Contour Error Compensation Research Articles

Real-time arc length parameter-based integrated control strategy of contour error compensation for free-form curve CNC machining

Real-time arc length parameter-based integrated control strategy of contour error compensation for free-form curve CNC machining

Research on a novel integrated control strategy for contour error compensation of biaxial CNC machining

Research on a novel integrated control strategy for contour error compensation of biaxial CNC machining

A Feedrate Planning Method in CNC System Based on Servo Response Error Model

Reducing servo response error and further making reduction on contour error is crucial for high-precision computer numerical control (CNC) machine tools. For a permanent magnet synchronous motor (PMSM) servo system, there is always a response lag in feedrate tracking, which would introduce response error into the machining trajectory. Therefore, it is necessary to improve the performance of feedrate planning and interpolation for trajectory path. In this paper, a novel contour error compensation strategy is proposed. Compared with the mainstream methods, the proposed method offers a simplified alternative to existing contour error estimation techniques. Through a three-closed-loop control structure of a PMSM servo system, a response error model is founded. Afterwards, an improved S-model feedrate planning method is introduced according to the servo response error compensation. This predicted error is subsequently compensated in each interpolation cycle, resulting in a reduction of contour error. Finally, simulations and experiments are performed to demonstrate that the contour error can be reduced in both the ‘∞’-shaped Non-Uniform Rational B-Spline (NURBS) curve path and the butterfly-shaped NURBS curve path using the proposed method.

Application of fuzzy control based feed rate strategy design in NC machining error automatic compensation

With the continuous development of manufacturing industry, the application range of NC machining technology has been further expanded. The contour accuracy is strongly related to the NC machining quality as a key machine tool performance indicator. Its application efficiency is plainly low as the majority of offline compensation-based contour accuracy adjustments rely heavily on manual experience. Moreover, the isolated research on automatic error compensation and its combination with algorithms does not start with the characteristics of contour accuracy in data processing. Therefore, based on the advantages of strong the robustness of the fuzzy algorithm and the high effectiveness of parameter adjustment, an automatic compensation method for NC machining contour error based on fuzzy control is proposed. The contour error prediction model is designed according to the machining path, and then the automatic compensation strategy for contour error under fuzzy control is designed based on the feed speed. The results showed that under this method, the contour error can reach a maximum of 0.06 and a minimum of 0.025, which was 0.015 lower than the minimum contour error of genetic algorithm. This indicated that the method greatly reduced the CNC machining contour error and improved the contour accuracy, as well as reducing the time cost of contour error compensation, improving the efficiency of contour error compensation, and realizing the automation of error compensation control capability. This is helpful for advancing CNC machining automation technology and supporting the intelligent development of machinery manufacturing.

Real-time estimate and control contour errors for five-axis local smoothed toolpaths based on airthoid splines

Five-axis linear commands are blended as the local smoothed toolpaths by inserting clothoid and airthoid splines at corners in five-axis CNC machining. The contour error is the bottleneck to achieve the precise dimension of the machined parts, when following the local smoothed toolpaths. This paper presents a contour error estimation and control method for the five-axis smoothed toolpaths with airthoid splines, according to the geometric characteristics of the toolpaths. The tool-tip contour error is analytically calculated based on the expression of the smoothed toolpaths. Consequently, the tool-orientation contour error is obtained by synchronizing the tool-orientation contour point with the tool-tip item based on the motion time through the designed time scale coefficient, when the toolpaths are scheduled by the time-synchronization scheme. Furthermore, a contour error compensation strategy is constructed to adaptively determine the compensator gain. It can be qualified to maximally eliminate the contour errors and steadily hold the control stability of the feed drives, in spite of the modeling error between the nominal and actual control models. The simulation and experiment results show that the estimation algorithm has higher accuracy than traditional methods, and the compensation strategy effectively eliminates the five-axis contour error.

Five-Axis Contour Error Control Based on Numerical Control Data

Improving contour accuracy is one of the significant goals of industrial machining. This paper proposes a contour error estimation and compensation algorithm for five-axis computer numerical control (CNC) machine tools based on modified numerical control (NC) codes. The expected path analyzed by NC data and the actual trajectory collected by sensors are spatially mapped by the hidden Markov model (HMM). Next, an evaluation function that hybrids the tool tip position and tool orientation change trend is proposed as the index of contour error estimation. Finally, spatial iterative learning control (ILC) is used to compensate the contour error, and high-precision machining instructions are obtained after multiple iterations. Experiments with different trajectories are performed on a five-axis platform to verify the proposed algorithm’s effectiveness. The results show that the proposed algorithm without using planned trajectories, has the same good control effect as traditional methods, which must know the planning trajectory for simple trajectories. At the same time, the method proposed in this paper has better performance than existing algorithms based on tool tip position nearest principle at sharp corners. In conclusion, on the basis of not depending on the planning trajectories, this method has a better compensation effect for the overall accuracy of trajectories and is easier to implement in industrial applications.

Adaptive nonsingular terminal sliding mode control of robot manipulator based on contour error compensation

To achieve accurate contour tracking of robotic manipulators with system uncertainties, external disturbance and actuator faults, a cross-coupling contour adaptive nonsingular terminal sliding mode control (CCCANTSMC) is proposed. A nonsingular terminal sliding mode manifold is developed which eliminates the singularity completely. In order to avoid the demand of the prior knowledge of system uncertainties, external disturbance and actuator faults in practical applications, an adaptive tuning approach is proposed. The stability of the proposed control strategy is demonstrated by the finite-time stability theory. Then, the developed controller combines adaptive nonlinear terminal sliding mode control (ANTSMC) of joint trajectory tracking and proportion–differentiation control of end-effector contour tracking by introducing the coupling factor between multiple axes based on Jacobian. Moreover, a unified framework of cross-coupling contour compensation and reference position pre-compensation is built. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control strategy.

Five-Axis Contour Error Control Based on Spatial Iterative Learning

In this paper, a contour error control strategy based on spatial iterative learning control (sILC) is developed for repetitive processing of five-axis computer numerical control (CNC) machine tools. A curve approximation method with an adaptive moving window is developed to achieve accurate tool position and orientation contour error estimation, and a five-axis contour error control strategy based on sILC is proposed. The compensation method is derived using an sILC algorithm to modify the geometric reference path instead of modifying the controller. The experimental results show that the proposed control strategy reduces contour errors of five-axis CNC machine tools, and it outperforms the traditional tracking error control. Note to Practitioners—This paper aims to propose an effective five-axis contour error control scheme. At present, most of the five-axis contour error control methods rely on the modification of the controller, which is not allowed in commercial CNC systems. Therefore, we propose a five-axis contour error compensation algorithm based on sILC, which modifies the system’s reference path. Experimental results show that the proposed method can reduce the five-axis contour errors, while maintaining the machining efficiency.

Contour error modeling and compensation of CNC machining based on deep learning and reinforcement learning

Contour error compensation of the computer numerical control (CNC) machine tool is a vital technology that can improve machining accuracy and quality. To achieve this goal, the tracking error of a feeding axis, which is a dominant issue incurring the contour error, should be firstly modeled and then a proper compensation strategy should be determined. However, building the precise tracking error prediction model is a challenging task because of the nonlinear issues like backlash and friction involved in the feeding axis; besides, the optimal compensation parameter is also difficult to determine because it is sensitive to the machining tool path. In this paper, a set of novel approaches for contour error prediction and compensation is presented based on the technologies of deep learning and reinforcement learning. By utilizing the internal data of the CNC system, the tracking error of the feeding axis is modeled as a Nonlinear Auto-Regressive Long-Short-Term Memory (NAR-LSTM) network, considering all the nonlinear issues of the feeding axis. Given the contour error as calculated based on the predicted tracking error of each feeding axis, a compensation strategy is presented with its parameters identified efficiently by a Time-Series Deep Q-Network (TS-DQN) as designed in our work. To validate the feasibility and advantage of the proposed approaches, extensive experiments are conducted, testifying that our approaches can predict the tracking error and contour error with very good precision (better than about 99% and 90% respectively), and the contour error compensated based on the predicted results and our compensation strategy is significantly reduced (about 60~85% reduction) with the machining quality improved drastically (machining error reduced about 50%).

Gain parameters optimization strategy of cross-coupled controller based on deep reinforcement learning

In this article, a deep reinforcement learning-based strategy for the optimization of gain parameters of a cross-coupled controller is proposed. First, to compensate the contour error caused by servo lag, a proportional–integral (PI)-type cross-coupled controller is designed, with its gain parameters being determined using the cut-off frequency of the contour error transfer function. Next, on the basis of a deep reinforcement learning algorithm, a neural network structure suitable for contour error compensation is established, through which the optimal gain parameters are obtained. Finally, some experiments are carried out, in which the optimal gain parameters sought through off-line learning schemes are applied to the biaxial motion control. The results indicate that the proposed gain parameters optimization strategy can effectively converge the gain parameters with the optimal intervals, and that the optimal gain parameters obtained by the proposed strategy can significantly improve the contour control accuracy in biaxial contour tracking tasks.

Dynamic contour error compensation in micro/nano machining of hardened steel by applying elliptical vibration sculpturing method

In this study, a novel dynamic contour error compensation technique has been proposed for the elliptical vibration cutting process achieved through the ultra-precision amplitude control. The influence of the contour error, triggered due to the inertial vibrations of the friction-less feed drive system, on the machining accuracy deterioration has been experimentally investigated. In order to reduce the contour error, a compensation method utilizing a real-time amplitude control in the elliptical vibration cutting process has been applied. In the proposed method, the dynamic motion error along the depth of cut direction is detected by utilizing the precise linear encoders installed on the feed drive system. The motion error in real-time is subsequently converted into cancelling amplitude command for the vibration control system of the ultrasonic vibrator, thus, guaranteeing that the envelope of the vibration amplitudes auto-tracks the dynamic reference position of the motion axis in the depth of cut direction. Due to this, a constant nominal depth of cut can be obtained even though the inertial vibrations disturb the feed drive control during machining. A series of experimental investigations have been conducted in order to analyze the machining performance by employing the proposed method. The maximum machining error is observed to significantly decrease from 0.6 to 0.04 μm by applying the proposed compensation method. Finally, the micro dimple array with a structural height from about 200 to 600 nm could be accurately fabricated with a maximum machining error of 36.8 nm, which verified the feasibility of the proposed amplitude control compensation method.

Prediction and Compensation of Contour Error of CNC Systems Based on LSTM Neural-Network

This article proposes a contour error estimation (CEE) and compensation method for computer numerical control (CNC) systems based on the long short-term memory neural network. This is achieved by performing modeling of each axis to predict the tracking error, calculating the actual trajectory, estimating the contour error, and modifying the reference trajectory. First, linear feature selection based on a simplified single-axis model and nonlinear feature selection based on a circular test are performed to achieve tracking error prediction. Then, a spline-approximation-based CEE method is proposed to estimate the contour error between the reference trajectory and the predicted trajectory. Finally, contour error compensation is performed on the reference trajectory before it is run on CNC systems. The proposed method is validated through experiments on a three-axis CNC system.

Residual learning of the dynamics model for feeding system modelling based on dynamic nonlinear correlate factor analysis

Feeding system modelling is the foundation for control strategy optimization, contour error compensation, etc., to improve the productivity and quality of a part. This paper proposes a novel residual learning approach for fitting the simulation error of the dynamics model of a machine tool feeding system. Then, the feeding system model consisting of the dynamics model and the residual model is constructed by integrating prior knowledge with statistical learning knowledge. The residual model is trained by using the training dataset generated from the dynamics model instead of using only the input and output data (i.e., the end-to-end data). In addition, a dynamic nonlinear correlate factor extraction method is proposed to extract the training dataset from the dynamics model and the reference data. Compared to the end-to-end data, the training dataset knows very well about the system’s nonlinear features owing to the internal prior knowledge of the dynamics model. Experiments conducted on a vertical milling centre confirm the effectiveness of the feeding system model in dynamic response prediction. Compared to the existing dynamics or data-driven modelling method, the proposed method can achieve higher prediction accuracy in nonlinear motion processes, such as the reverse process, and can obtain stable performance with respect to different feedrates owing to the residual learning approach.

Prediction-Model-Based Contouring Error Iterative Precompensation Scheme for Precision Multiaxis Motion Systems

In order to achieve both accurate contouring error estimation and excellent contouring control performance for multiaxis motion systems, this article proposes an online iterative precompensation control method based on a third-order contouring error prediction model. Specifically, the closed-loop dynamical model of each axis is first used to predict tracking errors at future sampling instants. And then the related contouring error of the multiaxis system at future time can be expressed by the predicted tracking error and the theoretical third-order model of the reference contour. To reduce the influence of modeling error and uncertain disturbances on the prediction performance of contouring error, the numerical calculation method is utilized to obtain absolutely accurate contouring error, through which the deviation between the proposed contouring error model and the accurate one can be corrected accordingly. Based on the accurate contouring error prediction model, the optimal contouring error compensation can be generated through online iterative calculation. To achieve excellent contouring performance, the compensation is added to the original reference contour as a kind of trajectory precompensation. Comparative experiments are carried out on an industrial three-axis machine tool. A series of contour tracking experiments consistently demonstrate that the proposed method can predicate the contouring error accurately. Additionally, the contouring motion performance can also be significantly improved in the case of a variety of different trajectories.

A feedrate optimization method for CNC machining based on chord error revaluation and contour error reduction

Interpolation of parametric curves is one of the most effective methods in high-performance computer numerical control (CNC) machining. Its precision highly depends on chord errors from feedrate scheduling and contour errors from real-time machining. In order to improve machining precision, a novel feedrate optimization method is proposed in this paper. The osculating circle (OC) method can effectively estimate the chord errors, but its precision degrades if the trajectory curvature changes dramatically. Therefore, an iterative algorithm based on OC method is developed to reevaluate the chord errors, which can upgrade the estimation precision and further improve the feedrate constraints. To reduce the contour error, feature zones on the trajectory are firstly selected according to the kinestates and a specified zone length. In each feature zone, the projection of tracking error onto the zone chord-line is calculated as a new vector, based on which an indirect contour error compensation method is proposed through refining the feedrate profile. To ensure that the contour error can be reduced, the compensation performance is pre-estimated before implementation. Finally, simulation results in different scenarios are presented to validate the high precision of the proposed method.

Chord error constraint based integrated control strategy for contour error compensation

As the traditional cross-coupling control method cannot meet the requirements for tracking accuracy and contour control accuracy in large curvature positions, an integrated control strategy of cross-coupling contour error compensation based on chord error constraint, which consists of a cross-coupling controller and an improved position error compensator, is proposed. To reduce the contour error, a PI-type cross-coupling controller is designed, with its stability being analyzed by using the contour error transfer function. Moreover, a feed rate regulator based on the chord error constraint is proposed, which performs speed planning with the maximum feed rate allowed by the large curvature position as the constraint condition, so as to meet the requirements of large curvature positions for the chord error. Besides, an improved position error compensation method is further presented by combining the feed rate regulator with the position error compensator, which improves the tracking accuracy via the advance compensation of tracking error. The biaxial experimental results of non-uniform rational Bsplines curves indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy in biaxial contour following tasks.

A New Analytical Path-Reshaping Model and Solution Algorithm for Contour Error Pre-Compensation in Multi-Axis Computer Numerical Control Machining

Abstract Reduction of contour error is crucial for multi-axis computer numerical control (CNC) machining to produce products with required geometric and dimensional accuracy. Although various contour error pre-compensation methods have been developed, few studies are dedicated to five-axis machines when compared with three-axis ones. In this paper, a new contour error pre-compensation method that integrates analytical prediction of contour error, optimal path-reshaping model, and decoupling solution algorithm is proposed for five-axis machining. First, by analyzing the dynamic responses of servo drive to the typical step and ramp signals, linear expression of servo tracking error with respect to the sequence of discrete axis positions is yielded for the prediction of contour error ahead of servo loops. Then, using the Taylor-series expansion and the pseudo-inverse matrix of the Jacobian function, a least-square optimization-based path-reshaping model that implies the satisfaction condition of zero contour error is analytically built. Thus, the complicated nonlinear contour error pre-compensation problem is converted into a simple quadratic programming problem. Concerning the effects of tool orientation reshaping on tool-tip contouring accuracy, a simple yet effective synchronous compensation strategy is subsequently proposed, through which both tool tip and tool orientation contour errors are reduced to near-zero without any iteration. To address the neighbor-dependence of the contour error compensation in adjacent cutter locations, a progressive solution algorithm with linear computational complexity is also briefly presented. Both numerical simulations and laboratorial experiments are conducted to validate the effectiveness of the proposed method.

A Practical Method of Modelling and Simulation for Ball End Mill CNC Grinding

The spherical cutting edge on the ball end mill directly affects its cutting performance. This paper presents a practical method for end mill rake/clearance face modelling. The rake face is a developed ruled surface to fulfill the desired normal rake angle. Revolution surface of the bottom curve on the rake face avoids the interference between the wheel with the designed rake face while grinding. An equidistance curve of the cutting edge on the sphere is deduced by the geodesic curve in order to adjust the position of the cutting edge. With this new modelling method as a platform, it is very helpful for model modification and contour error compensation. The measurement results show that the average value of contour error on spherical cutting edge of the machined sample is 0.01mm inspected by the tool measuring instrument. Its validity is verified by good agreement between the results computed and the data measured.

Real-time machining data application and service based on IMT digital twin

With the development of manufacturing, machining data applications are becoming a key technological component of enhancing the intelligence of manufacturing. The new generation of machine tools should be digitalized, highly efficient, network-accessible and intelligent. An intelligent machine tool (IMT) driven by the digital twin provides a superior solution for the development of intelligent manufacturing. In this paper, a real-time machining data application and service based on IMT digital twin is presented. Multisensor fusion technology is adopted for real-time data acquisition and processing. Data transmission and storage are completed using the MTConnect protocol and components. Multiple forms of HMIs and applications are developed for data visualization and analysis in digital twin, including the machining trajectory, machining status and energy consumption. An IMT digital twin model is established with the aim of further data analysis and optimization, such as the machine tool dynamics, contour error estimation and compensation. Examples of the IMT digital twin application are presented to prove that the development method of the IMT digital twin is effective and feasible. The perspective development of machining data analysis and service is also discussed.

Iterative learning contouring controller based on trajectory generation with linearly interpolated contour error estimation and Bézier reposition trajectory for computerized numerical control machine tool feed drive systems

In industrial applications, highly accurate mechanical components are generally required to produce advanced mechanical and mechatronic systems. In machining mechanical components, contour error represents the product shape quality directly, and therefore it must be considered in controller design. Although most existing contouring controllers are based on feedback control and estimated contour error, it is generally difficult to replace the feedback controller in commercial computerized numerical control machines. This article proposes an embedded iterative learning contouring controller by considering the linearly interpolated contour error compensation and Bézier reposition trajectory, which can be applied in computerized numerical control machines currently in use without any modification of their original feedback controllers. While the linearly interpolated contour error compensation enhances tracking performance by compensating the reference input with an actual value, the Bézier reposition trajectory enables smooth velocity transitions between discrete points in the reference trajectory. For performance analysis, the proposed controller was implemented in a commercial three-axis computerized numerical control machine and several experiments were conducted based on typical three-dimensional sharp-corner and half-circular trajectories. Experimental results showed that the proposed controller could reduce the maximum and mean contour errors by 45.11% and 54.48% on average, compared to embedded iterative learning contouring controller with estimated contour error. By comparing to embedded iterative learning contouring controller with linearly interpolated contour error compensation, the maximum and mean contour errors are reduced to 20.54% and 26.92%, respectively.