TMR prediction and correction in bit-patterned media recording

This paper proposes a utilization of multiple read heads to predict and correct a track mis-registration (TMR) in bit-patterned media recording (BPMR) based on the readback signals. We propose to use the signal energy ratio between the upper and lower tracks from multiple read heads to estimate the TMR level. Then, a pair of two-dimensional (2D) target and its corresponding 2D equalizer associated with the estimated TMR will be chosen to correct the TMR in the data detection process. Numerical results show that the proposed system can achieve a very high accuracy of TMR prediction, thus performing better than the conventional system, especially when TMR is severe.

Soft Intertrack Interference Cancellation for Two-Dimensional Magnetic Recording

We propose a detection strategy for the two-dimensional magnetic recording channel with multiple read heads, in which intertrack interference (ITI) is mitigated by a combination of linear combining and soft interference cancellation. The proposed strategy reduces the detection problem to a series of traditional one-dimensional detection problems, so that the existing iterative detection strategies based on turbo equalization may be leveraged. The performance of the proposed detector is compared with a previously reported detector, in which the ITI is suppressed linearly via a multiple-input equalizer. Numerical results demonstrate that the proposed detector outperforms the linear detector regardless of whether or not media noise is dominant, and further that the proposed detector is able to recover data from more tracks than is otherwise possible.

Capabilities and limitations of the self-calibration of angle encoders

At the Physikalisch-Technische Bundesanstalt (PTB), a self-calibration method for the fast and precise in situ calibration of angle encoders without recourse to external reference standards has been developed. It relies on a suitable geometric arrangement of multiple reading heads which read out the radial grating of the angle encoder at different angular positions. Fourier-based algorithms are used to analyse the measurement differences of pairs of heads to recover the graduation error of the grating. A comprehensive overview, both theoretical and experimental, of the capabilities and limitations of the self-calibration method is presented, including experimental data obtained with the high-precision primary angle standard of PTB. The evaluation and, where it is possible, correction of error influences due to lateral shifts of the centre of the encoder's grating during its rotation, including its eccentricity, the reading heads’ angular positions, and their non-uniform response, are discussed in detail, as well as the resulting uncertainty budget.

Self-Calibration of On-Axis Rotary Encoders

This paper presents a new self-calibration method for rotary encoders mounted on precision axes of rotation. By measuring encoder pulse widths in the time domain, the angular distance corresponding to each pulse is automatically derived from the spindle free-response dynamics. This method has three distinctive features: 1) instant calibration of the encoder error map without need for an angle measurement instrument; 2) wide applicability to general encoders without requiring multiple read-heads; 3) in-place calibration on the target rotary axis rather than the axis of another calibration system. Experiments and simulations have been conducted to characterize the calibration repeatability and accuracy.

Calibration of angle encoders using transfer functions

Classical approaches to the calibration of angle encoders typically make use of circle division by means of an auxiliary artefact and apply linear equation systems constrained by circle closure which are solved for the errors of the encoder and those of the artefact simultaneously. Lately, emphasis has been placed on Fourier methods, as Fourier approaches involving transfer functions have proved to be a powerful tool applicable to various high-precision measurement tasks. We present an in-depth treatment of the use of the Fourier approach including transfer functions for the calibration of angle encoders. Different weighting schemes for combining the measurements will be presented by which the uncertainty of the calibration of angle encoders can be substantially reduced. The method utilizes angle difference measurements and it can therefore also be applied to the calibration of angle encoders using suitable arrangements of multiple reading heads. The approach is used for calibrating an angle encoder in an experimental set-up by means of a five-sided calibration polygon with angle differences between the optical faces that are not integer fractions of the full circle. The calibration results, including an evaluation of the measurement uncertainty, are presented for different weighting schemes and it is shown that appropriate weighting leads to a reduction in the uncertainty up to a factor of 4.