Contour Error Estimation Research Articles

Accurate three-dimensional contouring error estimation and compensation scheme with zero-phase filter

Abstract Contour following is an important research topic for multi-axis CNC systems. In this paper, to simultaneously meet the challenges of accurate contouring error estimation and high-performance contouring control those are very significant for three-dimensional contouring following tasks, a numerical calculation based contouring error estimation and contour compensation scheme is proposed. Unlike any existing geometric approximation methods, the proposed scheme calculates the contouring error through a numerical calculation algorithm. Specifically, a cost function is defined as the spatial distance between the actual point and the point located on the reference contour. When the minimum value of the cost function is obtained through the numerical calculation, accurate contouring error vector can be obtained even under extreme contouring tasks with high-speed, large-curvature and sharp-corner. Then, the calculated contouring error is projected to each axis. After a zero-phase filter with low-pass characteristic, the axial contouring error is fed back to the corresponding axis as a kind of contour compensation. The added filter can effectively suppress the high-frequency noise widely existing in contouring error signal. Moreover, our proposed contour compensation scheme can be realized iteratively for further improvement of contouring performance. Various comparative experiments are performed to verify the effectiveness of the proposed contouring error estimation and compensation scheme. The results demonstrate that in comparison with traditional position loop CCC method, the proposed scheme can achieve not only nearly perfect contouring error estimation but also obvious promotion of contouring accuracy.

A novel dynamic contour error estimation and control in high-speed CNC

High-speed CNC machining requires high-precision servo response and dynamic performance of feed drives with better control parameters matched in coupled axis. In this paper, an electromechanical coupling system of multi-axis CNC machine tool feed drive model is established for servo parameter optimization and high-precision contour error improvement. The influences of the joint stiffness and the friction disturbance in servo dynamic have been considered. The disturbance parameter and joint stiffness have been identified by unbiased least squares scheme. The electromechanical coupling model is used to study the contour error estimation and compensation technology in high-speed machining. The multi-axis contour error is estimated by using Ferguson curve to approximate the curve between the interpolation points. The calculation is fast and accurate enough for contour error pre-compensation. Experiments prove that five-axis contour error can be effectively reduced by dynamics pre-compensation in high-speed CNC with better processing quality and stability improvement.

Contouring compensation control based on high accuracy contour error estimation for multi-axis motion systems

Multi-axis motion systems have been widely applied in industrial fields, and the contour error is an important indicator to measure the quality of the products. Contour error is defined as the orthogonal deviation of actual position from the desired tool path, and contouring control is a very useful method to reduce or eliminate it. In this study, by finding the reference point nearest to the current actual position, and then projecting the actual position onto the osculating plane at this reference point, a high-accuracy contour error estimation method is proposed. When the estimated contour error cannot be described as an analytic expression of tracking errors, the cross-coupling control (CCC) is not applicable. And, task coordinate frame approach (TCFA) has a relatively complex computation. In order to overcome these shortcomings, by compensating the axis component of contour error into each loop of the servo motor simultaneously, a simple and effective contouring compensation control method is proposed. Experiments are carried out on a real-time in-house-developed multi-axis motion system. The results show that the contour error estimated by using the proposed method is close to the true one, and the proposed contouring control method can achieve the proportional reduction of the contour error effectively.

Dual sliding mode contouring control with high accuracy contour error estimation for five-axis CNC machine tools

Five-axis CNC machine tools are widely used in the manufacturing of the complex parts, and the contour error is the key indicator for the accuracy of the final product. Contour error, by definition, is a geometrical quantity solely dependent on the current actual tool pose and the reference trajectory. Contouring control is the main method to reduce or eliminate it. In this paper, based on the geometrical information of the reference trajectory, a high accuracy contour error estimation method for five-axis machine tools is proposed. Then, to avoid the time-consuming calculation of the inverse and derivative of the Jacobian matrix, to reduce tracking and contour errors simultaneously as well as suppress the chattering in the control signal, a dual sliding mode contouring control method is proposed. The dual sliding surface is selected for each drive separately, which integrates the traditional PD-type tracking sliding surface, a PD-type contouring sliding surface consisting of the axis component of the contour errors, and the input signal together. Experiments are conducted on a tilting-rotary-table type five-axis CNC machine tool. The results demonstrate that the contour errors estimated using the proposed method are very close to the true ones, and compared with the traditional sliding mode controller, the proposed method can reduce the contour error and the chattering behavior effectively.

Design and analysis of a modular learning based cross-coupled control algorithm for multi-axis precision positioning systems

Increasing demand for micro/nano-technology related equipment resulted in growing interest for precision positioning systems. In this paper a modular controller combining cross-coupled control and iterative learning control approaches to improve contour and tracking accuracy at the same time is presented. Instead of using the standard error estimation technique, a computationally efficient and modular contour error estimation technique is used. The new controller is more suitable for tracking arbitrary nonlinear contours and easier to implement to multi-axis systems. Stability and convergence analysis for the proposed controller is presented with the necessary conditions. Effectiveness of the control design is verified with simulations and experiments on a two-axis positioning system. The resulting positioning system achieves nanometer level contouring and tracking performance.

Real time parameter based contour error estimation algorithms for free form contour following

The contour following task of a multi-axis servo system is one of the most important applications of modern Computer Numerical Control (CNC) machine tools, and is widely seen in many types of CNC machining. Hence, the reduction of contour error occurring in the contour following process is paramount and deserves more comprehensive investigation. In general, the calculation of precise contour error in real time is very challenging if not impossible, in free-form curve following tasks. To deal with such a problem, this paper proposes six real-time contour error estimation methods for free-form parametric curves. The feasibility of these methods is verified with several NURBS parametric curve contour following experiments. In addition, experimental results reveal that the proposed methods can provide more accurate contour error estimation for various free-form curves than the other estimation algorithms tested in the experiments. With the proposed contour error estimation approach, advanced motion control schemes can be designed to efficiently reduce contour errors of contour following tasks.

A generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes

High-accuracy contouring error estimation is the premise of effective contouring error control. However, two key factors make it complex to estimate contouring error for multi-axis machines with rotary axes: the nonlinear kinematics and the synchronization requirement of the tool tip position and tool orientation. This paper proposes a generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes. The nearest reference tool pose to the actual one is searched at first, and then the corresponding contouring error components on each axis are estimated by using linear ratio estimation, where the tool tip position and tool orientation are naturally synchronized to one same pose on the desired trajectory. The advantage of the proposed contouring error estimation algorithm is that only the interpolated reference poses and drive commands are needed in the calculation, which increases the generality of the algorithm to different trajectory types and machine topologies. On the other hand, the calculation load is reduced when compared with existing iterative multi-axis contouring error estimation approaches. Simulation results on both five- and four-axis machines show that the proposed contouring error estimation algorithm can estimate axis components of contouring errors with high accuracy. Experiment results on an in-house developed five-axis experiment platform verify the effectiveness of the proposed algorithm.

Cross-coupled controller design for triaxial motion systems based on second-order contour error estimation

The cross-coupled control (CCC) is widely applied to reduce contour errors in contour-following applications. In such situation, the contour error estimation plays an important role. Traditionally, the linear or second-order estimation approach is adopted for biaxial motion systems, whereas only linear approach is available for triaxial systems. In this paper, the second-order contour error estimation, which was presented in our previous work, is utilized to determine the variable CCC gains for motion control systems with three axes. An integrated stable motion control strategy, which combines the feedforward, feedback and CCC controllers, is developed for multiaxis CNC systems. Experimental results on a triaxial platform indicate that the CCC scheme based on the second-order estimation, compared with that based on the linear one, significantly reduces the contour error even in the conditions of high tracking feedrate and small radius of curvature.

A tool path generation and contour error estimation method for four-axis serial machines

Although four-axis machines are widely used in welding, carving, and cutting revolving parts, much fewer four-axis tool path generation and contour error estimation researches have been studied when compared with five-axis ones. This paper proposes an off-line tool path generation and an on-line contour error estimation method for four-axis serial machines that are used for welding spatial intersecting curves on revolving parts. First, the kinematics module is derived, followed by proposing the tool path generation algorithm. The tool tip positions are represented by using a third order B-spline, while the tool orientations are represented by a third order polynomial-spline. Both splines, which form the C2 continuous tool path, are fitted to the curve length parameter of the tool tip positions. When compared with existing multi-axis trajectory generation methods, the proposed method is greatly simplified by mapping the tool pose commands from the Cartesian coordinate frame to the cylindrical coordinate frame. In the proposed contour error estimation method, the tool tip position contour error is estimated at first, followed by calculating the relative tool orientation contour error which is synchronized with the tool tip position contour error to one same pose on the desired trajectory. The proposed tool path generation and contour error estimation methods are experimentally verified on a four-axis welding machine controlled by an in-house developed CNC system. Experiment results show that the desired trajectory can be tracked continuously and steadily. The contour error can be estimated with high accuracy and reduced by 50% after performing on-line compensation.

A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools

Nonlinear and configuration-dependent five-axis kinematics make contouring errors difficult to estimate and control in real time. This paper proposes a generalized method for the on-line estimation and control of five-axis contouring errors. First, a generalized Jacobian function is derived based on screw theory in order to synchronize the motions of linear and rotary drives. The contouring error components contributed by all active drives are estimated through interpolated position commands and the generalized Jacobian function. The estimated axis components of contouring errors are fed back to the position commands of each closed loop servo drive with a proportional gain. The proposed contouring error estimation and control methods are general, and applicable to arbitrary five-axis tool paths and any kinematically admissible five-axis machine tools. The proposed algorithms are verified experimentally on a five-axis machine controlled by a modular research CNC system built in-house. The contouring errors are shown to be reduced by half with the proposed method, which is simple to implement in existing CNC systems.

Cross-coupled Controller Based on High-precision Contouring Error Estimation

Cross-coupled Controller Based on High-precision Contouring Error Estimation

Multiaxis Contour Control—the State of the Art

Contour control is an important task for many motion control applications. This paper reviews the state-of-the-art control methods in academic research for contour tracking, including individual axis tracking control, cross coupled control and its variants, and other contour control methods, such as neural networks and velocity field control. Different methods for contour error estimation are also reviewed. Areas for future multiaxis contour control research are discussed.

Adaptive Error Control Algorithm for High Speed Two-Axis CNC Contouring

The computerized numerical control (CNC) machining program usually contains a large number of small line segments. The CNC controller must generate a smooth and optimized motion profile to achieve high speed and high precision machining. This paper proposed an adaptive contour error control algorithm. The curvature radius of the tool path is obtained by analyzing the geometry relationship. The algorithm uses the curvature information and a simplified servo error model to realize contour error estimation and adaptive control. The target feet rate filter (TFF) and planning unit merging (PUM) are introduced to obtain a smooth profile. Experiments result demonstrated the efficiency of the proposed algorithm.

Real-time contouring error estimation for multi-axis motion systems using the second-order approximation

To reduce contour error in contour-following tasks, a common approach is to design a controller based on the contour error information. Hence, real-time contouring error estimation plays an important role in contour-following control. However, the available second-order estimation formulas only apply to biaxial motion systems, and cannot be generalized to handle arbitrary contours tracked by multi-axis motion systems. In this paper, a point-to-curve distance function is defined, and its properties are investigated, especially, its second-order Taylor approximant is derived. On this basis, a novel second-order approach for calculating contour errors of arbitrary contours in real time is proposed. The inter-correlations between the present approach and four commonly used ones are classified. Simulation and experimental results demonstrate the effectiveness of the proposed contour error estimation algorithm.

Free-Form Two-Dimensional Contour Error Estimation Based on NURBS Interpolation

Contouring control is in wide use in the manufacturing industry. To achieve accurate contouring control, accurate control error estimation is necessary. However, for free-form contours, there is a lack of effective algorithms for accurately estimating contour errors. This paper proposes a new algorithm for contour error estimation based on NURBS interpolation (CEEBNI). The reference input points closest to the current position is searched. Based on the NURBS interpolation, certain discrete reference input points are then used to reconstruct the NURBS curve. Finally, the contour error is estimated based on the minimum distance between the current position and this NURBS curve. Simulation results indicate that proposed algorithm gives excellent result in the estimation of the contour error.

Iterative Learning Cross-Coupled Control for XY Table Based on Real-Time Contour Error Estimation

The contour accuracy of XY table directly driven by two linear motors was influenced by the complicated reel-time contour error model of free-form curves, uncertainty external disturbance and dynamic matching between X axis and Y axis. To establish XY table model that easily calculated and suitable for free-form curves, real-time contour error estimate method was adopted. In order to reduce uncertainty external disturbance and dynamic matching between X axis and Y axis, the iterative learning cross-coupled controller (ILCCC) was designed for current compensation on X axis and Y axis. Simulation results show that the control scheme can enhance the robustness of the system, and effectively improve the XY table of contour precision.

Performance analysis of cross-coupled controllers for CNC machines based upon precise real-time contour error measurement

Experimental results from the implementation of a cross-coupled control scheme on a 3-axis CNC mill governed by an open-architecture software controller are presented. Unlike prior cross-coupling schemes, which depend on osculating-circle approximations to the commanded toolpath for real-time contour error estimation, the proposed scheme is based on essentially exact contour error computations for free-form curved paths. The implementation illustrates the feasibility of precise real-time contour error computation with a modest (300 MHz) CPU and a 1024 Hz sampling frequency. For a P-type controller and paths with strong curvature variation, the new scheme ensures much better diminution of contour error than earlier methods. The contour error is observed to decrease monotonically as the relative gain is increased, up to a critical gain value that incurs instability. For PI-type controllers, the comparative contour error reduction is more modest, due to their effective suppression of steady-state position error along the path. In practice, the exact contour error measure permits accurate tracking of strongly curved paths using a simple P-type controller, with smaller feedrate fluctuations than a PI-type controller incurs.

A Novel Contour Error Estimation for Position Loop-Based Cross-Coupled Control

Reduction of contour error is the main control objective in contour-following applications. A common approach to this objective is to design a controller based on the contour error directly. In this case, the contour error estimation is a key factor in the contour-following operation. Contour error can be approximated by the linear distance from the actual position to the tangent line or plane at the desired position. This approach suffers from a significant error due to linear approximation. A novel approach to contour error calculation of an arbitrary smooth path is proposed in this paper. The proposed method is based on coordinate transformation and circular approximation. In this method, the contour error is represented by the coordinate of the actual position with respect to a specific virtual coordinate frame. The method is incorporated in a position loop-based cross-coupled control structure. An equivalent robust control system is used to establish stability of the closed-loop system. Experimental results demonstrate the efficiency and performance of the proposed contour error estimation algorithm and the motion control strategy.

Contouring controller design based on iterative contour error estimation for three-dimensional machining

Recently, there has been a growth of interest in high precision machining in multi-axis feed drive systems, subjected to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. To guarantee high precision machining in modern computer numerical controlled (CNC) machines, CNC's controllers do its control efforts to reduce contour error. One of the common approaches is to design a controller based on the estimation of contour error in real time. However, for complex contours with severe curvatures, there is a lack of effective algorithms to calculate contour errors accurately. To address this problem, this paper proposes an accurate contour error estimation procedure for three-dimensional machining tasks. The proposed method is based on an iterative estimation of the instantaneous curvature of the reference trajectory and coordinates transformation approach, and hence, it is effective for complex reference trajectories with high curvatures. In addition, contour error controller is presented to reduce the estimated contour error. The feasibility and superiority of the proposed model as well as contour error controller are demonstrated through experimental system using a desk-top three-axis CNC machine.

Contouring accuracy improvement using a tangential contouring controller with a fuzzy logic-based feedrate regulator

In contour-following tasks, contour error reduction is an issue of much concern. Generally speaking, contour error is caused by the mismatched dynamics between each axis. To reduce the contour error, many previous studies have focused on developing proper controllers and/or more accurate contour error estimation algorithms. An alternative method for reducing contour errors is to exploit the idea of desired feedrate adjustment. This paper proposes using the approximate contour error information to develop a fuzzy logic-based feedrate regulator, which adjusts the value of the desired feedrate. Moreover, to further reduce contour error, an integrated motion control scheme is also developed. This scheme consists of a position loop controller with velocity command feedforward, a tangential contouring controller (TCC), a real-time contour error estimator, and the proposed fuzzy logic-based feedrate regulator. Several experiments on free-form contour-following tasks are conducted to evaluate the performance of the proposed approach. The experimental results clearly demonstrate the effectiveness of the proposed approach.