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 aimi...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.展开更多
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 propa...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.展开更多
Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-v...Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-varying,nonlinear,and strongly coupled characteristics of parallel machining modules.In addition,the time delay in the system reduces the timeliness of the feedback data,thereby making online contour error calculations and compensation particularly difficult.To solve this problem,the generation mechanism of the time delay of the feedback data and contour error is revealed,and a systematic method for the identification of the time-delay parameter based on Beckhoff’s tracking error calculation mechanism is proposed.The temporal alignment between the position commands and feedback data enables the online calculation of the contour error.On this basis,the tracking error of the drive axes(an important factor resulting in end-effector contour errors)is used for the contour error calculation.Considering the ambiguous parameter-setting logic of the servo drive,the servo parameter is calculated in reverse using the steady-state error to obtain the tracking error model of the drive axes.Furthermore,combined with the system time-delay model,an online correction method for the tracking error estimation model is established.To achieve an accurate mapping of the drive-axis tracking error and end-effector contour error,a bounded iterative search method for the nearest contour point and online calculation model for the contour error are respectively established.Finally,an online compensation controller for contour error is designed.Its effectiveness is verified by a machining experiment on a frame workpiece.The machining results show that the contour error reduces from 68μm to 45μm,and the finish machining accuracy increases by 34%.This study provides a feasible method for online compensation of contour error in a system with time delay.展开更多
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 ...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.展开更多
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 analy...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.展开更多
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 co...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.展开更多
In conventional cross-coupled controller design,the method usually ignored the inherent characteristic of time-vary-ing parameters and model uncertainties in system.In this paper,a cross-coupled controller(CCC)using a...In conventional cross-coupled controller design,the method usually ignored the inherent characteristic of time-vary-ing parameters and model uncertainties in system.In this paper,a cross-coupled controller(CCC)using an H~∞control scheme has been proposed to reduce the contouring error for an X-Y table.Furthermore,the proposed CCC design,which is a typical Multi-Input Multi-Output(MIMO)system with linear time varying(LTV)characteristics,has been verified as being internally stable.The simulations are carried on Matlab simulink to verify the proposed method,and the results showed that the proposed method can reduce the contouring error significantly compared with the conventional one.展开更多
A design approach for online pre-compensation of three-axis cross-coupled contour errors with mismatched dynamics is proposed.In the context of cross-coupled contour control design,online pre-compensation of contour e...A design approach for online pre-compensation of three-axis cross-coupled contour errors with mismatched dynamics is proposed.In the context of cross-coupled contour control design,online pre-compensation of contour errors is commonly employed.However,establishing a specific relationship between contour errors is challenging for mismatched computer numerical control(CNC)systems.Therefore,the design of interpolation methods for mismatched systems remains crucial,as most existing systems struggle to be adjusted to match seamlessly.This study introduces an online pre-compensation scheme for cross-coupled contour errors in three-axis motion,which constitutes a compensation system for real-time correction of contour error estimation.The coupling control structure,based on a speed loop,comprises a proportion integration differentiation(PID)control feedback controller,a feedforward controller,and an online pre-compensation cross-coupled contour controller.The experimental results demonstrate that the proposed three-axis cross-coupled contour error pre-compensation scheme significantly enhances the contour accuracy compared to traditional cross-coupled control systems.Moreover,the proposed cross-coupled contour error pre-compensation controller exhibits superior contour performance over conventional cross-coupled controllers when tracking high-order curvature bending paths.展开更多
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-orde...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.展开更多
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 e...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.展开更多
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 b...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.展开更多
基金the National Natural Science Foundation of China(Grant Nos 51515081 and 51675081)National Science and Tech-nology Major Project of China(Grant No 2016ZX04001-002)+2 种基金Innovation Project for Supporting High-level Talent in Dalian(Grant No 2016RQ012)Science Fund for Creative Research Groups(Grant No 51621064)the Fundamental Research Funds for the Central Universities(Grant NoDUT17LAB13)
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China(Grant Nos.52375018,92148301).
文摘Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-varying,nonlinear,and strongly coupled characteristics of parallel machining modules.In addition,the time delay in the system reduces the timeliness of the feedback data,thereby making online contour error calculations and compensation particularly difficult.To solve this problem,the generation mechanism of the time delay of the feedback data and contour error is revealed,and a systematic method for the identification of the time-delay parameter based on Beckhoff’s tracking error calculation mechanism is proposed.The temporal alignment between the position commands and feedback data enables the online calculation of the contour error.On this basis,the tracking error of the drive axes(an important factor resulting in end-effector contour errors)is used for the contour error calculation.Considering the ambiguous parameter-setting logic of the servo drive,the servo parameter is calculated in reverse using the steady-state error to obtain the tracking error model of the drive axes.Furthermore,combined with the system time-delay model,an online correction method for the tracking error estimation model is established.To achieve an accurate mapping of the drive-axis tracking error and end-effector contour error,a bounded iterative search method for the nearest contour point and online calculation model for the contour error are respectively established.Finally,an online compensation controller for contour error is designed.Its effectiveness is verified by a machining experiment on a frame workpiece.The machining results show that the contour error reduces from 68μm to 45μm,and the finish machining accuracy increases by 34%.This study provides a feasible method for online compensation of contour error in a system with time delay.
文摘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.
基金supported by the Chinese National Natural Science Foundation under Grant(51375056)the Beijing Natural Science Foundation under Grant(3142009)the key of Beijing Natural Science Foundation under Grant(KZ201211232039)
文摘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.
基金supported by the Science Foundation of the Education Office of Gansu Province of Chinaunder Grant No.0914-01
文摘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.
文摘In conventional cross-coupled controller design,the method usually ignored the inherent characteristic of time-vary-ing parameters and model uncertainties in system.In this paper,a cross-coupled controller(CCC)using an H~∞control scheme has been proposed to reduce the contouring error for an X-Y table.Furthermore,the proposed CCC design,which is a typical Multi-Input Multi-Output(MIMO)system with linear time varying(LTV)characteristics,has been verified as being internally stable.The simulations are carried on Matlab simulink to verify the proposed method,and the results showed that the proposed method can reduce the contouring error significantly compared with the conventional one.
文摘A design approach for online pre-compensation of three-axis cross-coupled contour errors with mismatched dynamics is proposed.In the context of cross-coupled contour control design,online pre-compensation of contour errors is commonly employed.However,establishing a specific relationship between contour errors is challenging for mismatched computer numerical control(CNC)systems.Therefore,the design of interpolation methods for mismatched systems remains crucial,as most existing systems struggle to be adjusted to match seamlessly.This study introduces an online pre-compensation scheme for cross-coupled contour errors in three-axis motion,which constitutes a compensation system for real-time correction of contour error estimation.The coupling control structure,based on a speed loop,comprises a proportion integration differentiation(PID)control feedback controller,a feedforward controller,and an online pre-compensation cross-coupled contour controller.The experimental results demonstrate that the proposed three-axis cross-coupled contour error pre-compensation scheme significantly enhances the contour accuracy compared to traditional cross-coupled control systems.Moreover,the proposed cross-coupled contour error pre-compensation controller exhibits superior contour performance over conventional cross-coupled controllers when tracking high-order curvature bending paths.
基金supported by the National Natural Science Foundation of China(Grant Nos.51325502 and 51405175)the National Basic Research Program of China("973"Project)(Grant No.2011CB706804)the National Science and Technology Major Projects of China(Grant No.2012ZX04001-012-01-05)
文摘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.
基金This work is supported by the National Science and Technology Major Project of China(Grant No.2015ZX04005006)the Science and Technology Major Project of Zhongshan City,China(Grant Nos.2016F2FC0006 and 2018A10018).
文摘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.
文摘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.
