Optical Linear Encoder Research Articles

A novel peak positioning method for nanometer displacement measurement by optical linear encoder

In the field of precision measurement, subdividing displacement within the grating period to achieve high precision and high resolution remains a significant challenge. For subdivision, traditional optical linear encoders need complex coding and complicated optical systems, which struggle to meet the demands of nanometer measurement. In this paper, based on the fundamental principles of grating displacement measurement, a high-precision peak positioning method from grating images is proposed for linear displacement measurements with nanometer resolution and submicron accuracy. By utilizing a local gradient interpolation algorithm to optimize curves, it could further improve the accuracy of displacement measurement. Experiments demonstrate that this method achieves a resolution of 2 nm and an accuracy of ± 0.1 μm in a range of 50 mm using a grating with a 20 μm period. This sets the groundwork for subdividing optical linear encoders further, the resolution and accuracy could be further improved by optimizing the subdivision method.

Error Analysis of an Economical On-Site Calibration System for Linear Optical Encoders

A calibration system was designed to evaluate the accuracy of linear optical encoders at the micron level in a fast and economical manner. The system uses a commercial interferometer and motor stage as the calibrator and moving platform. Error analysis is necessary to prove the effectiveness and identify areas for optimization. A fixture was designed for the scale and interferometer target to meet the Abbe principle. A five-degree-of-freedom manual stage was utilized to adjust the reading head in optimal or suboptimal working conditions, such as working distance, offset, and angular misalignment. The results indicate that the calibration system has an accuracy of ±2.2 μm. The geometric errors of the calibration system, including mounting errors and non-ideal motions, are analyzed in detail. The system could be an inexpensive solution for encoder manufacturers and customers to calibrate a linear optical encoder or test its performance.

A Method for Reducing Sub-Divisional Errors in Open-Type Optical Linear Encoders with Angle Shift Pattern Main Scale

In this research, a novel approach is presented to enhance the precision of open-type optical linear encoders, focusing on reducing subdivisional errors (SDEs). Optical linear encoders are crucial in high-precision machinery. The overall error in optical linear encoders encompasses baseline error, SDE, and position noise. This study concentrates on mitigating SDEs, which are recurrent errors within each pitch period and arise from various contributing factors. A novel method is introduced to improve the quality of sinusoidal signals in open-type optical linear encoders by incorporating specially designed angle shift patterns on the main scale. The proposed method effectively suppresses the third order harmonics, resulting in enhanced accuracy without significant increases in production costs. Experimental results indicate a substantial reduction in SDEs compared to traditional methods, emphasizing the potential for cost-effective, high-precision optical linear encoders. This paper also discusses the correlation between harmonic suppression and SDE reduction, emphasizing the significance of this method in achieving higher resolutions in optical linear encoders.

Methods for the Automated Determination of Sustained Maximum Amplitudes in Oscillating Signals

Abstract Machine condition monitoring has been proven to reduce machine downtime and increase productivity. The state-of-the-art research uses vibration monitoring for tasks such as maintenance and tool wear prediction. A less explored aspect is how vibration monitoring might be used to monitor equipment sensitive to vibration. In a manufacturing environment, one example of where this might be needed is in monitoring the vibration of optical linear encoders used in high-precision machine tools and coordinate measuring machines. Monitoring the vibration of sensitive equipment presents a unique case for vibration monitoring because an accurate calculation of the maximum sustained vibration is needed, as opposed to extracting trends from the data. To do this, techniques for determining sustained peaks in vibration signals are needed. This work fills this gap by formalizing and testing methods for determining sustained vibration amplitudes. The methods are tested on simulated signals based on experimental data. Results show that processing the signal directly with the novel Expire Timer method produces the smallest amounts of error on average under various test conditions. Additionally, this method can operate in real-time on streaming vibration data.

A Method to Improve Mounting Tolerance of Open-Type Optical Linear Encoder.

Accuracy becomes progressively important in the wake of development in advanced industrial equipment. A key position sensor to such a quest is the optical linear encoder. Occasionally, inappropriate mounting can cause errors greater than the accuracy grade of the optical linear encoder itself, especially for open-type optical linear encoders, where the mounting distance between the reading head and main scale must be accurately controlled. This paper analyzes the diffraction fields of a traditional scanning reticle made by amplitude grating and a newly designed combined grating; the latter shows a more stable phase in mathematical calculation and simulations. The proposed combined gratings are fabricated in a laboratory and assembled into the reading heads. The experimental results indicate that the mounting tolerance between the reading head and the main scale of the optical linear encoder can be improved.

A Variable Configuration Force Sensor With Adjustable Resolution for Robotic Applications

Multitask measurements with different measuring ranges and resolutions have put forward higher requirements for force sensors. This article presents a novel variable configuration approach to develop an adjustable-resolution force sensor with a compact force-sensitive structure. Unlike the traditional strain gauge-based force measurement, the external force is detected through measuring the displacement of the deformed structure with a precision optical linear encoder. This approach can enable variable measuring range and force resolution through the continuous adjustment of structural stiffness. Specifically, the stiffness adjustment is implemented by changing the second moment of area of the sensor structure through rotating its build-in flexure beam shafts. Analytical models are established to provide the theoretical basis for analysis and design of the sensor. Furthermore, the validity of the design is evaluated with finite element simulations. Finally, a sensor prototype is developed for performance evaluation, and applied for the wire bond pull tests to evaluate the bond strength on the printed circuit board assembly. Experimental results show that it is effective to change the measuring range and force resolution of the developed force sensor through the stiffness adjustment.

Performance Analysis of an Experimental Linear Encoder’s Reading Head under Different Mounting and Dynamic Conditions

The performance of an optical linear encoder is described and evaluated by certain parameters such as its resolution, accuracy and repeatability. The best encoder for a particular application, just like other sensors, is usually selected according these parameters. There are, however, many side effects that have a direct influence on the optimal operation of an encoder. In order to understand how to minimize these harmful effects, a deeper knowledge of an encoder’s performance and a method for determining these factors are necessary. The main aspects of an encoder’s accuracy, resolution and repeatability are briefly reviewed in this paper. Discussed and developed in previous work, the experimental reading head for a Moiré effect-based optical linear encoder is used for the experimental analysis of the influence of different reading head designs on an encoder’s performance under various mounting inaccuracies and dynamic conditions.

Thrust Force Calculation and Analysis for the Permanent Magnet Linear Motor Motion System Considering the Encoder Errors

In this article, we present the effects of encoder errors caused by the mechanical torsional vibrations on the characteristics of the thrust force for the permanent magnet linear motor (PMLM) motion system. First, the effects of the mechanical vibrations on the encoder errors are analyzed. Then, the three-phase current is calculated, considering the nonlinearity of the drive circuit. Based on Maxwell's equations and a Schwarz–Christoffel method, the analytical model of the magnetic field in airgap is established taking into account the slot effect. Finally, the thrust force considering the encoder errors is analytically presented using the electromagnetic energy method, and the experimental verification is carried out. The results show that the mechanical torsional vibrations will produce different kinds of encoder errors for the optical linear encoder. These encoder errors will be coupled with the harmonics in the magnetic field. Consequently, lots of new thrust harmonics appear, affecting the characteristics of the thrust force and the performance of the PMLM motion system.

Development and Experimental Research of Different Mechanical Designs of an Optical Linear Encoder's Reading Head.

Optical linear encoders are widely used in manufacturing. They are accurate and have a relatively high resolution and good repeatability. However, there are a lot of side effects, which have an inevitable impact on the performance of an encoder. In general, the majority of these effects could be minimized by the appropriate design of an encoder’s reading head. This paper discusses the working principle of and commonly occurring errors in optical linear encoders. Three different mechanical designs are developed and implemented in the experimental reading head of the linear encoder in order to evaluate how mechanical construction influences the displacement measurement accuracy and total performance of the encoder.

Thermal and Geometric Error Compensation Approach for an Optical Linear Encoder.

Linear displacement measuring systems, like optical encoders, are widely used in various precise positioning applications to form a full closed-loop control system. Thus, the performance of the machine and the quality of its technological process are highly dependent on the accuracy of the linear encoder used. Thermoelastic deformation caused by a various thermal sources and the changing ambient temperature are important factors that introduce errors in an encoder reading. This work presents an experimental realization of the real-time geometric and thermal error compensation of the optical linear encoder. The implemented compensation model is based on the approximation of the tested encoder error by a simple parametric function and calculation of a linear nature error component according to an ambient temperature variation. The calculation of a two-dimensional compensation function and the real-time correction of the investigated linear encoder position readings are realized by using a field programmable gate array (FPGA) computing platform. The results of the performed experimental research verified that the final positioning error could be reduced up to 98%.

Position sensor for active magnetic bearing with commercial linear optical encoders

Active magnetic bearings are used in a number of applications but their disadvantage is the high asynchronous error due to sensor noise amplification. In this paper a new radial position sensor for active magnetic bearings (AMB) based on linear optical encoders is presented. A commercial encoder scanning head faces a round scale with concentric, coplanar lines on its face. Because such a scale is not readily available, it is made by high precision micro machining and different options are compared. In experiments a measurement noise of 3.5 nm at 10 kHz bandwidth is achieved. In addition, a magnetic bearing is built to demonstrate the sensor in closed-loop.

Evaluation of the pitch deviation of a linear scale based on a self-calibration method with a Fizeau interferometer

A self-calibration method, in which the wavefronts of zeroth and first-order diffracted beams from a scale grating measured by a Fizeau interferometer are employed, is applied for the evaluation of the pitch deviation of a reflective-type linear scale with a grating pitch of 2.048 μm used in a commercial interferential scanning-type optical linear encoder. One of the advantages of the self-calibration method is that the pitch deviation of a scale grating can be evaluated while measuring the out-of-flatness of the scale grating under inspection and the Z-directional out-of-flatness (surface profile) of the reference optical flat in the Fizeau interferometer. Meanwhile, in a practical case, the self-calibration method is valid under the condition where the out-of-flatness of the scale grating is on the same order or less than that of the reference optical flat in the Fizeau interferometer. In this paper, theoretical analysis and numerical calculations are thus carried out to investigate the influence of the out-of-flatness of the scale grating on measurement of the pitch deviation and the out-of-flatness of the reference optical flat. Some experiments with a linear scale from a commercial interferential scanning-type linear encoder are also carried out to verify the feasibility of the self-calibration method for the evaluation of the pitch deviation of the scale having an out-of-flatness of approximately 600 nm over the analyzed area.

Experimental Investigation of Linear Encoder’s Subdivisional Errors under Different Scanning Speeds

Optical encoders are widely used in applications requiring precise displacement measurement and fluent motion control. To reach high positioning accuracy and repeatability, and to create a more stable speed-control loop, essential attention must be directed to the subdivisional error (SDE) of the used encoder. This error influences the interpolation process and restricts the ability to achieve a high resolution. The SDE could be caused by various factors, such as the particular design of the reading head and the optical scanning principle, quality of the measuring scale, any kind of relative orientation changes between the optical components caused by mechanical vibrations or deformations, or scanning speed. If the distorted analog signals are not corrected before interpolation, it is very important to know the limitations of the used encoder. The methodology described in this paper could be used to determine the magnitude of an SDE and its trend. This method is based on a constant-speed test and does not require high-accuracy reference. The performed experimental investigation of the standard optical linear encoder SDE under different scanning speeds revealed the linear relationship between the tested encoder’s traversing velocity and the error value. A more detailed investigation of the obtained results was done on the basis of fast Fourier transformation (FFT) to understand the physical nature of the SDE, and to consider how to improve the performance of the encoder.

Dynamic Behaviour Analysis of Optical Linear Encoder under Mechanical Vibrations

Mechanical vibrations are probably inevitable and occur in more or less all machine tools and other technological equipment. In case the linear encoder is used for moveable parts positioning in such machines, vibrations could cause additional errors. This paper investigates the dynamic behavior of the optical linear encoder under mechanical vibrations. Potentially the most harmful frequencies are determined experimentally, and the corresponding mode shapes are simulated by using finite element method (FEM). Obtained results describe tested encoder`s construction dynamic response to external excitation and could be used to improve its design.

Measurement bias in estimates of system power during a vertical jump

ABSTRACT This investigation sought to quantify the level of measurement agreement in system force, velocity and power values derived across three commonly applied assessment techniques during a countermovement jump (CMJ). Twenty-five male national representative athletes completed three CMJs under unloaded (0%1RM) and loaded (40%1RM) jump conditions. Associated values of force, velocity and power were captured simultaneously from either a linear optical encoder (LOE) or force plate (FP) and then compared to the gold-standard reference values derived from a combined force plate and three-dimensional motion capture system (FPMC). The LOE significantly (p < 0.001) overestimated and failed to meet the minimum level of relatedness (<0.80) for measures of peak velocity, peak force, peak power and mean power across both conditions compared to the FPMC reference values. A reduction in measurement dispersion and bias was, however, evident during the loaded condition. The FP significantly (p < 0.05) underestimated mean and peak power across both conditions, yet measurement bias and dispersion remained consistent. These findings highlight a disparity in measurement agreement in force, velocity and power values across alternative assessment techniques and loads. Such variance in measurement agreement will uniquely alter derived force-velocity profiles, and thus the prescription of training loads to maximise system power during unrestricted CMJs.

Analysis of geometric and thermal errors of linear encoder for real-time compensation

Thermal errors that cause temperature deformations is one of the main factors that influence the accuracy of precision machines. Displacement measuring systems are used in robotics, precision machine tools and other technological equipment, where exist abundant heat sources. The accuracy of linear encoder is affected by both: thermal sources and the changing external ambient temperature. Therefore, thermo-elastic deformations occurring due to the changes in the ambient temperature is an important factor that should be estimated in the process of machine operation. This article presents a study on the thermal errors of optical linear encoder. Compensation of thermal errors is considered a more convenient, effective and economical way in comparison to the ways of thermal error handling and reduction. On the basis of analytic calculations, digital FEM analysis and experimental research, the models of thermal errors that are used for the real-time compensation are determined. The methodology of thermal error compensation, which could be easily realized in a linear encoder itself is presented in the article.

Variability and Impact of Self-Selected Interset Rest Periods During Experienced Strength Training.

We investigated the variability of strength trained athletes' self-selected rest periods between sets of heavy squat training. Sixteen strength-trained male athletes (Mage = 23, SD = 3 years) completed two squat training sessions 48 hours apart. Each training session consisted of five sets of 5RM squats, interspersed with self-selected interset rest periods. A Gymaware linear optical encoder collected kinetic data for each squat and temporal data for each interset rest period. The participants' subjective ratings of the experience were taken before (Readiness to Lift [RTL]) and after (Rating of Perceived Effort [RPE]) each set. Mean total rest time and mean power output differed significantly between sessions. For both sessions, interset rest period increased, and power output decreased between Sets 3, 4, and 5 (95% CI range [-101, -17]) compared with Set 1. In both sessions, RPE increased significantly in Set 3 compared with Set 1 (95% CI range = [0.68, 2.19]), while RTL decreased significantly from Set 3 (95% CI range [-2.99, -0.58]) compared to Set 1. Interset rest period and power output demonstrated fair reliability between sessions (mean intraclass correlation coefficient = 0.55), while RPE and RTL demonstrated good and excellent reliability, respectively (mean intraclass correlation coefficient = 0.63 and 0.80). In conclusion, highly trained strength athletes demonstrated a significant difference in their between session power output and total rest time when using self-selected interset rest periods, despite stability in their subjective ratings of fatigue and effort. Interset rest periods can be self-selected reliably to complete strength training in heavy squat protocol; however, power output may decline during the set.

Development of a digital interpolation module for high-resolution sinusoidal encoders

This paper presents a digital interpolation module for high-resolution sinusoidal encoders. The proposed strategy performs phase-shifting manipulation on the sinusoidal encoder signals, and takes advantage of the linear sections of the absolute values of the phase-shifted sinusoidal signals. Thus, an approximately linear signal is obtained, from which the displacement can be linearly determined. Simulation result shows that the theoretical error of the proposed interpolate strategy is within 0.072° over the 360° signal period. Furthermore, a digital interpolation module is developed by implementing the interpolate strategy in a field-programmable gate array (FPGA), and performance evaluation experiments are carried out by applying it to a linear optical encoder with a pitch of 20 μm. The effectiveness of the digital interpolation module has been validated by both simulation results and experimental results.

Ratiometric-Linearization-Based High-Precision Electronic Interpolator for Sinusoidal Optical Encoders

Electronic interpolation is the key technology for further improving the measurement resolution of optical encoders. In this paper, an electronic interpolator based on the ratiometric linearization conversion method is presented. The proposed method converts the sinusoidal encoder signals into a nearly perfectly linear output signal through mathematical manipulation that only involves basic operations of addition, subtraction, multiplication, and division. Thus, the displacement can be precisely determined using a simple linear equation. Furthermore, quadrature interpolation pulses are also generated from the linear output signal by using the amplitude subdivision method. Since the linearization procedure is based on the ratiometric operation, interpolation accuracy is independent of amplitude fluctuation of the encoder signals. Theoretical analysis shows that the nonlinear error of the proposed interpolator is below ±0.0034 rad over a signal period of 2 π rad, which corresponds to an interpolation error of ±0.0108 μ m for a linear optical encoder with a pitch of 20 μ m. In the experiment, the proposed strategy is successfully implemented within a field programmable gate array, and applied to a 20 μ m-pitch optical encoder. Experiments are performed to demonstrate the effectiveness of the proposed method.

Error analysis and compensation of an optical linear encoder

Optical linear encoder error is of a great concern for its wide applications. Temperature plays an important role in the realistic environment error factors, and influences the encoder's accuracy. In this study, an incremental optical linear encoder error model is built and estimated by a prior analysis, error processing of least-square fitting, empirical mode decomposition and cross-correlation methods. The errors of the different temperatures can be used for error separation during the cross-correlation calculation. The experimental measurement with different temperatures is carried out, and analysed by the authors’ model. Finally, an ‘ad hoc’ compensation formula is obtained and demonstrated.