Contour Error Research Articles

Servo X-Y biaxial feed system of flux switching permanent magnet linear motor.

As both magnets and coils are arranged in the motor primary, a short primary long secondary flux switching permanent magnet linear motor (FSPMLM) is favorable to construct a feed system, especially for long distance, multi-axis applications. A novel FSPMLM with a complementary primary module and end-PM topology is proposed to directly drive a biaxial feed system, and the whole structure is presented. To consider the influence of temperature raise on motor performance, magnetic-thermal coupling finite element analysis is employed, and then, the motor dimensions are optimized by the response surface method. With the same 500 N rated force and 1.5 m/s rated speed of the two FSPMLMs, the biaxial prototype is fabricated. Considering the two-axis synchronization, the control system is constructed by using a commercial motion controller and servo drivers. Monoaxial and biaxial feeding experiments are carried out simultaneously. Both X and Y axes exhibit sufficient force capability for well dynamic response, and the positioning error is less than 0.14 mm. Biaxial diamond and circular trajectories are conducted, and the contour errors are less than 0.88 mm. It can be seen that the proposed FSPMLM feed system is featured with favorable performance and competitiveness for applying in various industrial applications.

A Model Predictive Contouring Error Precompensation Method

Contouring error has a significant effect on machining accuracy. In this paper, a model predictive contouring error precompensation method is presented that performs model-based error precompensation with feedback and constraints. The proposed method uses the predicted contouring error without compensation obtained by simulation, as the reference trajectory of the model predictive compensator. It then calculates the compensation signal using a constrained model predictive control algorithm and adds it to the original reference position as the new system input. Experiments were conducted on an X–Y table to compare the proposed method with a traditional cascaded proportional-integral (PI) controller and two existing contouring error precompensation methods. The experimental results show that higher contouring accuracy can be achieved with the proposed method for both sharp corners and free-form curves.

A Comparison Strategy for Improving the Precision of Contour Error Estimation

Contour error estimation is one of the most important tasks in contour following control. The general way to estimate the contour error is by carrying out curve approximation at the current reference point. But it will suffer a loss of precision in large tracking lag condition. To improve the accuracy of estimation, iteration of the approximation process is usually inevitable. In this paper, a comparison strategy is proposed to ameliorate the accuracy of traditional contour error estimation. By searching the optimal reference point, then directly performing estimation near the neighbor of real contour error point, the estimation accuracy can be improved and the iteration process can be avoided. Principles and details of the proposed strategy are discussed by numerical simulations. The verification experiments are implemented by employing linear and circular based contour error estimation methods. The proposed strategy exhibits better universal estimation performance compared with several advanced algorithms and is easy to implement on external computer. The compensation results of ellipse path following task show the feasibility and efficiency of the proposed comparison strategy.

A novel causation analysis method of machining defects for five-axis machine tools based on error spatial morphology of S-shaped test piece

In the acceptance process of newly developed five-axis machine tools (FAMTs), it is urgent for machine tool builders to understand the main causes of machining defects on S-shaped test piece. This paper proposes a novel causation analysis method based on error spatial morphology of S-shaped test piece to decouple the key geometric error parameters causing contour errors of test piece. Firstly, based on multi-body system (MBS) theory, tool axis surface error model of a FAMT is set up. In order to eliminate the effect of theoretical error on contour error of S-shaped test piece, the optimized tool path is planned based on the three-point tangential method. Then, the NC instruction is calculated, and error spatial model is established to characterize contour error of the test piece by considering tool setting position. As a basis, error spatial morphologies of test piece are drawn and the relationships between geometric error parameters and error spatial morphologies are analyzed. In order to decouple the key geometric error parameters affecting contour error of test piece, the causation analysis method of local error and global error are presented. After repairing the local and global key error parameters of the test piece obtained from these two analysis methods respectively, the local machining errors are reduced by more than 80%, and the global machining error is not beyond the tolerance. Finally, the cutting experiments of S-shaped test piece on the FAMT XKAS2525 × 60 are implemented. Error detection results of the cutting test piece are basically the same as that shown in error spatial morphologies of test piece, which verifies the correctness of error spatial model for the test piece. After compensating the global key error parameters obtained from the causation analysis method of global error in CNC system, the detection results of re-cutting test piece under the same conditions indicate the test piece has very few points that are not within the tolerance range, and detection results after compensation and global repaired results are almost similar, which verifies the feasibility and correctness of the proposed analysis method. Therefore, it is obvious that the presented method bridges between geometric characteristics of S-shaped test piece, geometric errors of machine tool, and machining defects of test piece and provides a comprehensive error analysis method in the acceptance and performance testing of FAMTs by using the S-shaped test piece. Thus, this study is of great significance for improving the accuracy evaluation method and enhancing the design accuracy of FAMTs.

MPCC-Based Set Point Optimisation for Machine Tools

Numerical control code is typically used for manufacturing a workpiece using machine tools. Most state-of-the-art approaches decouple the set point optimisation into two steps: the geometry and the feed rate optimisation that does not necessarily result in time-optimal set points for the desired geometry. Given the originally programmed geometry through the numerical control code, dynamic constraints of the machine tool, and maximum permissible contour error for the optimisation, a model predictive contouring control based set point optimisation approach is developed to generate time-optimal set points for machine tools globally. A suitable error definition and its linearisation are used whereby the optimisation problem can be represented by a quadratic programming problem with linear constraints. Compared to most state-of-the-art methods, a direct approach is presented and no previous geometry optimisation step is required. Depending on the demands of accuracy, different maximum contour error constraints and penalisation as well as various maximum permissible axis velocities and accelerations are presented and tested on a test bench. The method is shown to be adaptable to different demands on the set points, and the contour errors can be affected by either the constraints or penalising factors.

A LADRC based fuzzy PID approach to contour error control of networked motion control system with time‐varying delays

AbstractThis paper investigate the contour error control problem for networked multi‐axis motion system (NMAMS) with time‐varying delays. Firstly, the uncertainties induced by the delays are modeled as a part of the total disturbance, and a linear active disturbance rejection controller (LADRC) is designed for the uniaxial trajectory tracking control. In the LADRC, a linear extended state observer (LESO) is designed to estimate the system state and the total disturbance simultaneously, and the effect of the total disturbance is eliminated by the designed linear feedback error control law. Then, the classical contour error estimation method is adopted, and a fuzzy PID controller is designed to compensate the contour error to achieve a better contour tracking performance. Finally, experiments are provided to verify the effectiveness of the proposed method.

Analysis of friction error in CNC machine tools based on electromechanical characteristics

Friction is a kind of inherent and nonlinear disturbance in feed systems, which inevitably deteriorates motion accuracy at velocity reversal. Position error caused by friction is integrally effected by three aspects of feed drives, including command, control, and mechanical subsystems. Unfortunately, the traditional analyses hardly consider all mentioned aspects. Especially, no research has been reported on control characteristic at reverse motion. The purpose of this paper is to reveal the generation mechanism of friction error of a feed drive based on the commercial computer numerical control with three-loop control structure and velocity feedforward and proportional–proportional–integral controllers. Firstly, the generation process of the friction error at velocity reversal is profoundly investigated. Based on it, a simplified control model is conducted to explain transition from presliding to sliding regimes. It is the bond of analyzing friction error from command, control, and mechanical subsystems. Subsequently, the processes of presliding, acceleration, and adjustment stages are analyzed. Moreover, analytical formulas are derived to predict the durations of three stages and describe the shape of friction error. Then, the contour errors of linear and circular motion caused by friction can be predicted online. Experiments are introduced to verify the effectiveness of the proposed methods and formulations.

Contour Error Control of X-Y Platform Based on Nominal Model in Polar Coordinate System

In the case of the x-y linear motor platform, the contour error model of the nonlinear dynamic and curve trajectory is relatively complicated, and the traditional control system does not have the problem of systematic adjustment of parameters, and the precision of the contour is affected when machining. In this paper, the dynamic model of the system is modeled under the polar coordinate system, and the polar coordinate contour error nonlinear model of the linear motor x-y platform is obtained. At the same time, the nonlinear model application is based on the theory of sliding mode control, which makes the error of the system close to zero and can have good robustness. The theoretical derivation and simulation platform verification results show that the control system designed in this paper can improve the precision of the contour machining of the linear motor x-y platform.

Sensitivities of input parameters for predicting stability of soil slope

The infinite slope stability model is the basis for predicting the slope stability; however, the fundamental theory requires various input parameters. The objective of this study is to suggest a reasonable method for assuming input parameters in difficult measurement areas. The referred values are used to perform the sensitivity analysis, which found the influence degree of each parameter on the output result. Both slope angle and soil depth are shown to be highly affected parameters in the infinite slope stability model. To gather the real values of the slope angle, soil depth, and water table height, field tests are carried out and the remaining values are estimated from laboratory test results. The geostatistical method is applied to predict the distribution of input parameters over the entire study area based on the measured data, and the safety factor in the objective area is calculated. To observe fluctuations in the safety factor, the input parameter values are changed to single values representing the average, maximum, and minimum measured values. Then the contour map, histogram, and error ratios are established using the deduced safety factors. This study suggests considerations needed to determine the input parameters and a reasonable method when assuming factors.

Contour error–bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools

In this paper, a new generalized parametric interpolation method is proposed for optimized five-axis machining with the consideration of both the machine contour errors and the feedrate fluctuation elimination. An analytic processing is presented for linearization of contour errors with respect to feedrate limit. For machine configuration, explicit analytical modeling of the contour error and the tracking error with respect to feedrate is presented; thus, the error constraint problem is nicely converted to a kinematic constraint problem. On this basis, an accurate feedrate upper limit with confined contour errors is further determined by using a shifted Frenet frame with linear computational complexity. With the consideration of both the motion smoothness and machining efficiency, a time-based optimization algorithm is proposed for time-optimal feedrate scheduling. For eliminating the feedrate fluctuation, a new real-time interpolation algorithm is developed for free derivation between the path parameter and the arc length for smoothed five-axis tool path generation. Laboratory testing experiments were conducted for validation and were presented in the paper. And the experimental results indicate that the proposed feedrate interpolation method is capable of confining both the tool tip contour error and tool orientation contour error simultaneously, as well as maintaining a satisfactory interpolation performance in both computation efficiency and accuracy. The presented methods can be used for five-axis machining and the feedrate optimization of complex part machining.

Iterative NC program modification and energy saving for a CNC machine tool feed drive system with linear motors

This study proposes a design of iterative learning contouring controller (ILCC) by considering actual contour error compensation (ACEC) to enhance the contouring performance of CNC machine tool feed drive systems with linear motors. The ACEC with linear and circular interpolation is designed to estimates contour error precisely. The proposed control iteratively modifies the numerical control (NC) programs for each drive axis to reduce a contour error. Hence, the proposed approach can be directly applied for a commercial CNC machine tool with linear motors currently in use without any modification of their original controllers. Both of linear and circular interpolations are verified by simulation in both air-cutting and machining condition. The simulation is conducted for a non-smooth rhombus and circular trajectory. The effectiveness of the proposed methods has been experimentally verified through a CNC machine tool with linear motors for a non-smooth rhombus trajectory. Experimental results show that the proposed controller could reduce the maximum and mean contour errors by 94.58% and 88.67% on average, respectively. The proposed method improved the control input variance by 37.9%, and consequently energy consumption was reduced by 11.7% compared with the original NC program.

Measurement method of Wolter-I type mandrel based on a contact-type profilometer

Contraposing the surface quality testing of a Wolter-I type mandrel after ultraprecise turning, we propose a measuring method based on a contact-type profilometer and fabricate an adjusting device to assist in measurements. By coordinating probe translational motion in the Z and Y directions, this device provides 6 degrees of freedom. Extracting the feature point on the curve of a meridian section contour, the measurement data of the two aspherical surfaces that constitute a Wolter-I type mandrel can be segregated. This feature point is used as a reference point to make the measurement coordinate and machine coordinate systems coincide with each other in order to calculate the dimensional errors of the mandrel. By choosing samples of different lengths, some property indexes of the mandrel surface, such as roughness, waviness, and form error, can be extracted from the contour error signals via the wavelet transform method. This proposed method can solve the problem that the aspheric surface dimension error and contour form error of the Wolter-I mandrel surface cannot be measured by the profilometer when the aspheric reference vertex cannot be determined. Using this method, only one measuring instrument is required to evaluate the mandrel after diamond turning, which can improve the measurement efficiency, and cover the full spatial wavelength range from the figure error to the surface roughness. In addition, this method has the potential to achieve the in situ measurement of the surface of the Wolter-I type ultra-precision mandrel.

A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision.

Periodic health checks of contouring errors under unloaded conditions are critical for machine performance evaluation and value-added manufacturing. Aiming at breaking the dimension, range and speed measurement limitations of the existing devices, a cost-effective knowledge-driven approach for detecting error motions of arbitrary paths using a single camera is proposed. In combination with the PNP algorithm, the three-dimensional (3D) evaluation of large-scale contouring error in relatively high feed rate conditions can be deduced from a priori geometrical knowledge. The innovations of this paper focus on improving the accuracy, efficiency and ability of the vision measurement. Firstly, a camera calibration method considering distortion partition of the depth-of-field (DOF) is presented to give an accurate description of the distortion behavior in the entire photography domain. Then, to maximize the utilization of the decimal involved in the feature encoding, new high-efficient encoding markers are designed on a cooperative target to characterize motion information of the machine. Accordingly, in the image processing, markers are automatically identified and located by the proposed decoding method based on finding the optimal start bit. Finally, with the selected imaging parameters and the precalibrated position of each marker, the 3D measurement of large-scale contouring error under relatively high dynamic conditions can be realized by comparing the curve that is measured by PNP algorithm with the nominal one. Both detection and verification experiments are conducted for two types of paths (i.e., planar and spatial trajectory), and experimental results validate the measurement accuracy and advantages of the proposed method.

Virtual prediction and constraint of contour errors induced by cutting force disturbances on multi-axis CNC machine tools

This paper presents a strategy to virtually predict and constrain the contouring errors contributed by cutting force disturbances on feed drives. The tracking errors on each feed drive are predicted as a linear function of tangential feed by evaluating the product of estimated power spectrum of cutting forces and disturbance frequency response function along the tool path in virtual CAM environment. The corresponding tool tip contouring and tool axis orientation errors are estimated and constrained by scaling the feed along the tool path. The algorithm is experimentally illustrated to improve the machining accuracy on a 5 Axis CNC machine tool.

Synthesis of the neural coordinated control algorithm for the model of CNC machine

Objectives: Increase quality factor of the CNC machine model in comparison with the Uncoupled System by synthesizing Neural Coordinated Control. Synthesis: We synthesized the Neural Coordinated Control algorithm based on the coordinated control algorithm and neural control. Experiment: Using mathematical modeling we compared the synthesized algo-rithms and the uncoupled system using the following criteria: contour error, contour speed error, and score function. Results: The four NCC algorithms were synthesized and trained. The experiment shows that synthesized algorithms have better score function values and better quality factor values in comparison to the reference Uncoupled System. Conclusion: The quality factor of the CNC machine model was successfully in-creased by using the synthesized Neural Coordinated Control algorithm.

Measurement and compensation of diamond tool’s contour error by using a white light interferometer for ultra-precision turning of freeform surfaces

Measurement and compensation of diamond tool’s contour error by using a white light interferometer for ultra-precision turning of freeform surfaces

Binocular Vision-based Three-dimensional Contouring Error Calibration Method for NC Machine Tools

Binocular Vision-based Three-dimensional Contouring Error Calibration Method for NC Machine Tools

Precise Contour Control of Biaxial Motion System Based on MPC

In order to realize accurate and fast contour tracking of biaxial motion system and ensure the smoothness of its path, this paper proposes a model predictive contour control strategy suitable for biaxial system based on the idea of unified modeling. The two permanent magnet synchronous motors driving the biaxial system are considered as a whole to build a unified model. Based on the unified model, a compact model predictive controller is designed, where the contour error, the tracking error, the control increment and the position increment are introduced into the cost function simultaneously, realizing the multivariable collaborative optimization control. In addition, to obtain the better dynamic response and steady-state performance, a method of real-time adaptive adjustment of the position increment weight coefficient and the control increment weight coefficient is proposed. At the same time, considering the constraints, a posteriori constraint limitation network with the current control increment is proposed. Furthermore, the closed-loop stability analysis of the model predictive contour control system is carried out according to the optimal control principle. The experimental results show that the proposed control strategy can not only track the trajectory accurately at steady state, but also improve the transient contour tracking performance.

Monocular-vision-based contouring error detection and compensation for CNC machine tools

Contouring error detection for machine tools can be used to effectively evaluate their dynamic performances. For the state-of-the-art non-vision measurement devices, they have limitations on arbitrary and high cross-scale contouring error measurement (e.g., ball-bar and cross-grid encoder). Besides, error motions of irrelevant axes are inevitably introduced in the measurement process (e.g., ball-bar, R-test). The vision-based method provides a promising way to address the problems. In this paper, to further the study, a cost-effective monocular-vision-based two-dimensional arbitrary contouring error detection method is proposed. Compared to the existing vision-based method, the main progress is to use the idea of error distribution to simultaneously extend the measurable working range and traverse speed. The basic idea of the proposed method is to improve the measurable traverse speed by sacrificing field of view (FOV), and to deduce the wide range contouring error using priori information. Both experiments for the detection and compensation of contouring error are performed in a CNC machine tool. The contouring error detection results, in contrast to the cross-grid encoder, show that the average detecting error at feed rate of 5000 mm/min is about 4 μm, which verifies measurement accuracy and feasibility of the proposed method. Besides, the compensation results show that the maximum and average contouring error measured after compensation at 5000 mm/min decrease by 66.39% and 56.47%, respectively, which validate the potential of the proposed method in effectively improving machine tool's dynamic performance.

Neural Network-Based Real Time PID Gain Update Algorithm for Contour Error Reduction

In this study, a novel neural network-based proportional-integral-derivative (PID) controller gain update algorithm is presented. The proposed algorithm aims to improve the machining quality and efficiency by adjusting the PID gains in real time in order to minimize the contour error. Automatic PID gain tuning algorithms are desired as it can increase the machining efficiency while improving the machining quality. Unlike conventional tracking error-based PID gain update algorithms, the proposed algorithm is based on the contour error and thus, it is more suitable for machine tools. Furthermore, the contour error-based approach enables a scalar representation of the system errors, which leads to a significant reduction in the required computational load. Compare to conventional neural network-based gain tuning algorithms, which often requires two neural networks per axis for automatic PID gain update, the proposed algorithm can update the gains of the a multi-axis system using a single neural network. The experimental results with a 3-degrees of freedom (DOF) Cartesian machine shows a clear reduction in both the contour and tracking errors.