Error Compensation Research Articles

Recent Patents of Thermal Error Modeling and Thermal Error Prediction of CNC Machine Tool Spindle

: With the development of machine tools to high precision and high automation, thermal error has become the key reason to hinder the improvement of thermal stability of machine tools. The spindle electrothermal error is an important factor affecting the machining accuracy of highspeed CNC machine tools. The thermal error model of a high-speed motorized spindle is established to compensate the thermal error, which can effectively improve the influence of thermal error on the machining accuracy of machine tools. The thermal displacement during the operation of motorized spindle is the main reason that affects the machining stability and precision of motorized spindle. The thermal error compensation of CNC machine tool spindle can improve the machining efficiency, the machining quality of parts and the service life of CNC machine tools. This paper summarizes the representative patents and papers on thermal error modeling and thermal error prediction in China. By summarizing a large number of patents and papers on modeling, prediction and compensation of thermal error of spindle of CNC machine tools, the modeling method is analyzed and the development trend is discussed. The improvement of thermal error modeling method of CNC machine tool spindle has an important influence on improving machining accuracy, efficiency, and stability. Therefore, in the future, there will be more and more patents for thermal error modeling of CNC machine tools and spindles.

Finite-time event-triggered tracking control for quadcopter attitude systems with zero compensation technology

This paper primarily investigates the event-triggered tracking control problem for quadcopter attitude systems, utilizing finite-time zero compensation technology. Unlike existing research results, a zero compensation technology is proposed to solve non-affine control input problems such as saturation, dead zones, and gaps. The command filtered compensation technology is used to solve ’differential explosion’ and filtering errors. A novel Tanh type filter and a neural network are employed to approximate virtual control signals and account for un-modeled dynamics, respectively. Moreover, the finite-time convergence theory is used to prove that the state, tracking error, and filtered error compensation signals in the entire closed-loop system converge to an arbitrarily small neighborhood of the equilibrium origin. Finally, the advantages of the proposed control algorithm in improving tracking accuracy and reducing communication load were demonstrated through simulation.

A Localization Method Based on Multi-Area Selection and Error Compensation for Indoor Wireless Sensor Network

A Localization Method Based on Multi-Area Selection and Error Compensation for Indoor Wireless Sensor Network

Predictive Current Error Compensation Based Strong Robust Model Predictive Control for PMSM Drive Systems

Predictive Current Error Compensation Based Strong Robust Model Predictive Control for PMSM Drive Systems

Digital-driven in-situ monitoring for thermally-induced volumetric errors of CNC machine tools

In order to realize the in-situ monitoring of thermally-induced volumetric errors of CNC machine tools, a digital twin system is designed and developed through combined programming of C#, ANSYS, and MATLAB. The thermal error mapping models are constructed through superposing the axis motion-induced thermal errors and the spindle rotation-induced thermal deformations. The models of axis motion-induced thermal errors are established based on the orthogonal polynomial tabular modeling method, and real-timely corrected through correction models which are constructed based on the predicted and measured errors. The spindle rotation-induced thermal deformations are obtained via digital twin for thermal characteristics of the spindle system. The error distributions are generated by MATLAB through pre-creating the DLL file. Experimental results show that the prediction accuracy of digital twin-driven in-situ monitoring for thermally-induced volumetric errors is greater than 95 %, which effectively improvs the prediction accuracy of thermally-induced volumetric errors of CNC machine tools and provides a basis for thermal error compensation.

Resonance-State Temperature Compensation Method for Ultrasonic Resonance Wind Speed and Direction Sensors

To achieve high-precision wind speed and direction measurements in complex environments, a resonance-state temperature compensation method is proposed based on an ultrasonic resonance principle. This method effectively addresses the issue of sound velocity compensation errors caused by the temperature difference between the internal and external environments when using an internal temperature sensor for temperature compensation. By utilizing an adaptive resonance-state tracking model, the resonance frequency shift issues under varying conditions such as altitude, pressure, and temperature are mitigated. This approach ensures that the resonance frequency is strongly correlated with temperature, enabling temperature compensation through resonance frequency alone, without the need for a temperature sensor. The experimental results indicate that the resonance frequency variation rate with temperature for the resonance-state temperature-compensated ultrasonic resonance wind speed and direction sensor is approximately 0.08 kHz/°C. The wind speed measurement accuracy is ±0.3 m/s (≤15 m/s)/±2.3% (15 m/s~50 m/s), which is superior to the measurement accuracy of traditional ultrasonic wind speed and direction sensors (±0.5 m/s (≤15 m/s)/±4% (15 m/s~50 m/s)). The consistency of wind speed measurement is ≤±0.3%, representing an improvement of approximately 3% compared to ultrasonic resonance wind speed and direction sensors without resonance-state temperature compensation.

Observer-Based Event-Triggered Fuzzy Control for Switched Multi-Agent Systems with State Constraints and Sensor Faults

In this paper, we consider the output feedback event-triggered tracking control problem for a class of switched nonlinear multi-agent systems (MASs) with sensor faults and state constraints. For unknown nonlinear functions in the system, fuzzy logic systems are used to approximate them. To address sensor faults, sensor error compensation coefficients are designed to compensate for the errors caused by sensor faults. Meanwhile, state observer is designed to estimate the unmeasurable states in the system, providing necessary information for control design. Based on directed switching networks containing a directed spanning tree, an event-triggered output feedback controller is designed to enable the MAS to track the leader agent. By constructing a suitable barrier Lyapunov function, the stability of the system is analyzed, and it is proved that the consensus tracking can be achieved without violating the state constraints, the uniform boundedness of all the closed-loop system signals is ensured and the Zeno behavior can be eliminated. Finally, the effectiveness of the proposed algorithm is verified through a simulation example.

A novel TDE error compensation method based on manipulator time-delay control

A novel TDE error compensation method based on manipulator time-delay control

Research on Pose Error Modeling and Compensation of Posture Adjustment Mechanism Based on WOA-RBF Neural Network

This paper is aimed to address the issue of decreased accuracy in the ship block docking caused by the structural errors of posture adjustment mechanism. First, inverse kinematic analysis is performed to investigate the sources of static errors in the mechanism. Subsequently, based on the closed-loop vector method, a pose error model for the moving platform is established, which includes eight categories of error terms. The impact of various structural errors on the pose accuracy of the moving platform is then compared and analyzed under both single-limb and multi-limb configurations. Therefore, a compensation method based on the whale optimization algorithm optimized radial basis function neural network is proposed. By transforming pose errors into actuator length errors, it establishes a predictive model between the theoretical pose of the dynamic platform and actuator length errors. After optimizing the network parameters, it yields the actuator length compensation to correct the actual pose of the dynamic platform. Simulation and experimental results validate the effectiveness of this method in enhancing the motion accuracy of the parallel mechanism. The mean pose accuracy of the moving platform is improved by 85.07%, demonstrating a significant compensation effect.

High-Speed and Low-Noise Gear Finishing by Gear Grinding and Honing: A Review

AbstractGears are important mechanical parts for transmitting power and play an increasingly important role in the machinery industry. The electric vehicle industry developed rapidly and became a vital development field of the automotive industry over the past few years. The conversion of energy increases the requirements for electric vehicle transmissions, which promotes the development of high-speed and low-noise transmission gear. This paper elaborates on the research progress of high-speed and low-noise gear finishing methods. Firstly, this review analyses the machining requirements, finishing, and specific machining technologies of high-speed and low-noise gears. The importance of gear grinding and honing in high-speed and low-noise gear machining is highlighted. Secondly, the applications of gear grinding and honing in gear modification, error compensation, and texture control are analyzed. Furthermore, the role of precision machining technology in improving gear performance is clarified. Finally, the design and processing methods of the modified tooth flank for gear modification are summarized. In addition, the influence of tooth surface texture on noise is described, and the texture change methods are explored. The well-known open problems of gear finishing are finally identified, and some new research interests are also pointed out. This review will provide valuable references for further research on gear finishing.

Study on the analytical verification method of geometric error models

Abstract Geometric error compensation is a widely used and effective approach for enhancing the accuracy of Coordinate Measuring Machines (CMMs) and Computer Numerical Control (CNC) machines. The research in this field primarily focuses on the challenging task of developing geometric error modelling techniques. Currently, there are several well-established methods for modelling geometric errors. However, there is scarce availability of methods that can validate the established geometric error models. Therefore, this article proposes an analytical validation method for geometric error models based on the error transformation equation. The principle of the method is elaborately explained, and its correctness is verified through specific model verification example. The method proposed in this article enables rapid and accurate model correction and iteration, effectively reducing the economic and time costs of model validation in the current geometric error compensation process. Therefore, the method provides guidance for standardising the modelling process and could be widely applied to various structural forms of measurement and machining systems.

Adaptive Weighted Particle Swarm Optimization for Controlling Multiple Switched Reluctance Motors with Enhanced Deviatoric Coupling Control

Switched reluctance motors (SRMs) are widely used in industrial applications due to their advantages. Multi-motor synchronous control systems are crucial in modern industry, as their control strategies significantly impact synchronization performance. Traditional deviation coupling control structures face limitations during the startup phase, leading to excessive tracking errors and exacerbated by uneven load distribution, resulting in desynchronized motor acceleration and increased speed synchronization errors. This study proposes a modified deviation coupling control method based on an adaptive weighted particle swarm optimization (PSO) algorithm to enhance multi-motor synchronization performance. Traditional deviation coupling control applies equal reference torque inputs to each motor’s current loop, failing to address uneven load distribution and causing inconsistent accelerations. To resolve this, a gain equation based on speed deviation is introduced, incorporating self-tracking error and gain coefficients for dynamic synchronization error compensation. The gain coefficients are optimized using the adaptive weighted PSO algorithm to improve system adaptability. A simulation model of a synchronization control system for three SRMs was developed in the Matlab/Simulink R2023b environment. This model compares the synchronization performance of traditional deviation coupling, Fuzzy-PID improved structure, and adaptive PSO improved structure during motor startup, sudden speed increases, and load disturbances. The validated deviation coupling control structure achieved the initial set speed in approximately 0.236 s, demonstrating faster convergence and a 6.35% reduction in settling time. In both the motor startup and sudden speed increase phases, the two optimized methods outperformed the traditional structure in dynamic performance and synchronization accuracy, with the adaptive PSO structure improving synchronization accuracy by 54% and 37.17% over the Fuzzy-PID structure, respectively. Therefore, the PSO-optimized control system demonstrates faster convergence, improved stability, and enhanced synchronization performance.

Machining error compensation of free-form surfaces by combination of ordinary kriging method and mirror compensation method

ABSTRACT Improving the accuracy and efficiency of free-form surface machining is a common goal of modern manufacturing. In this study, a compensation method combining the ordinary kriging method based on sequential quadratic programming method optimization (SQP-OK) and the mirror compensation method for machining errors of free-form workpieces was applied, with the aim of significantly improving the workpiece machining accuracy. Machining errors on the surface of the workpiece were predicted utilizing the SQP-OK after the workpieces were completed with semi-finishing machining based on the on-machine measurement (OMM) results of the workpiece. Based on the prediction result, the mirror compensation method was applied to calculate the compensation points. Free-form workpieces were compensated for by modifying the NC code for semi-finishing. To verify the effectiveness of the proposed method, two free-form workpieces were machined with computer numerical control (CNC) compensation, applying the proposed method and the method modifying the overall machining allowance. The experimental results revealed that the compensation method proposed in this paper reduced the average value of the machining errors decreased by 28.6% in absolute value, 31.1% in maximum undercut, and 28.8% in maximum overcut for the free-form workpiece, respectively, compared with the compensation method of modifying the overall machining allowance.

Gaze-Contingent Layered Optical See-Through Displays with a Confidence-Driven View Volume.

The vergence-accommodation conflict (VAC) presents a major perceptual challenge for head-mounted displays with a fixed image plane. Varifocal and layered display designs can mitigate the VAC. However, the image quality of varifocal displays is affected by imprecise eye tracking, whereas layered displays suffer from reduced image contrast as the distance between layers increases. Combined designs support a larger workspace and tolerate some eye-tracking error. However, any layered design with a fixed layer spacing restricts the amount of error compensation and limits the in-focus contrast. We extend previous hybrid designs by introducing confidence-driven volume control, which adjusts the size of the view volume at runtime. We use the eye tracker's confidence to control the spacing of display layers and optimize the trade-off between the display's view volume and the amount of eye tracking error the display can compensate. In the case of high-quality focus point estimation, our approach provides high in-focus contrast, whereas low-quality eye tracking increases the view volume to tolerate the error. We describe our design, present its implementation as an optical-see head-mounted display using a multiplicative layer combination, and present an evaluation comparing our design with previous approaches.

Balancing precision and efficiency: an approximate multiplier with built-in error compensation for error-resilient applications

Balancing precision and efficiency: an approximate multiplier with built-in error compensation for error-resilient applications

The Analysis and Compensation Experiment of Linear Feed Axis Positioning Error Based on Matrix Operation

The positioning accuracy of the linear feed axis is a key factor affecting the machining accuracy of CNC machine tools. The generation process of the positioning error of the linear feed axis is expounded. The Z axis of the vertical linear feed axis of the machining center is the research object, the positioning error analytical matrix is established, and the positioning error calculation of the Z axis of the vertical linear feed axis is completed based on the principle of solving the inhomogeneous linear equation. The positioning error detection of the vertical linear feed axis Z axis of the CNC machining center is carried out. Based on the characteristics of the error detection data, an error compensation model is constructed. , the variance of the positioning error detection point after compensation is reduced to 1.562, which meets the needs of precision machining.

Calculation of Tool Offset and Tool Radius Errors Based on On-Machine Measurement and Least Squares Method in Ultra-Precision Diamond Turning

Metal mirrors will be widely used in the coming decades. Therefore, as one of the enabling technologies for metal optical freeform surface manufacturing, ultra-precision (UP) diamond turning error compensation has become a research hotspot. However, for the tool offset error and tool radius error, which are the main errors in UP diamond turning, no precise and efficient calculation method has been found in the literature. In this study, a more precise and efficient algorithm was developed and validated in three ways using on-machine measurement data and profilometer measurement data. After one compensation, the tool offset error can be reduced to below 0.1 μm, and the tool radius error can be reduced to below 1 micrometer, which will significantly improve the UP turning accuracy and efficiency of optical parts.

Error compensation and path planning for sheet metal bending process based on improved modeling algorithms

Error compensation and path planning for sheet metal bending process based on improved modeling algorithms

Modeling and Simulation of Wide-Frequency Characteristics of Electromagnetic Standard Voltage Transformer

To achieve the broadband applicability of standard voltage transformers in “dual high” power systems, an equivalent circuit model of the standard voltage transformer is first established. Using the complex magnetic permeability method and utilizing existing core parameters, the excitation impedance values are obtained. Next, based on the equivalent circuit model, the no-load error function of the standard voltage transformer is analyzed, and through simulation, the no-load error response curve of the standard voltage transformer in the frequency range of 20 Hz to 3000 Hz is derived. The simulation results indicate that within the 20 Hz to 700 Hz range, both the no-load ratio error and the no-load angular error meet the accuracy requirements, with the ratio error within ±0.05% and the angular error within 2′. Additionally, the derivation of the error transfer function demonstrates the correlation between the no-load error values and the number of turns and cross-sectional area of the standard voltage transformer. Simulation results, obtained by increasing and decreasing the number of turns and cross-sectional area by 10%, provide valuable insights for the error compensation and structural design of standard voltage transformers.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.