Adaptive estimation and nonlinear variable gain compensation of the contouring error for precise parametric curve following

Contour following is one of the most important issues faced by many computer-numerical-control(CNC) machine tools to achieve high machining precision. This paper presents a new real-time error compensation method aiming at reducing the contouring error caused by facts such as servo lag and dynamics mismatch in parametric curved contour-following tasks. Due to the lack of high-precision contouring-error estimation method for free-form parametric curved toolpath, the error can hardly be compensated effectively. Therefore, an adaptive accurate contouring-error estimation algorithm is proposed first, where a tangential-error backstepping method based on Taylor's expansion is developed to rapidly find the closest point on the parametric curve to the actual motion position. On this foundation, the contouring error is compensated using a proposed nonlinear variable-gain compensation method, where the compensation gain is obtained according to not only the contouring-error magnitude but also its direction variation. The stability of the system after compensation is analyzed afterwards according to the Jury stability criterion.By design of the compensator in accordance with the presented contouring-error compensation method as well as the stability analyzation result, the balance between the response speed and the contour control stability can be effectively made. Experimental tests demonstrate the feasibility of the presented methods in both contouring-error estimation and contour-accuracy improvement.Contributions of this research are significant for enhancing the contour-following performance of the CNC machine tools.

A pre-compensation method of the systematic contouring error for repetitive command paths

For a repetitive command path, pre-compen- sating the contouring error by modifying the command path is practical. To obtain the pre-compensation value with better accuracy, this paper proposes the use of a back propagation neural network to extract the function of systematic contouring errors. Furthermore, by using the extracted function, the contouring error can be easily pre- compensated. The experiment results verify that the proposed compensation method can effectively reduce contouring errors.

TWO-COORDINATE DUAL-SERVO CONTOURERROR COMPENSATION TECHNOLOGY FOR ULTRA-PRECISION MANUFACTURING

A technology of two-coordinate dual-servo(TCDS) is proposed. Using this technology which is based on error compensation, workpieces of higher contour accuracy could he turned on ultra-precision machine tool with Poor dynamic performances. The principle, constitute and operation of a TCDS system are described. Mathematical proof and experiments are achieved in addition.

Research of contour error compensation control for X-C non-circular grinding in polar coordinates

In the X-C linkage grinding of non-circular parts,the computation and control method of contour error in polar coordinates platform is different with that in the XY coordinates platform.To solve this problem,the analysis of the definition and computation methods for contour error and track error in polar coordinates platform will be made.Through the relative lead-lag relation of the linkage axes in the grinding process,the range of the estimation contour error is narrowed and a contour error calculation model is constructed.Then the contour compensation controllers along contour error direction and trajectory tracking error direction are designed respectively,and the error compensation decoupling matrix of the X-C linkage axes is given as well.In the end of this paper,we take the machining of the cylinder contour in Wankel rotary piston engine as an example.A simulation experiment of contour error compensation control based on relative lead-lag quantity is made.The result shows that the designed contour compensation controller can increase the contour machining accuracy effectively.

Research on Contour Error Based on CNC Multi-axis Motion Control System

The contour error was analyzed based on CNC multi-axis motion control, the contour error model was obtained focused on beeline and different radius of curvature and common contour of curve, for a CNC biaxial motion control system and the mechanism of producing contour error and the relationship between tracking error and contour error were presented. The theoretical and practical significance of modeling error and controlling error in motion control systems was carried out.

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.

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 B-splines curves indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy in biaxial contour following tasks.

A HEURISTIC PATH-PLANNING METHOD FOR ENHANCING MACHINE-TOOL CONTOUR-FOLLOWING

The machine-tools performances within the framework of high-speed machining both depend on the design of the reference trajectory and on the tuning of the servo controllers. The reduction of the contouring error can be achieved by adapting the feedrate to the path profile. An alternative method consists of smoothing the spatial trajectory that allows to decrease the cycle time. A path smoothing technique is provided, which uses an analogy with racing-car piloting. The trajectory is modified pointwise according to a set of rules and is designed using fuzzy control.